What are the values of x and y in the figure?

By using the property of congruency of triangles,

[tex]\angle V \cong \angle S[/tex] has been proved

What is congruency of triangles?

Two triangles are said to be congruent if the corrosponding angles are equal and the corrosponding sides are equal.

There are different axioms of congruency. They are

SSS axiom, SAS axiom, AAS axiom, ASA axiom, RHS axiom

UV [tex]\cong[/tex] ST [Given]

QR [tex]\cong[/tex] PQ [Given]

QT [tex]\cong[/tex] QU [Given]

PV [tex]\cong[/tex] RS [Given]

PT = PQ + QT [Additive Property of Length]

RU = QR + QU [Additive Property of Length]

PT = QR + QU [Substitution]

PT = RU [Transitive Property of Equality]

TV = UV + TU [Additive Property of Length]

SU = ST + TU [Additive Property of Length]

TV = ST + TU [Substitution]

SU = TV [Transitive Property of Equality]

[tex]\angle[/tex]SUR [tex]\cong[/tex] [tex]\angle[/tex]VTP [QT = QU]
[tex]\Delta USR \cong \Delta TVP[/tex] [SAS axiom]

[tex]\angle V \cong \angle S[/tex] [Corrosponding parts of congruent triangles are congruent]

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Answer:

x<3

Step-by-step explanation:

;)

Answer:

f(x) = 500+40m

Step-by-step explanation:

500 = initial

40m because she deposits 40 each month

Mrs. Jones will make 55 wax warmers when she produces 77 candles.

The given table shows the ratio of the number of candles to the number of wax warmers she makes.

Let's assume that "x" wax warmers will she make when she makes 77 candles

According to the given question, we can write the ratio would be as:

7 Candles : 5 Wax Warmers = 77 Candles : x Wax Warmers

⇒ 7/5 = 77/x

⇒ 7x = (77)(5)

Divided by 7 on both sides of the above equation,

⇒ x = (77)(5)/7

⇒ x = 11 × 5

Apply the multiplication operation, we get

⇒ x = 55

Thus, when she makes 77 candles, she will also produce 55 wax warmers.

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Answer:

associative property of multiplication

Step-by-step explanation:

Given graph will be a line parallel to [x] axis.

The general equation of a straight line is -

y = mx + c

where -

[m] → is slope of line which tells the unit rate of change of [y] with respect to [x].

[c] → is the y - intercept i.e. the point where the graph cuts the [y] axis.

Other possible equations of lines are -

For any function y = f(x), Domain is the set of all possible values of [y] that exists for different values of [x]. Range is the set of all values of [x] for which [y] exists.

We have Mrs. Rao pays the same amount each month for Internet service.

Assume that he pays amount [k], each month. Then, we can write the equation representing the graph as -

y = k

The graph will be a line parallel to [x] axis.

Therefore, the given graph will be a line parallel to [x] axis.

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It is a supposition that it is true if two points are equally far apart from a third point and the three points are collinear.

If three or more points lie on a single straight line, they are said to be collinear. An axis is a term used to describe a line on which points are located, particularly if that line is connected to a triangle or other geometric shape. Since two points determine a line, two points are trivially collinear.

Collinear points are those that are situated along a  identical straight line.

The supposition is correct since all three points are located on the same line.

if the two points create a straight angle that includes the third point, then the conjecture is true.

If the two points do not create a straight angle with the third point, then the conjecture is false.

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Answer:

A

Step-by-step explanation:

y = - 2² + 4

y = - 4 + 4

y = 0

(2,0)

The equation that has a real zero at x = 2 is y = -[tex]2^x[/tex] + 4.

Option A is the correct answer.

An equation contains one or more terms with variables connected by an equal sign.

Example:

2x + 4y = 9 is an equation.

2x = 8 is an equation.

We have,

The graph shows an x-intercept at x = 2, which means that the function has a real zero at x = 2.

Now,

We can check which of the given equations has this property by plugging in x = 2 and seeing if the corresponding y-value is zero.

For y = [tex]-2^x[/tex] + 4,

y = -2² + 4 = 0

This equation has a real zero at x = 2.

For y = 2^x,

y = 2² = 4,

This equation does not have a real zero at x = 2.

For y = log₂(x + 2) + 1,

y = log₂(2 + 2) + 1 = log₂4 + 1 = 3

This equation does not have a real zero at x = 2.

For y = log₂(-x + 2),

-x + 2 < 0, which means that x > 2.

This equation does not have a real zero at x = 2.

Therefore,

The equation that has a real zero at x = 2 is y = -[tex]2^x[/tex] + 4.

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The combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.

We have the following information:

A sandwich hop serve 4 ounce of meat and 3 ounce of cheese on each sandwich. After making sandwiches for an hour the hop owner has used 91 combined ounce of meat and cheese.

Now, we know the combined ounces of meat and cheese for 1 sandwich will be given as follows:

Ounces of meat + ounces of cheese

4+3

7 ounces

Now, in an hour 91 ounces of combined cheese and meat are used.

So, we have the following expression:

Number of sandwiches made in 1 hour = Total ounces used/ounces used in 1 sandwich

Number of sandwiches = 91/7

Number of sandwiches = 13

Ounces of meat used in 13 sandwiches = 13*4

Ounces of meat used in 13 sandwiches = 52 ounces

Ounces of cheese used in 13 sandwiches = 13*3

Ounces of cheese used in 13 sandwiches = 39 ounces

Hence, the combined ounces of meat and cheese used on each sandwich is 7 ounces and the combined ounces of meat on all sandwiches is 52 ounces and that of cheese on all sandwiches is 39 ounces.

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Answer:

The total surface area is 3860 ft^2

The total volume is 22,500 ft^3

Step-by-step explanation:

See attached worksheet.

The house needs to be broken up into separate rectangles and triangles, as shown on the worksheet.  Individual calculations of the area and volume are then added for a total number for both volume and surface area.

Answer:

Step-by-step explanation:

20 5 dollar

20 10 dollar

32 hundred dollar

For this problem there are $44.55 Shen paid.

What is sale price?

The cost following a discount applied to the original cost. This item is being sold for $8.00. We must first calculate the discount amount if the discount is a percentage: • Original price x discount rate equals the discount amount.

Given:

An item is regularly priced at $81.

Shen bought it on sale for 45% off the regular price.

The formula for calculating the sales price of an item is:

s = p - (p x d)

Where:

s is the sales price: what we are calculating in this problem.

p is the regular price of the item: $81 for this problem.

d is the discount rate: 45% for this problem. "Percent" or "%" means "out of 100" or "per 100", Therefore 45% can be written as  45/100.

Substituting and calculating  s gives:

[tex]s = 81 - (81 *\frac{45}{100}) \\s = 81 - (36.45)\\s = 44.55[/tex]

s = $44.55

Hence, for this problem there are $44.55 Shen paid.

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The area of the figure that is made up of a semicircle and a triangle is 63.25  square feet .

In the question ,

it is given that ,

a figure is made up of a semicircle and a triangle ,

the diameter of the given semicircle is = 10 ft ,

So , the radius of the given semicircle is = 10/2 = 5 ft .

hence the area of the semicircle will be = (πr²/2)

= 3.14×(5)²/2

= 39.25 square feet

the base of the triangle is given to be = 8 ft ,

the height of the triangle is given to be = 6 ft ,

So , the area of the triangle is = (1/2)×b×h = (1/2)×8×6 .

= 4 × 6

= 24 square feet .

So , the area of the figure = area of semicircle +  area of triangle

= 39.25 + 24

= 63.25 .

Therefore , the area of the figure is = 63.25 square feet .

The given question is incomplete , the complete question is

A figure is made up of a semicircle and triangle. The diameter of the semicircle is 10ft, the base of the triangle is 8 ft and the height is 6 ft. What is the area of the figure ?

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Answer: 2 miles

Step-by-step explanation:

Answer:

domain=5,12,3

range=0,4,-3

Whenever a probability sample is drawn from a population, it is not enough to simply report the sample's descriptive statistics, for these measures contain a certain degree of error due to the sampling process.

Thus the answer is ‘ true’.

A population is any entire group that has at least one trait in common that is relevant to a given issue or experiment in statistics.

A probability sample is one that is drawn using a method of random selection that is compatible with the known odds for each member of the population to be selected, and that takes these probabilities into account when generating estimates from the sample.

If the chosen sample does not accurately reflect the total population of data, there has been a sampling error, which is a statistical error resulting from sampling.

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To make the quadratic polynomial x² + 18x into a perfect square, we add 81 to it.

A quadratic polynomial is a polynomial in which the highest power of the unknown is 2.

A perfect square is a number suvh that it is equal to another number multiplied by itself

Since we have the quadratic polynomial x² + 18x, and we wnat to convert it to a perfect square.

To be a perfect square, we want it in the form (x + a)² = x² + 2ax + a²  (1)

Compring the quadratic polynomial with equation (1), we have that

2a = 18

a = 18/2

a = 9

⇒ a² = 9² = 81

So, substituting a = 9 into equation (1), we have

(x + a)² = x² + 2ax + a²

(x + 9)² = x² + 2(9)x + 9²

= x² + 18x + 81

Thus we see that to make  x² + 18x into a perfect square, we add 81 to it.

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Answer:

see explanation

Step-by-step explanation:

(c)

ratio of

boys : total students

= 182 : 260 ( divide both parts by 26 )

= 7 : 10

number of girls = 260 - 182 = 78

ratio of

girls : total students

= 78 : 260 ( divide both parts by 26 )

= 3 : 10

Answer:

She can make 12 pizzas

Step-by-step explanation:

There are 2 halves in a pound, so you'll need to do 6 × 2 = 12.

Answer:

- 51

Step-by-step explanation:

substitute x = - 2 into the expression

2x³ - 4x² + 8x - 3

= 2(- 2)³ - 4(- 2)² + 8(- 2) - 3

= 2(- 8) - 4(4) - 16 - 3

= - 16 - 16 - 19

= - 32 - 19

= - 51

Answer: True

Step-by-step explanation:

If I remember not to mistake y=x is the parent functions. So y=b is the parent function! So this question is true.

The rate of change is 2 and initial value is 3.

Given points A (0,3) B(2,7)

What is the slope of line joining between point A and point B

if let's suppose A(x1,y1) B(x2,y2)

then slope(m) = y2-y1/x2-x1

x1=0,y1=3

x2=2 y2= 7

slope(m) = 4/2 = 2

The ratio between the change in the values of the y variables and the change in the values of the x variables is known as the rate of change. The rate of change is the slope of the line if the rate of change is linear and constant.

Rate of change of linear function is also know as slope of that linear function.

So here slope itself is the rate of change.

Initial value is 3 as Coordinate of A is (0,3).

Given Question is incomplete Complete Question here

A relation is plotted as a linear function on the coordinate plane starting at point A (0, 3)and ending at point B (2, 7) .

What is the rate of change for the linear function and what is its initial value?

Select from the drop-down menus to correctly complete the statements.

The rate of change is____ and the initial value is___ .

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The measure of angle V i.e. [tex]m\angle V[/tex] is [tex]60^\circ[/tex].

For the triangle TUV ([tex]\triangle TUV[/tex]), all the sides are of same length i.e. 9. So we can consider this as an equilateral triangle.

We know for an equilateral triangle all of the angles are of same measure.

Now the sum of all angles of a triangle is [tex]180^\circ[/tex] and there are 3 angles in a triangle. So, each angle will be of measure [tex]60^\circ[/tex].

Therefore the measure of [tex]\angle V[/tex] i.e. [tex]m\angle V[/tex] is [tex]60^\circ[/tex].

Also the basic three properties of an equilateral triangle are:

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The triangles ΔUST and ΔVRQ are congruent to each other by the SSS postulates.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

In triangles ΔUST and ΔVRQ, then we have

TU = QV (Given)

ST = QR (Given)

UV = SR

Add RU on both sides, then we have

UV + RU = SR + RU

RV = SU

The triangles ΔUST and ΔVRQ are congruent to each other by the SSS postulates.

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If someone tells me "keep dreaming :)", I would likely respond by thanking them for their encouragement and expressing my determination to continue pursuing my dreams. I might also share some of my aspirations and plans for achieving them, and encourage the other person to do the same. Depending on the context and tone of the conversation, I might also make a joke or offer a playful response, such as "I will, and I'll make sure to dream big!"

Answer: He will work for 19 days.

Step-by-step explanation:

If Nicholas has 234 dollars and the computer he wants to put is 899 dollars, you have to subtract to see how much he has to take the loan from his parents in order to buy the computer.

899 - 234 = 665

He took a loan of 665 dollars from his parents

To figure out how many days he needs to work to pay that amount, you divide the amount he earns each day with the amount of loan he took.

So 665 divided by 35 = 19

He has to work 19 days to pay off the 665 dollar loan he took from his parents.

We can check this answer by multiplying 35 x 19 , which equals to 665.

Hope this helps!

Answer:

  24.98 units

Step-by-step explanation:

You want the perimeter of triangle ABC with vertices A(-5, 4), B(1, -2), and C(3,6).

The distance between two vertices can be found using the formula ...

  d = √((x2 -x1)² +(y2 -y1)²)

The  distance between A and B is ...

  d = √((1 -(-5))² +(-2 -4)²) = √(6² +(-6)²) = 6√2 ≈ 8.485

The attached spreadsheet performs the same calculation on all the pairs of points. (The distance from each point to the one below it is listed.)

The perimeter of the triangle is the sum of the segment lengths. That is also shown in the spreadsheet.

  P = AB +BC +CA

  P = 8.485 +8.246 +8.246 ≈ 24.98

The perimeter of triangle ABC is about 24.98 units.

__

Additional comment

When calculations are repetitive, we like to let a spreadsheet do them.

Answer:

The length of side B is 6.25, The length of side A is 8.75, The scale factor is 0.25

Step-by-step explanation:

Divide the left side of the first model by the left side of the scaled version

60 / 15 = 4

divide side A and B by the result

35 / 4 = 8.75

25 / 4 = 6.25