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4 years ago

The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain?

1 answer:

6 0

The domain of a function contains the x-values of the function while the range of the function contains the y-values of the function. In this case, we substitute 25 and 64 to y. Then,
25 = k2 + 2 k + 1 (k-4) * (k+6) = 0
64 = k2 + 2 k + 1 (k-7) * (k+9) = 0
hence the domain is {-9,-6, 4,7}

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5x + 10 = 20

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To solve for x, we must first isolate the term containing x which in this problem is 5x.

Since 10 is being added to 5x, we subtract 10 from both sides of the equation to isolate the 5x.

On the left, the +10 and -10 cancel out and on the right, 20 - 10 is 10 and we have 5x = 10.

Now we can finish things off by just dividing both sides of the equation by 5. On the left the 5's cancel and on the right, 10 divided by 5 is 2 so x = 2.

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4 years ago

Two triangular prisms are similar. The perimeter of each face of one prism is double the perimeter of the

shepuryov [24]

The area of a shape is the amount of space it can occupy.

The surface area of the larger prism is 4 times the surface area of the smaller prism.

Let the dimension of one side of the smaller prism be: l and w

Let the dimension of one side of the bigger prism be: L and W

So, we have:

$L = 2l$

$W =2w$

The area of these corresponding sides are:

$A_1 =l \times w$ ---- the first

$A_1 = lw$

While, the area of the second is:

$A_2 =2l\times 2w\\$

$A_2 =4lw$

The ratio of these two sides are:

$Ratio = A_1 : A_4$

This gives

$Ratio = lw : 4lw$

Cancel out common terms

$Ratio = 1 : 4$

Express as fractions

$Ratio = \frac 14$

Also, we have:

$Ratio = \frac{Small}{Large}$

This gives

$\frac{Small}{Large} = \frac 14$

Cross multiply

$Large = 4 \tiimes Small$

$Large = 4\4Small$

Hence, option (c) is true

Read more about areas at:

brainly.com/question/6465134

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2 years ago

What is a synthetic material made of?

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3 years ago

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3 years ago

Coach kunal stacks all of the tennis balls in a square pyramid. The number of tennis balls, P(n), in n layers of the square pyra

Zolol [24]

Answer:

D. 9

Step-by-step explanation:

We are told in the question that: The number of tennis balls represented by P(n), in n layers of the square pyramid is given as

P(n) = P(n - 1) + n²

Let's take the first layer

n = 1

P(1) = P(1 - 1) + 1²

P(1) = 1 tennis ball.

It is important to note that the first layers we have one tennis ball.

Let's take the second layer

n = 2

P(2) = P(2 - 1) + 2²

P(2) = P(1) + 2²

Note that: P(1) above = 1

P(2) = 1 + 2²

P(2) = 5 tennis balls

It is important to note that the second layer we have five tennis balls

Let's take the third layer

n = 3

P(3) = P(3 - 1) + 3²

P(3) = P(2) + 3²

Note that: P(2) above = 5

P(3) = 5 + 3²

P(3) = 14 tennis balls

It is important to note that the second layer we have fourteen tennis balls

Let's take the fourth layer

n = 4

P(4) = P(4 - 1) + 4²

P(3) = P(4 - 1) + 4²

P(3) = P(3) + 4²

Note that: P(3) above = 14

P(3) = 14 + 4²

P(3) = 30 tennis balls

It is important to note that the fourth layer we have thirty tennis balls

Hence, the number of tennis balls from the first four layers will be: 1, 5, 14, 30,

So, the number of tennis balls that Coach Kunal could not have is 9.

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3 years ago