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2 years ago

H(n)=n^2-1; find h(4)

Mathematics

2 answers:

LiRa [457]2 years ago

7 0

Answer:

h(4)=4²-1

=16-1

=15

hope it helps.

shtirl [24]2 years ago

4 0

Answer:

h(4) = 7

Step-by-step explanation:

given ,

h(n) = n^2 ‐ 1

if, h(4) = 4^2 ‐ 1

or, h(4) = 16‐1

or, h(4) = 15

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Round the following to the nearest cent: $16.997

Paul [167]

$\$16.99\underbrace{7}_{>5}\approx\$17.00$

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2 years ago

Alberta has 5 shirts and 4 pants. 3 of the shirts are her favorite and 2 of the pants are her favorite. If Alberta chooses an ou

tiny-mole [99]

Answer:

$\frac{3}{10}$

Step-by-step explanation:

In probability, "AND" means "multiplication" and

"OR" means "addition".

We want the probability that she picks FAVORITE SHIRT "AND" FAVORITE PANT.

Probability that she picks favorite shirt = 3/5

Probability that she picks favorite pants = 2/4 = 1/2

Since, "AND", we "multiply" both to get:

3/5 * 1/2 = 3/10

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3 years ago

1. Solve proportion 12/15 = 18/b

omeli [17]

We solve the as follows:

<span>1. Solve proportion 12/15 = 18/b
</span>( 12/15 = 18/b ) b<span>
( 12b/15 = 18 ) 15/12
b = 18(15/12)
b = 45/2

2. Solve equations

A. -x + 4 = x +6
</span>-x + 4 - x = x +6 - x
<span>-2x + 4 - 4 = 6 - 4
-2x = 2
x = -1

B. 5n + 7 =7(n+1) -2n
5n + 7 = 7n + 7 - 2n
5n -7n + 2n = 7 - 7
0 = 0

C. -4(p+2) + 8 = 2(p-1) - 7p + 15
-4p - 8 + 8 = 2p - 2 - 7p + 15
-4p + 7p - 2p = -2 + 15 + 8 - 8
p =13

3. Solve a/b x - c = 0 for x
</span>a/b x - c = 0
( a/b x = c ) b/a
x = bc / a

3 0

3 years ago

You have D dollars to buy fence to enclose a rectangular plot of land (see figure at right). The fence for the top and bottom co

alex41 [277]

The perimeter of the rectangular plot of land is given by the expression below

$P=2x+2y$

On the other hand, since the available money to buy fence is D dollars,

$\begin{gathered} D=4(2x)+3(2y) \\ \Rightarrow D=8x+6y \\ D\rightarrow\text{ constant} \end{gathered}$

Furthermore, the area of the enclosed land is given by

$A=xy$

Solving the second equation for x,

$\begin{gathered} D=8x+6y \\ \Rightarrow x=\frac{D-6y}{8} \end{gathered}$

Substituting into the equation for the area,

$\begin{gathered} A=(\frac{D-6y}{8})y \\ \Rightarrow A=\frac{D}{8}y-\frac{3}{4}y^2 \end{gathered}$

To find the maximum possible area, solve A'(y)=0, as shown below

$\begin{gathered} A^{\prime}(y)=0 \\ \Rightarrow\frac{D}{8}-\frac{3}{2}y=0 \\ \Rightarrow\frac{3}{2}y=\frac{D}{8} \\ \Rightarrow y=\frac{D}{12} \end{gathered}$

Therefore, the corresponding value of x is

$\begin{gathered} y=\frac{D}{12} \\ \Rightarrow x=\frac{D-6(\frac{D}{12})}{8}=\frac{D-\frac{D}{2}}{8}=\frac{D}{16} \end{gathered}$ <h2>Thus, the dimensions of the fence that maximize the area are x=D/16 and y=D/12.</h2><h2>As for the used money,</h2> $\begin{gathered} top,bottom:\frac{8D}{16}=\frac{D}{2} \\ Sides:\frac{6D}{12}=\frac{D}{2} \end{gathered}$ <h2>Half the money was used for the top and the bottom, while the other half was used for the sides.</h2>

7 0

10 months ago

Graph the function by first finding its zeroes. <br> y = x3- 2x2 + x

CaHeK987 [17]

Answer:

The zeros of the function are;

x = 0 and x = 1

Step-by-step explanation:

The zeroes of the function simply imply that we find the values of x for which the corresponding value of y is 0.

We let y be 0 in the given equation;

y = x^3 - 2x^2 + x

x^3 - 2x^2 + x = 0

We factor out x since x appears in each term on the Left Hand Side;

x ( x^2 - 2x + 1) = 0

This implies that either;

x = 0 or

x^2 - 2x + 1 = 0

We can factorize the equation on the Left Hand Side by determining two numbers whose product is 1 and whose sum is -2. The two numbers by trial and error are found to be -1 and -1. We then replace the middle term by these two numbers;

x^2 -x -x +1 = 0

x(x-1) -1(x-1) = 0

(x-1)(x-1) = 0

x-1 = 0

x = 1

Therefore, the zeros of the function are;

x = 0 and x = 1

The graph of the function is as shown in the attachment below;

8 0

2 years ago