The graph showsf(x)and its transformationg(x).

What is the function equation for g(x)?

Answer:

Step-by-step explanation:

7/8
------
3/10

use the fraction rule: 7x10/8x3- 35/12

try that, im not sure if its fully correct

Answer:

50x + 9500 ≤ 27500

x ≤ 360

Step-by-step explanation:

50x + 9500 ≤ 27500  Subtract 9500 from both sides

50x + 9500 - 9500 ≤ 27500 - 9500

50x ≤ 18000  Divide both sides by 50

[tex]\frac{50x}{50}[/tex] ≤ [tex]\frac{18000}{50}[/tex]

x ≤ 360

The volume of the triangular prism is 308 in³

Volume is defined as the space occupied within the boundaries of an object in three-dimensional space. It is also known as the capacity of the object.

Given that, Alfred made a container shaped like a triangular prism,

Given are the dimensions, 14 in., 4 in. and 11 in.

Volume of a triangular prism = BxHxL/2

= 14x4x11/2 = 616/2 = 308 in³

Hence, The volume of the triangular prism is 308 in³

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The mark that is required to receive an A on the test is; 75.68

The formula for z-score here with the parameters given is;

z = (x' - μ)/σ

where;

x' is sample mean

μ is population mean

σ is standard deviation

We are given;

p-value = 10% = 0.1

μ = 68

σ = 6

Now, from z-score tables, the z-score at a p-value of 0.1 is z = 1.28. Thus;

1.28 = (x' - 68)/6

x' = 68 + (1.28 * 6)

x' = 75.68

We conclude that this value is the mark required to receive an A on the test.

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The required probability of getting exactly 3 heads is 0.3.

Probability can be defined as the ratio of favorable outcomes to the total number of events.

here,
Total sample space = 2×5 = 10
Favorable outcome (3 heads) = 3
Probability is given of getting exactly 3 heads
= favorable outcome / total sample space

Substitute the value in the above equation
= 3 / 10
= 0.3

Thus, getting the 3 heads while tossing a coin 5 times has a probability of 0.3.

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Therefore , the speed of shadow moving down the wall when he is 5 feet from the wall is 8/3 ft/sec.

A method of determining a function's derivative is differentiation. Mathematicians use the technique of differentiation to determine the instantaneous rate of change in a function based on one of its variables. The most typical example is velocity, which is the rate at which a distance changes in relation to time.

Here,

ΔABC & ΔDBE

=> AC/DE = BC/BE

=> h/6 = 20 /20-x

=> h = 120/20-x

Differentiate w.r.t  to t

=> dh/dt = [tex]\frac{120}{{(20-x)}^{2} }[/tex] * dx/dt

given the man is walking towards wall at the rate of 5 ft/s

thus, dx/dt =5 ft/s

=>dh/dt =  [tex]\frac{120}{{(20-5)}^{2} }[/tex] * 5

=>dh/dt =  8/3 ft /sec

Therefore , the speed of shadow moving down the wall when he is 5 feet from the wall is 8/3 ft/sec.

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Answer:

-48y+24

Step-by-step explanation:

−6⁢(⁠4y + 4y + (−4)⁠)

=-6(8y+-4)

=-48y+24

Answer:

-48y + 24

Step-by-step explanation:

−6⁢(⁠4y + 4y + (−4)⁠) =

= −6⁢(⁠8y - 4)

= -48y + 24

A proportional relationship is when a change in one variable results in a change in the other variable in a consistent manner.

similar to direct variation in the form

y = k × x

where,

y = dependent variable

x = independent variable

k = constant.

The relationship between how much Steven charges and time is a proportional relationship because the rate of change between the two variables is constant. This can be seen in the equations:

For 3 hours: cost = 15.75

For 5 hours: cost = 26.25

The rate of change can be calculated by dividing the difference in costs (26.25 - 15.75) by the difference in time (5 hours - 3 hours) which equals a rate of 5.50 per hour. This rate remains constant for all other time increments, making it a proportional relationship.

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Answer:

j = - 8

Step-by-step explanation:

1 - j/4 - 3

1 is also 4/4

so

4/4 - j/4 = 3

4 - j/ 4= 3

multiply by 4 on both sides

which gets you

-j  + 4 = 12

minus 4 from both sides

-j = 8

j = -8

Answer:j=-8 I hope this helps

Step-by-step explanation:

1-j/4=3

Multiply both sides of the equation by 4

which gives you

4-j=12

Move the constant to the right-hand side and change its sign
-j=12-4

Subtract the numbers

-j=8

Change the signs on both sides of the equation

j=-8 - This is your answer

Answer:

Step-by-step explanation:

g(x) = (-x)1/2

Answer:0.41

Step-by-step explanation:

Factor by grouping: 16x³ +28x² - 28x - 49 = 0 is  (4x² - 7) (4x - 7) = 0

Large polynomials can be divided into groups based on a common factor. As a result, we may factor each distinct group and then merge like words. We refer to this as factoring by grouping.

We have the equation,

16x³ +28x² - 28x - 49 = 0

In order to solve the equation by using factor by grouping:

We find common terms in between,

So, we arrange the terms,

16x³ +28x² - 28x - 49 = 0

4x² (4x - 7) -7 (4x - 7) = 0

Here, we have common term (4x-7).

Factor out the common binomial.

(4x² - 7) (4x - 7) = 0

Therefore, (4x² - 7) (4x - 7) = 0 is the factor.

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Answer:

a. -4

b. 1/4

Step-by-step explanation:

a. [tex]\textrm{slope}_{||} = \dfrac{\textrm{rise}}{\textrm{run}} = \dfrac{-4}{1} = -4[/tex]

b. [tex]\textrm{slope}_\perp = \dfrac{-1}{\textrm{slope}_{||}} = \dfrac{-1}{-4} = \dfrac{1}{4}[/tex]

We can arrange the group in 120960 different ways.

Given,

Number of adults = 7

Number of children = 4

We have to find the number of ways they can stand when no two children are allowed to stand together;

Here,

Arrange 7 adults in a row of 7 ; 7

Number of arrangements = 7! = 5040

Consider that there are four possible placements for a child, but only one youngster can be placed in each of them: on either side of the row of adults, or in between two adults.

Consequently, pick one place for each youngster from the possibilities below: 4 for the first adult, 3 for the second,... the final adult's two options are = 4 × 3 × 2 = 24 arrangements

Add the two groupings together =  5040 × 24 = 120960

Therefore,

There is 120960 ways to arrange the standing position of the group.

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Answer:

x = 3[tex]\sqrt{7- x}[/tex]

Step-by-step explanation:

so what you do here is move the x to the other side.

X^2 = 63 - x

then you square root both sides

so [tex]\sqrt{x^{2} }[/tex] and [tex]\sqrt{63 - x}[/tex]

so you end up with

x =   [tex]\sqrt{63 - x}[/tex]

so now we ask what can we take out? 9 times 7 is 63 and 9 is a perfect square so when we take the square root of that, we end up with

x = 3[tex]\sqrt{7- x}[/tex]

have a good day :)

The value of k for the function k f( 3 ) = 7 f( 2 ) is 2

What is a Function ?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

According to the given information

We are given with the function

f( x ) = 2 -3x

f ( 3 ) = 2 - 3(3)

        = 2 - 9

f ( 3 ) = -7

f ( 2 ) = 2 - 2(2)

        = 2 - 4

f ( 2 ) = -2

We are given

k f( 3 ) = 7 f( 2 )

k ( -7 ) =  7 ( -2 )

k = 2

The value of k for the function k f( 3 ) = 7 f( 2 ) is 2

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987.6 million written in scientific notation is 9.876 × [tex]10^{8}[/tex]

What is scientific notation?

Scientific notation is basically a shortcut for writing numbers. It is a method of expressing real numbers in terms of a significand, multiplied by a power of 10.

When using scientific notation, you're allowed to simplify all the zeros that you have in the number by writing the number as a product of a number and a power of 10. 987.6 million in exponential form is [tex]a^{b}[/tex], a is the base, and b is called the exponent . The term [tex]a^{b}[/tex] is called the exponential expression. 987.6 million = 9.876 x 100,000,000 = 9.876 ×[tex]10^{8}[/tex].

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Answer:

Below

Step-by-step explanation:

3x+15      <==== factor out '3'

3 * ( x+5)       done !

The value of x for the given figure is 2.35 if triangle ΔCDG~ ΔEDF

Three edges and three vertices define a triangle as a polygon. One of geometry's fundamental shapes is this one. The designation "triangle ABC" refers to a triangle containing the vertices A, B, and C. When three points are non-collinear in Euclidean geometry, they each produce a distinct triangle and plane. Since it was first described on the first page of Euclid's Elements, the vocabulary for classifying triangles is more than two thousand years old. Modern categorization names are either literal transliterations of Euclid's Greek or their Latin interpretations.

A closed triangle has 3 sides, 3 angles, and 3 vertices. It is a 2-dimensional shape. Polygons include triangles as well. ABC is used to signify a triangle in the previous illustration.

FD/DC=ED/DG

2x+7/48=5x-2/40

40(2x+7)=48(5x-2)

80x+280=240x-96

160x=376

x=2.35

Therefore, The value of x for the given figure is 2.35 if triangle ΔCDG~ ΔEDF

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The value of y in the equation y=x2+2x+5 when x=3 is y= 20

Simplifying algebraic expressions is the same idea, except you have variables (or letters) in your expression.

simplification is reducing the expression/fraction/problem in a simpler form. It makes the problem easy with calculations and solving

y=x^2+2x+5

mathematically, x=3

substitute the valve of x=3 into the equation

y= 3^2 + 2(3) + 5

y= (3x3) + 2(3) +5

Evaluate the value of y by adding the numbers together

y= 9 + 6+ 5

y= 20

Therefore, the value of y in the equation y=x^2+2x+5  is 20

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The value of x is equal to 2, for the figure A which maps to figure B with a scale factor of 2 1/2 .

Scale factor is the ratio between the scale of a given original object and a new object, which is its representation but of a different size either bigger or smaller.

From the question, figure A maps to figure B with a scale factor of 2 1/2 which implies that figure B was made bigger by multiplying with 2 1/2 , so we can evaluate for the value of x as follows:

2 1/2 = 5/2

x = 5 ÷ (5/2) {changing division to multiplication}

x = 5 × 2/5 {cancel out 5}

x = 2

Therefore, the value of x is equal to 2, using the scale factor of 2 1/2 for figure A and figure B.

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Answer:

b = [tex]\sqrt{2p/a}[/tex]

Step-by-step explanation:

The given equation is:

p=1/2ab^2

Multiply by 2 on both sides

2p = ab^2

Then divide by a on both sides,

b^2 = 2p/a

take square root on both sides, then we can get subject of b,

b = [tex]\sqrt{2p/a}[/tex]

Hence, the subject of the given equation make the value of b is b = [tex]\sqrt{2p/a}[/tex]

The subject of an equation is the value that is being solved for. An equation is a mathematical statement consisting of an equality sign (=) between two expressions that have the same value. The expression on the left side of the equality sign is called the left-hand side, while the expression on the right side of the equality sign is called the right-hand side. The left-hand side of the equation can be thought of as what is being solved for, while the right-hand side of the equation can be thought of as the clues or tools that are used to solve for the left-hand side. For example, in the equation 3x + 1 = 7, the subject of the equation is the variable x, which is the value that is being solved for.

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Step-by-step explanation:

The lateral surface area of a cone is A = π r L, where L = √(r² + h²) is the slant height.

The lateral surface area of a cylinder is A = 2 π r H.

The area of the cylinder's base is A = π r².

The total area is therefore:

A = π r L + 2 π r H + π r²

A = π r² + (π L + 2 π H) r

The total cost of painting the surface is Rs. 1531.20 at a rate of Rs. 140 per 100 cm². Therefore the total surface area is:

A = Rs. 1531.20 / (Rs. 140 / 100 cm²)

A = 1093.71 cm²

Plug in and solve for r:

1093.71 = π r² + (10π + 42π) r

348.14 = r² + 52r

r² + 52r − 348.14 = 0

r = [ -52 ± √(52² − 4(1)(-348.14)) ] / 2

r = [ -52 ± √(52² − 4(1)(-348.14)) ] / 2

r = (-52 ± 64) / 2

r = -58 or 6

Since r > 0, r = 6.

Solve for h:

L² = r² + h²

10² = 6² + h²

h = 8 cm

Answer:

3y, 9y²

Step-by-step explanation:

We use laws of binomial

(a+b)²=a²+2ab+b²

From this, we get

15x × * × 2 = 90xy

2×*=6y

*=3y

Now, we square this term to get the last term

3y×3y=9y²

The system of inequalities that matches the graph is defined as follows:

The first solid line has a positive slope and goes through (-1, -3) and (0, 0). Everything to the left of the line is shaded, hence this is the upper bound of the interval, as it is a solid line, it is a closed interval.

This line has an intercept of zero and a slope of 3, as when x increases by one, y increased by 3, hence the constraint is defined as follows:

y ≤ 3x

he second dashed line has a negative slope and goes through (-2, 3) and (1, -3). Everything to the right of the line is shaded, meaning that this is the lower bound of the interval, with an open interval.

When x increased by 3, y decayed by 6, hence the slope of the line is of:

m = -6/3 = -2.

Then:

y = -2x + b.

When x = 1, y = -3, then the intercept is given as follows:

-3 = -2 + b

b = -1.

Thus the constraint is of:

y > –2x – 1.

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Answer:

Step-by-step explanation:

3/6 + 1/4,  6/12 + 3/12,    12/24 + 6/24,    18/36 + 9/36

The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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The equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

What is the isolation of a variable in an equation?

Equations are relations between two quantities involving variables raised to multiple powers, making up terms along with numerals.

Isolation is the process of moving one variable to one-side of the equation and everything else on the other side of the equation.

How to solve the question?

In the question, we are given an equation, y = mx + b, and are asked to write m in terms of x, y, and b.

This means that we need to isolate the variable m, to get an expression equal to m.

The isolation of the variable m can be done as follows:

y = mx + b,

or, y - mx = mx + b - mx {Subtracting mx from both sides},

or, y - mx = b {Simplifying},

or, y - mx - y = b - y {Subtracting y from both sides},

or, -mx = b - y {Simplifying},

or, (-mx)/(-x) = (b - y)/(-x) {Dividing both sides by (-x)}

or, m = (y - b)/x {Simplifying}.

Thus, the equation y = mx + b, when isolated for the variable m, gives us m in terms of x, y, and b, as m = (y - b)/x.

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