The bill for the repair of a car was $357. The cost for the parts was $285. The cost of labor was $32 per hour. Use an equation to find out how long it took for the mechanic to repair the car?​

The value of unknown number y for the equation  8 superscript y baseline = 16 superscript (y+2) is -8.

When the power of a number is raised by another number, then multiply both the powers and the result of this product keep as the power of the number.

Let suppose there is a number a. For this number the above rule can be given as,  

[tex](a^m)^n=a^{m\times n}\\(a^m)^n=a^{mn}[/tex]

The expression which consist unknown variable y is given as,

[tex]8^y=16^{y+2}[/tex]

The above equation can be written as,

[tex](2\times2\times2)^y=(2\times2\times2\times2)^{y+2}\\(2^3)^y=(2^4)^{y+2}\\(2)^{3y}=(2^)^{4y+8}[/tex]

As the base of both side of the equation is same. Thus, the value of their exponent can be compared.

[tex]3y=4y+8\\4y-3y=-8\\y=-8[/tex]

Thus, the value of unknown number y for the equation  8 superscript y baseline = 16 superscript (y+2) is -8.

Learn more about the  power raised by another number here;

https://brainly.com/question/960886

It would take Jenna half an hour, or 30 minutes, to run 3 km.

Hope this helps!

Answer:

x=7

Step-by-step explanation:

4x-8=2x-6

4x-2x=-6+8

2x=-14(divide both the sides by 2)

x=7

Answer:

d = 13

Step-by-step explanation:

Given:

m ∠ d = 27°

m ∠ a = 105°

t = 21°

Look at the picture I posted

Use sine law:

[tex]\mathrm{\dfrac{ sin\:a }{ A } = \dfrac{ sin\:B }{ b }}[/tex]

∠T = 180° - 27° - 105°

∠T = 48°

[tex]\mathrm{\dfrac{ sin\:48\° }{ 21 } = \dfrac{ sin\:D }{ d }}[/tex]

[tex]\mathrm{\dfrac{ sin\:48\° }{ 21 } = \dfrac{ sin\:27 }{ d }}[/tex]

Cross multiply

[tex]\mathrm{{d\:sin\:48\°} = { 21\:sin\:27\°}}[/tex]

Solve for d

[tex]\mathrm{d = \dfrac{ 21\:sin\:27\° }{ sin\:48\° }}[/tex]

Evaluate trigonometric functions in the problem

[tex]\mathrm{d = \dfrac{ 21 \times 0.453990499739547 }{ 0.743144825477394 }}[/tex]

Multiply 21 and 0.453990499739547 to get 9.533800494530487

[tex]\mathrm{d = \dfrac{ 9.533800494530487 }{ 0.74314482547394 }}[/tex]

Divide 9.533800494530487 by 0.743144825477394

[tex]\mathrm{d = 12.828993983}[/tex]

d = 13

Rounded to the nearest integer: 13

Let's plug in both x and y values in the equation and check if the inequality is true...

[tex]\red{ \rule{35pt}{2pt}} \orange{ \rule{35pt}{2pt}} \color{yellow}{ \rule{35pt} {2pt}} \green{ \rule{35pt} {2pt}} \blue{ \rule{35pt} {2pt}} \purple{ \rule{35pt} {2pt}}[/tex]

[tex](4,1) \\ y \leqslant x + 1 \\ y < - \frac{x}{2} - 1[/tex]

Substitute x as 4 and y as 1

[tex]1 \leqslant 4 + 1 \\ 1 < - \frac{4}{2} - 1[/tex]

[tex]0 \leqslant 4 + 1 \\ 1 < - 2 - 1[/tex]

[tex]0 \leqslant 5 \\ 1 < - 3[/tex]

[tex]\purple{ \rule{300pt}{3pt}}[/tex]

[tex](0, - 3) \\ y \leqslant x + 1 \\ y < - \frac{x}{2} - 1[/tex]

Substitute x as 0 and y as -3

[tex] - 3 \leqslant 0 + 1 \\ - 3 < - \frac{0}{2} - 1[/tex]

[tex] - 3 \leqslant 1 \\ - 3 < - 0 - 1[/tex]

[tex] - 3 \leqslant 1 \\ - 3 < - 1[/tex]

Thus, Option B (0,-3) is the correct choice....

Answer:

First place a mark at your point. (x=2, y=3)

Step-by-step explanation:

Now when you look at the -3/4 that is called your rise over run so you will go down 3 and over 4 so your next point will be at (x=0, y=6) and then you connect your dots to make a line.

Answer:

i think c no is the correct answer

Answer:

x = 15

y = 1

Step-by-step explanation:

Answer:   $54.00

Explanation: Three percent of $180.00 is $5.40. So Bonnie receives $5.40 annually. In ten years, she will have $54 (multiply 5.40 by 10).

Hello!

2( 8u² + uv²w -1) + 2( 5u²-v^6) -2( 2v)

= 16u²  +  2uv²w  -2 + 10u² - 2v^6 -4v

=   2uv²w  - 2v^6  +  26u²   -4v -2      

Answer: 10

Step-by-step explanation:

4(2x-5)

distribute

8x-10

8x-10=8x-10

Answer:

Rate=8%

Step-by-step explanation:

Step 1: Write the given terms

Principal (p)=Rs15000

Rate(r)=?

Time(t)=2 1/2=5/2=2.5

Interest(i)=Rs3000

Step 2: Write the formula for calculating Simple interest

[tex]i = \frac{p \times r \times t}{100} [/tex]

Step 3: Make Rate(r) the subject of the equation in Step 2

[tex]by \: cross \: multiplcation \\ 100i = prt \\ divide \: both \: sides \: by \: pt \: to \: have \\ \frac{100i}{pt} = r[/tex]

Step 4: Use the new equation for r to get the rate by substitution

[tex]r = \frac{100i}{pt} \\ r = \frac{100 \times 3000}{15000 \times 2.5} \\ r = \frac{300000}{37500} \\ r = 8[/tex]

Hence, the rate of the simple interest is 8%

Answer:

30 × 24 = 720 inches

since there are 12 inches in a foot

720 ÷ 12 = 60

60 feet converted to yards is 20 yards

50 - 20 = 30

they should have 30 yards of string left over

Answer:

D, it admits 4 complex roots

Step-by-step explanation:

Based on what you've written;

f(x) can be rewritten by adding the light terms together as;

f(x)=2x⁴-16x+1768.68

By graphing this function on an app, since i cannot possibly simplify this equation or use a calculator;

we observe that this function does not intersect the x-axis at any point, hence it does not admit any real roots.

So your answer must be D.

ps: Regardless if you forgot any x's in your equation and if f(x) was actually defined by,

f(x)=2x⁴-9.32x³+1772x²-16x+6

This equation also admits 4 complex roots and does not intersect the x-axis

Answer:

D [tex]\angle O\cong\angle S[/tex]

Step-by-step explanation:

[tex]\angle O\cong\angle S[/tex]

Hope it helps you in your learning process.

Answer:

True

Step-by-step explanation:

Answer:

true

Step-by-step explanation:

Step-by-step explanation:

please mark me as brainlest

See picture for math work and answer.

Answer:

dy/dx=sec^2^(x)-(-csc^2(x)

=sec^2(x)+ csc^2(x)

so solution is E

Answer:

e) sec^2x+csc^2x

Step-by-step explanation:

I explained your answer in the sent photo

Answer:

  D.  20 cm

Step-by-step explanation:

The volume of a rectangular prism is given by the formula ...

  V = LWH

__

For the dimensions given, we have ...

  15000 cm³ = (30 cm)(25 cm)H

  15000/750 cm = H = 20 cm

The height of the box is 20 cm.

Answer: Length  =  9.434

Step-by-step explanation: Input Data :

Point 1

(

x

A

,

y

A

)

= (-4, 5)

Point 2

(

x

B

,

y

B

)

= (4, 0)

Objective :

Find the distance between two given points on a line?

Formula :

Distance between two points =

√

(

x

B

−

x

A

)

2

+

(

y

B

−

y

A

)

2

Solution :

Distance between two points =

√

(

4

−

−

4

)

2

+

(

0

−

5

)

2

=

√

8

2

+

(

−

5

)

2

=

√

64

+

25

=

√

89

= 9.434

Distance between points (-4, 5) and (4, 0) is 9.434

Answer:

288 girls and 192 boys

Step-by-step explanation:

Ratio of boys to girls is 6:9

So, first find the total parts they are dividied into. 6+9= 15

480/15= 32. So one part has 32 students.

The boys are of 6 parts of 15 (as in the ratio). So 32 x 6= 192 boys.

girls are 32 x 9= 288 girls

they add to 480.

Step-by-step explanation:

Given,

x = 4

2x - 4y = 20

Now,

2x - 4y = 20

or, 2×4 - 4y = 20

or, 8 - 4y = 20

or, -4y = 20 - 8

or, y = 12/-4

or, y = -3

therefore, y = -3

Answer:

(x,y)=(4,-3)

Step-by-step explanation:

2x-4y=20

x=4

substitute the given value of x into the equation

2×4-4y=20

solve the equation for y

y=-3

A possible solution of the system is the ordered pair

(x,y)=(4,-3)

CHECK SOLUTION!

2×4-4×(-3)=20

4=4

simplyfy the quality

20=20

4=4

since all of the qualities are true, the ordered pair is the solution of the system

(x,y)=(4,-3)

hey hi I hope this helps

Answer:

8 number of visits will be the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card

Step-by-step explanation:

                             Price without Discount Card   Price with Discount Card

Ticket (12 & Under)        $10                                             $8

Adult's Ticket                  $15                                           $12

Let x be the number of visits

Price without discount card for 2 adults and 1 child ticket

Price without discount for x visits = [tex]x(15 \times 2+ 10)=40x[/tex]

Price with discount for x visits =[tex]57+ x(12 \times 2+ 8)=57+32x[/tex]

Now to find For what number of visits will the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card

57+32x< 40x

57<8x

7.1<x

So, 8 number of visits will be the total cost of the visits (including the price of the discount card) be less expensive for a family of 2 adults and 1 child if they have purchased the discount card

Answer:

2.13333

Step-by-step explanation:

2x180 over 168.75

I AM NOT SURE OF THE ANSWER THO

Answer:

1.20 ÷ 4 = 0.30 per unit

Please mark as brainliest;)

Answer:

273 K, 0 C, 32 F

This is freezing temperature for all 3 systems.

Answer:

A

Step-by-step explanation: