24. A car costs $21,435. Each year the car depreciates (decreases in value) by 8%. How much will
the car be worth after 10 years?

Answer:

Step-by-step explanation:

14.

A.  

x = 5.0081818181..

10x = 50.08181818181....

100x = 500.81818181818...

100x - x = 500.8181818... - 5. 008181818....

99x = 495.81

[tex]x = \frac{495.81}{99} = \frac{495.81 \times 100}{99 \times 100} \\\\\\x= \frac{49581}{9900}[/tex]

[tex]x = \frac{5509}{1100}[/tex]

14.

B.

[tex]\sqrt{50} - \sqrt{98} + \sqrt{162} \\\\\sqrt{ 2 \times 25} - \sqrt{ 2 \times 49} + \sqrt{2 \times 81}\\\\\sqrt{ 2 \times 5^2} - \sqrt{ 2 \times 7^2} + \sqrt{2 \times 9^2}\\\\5\sqrt2 - 7 \sqrt 2 - 9 \sqrt 2\\\\\sqrt{2} ( 5 - 7 + 9 ) \\\\7\sqrt2[/tex]

15.

[tex]\frac{3 + \sqrt5}{4 - 2\sqrt 5} \\\\= \frac{3 + \sqrt5}{4 - 2\sqrt 5} \times \frac{4 + 2\sqrt5}{4 + 2\sqrt5}\\\\[/tex]                           [tex][ \ rationalizing \ the \ denominator \ ][/tex]

[tex]=\frac{(3 + \sqrt5)(4 + 2\sqrt5)}{(4 -2 \sqrt5)(4 + 2\sqrt5)}\\\\=\frac{12 + 6 \sqrt5 + 4\sqrt5 + 2(\sqrt5)^2}{(4)^2 - (2\sqrt5)^2}[/tex]                    [tex][ \ (a - b)(a +b) = a^2 - b^2 \ ][/tex]

[tex]=\frac{12 + 10 + 10\sqrt5}{16 - (4 \times 5)}\\\\=\frac{22 + 10\sqrt5}{16 - 20 }\\\\=\frac{22+ 10 \sqrt5 }{-4}[/tex]

[tex]= \frac{11}{-2} + \frac{5 \sqrt5}{-2}\\\\= -\frac{11}{2} + \frac{-5 }{2} \sqrt5\\\\[/tex]

[tex]a = - \frac{11}{2} , \ b = -\frac{5}{2}[/tex]

16

[tex]\frac{\sqrt7 + 1 }{\sqrt7 - 1} - \frac{\sqrt7 - 1}{\sqrt7 + 1}\\\\[/tex]

[tex]\frac{(\sqrt 7 + 1 )( \sqrt7 + 1)}{(\sqrt7 - 1 )(\sqrt7 + 1)} - \frac{(\sqrt7 - 1)(\sqrt 7 - 1)}{(\sqrt7 + 1)(\sqrt7 - 1)}[/tex]     [tex][ \ LCM \ of \ denominators : (\sqrt7 -1)(\sqrt7 + 1) \ ][/tex]

[tex]\frac{(\sqrt 7 + 1 )^2 -( \sqrt7 - 1)^2}{(\sqrt7)^2 - 1^2}[/tex]                     [tex][ \ (a \pm b)(a \pm b) = (a \pm b)^2 \ (a-b)(a+b) = a^2 - b^2 \ ][/tex]

[tex]=\frac{(7 + 1 + 2\sqrt7) - ( 7 + 1 - 2\sqrt7)}{7 - 1}\\\\=\frac{8 + 2\sqrt7 - 8 + 2\sqrt7}{6}\\\\= \frac{4 \sqrt7}{6}\\\\= \frac{2 \sqrt 7}{3}[/tex]

Answer:

25

Step-by-step explanation:

Moving it down does not change the length.

Answer:

True

Step-by-step explanation:

Supplementary angles are angles that add up to 180 degrees (straight line). *5 degrees + x create a straight line.

Answer:

The given theorem proves that the door is not a rectangle right now since, the door came out of shape, it can be proved by the Pythagorean theorem. If the length is set to a certain shape, and the width is set to a certain shape, and drawn to diagonals. If solved by the Pythagorean Theorem, if the length of two diagonals are similar then and only then the door would be a rectangle.

Hope this helps!

Answer:

11 years

Step-by-step explanation:

Double of the amount deposited = $350 × 2 = $700

First, convert R as a percent to r as a decimal

r = R/100

R = 6.3%

Hence,

r = 6.3/100

r = 0.063 per year,

Then, solve the equation for t = time, the formula is given as:

t = ln(A/P) / r

A = Doubled amount = $700

P = Principal = Initial amount = $350

t = ln(700.00/350.00) / 0.063

t = 11.002 years

Approximately , t = 11 years

Therefore, it will take 11 years for your money to double.

Answer:

The fourth coefficient is 4.

Step-by-step explanation:

Pascal's Triangle in this case has 5 rows of coefficients because the highest power in (y + w)^4 is 4.  4 plus 1 is 5.

     Here's the appropriate Pascal's Triangle:

     1

    1  1

   1  2  1

 1   3  3   1

1  4  6  4    1          Use this row when expanding the 4th power of (v + w).

Notice that in the given expansion, the coefficients are

1, 4, 6, 4  1

This corresponds to the last (5th) row of Pascal's Triangle (above).

So the correct coefficient to be placed in the box is 4.

Answer:

8

Step-by-step explanation:

4/x=3/6

4=3/6x

4*6=3x

24/3=x

8=x

Please mark me as brainliest

Answer:

Aaron = 54

Bola = 18

Step-by-step explanation:

Let

[tex]A \to Aaron[/tex]

[tex]B \to Bola[/tex]

From the first statement, we have:

[tex]A = 3B[/tex]

After given Bola 6 sweets,

[tex]A - 6 = 2(B + 6)[/tex]

Required

The initial number of sweets each has

Substitute [tex]A = 3B[/tex] in [tex]A - 6 = 2(B + 6)[/tex]

[tex]3B - 6 = 2(B + 6)[/tex]

Open bracket

[tex]3B - 6 = 2B + 12[/tex]

Collect like terms

[tex]3B -2B = 12+6[/tex]

[tex]B = 18[/tex]

Substitute [tex]B = 18[/tex] in [tex]A = 3B[/tex]

[tex]A = 3 * 18[/tex]

[tex]A = 54[/tex]

Answer:

5

Step-by-step explanation:

Evaluate and substitute:

Sqrt of 7 - (-18)

Sqrt of 7 + 18 = 25

Sqrt of 25 = 5

Therefore, our answer!

Hope this helps, best of luck! :p

Answer: I did it in the explanation thingy-

Step-by-step explanation:

Step 1. 8792 - 6886 = 1906

Step 2. 12 x 9 108

That... OR the answer is 205848X

The solution of the expression as a single power is X²⁹.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given expression is (x⁴)(x¹⁰)/(x³)⁵. The equation will be solved by the property of exponents.

E = (x⁴)(x¹⁰)/(x³)⁵

Add all the powers of the same base x.

E =  (x⁴)(x¹⁰)/(x¹⁵)

E = x⁽⁴⁺¹⁰⁺¹⁵⁾

E = x²⁹

Therefore, the solution of the expression as a single power is X²⁹.

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Answer:

Step-by-step explanation:

.....

Answer:

34,833.21 ft³

Step-by-step explanation:

Volume of a cylinder = πr²h

r is the radius

h is the height

Given

height h = 19 3/4 ft

d = 1 1/5h

d = 6/5 * h

d = 6/5 * 19 3/4

d = 6/5 * 79/4

d = 474/20

radius r = 474/20 * 1/2

radius r = 474/40

radus r = 11 34/40

radus r = 11 17/20 ft

Get the volume

V = 3.14 * (474/40)² * 79/4

V = 3.14 * 561.69 * 19.75

V = 34,833.20535

Hence the volume of the cylinder to the nearest hundredth is 34,833.21 ft³

Answer:

R = 13%

Step-by-step explanation:

P = $4000

I = $780

T = 18 months = 18/12 years

[tex]I = \frac{PRT}{100} \\\\780 = \frac{ 4000 \times R \times \frac{18}{12}}{100}\\\\780 = \frac{6000 \times R }{100}\\\\780 = 60R\\\\R = \frac{780}{60} = 13 \%[/tex]

Answer:

gloves cost $5

hats cost $4

Step-by-step explanation:

four pairs of gloves and four hats for $36.00

4g + 4h = 36

three pairs of gloves and four hats for $31.00

3g + 4h = 31

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

Subtract the second equation from the first

  4g + 4h = 36

-( 3g + 4h = 31 )

––––––––––––

   g           = 5

gloves cost $5

substitute for g = 5 into either equation

4(5) + 4h = 36

20 + 4h = 36

Subtract 20 from both sides

4h = 16

Divide both sides by 4

h = 4

hats cost $4

Answer:

Question 1: d. (3, 7)

Question 2: b. (5, 1)

Question 3: b. (6, –4)

Step-by-step explanation:

Question 1:

Solve this system of equations using any method.

4x – y = 5

3x + y = 16

Add the equations.

7x = 21

x = 3

4(3) - y = 5

-y = -7

y = 7

d. (3, 7)

Question 2:

Solve the following system of equations.

d + e = 6

d – e = 4

Add the equations.

2d = 10

d = 5

5 + e = 6

e = 1

b. (5, 1)

Question 3:

Solve the following system of equations by linear combination:

4x + 3y = 12

y = x – 10

4x + 3y = 12

-x + y = -10

Multiply the second equation by 4 and add to the first equation.

          4x + 3y = 12

(+)      -4x + 4y = -40

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

                  7y = -28

y = -4

-4 = x - 10

x = 6

b. (6, –4)

Answer:

1

Step-by-step explanation:

additive identity =1/2

multiplicative =2

Product = 1/2*2

So the answer is 1

Answer:

If the question is asking which line is the radius then yes

Step-by-step explanation:

Answer:

Step-by-step explanation:

Distance traveled by walking = x

i) The distance Mary run = 2 *x = 2x

ii) Distance traveled by bus = 65 m more than the distance she ran

                                             = 65 m more than 2x

Distance traveled by bus  = 2x + 65

Total distance traveled = 600 m

x + 2x + 2x +65 = 600

            5x + 65 = 600

                   5x = 600 - 65

                   5x = 535

                     x = 535/5

x = 107

Distance Mary walked = 107 m

To find the y-intercept, plug in 0 for x and you solve to get 8

y=−2x+8

y=−2(0)+8

y=0+8

y=0

To find the x-intercept, plug in 0 for y and you solve to get 4

y=−2x+8

0=−2x+8

2x=8

x=0

Answer:

$128

Step-by-step explanation:

2/5 × $40= $16

$16×8= $128

Answer:

118

Step-by-step explanation:

Answer:

jojo reference

Step-by-step explanation:

Answer:

B. X= 5 + 3i

5 + 3i

Step-by-step explanation:

We are given the quadratic equation

x² - 10x = -34

x² - 10x + 34 = 0

Using Almighty formula

x = -b ± √b² - 4ac/2a

When given equation: ax² + bx + c

Where: a = 1, b = -10 , c = 34

x = -10 ± √-10² - 4 × 1 × 34/2 × 1

x = 10 ± √100 - 136/2

x = 10 ± √-36 /2

x = 10/2 ±. √-36/2

x = 5 ± 6i /2

x = 5 ± 3i

Hence: the roots of the equation are:

x = 5 - 3i , x = 5 + 3i

The expression [tex]2- \dfrac{x-1}{x+2}[/tex]  is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].

We have to find, which equation is equivalent to the given expression.

The given expression is,

[tex]= 2- \dfrac{x-1}{x+2}[/tex]

To determine the equivalent expression following all the steps given below.

                   [tex]\rm = 2-\dfrac{x-1}{x+2}\\\\= \dfrac{2(x+2) - (x-1)}{x+2}\\\\= \dfrac{2x+4-x+1}{x+2}\\\\[/tex]

                    [tex]= \dfrac{2x+4-x+1}{x+2}\\\\= \dfrac{x+5}{x+2}\\\\[/tex]

                    [tex]=\dfrac{x+5}{x+2}\\\\= \dfrac{x+ 2+3}{x+2}\\\\[/tex]

                    [tex]= \dfrac{x+2}{x+2} + \dfrac{3}{x+2}\\\\= 1 + \dfrac{3}{x+2}[/tex]

Hence, The expression [tex]2- \dfrac{x-1}{x+2}[/tex]  is equivalent to [tex]1 + \dfrac{3}{x+2}[/tex].

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Answer: 4 thousands, 5 hundreds, 7 tens

Step-by-step explanation: 4,570 is pretty easy to break down. The first place value is 0 so nothing for that. As you have it there the tens place values has 7. Next is hundreds and there's a 5 there so 5 hundreds. If the number is 4,570 then it should be 4 thousands not three.

Answer:

7.9m

Step-by-step explanation:

We solve using the Trigonometric function of Tangent

tan θ = Opposite/Adjacent

Opposite = x

Adjacent = 7.05m

We solve for x

tan 42 = x /7.05m

Cross Multiply

tan 42 × 7.05 = x

x = 6.3478485123m

Approximately = 6.35m

Height of the statue = x + 1.55

Hence, = 6.35m + 1.55m

= 7.9m

The height of the statue = 7.9 meters

Answer:

Cost of case = $5

Step-by-step explanation:

x = cost of camera and y = cost of case

x = y + 90

x + y = 100

y + 90 + y = 100

2y = 10

y = 5

x = y + 90

x = 5 + 90

x = 95

Therefore, the cost of the camera is $95 and the cost of the case is $5.

The cost of case is 5 dollars.

The equation is the defined as mathematical statements that have a minimum of two terms containing variables or numbers is equal.

Let,

Cost of camera = a and

Cost of case = b

Given that, camera and a case cost 100 dollars

a + b = 100

Since, the camera cost 90 more dollars than the case

So, a = b + 90

Substitute the value in the equation a + b = 100

b + 90 + b = 100

2b = 10

Divided by 2 both the sides

b = 5

Substitute the value of b in equation

a = b+ 90

a = 5 + 90

a = 95

So, the cost of the camera is $95 and the cost of the case is $5.

Hence, the cost of the case is 5 dollars.

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the answer is c because you have to take the zf an time it by the zd

Answer:

C

Step-by-step explanation:

for the top of the triangle it has to be 40 and angle d has been declared as 88

so it is 40+88 = 128    now 180 -128 = 52 so the answer is C