When dividing two numbers written in exponential notation, what do you do with the exponents of 10?

9)

If y varies directly with x and y = -3 when x = 6, find y when x = 14.

We know if y varies directly with x, we get the equation

y ∝ x

y = kx

k = y/x

where k is called the constant of variation.

we are given y = -3 when x = 6

so substitute y = -3 and x = 6 to determine 'k'

k = y/x

k = -3/6 = -1/2

Now we have to find y when x = 14

so substituting x = 14 and k = -1/2 to find y

y = kx

y =  -1/2 × 14 = -7

Therefore, the value of y = -7 when x = 14

10) If y is directly proportional to x and y = 4 when x = 3, find x when y = -12.

we are given y = 4 when x = 3

so substitute y = 4 and x = 3 to determine 'k'

k = y/x

k = 4/3

Now we have to find x when y = -12

so substituting y = -12 and k = 4/3 to find x

y = kx

x = y/k

x = [-12] / [4/3] = [-12×3] / [4]

x = -36/4

x = -9

Therefore, the value of x = -9 when x = 3

11)

If y varies directly with x and y = -6 when x = 2, find the constant of variation.

We are given

y = -6

x = 2

so substitute y = -6 and x = 2 in the equation

k = y/x

k = -6/2

k = -3

Therefore, the value of the constant of variation will be:

Answer:

Step-by-step explanation:

When we are given a function in this format, we substitute the x value in the equation. F(x) is simply another way of saying y.

if x = -8

6 (2 - -8)

6(10)

60

Answer:

C. y=5x+14

Step-by-step explanation:

Solve using this formula: y=mx+b

4 = (5) (-2) + b

4 = -10 + b

+10  +10

14 = b

Then you will plug in what you found for b in:

y=5x+14

Answer: y = -2/3x + 5/3

Step-by-step explanation:

Answer:

i believe the y intersept is -4

Answer:

18y+30y+14y+150°+142=540

62y+292=540

subtract 292 from both sides

62y= 248

divide 62

y=4°

Answer:

You already have the answer so ima just get the points

Have a good night

Answer:

6 miles

Step-by-step explanation:

Li can walk 6 miles if you divide 135 and 45 you'll get 3 finally if you multiply 2 and 3 you'll get 6 So in total Li walks 6 miles

Answer:

[tex] \frac{30}{100} = \frac{33}{x} \\ 30x = 3300 \\ x = \frac{3300}{30} = 110[/tex]

Answer: The total cost of their meal with tax= $23.49

Step-by-step explanation:

Given: Cost of the three dinners before tax = $21.65

Tax = 8.5%

Tax amount = 8.5% of ( Cost of the three dinners before tax)

= (0.085) x 21.65        [0.085 = 8.5%]

= $1.84025 ≈ $ 1.84

The total cost of their meal with tax = Cost + Tax amount

= 21.65 + 1.84

= $23.49

Hence, the total cost of their meal with tax= $23.49

Answer:

y = 7/4x

Step-by-step explanation:

All you have to do is find the slope by using the formula change in y divided by change in x of the two points. You can see that y goes up by 14 when x goes up by 8. This means that the slope is 14/8, or 7/4.

The equation would then be y = 7/4x

Answer:

[tex](4n + 3) - (3 {n}^{2} + 2) \\ = 4n + 3 - 3 {n}^{2} - 2 \\ = - 3 {n }^{2} + 4n + 1 \\ ( - 3 {n}^{2} - 3n) - (1n + 1) \\ - 3n(n + 1) - 1(n + 1) \\ (n + 1)( - 3n - 1) \\ n = - 1 \\ n= \frac{1}{ - 3} [/tex]

Answer:

[tex]f(n) - g(n) = (4n + 3) - (3 {n}^{2} + 2) \\ = 4n + 3 - 3 {n}^{2} - 2 \\ = \boxed{4n - 3 {n}^{2} + 1}[/tex]

Answer:

x+8.95 and x+24.55

Step-by-step explanation:

im not going to do this

Answer:

The value of x = 12.

Step-by-step explanation:

We know that two angles are termed as supplementary when the sum of the measure of their angles is 180°.

We also know that a straight line angle measures 180°.

It is clear that the angles 72° and 9x° line on a straight line. Thus, the sum of the measure of their angles is 180°.

Therefore,

9x° + 72° = 180°

9x° = 180° - 72°

9x° = 108

divide both sides by 9

9x/9 = 108/9

x = 12

Therefore, the value of x = 12.

Answer:

Step-by-step explanation:

F(x) is simply another way of saying y. We are given the x value of -10. We can substitute this in for x and find y.

f(-10) = 7(-10) - 5

f(-10) = -70 - 5

f(-10) = -75

Answer:

Rewrite the equation in term of  

x

and  

y

.

f

(

x

)

=

2

x

2

−

7

x

+

5

Rewrite the equation in vertex form.

Tap for fewer steps...

Complete the square for  

2

x

2

−

7

x

+

5

.

Tap for more steps...

2

(

x

−

7

4

)

2

−

9

8

Set  

y

equal to the new right side.

y

=

2

(

x

−

7

4

)

2

−

9

8

Use the vertex form,  

y

=

a

(

x

−

h

)

2

+

k

, to determine the values of  

a

,  

h

, and  

k

.

a

=

2

h

=

7

4

k

=

−

9

8

Find the vertex  

(

h

,

k

)

.

(

7

4

,

−

9

8

)

Step-by-step explanation:

Answer:

F

Step-by-step explanation:

Square root of 10 is 3.16

Answer:

24,000

Step-by-step explanation:

Answer:

24,000

Step-by-step explanation:

Every kilogram is 1,000 grams

Answer:

multiply and see what you get

Answer:

15 m

Step-by-step explanation:

Given that :

Change in distance is the same each time Ballon is lowered ;

Number of times Ballon is lowered = 5 times ;

Total change in distance = 75 m

Change in distance per time lowered equals ;

(Total change in elevation / Numbe rof times Ballon is lowered)

75m / 5

= 15 m

Hence, Ballon height changes by 15 m each time it is lowered.

The integer gives the lowering rate.

Answer:

y+4+−4=−6x−36+−4

y=−6x−40

y=−6x−40

slope is -6

y intercept is -40

Answer:

y = -6x - 40

in standard form its:

y + 6x = -40

Step-by-step explanation:

Answer: A

Step-by-step explanation:

Answer:

2.)  "My parents will be very disappointed in me."

Step-by-step explanation:

This is the only explanation that will get you out of any bad situations.

1.) I'll try it once: if you try it once, you'll be hooked on it forever.

2.) Correct answer: Only way to get out of a situation like this affectively.

3.) My friends and I prefer weed: This would still suggest you still use drugs.

(I think it's smart to post it in math! :)

Answer:

The values of a and b are:

Step-by-step explanation:

We know that the slope-intercept form of the line equation

y = ax+b

where

From the diagram of the line graph, we can fetch the two points

Determining the slope between (0, 2) and (-1, 0)

[tex]\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]\left(x_1,\:y_1\right)=\left(0,\:2\right),\:\left(x_2,\:y_2\right)=\left(-1,\:0\right)[/tex]

[tex]a=\frac{0-2}{-1-0}[/tex]

[tex]a=2[/tex]

Thus, the value of a = 2

We know that the value of the y-intercept can be determined by setting x = 0, and determining the corresponding value of y.

From the graph, it is clear

at x = 0, y = 2

Thus, the y-intercept b = 2

now substituting a = 2 and b = 2 in the slope-intercept form of the line equation

y = ax+b

y = 2x + 2         ∵ a = 2 , b = 2

Thus, the line of equation is:

y = 2x+2

now comparing with y = ax+b

Here:

a = 2

b = 2

Therefore, the values of a and b are:

Answer:

No, it is A for the first question and C for the last one

Step-by-step explanation:

Answer:

yes

Step-by-step explanation:

1/9= .111111111111 repeating

I don't know the second one sorry but the first one is 92. Plug -4 in for x and you get 92

Answer:

f(-4) = 3×(-4×-4) - 10 ×(-4) + 4

= 3×16 + 40 + 4

= 48 + 44

= 92

Answer:

First Option: y = 1/2x + 8

Step-by-step explanation:

for lines to be parallel they must have the same slopes

Answer:

B. 25

Just use Photomath in those questions

Answer:

B) N=25

Step-by-step explanation:

the distance between -53 and -28 is positive 25