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3 years ago

4y p(y) => + 5. If y = 4, then what is the value of p(y)? 9 7 13 37

Mathematics

1 answer:

Leni [432]3 years ago

3 0

9514 1404 393

Answer:

C. 13

Step-by-step explanation:

Put 4 where y is in the equation and do the arithmetic.

$p(y)=\dfrac{4y}{2}+5\\\\p(4)=\dfrac{4(4)}{2}+5 = \dfrac{16}{2}+5=8+5\\\\\boxed{p(4)=13}$

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What is −3/8÷7/12 ?

RSB [31]

Answer:

-9/14

Step-by-step explanation:

This is my simplest-

Do the keep-change-flip method for this problem (and also any problem involving this)

KEEP -3/8

CHANGE the division sign to multiplication

FLIP the last fraction. 7/12 to 12/7

Now solve the problem by multiplying the fractions

-3/8 × 12/7 =

-3 × 12 = -36

8 × 7 = 56

-36 / 56 =

Simplify it by dividing the numerator (up of the line) and denominator (below the line) to get -9/14

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3 years ago

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It is estimated that the average amount owed for student loans in 2010 was $25,250 per student. If the interest rate for studen

Nostrana [21]

Given:
loan amount: 25,250
original interest rate: 3.4%
new interest rate: 6.8%
term: 10 years.

Assuming that simple interest formula is used.
I = P * r * t
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P = principal
r = interest rate
t = term/time

I = 25,250 * 3.4% * 10 years
I = 8,585

I = 25,250 * 6.8% * 10 years
I = 17,170

17,170 - 8,585 = 8,585 Additional interest paid using the new interest rate.

Using an online loan repayment calculator: Here are the following data:
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Loan Balance:$25,250.00
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Loan Interest Rate:3.40%
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6 0

3 years ago

Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha

Pavel [41]

Answer:

$(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14$ .

(Expand to obtain an equivalent expression for the sphere: $x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0$ )

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

$\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}$ .

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

$\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}$ .

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between $\left(x_1, \, y_1, \, z_1\right)$ and $\left(x_2, \, y_2, \, z_2\right)$ would be:

$\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right)$ .

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

$\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}$ .