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3 years ago

There are 4 consecutive integers that add up to 154. what is the least of these integers?

Mathematics

2 answers:

ElenaW [278]3 years ago

6 0

I guesstimated and checked my answer to get 37.
37 + 38 + 39 + 40

Ilia_Sergeevich [38]3 years ago

5 0

Step One
Set up the equation.
Let x be the smallest number. A consecutive integer is one that follows after another number that is smaller. The difference between the two numbers is one.

x + x + 1 + x + 2 + x + 3 = 154

Step Two
Collect all the like terms on the left.
4x + 6 = 154

Step 3
Solve
4x + 6 = 154 Subtract 6 from both sides.
4x = 154 - 6
4x = 148 Divide by 4
x = 148 / 4
x = 37
The smallest number is 37 <<<<< answer.

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Which set of steps will translate f(x)=6x to g(x)=6x-5-7

Maurinko [17]

THIS IS THE COMPLETE QUESTION BELOW;

Which set of steps will translate f(x) = 6x to g(x) = 6x – 5 – 7?

Shift f(x) = 6x five units to the left and seven units up.

Shift f(x) = 6x five units to the right and seven units down.

Shift f(x) = 6x seven units to the right and five units up.

Shift f(x) = 6x seven units to the left and five units down.

Answer:

Shift f(x)=6x five units to the left and seven units down.

Step-by-step explanation:

We are told to translate the function below

f(x) = 6x to g(x) = 6x – 5 – 7

Which means the process to translate f(x) into g(x) is required.

According to the translation rule

f(x)-------->f(x)+a

If a<0 it shift to downward

If a>0 it shift to upward

Then we have

(X,y) ----->((x - 5, y)

There is a shift by x coordinates towards left by 5 units

then we would have the function as

f'(x) = 6(x-5)

Following the translation rule there is a shift by the function by 7 units downward direction then we have

(x,y) ----->(x,y -7)

Then we have g(x) = 6x – 5 – 7 as our translation product.

Therefore, shift f(x)=6x five units to the left and seven units down.

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3 years ago

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3 years ago

A cylinder vase has a height of 10 inches and a diameter of 3 inches. If the water raises to 9/10 of the way to the top, approxi

goblinko [34]

Answer:

The volume of water in the vase is $64 in^3$

Step-by-step explanation:

A cylinder vase has a height, h, of 10 inches and its diameter of 3 inches. This means that its radius, r, is:

r = 3 / 2 = 1.5 inches

To find the volume of the water in the vase if the water raises to 9/10 of the way to the top, we first have to find the volume of the vase when it is filled with water and then, find 9/10 of that volume.

The volume of a cylinder is given as:

$V = \pi r^2h$

The volume of the vase will be:

$V = \pi * 1.5^2 * 10\\V = 70.69 in^3$

Hence, the volume of the water in the vase when it is 9/10 filled is:

$\frac{9}{10} * 70.69 = 63.62 in^3$

Approximating to the nearest cubic inch, the volume of water in the vase is $64 in^3$

5 0

3 years ago