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3 years ago

8

What is the slope of the line that passes through the points (-6, 8) and (−16,33)? Write your answer in simplest form.

1 answer:

Leni [432]3 years ago

4 0

Answer:

$-\frac{5}{2}$

Step-by-step explanation:

$\frac{change in Y}{change in X}$

plug in points:

$\frac{8-33}{-6+16}$

$\frac{-25}{10}$

Simplify:

$-\frac{5}{2}$

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Which of the following expressions is equivalent to 1/3 ÷ 3/4

REY [17]

The right answer is D 1/3x4/3

7 0

3 years ago

Prove the divisibility of the following numbers: 5^23−5^21 by 24

vodka [1.7K]

5^23 - 5^21 = 5^(21+2) - 5^21
5^23 - 5^21 = 5^21*5^2 - 5^21*1
5^23 - 5^21 = 5^21*(5^2 - 1)
5^23 - 5^21 = 5^21*(25 - 1)
5^23 - 5^21 = 5^21*24
5^23 - 5^21 = 24*5^21
5^23 - 5^21 = 24*k

The original number is in the form 24k where k = 5^21, so this proves that the original number is a multiple of 24

6 0

4 years ago

Read 2 more answers

How to solve 2x^2 -x -6 =0

gtnhenbr [62]

Answer:

<h2>x = -1.5 or x = 2</h2>

Step-by-step explanation:

$2x^2-x-6=0\\\\2x^2+3x-4x-6=0\\\\x(2x+3)-2(2x+3)=0\\\\(2x+3)(x-2)=0\iff2x+3=0\ \vee\ x-2=0\\\\2x+3=0\qquad\text{subtract 3 from both sides}\\2x=-3\qquad\text{divide both sides by 2}\\\boxed{x=-1.5}\\\\x-2=0\qquad\text{add 2 to both sides}\\\boxed{x=2}$

4 0

3 years ago

What is 2 (log Subscript 3 Baseline 8 + log Subscript 3 Baseline z) minus log Subscript 3 Baseline (3 Superscript 4 Baseline min

Ilya [14]

Answer:

Value of expression in single logarithm is $\log_3\left(2z^2\right)$ .

Step-by-step explanation:

Given expression is,

$2\left(\log_3\left(8\right)+\log_3\left(z\right)\right)-\log_3\left(3^4-7^2\right)$

Now using logarithmic rule to solve the expression as follows,

Applying product rule of logarithmic,

$\log_c\left(a\right)+\log_c\left(b\right)=\log_c\left(ab\right)$

Therefore,

$2\log_3\left(8z\right)-\log_3\left(3^4-7^2\right)$

Applying power rule of logarithmic,

$a\log_c\left(b\right)=\log_c\left(b^a\right)$

Therefore,

$\log_3\left(\left(8z\right)^2\right)-\log_3\left(3^4-7^2\right)$

$\log_3\left(\left(64z^2\right)\right)-\log_3\left(3^4-7^2\right)$

Applying quotient rule of logarithmic,

$\log_c\left(a\right)-\log_c\left(b\right)=\log_c\left(\frac{a}{b}\right)$

Therefore,

$\log_3\left(\dfrac{\left(64z^2\right)^2}{3^4-7^2}\right)$

Simplifying,

$\log_3\left(\dfrac{\left(64z^2\right)^2}{81-49}\right)$

$\log_3\left(\dfrac{\left(64z^2\right)^2}{32}\right)$

$\log_3\left(2z^2\right)$

Therefore value of expression is $\log_3\left(2z^2\right)$

6 0

4 years ago

Read 2 more answers

If f(x) = 3x² - 4 and g(x)= x+2, find (f - g)(x).

evablogger [386]

Answer:

D. 3x² - x - 6

Step-by-step explanation:

If f(x) = 3x² - 4 and g(x)= x+2, find .

We know that (f - g)(x) = f(x) - g(x)

Then

(f - g)(x) = (3x² - 4) - (x+2)

= 3x² - 4 - x - 2

= 3x² - x - 4 - 2

= 3x² - x - 6

7 0

2 years ago