Which of the images above represents a proof of the Pythagorean Theorem? Explain your choice, and then explain how the figure proves the Pythagorean Theorem.

Answer:

D: 3780 square feet

Step-by-step explanation:

Let the length be L. Let the width be W.

The area of a rectangle is length times width, so

A = LW

The area is 420 square feet, so

LW = 420

Now you multiply the length by 3 and multiply the width by 3.

The length is now 3L, and the width is now 3W.

The area of the new rectangle is the new length times the new width.

new area = 3L * 3W

new area = 3 * 3 * LW

new area = 9 * LW

LW was the original area, and it is 420 square feet, so the new area is 9 times the old area.

new area = 9 * 420 square feet

new area = 3780 square feet

Answer:

3x6=18

Step-by-step explanation:

3x6=18

6 times as old is the same as saying TIMES by 6 :)

Joe's age can be found using the equation 'Joe's Age = 6 * 3', as Joe is 6 times as old as Mike, and Mike is 3 years old.

The question presents a situation where Joe is 6 times as old as Mike. We know that Mike is 3 years old, so to find Joe's age, we need to multiply Mike's age by 6. This situation can be expressed by the following equation: Joe's Age = 6 * Mike's Age.

Replacing 'Mike's Age' with the given value (3 years), we get: Joe's Age = 6 * 3

Therefore, the equation to find Joe's age is Joe's Age = 6 * 3.

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Answer:

19.25ft

Step-by-step explanation:

area = length x width so 3.5 x 5.5 = 19.25

Answer:

The area of the frame is 19.25 feet.

Step-by-step explanation:

We can see from the information that the wooden frame is a rectangle since length and breadth are unequal.

breadth = 3.5 ft

length = 5.5 ft

The formula for area of a rectangle is = A = L x b

Area = 3.5 * 5.5

Area = 19.25 feet

Answer:

10 ounces

Step-by-step explanation:

10 ounces of iodine are worth 30 cents so the mixture can be sold for 20 cents an ounce.

Arithmetic operations can also be specified by adding, subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Let n be the ounces of 30 cents worth of iodine.

To determine the mixture to be worth 20 cents per ounce.

The value of 50 ounces of 18-cent iodine is

⇒ (50)(18) = 900 cents of iodine.

A (50+n) mixture of iodine is produced by combining 50 ounces of 18-cent iodine with n ounces of 30-cent iodine.

Similarly, n ounces of 30-cent iodine is worth 30n.

So, the price of 50+n ounces of 20-cent iodine (50+n)20

⇒ 30x + 900 = 1000 + 20x

Rearrange the likewise terms and apply the arithmetic operations,

⇒ 10x = 100

⇒ x = 10

We can estimate that in order to sell the mixture for 20 cents per ounce, we should combine 10 ounces of iodine worth 30 cents.

Hence, 10 ounces of iodine are worth 30 cents so the mixture can be sold for 20 cents an ounce.

Learn more about Arithmetic operations here:

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Answer:

40% reduction

Step-by-step explanation:

To answert this, we need to find how much of the price is each percentage. This can be found my subtracting the percent from 100:

Sale price: 100 - 20 = 80

Last day price: 100 - 25 = 75

Now we need to multiply these two values together, remembering to divide both numbers by 100 first:

80 ÷ 100 = 0.8

75 ÷ 100 = 0.75

0.8 * 0.75 = 0.6

Then multiply by 100 to find the percentage:

0.6 * 100 = 60

60% is the end price, but to find the overall reduction we need to subtract this value from 100:

100 - 60 = 40

So there was a 40% reduction on the price.

Answer: travis can afford the compact car but not the coupe

Step-by-step explanation:

Answer:

Travis can afford the compact car.

Step-by-step explanation:

The EMI formula is :

[tex]\frac{p*r*(1+r)^{n} }{(1+r)^{n}-1 }[/tex]

In first case:

p = 10800

r = 6/12/100=0.005

n = 4*12 = 48

Putting values in the formula we get:

[tex]\frac{10800*0.005*(1+0.005)^{48} }{(1+0.005)^{48}-1 }[/tex]

= $254

We can see that Travis can afford the compact car because the EMI is less than $260.

In second case:

p = 11300

r = 6/12/100=0.005

n = 4*12 = 48

Putting values in the formula we get:

[tex]\frac{11300*0.005*(1+0.005)^{48} }{(1+0.005)^{48}-1 }[/tex]

= $265.75

We can see that the coupe will have an EMI of $265.75 which is higher than the amount that Travis can afford.

Hence, Travis can afford a compact car.

Answer:

0.14 s

Step-by-step explanation:

s = -2.7 t² + 40t + 6.5

Let s = 12

12 = -2.7t² + 40t + 6.5     Subtract 12 from each side

-2.7t² + 40t + 6.5 - 12 = 0

      -2.7t² + 40t - 5.5 = 0

Apply the quadratic formula

[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

a = -2.7; b = 40; c = -5.5

[tex]x = \frac{-40\pm\sqrt{40^2 - 4\times (-2.7) \times (-5.5)}} {2(-2.7)}[/tex]

[tex]x = \frac{-40\pm\sqrt{1600-59.4}}{-5.4}[/tex]

[tex]x = \frac{-40\pm\sqrt{1540.6}}{-5.4}[/tex]

[tex]x = \frac{-40\pm 39.25}{-5.4}[/tex]

x = 7.41 ± 7.27

x₁ = 0.14; x₂ = 14.68

The graph below shows the roots at x₁ = 0.134 and x₂ = 14.68.

The Moon’s surface is at -12 ft. The ball will be 12 ft above the Moon’s surface (crossing the x-axis) in 0.14 s.

The second root gives the time the ball will be 12 ft above the Moon’s surface on its way back down.

Answer:

2 out of 4.  2/4

Step-by-step explanation:

There are 2 sides to each coin, there are two coins so all sides add up to 4.

The probability that both coins will display tails is:

P = 0.25

A fair coin has two possible outcomes, tails and heads, both with the same probability.

Then the probability of getting tails is:

p = 0.5

So, the probability for each coin (of getting tails) is:

p₁ = 0.5

p₂ = 0.5

The joint probability (this is, the probability that both of the above events happen at the same time) is the product between the individual probabilities:

P = p₁*p₂ = 0.5*0.5 = 0.25

If you want to learn more about probability, you can read:

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Answer:

6300 = s * 3

s=2100

Step-by-step explanation:

s =steps per mile

steps = steps per miles * miles

6300 = s * 3

This is the equation.

Divide each side by 3.

6300/3 = s3/3

2100 /s

Answer:

6300/3=s

s=2100

Step-by-step explanation:

six thousand three hundred over 3 equals s

s equals two thousand one hundred

Answer:

2/10

Step-by-step explanation:

2/10

The probability that Mike would pick two prime numbers from the stack of 10 cards without replacement is 2/15.

The probability of picking two prime numbers from a stack of 10 cards without replacement can be calculated by finding the probability of picking a prime number on the first draw and a prime number on the second draw, given that the first draw was successful.

There are four prime numbers among the 10 cards (2, 3, 5, and 7). So, the probability of picking a prime number on the first draw is 4/10.

Since we do not replace the first card, there are now 9 cards left in the deck, with 3 prime numbers. So, the probability of picking a prime number on the second draw, given that the first draw was successful, is 3/9.

To find the overall probability, we multiply the probabilities of the individual events: (4/10) * (3/9) = 12/90 = 2/15.

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Answer:

-38

Step-by-step explanation:

Answer:

Yes, they are similar. The answer you would click is Yes, the corresponding sides are proportional.

Step-by-step explanation:

The second figure is a dilation of the first, making them similar. The dilation is by a factor of 2 and a half.

To factor the trinomial x²-4x-32, follow the steps to identify coefficients, find suitable numbers, split the middle term, and factor by grouping. The answer is (x+4)(x-8).

To factor the trinomial x²-4x-32, you can follow these steps:

Identify the coefficients of the quadratic terms: a = 1, b = -4, and c = -32.

Find two numbers that multiply to c (a*c = -32) and add up to b (-4).

Split the middle term using these numbers: x²-4x-32 becomes x²-8x+4x-32.

Factor by grouping: (x²-8x) + (4x-32) = x(x-8) + 4(x-8) = (x+4)(x-8).

Answer:

The total surface area of the square pyramid is [tex]SA=400\ mm^2[/tex]

Step-by-step explanation:

we know that

The surface area of a square pyramid is equal to the area of the square base plus the area of four triangular faces

so

[tex]SA=10^{2} +4[\frac{1}{2}(10)(15)][/tex]

[tex]SA=400\ mm^2[/tex]

Answer:

Step-by-step explanation:

Given that two points (-5,-9) and (-5,13)

We have to find the differences between these points

Both the points have -5 as x coordinate.

But y coordinate is negative for first one while positive for second one.

Also dimension is 9 units down for I point while for ii point it is 13 units up.

The first point lies in the III quadrant while II point lies in the II quadrant.

Both the points are located with a distance of 5 units from x axis to the left of x axis.

But first point is 9 units down y axis and ii point is 13 units up the y axis.

Distance between them is 22 units.

Answer: The difference between the points (-5,-9) and (-5,13) is 22 units.

Explanation:

Since we have given that

(-5,-9) and (-5,13)

As we can see that the points are along the x-axis as the x-coordinate are same in both the points.

So, to find the difference between the points we just need to get the distance between the y- coordinates.

[tex]13-(-9)\\\\=13+9\\\\=22\ units[/tex]

Hence, the difference between the points (-5,-9) and (-5,13) is 22 units.

Answer:

6 feet above the deck

6 is in the tenths place.

Written Form: 0.6

Answer: choice C, 18

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

Explanation:

We don't know how long each little horizontal piece is, but we do know that the smaller horizontal pieces combine to fully span 5 units across. The top and bottom sides effectively are both 5 units long. Think of a rectangle. Similarly, the same happens with the vertical pieces as well. They combine to get 4.

We have a figure with a perimeter similar to a rectangle that is 4 by 5, the perimeter being 4+5+4+5 = 9+9 = 18

Alternatively, you can use the formula

P = 2*L + 2*W or P = 2*(L+W)

Plug in L = 5 and W = 4 as the length and width to get P = 18 for the perimeter

a= 92(18) =1656

Area= 1656m

p= 2(92+18) =220

Perimeter= 220m

Answer:

You would use a = 12

Step-by-step explanation:

The b value is the coefficient that is in front of the x term, that does not have an exponent of 2. It's simply the x term (not the x^2 term)

We're told that b = 15 is used, but we see that -15 is in front of the x term. To fix this contradiction, add 15x to both sides so that you move the x term to the right side

-15x+22 = 12x^2

-15x+22+15x = 12x^2+15x

22 = 12x^2+15x

Now subtract 22 from both sides to move that term over as well

22-22 = 12x^2 + 15x - 22

0 = 12x^2 + 15x - 22

12x^2 + 15x - 22 = 0

12x^2 + 15x + (-22) = 0

The last equation is in the form ax^2 + bx + c = 0 with

a = 12, b = 15, c = -22

Answer:

The adults shadow is 4.8 ft

Step-by-step explanation:

We can use ratio's to solve this problem

12 ft hoop             6ft adult

--------------         = -----------------

9.6 ft shadow      x ft shadow

Using cross products

12 * x = 9.6 * 6

12x = 57.6

Divide each side by 12

12x/12 = 57.6 /12

x = 4.8 ft

Answer:

z5

Step-by-step explanation:

Answer:

z is your answer! :)

100% --> 14

30% --> x

100x = 420

x= 420/100

x=4.2

Answer:

The answer is 4.2

Step-by-step explanation:

Always remember that when they use the word of, it means you have to multiply. So 14 times 0.3 is 4.2

Answer:

m = 35/3  or 11 2/3

Step-by-step explanation:

1/3=12-m

Subtract 12 from each side

1/3 - 12 = -m

Get a common denominator

1/3 - 12*3/3 = -m

1/3 - 36/3 = -m

-35/3 = -m

Multiply by -1

-1* -35/3 = -1 *-m

35/3 = m

Changing to a mixed number

3 goes into 35    11  times with 2 left over

11 2/3

[tex]12-m=\dfrac{1}{3}\qquad\text{subtract 12 from both sides}\\\\-m=-11\dfrac{2}{3}\qquad\text{change the signs}\\\\\boxed{m=11\dfrac{2}{3}}[/tex]

Answer:

 [tex]x^3 + 8x^2 + 11x-20[/tex]

Step-by-step explanation:

f(x) = x^2 + 3x − 4

g(x) = x + 5

To find f(x) * g(x) we multiply f(x) with g(x)

[tex]f(x) * g(x) = (x^2 + 3x -4) * (x+5)[/tex]

First multiply each term in f(x) and multiply with x+5

x^2 times x+5 becomes [tex]x^3+5x^2[/tex]

3x times x+5 becomes [tex]3x^2 + 15x[/tex]

-4 times x+ 5 becomes -4x -20

so f(x) * g(x) = [tex]x^3 + 5x^2 +3x^2 + 15x -4x -20[/tex]

Combine like terms

f(x) * g(x) = [tex]x^3 + 8x^2 + 11x-20[/tex]

Answer:    [C]:    " x³ + 8x² + 11x − 20 " .

______________________________________________________

Step-by-step explanation:

______________________________________________________

Given:      "  f(x) =  x² + 3x − 4 " ;   and

                " g(x) =  x + 5  "  ;

Find:         "  f(x) ⋅ g(x) "  :

______________________________________________________

    f(x) ⋅ g(x) =

     " (x² + 3x − 4) (x + 5) " ;

     ↔  " (x + 5) (x² + 3x − 4) " ;

______________________________________________________

Note:  " (a + b) (c + d + e)  =  ac + ad + ae + bc + bd + ae " ;

______________________________________________________

 →  " (x + 5) (x² + 3x − 4)

             =  (x * x²) + (x * 3x) + (x*-4) + (5*x²) + (5*3x) + (5*-4) " ;

             =  (x³) + (3x²)  + (-4x) + (5x²) + (15x) + (-20) ;

             =   x³  + 3x² − 4x + 5x² + 15x − 20 ;

 →  Combine the "like terms" :

          + 3x² + 5x²  =  + 8x²  ;

           − 4x + 15x   = + 11 x ;

______________________________________________________

 → And rewrite:

______________________________________________________

        →   "  x³ +  8x²  +  11x  − 20 " ;

______________________________________________________

       →  which is:  Answer choice:  [C]:   " x³  +  8x²  +  11x  −  20 " .

______________________________________________________

     Hope this helps!

        Best wishes!

______________________________________________________

I'm not sure if this is correct.

200/5x

Answer:200-10x= y

Step-by-step explanation:

5%= .05 so 200*.05= $10 Per year

so the equation would look something like

200-10x= y

x= how old the bike is

y= is your answer

To calculate 1/3 ÷ 4/5, switch the division operation to multiplication by flipping the second fraction. This gives us 1/3 * 5/4, which simplifies to 5/12.

In mathematics, when we're asked to divide fractions, we often use the method of multiplying by the reciprocal of the second fraction.

In this case, the question asks you to perform the division operation of 1/3 ÷ 4/5.

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Answer:

BD = 8 cm

Step-by-step explanation:

Diagonals of trapezoid divides each other in equal ratio.

if ABCD is a trapezoid and the diagonals AC and BD  intersect at point O

then we have

[tex]\frac{AO}{OC} =\frac{OB}{OD}[/tex]

it is given that

[tex]\frac{AO}{OC} =\frac{3}{1}[/tex] and BO=6 cm

so we can write

[tex]\frac{3}{1} =\frac{6}{OD}[/tex]

cross multiply

[tex]3 OD=6[/tex]

divide both side by 3

OD= 2 cm

now we have

BD = BO +OC

BD = 6 cm + 2 cm

BD= 8 cm

Step-by-step explanation:

The ratios of the sides is the same.

3OD=OB

Let y be the length of OD

Therefore,

3y=6

y=2,

meaning OD is 2.

OB+OD=DB

BD=6

ANSWER:

BD=8

Answer:

$354,000

Step-by-step explanation:

Since six percent in decimal is .06, all we have to do is multiply that by 5900000. When multiplied this would leave our answer to be $354,000. This is the answer unless we're missing any decimals, that would relate to the part of the question where it says round to the nearest cent.

The slope-intercept form of the equation, which represents how much allowance Hari receives based on the number of chores he does, is y = 0.5x + 9. Here, the slope of 0.5 represents the amount Hari earns per chore, and 9 is the base amount Hari receives irrespective of the chores.

The given scenario provides us with two points (22, $20) and (6, $12) where the number of chores is the x-coordinate and the allowance is the y-coordinate. We can use these points to find the slope of the line:

Slope (m) = (y2 - y1) / (x2 - x1)= ($20 - $12) / (22 - 6) = $8 / 16 = $0.5,

Next, we use the slope and one of the points to find the y-intercept: y = mx + b so $20 = ($0.5 * 22) + b, solving for b gives us b = $20 - $11 = $9, which is our y-intercept.

So, the equation of the line in slope-intercept form is y = 0.5x + 9

This equation states that Hari earns $0.5 per chore and gets a guaranteed $9 even if he does no chores.

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