5. A negative number squared decreased by 7 times that number is 30. Find the number

What is the function g(x) created from f(x) = x^2 by moving the graph left 9 units, vertically stretching it by a factor of 4, a

MariettaO [177]

Given:

The parent function is $f(x)=x^2$

We need to determine the function g(x) created from the function f(x) by moving the graph left 9 units, vertically stretching it by a factor of 4, and shifting the graph up 5 units.

Shift left 9 units:

The rule to shift the graph c units to the left is given by

$y=f(x+c)$

where c is the positive real number.

Hence, to shift the graph 9 units to the left is given by

$f(x)=(x+9)^2$

Vertical stretch by a factor of 4:

The rule to stretch the graph vertically by a factor of c is given by

$y=cf(x)$

where $c>1$

Hence, to stretch the graph vertically by a factor of 4, we have;

$f(x)=4(x+9)^2$

Shifting 5 units up:

The rule to shift the graph c units upward is given by

$y=f(x)+c$

where c is the positive real number.

Hence, to shift the graph 5 units upward is given by

$f(x)=4(x+9)^2+5$

Therefore, the function $g(x)=4(x+9)^2+5$ is created from the graph $f(x)=x^2$ by moving the graph left 9 units, vertically stretching it by a factor of 4 and shifting up 5 units.

Hence, the graph g(x) is $g(x)=4(x+9)^2+5$

5 0

3 years ago

A conical pile of road salt has a diameter of 112 feet and a slant height of 65 feet. After a storm, the linear dimensions of th

QveST [7]

we know that

the volume of a cone is equal to

$V= \frac{1}{3} \pi r^{2}h$

in this problem

the radius is equal to

$r= \frac{112}{2}= 56ft$

1) Find the height of the cone before the storm

Applying the Pythagorean Theorem find the height

$h^{2} = l^{2}-r^{2}$

$l=65 ft$

$h^{2} = 65^{2}-56^{2}$

$h^{2} = 1,089$

$h=33 ft$

2) Find the volume before the storm

$V= \frac{1}{3}*\pi* 56^{2}*33$

$V=34,496\pi\ ft^{3}$

3) Find the volume after the storm

After a storm, the linear dimensions of the pile are 1/3 of the original dimensions

so

r=(56/3) ft

h=(33/3)=11 ft

$V= \frac{1}{3}*\pi* (56/3)^{2}*11$

$V= 1,277.63\pi\ ft^{3}$

4) Find how this change affect the volume of the pile

Divide the volume after the storm by the volume before the storm

$\frac{1,277.63 \pi }{34,496 \pi } = \frac{1}{27}$

therefore

the answer part a) is

The volume of the pile after the storm is $\frac{1}{27}$ times the original volume

Part b) Estimate the number of lane miles that were covered with salt

5) Find the amount of salt that was used during the storm

$=34,496 \pi - 1,277.63 \pi \\= 33.218.37 \pi \\= 104,358.59\ ft^{3}$

6) Find the pounds of road salt used

$104,358.59*80=8,348,687.2\ pounds$

7) Find the number of lane miles that were covered with salt

$8,348,687.2/350=23,853.39 \ lane\ miles$

therefore

the answer part b) is

the number of lane miles that were covered with salt is $23,853.39 \ lane\ miles$

Part c) How many lane miles can be covered with the remaining salt? Round your answer to the nearest lane mile

the remaining salt is equal to $1,277.63\pi\ ft^{3}$

$1,277.63\pi\ ft^{3}=4,013.79\ ft^{3}$

8) Find the pounds of road salt

$4,013.79*80=321,103.20\ pounds$

9) Find the number of lane miles

$321,103.20/350=917.44 \ lane\ miles$

therefore

the answer part c) is

the number of lane miles is $917 \ lane\ miles$

7 0

4 years ago

What is the value of 17-2(5-3)

Shkiper50 [21]

Answer:

13

Step-by-step explanation:

17-10+6

7+6=13

hope it helps

5 0

3 years ago

Help help help help help

attashe74 [19]

Answer:

i dont now

Step-by-step explanation:

inde man kona ka balo sorry

7 0

3 years ago

Read 2 more answers

George decides to walk from his home to Tina's house down the street. On the way,

hichkok12 [17]

Answer:

The coordinates of the gas station are (5, 9)

Step-by-step explanation:

As given,

George begins at (2,3), ends at (9,17), and stops at the gas station at (x,y). If the part to part ratio is 3:4

A P B

(2, 3) (x, y) (9, 17)

3 : 4

we use the Interval Division formula :

If P(x,y) lies on the interval A(x1,y1), B(x2,y2) such that AP:PB=a:b, with a and b positive, then

x= $\frac{bx1 + ax2}{a + b}$

y= $\frac{by1 + ay2}{a + b}$

Here , (x1, y1) = (2, 3)

(x2, y2) = (9, 17)

a : b = 3 : 4

⇒ x= $\frac{bx1 + ax2}{a + b}$ = $\frac{4(2) + 3(9)}{3 + 4} = \frac{8 + 27}{7} = \frac{35}{7} = 5$

y= $\frac{by1 + ay2}{a + b}$ = $\frac{4(3) + 3(17)}{3 + 4} = \frac{12 + 51}{7} = \frac{63}{7} = 9$

∴ The coordinates of the gas station are (5, 9)

3 0

3 years ago