MATHEMATICS HIGH SCHOOL

What is the equation of a line that passes through the points (3, 6) and (8, 4)?

Answers

Answer 1
Answer:

Answer:

2x + 5y = 36 in standard form

Step-by-step explanation:

m = (y_(2) -y_(1) )/(x_(2) -x_(1) )

y - y_(1) = m( x - x_(1) )

~~~~~

(3, 6)

(8, 4)

m = -(2)/(5)

y - 6 = -(2)/(5) ( x - 3 )

y = -(2)/(5) x + (36)/(5) in slope-intercept form

2x + 5y = 36 in standard form
Answer 2
Answer:

Answer:

D.

Step-by-step explanation:

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Find the area of a circle circumscribed about an equilateral triangle whose side is 18 inches long.a. 81
b. 108
c. 243

Answers

The\ area\ of\ a\ circle:A_O=\pi r^2\ \ \ \ /r-a\ radius/\nThe\ length\ of\ a\ radius\ of\ a circle\ circumscribed\ about\ an\nequilateral\ triangle:r=(a\sqrt3)/(3)\ \ \ /a-a\ lenght\ of\ a\ side\ the\ triangle\n-------------------------------\nr=(18\sqrt3)/(3)=6\sqrt3\ (in)\n\nA_O=\pi\cdot\left(6\sqrt3\right)^2=\pi\cdot6^2\cdot\left(\sqrt3\right)^2=\pi\cdot36\cdot3=108\pi\ (in^2)\n\n\pi\approx3.14\n\ntherefore\n\nA_O\approx108\cdot3.14=339.12\ (in^2).....
See attached for work.
s=18\rightarrow r=6\sqrt3\rightarrow A_\odot=\pi(6\sqrt3)^2=\boxed{108\pi\ in^2}

During her first year of college, Sara put $2000 in the bank to save for a trip to Italy after graduation. The money earned 3% simple annual interest. After 4 years, how much money did she have in the bank for her trip?

Answers

Answer:

2,240

Step-by-step explanation:

Sara will have US$ 2,251.02 in the bank after 4 years for her trip to Italy.

Step-by-step explanation:

1. Let's review the data given to us for solving the question:

Investment of Sara during her 1st year of college = US$ 2,000

Duration of the investment = 4 years

Annual interest rate = 3%

2. Let's find the future value of this investment after 4 years, using the following formula:

FV = PV * (1 + r) ⁿ

PV = Investment of Sara during her 1st year of college = US$ 2,000

number of periods (n) = 4

rate (r) = 3% = 0.03

Replacing with the real values, we have:

FV = 2,000 * (1 + 0.03) ⁴

FV = 2,000 * (1.03) ⁴

FV = 2,000 * 1.12550881

FV = 2,251.02

Sara will have US$ 2,251.02 in the bank after 4 years for her trip to Italy. Later you round the answer and that gives you 2,240

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a lotStep-by-step explanation:

A person is 5 feet tall is standing 132 feet from the base of the tree , and tree casts a 143 foot shadow. The persons shadow is 11 feet in length. What is the height?

Answers

the height of the tree is 65 feet.
I did not understand what is the question

A1 = -5 and a4 = -23 find a23

Answers

It’s minus 6…so that should get you your 23rd number, 138

The value pi/4 is a solution for the equation 3 sqrt 2 cos theta+2=-1

Answers

Answer:

FALSE

Step-by-step explanation:

3\sqrt2\cos\theta+2=-1\n\n\text{Method 1}\n\n\text{Put}\ \theta=(\pi)/(4)\ \text{to the equation and check the equality:}\n\n\cos(\pi)/(4)=(\sqrt2)/(2)\n\nL_s=3\sqrt2\cos(\pi)/(4)+2=3\sqrt2\left((\sqrt2)/(2)\right)+2=((3\sqrt2)(\sqrt2))/(2)+2\n\n=((3)(2))/(2)+2=3+2=5\n\nR_s=-1\n\nL_s\neq R_s\n\n\boxed{FALSE}

\text{Method 2}\n\n\text{Solve the equation:}\n\n3\sqrt2\cos\theta+2=-1\qquad\text{subtract 2 from both sides}\n\n3\sqrt2\cos\theta=-3\qquad\text{divide both sides by}\ 3\sqrt2\n\n\cos\theta=-(3)/(3\sqrt2)\n\n\cos\theta=-(1)/(\sqrt2)\cdot(\sqrt2)/(\sqrt2)\n\n\cos\theta=-(\sqrt2)/(2)\to\theta=(3\pi)/(4)+2k\pi\ \vee\ \theta=-(3\pi)/(4)+2k\pi\ \text{for}\ k\in\mathbb{Z}\n\n\text{It's not equal to}\ (\pi)/(4)\ \text{for any value of }\ k.

How to solve this problem

Answers

Since they are congruent, all will be the same value.

c = 3
∠d = 38°  (asked for the angle)
g = 5
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