The surface area of the triangular prism pictured below is 204 square centimeters. What is the height of the prism?

The statement that "In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex" is always true

The statement is given as:

In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex.

As a general rule;

If any two angles are congruent in a triangle, then it means that the sides that opposite the two congruent angles are congruent sides.

The above is an illustration of the base angle theorem

The base angle theorem goes hand-in-hand with the isosceles triangle theorem which is illustrated by the given statement

Hence, the statement that "In an isosceles triangle, the perpendicular bisector of the base is also the angle bisector of the opposite vertex" is always true

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Answer: In the first graph, you plug in the numbers, so the rule would be "+9" and the term would be 9 for the first one, the second term is 18 and the rule stays the same. In the second one, the rule is that they each go up by (+7)

I hope that helps :)

Answer: an acute angle so it bout 55

Step-by-step explanation:

The length of the square base is thus [tex]2 x 3\sqrt{2}/2 = 3\sqrt{2}[/tex] = A

Consequently, a hemisphere is a 3D geometric object that is made up of half of a sphere, with one side being flat and the other being a bowl-like shape. It is created by precisely cutting a spherical along its diameter, leaving behind two identical hemispheres.

EXPLANATION; Let ABCDE be the pyramid with ABCD as the square base. Let O and M be the center of square ABCD and the midpoint of side AB respectively. Lastly, let the hemisphere be tangent to the triangular face ABE at P.

Notice that triangle EOM has a right angle at O. Since the hemisphere is tangent to the triangular face ABE at P, angle EPO is also 90 degree. Hence, triangle EOM is similar to triangle EPO.

OM/2 = 6/EP

OM = 6/EP x 2

OM = [tex]6\sqrt{6^2 - 2^2} x 2 = 3\sqrt{2}/2}[/tex]

The length of the square base is thus [tex]2 x 3\sqrt{2}/2 = 3\sqrt{2}[/tex] = A

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Answer:

Fe2 is elemental iron and Fe2O3 is a compound

Answer:

Step-by-step explanation:

Fe2 is elemental iron and Fe2O3 is a compound of iron and oxygen.

Answer:

k = 4.33

Step-by-step explanation:

Cos 30 = 0.8660

Tan 60 = 1.732

2 Tan 60 = 2 (Tan 60)

2 Tan 60 = 2 (1.732)

2 Tan 60 = 3.464

Cos 30 + Tan 60  = 0.8660 + 3.464 = 4.33

k = 4.33

Answer: x=36

Step-by-step explanation: a straight line is 180 degrees. on one side, it is 144 degrees. 180-144 = 36.

Answer:

d:1

Step-by-step explanation:

the answers will always be negative and the other side will always be positive

The volume of the sphere is 2144.7cm³.

Given that a sphere with radius 8 cm.

As we all know that the volume of sphere is 4/3πr³.

We will find the volume of sphere by substituting the value of radius in the formula, we get

Volume=4/3 πr³

Now, we will substitute r=8 cm in above formula, we get

V=(4/3)π(8 cm)³

V=(4/3)π(512)cm³

Now, we will simplify this by multiply by 4, we get

V=(2048/3)πcm³

Now, we will simplify it by dividing it with 3, we get

V=682.66π cm³.

As we know, the value of π is 3.14.

So, we will substitute this value and simplify it, we get

V=682.66×3.14

V=2144.66 cm³

Hence, the volume of the sphere when the radius is 8cm is 2144.7 cm³.

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Answer:

Step-by-step explanation:

Answer: x=64/7 Step-by-step explanation: 4x+3=64 7x=64

4x=−64

Divide both sides by 4.

x=

4

−64

​

Divide −64 by 4 to get −16.

x=−16

x(5) is approximately equal to 1.466.

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When two random variables X and Y are considered to be independent, it means that neither X's distribution nor Y's values have any bearing on the other.

A random variable is a variable used in an experiment, such as the number of coin tosses or card draws. An independent random variable is a random variable in your experiment that doesn't affect the other random variables. In other words, it has no impact on the likelihood that another event will occur. For illustration, suppose you randomly selected 50 bags of sugar from various grocery stores in order to determine the average weight of a bag of sugar. The factors are independent since you wouldn't anticipate the weight of one bag having an impact on another. A dependent random variable, on the other hand, does have an impact on the probability of other random variables.

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The perimeter of the quadrilateral is approximately 50.47 units

Given the vertices of the quadrilateral: H(– 4,6), I(4,9), J(2,3), K(7, – 4).

Let us calculate the distances of HI , IJ , JK and KH

[tex]{\displaystyle HI={\sqrt {(4-(-4))^{2}+(9-(6))^{2}}}.}[/tex]

or, HI = 17 units

[tex]{\displaystyle IJ={\sqrt {(2-(4))^{2}+(3-(9))^{2}}}.}[/tex]

or, IJ = 10

[tex]{\displaystyle JK={\sqrt {(7-(2))^{2}+(-4-(3))^{2}}}.}[/tex]

or, JK = √74 = 8.602... ≈ 8.60

[tex]{\displaystyle KH={\sqrt {(7-(-4))^{2}+(-4-(6))^{2}}}.}[/tex]

or, KH = √221 = 14.866... ≈ 14.87

Now perimeter = HI + IJ + JK + KH

or, perimeter = 8.60 + 14.87 + 10 + 17 = 50.47 units.

Therefore the perimeter of the quadrilateral is 50.47 units.

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Answer:

30J + 15S = $1,200

Step-by-step explanation:

Since Jason earns $30 per computer and Sandra earns $15 per computer therefore the equation will be written as $30J + $15S = base salary per month.

30J + 15S = $1,200

The ordered pairs of the given graph are;

(-2, 3), (4, 2), (0, -3), (2, -5), (-5, -4)

An ordered pair is defined as a composition of the x coordinate and the y coordinate, having two values written in a fixed order within parentheses.

Ordered Pair = (x, y)

Where;

x = abscissa, the distance measure of a point from the primary axis “x”

y = ordinate, the distance measure of a point from the secondary axis “y”

Thus the ordered pairs of the given graph are;

(-2, 3), (4, 2), (0, -3), (2, -5), (-5, -4)

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The information is no complete yet. The additional fact that is needed to prove that both triangles are congruent by SAS is: AD ≅ CD.

The Side-Angle-Side (SAS) is a triangle congruence theorem that is used to prove that two triangles are congruent to each other if they have two pairs of corresponding congruent sides and a pair of included congruent angles.

The diagram given gives us the following information:

A pair of congruent sides - BD ≅ BD

A pair of congruent angles - <ADB ≅ CDB.

Thus, the information is no complete yet. The additional fact that is needed to prove that both triangles are congruent by SAS is: AD ≅ CD.

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Answer: FIRST ONE IS -1/7

The second one is 1

Step-by-step explanation:

Step-by-step explanation:

2x + 3x = -25

5x = -25

x = -25 / 5

x = -5

The length of rectangle is (x - 5).

We are given-

Area of rectangle = [tex]x^{3} - 5x^{2} + 3x - 15[/tex]

Width of rectangle = [tex]x^{2} + 3[/tex]

Using the formula, the length will be calculated by rewriting the formula as -

Length = Area/width

Keep the values in formula to find the length of rectangle.

Length = [tex]\frac{x^{3} - 5x^{2} + 3x - 15}{x^{2} + 3}[/tex]

In numerator, separating the common values and rewriting the equation -

Length = [tex]\frac{x^{2} (x - 5) +3 (x - 5)}{x^{2} + 3}[/tex]

Rewriting the equation to for ease of solving to find the length of rectangle -

Length = [tex]\frac{(x^{2} +3)(x - 5)}{(x^{2} +3)}[/tex]

Cancelling [tex](x^{2} + 3)[/tex] as it is common in both numerator and denominator. Now, we will get the value of length of rectangle.

Length = (x - 5)

Hence, the length of rectangle is (x - 5).

The complete question is -

The area of a rectangle is [tex]x^{3} - 5x^{2} + 3x - 15[/tex], and the width of the rectangle is [tex]x^{2} + 3[/tex]. If area = length × width, what is the length of the rectangle? x + 5 x – 15 x + 15 x – 5

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Answer:

The person runs 30km/h or 30000m/h

Step-by-step explanation:

First let's find speed per minute

➟ 1500/3

➟ 500

Now let's calculate speed per hour

1 hour = 60 minutes

➟ 500 × 60

➟ 30,000 meters

If you would like the meters to be in miles

then Formula divide the meter value by 1000

➟ 30000/1000

➟30

∴ The person runs 30km/h or 30000m/h

The speed of the person is 300 km/hour.

Speed is the ratio of distance and time.

It shows how fast an object is moving at a given time.

We have,

Distance covered in 3 minutes = 1500 meters.

1 hour = 60 minutes

3 minutes = 15000 meter

Multiply 20 on both sides.

60 minutes = 300,000 meter

1 km = 1000 meter

Multiply 300 on both sides.

300 km = 300,000 meter

Now,

60 minutes = 300 km

Speed = 300 km/hour

Thus,

300km/hour is the speed of the person.

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Based on the raw score of 82, and the 70th percentile passing, we can infer that as regards 82 being a passing score, No, it might have a percentile rank less than 70.

The passing score is one that is in the 70th percentile or higher. This means that the raw score that a student gets needs to be considered higher than 70% of the rest of the scores.

There is a chance that the exam was so easy that most people got good scores. If that were the case, then a score of 82 can be below the 70th percentile which means that the candidate would not pass.

Options for this question are:

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The fence is 33 feet long when measured in yards.

Here,

In order to erect a fence around a rectangular flower garden on his property, Craig has 72 feet of material.

If the fence must be 3 feet in width, then, assuming he uses the entire 72 feet of material, we must determine the fence's length in yards.

What is the rectangle's perimeter?

The rectangle's perimeter is 2 (l + b). l being the length. b=breadth (width).

Now,

A rectangular flower bed should be x feet long.

(Length + Width)2 = the perimeter of a rectangular flowerbed.

72 = 2 (x + 3)

36 = x + 3

x = 33 feet

Hence, The fence is 33 feet long when measured in yards.

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Answer:

(25,20) , (45,36)

Step-by-step explanation:

I THINK??

The statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2  for n > 2

The function definition is given as

f(n) = -4 +2n for n > 1

Start by calculating f(2), f(3) and f(4)

So, we have

f(2) = -4 +2(2)

f(2) = 0

f(3) = -4 +2(3)

f(3) = 2

f(4) = -4 +2(4)

f(4) = 4

In the above computation, we can see that the sequence is an arithmetic sequence with a common difference of 2

So, we have

f(n) = f(n - 1) + 2

Also, we have

f(1) = -4 +2(1)

f(1) = -2

Hence, the statement that is the recursive definition of f is f(1) = -2 f(n) = f(n - 1) + 2  for n > 2

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