find the area of a circle

If Zachary purchased a computer for ​$1600 on a payment plan. five months after he purchased the​ computer, his balance was ​$900. eight months after  his balance was ​$480.  The equation that models the balance y after x​ months is: y = -140x + 1600.

Month    Balance

0            1600

5              900

8              480

Slopes:

(1600 - 900) / 5  = 700 / 5 = 140

(1600 - 480) / 8 = 1120 / 8 = 140

(900 - 480 ) /  - 3 = - 140

Hence,

y = -140x + 1600

Therefore the equation is y = -140x + 1600.

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Answer: y - 3 = -2(x + 2)

Answer:

5/4

Step-by-step explanation:

There is a rule that dividing by a fraction is the same as multiplying by the reciprocal.

So:

[tex]\frac{5/6}{2/3} = \frac56 \cdot \frac32 = \frac{15}{12} = \frac54[/tex]

Answer:

Step-by-step explanation:

ur mom

Answer:

16/3.

Step-by-step explanation:

5 1/3

First multiply 5 by 3.

This gives 15.

Now add the numerator of the fraction (1) to 15

- to give 16.

The improper fraction is 16/3.

Answer: 188.6 seconds which is rounded to 189 seconds or 3 minutes and 9 seconds

Step-by-step explanation:

Since we see that a time is given for 1 mile, to find the other distance we multiply the time for 1 mile (49.7 seconds) by the distance required (3.8 miles)

It can be also written like this:

1 mile -------> 49.7 seconds

3.8 miles-------> 49.7 seconds x 3.8 miles = 188.6 seconds rounded to 189 seconds. If asked for minutes, it can be written as 3 minutes and 9 seconds

Hope this helps!

Answer:

  ∠ABD = 19.5°

  ∠ABE = 160.5°

Step-by-step explanation:

Given angle ABC = 39° and its bisector BD, you want the measures of angle ABD and ABE, its supplement.

An angle bisector divides an angle into two equal parts, each with half the measure of the whole.

  ∠ABD = 1/2∠ABC

  ∠ABD = 1/2(39°)

  ∠ABD = 19.5°

The angles of a linear pair are supplementary: they total 180°. Angles ABD and ABE form a linear pair.

  ∠ABE = 180° -∠ABD

  ∠ABE = 180° -19.5°

  ∠ABE = 160.5°

5 3/4 = 5.75

8 1/2 = 8.50

2 1/4 = 2.25

Volume = width × height × length

? = (5.75)(8.50)(2.25)

volume = 109.96875

in fraction form = 109 31/32

The dimensions of the windowpane = 5 inches x 5 inches

This means the windowpane is square in shape.

Now, for the triangle,

Sides of the triangle = 5 inches each

Diagonal of the Square = Hypotenuse of the Triangle

The diagonal of a square is given by = [tex]\sqrt{2}[/tex] x side of the square = 5[tex]\sqrt{2}[/tex] inches

So, the perimeter of the one triangle = 5 + 5 + 5[tex]\sqrt{2}[/tex] = 10 + 5[tex]\sqrt{2}[/tex]

= 5(2+[tex]\sqrt{2}[/tex]) Inches

= 5(2+1.414)

= 17.07 inches (Approx.)

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All three triangles are congruent as, △ABC ≅ △ACD ≅ △CBD under AA condition

So, in the given image filling the blanks as follows:

(A) ∠ACB = ∠CDA = ∠CDB = 90° (Definition of right triangles)

(B) Triangle angle sum theorem:

It is enough to prove that:

(C) C.P.C.T (Corresponding parts of congurent triangles)

(D) △ABC ≅ △ACD ≅ △CBD under AA condition.

Therefore, all three triangles are congruent as, △ABC ≅ △ACD ≅ △CBD under AA condition

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Answer:A

Step-by-step explanation:

Step-by-step explanation:

we need to remember the formula for the circumference of a circle :

2×pi×r

or

2×r × pi

what is 2×r ? the double radius ? 2 times the radius is the diameter.

so, we know

diameter × pi = 34 ft

diameter = 34/pi = 10.82253613... ft

Answer:

See below

Step-by-step explanation:

72 %  is .72 in decimal

.72 x = 50 oz     Divide both sides by .72

X = 50 / .72 = 69.44 oz     ( or 69  4/9 oz )

Using similarity of triangles, the length of side GH is given as follows:

GH = 18.

Similar triangles have congruent angle measures, thus the measures of the side lengths are proportional.

In this problem, triangles CAD and HGD are similar, and the equivalent sides are given as follows:

Hence the following proportional relationship is established:

x/12 = 45/30

Applying cross multiplication, we can solve for x, which is the length of side GH, as follows:

30x = 45 x 12 (simplifying by 30)

x = 1.5 x 12 (multiply 1.5 and 12).

x = 18. (which is the length of side GH).

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First, draw a diagram to visualize the situation:

As we can see, the difference between the x-coordinates of the points is the length of one leg of a right triangle, and the difference between the y-coordinates is the length of the other leg.

Then, for the given points (-5,4) and (8,-3), the distance given by the Pythagorean Theorem is:

Therefore, the distance between the points (-5,4) and (8,-3) is: √218.

Answer:

The prime factorization of 21 is;

Explanation:

We want to find the prime factorization of 21;

The number 21 is a product of 3 and 7;

since 3 and 7 are both prime number, then the prime factorization of 21 is;

Given: 5 kg bag of grass seed covers 650 m2

To find:

Bags to seed 60m-80m field

Solution:

Area of football field- 60x80=4800m²

Bags required-

Since 650 m² is covered by 5kg

So, 4800m² will be covered by-

=4800/650x5

= 36.9 bags

Therefore, 40 bags are required to seed a 60m-by-80m football field.

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Answer:

B)4+5×(3^2-9)÷3^2 C)

Step-by-step explanation:

(a) Hans bought 11 pounds of rice for $5.

How many dollars did he pay per pound of rice?

the unit price is given by the total price divided by the total weight, therefore:

He payed $0.45 per pound of rice

(b) It takes 16 pounds of seed to completely plant a 3-acre field.

How many pounds of seed are needed per acre?

the pounds of seed per unit area is given by the total pounds used to plant the total acres

so, the answer is 5.33 pounds per acre

When Kara is sorting buttons by length for a craft project  and the line plot shows the length of each button. If Kara lines up all the 3/4 inches buttons, then the total length is  [tex]2\frac{1}{4}[/tex] inches

The length of the button = 3/4 inches

Number of 3/4 inch buttons = 3 buttons

Then the total length = Number of 3/4 inch buttons × The length of the button

Substitute the values in the equation

The total length = 3×(3/4)

= 9/4 inches

Convert the simple fraction to the mixed fraction

9/4 inches = [tex]2\frac{1}{4}[/tex] inches

Hence, when Kara is sorting buttons by length for a craft project  and the line plot shows the length of each button. If Kara lines up all the 3/4 inches buttons, then the total length is  [tex]2\frac{1}{4}[/tex] inches.

The complete question is

Kara is sorting buttons by length for a craft project. the line plot shows the length of each button. if Kara lines up all the 3/4-inch button, what would be the total length?

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It takes 1.75 minutes to an average customer to wait

The waiting times standard deviation is 1.01

The percentage of a customer wait under a minute is 28.57%

42.86% customers wait more than two minutes

Uniform distribution: n probability theory and statistics, the continuous uniform distribution or rectangular distribution is a family of symmetric probability distributions. The distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds.

Display the 1.00 area under the curve.

The rectangle has a length of 3.5 - 0 = 3.5.

The rectangle's height is 1/3.5.

To determine the area, multiply:

3.5 * 1/3.5 = 1

How long does the average customer have to wait for an elevator?

EV stands for average between high and low.

= (0+3.5)/2

= 1.75

What is the waiting time's standard deviation?

Standard deviation is equal to sqrt(b-a2/12).

= sqrt((3.5-0)^2/12)

= 1.01

What percentage of customers wait under a minute?

It is x/(b-a) = 1/ for less than (3.5-0)

1/3.5

= 28.57%

How many customers wait more than two minutes?

It is 1 - x for greater than (b-a)

(3.5-2)/3.5

= 1.5/3.5

= 42.86%

It takes 1.75 minutes to an average customer to wait

The waiting times standard deviation is 1.01

The percentage of a customer wait under a minute is 28.57%

42.86% customers wait more than two minutes

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Answer:

$3015

Step-by-step explanation:

Answer:

$3015

Step-by-step explanation:

Comment

She earned 9% of 33500

To replace th4 % sign, you always divide the number given by 100.

So 9% as a decimal is 9/100 = 0.09. Notice where the 100 goes. It is right underneath the 9. So you are dividing by 100.

So she earned

0.9 * 33500          =      $3015

Answer:

x=65

y=32

Step-by-step explanation:

2x+x-15=180

combine like terms

3x-15=180

add 15 to both sides

3x=195

divide both sides by 3

x=65

now y's

4y+y+20=180

combine like terms

5y+20=180

subtract 20 from both sides

5y=160

divide both sides by 5

y=32

Answer:

x = 65

y = 32

Step-by-step explanation:

2x + (x - 15) = 180

2x + x - 15

3x - 15 = 180

     +15    +15

-------------------

3x = 195

÷3      ÷3

----------------

x = 65

4y + (y + 20) = 180

4y + y + 20 =180

5y + 20 = 180

      -20    -20

---------------------

5y = 160

÷5     ÷5

---------------

y = 32

2x + (x - 15) + 4y + (y + 20) = 360

2(65) + (65 - 15) + 4(32) + (32 + 20) = 360

130 + 50 + 128 + 52 = 360

180 + 180 = 360

360 = 360

I hope this helps!

How are the algebraic expressions divided?

a) (4x4-12x³ + 7x² + 3x - 2) by (2x²-3x-2) = (2x-1) (x-1)

Factorization of the numerator ,

[tex]4x^4-12x^3 + 7x^2 + 3x - 2\\\\= (4x^4+ 7x^2 - 2) -12x^3+3x\\\\= (4x^4- x^2+ 8x^2 - 2) -12x^3+3x\\\\=(4x^4- x^2)+ (8x^2 - 2) -12x^3+3x\\\\= x^2(4x^2- 1)+ 2( 4x^2 - 1) -12x^3+3x\\\\=(4x^2- 1)(x^2+2)-12x^3+3x\\\\=(4x^2- 1)(x^2+2)+(-12x^3+3x)\\\\=(4x^2- 1)(x^2+2)-3x(4x^2-1)\\\\=(4x^2- 1)(x^2+2-3x)\\\\=(4x^2- 1)(x^2-x-2x+2)\\\\=(4x^2- 1)((x^2-x)+(-2x+2))\\\\=(4x^2- 1)(x(x-1)-2(x-1))\\\\=(4x^2- 1)(x-1)(x-2)\\\\=(2x+1)(2x-1)(x-1)(x-2)[/tex]-----(1)

Factorization the denominator ,

[tex](2x^2-3x-2)\\\\= (2x^2+x-4x-2)\\\\= (2x^2+x)+(-4x-2)\\\\=x(2x+1)-2(2x+1)\\\\=(2x+1)(x-2)[/tex]                          ----(2)

Divide (1) by (2)

= [tex]\frac{(2x+1)(2x-1)(x-1)(x-2)}{(2x+1)(x-2)}[/tex]

= (2x-1) (x-1)

b) (x² + 4y¹) by (x² + 2y²-2xy)

[tex]\frac{x^{2} +4y}{x^{2} +2y^{2} -2xy}[/tex]

This is the simplest form of the algebraic expression.

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Answer:

12 Blueberries and 4 Strawberries

Step-by-step explanation:

12+4 = 16 and 12:4 = 3:1

Answer:

3, 9, 19

Step-by-step explanation:

substitute n = 1, 2, 3 into the nth term formula

n = 1 : 2(1)² + 1 = 2(1) + 1 = 2 + 1 = 3

n = 2 : 2(2)² + 1 = 2(4) + 1 = 8 + 1 = 9

n = 3 : 2(3)² + 1 = 2(9) + 1 = 18 + 1 = 19

the first 3 terms are 3, 9, 19

By following the steps below, we can plot the graph of →

y = 5 cos(2x + π/3) - 1

The trigonometric functions (also called circular functions, angle functions) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.

Given is the following function -

y = 5 cos(2x + π/3) - 1

We have -

y = 5 cos(2x + π/3) - 1

We can sketch the function as follows -

Let y = cos(x)

       y = 5 cos(x)

        y = 5 cos(2x)

        y = 5 cos(2x + π/3). This will shift the graph along the negative

        [x] - axis by π/3.

Therefore, by following the steps above, we can plot the graph of →

y = 5 cos(2x + π/3) - 1

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Answer:  between $42 and $54 including both endpoints.

In symbolic form we can say [tex]42 \le p \le 54[/tex] where p is the final price after the discount is applied.

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

Explanation:

10% off means you save 10% but pay the remaining 90%

Then convert 90% to decimal form to get 0.90

If the original price is $60, then the final price is 0.90*60 = 54 dollars.

In other words,

10% of 60 = 0.10*60 = 6 dollars saved

60-6 = 54 is the final price

---------------------

If the discount is 30% then you pay the remaining 70%

0.70*60 = 42

Or you can think of it like this

30% of 60 = 0.30*60 = 18 dollars saved

60-18 = 42 dollars is the final price

---------------------

Let's summarize with this chart:

[tex]\begin{array}{|c|c|c|} \cline{1-3}\text{Discount} & \text{Amount Saved} & \text{Final Price}\\\cline{1-3}10\% & \$6 & \$54\\\cline{1-3}30\% & \$18 & \$42\\\cline{1-3}\end{array}[/tex]

Therefore, the final price after the discount is between $42 and $54 including both endpoints.

Side note: The jump from 10% to 30% is "times 3"; so is the jump from $6 to $18 in the "amount saved" column of the table.

Percent increase by 35.71%

What is Profit and Loss ?

Profit and loss (P&L) statement refers to a financial statement that summarizes the revenues, costs, and expenses incurred during a specified period, usually a quarter or fiscal year.

Given,

cost price of a boat is = $2800

selling price of a boat is = $3800

There is profit since C.P is less than S.P.

so, Profit = S.P - C.P

               = $3800 - $2800

               = $1000

Now, find profit percent i.e, Profit% = (Profit / C.P) * 100

=> Profit % = (1000 / 2800)*100

                 = 35.71%

Therefore, Percent increase by 35.71%

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