True or false? Any two right triangles with the same hypotenuse have the same area.
Explain your reasoning.

The volume of the square pyramid is 32.49 cubic mm.

Volume is defined as the space occupied by any object in the three-Dimensions. All three parameters are required for the volume like length, width, and height of cube or cubes.

Given that crystal is cut into a shape formed by two square pyramids joined at the base. Each pyramid has a base edge length of 5.7 mm and a height of 3 mm.

The volume of the pyramid will be calculated as below:-

V = ( L W H ) / 3

V = ( 5.7 x 5.7 x 3 ) / 3

V = 32.49 cubic mm

Therefore, the volume of the square pyramid is 32.49 cubic mm.

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The expressions that can be used to determine the area of the rectangle are:

12 x 7

7 . 10 + 7 . 2

The expressions that can be used to determine the perimeter of the rectangle are:

2 x (12 + 7)

7 + 12 + 7 + 12

2 . 7 + 2 . 12

The expression that cannot be used to find either the area or the perimeter of a rectangle is: 7 + 12

A rectangle is a 2-dimensional quadrilateral with four right angles that sum up to 360 degrees. A rectangle has two diagonals which bisect each other at right angles.

The area of a rectangle is the product of the width and the length.

Area of a rectangle = length x width

12 x 7 = 84 units²

7 . 10 + 7 . 2

70 + 14 = 84

The perimeter of a rectangle is the distance round the rectangle.

Perimeter of a rectangle = 2 x (length + width)

2 x (12 + 7)

2 x 19 = 38 units

7 + 12 + 7 + 12 = 38

2 . 7 + 2 . 12

14 + 24 = 38

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The value of the expression (g ₀ f) (1/2) is 15/4

In this question, we have been given two functions f(x) = x² + 1 and             g(x) = 3x.

We need to evaluate an expression. (g ₀ f) (1/2)

We know that the composite function is a function where the output of one function becomes the input of another function.

First we find the composite function (g ₀ f) (x)

(g ₀ f) (x)

= g(f(x))

= 3(f(x))

= 3 (x² + 1 )

= 3x² + 3

So, (g ₀ f) (x) = 3x² + 3

Now, we find the value (g ₀ f) (1/2)

(g ₀ f) (1/2)

= 3(1/2)² + 3

= 3(1/4) + 3

= 3/4 + 3

= 15/4

Therefore, the value of the expression (g ₀ f) (1/2) is 15/4

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Step-by-step explanation:

9y=-72-4×

put x =1

9y=-72-4×1

9y=-72-4

9y=-76

Two triangles with three pairs of corresponding congruent angles are congruent: Always TRUE

So, the statement says that:

Therefore, "two triangles with three pairs of corresponding congruent angles are congruent" is Always TRUE.

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The arithmetic mean a n of the given terms  a n₋₁ =100, an ₋₁ =140 is

a (n) = 20.

a n₋₁ =100, an ₋₁ =140

a (n) = (140-100)/2

a (n) = 20

The arithmetic mean is the most straightforward and widely used method of calculating a mean or average. It only requires adding up a group of figures, then dividing the result by the entire amount of figures in the series. Consider the numbers 34, 44, 56, and 78 as an example. It totals 212.

The mean or arithmetic average are other names for the arithmetic mean. It is determined by adding up each number in a particular data set, then dividing the result by the overall number of items in the data set. For uniformly distributed integers, the middle number serves as the arithmetic mean (AM).

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Answer:

625,3125,15625

Step-by-step explanation:

Because it is ×5, so 125×5=625, 625×5=3125...

The time that it will take for the object to be 4 feet above the valley floor will be 4 seconds.

It should be noted that the object is dropped from the observation deck, its height h in feet, after t seconds, is given by h=-16² +260.

Therefore, the time that it will take for the object to be 4 feet above the valley floor will be:

h=-16² +260.

4 = -16t² + 260

4 + 16t² - 260 = 0

16t² - 256 = 0

Collect like terms

16t² = 256

t² = 256/16

t² = 16

t = ✓16

= 4

The time is 4 seconds.

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On simplifying the given equation, the answer is

[tex]\frac{{9x^{2} - 15x^{2} + 4x}}{{x^{2} (x-1)} }[/tex]

Solving a math issue is the same thing as simplifying an equation. You basically strive to write an expression as simply as you can when you simplify it. At the conclusion, there shouldn't be any more multiplying, dividing, adding, or removing to perform.

Finding the value or values that make the equation—or math sentence—true is the process of solving.

[tex]6 + [\frac{x+5}{x^{2}} + \frac{3x - 10}{x-1} ]\\[/tex]

On simplifying it,

[tex]6 + \frac{(x+5)(x-1) + (3x-10x^{2} )}{x^{2} (x-1)} \\\\6 + \frac{x^{2} -x + 5x +3 x^{3} - 10x^{2} }{x^{2} (x-1)} \\\\6 + \frac{3x^{3} -9x^{2} + 4x }{x^{2} (x-1)} \\\\\frac{6x^{3} - 6x^{2} + 3x^{3} - 9x^{2} +4x }{x^{2} (x-1)} \\\\\frac{9x^{2} - 15x^{2} + 4x}{x^{2} (x-1)}[/tex]

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The simplification of the expression 3(x + 3y) - 5(x -y) is  -2x + 14y.

According to the given question.

We have an expression

3(x + 3y) -5(x -y)

As we know that, the simplification of an expression means to write an equivalent expression which contains no similar terms.

Therefore, the simplificantion of the expression  3(x + 3y) - 5(x -y) is given by

3(x + 3y) - 5(x -y)

= 3x + 9y - 5x + 5y     (by distributive rule)

= 3x - 5x + 9y + 5y

= -2x + 14y                    (adding and subtracting the like terms)

Hence, the simplification of the expression 3(x + 3y) - 5(x -y) is  -2x + 14y.

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Step-by-step explanation:

you don't know the Pythagoras formula yet ?

this is something you need to remember for life. this you will encounter everywhere (not just in school) :

c² = a² + b²

in a right-angled triangle c is the Hypotenuse (the side opposite of the 90° angle). a and b are the legs of the triangle.

4.

the legs of this right-angled triangle are the pole and the ground distance to the cable fixture on the ground.

the cable itself is the Hypotenuse (as the right angle is the angle between the pole and the ground distance).

so,

cable² = 8² + 6² = 64 + 36 = 100

cable = sqrt(100) = 10 m

5.

here we have a right-angled triangle with the direct distance between the points being the Hypotenuse, and the x and y coordinate differences are the legs.

so, we have

distance² = (3 - -3)² + (0 - -1)² = 6² + 1² = 36 + 1 = 37

distance = sqrt(37)

please note that since we are squaring, the direction of the differences and their signs do not matter. the square will turn positive and negative distances into positive numbers.

Answer:

base :6 units

height:4units

area of a triangle: 1/2 ×b×h

1/2× 6×4=12

12sqaure units should be the area

Answer:

The square root of 48 to the nearest tenth is 6.9

The difference in height between 30 meters up the cliff and 87 meters up the cliff will be 57 meters.

The distance between the albatross flying at 100 meters above the surface of the ocean and the shark swimming 30m below the surface is 130 meters.

It should be noted that the distance in height between 30 meters up the cliff and 87 meters up the cliff will be:

= 87 - 30

= 57 meters.

The distance between the albatross flying at 100 meters above the surface of the ocean and the shark swimming 30m below the surface will be:

= 100 - (-30)

= 100 + 30

= 130 meters

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Answer:

d) (-2)⁶/(-2)⁴

Step-by-step explanation:

Given that,

→ (-2)⁴/(-2)²

→ 16/4 = 4

Then the equivalent expression is,

→ (-2)⁶/(-2)⁴

→ 64/16 = 4

Hence, option (d) is correct.

Answer: 140°

Step-by-step explanation:

x = 11

5 x 11 = 55

55 - 15 = 40

The 5x-15 = 40°

tHe 3x+7 is opposite, so it also equals 40°

40 + 40 = 80°

360° - 80° = 280

280 divided by 2 = 140°

An unbiased statistic is one in which the average value of the statistic is equal to the population parameter.

Unbiased Statistic/estimator is defined as the accurate statistic that is used in approximation a population parameter.

In the above statement the word "accurate" means that it should be neither greater than nor less than the population parameter.

If the average value is less than  the population parameter  or greater than the population parameter then the statistic will be termed as "biased".

Therefore , An unbiased statistic is one in which the average value of the statistic is equal to the population parameter.

The correct option is (d) equal to.

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Answer:

114

Step-by-step explanation:

If you use the probability of statistics equation ax+bx+cx=x^3 and plugin the numbers you will get 114 as your answer.

The solution of the given equation 3/x = 5 is at x = 3/5.

According to the given question.

We have an equation 3/x = 5.

As we know that, an equation is a condition on a variable such that two expressions in the variable should have equal value.

Here, we have to find the solution of the equation 3/x = 5 is given by

3/x = 5

⇒ 3 = 5x        (multiplying x both the sides)

⇒ 3/5 = x       (dividing both the sides by 5)

⇒ x = 3/5

Hence, the solution of the given equation 3/x = 5 is at x = 3/5.

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Answer: 1) x=20°      2) x=50°

Step-by-step explanation:

1)

[tex]x+20+x+30=90\\2x+50=90\\2x+50-50=90-0\\2x=40\\Divide\ both\ parts\ of \ the\ equation\ by\ 2:\\x=20^0[/tex]

2)

The sum of adjacent angles is always 180 degrees.

[tex]x+80+x=180\\2x+80=180\\2x+80-80=180-80\\2x=100\\Divide\ both \ parts\ of\ the\ equation\ by\ 2:\\x=50^0[/tex]

The difference is a binomial with a degree of 6.

What is Degree of polynomial?

The highest power of the variable in a polynomial is called the degree of the polynomial.

The polynomials are given as;

(a³b + 9a²b² - 4ab⁵) and (a³b - 3a²b² + ab⁵)

Now, The difference of the polynomial calculated as;

(a³b + 9a²b² - 4ab⁵) - (a³b - 3a²b² + ab⁵)

a³b + 9a²b² - 4ab⁵ - a³b + 3a²b² - ab⁵

12a²b² - 5ab⁵

Hence, Degree of polynomial = 1 + 5 = 6

So, The difference is a binomial with a degree of 6.

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The C-intercept at (0, 180) and r- intercepts at (6, 0), (-6, 0), and (5, 0).

The points on each axis where the function crosses will be the intercepts. Therefore, the p-intercept will be at the point where r = 0, and the r-intercepts will be at the point where C = 0.

We have been given the function as

C(r) = (r-6)(r+6)(r-5)

We have to determine the C-intercept and r- intercepts.

We should plug in 0 for r and solve.

Solving for the C-intercept

Plug in 0 for r.

C(0) = (0-6)(0+6)(0-5)

C(0) = 180

The C-intercept is (0, 180)

Solving for the r-intercepts, we get

Set the function equal to 0.

0 = (r-6)(r+6)(r-5)

Solve for the zeros.

(r-6) = 0 ⇒ r = 6

(r+6) = 0 ⇒ r = -6

(r-5) = 0 ⇒ r = 5

The r-intercepts are (6, 0), (-6, 0), and (5, 0)

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Given that ∠1 and ∠2 are supplementary, the measure of ∠1 is 79 degree.

Hence, option D)79° is the correct answer.

Supplementary angles refer to the pair of angles that sum up to 180 degree.

Given the data in the question;

Since ∠1 and ∠2 supplementary angles, they will  sum up to 180 degree.

∠1 + ∠2 = 180°

(2y + 9) + (3y - 4) = 180

Solve for y

2y + 9 + 3y - 4 = 180

5y + 5 = 180

5y = 180 - 5

5y = 175

y = 175/5

y = 35

Hence, the measure of ∠1 will be;

∠1 = 2y + 9

∠1 = 2(35) + 9

∠1 = 70 + 9

∠1 = 79°

Given that ∠1 and ∠2 are supplementary, the measure of ∠1 is 79 degree.

Hence, option D)79° is the correct answer.

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Answer:

C

Step-by-step explanation:

Based on the fact that Jessica wants to attach ribbons around her wardrobe, the amount more of ribbons that she needs is 5/6 meters of ribbons

Find out the distance wound Jessica's wardrobe:

= 1¹/₃ + ²/₃ + 1¹/₃ + ²/₃

= 58 / 12

= 4 ⁵/₆ meters

The amount more that Jessica needs is therefore:

= 4 ⁵/₆ - 4

= 5/6 meters of ribbons

In conclusion, Jessica needs 5/6 meters of ribbons

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Answer:

C

Step-by-step explanation:

Because they are two in a addiction like A+B, but they are elevated to the second.

If the solution was D we would have one square in all the espression.

The expression for missing term is (d - e)². The correct option is (A).

Pythagoras theorem states that in a right angled triangle, the sum of the squares of the perpendicular and base is equal to the square of the hypotenuse. It can be written as h² = p² + b².

The 8th step of the problem is given below,

(1 + d²) + (e² + 1) = d² - 2de + e²

Comparing it with the 7th step (√(1 + d²))² + (√(e² + 1))² = ?

It can be found that the missing term is,

d² - 2de + e²

= (d - e)²

Hence, the missing term in the 7th step is given as  (d - e)².

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Answer: 12

Step-by-step explanation: You're welcomed

The quotient of the decimal numbers 57.15 and 4.5 is 12.7.

The given decimal numbers are 57.15 and 4.5.

In arithmetic, a quotient is a quantity produced by the division of two numbers. The quotient has widespread use throughout mathematics, and is commonly referred to as the integer part of a division, or as a fraction or a ratio.

Here, 57.15/4.5

4.5|57.15|12.7

     57.15
  _______
       0

Therefore, the quotient of the decimal numbers 57.15 and 4.5 is 12.7.

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The distance the slower and faster car travelled are 360 km and 432 km respectively.

Two cars start at the same time from two towns 792 kilometres apart and meet in 9 hours.

One car can travel 8 km faster than the other car.

let

x = speed of the slower car

x + 8 = speed of the faster car

The cars meet in 9 hours and both cover a distance of 792 km.

Therefore,

speed = distance / time

distance = time × speed

Hence,

9x + 9(x + 8) = 792

9x + 9x + 72 = 792

18x = 792 - 72

18x = 720

divide both sides by 18

x = 720 / 18

x = 40

Therefore,

speed of the slower car = 40 km per hour

speed of the faster car = 48 km per hour

Hence,

how far the slower car go(distance) = 40 × 9 = 360 km

how far the faster car go(distance) = 48 × 9 = 432 km

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The value of ((1*2)*3) is 0

From the information given, we have the real number operation as;

(a*b) = (a+b)/ (a-b)

Given the expression;

((1*2)*3)

Now, let's solve the bracket first, we have;

( 1 * 2 )

Where;

a = 1

b = 2

( 1 * 2 )  = ( 1 + 2 ) / 1 - 2

Simplify further

= 3/ -1

= -3

Substitute into the operation;

( -3 * 3)

Where;

a = -3

b = 3

( -3 * 3) = ( -3 + 3) / -3 - 3

Simplify further

= 0/ -6

= 0

Thus, the value of ((1*2)*3) is 0

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