Write an exponential function to model each situation. Find each amount after the

specified time.


A population of 1,236,000 grows 1.3% per year for 10 years

There are 3 right triangles in this picture, and they are all mutually similar.

• the smallest triangle has legs 4 and y, and hypotenuse z

• the middle one has legs y and 16, and hypotenuse x

• the largest one has legs z and x, and hypotenuse 16 + 4 = 20

Note the order in which I've listed the sides (shortest to longest). Because these triangles are similar, the corresponding sides occur in a fixed ratio. In particular, we have

4/y = y/16 = z/x … (ratios of each side of the smallest and middle triangles)

4/z = y/x = z/20 … (ratios of the sides of the smallest and largest triangles)

y/z = 16/x = x/20 … (ratios of the sides of the middle and largest triangles)

We just want to find x, which we can do easily with the last equality,

16/x = x/20

Solve for x :

20 • 16/x = 20 • x/20

320/x = x

x • 320/x = x • x

320 = x²

⇒   x = √320 = √(64 • 5) = 8√5

Answer:

y=(5/3)x + 5

Step-by-step explanation:

Every line is in the form: y = ax+b. If some points are on this line, they satisfy this equation. So we can write:

-5 = a(-6) + b

0 = a(-3) + b

It's a system of equations. We can solve them by subtracting the second equation from the first:

-5-0 = -6a - (-3a) + b - b

That becomes:

-5 = -3a

Therefore:

a = 5/3

Now we plug this value in the second equation of the system, and find the value of b:

0 = 5/3*(-3) +b

b=5

The final line equation will be: y=(5/3)x + 5

y = [tex]\frac{5}{3}[/tex]x + 5

First, find the slope. The formula to find slope can be defined as [tex]\frac{y_2-y_1}{x_2-x_1}[/tex].

Given points (-6, -5) and (-3, 0), we can substitute those values in and find that the slope for this line will be [tex]\frac{5}{3}[/tex].

Using slope-intercept form, our equation so far is y = [tex]\frac{5}{3}[/tex]x + b. To find b, we substitute the coordinates of any point and solve. Doing so gets us a value of 5 for b.

Therefore, our final answer is y = [tex]\frac{5}{3}[/tex]x + 5.

Answer:

644.972

Step-by-step explanation:

6x100=600

4x10=40

4x1=4

9x(1/10)=0.9

7x(1/100)=0.07

2x(1/1000)=0.002

add all of these values up. hope this helps!

Answer:

the third angle is 50 degress

Step-by-step explanation:

the angle sum property states that the sum of all the interior angles of a triangle is 180.

therefore : 30 + 100 + x = 180

x = 180 - 130

x = 50

Answer:

y = -5/6x + 3

Step-by-step explanation:

Answer:

The ratio of their radius is [tex]2:3[/tex]

Step-by-step explanation:

Volume of cylinder is [tex]\pi r^2h[/tex], where r is radius and h is height

We have

The heights of two cylinders are in the ratio of [tex]5:3[/tex]

[tex]\frac{h_1}{h_2} =\frac{5}{3}[/tex]

The volume are in the ratio [tex]20:27[/tex]

[tex]\frac{V_1}{V_2} =\frac{20}{27}\\\\\frac{\pi r_1^2h_1}{\pi r_2^2h_2} =\frac{20}{27}\\\\\frac{ r_1^2}{ r_2^2}\times \frac{3}{5} =\frac{20}{27}\\\\\frac{ r_1^2}{ r_2^2} =\frac{4}{9}\\\\\frac{ r_1}{ r_2} =\frac{2}{3}[/tex]

The ratio of their radius is [tex]2:3[/tex]

Answer:

2 : 3

Step-by-step explanation:

Let,

Radius of cylinder 1 = R

Radius of cylinder 2 = r

Now,

We know that

Volume of cylinder = πr²h

=> πR²h/πr²h' = 20/27

=> R² × 5/r² × 3 = 20/27

=> R²/r² = 20/27 × 3/5

=> R²/r² = 4/9

=> R/r = √(4/9)

=> R/r = 2/3

=> R : r = 2 : 3

S(0,-2)

i.e

[tex]\\ \sf{:}\Rrightarrow 0-4=-4[/tex]

New co-ordinates are

Answer:

-5/4

Step-by-step explanation:

4x-5y=10

-5y=-4x-10

-5y/-5=-4/-5-10/-5

y=4/5+2

perpendicular slope is -5/4

Answer:b

Step-by-step explanation:

Answer:

1/6

Step-by-step explanation:

Apply the distributive property.

1/3 x 1/6 = 2/36

1/3 x 5/12 = 5/36

Add the products.

2/36 + 5/36 = 7/36

Subtract the result by the 1/36.

7/36 - 1/36 = 6/36

Simplify the fraction.

6/36 = 1/6

-hope it helps

Answer:

6 cups of chocolate chips

Step-by-step explanation:

2:5 5+4=9 so add 4 to each side of the ratio

6:4

Answer:

Step-by-step explanation:

The coordinates of the graph representing the given situation are listed below

A (0 ,400)

B ( 1 ,350 )

C (2,300)

D(3,250)

 E(4, 200)

 F(5, 150)

 G(6, 100)

  H(7, 50)

  I (8, 0)

The graph attached shows the nature of the graph.

Answer: 9/11 diveded by 3/4

Step-by-step explanation: divde to get middle answer

Answer:

(y/5)-6

Step-by-step explanation:

quotient is dividing, less than is subtracting

Answer:

x=1 y=1 z=1

Step-by-step explanation:

3+3+3=9

and

3x+3y+3z=9

========================================================

Explanation:

1/6 cup of glitter is needed for each 1/3 cup of glue. We want that "1/3 cup of glue" to be "1 cup of glue". So we'll multiply each part by 3.

The ratio 1/6 : 1/3 updates to 1/2 : 1 to tell us that we need 1/2 cup of glitter to pair with 1 cup of glue.

Answer:

5

Step-by-step explanation:

So lets do this slowley

3x3=9

9x3=27

27x3=81

81x3=243

It took 5 threes or 3x3x3x3x3 to get 243

Answer:

y=81, try that for answer

Answer:

12

Step-by-step explanation:

Set up equation like this with x being the number

X / (3/5) = 20

X * (5/3) = 20

so multiply both sides by 3/5 so

X = 20 (3/5)

therefore,

X = 12

we can check to make sure this is right by plugging it back in:

12 / (3/5) = 20 so it is true

Answer:

Step-by-step explanation:

The answer would be 6 because you would count the distance like it says!

Answer:

2nd option

Step-by-step explanation:

Given f(x) then the graph of f(x + a) is a horizontal translation of f(x)

• If a > 0 then a shift left of a units

• If a < 0 then a shift right of a units

g(x) = f(x + 4)

Is the graph of f(x) shifted 4 units to the left

answer

2.5

Step-by-step explanation:

that is what I got so

Answer:

[tex] \frac{3}{7} \times \frac{3}{7} = \frac{9}{49 } [/tex]

Multiply the percentage by the allowable amount:

180% = 1.80

20 x 1.80 = 36

Answer: 36 mg

Step-by-step explanation:

an object and its shadow create a right-angled triangle.

2 objects and their shadows create 2 similar right-angled triangles.

that means the angles are the same, and the side lengths of one triangle all correlate with the corresponding side lengths of the other triangle via the same factor.

so,

42 × f = 6

f = 6/42 = 1/7

the length of Joel's shadow is then

20 × f = 20 × 1/7 = 2.857142857... ft

Based on the cost of the shirt and the rebate applied, the customer would pay  Rs. 233.75

A rebate is a discount on the price of a good so the shirt will be discounted by 15%.

= 275 x 15%

= Rs. 41.25

The price the customer will pay is therefore:

= Cost of shirt - Discount

= 275 - 41.25

= Rs. 233.75

In conclusion, the customer will pay Rs. 233.75

Find out more on discounts at https://brainly.com/question/889098.