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2 years ago

What is the vertex of f(x) = | 8x + 8| - 3?

Mathematics

1 answer:

Harman [31]2 years ago

3 0

Answer:

Step-by-step explanation:

Vertex of y = |x| have the coordinates (0, 0).

f(x) + n - shift the graph n units up

f(x) - n - shift the graph n units down

f(x + n) - shift the graph n units to the left

f(x - n) - shift the graph n units to the right

nf(x) - stretches/shrinks vertically

f(nx) - stretches/shrinks horizontally

We have

f(x) = |8x + 8| - 3 = |8(x + 1)| - 3 = |8| · |x+1| - 3 = 8|x + 1| - 3

g(x) = |x| → f(x) = 8g(x + 1) - 3

vertically streched by 8 (0, 8 · 0) → (0, 0)

shifted 1 unit to the left (0 - 1, 0) → (-1, 0)

shifted 3 units down (-1, 0 - 3) → (-1, -3)

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40 is what percent of 32

Jobisdone [24]

40 = x% of 32

32x = 40
x = 40/32
x = 1.25

multiply by 100 to convert to percentage...

x = 125%

40 is 125% of 32

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2 years ago

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What is the volume of the composite figure? Express the

Papessa [141]

Answer:

$V=312\pi\ mm^{3}$

Step-by-step explanation:

we know that

The volume of the composite figure is equal to the volume of a semi-sphere plus the volume of the cone

$V=\frac{4}{6}\pi r^{3} +\frac{1}{3} \pi r^{2} h$

we have

$r=6\ mm$

$h=14\ mm$

substitute

$V=\frac{4}{6}\pi (6)^{3} +\frac{1}{3} \pi (6)^{2} (14)$

$V=144\pi +168\pi$

$V=312\pi\ mm^{3}$

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2 years ago

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Ava volunteers at an animal shelter with 6 cats. She has 15 cat treats. She gives each cat the same number of treats, and she gi

Delvig [45]

Answer:

Ava gives each cat __2__ treats. __3___ treats are left.

Step-by-step explanation:

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2 years ago

Winston drove 70 mph. If he drives for 3.5 hours how many miles will Winston drive?

Fofino [41]

This problem can be solved using two equations:
The first represents the total trip, which is the miles driven in the morning added to those in the afternoon. Let's call the hours driven in the morning X and the hours driven in the afternoon Y. We get: X + Y = 248.
The second equation relates the miles driven in the morning compared to the afternoon. Since 70 fewer miles were driven in the morning than the afternoon, then X = Y - 70.
Now substitute the equation for morning hours (equation 2) into the total miles equation (equation 1). We get:
(Y - 70) + Y = 248
2Y - 70 = 248
2Y = 318
Y = 159
We know that Winston drove 159 miles in the afternoon.

To find the morning hours, just substitute 159 into the equation for morning hours (equation 2)
X = 159 - 70
X = 89
We now know that Winston drove 89 miles in the morning.

We can check our work by plugging both distances into the total distance equation: 89 + 159 = 248

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1 year ago

A rectangular room is twice as long as it is wide, and its perimeter is 48 meters. Find the width of the room.

Dimas [21]

Answer:

The width of the rectangular room =x= 8

Step-by-step explanation:

Given: A rectangular room is twice as long as it is wide, and its perimeter is 48 meters.

To find: The width of the room.

Solution: Let the width of the rectangular room= x meters, then the length of the rectangular room will be = 2x.

Now, Perimeter of rectangular room=2(l+b)

⇒48=2(2x+x)

⇒24=3x

⇒x=8 meters

Then, the width of the rectangular room =x= 8 meters and the breadth of the rectangular room=2x=2(8)=16 meters.

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2 years ago

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