Marsha bought a pencil for $2.81 and a drink for $3.67. She paid with a $20 bill. How much change should Marsha have received?

Answer:

[tex]y=\frac{15\sqrt{3} }{4}[/tex]

Step-by-step explanation:

Well what you have here are two right triangles within another right triangles created by an altitude. This results in 3 similar triangles (see attached for reference)

As a result , using the properties of similar triangles, and taking ratios of their sides of the medium triangle and the largest triangle, we can form the following relationship:

[tex]\frac{b}{z}=\frac{y}{x} = \frac{z}{a+b}[/tex]  (we know that a+b = 15), hence the equation becomes:

[tex]\frac{b}{z}=\frac{y}{x} = \frac{z}{15}[/tex]  ----------eq 1

If we consider the largest triangle, we will see that

cos 30° = z / 15

but from our special angles (see second attachment) we know that cos 30° = (√3)/2

hence

(√3)/2 = z / 15

z = (15√3) / 2 --------eq 2

from the same largest triangle, we will also see that

sin 30° = x / 15

similarly from our special angles, we know that sin 30° = 1/2

hence,

1/2 = x/15

x = 15/2 --------eq 3

now that we have values for x and z, we can neglect the first term of equation 1 and form an equality with x, y and z

[tex]\frac{y}{x} = \frac{z}{15}[/tex]

[tex]y = x\frac{z}{15}[/tex]  (substituting the values for x and z that we found above)

y = (15/2) · [ (15√3) / 2] / 15

y = (15√3) / 4

[tex]y=\frac{15\sqrt{3} }{4}[/tex]

Answer:

They are inverses since both composition equal x.

Step-by-step explanation:

Given the functions, f(x) = 3x + 1 and g(x) = (x-1) / 3, to check if they are inverses functions, we are to find the inverse of one of the function and check if it will give us the other function.

Let's look for the inverse of f(x).

Given f(x) = 3x+1

Let y = f(x) so that y = 3x+1

Replace y with x

x = 3y+1

Make y the subject of the formula of the resulting equation;

3y = x-1

y = (x-1)/3

The new function of x will be the inverse of f(x)

Hence f^-1(x) = (x-1)/3 = g(x)

Another way to check is to find their composition. Let's find f(g(x) and g(f(x)

F(g(x)) = f((x-1)/3)

Replace x with (x-1)/3 in f(x)

F(g(x)) = 3[(x-1)/3]+1

F(g(x)) = x-1+1

F(g(x)) = x

Similarly for g(f(x));

g(f(x)) = g(3x+1)

Replace x in g(x) with 3x+1

g(3x+1) = (3x+1-1)/3

g(3x+1) = 3x/3

g(3x+1) = x.

Since g(f(x)) = f(g(x)) = x, hence f(x) and g(x) are Inverses functions

Answer:

(3z + 1)(3z + 4)

Step-by-step explanation:

[tex]9 {z}^{2} + 15z + 4 \\ = 9 {z}^{2} + 3z + 12z+ 4 \\ = 3z(3z + 1) + 4(3z + 1) \\ = (3z + 1)(3z + 4)[/tex]

Answer:

x=1+/- the square root of 89

Answer:

x=1+ (square root of 89)

Step-by-step explanation:

Answer:

KCC off KCC off off egg LLC

Answer:

rational

Step-by-step explanation:

3by3=3/3

= 1

1 is not eq. to 9

and 3/3 is 1

and 1 is rational no.

Answer:

R/4 - 1.4 =1.58

R/4 = 1.58 + 1.4

R/4 =2.98

r=11.92

Step-by-step explanation:

Answer:

(x² + 18) units²

Step-by-step explanation:

Area of a rectangle = l*w

There are two shaded rectangles found inside the large rectangle. Let us represent the smaller shaded one as Rectangle 1, the bigger shaded rectangle as Rectangle 2.

Below are the dimensions and area if each of them:

Rectangle 1 (small shaded rectangle):

l = x

w = x

Area = x * x = x² units²

Rectangle 2 (bigger shaded rectangle):

l = 9

w = 2

Area = 9*2 = 18 units²

Total area of the shaded rectangles = x² + 18 = (x² + 18) units²

Answer:

72in

Step-by-step explanation:

area=length x width

a=8x9

Answer:

In ∆ABD and ∆ACD

<BAD =<CAD ( each are half of <A )

<D=<D ( each equal to 90°)

AD = AD ( common)

So ∆ ABD is congruent to ∆ ACD.

Then AB =AC (by C.P.C.T)

Hence,∆ABC is an iso - sceles triangle.

answer

212 - 147 = () times 3.75

147 × 4.25 =

add them together and that's the total amount

Answer:

Horizontal compression

Step-by-step explanation:

Just took a test

Answer: horizontal compression

Step-by-step explanation:

Edge

Answer:

[tex]f^{-1}(0)=6[/tex]

Step-by-step explanation:

So, we have the graph y=f(x).

And we want to find:

[tex]f^{-1}(0)[/tex]

Remember that the inverse of a function is simply the x-values and y-values swapped. To see this, let's let our inverse equal y:

[tex]f^{-1}(0)=y[/tex]

This means that we have the point:

[tex](0,y)[/tex]

So, to find our solution, we will swap the x- and y-coordinates. This gives us:

[tex](x,0)[/tex]

So, simply need to find the x-coordinate such that y is 0.

From our graph, we can see the point (6,0). In other words:

[tex]f(6)=0[/tex]

So:

[tex]f^{-1}(0)=6[/tex]

And we're done!

Answer:

Step-by-step explanation:

-18 is a integer because it has negative sign

☽------------❀-------------☾

Hi there!

~

-18 is an integer number because of the " - " sign. I hope the picture will explain why -18 is an integer number!

❀Hope this helped you!❀

☽------------❀-------------☾

Answer:

The answer is C

Step-by-step explanation:

You have to find the pattern, in this case it's 4,5,6, then 7

Hope this helps! :)

Answer:

its actualy D

Step-by-step explanation:

Answer:

[tex]\theta = 148.8[/tex]

Step-by-step explanation:

Given

[tex]R_x = -419[/tex]

[tex]R_y = -253[/tex]

[tex]R = 490[/tex]

Required

Determine the value of [tex]\theta[/tex]

Since, [tex]\theta[/tex] is counter clockwise from x axis;

The relationship between [tex]\theta[/tex], [tex]R_x[/tex] and R is

[tex]cos\theta = \frac{R_x}{R}[/tex]

Substitute values for Rx and R

[tex]cos\theta = \frac{-419}{490}[/tex]

[tex]cos\theta = -0.8551[/tex]

Take arccos of both sides

[tex]\theta = cos^{-1}(-0.8551)[/tex]

[tex]\theta = 148.770784108[/tex]

[tex]\theta = 148.8[/tex] (Approximated)

Answer:

actually a 56 pound bag cost =9

so one pound bag cost =9/56=0.16 cents

Step-by-step explanation:

Answer:

50 penguins

Step-by-step explanation:

Let the total number of penguins = x

30% of x = 15

[tex]\frac{30}{100}*x=15\\\\\\x=15*\frac{100}{30}\\\\x=50[/tex]

Answer:

50

Step-by-step explanation:

15 x 100 equals 1500

1500 divided by 30 equal 50

Hopefully this helps you :)

pls mark brainlest ;)

The general form of the number is 28,700. The correct option is A.

Any value between 1.0 and 10.0 that can be expressed as a decimal number and multiplied by a power of 10 is referred to as being in standard form.

The given number is 2.87 x 10⁴. The general form of the number can be written as:-

2.87 x 10⁴ = 2.87 x 10000

2.87 x 10⁴  = 28700

Multiply 2.87 by 10000 we will get the general form 28700 for the number.

Therefore, the general form of the number is 28,700. The correct option is A.

To know more about the standard form of the number follow

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Answer:

the answer is .5 i think

Answer:

23

Step-by-step explanation:

Step 1:

3 - -5 (4)

Step 2:

3 - (-20)

Step 3:

3 + 20

Answer:

23

Hope This Helps :)

Answer:

Distributive Property.

Step-by-step explanation:

You distribute the 2 to each of the terms.

Answer:

Hey there!

A good estimation is one dollar.

2 pairs of shoes for 14 dollars= 28 dollars

29-28=1 dollars.

Hope this helps :)

Answer:

2r - 15

Step-by-step explanation:

product of 2 and r is 2r and then minus by 15. im sorry if this is wrong haha

The algebraic expression for the statement"15 less than the product of 2 and r" will be 2r-15.

A phrase is considered a mathematical expression if it contains at least two numbers or variables and one or more mathematical operations. Mathematicians can multiply, divide, add, or subtract. An expression is structured as follows: Number/variable, mathematical operator, and expression.

It is given that the expression is, "15 less than the product of 2 and r."

Let the expression is equated to x in order to represent,

x=15 less than the product of 2 and r

x=2r-15

Thus, the algebraic expression will be 2r-15.

Learn more about the expression here:

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Answer: (A)=10x5−29x4+33x3−18x2−18x+27

Step-by-step explanation:

How i solved it was by simplifying each answer there was available and (A) was the most compatiable answer!

=(2x+−3)(5x4+−7x3+6x2+−9)

=(2x)(5x4)+(2x)(−7x3)+(2x)(6x2)+(2x)(−9)+(−3)(5x4)+(−3)(−7x3)+(−3)(6x2)+(−3)(−9)

=10x5−14x4+12x3−18x−15x4+21x3−18x2+27

=10x5−29x4+33x3−18x2−18x+27

Answer:

=(2x+−3)(5x4+−7x3+6x2+−9)

=(2x)(5x4)+(2x)(−7x3)+(2x)(6x2)+(2x)(−9)+(−3)(5x4)+(−3)(−7x3)+(−3)(6x2)+(−3)(−9)

=10x5−14x4+12x3−18x−15x4+21x3−18x2+27

=10x5−29x4+33x3−18x2−18x+27

Step-by-step explanation:

Answer: It is 20 m, multiply each number by 1.25

Answer:

$4.42!

Step-by-step explanation:

Just add all the prices together then divide by 2!

$1.10 * 2 + $3.79 + $0.95 * 3 = $8. 84

$8.84 ÷ 2 = $4.42!

Answer:64

Step-by-step explanation:multiply the two numbers

Answer:

Step-by-step explanation:

16=k

The value of k from the given equation is 16.

In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.

The given equation is 28=8k+12-7k.

The solution of an equation is the set of all values that, when substituted for unknowns, make an equation true.

Here, 28=k+12

k=28-12

k=16

Therefore, the value of k from the given equation is 16.

To learn more about an equation visit:

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