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2 years ago

14

The value of y varies directly as the square of x and y=27 when x=9. Find the equation that represents this relationship. Report

the proportionality constant as a reduced fraction when necessary.

1 answer:

Alik [6]2 years ago

5 0

Answer:

im positive the answer is Y=1/3x2

Step-by-step explanation:

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I need help with these

IrinaVladis [17]

Let x be the number.
"twelve decreased by twice a number" ---> 12 - 2x
"8 times the sum of number and 4" ---> 8(x + 4)
12 - 2x = 8(x + 4)
12 - 2x = 8x + 32 (distributive property)
12 = 10x + 32 (add 2x to both sides)
-20 = 10x (subtract 32 from both sides)
x = -2 (divide both sides by 10)

6 0

2 years ago

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Please help me with these two questions, 10 points for each so in total 20!!

saul85 [17]

Answer:

$\large\boxed{Q2.\qquad C.\ -2x+y=-2}\\\boxed{Q4.\qquad C.\ y=3x+12}$

Step-by-step explanation:

Q2:

The point-slope form of an equation of a line:

$y-y_1=m(x-x_1)$

m - slope

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (4, 6) and (6, 10). Substitute:

$m=\dfrac{10-6}{6-4}=\dfrac{4}{2}=2$

$y-6=2(x-4)$ <em>use distributive property</em>

$y-6=2x-8$ <em>add 6 to both sides</em>

$y=2x-2$ <em>subteact 2 from both sides</em>

$-2x+y=-2$

Q4:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

Put the slope m = 3 and the coordinateso f the point (-2, 6) to the point-slope form of an equation of a line:

$y-6=3(x-(-2))$

$y-6=3(x+2)$ <em>use distributive property</em>

$y-6=3x+6$ <em>add 6 to both sides</em>

$y=3x+12$

4 0

2 years ago

What is the third term of the sequence defined by the recursive rule f(1)=3 f(n)=f(n-1)+4

snow_tiger [21]

What is the third term of the sequence defined by the recursive rule f(1)=3 f(n)=f(n-1)+4

Need f(2):

f(2)=f(2-1)+4
f(2)=f(1)+4
f(2)=(3)+4=7

FIND f(3):
f(3)=f(3-1)+4
f(3)=f(2)+4
f(3)=(7)+4
f(3)=11

5 0

3 years ago

Which expression is equivalent to (x+4)^2

Inessa05 [86]

Answer:

(x+4)(x+4)

Step-by-step explanation:

5 0

3 years ago

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Find the angle between u = (8.- 3) and v = (-3,- 8) Round to the nearest tenth of a degree.

Nimfa-mama [501]

Answer:

<h2>90°</h2>

Step-by-step explanation:

First you must calculate the module or the magnitude of both vectors

The module of u is:

$|u|=\sqrt{(8)^2 + (-3)^2} \\\\|u|=\sqrt{64 + 9}\\\\|u|=8.544$

The module of v is:

$|v|=\sqrt{(-3)^2 + (-8)^2} \\\\|u|=\sqrt{9 + 64}\\\\|u|=8.544$

Now we calculate the scalar product between both vectors

$u*v = 8*(-3) + (-3)*(-8)\\\\u*v = -24+ 24=0$

Finally we know that the scalar product of two vectors is equal to:

$u*v = |u||v|*cos(\theta)$

Where $\theta$ is the angle between the vectors u and v. Now we solve the equation for $\theta$

$0 = 8.544*8.544*cos(\theta)\\\\0 = cos(\theta)\\\\\theta= arcos(0)\\\\\theta=90\°$

the answer is 90°

Whenever the scalar product of two vectors is equals to zero it means that the angle between them is 90 °

5 0

3 years ago

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