Which of the following theorems verified that angle xyz is congruent too angle uwv?

Answer:

y = 4.  So this is your width.

Step-by-step explanation:

Use the distributive property to do 2(2y-3) = 2*2y-2*3 = 4y-6. So we have

4y-6+2y = 18.  Combine like terms 4y and 2y to get 6y.

6y-6 = 18.  Add 6 to both sides to solve for 6y

6y = 24.   Divide by 6 to solve for y

y = 4.  So this is your width.

length = x

           ________________

          |                            |

     y   |                            |  width = y

          |                            |

          _________________

                       x

The width of the rectangle is determined to be 4 inches.

To find the width of the rectangle, we need to set up equations based on the information given. The length (L) is described as being 3 inches less than twice the width (W), so we can express that as L = 2W - 3. The perimeter (P) of a rectangle is calculated as P = 2L + 2W. We are told the perimeter is 18 inches, so we have 18 = 2(2W - 3) + 2W. Simplifying this equation, we get 18 = 4W - 6 + 2W, which combines to 18 = 6W - 6. Adding 6 to both sides gives us 24 = 6W, and dividing both sides by 6 yields W = 4 inches. Therefore, the width of the rectangle is 4 inches.

The process used here is similar to working through proportions and scale factors. For instance, if one is working with scale models, as in the miniature fish pond example, the scale factor is used to determine the dimensions in the model based on actual size dimensions. However, in this case, the given equations allowed us to find the width directly.

The volume of the space outside the pyramid but inside the prism is 250 cubic centimeters.

To find the volume of the space outside the pyramid but inside the prism, we first need to determine the volumes of both the prism and the pyramid.

The prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. The volume of a rectangular prism is calculated by multiplying the base area by the height. In this case, the base area is 5 cm * 5 cm = 25 square centimeters. Therefore, the volume of the prism is 25 cm² * 12 cm = 300 cubic centimeters.

The pyramid has the same square base as the prism, with sides measuring 5 centimeters. However, its height is half that of the prism, which is 12 cm / 2 = 6 centimeters. The volume of a pyramid is calculated by multiplying the base area by one-third of the height. In this case, the base area is 25 cm², and one-third of the height is 6 cm / 3 = 2 centimeters. Therefore, the volume of the pyramid is 25 cm² * 2 cm = 50 cubic centimeters.

To find the volume of the space outside the pyramid but inside the prism, we subtract the volume of the pyramid from the volume of the prism: 300 cubic centimeters - 50 cubic centimeters = 250 cubic centimeters.

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Given the provided conditions, we set up an equation to determine the width and length of the indoor football field. After simplifying the appropriate mathematical expressions, we find that length of the football field is 66 yards.

In this problem, we're solving for the length of an indoor football field. We know that the perimeter of a rectangle is given by [tex]2L + 2W[/tex] (twice the length plus twice the width) and the length is said to be 45 yards longer than the width. Therefore, we would describe the length as 'W + 45'

Let's represent the width as W and thus the length as W + 45. Substituting these into our perimeter equation we get [tex]2(W) + 2(W +45) = 174.[/tex] Simplifying gives [tex]4W + 90 = 174[/tex]

Subtracting 90 from both sides gives 4W = 84. Thus, W = 21. Substituting this value back into our equation for the length gives us L = 21 + 45 which equals 66 yards. Therefore, the length of the indoor football field is 66 yards.

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Answer: 1/6

Step-by-step explanation:

Lets say two points are (a,b) and (c,d)

the slope that cross these two points is: (b-d)/(a-c) or (d-b)/(c-a) → either one is fine, but make sure the one you are subtracting is the one from the same point.

Hope it helped!

Answer:

The slope formula is [tex]\frac{y_{2}- y_{1} }{x_{2} -x_{1} }[/tex]

The slope of (1, 9) and (-5, 8) is 1/6

Step-by-step explanation:

(9 - 8)/( 1 - [-5]) = 1/6

Answer:

m = [tex]\frac{1}{4}[/tex]

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 )

y = - 4x + 7 is in this form with slope m = - 4

Given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-4}[/tex] = [tex]\frac{1}{4}[/tex]

Hence the value of m = [tex]\frac{1}{4}[/tex]

Answer:

x = - 8, x = 8

Step-by-step explanation:

Given

x² - 64 = 0 ( add 64 to both sides )

x² = 64 ( take the square root of both sides )

x = ± [tex]\sqrt{64}[/tex] = ± 8

Answer:

(x+2)^{2} +5(x+2)-6=0

Let

u=(x+2)

Substitute in the expression

(u)^{2} +5(u)-6=0

therefore

the answer is

(u)^{2} +5(u)-6=0 is equivalent to (x+2)^{2} +5(x+2)-6=0

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Hello there!

X = 67°

Answer and work are provided in the image attached.

Answer:

6

Step-by-step explanation:

For both to be chosen the other spot can be taken by any of the other 6 people in the row. So six possibilities

Answer:

A. [tex]^6C_1=6[/tex]

Step-by-step explanation:

Given,

The total number of people = 8,

The number of people have to chosen = 3,

Since, me and my friend both have to be chosen,

So, the remaining number of people = 8 - 2 = 6,

And, the number of remaining number of people have to be chosen = 3 - 2 = 1

Also, the order does not matter,

Hence, the total way of choosing = Total combination of me and my friend × total combination of choosing 1 person out of 6 people

[tex]=^2C_2\times ^6C_1[/tex]

[tex]=1\times ^6C_1[/tex]

[tex]=6[/tex]

Option A is correct.

let's convert the 0.05 to a fraction first, so we have two decimals, so our fraction will have two zeros then.

[tex]\bf 0.\underline{05}\implies \cfrac{005}{1\underline{00}}\implies \cfrac{1}{20} \\\\[-0.35em] ~\dotfill\\\\ 10\div 0.05\implies \cfrac{10}{1}\div \cfrac{1}{20}\implies \cfrac{10}{1}\cdot \cfrac{20}{1}\implies 200[/tex]

Answer:

Step-by-step explanation:

Let x - y = A

A^4 - A^2

A^2 ( A^2 - 1)

A^2 (A + 1)(A - 1)

(x - y)^2 (x - y + 1)(x - y - 1)

If I have not thought out the question properly please leave me a note.

Answer:  Point, Point, Line

Step-by-step explanation:

A plane and a line intersect at a point .  Think of a piece of paper as a plane and a pen as a line.  What happens when you push the pen through the paper?  It creates a point!

Two lines intersect at a point .

Two planes intersect at a line . Think of a piece of paper laid horizontally on a table and another piece of paper standing on it vertically.  What can you draw at the places of intersection? A line!

Answer:

28 deg

Step-by-step explanation:

Reference angle is the smallest angle formed by the terminal ray, x-axis, and origin. So at 180 you are on the x-axis so just for this question you have to do 180-152=28.

The reference angle should be a positive between 0 and 90 degrees.

Answer:

12) 154   squared meters

13) 307  cm^2

Step-by-step explanation:

12) A circle has area pi*r^2

r is half the diameter so half of 14 is 7

pi in this case is 22/7

A=22/7 * (7)^2

A=22/7  * 49

A=22     *49/7

A=22     *7

A=154 squared meters

13)  Area of rectangle is 10(18)=180

      Area of half a circle is .5*pi*r^2=.5*pi*9^2  

       Adding the two areas together would result in a total area of 307.2 squared centimeters

Answer:

V≈4.19ft³

Step-by-step explanation:

The volume of a sphere with a radius of 1 foot is 4.19ft³.

In order to find this:

V=4

3πr3=4

3·π·13≈4.18879ft³

[tex]V=\dfrac{4}{3}\pi r^3\\\\V=\dfrac{4}{3}\cdot3.14\cdot 1^3\approx4.19\text { ft}^3[/tex]

Answer: 88 inches

Step-by-step explanation:

Given : A bicycle tire is 28 inches in diameter. approximately.

To find the distance traveled by the bicycle each time the wheel goes around we need to find the circumference of the tire.

The circumference of a circle : [tex]\pi d[/tex], where d is the diameter of the circle.

Now, the circumference of tire : [tex]\dfrac{22}{7} \times(28)=88[/tex]

Hence, the distance traveled by the bicycle each time the wheel goes around  =88 inches.

The wheel moves forward each time, in a single round it will cover distance of 88 inches.

Given information:

The diameter of the tire is 28 inches.

Now, if we need to find the distance covered by the tire in one round, we need to understand that the tire will cover exactly same distance as it's circumference in one round.

So, the distance will be equal to its circumference :

[tex]D=\pi\times d[/tex]

Hence, distance covered (D)

[tex]D=3.14\times 28\\D=88[/tex]

Hence, when the wheel move forward each time the in a single round it will cover 88 inches.

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Answer:

Practical probability:  9 / 20 = 45%

Theoretical probability: 3 / 6 = 50%

Step-by-step explanation:

So, we have 20 rolls:

1 5 3 2 3 6 5 6 3 3 4 4 1 3 6 5 3 2 2 6

Out of which we have 9 even numbers: 2 6 6 4 4 6 2 2 6

So, the practical probability is 9 / 20 or 45%

The theoretical probability is:

Possible outcomes (6): 1 2 3 4 5 6

Even numbers possible (3): 2 4 6

P = 3 / 6 = 50%

The practical probability is a bit lower (45%) than the theoretical probability (50%) but that's most probably due to the low number of rolls, it's just one roll away from being on target.  With a greater number of rolls, the student would get closer to the theoretical probability.

Answer:

The first number is 8

Step-by-step explanation:

Let

x -----> the first number

y ----> the second number

x=3y-4 ----> equation A

3+2x-2y=11 ----> equation B

Substitute equation A in equation B and solve for y

3+2(3y-4)-2y=11

3+6y-8-2y=11

4y=11+5

y=16/4=4

Find the value of x

x=3(4)-4=8

Answer:

7

Step-by-step explanation:

Blue is 7 and the Red is 7

Answer:

7

Step-by-step explanation:

we can take a peek at two of those lines  hmmm say y = 5x + 3 and y = 5x + 7.

let's notice, those two equations for those lines are in slope-intercept form, so let's solve the system.

since y = y then

5x + 3 = 5x + 7

3  = 7    what the?

well, notice, both lines have the same slope of 5, but different y-intercept, one has it at y = 3 and the other at y = 7, what does that mean?

it means that both lines are parallel to each other, one may well be above the other, but both are parallel, and since a solution to the system is where their graphs intersect, well, parallel lines never touch, so a system with two parallel lines has no solutions.

The two lines are parallel.

We have a girl Deedra who has the equations for lines A and B. When she solved for the point where these two lines intersect, she ended up with the equation 3 = 7.

We have to investigate what it tells about the nature of lines.

The slope intercept form of an equation of line is -

y = mx + c

Let's assume we have two lines with their equations be -

[tex]y_{1} = m_{1} x_{1} + c\\y_{2} = m_{2} x_{2} + d[/tex]

To find the intersecting points of these two lines, then -

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

Therefore -

[tex]m_{1} x_{1} +c =m_{2} x_{2} +d\\[/tex]

Now, in the question she found out that 3 =7 which is same c = d. To fulfill this condition, the slope of these two lines should be equal. Hence, we can conclude that the two lines are parallel.

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Answer:

I’m not sure, but I think it’s C

Answer:

no solutions

Step-by-step explanation:

-4x-4=-4(x+2)​

Distribute the negative

-4x-4 = -4x-8

Add 4x to each side

-4x+4x-4 = -4x+4x-8

-4 = -8

Since this is not true there are no solutions

Answer:

unlikley

Step-by-step explanation:

Answer:

x<11

Step-by-step explanation:

Subtract by 2 both sides of equation.

2-2x-2>-20-2

Simplify.

-2x>-22

Multiply -1 from both sides of equation.

(-2x)(-1)<(-22)(-1)

Simplify.

2x<22

Divide by 2 from both sides of equation.

2x/2<22/2

Simplify, to find the answer.

22/2=11

x<11 is the correct answer.

To solve the inequality 2 - 2x > -20, we isolate the variable term by adding 2x to both sides, subtracting 2, and then dividing by 2 to find that the solution is x < 11.

To solve the inequality 2 - 2x > -20, we can follow these steps:

The solution to the inequality is x < 11.

Answer:

The true statements are,

x ∈ B

x ∉ C

x ∈ A ⋃ B

x ∈ A ⋂ B

x ∈ A ⋃ C

Step-by-step explanation:

From the figure we can see three sets A, B, C

Check all options

1)  x ∉ A

From the figure we get, x is an element of A

x ∉ A is False

2)  x ∈ B

From the figure we get, x is an element of B

x ∉ B is True

3)  x ∉ C

From the figure we get, x is not an element of C

x ∉ C is True

4). x ∈ A ⋃ B

From the figure we get, x is an element of A ⋃ B

x ∈ A ⋃ B  is True

5). x ∈ A ⋃ C

From the figure we get, x is an element of A ⋃ C

x ∈ A ⋃ C  is True

6).x ∈ A ⋂ B

From the figure we get, x is an element of A ⋃ B

x ∈  A ⋂ B   is True

Answer:

Everything is true expect for the first answer choice .

Step-by-step explanation:

Step-by-step explanation:

a = x^2 - 1

b = 2x

c = x^2 + 1

The Pythagorean theorem states

a^2 + b^2 = c^2

Let's find a^2 and b^2 and add them to get a^2 + b^2:

a^2 = (x^2 - 1)^2 = x^4 - 2x^2 + 1

b^2 = (2x)^2 = 4x^2

a^2 + b^2 = x^4 - 2x^2 + 1 + 4x^2 = x^4 + 2x^2 + 1

Now let's find c^2:

c = x^2 + 1

c^2 = (x^2 + 1)^2 = x^4 + 2x^2 + 1

We see that both a^2 + b^2 and c^2 equal x^4 + 2x^2 + 1, so we have shown that the triangle is a right triangle.

We can see that a² + b² = c² = x⁴ + 2x² + 1, indicating that the triangle is a right triangle.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometric function.

According to Pythagoras, the sum of the squares of two sides equals the square of the longest side.

Given data;

a = x² - 1

b = 2x

c = x² + 1

According to the Pythagorean theorem;

[tex]\rm a^2 + b^2 = c^2[/tex]

Let's find a^2 and b^2 and add them to get a^2 + b^2:

[tex]\rm a^2 = (x^2 - 1)^2 \\\\ a^2 = x^4 - 2x^2 + 1 \\\\ b^2 = (2x)^2 \\\\ b^2 = 4x^2\\\\[/tex]

Left hand side:

[tex]\rm a^2 + b^2 = x^4 - 2x^2 + 1 + 4x^2 \\\\ a^2 + b^2 =x^4 + 2x^2 + 1[/tex]

Right hand side:

[tex]\rm c^2 = (x^2 + 1)^2 \\\\ c^2 = x^4 + 2x^2 + 1[/tex]

L.HS.=R.H.S

Hence,the given triangle is a right angled triangle.

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The federal courts that the Constitution gives the Congress the power to create are federal courts: lower than the Supreme Court.

Federal courts can be described as lower courts having limited jurisdiction. This implies that they are only authorized to hear cases that arise under the federal statues in the United States.

The Supreme Court is the highest court. District courts are the lowest federal courts.

Therefore, the federal courts that the Constitution gives the Congress the power to create are federal courts: lower than the Supreme Court.

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The U.S. Constitution allows Congress to establish federal courts lower than the Supreme Court, but not higher, equal to, or unaffected by it. The Supreme Court is the highest court in the U.S. judiciary.

The Constitution gives Congress the power to create federal courts that are lower than the Supreme Court. According to Article III, Section 1 of the Constitution, 'The judicial Power of the United States, shall be vested in one supreme Court, and in such inferior Courts as the Congress may from time to time ordain and establish.'

The Constitution does not give Congress the power to create courts that are higher than, equal to, or unaffected by the Supreme Court. The Supreme Court is the highest court in the U.S. judicial system, and all lower courts must follow the legal precedents set by it.

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Answer:

-2

Step-by-step explanation:

The only domain problems are going to come from the square root you have there. You only want to square root 0 or positive numbers,. In other words, you want x+2 to be greater than 0 or equal to 0.

x+2>=0

x>=-2

So x has to be greater than ot equal to 0

[tex]{_8C_3}\cdot 3!=\dfrac{8!}{3!5!}\cdot 6=\dfrac{6\cdot 7\cdot 8}{6}\cdot6=336[/tex]

There are 336 ways we can choose and arrange the trophies.

The answer is option D. 336

calculation:-

   ₃C⁸.3! = 8!/3!5!.6 = (6.7.8)/6.6 = 336

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