QUAD ABCD is a rectangular shape whose diagonals meet at point P. AC is 4x-13 and DP is x + 7.
Can you show that the quadrilateral ABCD is a parallelogram given the provided information?When one set of opposing sides in a quadrilateral are congruent and parallel, the quadrilateral is a parallelogram. ABCD is a parallelogram if — BC — AD and — BC — AD. A quadrilateral becomes a parallelogram if its diagonals are bisected by one another.
In QUAD ABCD, DP equals x + 7 and AC is 4x-13.
4x - 13 is x + 7 + x + 7
4x - 13 = 2x+14
2x-13 = 14.
hence,
The value of x is 13.5.
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Sabreena is playing a card game, and the odds of her winning after drawing the next card are 5:7. What is the probability of her not winning? Enter your answer as a decimal rounded to the nearest thousandth, like this: 0.423
The probability that Sabreena is going to lose is given as 0.5833
How to solve for the probabilityProbability is a measure of the likelihood of a specific event or outcome occurring. It is typically expressed as a decimal number between 0 and 1, or as a percentage between 0% and 100%.
A probability of 0 indicates that an event is impossible and will never occur, while a probability of 1 indicates that an event is certain and will always occur.
If the odds that Sabreena has of winning in this game is 5: 7, this is written as 5 / 7
In this case, the odds of Sabreena winning are 5:7,
so the probability of winning is 5/(5+7)
the probability of not winning is 1 - 5/12
The probability of not winning is approximately 0.5833
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A rigid body exists in an n-dimensional space. How many coordinates are needed to specify the position and orientation of this body in this space
The number of coordinates needed to specify the position and orientation of a rigid body in an n-dimensional space is n.
A rigid body is an object that maintains its shape and size while in motion. In order to specify the position and orientation of a rigid body in an n-dimensional space, we need to know its coordinates in each of the n dimensions. The coordinates describe the location of the body in the space and the orientation of the body relative to the space's coordinate system. Thus, n coordinates are required to fully specify the position and orientation of a rigid body in an n-dimensional space.
However, it is important to note that if the rigid body is placed in a space that's non-Euclidean, other parameters could be necessary to fully describe the rigid body position and orientation.
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Can the inverse of a function be the same function?
Answer:
Yes
Step-by-step explanation:
y = x has the inverse x = y
A building with a height of 48 meter casts a shadow that is 30 meter long. A person standing next to the building casts shadow that is 0.8 meter long. How tall is the person
The height of the person is approximately 0.426 meters or 42.6 cm.
We can use the concept of similar triangles to solve this problem. The height of the building and the length of its shadow form a right triangle, with the height as the opposite side and the shadow as the hypotenuse. The person and their shadow also form a similar right triangle, with the height of the person as the opposite side and the shadow as the hypotenuse.
We can set up the following proportion:
(Height of building)/(length of shadow) = (height of person)/(length of shadow)
48/30 = h/0.8
Solving for h, we get:
h = (48/30) * 0.8 = 0.533 * 0.8 = 0.426
Therefore, the height of the person is approximately 0.426 meters or 42.6 cm.
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PLEASE HELPPPP! Round to the nearest tenth, then find the sum. 0.92 + 5.37 2. Round to the nearest whole number, then find the difference. 6.3 − 2.8 3.Round to the nearest tenth, then find the difference. 13.56 − 10.02 4.Oliver did the high jump three times. His scores were 7.032 feet, 2.485 feet, and 4.59 feet. How many feet did he jump in total? 5.Clark ran the hurdles in 57.403 seconds. Grant ran the hurdles in 55.78 seconds. What is the difference between the two times? 6.Round to the nearest tenth, then find the sum. 13.46 + 7.84 + 2.59 7.Round to the nearest whole number, then find the difference. 1,472.63 − 975.28 8.Round to the nearest whole number, then find the sum. 38.24 + 14.53 + 8.93 9.Round to the nearest whole number, then find the sum. 16.4 + 12.8
Answer:
6.3
3
3.6
14
1.6
23.9
498
62
29
Step-by-step explanation:
0.9+5.4=6.3
6-3=3
13.6-10=3.6
7.032+2.485+4.59=14.107
57.403−55.78=1.623
13.5+7.8+2.6=23.
1,473−975=498
38+15+9=62
16+13=
Answer:
1. 0.92 rounds to 0.90 and 5.37 rounds to 5.40 (0.9 + 5.4 = 6.3)
2. 6.3 rounds to 6 and 2.8 rounds to 3 (6 - 3 = 3)
3. 13.56 rounds to 13.60 and 10.02 rounds to 10 (13.6 - 10 = 3.6)
4. 7.032 + 2.485 + 4.59 = 14.107
5. 57.403 - 55.78 = 1.623
6. 13.46 rounds to 13.50, 7.84 rounds to 7.80 and 2.59 rounds to 2.60 (13.5 + 7.8 + 2.6 = 23.9)
7. 1,472.63 rounds to 1,473 and 975.28 rounds to 975(1,473 - 975 = 498)
8. 38.24 rounds to 38, 14.53 rounds to 15 and 8.93 rounds to 9(38 + 15 + 9 = 62)
9. 16.4 rounds to 16 and 12.8 rounds to 13(16 + 13 = 29)
(some may be wrong but i did my best)
Warren is tiling his bathroom. He wants to cut three different sizes of square tiles. Tile A must be square inches, tile B must be square inches, and tile C must be square inches. He needs to know the side length of each tile. Part A In the table, note your guesses and checks to find the length of tile A, which has an area of square inches. Estimate the value to five decimal places
The length of tile A is 2.36068 inches.
The quantity of square units required to completely fill a square is known as the area of a square.
The region that lies inside the confines of a flat item or a two-dimensional figure is generally referred to as the area.
The measurement is made using square units, with square meters serving as the standard unit (m^2).
The square unit serves as the unit of area.
Let us recall that the area of a square is given by;
A = side^2
This is because, all the sides of a square are equal hence
When A = 5 square inches
5 = side^2
side = √5
side = 2.36068 inches
Therefore, The length of tile A is 2.36068 inches.
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Consider the differential equation dy/dx=xy^4.
(b) Find ⅆ2yⅆx2 in terms of x and y. Determine the concavity of all solution curves for the given differential equation in Quadrant II. Give a reason for your answer.
(c) Find the particular solution y=f(x) to the given differential equation with initial condition f(4)=−1.
The differential equation [tex]\frac{dy}{dx} = xy^{4}[/tex] is considered and the solutions for the following questions are found.
What is a differential equation?
A differential equation is an equation that links the derivatives of one or more unknown functions. Differential equations contain derivatives, which might be either partial derivatives or ordinary derivatives.
The differential equation describes a relationship between the variable that is constantly varying with respect to the change in another quantity, and the derivative represents a rate of change.
Given,
[tex]\frac{dy}{dx} = xy^{4}[/tex]
a) Now finding [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^{4} + 4xy^{3} \frac{dy}{dx}[/tex] = [tex]y^{4} + 4xy^3 (xy^4) = y^4 + 4x^2y^7[/tex]
In quadrant II, the values of x < 0 and the values of y >0.
So [tex]\frac{d^{2} y}{dx^{2} }[/tex] = [tex]y^4 + 4x^2y^7[/tex] > 0 for all values of x and y in quadrant II.
Therefore the concavity is up for of all solution curves of the given differential equation.
b)
[tex]\frac{dy}{dx} = xy^{4}\\\\\frac{dy}{y^4} =x dx\\\\\int {\frac{dy}{y^4} } \, = \int {x} \, dx \\\\\frac{y^{-4+1} }{-4+1} = \frac{x^{2} }{2} + c\\\\\frac{y^{-3} }{-3} = \frac{x^{2} }{2} +c[/tex]
Now it is given that initial condition is f(4) = -1
So substituting x =4 and y = -1 is the above equation to find c, we get
[tex]\frac{-1^{-3} }{-3} = \frac{4^2}{2} +c \\\\\frac{1}{3} = 8 + c\\\\c = \frac{1}{3} - 8 = \frac{-23}{8}[/tex]
Therefore the solution y = f(x) is to the given differential equation with initial condition f(4)=−1.
[tex]\frac{y^{-3} }{-3} = \frac{x^{2} }{2} -\frac{23}{8}\\ \\ \frac{1}{3y^3} = \frac{46 - 8x^2 }{16} = \frac{23 - 4x^2 }{8}\\\\y = \sqrt[3]{\frac{8}{3(23-4x^2)} }[/tex]
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10. Find the solution set for the following
y=x²-3x-4
y-x=-4
Answer:
I have no idea tbh I need help with this too
Step-by-step explanation:
PLEASE HELP!!!!!!!!!!!!!!!
9 people audition for a choir. The choir director must choose one soprano, one alto,
and one tenor.
In how many ways can the director fill these positions?
The numbers of ways that the director fill these positions is 504 ways.
What is the position about?There are a few different ways to approach this problem, but one possible method is to use the combination formula.
To fill the position of soprano, the director has 9 choices. After selecting one soprano, the director is left with 8 singers to choose from for the alto position. Then, the director has 7 singers to choose from for the tenor position.
So, the total number of ways the director can fill these positions is:
9 × 8 × 7
= 504 ways.
Alternatively, One can also use the permutation formula to solve the question. The formula of permutation is (n!/(r!(n-r)!)), where n is the total number of items to choose from, and r is the number of items to be chosen.
For this case n is 9, and r is 3, so the permutation would be:
(9!/(3!(9-3)!)
= (987)/(321)
= 504
Therefore, In both cases, the answer is 504 ways.
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What is a plot point example?
A plot point example contains a point in a story that defines the turning point in the story.
What is a plot point?A story's plot point is a crucial turning moment that occurs during the narrative. The tale and the characters may be developed and advanced using these ideas.
Why are plot points necessary in stories?Plot points offer your tale movement by advancing the plot and dragging the reader along. 'A particularly crucial portion of a storyline of a work of fiction,' according to the definition of a plot point. Never undervalue the significance of your framework, even if your book is contemplative or literary.
An example of plot point is :
In a story about a young girl who is trying to save her village from an impending monster attack, the plot point may occur when the girl discovers an ancient artifact that gives her the power to defeat the monster. This event marks a significant turning point in the story, as it sets the stage for the girl to take on the monster and potentially save her village.
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How do you solve a linear equation step by step?
Linear equations are mathematical equations that involve one or more variables. These equations can be solved by following a few simple steps:
How to solve linear equationsIdentify the constant and the coefficient of the variable.Use the coefficient to divide both sides of the equation by the same number.Subtract the constant from both sides of the equation.Divide both sides of the equation by the coefficient of the variable.Check your solution by substituting it back into the original equation.Linear equations can be used to solve a wide range of mathematical problems and are an essential part of any mathematics curriculum.
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what is 0.133 with a bar over 33
Answer:
2/15
Step-by-step explanation:
make x= 0.13
multiply it by 10^1 .
10x = − 1.33
subtract x from 10x
10x−x =
1.33 - 0.13
9x = 1.2
divide both sides by 9 to get x as a fraction
x = 1.2/9 =
12/90 =
2/15
httpssocraticorgquestionshowdoyouconvert0133beingrepeatedtoafraction#242780
A bar over a digit in a decimal number, such as 0.133 with a bar over the 3, indicates that the number is a repeating decimal. In this case, 0.133 is a repeating decimal and the digit 3 is repeating infinitely.
What is repeating decimal?A repeating decimal is a decimal number whose digits are periodic and repeat infinitely. They are also called recurring decimals. For example, 0.333... is a repeating decimal, with the digit 3 repeating indefinitely. The same goes for 0.666... and so on. They can also be represented in the form of a fraction, where the numerator is the repeating decimal and the denominator is a power of 10 with a 1 followed by as many zeroes as the number of digits in the repeating block. Repeating decimals can also be represented with a bar over the repeating block of digits, for example 0.133 with a bar over the 3, indicating that the digit 3 is repeating infinitely. It's also written as 0.133(3) where (3) means the repeating decimal. Another way is to use a dot above the repeating digit.To learn more about decimal refer:
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A regular heptagon has a radius of approximately 27.87 cm and the length of each side is 24.18 cm. What is the approximate area of the heptagon rounded to the nearest whole number
Rounded to the nearest whole number, the approximate area of the heptagon is 555 sq cm.
A heptagon is a seven-sided polygon. To find the area of a regular heptagon, we can use the formula:
Area = (7/4) * (perimeter) * (apothem)
where "perimeter" is the length of the heptagon's circumference and "apothem" is the distance from the centre to the midpoint of one of its sides. The radius of the heptagon is the apothem, which is 27.87 cm.
The perimeter of the heptagon can be calculated by multiplying the length of one side by the number of sides:
Perimeter = 24.18 cm * 7 = 168.26 cm
Now we can substitute these values into the area formula:
Area = (7/4) * 168.26 * 27.87
Area = approximately 554.55 sq cm.
Rounded to the nearest whole number, the approximate area of the heptagon is 555 sq cm.
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6x + y = 20
x - 4y = -5
The value of [tex]x[/tex] is [tex]3[/tex] and [tex]y[/tex] is [tex]2[/tex]
The given equations are
[tex]6x+y=20\\x-4y=-5[/tex]
We need to find the value of [tex]x[/tex] and [tex]y[/tex]
First let's take equation [tex]2[/tex] and we can simplify it
[tex]x-4y=-5\\x=-5+4y[/tex]
Now, let's substitute the value of [tex]x[/tex] in equation [tex]1[/tex], that is
[tex]6x+y=20\\6(-5+4y)+y=20[/tex]
We can open the bracket and simplify
[tex]=-30+24y+y=20\\=-30+25y=20\\=25y=20+30\\=25y=50\\=y=\frac{50}{25} \\y=2[/tex]
Now we can substitute the value of [tex]y[/tex] in equation [tex]x-4y=-5[/tex]
[tex]x-4(2)=-5\\x-8=-5\\x=-5+8\\x=3[/tex]
The complete question is find the value of [tex]x[/tex] and [tex]y[/tex] from the given equations.
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How do you solve the equation 5t 3 3t 5?
By solving the equation 5t - 3 = 3t - 5 we get the equation is true when t = -1. So the solution is t = -1.
To solve the equation 5t - 3 = 3t - 5, you can use algebraic manipulation to isolate the variable on one side of the equation.
The first step is to get all the terms with the variable on one side of the equation and all the constant terms on the other side.
5t - 3 = 3t - 5
adding 3 to both sides:
5t = 3t - 2
subtracting 3t from both sides:
2t = -2
then divide both sides by 2:
t = -1
So the solution is t = -1, meaning that when t = -1, the equation is true.
--The question is not clear, answering to the question below--
"How do you solve the equation 5t - 3 = 3t - 5?"
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What is the solution to the system of equations below x y 7 and x 2y 11?
The solution to the system of equations is x = 3 and y = 4.
this question is related to system of equations ,
the equations are,
x + y = 7 .......[1]
x + 2y = 11
x= 11 - 2y
now, place the value of x in equation 1,
(11 - 2y) + y = 7
11 - 2y +y = 7
11 - y = 7
- y = 7 - 11
- y = - 4
y = 4
now to find the value of x, place the value of y in equation 1
x + 4 = 7
x = 7 - 4
x = 3.
so, the value of x and y is 3 and 4.
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I need help this makes no sense
Answer:
∠ SQT = 63°
Step-by-step explanation:
since QS bisects ∠ RQT , then
∠ RQS = ∠ SQT = 7x + 7
then
∠ RQS + ∠ SQT = ∠ RQT , that is
7x + 7 + 7x + 7 = 9x + 54
14x + 14 = 9x + 54 ( subtract 9x from both sides )
5x + 14 = 54 ( subtract 14 from both sides )
5x = 40 ( divide both sides by 5 )
x = 8
Then
∠ SQT = 7x + 7 = 7(8) + 7 = 56 + 7 = 63°
How do you solve this?.....Katherine has a loyalty card good for a 3% discount at her local grocery store. What number should she multiply the prices on the tags by to find the price she would have to pay, before tax, in one step?
Answer:
Step-by-step explanation:
To find the number Katherine should multiply the prices on the tags by to find the price she would have to pay before tax, we need to calculate the inverse of the discount percentage, which is 1 - (discount percentage / 100).
Given that the discount is 3% and we want to find the price after the discount, that means:
1 - (3/100) = 1 - 0.03 = 0.97
So, the number Katherine should multiply the prices on the tags by to find the price she would have to pay, before tax, in one step, is 0.97. Multiplying the price of an item by 0.97 is equivalent to subtracting 3% from the original price, which is the same as finding the final price after the discount.
For example, if an item is priced at $10, Katherine can multiply this by 0.97 to find that the final price she would have to pay before tax is $9.7
10*0.97 = 9.7
Selena has 9 homemade bracelets for $12 each then 14 bracelets for $8 each. How much did she make in sales?
(Use the correct operation or combination of operations to solve the problem)
She will make a total profit of $220. Profits are amounts of money paid to a person with the right of immediate occupation for using the land when no permission has been granted for that use.
What are the different types of profit?Profit is the term used to describe the monetary gain experienced when the revenue from a commercial activity outpaces the costs, costs, and taxes incurred to support the activity in question. There are three primary ways to measure profit. These include operating profit, net profit, and gross profit. Gross profit and operating profit are indicators of how efficiently your company uses its resources to produce its goods and run day-to-day operations.
number of bracelets sold for $12 each=9
number of bracelets sold for $8 each=14
Total profit=9x12+8*14=$220
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Determine whether the lines tangent to the curve at the x-intercepts of the curve are parallel. Show the analysis that leads to your conclusion.
For the curve [tex]x^{2} +xy+y^{2} = 27[/tex] , the line tangents to the curve at the x intercepts of the curve are parallel .
The Slope of tangent line to a function at any point is denoted by [tex]\frac{dy}{dx}[/tex] .
The Curve is given as ⇒[tex]x^{2} +xy+y^{2} = 27[/tex] ;
On differentiating both sides of the curve with respect to "x" ,
we get ;
the slope of the line as ⇒ [tex]Slope = \frac{dy}{dx} = -\frac{2x+y}{x+2y}[/tex] ;
Now for the x- intercepts , the value [tex]y = 0 ,[/tex]
On substituting [tex]y=0[/tex] in the curve [tex]x^{2} +xy+y^{2} = 27[/tex] ,
we get ;
[tex]x^{2} +x(0)+0^{2} =27[/tex]
On simplifying further ,
we get ;
[tex]x=\pm 3\sqrt{3}[/tex] ;
So , the two x intercepts of the curve are [tex](3\sqrt{3},0)[/tex] and [tex](-3\sqrt{3},0)[/tex] ;
to find the slopes , we substitute the values in the slope equation .
On substituting the values in the slope equation ,
we get ;
[tex]Slope_{(3\sqrt{3} ,0)} = -\frac{2(3\sqrt{3}) +9}{3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex] and
[tex]Slope_{(-3\sqrt{3} ,0)} = -\frac{2(-3\sqrt{3}) +9}{-3\sqrt{3} +2(0)}[/tex] = [tex]-2[/tex].
we see that the slope at both the intercepts is same ,
Therefore , the lines tangents of the curve at the x intercepts are parallel .
The given question is incomplete , the complete question is
Consider the curve defined by [tex]x^{2} +xy+y^{2} = 27[/tex] . Determine whether the lines tangent to the curve at the x - intercept of the curve are parallel .
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How do you find the value of 3 7?
Please I need the 3 of them
The following operations are used to transform the quadratic equation y = x² into parabolas in standard form:
Case 1
Horizontal translation, vertical translation. Horizontal stretch.
Case 2
Horizontal translation, vertical translation. Reflection in the x-axis, vertical stretch.
Case 3
Horizontal translation, vertical translation. Horizontal stretch.
How to determine the magnitude of horizontal and vertical translations for quadratic equations
In this question we find three cases of parabolas in standard form, that is, quadratic equations of the form:
y - k = a · (x - h)²
Where:
a - Vertex constant(h, k) - Coordinates of the vertex.This parabola is translated both horizontally and vertically by using the following definitions:
Horizontal translation
x → x - a, where a > 0 for rightward translation.
Vertical translation
y → y - b, where b > 0 for upward translation.
Horizontal dilation
f(x) → f(k · x), where k is a non-negative real number.
Vertical dilation
f(x) → k · f(x), where k is a non-negative real number.
Reflection in the x-axis
f(x) → - f(x)
The procedure is summarize below:
Write the original function, that is, the equation of the parabola with vertex at origin.Apply dilation, translation and reflection definitions.Finally, we summarize the procedure for each case:
Case 1
g(x) = x²
g(x) = [(1 / 2) · x²]
g(x) + 4 = [(1 / 2) · (x - 2)]²
Horizontal shift: 2 units right, vertical shift: 4 units down. Horizontal stretch.
Case 2
f(x) = x²
f(x) = - (1 / 2) · x²
f(x) - 2 = - (1 / 2) · (x - 4)²
Horizontal shift: 4 units right, vertical shift: 2 units down. Reflection in the x-axis, vertical stretch.
Case 3
h(x) = x²
h(x) = 2 · x²
h(x) - 5 = [2 · (x + 2)]²
Horizontal shift: 2 units left, vertical shift: 5 units up. Horizontal stretch.
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What is undecidable problem give two examples?
An undecidable problem is one for which it has been demonstrated that it is impossible to develop an algorithm that always leads to the correct yes-or-no answer. Two examples are:
The Whitehead problem The halting problemWhat the halting problem?The halting problem is the problem of determining whether a computer programme will finish running or continue to run indefinitely based on a description of the programme and an input. Alan Turing demonstrated in 1936 that a general algorithm for solving the halting problem for all possible program-input pairs does not exist.
A "pathological" programme g, when called with some input, can pass its own source and input to f and then specifically do the opposite of what f predicts g will do. This case cannot be handled by any f. A key part of the proof is a mathematical definition of a computer and programme, known as a Turing machine; the halting problem is intractable over Turing machines.
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y
Which of the following best represents R = A - B?
A)
B)
R
The closing side of the triangle serves as the best representation of the resultant vector for the resultant R=A+B, so selecting option C would be the appropriate response.
what is vector ?A vector in mathematics is a quantity that has both magnitude and direction but no specific location. Illustrations of such numbers include velocity and acceleration. The term "vector" refers to something that has both magnitude and direction. When viewed geometrically, a vector can be thought of as a directed reference line, the direction of which is indicated by an arrow and whose length corresponds to the vector's magnitude. A quantity or phenomenon known as a vector has two distinct qualities that are its size and direction. Also included in the term is a description of how these values are represented geometrically or mathematically. Vectors are present in electromagnetic fields, as well as in weight, velocity, force, and velocity.
given
As stated in the issue, we must determine the resultant vector by adding vectors A and B.
The triangle law of vector addition, which states that the total is supplied by the triangle's closing side, can be used to calculate the vector's outcome.
Option C is the proper response, thus.
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How do you solve a 3 sided triangle?
It is impossible to solve a 3-sided triangle because triangles require 3 sides and 3 angles in order to be solved.
A triangle is a three-sided polygon, and the sum of its angles is always 180 degrees. In order to solve a triangle, you must know the length of all three sides and the measure of all three angles. If you know two sides and the angle between them (the angle opposite to one of the sides), you can use the Law of Sines to determine the other angle. If you know two angles and a side, you can use the Law of Cosines to determine the other two sides. With all three sides and angles known, you can use the Pythagorean Theorem to check your work. However, if you only have three sides, it is impossible to solve the triangle because you do not have enough information.
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Your neighbor pays you $17 for every two hours of work how many hours do you work if you earn $42.50
Answer:
To find the number of hours you work, you need to set up an equation using the information given. Let's say that the number of hours you work is x. The equation would be:
17(x/2) = 42.50
The parentheses around x/2 indicate that the division should be done before the multiplication. So, x/2 = 2.5. Multiplying both sides of the equation by 2 gives us:
x = 5
So, you work 5 hours.
Step-by-step explanation:
So, we know that you earn $17 per 2 hours. We also know that we earned $42.50. Now, we just need to find the hours! We can do this by using a cross multiply.
$17 is directly correlated to 2 hours of work. Therefore, to find the hourly wage we should divide it by 2:
$8.5 = 1 hour
$42.50 = x hours?
Now cross multiply:
$8.5x = $42.50
x = 5 hours
Therefore, your answer is 5 hours!
Hope this helps!
PLS HELP ME I ONLY HAVE 2 MINS TO ANSWER!!!!!!!!! ITS 100 PTS!!!!!
Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900. The following table shows the number of sales each salesman had during the first three weeks of this month.
Week 1 Week 2 Week 3
Salesman A 11 14 16
Salesman B 14 15 13
Salesman C 16 12 11
In which week(s), did Salesman C have a larger paycheck than both of the other salesmen? Select all that apply.
Week 3
None of the weeks.
Week 2
Week 1
In Week 1,
Salesman C got larger paycheck than Salesman A and Salesman B.
What is equation?Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.
Here,
2x – 5 and 13 are expressions
The sign that connects these two expressions is “=”.
In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable. That means, the equation 2x – 5 = 13 is satisfied only for x = 9.
Given,
Commission of salesman A per sale = $65
Commission of salesman B per sale = $40
Commission of salesman C per sale = $0
Salary of salesman A per week = $0
Salary of salesman B per week = $300
Salary of salesman C per week = $900
No. of sales × commission + salary = total earning
In week 1.
Earning of A
11 × $65 + $0 = $715
Earning of B
14 × $40 + $300 = $860
Earning of C
16 ×$0 + $900 = $900
In week 2.
Earning of A
14 × $65 + $0 = $910
Earning of B
15 × $40 + $300 = $900
Earning of C
12 ×$0 + $900 = $900
In week 3.
Earning of A
16 × $65 + $0 = $1040
Earning of B
13 × $40 + $300 = $820
Earning of C
111 ×$0 + $900 = $900
By the above calculation Salesman C received $900 in week 1 which is greater than Salesman A and Salesman B.
In week 2 and week 3 his paycheck is smaller than both of the other salesman.
Hence, Salesman C received larger paycheck than both of the other salesmen in Week 1.
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HELPPPPP
Jada rode her bike 5 days in a row. She rode the same distance each day. This model represents the situation. Each column represents one mile and the shaded parts of each column represent the fraction of a mile that Jada rode her bike each day.
Which expression can be used to determine the total distance in miles Jada rode her bike over the 5 days?
(A: 5 × 4/5
(B: 5 + 4/5
(C: 5 × 1/4
(D: 5 + 1/4
PLSSSS HELP
Answer: 5 x 4/5
Step-by-step explanation:
In each column there is 4/5 shaded . There are 5 columns .
So , 5 x 4/5
Answer:
A) 5 × 4/5
Step-by-step explanation:
The shaded part each column in the model represents what fraction of a mile that Jada rode her bike each day.
There are 5 columns.
Therefore, to determine the total distance in miles that Jada rode over the days, we can multiply the distance that she rode each day by the number of days that she rode that distance (5 days):
A) [tex]5 \textrm{ days} \times \dfrac{4}{5} \textrm{ mile each day}[/tex]
Aiden is a spice trader.
The price he charges for an order of cumin (in dollars) as a function of the size of the order (in kilograms) is graphed.
What is the approximate average rate at which the total cost increases, as the order size increases from 100 to 600 kilograms?
Approximately $2.40 per kilogramme is the average rate that the total cost rises as the order size does, from 100 to 600 kg.
How much is the average rate?The average rate of change is the average change rate of one thing in respect to another. Simply explained, a computation that divides the amount of change in one thing by the comparable amount of change in another is known as an average rate of change function.
How are average rates calculated?Divide the y-value change by the x-value change to determine the average rate of change. When analyzing changes in observable parameters like average speed or average temperature, finding that average rate of change is especially helpful.
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2. Write a factored form function, f(x) for a cubic function that has zeros (- 7, 0) and (3, 0)
The cubic equation in factor form f(x) = (x + 7) · (x - 3) · (x - r) contains zeros (- 7 , 0) and (3, 0), for r = 0: f(x) = (x + 7) · (x - 3) · (x - r).
How to derive a cubic equation in factor form
Cubic functions are polynomials with grade 3 and whose standard form is described by the following form:
y = a · x³ + b · x² + c · x + d
Where a, b, c, d are real coefficients. The factor form of a cubic function is described by the following definition:
y = a · (x - r₁) · (x - r₂) · (x - r₃)
Where:
a - Lead coefficient.r₁, r₂, r₃ - Real zeros.Replace all known variables in factor form of cubic equation: (a = 1, r₁ = - 7, r₂ = 3, r₃ = r)
f(x) = (x + 7) · (x - 3) · (x - r)
Variable r means that there is more than one answer concerning the expression, if we assume that r = 0, then the particular solution is f(x) = (x + 7) · (x - 3) · x.
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