Answer:
Step-by-step explanation:
Given Line equation is 4x+3y=12 and point (3,4)
Given condition two line are parallel
Parallel means two straight lines having same slope.
From the above condition we can use "point-slope" equation.
[tex]y-y_{1} =m(x-x_{1} )[/tex]
From the given line equation we can find slope easily.
We can rewrite the line equation as [tex]y=-\frac{4}{3} x+4[/tex]
We can compare the above equation as y=mx+b
slope [tex]m=-\frac{4}{3}[/tex] and point [tex](x_{1} ,y_{1} )[/tex]=(3,4) submit in slope-point equation.
Becareful while submit point in the slope point equation.
Note:(Many students do mistakes while submitting point.
[tex]y-4=-\frac{4}{3}(x-3)[/tex]
solve and get the answer
Equation of line is 4x+3y=24
How many different ID cards can be made if there are six digits on a card and no digit may be used more than once
On solving the provided question, we can say that by permutation If an ID card has six digits and each digit may only be used once, then 151,200 distinct ID cards can be created.
what is permutation?The permutation of a set in mathematics is essentially the rearranging of its elements if the set is already ordered, or the arrangement of its members in a linear or sequential order. The act of altering the linear order of an ordered set is referred to as a "permutation" in this context. The mathematical calculation of the number of possible arrangements for a given set is known as permutation. Permutation, in its simplest form, refers to the variety of possible arrangements or orders. The placement of the elements matters with permutations. The placement of items in a specific order is known as a permutation. Here, the set's components are sorted in either chronological order or linear order. like in the case of.
There are 6 digits on a card ( 0 - 9 ).
10 * 9 * 8 * 7 * 6 * 5 = 151,200
If an ID card has six digits and each digit may only be used once, then 151,200 distinct ID cards can be created.
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What is the nature of roots of quadratic equation x^2 =- 2x 1?
The nature of roots of quadratic equation x² = -2x + 1 is real and distinct.
The standard form of a quadratic equation is:
ax² + bx + c = 0
The discriminant is defined as:
D = b² - 4ac
Using the value of discriminant, we can determine the nature of roots of a quadratic equation.
If:
D > 0, the quadratic equation has two distinct real roots or the roots are real and distinct.
D = 0, the quadratic equation has 1 real equal roots or the roots are unique
D < 0, the quadratic equation has complex conjugate roots or the roots are imaginary.
In this case, the quadratic equation is:
x² = -2x + 1
transform it into the standard form:
x² + 2x - 1 = 0
Calculate the discriminant:
D = 2² - 4 (-1) = 8
Since D > 0, the roots are two distinct real roots.
Your question is incomplete, but most probably your question was:
What is the nature of roots of quadratic equation x² = -2x + 1?
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PLS HELP I HAVE NO IDEA
Complete the remainder of the table for the given function
y=x/2 + 5
Answer:
Step-by-step explanation:
(-2,4)
(0,5)
(2,6)
(4,7)
Answer: 4, 5, 6, 7,
Step-by-step explanation: From the formula y = x / 2 + 5
substitute x with the value -2
It becomes -2 / 2 + 5
that equals 4
then do the same for the rest
when x = 0
y = 0 / 2 + 5
y = 5
when x = 2
y = 2 / 2 + 5
y = 1 + 5
y = 6
when x = 4
y = 4 / 2 + 5
y = 2 + 5
y = 7
I hope this was helpful
pls solve me this functions question
On solving the provided question, we can say that - the value of the function is f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]; f(x) = x= it doesn't factor
what is function?The topic of numbers, formulae and associated structures, forms and the areas where they exist, quantities and their variations, and spaces where they exist are all included in the field of mathematics. An association between a collection of inputs, each of which has an output, is known as a function. A function is, to put it simply, a relationship between inputs and outputs, where each input has a single, specific outcome. A domain and a codomain, or scope, are assigned to each function. Typically, f is used to represent functions (x). input is x. Four different sorts of functions are available. Based on the following items: One-to-one functions, many-to-one functions, on functions, one-to-one functions, and within functions.
f(x) = [tex](x+3)^2 - 5[/tex]
f(x) = [tex]x^2 + 9 + 3x -5[/tex] = [tex]x^2 +3x +4[/tex]
f(x) = x= it doesn't factor
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Use the graph of the function to find the domain and range of f. (Enter your answer using interval notation.)
The domain and range of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.
What is vertex form of a quadratic function of graph?The vertex form of a quadratic function is f(x) = a(x - h)² + k, where (h, k) is the vertex of the parabola. The coefficient a determines whether the graph of a quadratic function will open upwards or downwards.
From the graph, vertex is (h, k)=(0, 4) and (x, y)=(2, 0)
Here, y= a(x - h)² + k
0=a(2-0)+4
-4=2a
a=2
Substitute, a=2 and (h, k)=(0, 4) in y= a(x - h)² + k, we get
y=2(x-0)²+4
y=2x²+4
So, f(x)=2x²+4
Find the domain by finding where the function is defined. The range is the set of values that correspond with the domain.
Domain: (-∞,∞),{x|x∈R}
Range: [4,∞),{y|y≥4}
Now,
(a) f(-3)= 2(-3)²+4=18
(b) f(2)= 2(2)²+4=12
(c) f(0)= 2(0)²+4=4
(d) f(3)= 2(3)²+4=18
Therefore, the domain and range of the functions are Domain: (-∞,∞),{x|x∈R} and Range: [4,∞),{y|y≥4}.
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Determine the Domain and Range of each graph, then decide if the graph is exponential growth or decay.
The required,
1. figure 1, domain and range are (0, ∞) and {25000, 0}, the graph shows the exponential decay.
2. figure 2, domain and range are (-∞, ∞) and {0, ∞}, the graph shows the exponential growth.
The function which is in format f(x) =aˣ where, a is constant and x is variable, the domain of this exponential function lies (-∞, ∞).
As mentioned in the question, the graph of two exponential functions are given, we have to determine the domain and range of both function and justify which graph shows the exponential growth and decay.
1.
A general exponential equation is given as,
y = aˣ
Graph 1, the graph shows the exponential decay because the value of the function is getting decreasing for the domain 0 to ∞. For this domain, the value of the function starts from point A which is at 25000 and ends at point B where y = 0, so the range is {25000, 0}.
Similarly,
Graph 2 shows exponential growth,
Domain and range are (-∞, ∞) and (0, ∞).
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3. ) Copy Center charges $0. 08 a page for machine fed copies and $0. 20 per page for hand-fed copies. I lagan's
bill for 80 copies of his movie script is $13. 00, how many copies of each type were made?
The number of machine fed copies are 25 and the number of hand fed copies are 55. This is solved forming simultaneous equations.
What are simultaneous equations?
Two or more algebraic equations that share variables, such as x and y, are said to be simultaneous equations. Since the equations are solved simultaneously, they are known as simultaneous equations. These equations alone could have an infinite number of solutions.
Given cost per page of machine fed copies = $0.08
cost per page of hand fed copies = $0.20
Let,
number of machine fed copies = x
number of hand fed copies = y
Given the total number of copies = 80
So we can write the equation as
x + y = 80 ⇒ (1)
It is also given that the total cost of the movie script is $13
So we can the equation as
0.08x + 0.20y = 13 ⇒ (2)
Solving the simultaneous equations (1) and (2)
From (1),
x = 80 - y
Substituting the above in (2)
0.08(80 - y) + 0.20y = 13
0.12y = 6.6
y = 55
x = 80 - 55 = 25
Therefore the number of machine fed copies are 25 and the number of hand fed copies are 55.
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.A car is traveling on a small highway and is either going 55 miles per hour or 35 miles per hour, depending on the speed limits, until it reaches its destination 200 miles away. Letting x represent the amount of time in hours that the car is going 55 miles per hour, and y being the time in hours that the car is going 35 miles per hour, an equation describing the relationship is: 55x+35y=200
A: If the car spends 2.5 hours going 35 miles per hour on the trip, how long does it spend going 55 miles per hour?
B: If the car spends 3 hours going 55 miles per hour on the trip, how long does it spend going 35 miles per hour?
C: If the car spends no time going 35 miles per hour, how long would the trip take? Explain your reasoning.
Answer:
This equation can be used to determine how long the car was traveling at each speed. You can solve for one of the variables by using algebraic techniques. For example, you could subtract 35y from both sides to get:
55x = 200 - 35y
Then divide both sides by 55 to get:
x = (200 - 35y)/55
This equation shows that the value of x (the time spent traveling at 55 mph) is determined by the value of y (the time spent traveling at 35 mph). If you know the value of y, you can use this equation to calculate the value of x.
To find the values of x and y that satisfy the equation, you will need to use additional information. For example, you could set up a system of equations and solve for x and y using techniques such as substitution or elimination.
Step-by-step explanation:
What it means when a function and its inverse is the same?
Step-by-step explanation:
it means that the graph of the function above y=x must be the mirrored image of the graph under y=x.
it means that the function applied to itself gives x.
f(f(x)) = x
e.g.
f(x) = 5 - x
f(f(x)) = 5 - (5 - x) = 5 - 5 + x = x
so, this f(x) is its own inverse.
pls help me on this question
1) false
2) false
3) true
4) true
5) true
Answer:
1 false,2 false,3 true,4 true,5 true
Can someone explain to me how to do this?
solve × ÷ - 2 = 7
x = ?
Answer: -14
Step-by-step explanation: When you have a problem like this all you do in multiply the answer and the number your given.
7x-2 that would by -14
You want to check your answer by changing X for -14 and you solve from there. Plus 2 negatives equal a positive.
Hope this helps!
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{\dfrac{x}{-2} = 7}[/tex]
[tex]\text{Multiply } \rm{ -2}\text{ to both sides}[/tex]
[tex]\mathsf{\dfrac{x}{-2}\times -2 = 7\times -2}[/tex]
[tex]\text{Simplify it}[/tex]
[tex]\mathsf{x = 7\times -2}[/tex]
[tex]\mathsf{x = -14}[/tex]
[tex]\huge\text{Therefore, your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{x = -14}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
Tierra is making steps for a doll house. She has cut a piece of wood that measures 1. 5 centimeters wide and 30 centimeters long. Each step will measure 15 millimeters by 4 millimeters. She will make 21 steps for her doll house. Which are the dimensions of the wood that remains after Tierra finishes making the 21 steps?
The dimensions of the wood that remains after Tierra finishes making the 21 steps is 1.185 cm by 21.6 cm
In Mathematics, dimensions are referred to as measures of size such as length, width, and height of an object or a shape.
A square has sides of equal dimensions.
A rectangle has length and width as its dimensions that define the area of a rectangle.
Also, dimension is used widely to term the figure as one-dimensional, two-dimensional or three-dimensional.
Wood = 1.5 cm by 30 cm
Each cut = .15 mm by 4 mm
Steps = 21
The remaining dimension is calculated as:
Remaining = 1.5 cm - 21 * .15 mm by 30 cm - 21 * 4 mm
Express mm as cm
Remaining = 1.5 cm - 21 * .015 cm by 30 cm - 21 * 0.4 cm
Evaluate the difference
Remaining = 1.185 cm by 21.6 cm
Hence, the dimensions of the wood that remains after Tierra finishes making the 21 steps is 1.185 cm by 21.6 cm
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5. The population of a town went from
100,000 to 137,000 in 5 years. What was
the percent increase in the town's
population
over that time?
A 7.4%
B 37%
C 73%
D 137%
Answer:B or A depending on if it went per year or overall
Step-by-step explanation:100 137, 137-100=37
37/5=7.4
If the original price is 125 pesos and the rate of discount is 25%, how much is the discount? with solution
Answer:
31.25
Step-by-step explanation:
25% * 125 = 25/100 * 125 = 1/4 * 125 = 31.25
If ABCD is dilated by a factor of the
coordinate of D' would be:
4-3
12
3
N
18
T
2
3
4
5
O
9 10
D'=([?]))
Enter
When ABCD is dilated by a factor of the coordinate of D' and the size of the coordinate point is, A"s coordinate would be (-6, -2) (-3, -1) .
what is coordinates ?When locating points or other geometrical objects precisely on a manifold, such as Euclidean space, a coordinate system is a technique that uses one or more integers or coordinates. Locating a point or item on a two-dimensional plane requires the use of coordinates, which are pairs of integers. Two numbers called the x and y coordinates are used to describe a point's location on a 2D plane. a collection of integers that represent specific locations. The figure often has two numbers. The first number denotes the front-to-back measurement, while the second number denotes the top-to-bottom measurement. For example, in (12.5), there are 12 units below and 5 above.
given
The coordinate point's size is specified as (-3, -1).
The coordinate A' will be supplied as follows if the coordinate A is dilatable by a factor of two: A' = (2(-3), 2(-1)) = (-6, -2)
Consequently, A"s coordinate would be (-6, -2)
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The table shows the heights y (in centimeters) of a plant after x weeks. Use the table to complete the statements.
x 0
4
8
y 17 29 41
The table shows pairs of values for the linear function f(x) = 3x
f(x)
-2
1
4
7
10
X
0
1
2
3
4
Which conjecture about linear functions in general is best supported by the
table?
Equal changes in the value of x
result in equal changes in the value
of y.
B. The difference between the x- ar
y-values in each ordered pair (x,
is a constant.
Answer:
the answer is. The answer is
57
Step-by-step explanation:
Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line. complete the diagram to show smaller and larger batches that would taste the same as lin's favorite blend. please
help it's due tomorrow
The ratios on the double line are 3:7, 6:14, 12:28 and 15:35.
What is the ratio?The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.
Given that, Lin makes her favorite juice blend by mixing cranberry juice with apple juice in the ratio shown on the double number line.
From the given double line, the ratio is 9:21.
Completed double line has the following ratios
3:7, 6:14, 12:28, 15:35
Therefore, the ratios on the double line are 3:7, 6:14, 12:28 and 15:35.
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50 points help me out
Answer:x=20
Step-by-step explanation: <2 and <3 must be equal, so set 3x-10 equal to x+30, once simplified you get x equal to 20.
Answer:
x = 20
Step-by-step explanation:
Angle 2 and 3 are alternate (interior) angles which means that they are equivalent to each other.
3x-10=x+30
-x -x
2x-10=30
+10 +10
2x=40
x=20
A line is parallel to y = -3x + 2 and
intersects the point (4, 3). What is the
equation of this parallel line?
y = [?]x + [ ]
Hint: Use the Point-Slope Form: y - y₁ = m(x -x1)
Then write the equation in slope-intercept form.
Enter
Answer:
the equation of line parallel to y=-3x+2
is y=-3x+k---(1)
Since,line(1) passes through point (4,3).
3=-3(4)+k
or,3=-12+k
or,k=3+12
:.k=15
Putting value of k in line (1), we get
y=-3x+15,which is the required eqn.
*mark me brainliest
PLEASE ANSWER ASAP WILL GIVE BRAINLIEST
Answer:
Translate(1.3, -1)
Scale Factor: 2/3
Step-by-step explanation:
First, perform a dilation about the origin. This will make the original shape smaller.
From the given diagram, we can see that R'S' is 10 units long. RS is 15 units long. Using this information, we can create this ratio.
[tex]\frac{10}{15}[/tex]
This means that Triangle R'S'T' is 2/3 of Triangle RST. Construct lines from the origin (the center of dilation) to each point on the original triangle. Then, find two thirds of that line. The new point will be the new y-coordinate.
The new coordinates will (approx.) be:
R = (-2, 4.7)
S = (-2, -5.3)
Only two coordinates are necessary to perform this translation. As per the graph, this triangle must shift approximately 1.3 units up and 1 unit to the left. Thus, the final translation is:
Translate(1.3, -1)
Scale Factor: 2/3
Is y 4 a horizontal asymptote?
Yes, the horizontal asymptote is at y = 4.
The term asymptote in math is known as a straight line that constantly approaches a given curve but does not meet at any infinite distance.
Here we have given the expression y = 4.
In order to find whether it is an horizontal asymptote or not, we have to plot it on the graph,
The first process is to label the graph with x and y axis.
And then we have to defines the scale for the for the graph.
Now, we have to input the expression y = 4 on the graph then we get the graph like the following.
While we looking into the given graph we have identified that the expression y = 4 makes the horizontal asymptote on the graph.
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please help i need help asap i have class in 2 hours pls
The value of x, given the angles next to the triangle, can be found to be 38 °
How to find the value of x ?To find the value of x, you first need to find the value of the other angles in the triangle.
Angles on a horizontal line add up to 180 degrees so the angle to the bottom left is:
= 180 - 134
= 46 °
The angle to the bottom right is:
= 180 - 84
= 96 °
The angles in a triangle add up to 180 ° so the value of x would be:
= 180 - 46 - 96
= 38 °
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Susan earns $10 per hour tutoring elementary students in math. She also earns $15 per
hour cleaning in the library. Her goal each week is to earn at least $240 while working no
more than 20 hours.
Let e represent the number of hours Susan works in one week tutoring elementary students,
and let c represent the number of hours Susan works in one week cleaning the library.
Which inequalities represent Susan's weekly goal of earning money?
Inequalities represent Susan's weekly goal of earning money are:
c + e ≤ 20
15c + 10e ≥ 240
What is an inequality?The term "inequality" in mathematics refers to a connection between two expressions or values that is not equal to each other. Inequality originates from an imbalance, thus. The majority of the time, size comparisons between two numbers on the number line are made.
The most notable instances of social inequality include those related to health care, social class, gender inequality, and wealth disparity. Comparatively speaking, some people in the healthcare system receive better and more skilled care. For these services, they are also likely to pay more.
Given that,
Susan earns $10 per hour tutoring elementary students in math.
She also earns $15 per hour cleaning in the library.
Her goal each week is to earn at least $240 while working not more than 20 hours.
Thus, the equation of inequality:
c + e ≤ 20
15c + 10e ≥ 240
Here, e represent the number of hours Susan works in one week tutoring elementary students.
c represent the number of hours Susan works in one week cleaning the library.
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Solve&Share-
The store sells boxes of adhesive
bandages. The boxes have: 12, 15, 18, 20, 25, 36, 40, 45,
50, 64, 75, or 100 bandages per box.
Which boxes have bandages that can be separated
into 2 first-aid kits with no leftover bandages?
Which boxes have bandages that can be separated into
5 first-aid kits with no leftover bandages?
Which boxes have bandages that can be separated into
10 first-aid kits with no leftover bandages?
Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method presented problem.
What is a unitary method?The term "unitary" refers to a single or separate unit or variable . As a result, this strategy's objective is to establish values in terms of a single unit. For instance, if a car travels 44 kilometres on two litres of gas, the unitary technique can be used to determine how many kilometers it will drive on one.
Here,
Given: Each box of bandages has three packs, with two bandages in each pack.
Now, determine how many bandages there are in two boxes.
Therefore, we solve using the unitary method:
One pack contains two bandages.
In 3 packs, there are therefore = 2*2 = 6 bandages.
One box contains three packs as stated.
Consequently, we multiply 2 by 6 to obtain the bandages in 2 boxes:
=> 2 * 6 = 12
Therefore, there are 12 bandages in 2 boxes, which is the answer to the unitary method's presented problem.
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Making connections between arithmetic sequences and linear function
Use the graph or the formula to write the equation of the line in a slope intercept form
On solving the provided question, we can say that - here in graph we have on solving equation [tex]x^2+ 3y^2 \\[/tex] = [tex]4+3 = 7[/tex]
What is equation?An equation is a formula in mathematics that joins two statements with the equal symbol = to represent equality. The definition of an equation in algebra is a mathematical statement proving the equality of two mathematical expressions. In the equation 3x + 5 = 14, for instance, the terms 3x + 5 and 14 are separated by an equal sign. The link between two phrases on either side of a letter is expressed mathematically. There is often only one variable, which is also the symbol. instance: 2x - 4 Equals 2.
here-
from graph, x= 2
y = 1
[tex]x^2+ 3y^2 \\[/tex]
[tex]4+3 = 7[/tex]
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Assuming that birthdays are distributed equally throughout the week, what is the probability that two people that have never met passing each other on the street were both born on a Friday is
1/7 2/7 1/49 2/49 4/49
Probability of Two people was born on Friday = 1/49
What is the definition of probability?
Possibility of happening an event is called probability. It is given by the ratio of favorable outcome to the total possible outcome. Probability is different kinds such as independent probability, dependent probability, conditional probability and so on.
What is the probability that two people were born on a Friday?
Assume that birthdays are equally distributed throughout the week.
probability of one people having birthday on Friday = 1/ 7
probability of another people has birthday on Friday = 1/7
probability of two people was born on Friday = 1/7× 1/7 = 1/ 49
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Identify like terms
24a - 12b + 4 - 8a
Answer:
The like terms in this expression are 24a and -8a, and -12b and 12b.
Step-by-step explanation:
The like terms 24a and -8a can be combined by adding the coefficients and the variables, which gives us 24a - 8a = 16a.
The like terms -12b and 12b can be combined by adding the coefficients and the variables, which gives us -12b + 12b = 0.
So the like terms in this expression are 24a, -8a, and -12b, 12b.
What are the three types of dilation?
Enlargements of the picture or reductions of the image are both types of dilations.
Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is a picture with the same shape as the original. However, there is a variation in the shape's size.
A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.
The angles of the dilated picture relative to the pre-image stay constant, which is one of the primary characteristics of dilated images.
Even in the enlarged picture, parallel and perpendicular lines are still discernible.
A dilated image's side's midway matches the pre-exactly. image's
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[need some help! will give brainlist!]
Write the terms in standard form. Then state the degree of the polynomial and the leading coefficient (LC).
It can be written in standard form as [tex]5x^2-2+3[/tex] and the degree of polynomial is 2 with leading coefficient as 2.5.
How do you format a standard form of writing?Ax+By=C is the usual form for two-variable linear equations. A standard form linear equation is, for instance, 2x+3y=5. When an equation is given in this format, finding both intercepts is fairly simple (x and y). When attempting to solve systems of two linear equations, this form is also very helpful.
What are some terms examples?The values on which mathematical operations take place in an algebraic expression are known as terms in mathematics. Let's explain with the help of a term example. This algebraic expression has terms 8x and 9, respectively.
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