F(x)=2x+6
G(x)=-5x-9
Find the product of f and g.
A.-10x^2-54
B.-10x^2-48x-54
C.-10x^2-12x-54
D.-10x^2+48x-54

Answer:

Option B.) 3 inches

Step-by-step explanation:

Let us first express some principles that we can use to solve our problem. Generally, the Volume of a Box is given by:

[tex]V=h*w*l[/tex]

where

[tex]V[/tex] : is the volume

[tex]h[/tex]   : is the height

[tex]w[/tex]   : is the width

[tex]l[/tex]   : is the length

Now we know that:

Volume of Box A ( [tex]V_{A}[/tex] )  is Equal to Volume of Box B ( [tex]V_{B}[/tex] ) so we have:

[tex]V_{A}=(2in)(3in)(6in)\\V_{A}=36 in[/tex]

So now we can find the Length ( [tex]l_{B}[/tex] ) of Box B easily, as we now the volume along with the height and the width, as follow:

[tex]V_{A}=V_{B}=36in\\\\36in = (3in)(4in)l_{B}\\\\36in=(12in)l_{B}\\\\l_{B}=\frac{36in}{12in}\\ \\l_{B}=3in[/tex]

So the Length of Box B is 3 inches, thus Option B. is correct.

Answer:

y=8x-69

Step-by-step explanation:

you would use the equation y-y1 = m (x - x1)

plug in m = 8 , y1 = 3, x1 = 9

now you have y - 3 = 8 (x-9)

distribute 8 --> y-3 = 8x - 72

add three to both sides to get y = 8x - 69

Answer:

[tex]y-3=8(x-9)[/tex]

Step-by-step explanation:

We are given that a line has a slope (m) of 8 and passes through the point (9,3).

We want to write the equation of this line.

There are three ways to write the equation of the line:

As the problem doesn't specify that we have to write the equation in a specific format, any one of the three work.

However, let's write it in point-slope form, as it is the easiest one to write in this case.  

As we are already given the point and the slope, we can plug them into the equation.

Starting with the slope, substitute 8 as m in the equation.

[tex]y-y_1=8(x-x_1)[/tex]

Now, substitute 9 as [tex]x_1[/tex] and 3 as [tex]y_1[/tex].

We get:

[tex]y-3=8(x-9)[/tex]

Answer:

30 minutes

Step-by-step explanation:

Let

y ---> the distance in miles    

x ---> the time in minutes

Remember that

[tex]1\ h=60\ min[/tex]

[tex]766\frac{2}{3}\ mi=\frac{766*3+2}{3}=\frac{2,300}{3}\ mi[/tex]

we have the ordered pairs

[tex](20,\frac{2,300}{3}),(60,2,300)[/tex]

Find the slope

[tex]m=(2,300-\frac{2,300}{3})/(60-20)[/tex]

[tex]m=(\frac{4,600}{3})/(40)[/tex]

[tex]m=\frac{4,600}{120}\\\\m=\frac{115}{3}\ mi/min[/tex]  

Find the linear equation in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=\frac{115}{3}[/tex]

[tex]point\ (60,2,300)[/tex]

substitute

[tex]y-2,300=\frac{115}{3}(x-60)[/tex]

[tex]y-2,300=\frac{115}{3}x-2,300\\\\y=\frac{115}{3}x[/tex]

Is a proportional relationship between the variables x and y (speed)

For y=1,150 miles

substitute the value of y in the linear equation and solve for x

[tex]1,150=\frac{115}{3}x\\\\x=1,150(3)/115\\\\x=30\ minutes[/tex]

Final answer:

It takes approximately 30 minutes for the shadow to travel 1,150 miles during a solar eclipse.

Explanation:

To determine the time it takes for the shadow to travel 1,150 miles, we can set up a proportion using the given information. Let's call the time it takes to travel 1,150 miles 't'. We can set up the proportion:

766.67 miles / 20 minutes = 1,150 miles / t

Now, let's solve for 't'. We can cross-multiply:

766.67 * t = 20 * 1,150

Divide both sides by 766.67:

t = (20 * 1,150) / 766.67

Simplifying the right side of the equation gives us:

t ≈ 30

Therefore, it takes approximately 30 minutes for the shadow to travel 1,150 miles.

Answer:

14 cm

Step-by-step explanation:

10 plus 8 plus 6

perimeter means add up the sides

Answer:

It's expected that Jason make 16 out of 20 free throws

Step-by-step explanation:

1. Let's review the information given to us to answer the question correctly:

Jason's free-throw scoring average = 80%

2. In a recent game Jason attempted 20 free throws. How many free throws would you expect him to make?

Free throws expected to make by Jason = 20 * 80%

Free throws expected to make by Jason = 16

Answer:Just add the top numbers on all of them :)

Step-by-step explanation:

Answer:

Step-by-step explanation:

28.80 = 360x%

28.80 / 360 = x%

0.08 = x%

8% = x <====

To find the sales tax rate, divide the sales tax amount ($28.80) by the cost of the item before tax ($360) to get 0.08. Multiplying this by 100 converts it to a percentage, thus, the sales tax rate is 8%.

The subject of your question is related to sales tax calculations, a topic under mathematics. To find the sales tax rate, we should divide the amount of sales tax by the original cost of the item, then multiply the result by 100 to get the percentage.

Here are step by step calculations:

Therefore, the sales tax rate is 8%.

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Answer:

the answer is b

Step-by-step explanation:

Answer:

13

Step-by-step explanation:

Answer:

16

Step-by-step explanation:

44+4=48

48/3=16

Volume of a rectangular prism is V = L x W x H

The length for the small prism is 6

The width for the small prism is 4

The height for the small prism is 3

So 6 x 4 x 3 = 72

The length for the large prism is 16

The width for the large prism is 9

The height for the large prism is 2

So 16 x 9 x 2 = 288

Now you add the two volumes together: 288 + 72 = 360 ft cubed.

[tex]\frac{5x-20}{14x^{2}-7x }[/tex]

Answer:

3 and 8

Step-by-step explanation:

6,240/3=2080

6,240/9=693.3333333.....

6,240/780

Answer:

The Total earning of Paula riddle from 6 pm to 11 pm is $7.25  

Step-by-step explanation:

Given as :

Paula riddle charges per hour before 9 pm = $2.25 per hour

Paula riddle charges per hour after 9 pm = $2.75  per hour

Let The Total earning of Paula riddle from 6 pm to 11 pm = $A

Now, According to question

∵ before 9 pm , charges = $2.25 per hour

The time spend between 6 pm to 9 pm = 3 hours

So, The charge between 6 pm to 9 pm = $2.25 per hours × 3 hours

i.e  The charge between 6 pm to 9 pm = $6.75

Again

After 9 pm , charges = $2.75 per hour

The time spend between 9 pm to 11 pm = 2 hours

So, The charge between 9 pm to 11 pm = $2.75 per hours × 2 hours

i.e  The charge between 9 pm to 11 pm = $5.5

So, The Total earning of Paula riddle from 6 pm to 11 pm =  charge between 6 pm to 9 pm + charge between 9 pm to 11 pm

i.e A = $6.75 + $5.5

Or, A = $7.25

So, The Total earning of Paula riddle from 6 pm to 11 pm = A = $7.25

Hence, The Total earning of Paula riddle from 6 pm to 11 pm is $7.25  Answer

Answer:

$7.25

Step-by-step explanation:

Answer:

Step-by-step explanation:

Six less than the product of 4 and a number is equal to 2:

n - the number

[tex]4n-6=2[/tex]    add 6 to both sides

[tex]4n-6+6=2+6[/tex]

[tex]4n=8[/tex]            divide both sides by 4

[tex]\dfrac{4n}{4}=\dfrac{8}{4}[/tex]

[tex]n=2[/tex]

Answer:8.300

Step-by-step explanation:

Answer:

8.36

the hundredth place is the second decimal place

Answer:

The equation y = 3x represents a proportional relationship, where y represents distance in miles, and x represents time in hours. The point (3, 9) represents that Alonso walks 9 miles in 3 hours. The point (5, 15) represents that Alonso walks 15 miles in 5 hours.

The graph of line y = 3x represents how much distance is covered in how much time.

Here x is the time and y represents distance traveled. So, for points (3, 9) and (5, 15), it represents that Alonso covered 9 units of distance in 3 units of time and 15 units of distance in 5 units of time.

The general equation of line is,

y = mx + c

where m is the slope and c is the intercept.

Now the given equation is,

y = 3x

This represents Alonso's walking speed.

So it is explained that y distance is covered in x time.

Hence for points (3,9),

x = 3

y = 9

So,

Alonso covered 9 units of distance in 3 units of time.

For point (5,15)

x = 5

y = 15

So,

Alonso covered 15 units of distance in 5 units of time.

Thus,for points (3, 9) and (5, 15), it represents that Alonso covered 9 units of distance in 3 units of time and 15 units of distance in 5 units of time.

To learn more about line:

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Answer:

When combining like terms the given expression turned to the simplest form of expression 3(x+z)+5

That is  4x+7z-x+5-(4z)=3(x+z)+5

Step-by-step explanation:

Given expression is 4x+7z-x+5-(4z)

To combining the given expression to solve it as below :

4x+7z-x+5-(4z)

=4x+7z-x+5-4z

=4x-x+7z-4z+5  ( combining the like terms of x and z )

=3x+3z+5 ( here adding the like terms )

=3(x+z)+5 ( taking the common factor )

Therefore 4x+7z-x+5-(4z)=3(x+z)+5

When combining like terms the given expression turned to the simplest form of expression 3(x+z)+5

That is  4x+7z-x+5-(4z)=3(x+z)+5

Answer:

To solve we must evaluate the expression. In order to evaluate, all you have to do to solve is replace the r with its value of 4 and multiply it by -3. Then, you must add that product to 8.

Step-by-step explanation:

-3r    + 8

-3(4) + 8

-12   + 8

-4

I hope this helps!

- sincerelynini

Answer:

-4

Step-by-step explanation:

-3r+8

-3(-4)+8

-12+8

-4

Answer:

His Age is 4 years old

Step-by-step explanation:

His brother is 7

Answer: 4

Step-by-step explanation:

If Tyler is 4 years old then his brother would be 7 and 7+4=11

Answer:

See attachment

Step-by-step explanation:

The given system is

2x-y=4

x-y=-2

We write the system in slope-intercept form:

y=2x-4

y=x+2

The first equation has slope of 2 and y-intercept at (0,-4)

When y=0, x=2.

We plot (0,-4) and (2,0) to graph this first equation.

The second equation has a slope of 1 and a y-intercept at (0,2)

Also when y=0, x=-2.

We plot (0,2) and (-2,0) and draw a straight line through them.

The graph of the system is shown in the attachment.

Answer:

25 feet

Step-by-step explanation:

In this problem, you would need to use the pythagorean theorem, a^2 + b^2 = c^2.

It doesn't matter which you decide to be a and which you decide to be b, but the diagonal line, or hypotenuse, must be c. In this case, that is the ladder.

Now you plug numbers into the equation. 20^2 + 15^2 = c^2.

Simplify the left side of the equation. 400 + 225 = c^2, 625 = c^2.

Now, since c is still squared, take the square root of both sides. c = 25.

Another way to solve this is using the special triangles. One of the easiest to remember is the 3-4-5 triangle. That is what this triangle is, once you factor out a 5 from all of the numbers (15/5=3, 20/5=4, 25/5=5). Them you just multiply whatever missing number you are looking for by the factor you took out (5 × 5 = 25).

Answer:

E

Step-by-step explanation:

The pattern is 3 letters before.

Answer: x = -1 and x = 1

Step-by-step explanation:

The solution to f(x) = g(x) is the point at which the two intersect , that is , the point at which they are equal. Checking through the table given ,it is only 9 and 12 that is common to both f(x) and g(x) .

Therefore : the solution to f(x) = g(x) is the point where x = -1 and x = 1

Answer:

Can some one help me with mine I’m failing

Step-by-step explanation:

Answer: 4000

Step-by-step explanation:

40(43+57)

40(100)

4000

Answer:

3600

Step-by-step explanation:

(43+47)*40

=90*40

=3600

Answer: [tex]f^{-1}[/tex] (x) = [tex]\frac{x+10}{7}[/tex]

Step-by-step explanation:

To find the inverse , all we need do is to make x the subject of the formula.

y = 7x - 10

Add 10 to both sides

y + 10 = 7x

divide both sides by 7

Therefore:

x = y + 10 / 7 , that is

[tex]f^{-1}[/tex] (x) = [tex]\frac{x+10}{7}[/tex]

Answer:

Step-by-step explanation:

y=7x-10  calculate x :  7x-10 =y

7x = y+10

x = 1/7 y +10/7

the inverse of y=7x-10 is ; y = 1/7 x +10/7

Step-by-step explanation:

to work out surface area you need to figure out the area of each face on the shape.

the first side is 7.5 x 9 = 67.5

there are two of these sides

this makes 135mm

the top side is (4.5 x 6) / 2

this makes 13.5

there are also two of these sides making 27mm

finally the back side is 4.5 x 9 = 40.5

there are only one of these sides

this makes 40.5mm

finally you need to add all these sides

135 + 27 + 40.5 = 202.5

the surface area is 202.5mm

Greater than bc the pieces is bigger