MATHEMATICS HIGH SCHOOL

Prove that the value of the expression
(3^5-3^4)(3^3+3^2) is divisible by 24

Answers

Answer 1

Answer:

Answer:

243

Step-by-step explanation:

(3^5 – 3^4) (3^3 + 3^2)

= (243 – 81) (27 + 9)

= (162) (36)

= 5832

24 = 8*3

because 832 can be divided by 8 and 5+8+3+2 = 18 is divisible by 3,

5832 is divisible by 24

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The equation shown below involves a perfect square trinomial. 4x2 + 20x + 25 = 7 Which of the following is a step in solving this equation? A. Take the square root of both sides B. Subtract 25 from both sides C. Square both sides D. Divide both sides by 4

How to estimate 518 + 372

Answers

Answer:

900

Step-by-step explanation:

518+372

We have to find the result by estimation

Estimate both the numbers to nearest hundreds

518 is estimated to nearest hundred= 500

372 is estimated to nearest hundred= 400

After adding, 500 and 400, we get

500+400=900

we get our answer 900

Hence, the correct answer is 900

It is 890 but if you estimate it would be 900

While waiting for a video game to download you notice that 30% of 32,000 kilobytes have been dowloaded so far

Answers

30% of 32000 will be 32000 multiplied by 0.3 which would equal 9600 kilobytes

30% and 32 000 kb have been downloaded so far.

Let the total be x.

(30/100)*x = 32000

0.3x = 32000

x = 32000/0.3

x ≈ 106 666.667 kb

So the total is ≈ 106 666.667 kb

Hope this helps.

Find the area of the shaded sector (It is 45 degrees with a radius of 7) Help!!!

Answers

Answer:

Step-by-step explanation:

The formula for the area of a sector is

$A_(s) =(\theta )/(360)*\pi r^2$

where theta is the angle given as 45 and r is the radius (7). Plugging in we get

$A_(s)=(45)/(360)*\pi (7)^2$

Simplify a bit to get

$A_(s)=(1)/(8)*49\pi$

which gives you, in terms of pi:

$A_(s)=(49\pi )/(8)$

or if you need to use the decimal form, rounded to the hundredths position:

A = 19.24

Complete the equation of the graphed linear function in point-slope form.y – (–2) = ___(x – ___)

Answers

$m = (y_(2) - y_(1))/(x_(2) - x_(1)) = (2 - (-2))/(2 - 1) = (2 + 2)/(1) = (4)/(1) = 4$

y - y₁ = m(x - x₁)
y - (-2) = 4(x - 1)
y + 2 = 4(x - 1)
y + 2 = 4(x) - 4(1)
y + 2 = 4x - 4
- 2 - 2
y = 4x - 6

Question is: Solve -7(x+6)=4(x+6)

Answers

$\huge\boxed{x=-6}$

Hey there! Our goal here is to isolate the variable on one side of the equation.

$\begin{aligned}-7(x+6)&=4(x+6)&&\smash{\Big|}&&\textsf{Start with the original equation.}\n-7x+(-7)(6)&=4x+4(6)&&\smash{\Big|}&&\textsf{Distribute.}\n-7x-42&=4x+24&&\smash{\Big|}&&\textsf{Multiply.}\n-7x-4x&=24+42&&\smash{\Big|}&&\textsf{Move the terms.}\n-11x&=66&&\smash{\Big|}&&\textsf{Combine like terms.}\nx&=\boxed{-6}&&\smash{\Big|}&&\textsf{Divide both sides by $-11$.}\end{aligned}$