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Step2247 [10]
3 years ago
6

WILL GIVE BRAINLY!! For the data in the table, does y vary directly with x? And if so write an equation for the direct variation

.
X= 16,32,48

Y= 4,16,16

A. yes; y=2x
B. yes; y=4x
C. yes; y=8x
D. no; y does not vary directly with x
Mathematics
1 answer:
lorasvet [3.4K]3 years ago
3 0
The correct answer is
A. Yes; y=2x
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Solving simultaneous equations with one quadratic, x^2+y^2=16 and y=x+3
Svetlanka [38]
If y=x+3, then in the first equation you have

x^2+(x+3)^2=x^2+(x^2+6x+9)=2x^2+6x+9=16

Rewriting a bit, you get

x^2+3x+\dfrac92=8

x^2+3x+\dfrac94+\dfrac94=8

\left(x+\dfrac32\right)^2=\dfrac{23}4

x=-\dfrac32\pm\dfrac{\sqrt{23}}2

Now, since y=x+3, you also get

y=-\dfrac32\pm\dfrac{\sqrt{23}}2+3=\dfrac32\pm\dfrac{\sqrt{23}}2

So, there are two solutions here:

(x,y)=\left(-\dfrac32+\dfrac{\sqrt{23}}2,\dfrac32+\dfrac{\sqrt{23}}2\right)
(x,y)=\left(-\dfrac32-\dfrac{\sqrt{23}}2,\dfrac32-\dfrac{\sqrt{23}}2\right)
7 0
3 years ago
Find the gradient of the line segment between the points (3,-2) and (5,-5). Give your answer in its simplest form.
Paraphin [41]

Answer:

2/7

Step-by-step explanation:

gradient y²-y¹/x²-x¹=4-2/4-(-3)

=2/7

{Taking (x¹,y,¹)=(-3,2)

and(x²-y²)=(4,4)

4 0
3 years ago
Solve for the two acute angles
sineoko [7]

Answer:

Angle A = 37 degrees, and Angle B = 53 degrees.

Step-by-step explanation:

We know that this is a right triangle, where angle C is 90 degrees. Since we know the sum of all these angles is 180 in any triangle, we can create an equation.

Angle A = 6x + 7

Angle B = 11x-2

Angle C = 90 degrees

A + B + C = 180

Substitute:

6x + 7 + 11x - 2 + 90 = 180

17x + 5 + 90 = 180

17x + 5 = 90

17x = 85

x = 5

Now substitute 5 for x in both acute angles and you will get your answer.

Angle A = 6(5) + 7

Angle A = 30 + 7

Angle A = 37

Angle B = 11(5) - 2

Angle B = 55 - 2

Angle B = 53

Angle A = 37 degrees, and Angle B = 53 degrees.

Hope this helps.

7 0
2 years ago
23,802 divided by 34 <br> HALP
lilavasa [31]

Answer:

700.058824 but rounded to the nearest tenth it would be 700.1.

Step-by-step explanation:

8 0
4 years ago
The function C(t) below relates outside temperature in degrees Fahrenheit to the number of cricket chirps per minute.
Maslowich
C(t) = 5t - 200
T = 5t - 200
5t = T + 200
t = (T + 200)/5
T(c) = (T + 200) / 5
8 0
3 years ago
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