F(j)=6j+5. <br> Find f(1/3)

Darius is a graphic designer he makes a sign for a company that has a width of 2 feet and a length of 2 feet 6 inches the compan

Sav [38]

Answer:

$\frac{1}{3}$

Step-by-step explanation:

Width of the sign made by Darius initially = 2 feet

Length of the sign = 2 feet 6 inches

Dimension of the flyer are 10 inches by 8 inches. Since, in original sign the measure of length is greater, therefore, the length of flyer is 10 inches and its width is 8 inches.

In order to find the scale factor we must convert the lengths and widths to same units. Lets convert the length and width of sign into inches.

Since, 1 feet = 12 inches

Length of the sign = 2 feet 6 inches = 2(12) + 6 inches = 30 inches

Width of the sign = 2 feet = 2(12) inches = 24 inches

Now we can find the scale factor by either comparing the lengths or widths of both the designs. Scale factor will be equal to the ratio of corresponding lengths/widths.

So, the scale factor would be:

Length of Flyer : Length of Sign

= 10 inches : 30 inches

= 1 : 3

= $\frac{1}{3}$

This shows, the length of flyer is $\frac{1}{3}$ times as that of the sign. So, the scale factor that Darius must use is $\frac{1}{3}$ . The length and width of the flyer are $\frac{1}{3}$ as that of the sign.

The same scale factor would result if we would have used the ratio of widths instead of the lengths.

Scale Factor = Width of Flyer : Width of sign

= 8 : 24

= 1 : 3

Therefore, Darius must type the scale factor of $\frac{1}{3}$ in his computer to get the size of the flyer.

7 0

3 years ago

What is the sum of the interior angles of the polygon pictured below?

kkurt [141]

3420°

explanation:

the equation of the sum of interior angles are (n-2)x180

polygon above has 21 sides so you sub n as 21 and plug the equation in the calculator

8 0

3 years ago

Read 2 more answers

A ball is thrown into the air from a height of 4 feet at time t = 0. The function that models this situation is h(t) = -16t2 + 6

katrin2010 [14]

Answer:

Part a) The height of the ball after 3 seconds is $49\ ft$

Part b) The maximum height is 66 ft

Part c) The ball hit the ground for t=4 sec

Part d) The domain of the function that makes sense is the interval

[0,4]

Step-by-step explanation:

we have

$h(t)=-16t^{2} +63t+4$

Part a) What is the height of the ball after 3 seconds?

For t=3 sec

Substitute in the function and solve for h

$h(3)=-16(3)^{2} +63(3)+4=49\ ft$

Part b) What is the maximum height of the ball? Round to the nearest foot.

we know that

The maximum height of the ball is the vertex of the quadratic equation

so

Convert the function into a vertex form

$h(t)=-16t^{2} +63t+4$

Group terms that contain the same variable, and move the constant to the opposite side of the equation

$h(t)-4=-16t^{2} +63t$

Factor the leading coefficient

$h(t)-4=-16(t^{2} -(63/16)t)$

Complete the square. Remember to balance the equation by adding the same constants to each side

$h(t)-4-16(63/32)^{2}=-16(t^{2} -(63/16)t+(63/32)^{2})$

$h(t)-(67,600/1,024)=-16(t^{2} -(63/16)t+(63/32)^{2})$

Rewrite as perfect squares

$h(t)-(67,600/1,024)=-16(t-(63/32))^{2}$

$h(t)=-16(t-(63/32))^{2}+(67,600/1,024)$

the vertex is the point (1.97,66.02)

therefore

The maximum height is 66 ft

Part c) When will the ball hit the ground?

we know that

The ball hit the ground when h(t)=0 (the x-intercepts of the function)

so

$h(t)=-16t^{2} +63t+4$

For h(t)=0

$0=-16t^{2} +63t+4$

using a graphing tool

The solution is t=4 sec

see the attached figure

Part d) What domain makes sense for the function?

The domain of the function that makes sense is the interval

[0,4]

All real numbers greater than or equal to 0 seconds and less than or equal to 4 seconds

Remember that the time can not be a negative number

6 0

3 years ago

Please help me with this

Zanzabum

Answer:

x=

−4y+32

9

Step-by-step explanation:

Let's solve for x.

y=

−9

4

x+8

Step 1: Flip the equation.

−9

4

x+8=y

Step 2: Add -8 to both sides.

−9

4

x+8+−8=y+−8

−9

4

x=y−8

Step 3: Divide both sides by (-9)/4.

−9

4

x

−9

4

=

y−8

−9

4

x=

−4y+32

9

I think this is the right answer.

6 0

3 years ago

If the check after the substitution of the answer doesn't work, does that mean that the result is incorrect for equation with va

Alecsey [184]

I don't understand what your point is. Mind posting a picture or something?

8 0

3 years ago

F(j)=6j+5. Find f(1/3)