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3 years ago

identify and equation in point-slope form for the line perpendicular to y=-1/2x-7 that passes through (-3,-2)

Mathematics

1 answer:

bazaltina [42]3 years ago

8 0

Answer:

y +2 = 2(x +3)

Step-by-step explanation:

The equation in point-slope form for a line with slope m through point (h, k) is ...

y -k = m(x -h)

The slope of your given line is the coefficient of x, -1/2. The slope of a perpendicular line will be the negative reciprocal of that: -1/(-1/2) = 2. So, you have m = 2, (h, k) = (-3, -2), and your desired equation is ...

y -(-2) = 2(x -(-3)) . . . . . . which can be simplified to ...

y +2 = 2(x +3)

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Rewrite the function f of x equals 7 times one half to the 3 times x power using the properties of exponents.

Artist 52 [7]

Answer:

f of x equals 7 times one eighth to the x power

Step-by-step explanation:

Given phrase,

function f of x equals 7 times one half to the 3 times x power,

$\implies f(x) = 7(\frac{1}{2})^{3x}$

By the power to power property of exponent,

That is,

$(a^m)^n=a^{m.n}$

$f(x) = 7((\frac{1}{2})^3)^x$

$f(x) = 7(\frac{1}{8})^x$

= f of x equals 7 times one eighth to the x power

8 0

3 years ago

What values of a and b make the equation true? StartRoot 648 EndRoot = StartRoot 2 Superscript a Baseline times 3 Superscript b

kramer

Option C: $a=3, b=4$ is the value of a and b

Explanation:

Given that the expression $\sqrt{648}=\sqrt{2^a\times3^b}$

We need to determine the value of a and b

Let us consider the term $\sqrt{648}$ and take the prime factorization of the term 648

Thus, we have,

648 divides by 2,

$648=2 \cdot 324$

324 divides by 2,

$648=2 \cdot 2 \cdot 162$

162 divides by 2,

$648=2 \cdot 2 \cdot 2 \cdot 81$

81 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 27$

27 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 9$

9 divides by 3,

$648=2 \cdot 2 \cdot 2 \cdot 3 \cdot 3 \cdot 3 \cdot 3$

Thus, we have,

$\sqrt{648}=\sqrt{2^{3} \cdot 3^{4}}$

Therefore, equating the powers of 2 and 3, we get,

$a=3, b=4$

Hence, the value of a and b is 3 and 4

Thus, Option C is the correct answer.

4 0

3 years ago

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What is the equation of the graphed line written in standard form?

IrinaVladis [17]

Y=2x+4
y=2x-4
and the last one is already in standard form

5 0

3 years ago

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HELP! WILL GIVE BRANLIEST!

iogann1982 [59]

10 in each do 10 times 3 then subtract total

6 0

3 years ago

Orlando is doing a math problem where he needs to dilate a triangle by a scale factor of four. The ordered pairs for his pre-ima

Rainbow [258]

Dilation refers to a non rigid motion where a figure is transform and its image has the same form but a different size measure.
Dilation is define by the rule (x,y)-- (kx, ky) where k represents the scale factor.

On this exercise is given that a triangle with vertices (-2,1), (8,4), and (3,0) was dilated by a scale factor of four, and it is asked to find the vertices of the image of the triangle after the dilation occurred.

Pre-image Image
(-2,1) -- (-2*4,1*4) -- (-8,4)
(8,4) -- (8*4,4*4) -- (32,16)
(3,0) -- (3*4,0*4) -- (12,0)

The coordinates representing the vertices of the triangle's image are (-8,4), (32,16), and (12,0); meaning that the ordered pair which is not a coordinate for a point in the triangle's image is (2,1).

5 0

2 years ago

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