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3 years ago

Angle ACB is an inscribed angle of circle P. Find x if angle ACB measures x° and arc ACB measures (x + 45)° .

1 answer:

8 0

According to the theorem of circles, angle ACB is equal to 1/2 of the explementary angle of angle APB. The explementary angle then is 360 - (x+45) or 315 - x where x is angle ACB. Hence x = 0.5 * (315-x). x is equal to 105 degrees.

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If Ms. P wants to withdraw $900 from an account earning 4% average annual interest rate at the start of each year for 7 years, h

Ksju [112]

Answer:

Amount he must have in his account today is $5,617.92

Step-by-step explanation:

Data provided in the question:

Regular withdraw amount = $900

Average annual interest rate, i = 4% = 0.04

Time, n = 7 years

Now,

Present Value = $C \times\left[ \frac{1-(1+i)^{-n}}{i} \right] \times(1 + i)$

here,

C = Regular withdraw amount

Thus,

Present Value = $C \times\left[ \frac{1-(1+i)^{-n}}{i} \right] \times(1 + i)$

Present Value = $900 \times\left[ \frac{1-(1+0.04)^{-7}}{ 0.04 } \right] \times(1 + 0.04)$

Present Value = $936 \times\left[ \frac{1 - 1.04^{-7}}{ 0.04} \right]$

Present Value = $936 \times\left[ \frac{1 - 0.759918}{ 0.04} \right]$

Present Value = 936 × 6.00205

Present Value = $5,617.92

Hence,

Amount he must have in his account today is $5,617.92

7 0

3 years ago

Find the approximate volume of a cone with radius 10 inches and a vertical height of 24 inches. ANSWERS: 414,565 in3 2,513 in3 6

OLEGan [10]

Answer:2,513in3

Step-by-step explanation:

7 0

4 years ago

What is 5/12 + 5/12?

agasfer [191]

Answer:

$\frac{5}{6}$

Step-by-step explanation:

1) Join the denominators.

$\frac{5 + 5}{12}$

2) Simplify.

$\frac{10}{12}$

3) Simplify.

$\frac{5}{6}$

Therefor, the answer is 5/6.

and in decimal from it will be, 0.8333333.

5 0

3 years ago

Solve for x in the equation.

labwork [276]

Answer:

The solution is $\displaystyle x=1\pm \sqrt{47}$ . Fourth option

Explanation:

Solve for x:

$2x^2+3x-7=x^2+5x+39$

Move all the terms from the right to the left side of the equation, a zero in the right side:

$2x^2+3x-7-x^2-5x-39=0$

Join all like terms:

$x^2-2x-46=0$

The general form of the quadratic equation is:

$ax^2+bx+c=0$

Solve the quadratic equation by using the formula:

$\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

In our equation: a=1, b=-2, c=-46

Substituting into the formula:

$\displaystyle x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(-46)}}{2(1)}$

$\displaystyle x=\frac{2\pm \sqrt{4+184}}{2}$

$\displaystyle x=\frac{2\pm \sqrt{188}}{2}$

Since 188=4*47

$\displaystyle x=\frac{2\pm \sqrt{4*47}}{2}$

Take the square root of 4:

$\displaystyle x=\frac{2\pm 2\sqrt{47}}{2}$

Divide by 2:

$\displaystyle x=1\pm \sqrt{47}$

First option: Incorrect. The answer does not match

Second option: Incorrect. The answer does not match

Third option: Incorrect. The answer does not match

Fourth option: Correct. The answer matches exactly this option

8 0

3 years ago

Which statement is true about comparing 5.37 and 5.4?

kap26 [50]

It’s either A or C I would pick A even though they don’t really make sense.

5 0

3 years ago