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2 years ago

What is the equation of the line that has a slope of -4 and passes through (2, -3)

Mathematics

1 answer:

slega [8]2 years ago

6 0

Answer:

y+3 = -4(x-2)

Step-by-step explanation:

We can use point slope form since we are given a point on the line and a slope,

Point slope form is

(y-y1) = m(x-x1) where m is the slope and (x1,y1) is a point on the line

(y- -3) = -4(x-2)

y+3 = -4(x-2)

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Simplify the following expression as much as you can use exponential properties. (6^-2)(3^-3)(3*6)^4

gtnhenbr [62]

Answer:

Simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

Step-by-step explanation:

We need to simplify the expression $(6^{-2})(3^{-3})(3*6)^4$

Solving:

$(6^{-2})(3^{-3})(3*6)^4$

Applying exponent rule: $a^{-m}=\frac{1}{a^m}$

$=\frac{1}{(6^{2})}\frac{1}{(3^{3})}(18)^4\\=\frac{(18)^4}{6^{2}\:.\:3^{3}} \\$

Factors of $18=2\times 3\times 3=2\times3^2$

Factors of $6=2\times 3$

Replacing terms with factors

$=\frac{(2\times3^2)^4}{(2\times 3)^{2}\:.\:3^{3}} \\=\frac{(2)^4\times(3^2)^4}{(2)^2\times (3)^{2}\:.\:3^{3}} \\$

Using exponent rule: $(a^m)^n=a^{m\times n}$

$=\frac{(2)^4\times(3)^8}{(2)^2\times (3)^{2}\:.\:3^{3}} \\=\frac{2^4\times 3^8}{2^2\times 3^{2}\:.\:3^{3}}$

Using exponent rule: $a^m.a^n=a^{m+n}$

$=\frac{2^4\times 3^8}{2^2\times 3^{2+3}}\\=\frac{2^4\times 3^8}{2^2\times 3^{5}}$

Now using exponent rule: $\frac{a^m}{a^n}=a^{m-n}$

$=2^{4-2}\times 3^{8-5}\\=2^{2}\times 3^{3}\\=4\times 27\\=108$

So, simplifying the expression $(6^{-2})(3^{-3})(3*6)^4$ we get $\mathbf{108}$

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2 years ago

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Answer:

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Carman used her knowledge of angle relationships to find the value of x in the diagram.what is the value of x ?

Sergeeva-Olga [200]

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Step-by-step explanation:

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2 years ago

A diver is swimming at -10m. he then descends 3 m and rises 6 m. at what new level is the diver swimming?

yaroslaw [1]

-10-3+6= -7

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3 years ago

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5. Kalen is trying to find the average of three measurements. The measurements are 13.8, 15.64, and 22.51. He adds the

Marrrta [24]

Answer:

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Step-by-step explanation:

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