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3 years ago

A line passes through ( 2, -1) and (4,5)

Mathematics

1 answer:

shusha [124]3 years ago

5 0

Answer:

A) $-3x+y=-7$

Step-by-step explanation:

Slope of the line:

$\frac{5-(-1)}{4-2} =\frac{6}{2} =3$

$y=mx+b$

$y=3x+b$

Plug in x and y values of any of the points.

$5=3(4)+b$

$5=12+b$

$b=-7$

Equation of the line:

$y=3x-7$

Subtract 3x from both sides:

$y-3x=-7$

$-3x+y=-7$

A is correct.

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How do you simplify this expression?

alisha [4.7K]

Solve the terms in parentheses first. We'll start on the denominator.

The denominator has an exponent for a fraction that also includes exponents. To multiply exponents within parentheses that are raised to a power, use this rule:

$(x^a)^b = x^{a \cdot b}$

Simplify the denominator:

$(\frac{3^4}{7^3} )^2 = \frac{3^8}{7^6}$

Solve the fractions in the numerator:

$(\frac{3}{5})^5 = \frac{3^5}{5^5}$

$(\frac{9}{7})^2} = \frac{9^2}{7^2}$

The problem should now read:

$\frac{\frac{3^5}{5^5} \cdot \frac{9^2}{7^2}}{\frac{3^8}{7^6}}$

There is a denominator in a denominator. We can bring that to the numerator of the overall fraction:

$\frac{\frac{3^5}{5^5} \cdot \frac{9^2}{7^2}}{\frac{3^8}{7^6}} = \frac{\frac{3^5}{5^5} \cdot \frac{9^2}{7^2} \cdot {7^6}}{3^8}}$

Using a calculator, simplify the numerator:

$\frac{3^5}{5^5} \cdot \frac{9^2}{7^2} \cdot {7^6} = \frac{19683}{7}$

The fraction should now read:

$\frac{\frac{19683}{7}}{3^8}$

There is a denominator in the numerator. This can be brought down to the overall denominator:

$\frac{\frac{19683}{7}}{3^8} = \frac{19683}{3^8 \cdot 7}$

Factor 19683:

$19683 = 3 \cdot3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 \cdot 3 = 3^9$

$\frac{19683}{3^8 \cdot 7} = \frac{3^9}{3^8 \cdot 7}$

Simplify the exponents:

$\frac{3^9}{3^8} = 3$

The following fraction will be your answer:

$\boxed{\frac{3}{7}}$

8 0

4 years ago

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Vlad1618 [11]

ANSWER

$< \: WRS \: \:and \: < \: \: VRT$

EXPLANATION

Vertical angles face each other directly opposite just like the angles formed on the opposite sides of the letter X.

Vertical angles, also called vertically opposite angles are equal.

From the above diagram,
$< \: WRS= < \: VRT$

because they are vertically opposite to each other.

The correct answer is B.

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3 years ago

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