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Answer:

x = [tex]\frac{(a+b)}{2}[/tex]

[tex]y=\frac{a-b}{2}[/tex]

Step-by-step explanation:

System of equations has been given as,

x + y = a ----------(1)

x - y = b ---------(2)

By adding equation (1) and (2)

(x + y) + (x - y) = a + b

2x = a + b

x = [tex]\frac{(a+b)}{2}[/tex]

By substituting these values in equation (2),

x - y = b

[tex]\frac{a+b}{2}-y=b[/tex]

[tex]\frac{a+b}{2}-b=y[/tex]

[tex]\frac{a+b-2b}{2}=y[/tex]

[tex]\frac{a-b}{2}=y[/tex]

Answer:

x= -2 , y = 4

then

R/ (-2)² - 8(4)

R/ 4-32

R/ -28

Step-by-step explanation:

4 Wrong Answers

[tex]Correct = 11*4=44[/tex]

[tex]Incorrect = Correct - 40 = 4[/tex]

Answer:

Complementary angles sum to 90°

Answer:

A)The angles in the smaller prism measure 90 degrees.

B)The perimeter of the rectangular bases changes by a factor of 2.  

E)The area of the rectangular bases changes by a factor of 4.

Step-by-step explanation:

The right rectangular prisms are similar.

Which statements are correct? Check all that apply.

A)The angles in the smaller prism measure 90 degrees.

B)The perimeter of the rectangular bases changes by a factor of 2.

C)The surface area changes by a factor of 8.

D)The larger prism has twice the volume of the smaller prism.

E)The area of the rectangular bases changes by a factor of 4.

Solution:

Two polygons are said to be similar if they have the same shape, the ratio of their sides are in the same proportion and they have the same size of angles.

A) Since the bigger prism has angles with measure of 90°, hence the angles in the smaller prism will also measure 90.

Option A is correct.

B) Perimeter of bigger prism base = 2(2.2 + 0.8) = 6

Perimeter of smaller prism base = 2(1.1 + 0.4) = 3

The perimeter of the rectangular bases changes by a factor of 2 (6 / 3).

Option B is correct.

C) Surface area of bigger prism = 2(3.2*0.8 + 2.2*0.8 + 3.2*2.2) = 22.72

Surface area of smaller prism = 2(1.6*0.4 + 1.1*0.4 + 1.6*1.1) = 5.68

The surface area does not change by a factor of 8 (22.72 / 5.68 ≠ 8)

Option C is wrong

D) Volume of bigger prism = 2.2 * 3.2 * 0.8 = 5.632

Volume of smaller prism = 1.1 * 1.6 * 0.4 = 0.704

The larger prism volume is not twice of the smaller prism

Option D is wrong

E) Area of bigger prism base = 2.2*0.8 = 1.76

Area of smaller prism base = 2.2*0.8 = 0.44

The area of the rectangular bases changes by a  factor of 4 (1.76 / 0.44 = 4)

Answer:

380

Step-by-step explanation:

280 coffe machine

15 bag multiple for 40= 600 - 15%= 540

540+280=820

1200-820=380

Answer:

A, C, D

Step-by-step explanation:

42 + 14 = 56

38 + 18 = 56

67 + 33 = 100

70 + 30 = 100

93 + 35 = 128

95 + 33 = 128

B)

40 + 22 = 62

32 + 10 = 42

62 ≠ 42

Answer:

x=-8

Step-by-step explanation:

Well subtract 10 on both sides

-4x=32

Div ide -4 on both sides

x=-8

Answer:

x = -8

Step-by-step explanation:

-4x + 10 = 42

       -10   -10

-4x = 32

/-4     /-4

x = -8

to check work, insert x into the normal equation

-4(-8) + 10 = 42

32 + 10 = 42

Answer:

what is the question?

Step-by-step explanation:

Answer:

The first step is to find the volume of the two hemispheres.

Step-by-step explanation:

[tex]\boxed{volume \: of \: sphere = \frac{4}{3} \pi {r}^{3} }[/tex]

Since the 2 hemispheres have the same radius, we can simply find the volume of a sphere.

Volume of sphere

[tex] = \frac{4}{3}( \pi)( {12}^{3} )[/tex]

[tex] = 2304\pi \: in^{3} [/tex]

Volume of solid

= volume of cylinder -volume of 2 hemispheres

Let's find the volume of the cylinder.

[tex]\boxed{voume \: of \: cylinder = \pi {r}^{2}h }[/tex]

Volume of cylinder

[tex] = \pi( {12}^{2} )(24)[/tex]

[tex] = 3456\pi \: in^{3} [/tex]

Thus, volume of solid

[tex] = 3456\pi - 2304\pi[/tex]

[tex] = 1152\pi[/tex]

[tex] = 1152(3.14)[/tex]

[tex] = 3617.28 \: in^{3} [/tex]

Answer:

Volume of solid = Volume of Sphere - Volume of cylinder

Volume = 4/3πr³ - πr²h

Volume = 4/3 • π • 12³ - π • 12² • 24

Volume = 4/3 • π • 1728 - π • 144 • 24

Volume = 4 • π • 576 - π • 3456

Volume = π(3456 - 2304)

Volume = π(1152)

Volume = 3619.11 in³

[tex] \\ [/tex]

Answer: sample of 100

:3

Answer:

16

Step-by-step explanation:

Square root of 2 is irrational. This has been proven by the Pythagoreans (there is a simple proof of that).

pi is also known to be irrational although the proof is a bit more demanding.

Square root of 10 can be written as a product of square root of 5 and square root of 2, which themselves are irrational. Any product involving an irrational number is irrational

Square root of 16 = 4. 4 can be written as a fraction 4/1, or 8/2, 16/4, etc. and therefore is rational by definition.

Answer:

see explanation

Step-by-step explanation:

length = [tex]\frac{60}{8}[/tex] = 7.5 in

scale factor = [tex]\frac{image}{original}[/tex] = [tex]\frac{8}{60}[/tex] = [tex]\frac{2}{15}[/tex]

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

length = [tex]\frac{192}{4}[/tex] = 48 cm

scale factor = [tex]\frac{omage}{original}[/tex] = [tex]\frac{4}{192}[/tex] = [tex]\frac{1}{48}[/tex]

Answer:

See below for answers

Step-by-step explanation:

y=5(2)ˣ

y=5(2)⁻²=5(1/2²)=5(1/4)=5/4

y=5(2)⁻¹=5(1/2¹)=5(1/2)=5/2

y=5(2)⁰=5(1)=5

y=5(2)¹=5(2)=10

y=5(2)²=5(4)=20

The total Amount of the mortgage is $400,545 if the closing costs are financed with the mortgage.

a) The down payment of Jason is 10% of $430,000 =$43,000b) The amount of the mortgage is the difference between the home value and the down payment.

Mathematically, $430,000 - $43,000 = $387,000.c) The closing costs are 3.5% of the mortgage. So, 3.5% of $387,000 is: 0.035 × $387,000 = $13,545.

Hence, the closing costs are $13,545. d) The total amount of the mortgage if they finance the closing costs with the mortgage is the sum of the amount of mortgage and the closing cost.

So, the total amount of the mortgage is: $387,000 + $13,545 = $400,545.Solution:a) Jason's down payment is 10% of the cost of the house, which is given as $430,000.

To calculate the down payment, multiply the cost of the house by 10%.Down payment = $430,000 x 10% = $43,000

Therefore, Jason's down payment is $43,000.b)

The amount of the mortgage is the difference between the total cost of the house and the down payment. The cost of the house is given as $430,000.

Thus, we have:Mortgage amount = Total cost - Down paymentMortgage amount = $430,000 - $43,000Mortgage amount = $387,000

Therefore, the amount of the mortgage is $387,000.c) The closing costs are 3.5% of the mortgage.

Using the mortgage amount calculated in part b), we can compute the closing costs as follows:Closing costs = 3.5% x Mortgage amountClosing costs = 3.5% x $387,000

Closing costs = $13,545

Therefore, the closing costs are $13,545.

d) If the closing costs are financed with the mortgage, we simply need to add the closing costs to the mortgage amount calculated in part b):Total amount of the mortgage = Mortgage amount + Closing costsTotal amount of the mortgage = $387,000 + $13,545

Total amount of the mortgage = $400,545

Therefore, the total amount of the mortgage is $400,545 if the closing costs are financed with the mortgage.

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Answer:

Razones trigonométricas inversas: cosecante, secante y cotangente. ... Dado un triángulo rectángulo, definimos la cosecante, la secante y cotangente de un ángulo como las razones inversas del seno, coseno y tangente, respectivamente.

Step-by-step explanation:

espero y te ayude

Answer:

7/25

Step-by-step explanation:

Answer:

133.33

Step-by-step explanation:

sorry if im incorrect

Answer:

800

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

what do you mean ?? its already written there

Answer:

The answer is 5

Step-by-step explanation:

The answer is 5 because the length across from the right angle is always the hypotenuse.

Answer:

6

Step-by-step explanation:

You would first divide 48/8 than you would get 8 baskets per minute.

Answer:

6

Step-by-step explanation:

Mario: 1 minute = 5 baskets and 5 x 6 = 30.

Chris: 1 minute = 6 baskets and 6 x 8 = 48.

Answer:

Im pretty sure it's 168

Step-by-step explanation:]

9 x 14 = 126

126 ÷ 0.75 = 168

Answer:

y = - [tex]\frac{4}{3}[/tex] x - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (- 3, 3) and (x₂, y₂ ) = (0, - 1) ← 2 points on the line

m = [tex]\frac{-1-3}{0+3}[/tex] = - [tex]\frac{4}{3}[/tex]

The line crosses the y- axis at (0, - 1 ) ⇒ c = - 1

y = - [tex]\frac{4}{3}[/tex] x - 1 ← equation of line

Answer: 9x^2-48x+64

I was wrong originally

I am so sorry

Step-by-step explanation:

(3x-8)(3x-8)

9x^2-24x-24x+64

9x^2-48x+64

Answer:

4.2

Step-by-step explanation:

took a bullet for the team

Elizabeth would need an interest rate of 4.25% to make a profit of $670, to the closest hundredth of a percent.

The interest earned on savings that are computed using both the original principal and the interest accrued over time is known as compound interest. A = P(1 + r/n)^nt, where P is the principal balance, r is the interest rate, n is the number of times interest is compounded annually, and t is the number of years, which is the formula for compound interest.

Given, Elizabeth is going to invest $480 and leave it in an account for 8 years.

from the formula of compound interest

A = P(1 + r/n) ^nt

in our case,

A =670

P = 480

t = 8

Thus,

670 = 480(1 + r)^8

r = 4.25%

Therefore, an interest rate, to the nearest tenth of a percent, would be 4.25% required in order for Elizabeth to end up with $670

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2√3+6√2

hope this helps :D

Answer:

Step-by-step explanation:

2√3+6√2

Answer:

71.88

Step-by-step explanation:

........................

So if 9 of the 32 are women, then everybody left would be a guy. That's 32 - 9 = 23 men. To turn that into a percentage, just divide the number of men by the total amount of people in the class: 23/32 = 71.875% which rounded is 71.88%

Answer:

169 3/4 in³

Step-by-step explanation:

v=l×w×h

v=8× 1 3/4× 12 1/8

21  7/32×8= 169 3/4 in³

Answer:

That would seem like a b

Step by step explanation: (>) means greater than and b is stating that element a is higher than element c