Find the area of the composite figure

Answer:

[tex]y = 4*5^x[/tex]

Step-by-step explanation:

Given

[tex](x_1,y_1) = (-3,\frac{4}{125})[/tex]

[tex](x_2,y_2) = (1,20)[/tex]

Required

Determine the exponential equation

An exponential equation is of the form: [tex]y = ab^x[/tex]

In: [tex](x_2,y_2) = (1,20)[/tex]

[tex]20 = ab^1[/tex]

[tex]20 = ab[/tex] ---- (1)

In: [tex](x_1,y_1) = (-3,\frac{4}{125})[/tex]

[tex]\frac{4}{125} = ab^{-3}[/tex] --- (2)

Divide (1) by (2)

[tex]20/\frac{4}{125} = \frac{ab}{ab^{-3}}[/tex]

[tex]20/\frac{4}{125} = b^4[/tex]

[tex]20*\frac{125}{4} = b^4[/tex]

[tex]5*125 = b^4[/tex]

[tex]625 = b^4[/tex]

Take 4th roots of both sides

[tex]\sqrt[4]{625} = b[/tex]

[tex]5 = b[/tex]

[tex]b = 5[/tex]

Substitute [tex]b = 5[/tex] in [tex]20 = ab[/tex]

[tex]20 = a * 5[/tex]

Solve for a

[tex]a = 20/5[/tex]

[tex]a = 4[/tex]

Hence, the equation is:

[tex]y = 4*5^x[/tex]

Answer:

Length of rectangle = 15 feet

Width of rectangle = 6 feet

Step-by-step explanation:

Given:

Perimeter of rectangle = 42 ft

Length of rectangle = 2[Width of rectangle] + 3

Find:

Value of length and width

Assume:

Width of rectangle = w

SO,

Length of rectangle = 2[w] + 3

Perimeter of rectangle = 2[l + b]

42 = 2[2w + 3 + w]

2[3w + 3] = 42

6w + 6 = 42

6w = 42 - 6

6w = 36

w = 36 / 6

w = 6

So,

Width of rectangle = 6 feet

Length of rectangle = 2[w] + 3

Length of rectangle = 2[6] + 3

Length of rectangle = 12 + 3

Length of rectangle = 15 feet

Answer:

After 16 months there will be a population of 1,944 insects.

Step-by-step explanation:

Since an insect population triples every 4 months, if the population started out with 24 insects, to determine how many insects would there be in 16 months, the following calculation must be performed:

X = 24 x 3 ^ (16/4)

X = 24 x 3 ^ 4

X = 1,944

Thus, after 16 months there will be a population of 1,944 insects.

Answer:

x = 6.25

Step-by-step explanation:

Suppose y = 2x  - 2.5. Find x when y = 10

this gives us the equation:

10 = 2x - 2.5

add 2.5 to both sides

2x = 12.5

divide both sides by 2

x = 6.25

Please LMK if you have questions.

Answer:

286°

Step-by-step explanation:

A circle is the locus of a point such that its distance from a fixed point (known as the center) is always constant. This distance is known as the radius of the circle.

A major arc is an arc larger than a semicircle, therefore its measure is greater than 180°. A minor arc is an arc smaller than a semicircle, therefore its measure is less than 180°.

The arc measure of [tex]\stackrel{\large{\frown}}{ACB}=angle\ about\ a\ point-\stackrel{\large{\frown}}{AB}[/tex]

The arc measure of [tex]\stackrel{\large{\frown}}{ACB}=360-74=286^o\\[/tex]

Answer:

C≈524.65m

Solving for C

C=πd=π·167≈524.64597m

Answer:

Step-by-step explanation:

I'm going to guess that 1/2 the size means the sides are 1/2 the size.

Square 1 has an area of 24. The sides are s, so the area is found by using s^2

The second square is made from sides that are 1/2 s

Area = 1/2 s * 1/2 s

Area = 1/4 s^2

Area 1 / area 2 = 24 / x^2 = s^2 / 1/4 s^2 =  1/0.25

Answer:

64.8 ft

Step-by-step explanation:

A square has all its sides equal

Therefore to get one side from its area is simply finding the square root of its area

√262.44=16.2ft

Having the one side then perimeter= to the four equal sides × the dimensions of one side

=4×16.2

=64.8 ft

Answer:

18

Step-by-step explanation:

Answer:

K-5

Step-by-step explanation:

Five less than K would be K-5.

Answer:

3^12

Step-by-step explanation:

(3^5)^2 / 3 − ^2 = 243^2/3−^2 = 59049 / 3−^2 = 59049/ 1 / 9 = 531441

= 3*3*3*3*3*3*3*3*3*3*3*3 = 3^12

Answer:

Last one. Combine like terms onto side of the equation.

Step-by-step explanation:

The first step in determining the solution to the system of equations,   [tex]y = -x^2 - 4x - 3[/tex]  and [tex]y = 2x + 5[/tex] , algebraically is to set the two equations equal as  [tex](-x^2 - 4x - 3) = 2x + 5[/tex], will be to set the equations equal to each other.

System of equations comprises of two or more equations of two or more variables and seeks common solutions to the equations.

We have,

  [tex]y = -x^2 - 4x - 3[/tex]  

  [tex]y = 2x + 5[/tex]

So, to determine solution to these System of equations,

We have to

Set the equations equal to each other and solve for the value of [tex]x[/tex],

i.e.

[tex]-x^2 - 4x - 3=2x+5[/tex]

[tex]-x^2-6x-8=0[/tex]

[tex]x^2+6x+8=0[/tex]

[tex]x^2+4x+2x+8=0[/tex]

[tex]x(x+4)+2(x+4)=0[/tex]

[tex](x+2)(x+4)=0[/tex]

⇒ [tex]x+2=0[/tex]

   [tex]x=-2[/tex]

   [tex]x+4=0[/tex]

  [tex]x=-4[/tex]

So, from the above solution we came to know that the first step in determining the solution to the given System of equations is to set the equations equal to each other.

To know more about System of equations click here

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9514 1404 393

Answer:

  3629.84 cm²

Step-by-step explanation:

Put the given numbers into the area formula and do the arithmetic.

The area of a sphere is given by ...

  A = 4πr²

  A = 4(3.14)(17 cm)² = 3629.84 cm²

The ball has a surface area of about 3629.84 cm².

Answer:

68

Step-by-step explanation:

Answer:

[tex] {x}^{2} - 2x + 3 = - 6x \\ = {x}^{2} - 2x + 6x + 3 = 0 \\ \\ = {x}^{2} + 4x + 3 = 0 \\ = (x + 1)(x + 3) \\ = x = - 1and \: x = - 3[/tex]

Answer:

13

Step-by-step explanation:

Since -5 is less than zero, we use the second equation, and substitute the -5 in for the x.

-2(-5)+3=13

Answer:

divide 8 by 4.16

Step-by-step explanation:

Answer:

52 cents

Step-by-step explanation:

Answer:

$81.25

Step-by-step explanation:

First find 35% of 125 which is 43.75

Next subtract 43.75 from 125

Your answer is $81.25

Answer:

Percent error = -4.02 (Approx.)

Step-by-step explanation:

Given:

Estimated pool dimension = 15 ft long and 35 ft wide

Actual pool dimension = 14.5 ft long and 34.75 ft wide

Find:

Percent error

Computation:

Area of Estimated pool = 15 x 35

Area of Estimated pool = 525 ft²

Area of Actual pool = 14.5 x 34.75

Area of Actual pool = 508.875 ft²

Percent error = [(Actual - Estimated) / Estimated]100

Percent error = [(508.875 - 525) / 525]100

Percent error = [(-21.125) / 525]100

Percent error = -4.02 (Approx.)

Answer:

25

Step-by-step explanation:

Ratios:

[tex]\frac{36}{100} =\frac{9}{x} \\\\36x=900\\x=25[/tex]

Double check:

25(0.36) = 9

Answer:

where is your figure please send it

Answer:

The answer is maybe going to be D which is 33 million

Step-by-step explanation:

New york is a big city

Answer:

12 prob

Step-by-step explanation:

Answer:

x < 0

Step-by-step explanation:

If you were to graph the function, you would get a parabola that opens down with the vertex at (0, 0).  So, the graph is increasing from -∞ to 0.

Answer:

Dec 10

Step-by-step explanation:

0.25 liter = 250 ml

4 ml * 3 = 12 ml

250/12 = 20.83 days

Nov 20 - Nov 30: 11 days

Dec 1 - Dec 9: 9 days

On December 9, she can still take her 3 doses.

By December 9, she will have taken 12 ml per day for 20 days for a total of 240 ml. She has 10 ml left for Dec 10th.

On Dec 10, she will take 2 doses of 4 ml and 1 dose of 2 ml, and she will finish the medicine.

9514 1404 393

Explanation:

Garment factory: workers may get paid by the number of pieces they complete.

__

Wood chopping: the worker gets paid by the number of cords of wood they produce, not by how long it takes.

__

Haircut -- the cost is the same (for the same type haircut) even if more time is spent

____

The above are instances where an individual worker gets paid by the piece they produce. There are numerous instances of companies getting paid by the job, regardless of the length of time or the quantity of materials required to do the job.

Lawn mowing -- the price is fixed each time the crew mows the lawn

Oil Change -- the cost of changing the oil in the car is not dependent on the time it takes or the amount of oil used

Car wash -- a fixed price is paid each time (at an automatic car wash)

Answer:

B

Step-by-step explanation:

I hope it is correct :)

Answer:

The answer is definitely B

Step-by-step explanation:

I just did this question on my test.