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nirvana33 [79]
3 years ago
14

⦁ Determine if the equation represents a direct variation. .8x = 1.6y ⦁ Suppose y varies directly with x. Write a direction vari

ation equation that relates x and y. Then find the value of y when x = 12. y=5 when x=2. ⦁ For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. X Y -6 9 1 -1.5 8 -12 ⦁ For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. X Y -2 1 3 6 8 11
Mathematics
2 answers:
Mkey [24]3 years ago
8 0
Part A:

Given that 

0.8x=1.6y\Rightarrow x= \frac{1.6}{0.8} y=2y

Thus, x = ky where k = 2.

Therefore, the given equation is a direct variation.


Part B:

If y varies directly as x, then y = kx.

Given that y = 5 when x = 2, then

5=2k \\  \\ \Rightarrow k=\frac{5}{2} =2.5 \\  \\ \Rightarrow y=2.5x

When x = 12, y = 2.5(12) = 30.



Part C:

If y varies directly as x, then y = kx.

Given that y = 9 when x = -6, then

9=-6k \\ \\ \Rightarrow k=-\frac{9}{6} =-\frac{3}{2} \\ \\ \Rightarrow y=-\frac{3}{2}x

It can be seen that the equation above satisfies all the rows of the given table, therefore, y varies with x for the data in the question and the equation for the direct variation is y=-\frac{3}{2}x



Part 4:

If y varies directly as x, then y = kx.

Given that y = 1 when x = -2, then

1=-2k \\ \\ \Rightarrow k=-\frac{1}{2} \\ \\ \Rightarrow y=-\frac{1}{2}x

It can be seen that the equation above does not satisfies the other rows of the given table, therefore, y does not vary with x for the data in the question.
nikklg [1K]3 years ago
8 0

Answer: Linear Functions Unit Test

1. Yes; y=1.625

2. no; y does not vary directly with x

3. Option D

4. Option A

5. 46/1; your car travels 46 miles in 1 hour

6. 1/3

7. -1/3

8. undefined

9. y-3=6(x-8)

10. y+6=-5/8(x+10)

11. y-16=8(x-2)

12. Option A

13. 3x+4y=12

14. y=2x+2

15. perpendicular

16. neither

17. y-3=-3/8(x+2)

18. The functions have the same shape. The y- intercept of y=|x| is 0, and the y- intercept of the second function is -9

19. The two graphs have the same shape but the second graph is shifted 5 units left

20. Option A

21. Option B

22. Positive correlation

These are the answers I put for the short answers

23. You can be confident in your prediction because the more your confident the more you'll have faith in yourself as an individual.

24. y=4.536+0.107*22

0.107*22=2.354

y=4.536+2.254

y=6.89

if rounded y=6.9

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If (1/4)^(x+y) = 256 and log₄(x-y) = 3, what are the exact values of x and y
andrew-mc [135]

Answer:

x = 30 and y = -34

Step-by-step explanation:

Given the following functions

(1/4)^(x+y) = 256... 1

log₄(x-y) = 3.... 2

From equation 2;

x-y = 4³

x-y = 64

x = 64 + y ... 3

Substitutw 3 into 1

From 1:

(1/4)^(x+y) = 256

(1/4)^(64+y+y) = 256

(1/4)^(64+2y) = 256

Take log₄ of both sides

64+2y log₄ (1/4) = log₄256

-(64+2y) = 4log₄4

-(64+2y) = 4

64+2y = -4

2y = -4 - 64

2y = -68

y = -34

Since

x = 64 + y .

x = 64 - 34

x = 30

Hence x = 30 and y = -34

6 0
3 years ago
10(2^×) + 7(3^×) = 6^× + 70​
Mkey [24]

Answer:

x = 2.81 and 2.096

Step-by-step explanation:

Given the expression

10(2^x) + 7(3^x) = 6^x + 70​

This can also be expressed as;

10(2^x) + 7(3^x) = (2*3)^x + 70

10(2^x) + 7(3^x) = 2^x*3^x + 70

Let a  = 2^x and b = 3^x

10a + 7b = ab + 70

10a + 7b - ab = 70

10a-ab + 7b - 70 = 0

a(10-b)+7(b-10) = 0

a(10-b)-7(10-b) = 0

a-7 = 0 and 10-b = 0

a = 7 and b = 10

Since a = 2^x

7 = 2^x

log 7 = log2^x

log7 = xlog2

x = log7/log2

x = 2.81

Similarly

10 = 3^x

log 10 = log 3^x

log 10 = xlog3

x = log 10/log 3

x = 1/0.4771

x = 2.096

Hence the values of x that satisfies the equation are 2.81 and 2.096

8 0
2 years ago
11/ 42 Marks
amm1812

Answer:

(a)x=128 degrees

(b)\angle APD\neq 116^\circ

Step-by-step explanation:

\angle ABD+\angle CBD =180^\circ$ (Linear Postulate)\\\angle ABD+116^\circ =180^\circ\\\angle ABD=180^\circ-116^\circ\\\angle ABD=64^\circ

(a) Now:

\angle AOD=2 \times \angle ABD$ (Angle at the centre is twice the  angle at the circumference)\\x=2 \times 64^\circ\\x=128^\circ

(b)

\angle APD=2 \times \angle ABD$ (Inscribed Angle Theorem)\\\angle APD=2 \times 64^\circ\\ \angle APD=128^\circ

\angle APD\neq 116^\circ

7 0
3 years ago
A metal bar is 7 5/8 inches long. If 9/32 inches is cut off one end, how long is the bar after the cut?
Blizzard [7]
7 11/32 inches i do believe
8 0
3 years ago
Read 2 more answers
1. Perry ran 30 miles more than DeShawn last month. Perry ran 46 miles. Write and solve an ADDITION equation to represent how ma
a_sh-v [17]

Answer:

30+46=76

Step-by-step explanation:

so you want to draw out a model and write the two numbers and add them.

3 0
3 years ago
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