Answer:
To solve this problem, we can set up the following equation:
2L + 2W = 64
We are told that the length of the rectangle is two more than double the width, so we can write the following equation:
L = 2W + 2
Substituting this equation into the first equation, we get:
2(2W + 2) + 2W = 64
Simplifying this equation, we get:
6W + 4 = 64
Subtracting 4 from both sides, we get:
6W = 60
Dividing both sides by 6, we get:
W = 10
The width of the rectangle is 10 feet.
To find the length of the rectangle, we can substitute this value back into the equation L = 2W + 2 to get:
L = 2(10) + 2
= 20 + 2
= 22
The length of the rectangle is 22 feet.
Therefore, the dimensions of the rectangle are 10 feet by 22 feet.
Step-by-step explanation:
what is an equation of the line that is parallel to y = - 5 x + 6 and passes through the point (-4,-1)
The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.
What is the equation of a parallel line?Let the equation of the line be ax + by + c = 0. Then the equation of the parallel line that is parallel to the line ax + by + c = 0 is given as ax + by + d = 0.
The equation of the line is given below.
y = - 5x + 6
The equation of the line that is parallel to the line y = - 5x + 6 is written as,
y = - 5x + c
The equation passes through (-4, -1), then we have
- 1 = - 5 (-4) + c
- 1 = 20 + c
- 21 = c
The equation of the line that is parallel to the line y = - 5x + c and passes through (-4, -1) will be y = - 5x - 21.
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A cake recipe calls for 2 1/3 cups of flour. If Gloria is planning on making 6 cakes for a bake sale, how many cups of flour will she need?
Answer: Gloria will need 14 cups of flour
Step-by-step explanation: 2 1/3 x 6 = 14
Between 2020 and 2021, the population of a town decreased by 35%
In 2021, the population of the town was 94,900
What was the population of the town in 2020?
Answer:
Step-by-step explanation:
Answer:
97611 is the correct answer
Find the measure of angle A,
The value of the Angle A is 74.3°.
What is Relation between angle and Side of a triangle?The longest side is in opposition to the longest angle, and the shortest side is in opposition to the smallest angle, respectively.
The opposite of the longest side is the greatest angle, while the opposite of the shortest side is the smallest angle. According to the sides of a triangle rule, the lengths of any two sides of a triangle must add up to more than the length of the third side.
The comparable sides are proportionate and the angles are same. The sides that are opposite the same angle are the corresponding sides. For instance, if two triangles have a 90-degree angle on each side, Triangle A's opposing side will match Triangle B's opposite side.
We know:-AB/sin(c)=AC/sin(a)=BC/sin(b)
8/sin(a)=5/Sin37°
Angle= 74.3°.
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Graph the solution to this inequality on the number line.
The
Using a straight line and either an open circle or a closed circle to indicate the end points, we can depict inequalities on a number line by displaying the range of integers.
How do you identify inequalities?By drawing a straight line and designating the end points with either an open circle or a closed circle, we can depict inequalities on a number line by illustrating the range of integers. An open circle indicates that it excludes the value. A closed circle indicates that it does contain the value.
Both equations and inequalities are mathematical phrases created by connecting two expressions. The equal sign (=) in an equation denotes that the two expressions are regarded as equal. In contrast, an inequality indicates that the two phrases are not always equal by using the symbols >,,, or.
With regard to the inequality expression
-3m + 5 > 14
5 from each side is subtracted.
-3m + 5 - 5 > 14 - 5
-3m > 9
Subtract -3 from both sides.
-3m/-3 < 9/-3
m < -3
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Kendra and Dalisay practice archery. Kendra hits the target 3 times every 5 misses. Dalisay hits the target 5 times every 7 misses. Who hits the target more?
Dalisay hits the target more.
What is Proportional?Any relationship that is always in the same ratio and quantity which vary directly with each other is called the proportional.
Given that;
Kendra hits the target 3 times every 5 misses.
And, Dalisay hits the target 5 times every 7 misses.
Since, Kendra hits the target 3 times every 5 misses.
Hence, In 1 misses Kendra hits the target = 3/5 times
= 0.6 times
And, Dalisay hits the target 5 times every 7 misses.
Hence, In 1 misses Dalisay hits the target = 5/7 times
= 0.74 times
Thus, Dalisay hits the target more.
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How do I even do this?
Answer:
going to have to to get the house ready
What is the domain of the function below?
A) x < 2
B) x ≤ 3
C) x ≥ 2
D) All Real Numbers
Answer:
I would say (option A)
Step-by-step explanation:
Domain is the set of x-values that can be inputted into function f(x).
We see that our x-values can be any number. Therefore, we have all real numbers as our domain:
→ A) x < 2.
Hope this helps!
A maple tree grows 1.5 feet each year. The table shows the yearly growth for a pibe tree
Comparing the maple tree and the pine tree growth information, the tree that grows faster is the pine tree.
How to find the tree that grow fasterA mathematical function called an exponential function is employed frequently in everyday life. It is mostly used to compute investments, model populations, determine exponential decay or exponential growth, and so on.
Exponential function is a type of function of the form: f(x) = a(b)^x. It is made up of 3 main parts
a = the starting or initial value
b = the base function
x = the exponents
Considering the given problem, b for maple is given as 1.5 and we calculate for pine using the data in the table. the equation is derived as follows
f(x) = a(b)ˣ
12 = a(b)¹
24 = a(b)²
dividing 24 = a(b)² by 12 = a(b)¹
b = 2
hence for pine tree the b is 2 which is greater than 1.5
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Find the inverse of y=3/(x+1) -2
The inverse of the function is y = 3/(x + 2) - 1
How to determine the inverse of the functionFrom the question, we have the following parameters that can be used in our computation:
y=3/(x+1) -2
Rewrite as
y = 3/(x + 1) - 2
Swap the positions of x and y
So, we have the following representation
x = 3/(y + 1) - 2
Next, we make y the subject of the formula
This gives
3/(y + 1) = x + 2
Take the inverse of both sides
(y + 1)/3 = 1/(x + 2_
So, we have
y = 3/(x + 2) - 1
Hence, the inverse is y = 3/(x + 2) - 1
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Graph the linear equation q(x)=-3x+1
The linear function q(x) = -3x + 1 is graphed and attached
How to graph the linear functionThe graph of the linear function is a straight line graph and the table of values used in making the plot is calculated as follows
For x = -20, q(x) = -3 * -20 + 1 = 61
For x = -10, q(x) = -3 * -10 + 1 = 31
For x = 0, q(x) = -3 * 0 + 1 = 1
For x = 10, q(x) = -3 * 10 + 1 = -29
For x = 20, q(x) = -3 * 20 + 1 = -59
Table of values
x y
-20 61
-10 31
0 1
10 -29
20 -59
These points are plotted in the cartesian coordinate by tracing the point of intersection of the x and y and marking it. Then the marked points are joined together to form a straight line
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Use the drop-down boxes to show a function in the form y = mx + b for the line that contains the points (–6.4, –2.6) and (5.2, 9).
The equation in the slope-intercept form is y = x + 3.8
What is a slope?
In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction.
Given:
A line that contains the points (–6.4, –2.6) and (5.2, 9).
If a line passes through two points (x₁ ,y₁) and (x₂, y₂) ,
then the equation of line is
y - y₁ = (y₂- y₁) / (x₂ - x₁) x (x - x₁)
So, the equation,
y + 2.6 = {(9 + 2.6)/(5.2 + 6.4)} (x + 6.4)
y + 2.6 = x + 6.4
y = x + 6.4 - 2.6
y = x + 3.8
Therefore, the equation y = x + 3.8 is in the slope-intercept form.
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If
f
(
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
x
)
f(x) is divided by
x
−
1
x−1?
Answer:
If
f
(
x
)
=
2
x
4
−
3
x
+
3
f(x)=2x
4
−3x+3, then what is the remainder when
f
(
√2 (2-2√10) how do you simplify
Answer:
2√2- 4√5
Step-by-step explanation:
√2 (2-2√10)
2√2- 2√20
2√2- 2√(4*5)
2√2- 2*2√5
2√2- 4√5
what is the value of q³?!
Answer:
-6
Step-by-step explanation:
You seem to want the value of q₃ in the matrix Q⁻¹.
Matrix inverseThe inverse matrix, Q⁻¹, is the transpose of the cofactor matrix, divided by the determinant. That makes q₃ = -q₂₁/det(Q):
q₃ = -(-2/3)/((-1(-1/9) -(-2/3)(-1/3))
q₃ = (2/3)/(1/9 -2/9) = (6/9)/(-1/9)
q₃ = -6
__
Additional comment
The transpose of the cofactor matrix of a 2×2 matrix is the original with the diagonal terms swapped, and the off-diagonal terms negated. Basically, the only math involved in computing the inverse is finding the determinant, and dividing by it.
You have a budget of $1,900 per week for employees. Employees are paid $11 per hour and work 40 hours per week. Ignore overhead, how many employees can you hire?
You can hire around 173 employees. Here's the calculation: $1,900 / ($11/hour * 40 hours/week) = 173.333..., which rounds down to 173.
Triangle ABC has vertices A(-3, 3), B(2, 5), and C(4, - 3).
a. What is the x-coordinate of the centroid of triangle ABC?
(-,5/3)
Answer:
Step-by-step explanation:
To find the x-coordinate of the centroid of triangle ABC, we need to take the average of the x-coordinates of the three vertices of the triangle. The x-coordinates of the vertices of triangle ABC are -3, 2, and 4, so the average of these three numbers is (-3 + 2 + 4) / 3 = (3) / 3 = 1.
Therefore, the x-coordinate of the centroid of triangle ABC is 1. The correct answer is (-,1). The given answer (-,5/3) is not the correct x-coordinate of the centroid.
if the length of the basketball court is (x+16) and the width is (x-2). what is the area
Answer:
[tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex]
Step-by-step explanation:
a basketball court is a rectangle, therefore its area is length x width.
the length given is (x+16)
the width given is (x-2)
substitute into the rectangular area equation:
length x width = (x+16)(x-2)= [tex]x^{2}[/tex]+14x-32
specific units (e.g. centimetres, meters, feet, etc) were not given so use the term 'units', and because we are dealing with area, use [tex]units^{2}[/tex].
therefore the answer is, [tex]x^{2}[/tex]+14x-32 [tex]units^{2}[/tex].
i hope that helps :)
Answer:
therefore the answer is, [tex]x^{2} +14x-32units^{2}[/tex].
Step-by-step explanation:
the number of geusts,g, coming for dinner is not 8
The number of guests, g, coming for dinner is not 8, is g ≠ 8.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
The expression,
the number of guests, g, coming for dinner is not 8.
That means,
Let the number is g.
According to the question,
the number is not equals to 8.
That means,
the expression in the numerator form,
g ≠ 8.
Therefore, the term in the mathematical form g ≠ 8.
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Lena had 149 dollars to begin with. She just spent k dollars. Using k, write an expression for the number of dollars she has left.
Therefore , the solution to the given problem of expression comes out to be 149-k =x be used it as its expression.
Define Expression .A mathematical expression is made up of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) It is possible to compare expressions and phrases. In English, a phrase by itself could contain an action, but it doesn't constitute a full sentence. In the phrase 4m + 5, for instance, the terms 4m and 5 are separated from the variable m by the arithmetic sign +.
Here,
Given : Lena has $149
she spends k amount of money
The money left be x
=> 149-k =x
Therefore , the solution to the given problem of expression comes out to be 149-k =x be used it as its expression.
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In a basket there are 18 tomatoes, 12 potatoes, and 8 carrots.identify the ratio of carrots and potatoes to tomatoes in all 3 forms.
Answer:
Step-by-step explanation:
Answer: 10:9, 10/9, 10 to 9.
Step-by-step explanation:
Lydia used 1/3 pound of peppers and 1/10 pound of cheese to make 3 pizzas. If Lydia uses the same recipe to make 1 pizza, how much cheese is needed?
Answer: Lydia used 1/3 pound of peppers and 1/10 pound of cheese to make 3 pizzas, which means that she used 1/3 / 3 = 1/9 pound of peppers and 1/10 / 3 = 1/30 pound of cheese per pizza.
If Lydia uses the same recipe to make 1 pizza, she will need 1/9 pound of peppers and 1/30 pound of cheese. Therefore, the amount of cheese needed is 1/30 pound.
Step-by-step explanation:
area of 6ft 10ft 14ft figure
Answer:
209.25
Step-by-step explanation:
Calculate the areas of the triangle, rectangle, and half circle, then add them together:
triangle = 1/2bh = 1/2(6)(10) = 30
rectangle = bh = (14)(10) = 140
half circle = 1/2πr² = 1/2(3.14)(5)² = 39.25
radius = r = D/2 = 10/2 = 5
Total area = 30 + 140 + 39.25 = 209.25
Answer:
209.25 ft²
Step-by-step explanation:
To find the total area of the figure you have to add the areas of the triangle, rectangle and the semi circle.
Area of the triangle.
[tex] \sf \: A = \frac{1}{2} \times base \times height \\ \sf \: A = \frac{1}{2} \times 6 \: ft \times10 \: ft \\ \sf \: A = \frac{1}{2} \times 60 \: {ft}^{2} \\ \sf \: A =30 \: {ft}^{2} [/tex]
Area of the rectangle.
[tex]\sf \: A =length \times width \\ \sf \: A =14 \: ft \times 10 \: ft \\ \sf A =140 \: {ft}^{2} [/tex]
Area of the semi circle.
[tex] \sf \: A = \frac{1}{2} \pi {r}^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times ( \frac{10}{2}) ^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times {5}^{2} \\ \sf \: A = \frac{1}{2} \times \pi \times 25 \\ \sf \: A = \frac{1}{2} \times 3.14 \times 25 \\ \sf \: A = \frac{1}{2} \times 78.5 \\ \sf \: A = 39.25 {ft}^{2} [/tex]
Add up all the areas to find the total area.
[tex] \sf \: Total \: Area = 30 {ft}^{2} + 140 {ft}^{2} + 39.25 {ft}^{2} \\ = 209.25 {ft}^{2} [/tex]
A system of linear equations with an infinite number of solutions is a(n).
_____system.
Answer:
It means that if the system of equations has an infinite number of solution, then the system is said to be consistent.
What is the value of 7/8+ (-2/3) - (-4)?
The value of fraction will be;
⇒ 101/24
What is mean by Fraction?A fraction is a part of whole number, and a way to split up a number into equal parts. Or, A number which is expressed as a quotient is called fraction. It can be written as the form of p : q, which is equivalent to p / q.
Given that;
The expression is,
⇒ 7/8+ (-2/3) - (-4)
Now,
Since, The expression is,
⇒ 7/8+ (-2/3) - (-4)
Simplify as;
⇒ 7/8 - 2/3 + 4
⇒ (21 - 16)/24 + 4
⇒ 5/24 + 4
⇒ (5 + 96) / 24
⇒ 101/24
Thus, The solution is,
⇒ 101/24
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1/3m = 12-m
Please explain step by step to get marked as brainliest.
Step-by-step explanation:
cross multiply
12-m(3m)= 1
12-3m²-1=0
multiply by -1
3m²+1-12=0
3m²= 11
m²= 11/3
m=√11/3.
What are the main things I need to know when doing variables on both sides of the equation?
Answer:
Make sure to keep track of the signs of the variables. If you add or subtract a variable on one side of the equation, you must do the same to the other side.
Don't forget to distribute if you have a variable inside parentheses. For example, if you have 3x + 2(x + 4) = 7, you would need to distribute the 2 to get 3x + 2x + 8 = 7.
When solving for a variable, make sure to perform the same operation on both sides of the equation to isolate the variable. For example, if you want to solve for x in the equation 3x + 2 = 7, you would need to subtract 2 from both sides to get 3x = 5.
In an acid-base titration, a base or acid is gradually added to the other until they have completely neutralized each other. Because acids and bases are usually colorless (as are the water and salt produced in the neutralization reaction), pH is measured to monitor the reaction. Suppose that the equivalence point is reached after approximately 100 mL of a NaOH solution have been added (enough to react with all the acetic acid present) but that replicates are equally likely to indicate from 95 to 104 mL to the nearest mL. Assume that volumes are measured to the nearest mL and describe the sample space. (a) What is the probability that equivalence is indicated at 100 mL? (b) What is the probability that equivalence is indicated at less than 100 mL? (c) What is the probability that equivalence is indicated between 98 and 102 mL (inclusive)?
Neglecting the fractional points and taking the whole number values for volume, the probability of getting equivalence point at 100 ml is 1/10. The probability of getting less than 100 ml is 1/2.
What is probability?The probability is the measurement of the chance of an event to happen. It is determined based on the total possibilities and criteria.
Given that the experiment trials got the values from 95 to 104. From 95 to 104, there are 10 numbers. Thus, the volume of the acid can be any of these 10.
Thus, total possibility = 10.
probability of getting 100 = 1/10
There are 5 volumes which are less than 100 here, [95, 99]. Thus, the probability = 5/10 = 1/2.
There are 5 values between 98 and 102 including these two values.
Hence, probability of getting these range = 5/10 = 1/2.
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A moving company wants to buy a new type of truck and needs to know the volume of the storage compartment before they can decide if they should purchase the truck. What’s is the volume of the storage compartment
Answer: jump off a cliff and shatter your bones
Step-by-step explanation:
Find the range of values of k for which the equation 4x² + 12x + k = 0 has no real roots.
Hello there!
Answer:
[tex](9, +\infty)[/tex]
Step-by-step explanation:
It has no real roots only if
[tex] \sqrt{b {}^{2} - 4ac } [/tex]
has no roots. That means that b² - 4ac is smaller than 0:
[tex]b {}^{2} - 4ac < 0 \\ 12 {}^{2} - 4 \times 4 \times k < 0 \\ 144 - 16k < 0 \\ 144 - 144 - 16k < - 144 \\ - 16k < - 144 \\ k > 9 \\ k \: \: \: in \: \: \: (9, +\infty)[/tex]
we can approach this from the standpoint of the discriminant, if the discriminant is negative then we only get complex roots or namely "imaginary" solutions or values, well, let's check before that happens, when the discriminant is 0.
[tex]\qquad \qquad \qquad \textit{discriminant of a quadratic} \\\\\\ y=\stackrel{\stackrel{a}{\downarrow }}{4}x^2\stackrel{\stackrel{b}{\downarrow }}{+12}x\stackrel{\stackrel{c}{\downarrow }}{+k} ~~~~~~~~ \stackrel{discriminant}{b^2-4ac}= \begin{cases} 0&\textit{one solution}\\ positive&\textit{two solutions}\\ negative&\textit{no solution} \end{cases}[/tex]
[tex]0=(12)^2 - 4(4)(k)\implies 0=144-16k\implies 16k=144 \\\\\\ k=\cfrac{144}{16}\implies k=9\hspace{5em} \stackrel{if~k > 9\textit{, then we land on negative territory}}{{\Large \begin{array}{llll} k > 9 \end{array}}}[/tex]