Triangle PQT and Triangle RSU are similar right triangles. Which proportion can be used to show that the slope of QT is equal to the slope of RS?

The four winning numbers are 24, 32, 27 and 37 respectively

It is important to note the following;

From the information given;

a. First number =  square root of 576

This is represented as

First number = √576

First number = 24

b. Second number =  multiple of 8 between 30 and 39

Second number = 32

c. Third number =  cube of 3

This is represented as;

Third number =  3³

Third number =  37

d. largest prime number less than 40

Fourth number = 37

Hence, the numbers are 24, 32, 27 and 37

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Answer:

Step-by-step explanation:

Multiply like this

2 x 2

How to do this

Just double 2

Answer:

multiplication is like doing repeated addition so let’s try doing 5x5

In repeated addition form it would be 5+5+5+5+5 which equals 25

I don’t know how to really explain it but I hope this helps!

Step-by-step explanation:

The smaller the sample size the greater the variability and higher the chance of getting an overestimate

From the given data

Median = $200,000

IQR = $100,000

The sample size for the median above to $250,000 is n =10

Because n=10 shows a sample with the fewest values, it is most likely that the sample median will be farther from the true median.

Answer : A) n = 10

The number of non-members is 12 and the number of members is 24.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

Let x be the number of members, and the number of non-members.

3x + 5y = 132

x = 2y

After solving the above two linear equations:

6y + 5y  = 132

11y = 132

y = 132/11

y = 12 non-members

x = 24 members

Thus, the number of non-members is 12 and the number of members is 24.

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Answer:

1

The answer is 1

When a line has a slope of 0, it means that the line is a horizontal line that is parallel to the x-axis. An equation that shows this is y = 0x + 2.

The slope of a line shows the change in the line and how it is shaped on the graph. If the slope of a line is 0, what it means is that the line has not slanting shape and is instead simply straight on the horizontal axis.

As a result of the line being a straight horizontal line, it will be parallel to the x-axis which is also a horizontal line.

Take the equation:

y = 0x + 2

y = 2

Y will be a horizontal line on y=2.

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Answer:

alphabet

Step-by-step explanation:

Answer:

Height = 36m

Step-by-step explanation:

As per the given data: Area of the triangle = 85m2

Base of the triangle = 5m

Height of the triangle = ? (x)

As we know, A = bh/2

by substituting the given values in the above equation, we get

85 = 5 * x/2

5x = 170

x = 36

date : 09-10-2022

The amount that Sidney will have in her account in 1 year is $ 95,704.

Given that:-

Principal amount = $85,450

Interest Rate = 12 % per annum

i = prt

Where,

i represents interest,

p represents the principal,

r represents the interest rate, and

t represents the time (in years)

Hence, putting the values in the formula of simple interest, we get,

i = 85450*(12/100)*1 = $ 10,254

Hence, the amount that Sidney will have in her account in 1 year is

85450 + 10254 = $ 95,704

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Answer:

209 out of 230 completed   that is   209/230 x 100% = 90.869 %     the rest did NOT complete   100% - 90.8% = 9.13 %

The height of the building to the nearest meter is 38 m.

In the question ,

it is given that

distance between the point and building is 80m

and the angle of elevation from the point to the top of the building is 25°

the figure formed from the data is shown below ,

where AB (h)is the height of the building .

So , From triangle ABC

tan25° = AB/BC

tan25° = h/80

simplifying further

we  get ,

h = 80*tan25°

h = 80*(0.466)

h = 37.28

h ≈ 38

Therefore , The height of the building to the nearest meter is 38 m.

The given question is incomplete , the complete question is

The angle of elevation of the top of a building from a point 80m away on level ground is 25° . Calculate the height of the building to the nearest meter.

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Answer:

3 millimeters : 2 meters

There ya go, happy to help! :)

Answer:

The scale of the drawing is 3 millimeters : 2 meters.

Step-by-step explanation:

olution

2a.

The graph of as described is given below (showing at least five points)

The (clear) graph that has the dashed line of asymptotes

The table will be

Bb.

o write the equation

We start from

Translate the graph up by 3 units

Translate the graph 4 units to the left

2c.

o get the equation of asymptotes

By algebra properties, the standard form with rational coefficients is the polynomial x³ - 11 · x² + 7 · x + 51, whose lead coefficient is 1 and comprise the roots 3 and 4 + i.

A polynomials of least degrees includes all the roots and the given lead coefficient, which can used in the following formula:

p = a · Π (x - rₐ)

Where:

If we know polynomial has rational coefficients, then the complex root 4 + i has a "twin" equal to 4 - i in accordance with the quadratic formula, otherwise the polynomial will have at least an irrational coefficient. Then, the least degree polynomial is introduced below:

p = 1 · (x - 3) · (x - 4 - i) · (x - 4 + i)

Then, we expand the expression by algebra properties:

p = (x - 3) · [x² - 8 · x - (16 - i²)]

p = (x - 3) · (x² - 8 · x - 17)

p = x³ - 8 · x² - 17 · x - 3 · x² + 24 · x + 51

p = x³ - 11 · x² + 7 · x + 51

The standard form is the polynomial p = x³ - 11 · x² + 7 · x + 51.

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Answer:

B) [tex](2,\infty)[/tex]

Step-by-step explanation:

Since we are given the graph of [tex]f'(x)[/tex], this gives us the value of the derivative, or the rate of change, of [tex]f(x)[/tex] given an x-value. For [tex]f(x)[/tex] to be increasing, then [tex]f'(x) > 0[/tex], which is a positive rate of change. As you may have noticed, when [tex]x > 2[/tex], the value of [tex]f'(x)[/tex] is positive. This means that f increases on the interval [tex](2,\infty)[/tex], or answer B.

Answer:

Step-by-step explanation:

1/2(12*5)=

1/2*60=

30 cm²

The number of units that must be produced and sold in order to break even will be 100.

At the break-even point, the cost of the revenue is equal to the cost of the manufacturing.

The break-even point is the point at which a business's costs and revenues are equal. R stands for the revenue, in dollars, from the sale of x units, and C stands for the cost, in dollars, of x units of a product.

C = 13x + 250 and R = 15.5x

By the definition of the break-even point, then the equation is given as,

13x + 250 = 15.5x

15.5x - 13x = 250

2.5x = 250

x = 250 / 2.5

x = 100

The number of units that must be produced and sold in order to break even will be 100.

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The numbers that represent the first 5 members selected is A. 24, 07, 59, 62, 20.

From the information, the members of a running club would like to survey the rest of the members to determine which 5K races the club should enter.

In this case, they decide to use a random number table to sample 10 of the 78 members. The numbers illustrated are 24000 75983 62200 91518 11198 88936.

Therefore, the appropriate numbers chosen will be (24) 000 (7) (59) 83 (62)(20)0.

The correct option is A.

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Applying the definition of the midpoint of a line and other properties, the proof that shows that AC ≅ CD is shown in the image attached below.

A line is divided into two equal parts by its midpoint. Thus, the midpoint of that line is that point where the line segment is bisected into two parts that are equal.

Given the image showing two lines that intersect each other at point C, the proof below shows that AC is congruent to CD:

1. C is the midpoint of line AE

C is the midpoint of line BD

AE is congruent to BD

(Reason: Given)

2. AC = CE; BC = CD

(Reason: Definition of midpoints)

3. AE = BD

(Reason: Definition of congruent segments)

4. AE = AC + CE;

BD = BC + CD

(Reason: Segment addition property)

5. AC + CE = BC + CD

(Reason: substitution property)

6. AC + AC = BC + BC

(Reason: substitution property)

7. 2AC = 2BC

(Reason: Simplify)

8. AC = CD

(Reason: division property)

9. AC ≅ CD

(Reason: definition of congruent segments).

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For the given figure, all the intersecting sides meet at right angles

The lengths of the vertical sides are 14, 8, and ?

Let the missing side = x

So,

so,

so, the answer will be the length of the missing side = 6 yd

Given function:

Finding x when f(x) = -4

Thus, the value of x is 3 and 5.

Here are some tips that may help you feel better:

1. Rest: Get plenty of sleep and rest as much as possible to allow your body to recover.

2. Hydration: Drink lots of fluids to stay hydrated and help flush out any toxins in your body.

3. Nutrition: Eat healthy foods that are easy to digest, such as soups, broths, and fruits.

4. Medication: Take any prescribed medication as directed and follow the instructions on the label.

5. Warmth: Use warm blankets and a hot water bottle to soothe aches and pains.

6. Avoiding stress: Stay away from stress as much as possible since it can interfere with your immune system's functioning.

7. Humidifier: Use a humidifier to help ease congestion and dryness in the air.It's also essential to see a doctor if your symptoms persist or worsen. Don't hesitate to seek medical attention if necessary.

Furthermore, the information given in the question, "x does not equal 12 and D isn't 95," seems unrelated to the context of the problem. It's unclear what information the question is asking for, so please provide more details if you have any.

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A) There are two parallel lines and a line that goes through them in this diagram. The line that goes through them causes perpendicular lines to form.

What are perpendicular lines?

Perpendicular lines are lines that intersect and create 90° angles. The two angles in this diagram are 90° due to this intersection.

B) There are two types of angles: supplementary and complementary: complementary angles are angles whose measurements add up to 90°. Supplementary angles are angles whose measurements add up to 180°. As you can see in this problem, the two angles (7x+11 and -1+8x) are 90°. When added they would equal 180°. These angles are supplementary.

C) Now that you know what supplementary angles are, you can use its characteristics to solve for x:

D) Now, solve for the two equations by plugging in x [you final answers should be 90]:

The midpoint of the fourth class interval is 0.51

The range of the fourth class is 0.48-0.54

So, to find the middle point of the class we use the following formula:

The average of the top and lower values of a specific class interval is referred to as the class midpoint (also known as the class mark). The class midpoint substitutes a range of values with a single value in a frequency distribution table. We can create a line graph for our data using the frequency and the class midpoint.

Midpoint = Upper limit+Lower limit/2

Upper limit = 0.54

Lower limit = 0.48

Substituting the values in the formula we get:

Midpoint = (0.54+0.48)/2

= 0.51

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Given the function is plotted on the graph and attached below.

You must choose x-values and insert them into the equation in order to graph a function. You will obtain a y-value if you enter those values into the equation. Your coordinates for a single point are made up of your x-values and your y-values.

To: Determine whether a graph reflects a function using the vertical line test. Check the graph to check if any vertical lines that were generated would repeatedly cross the curve. If such a line exists, the graph does not depict a function.

Hence the required graph is created .

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The statement that for two sets A and B, (A ∪ B)' = A' ∩ B' is true.

Let us check it with the help of an example.

Let A = {1,2,3,4,5,6} ,

B = {5,6,7,8,9,10} and ,

A universal set S = {1,2,3,4,....,15}

Now, we can write,

A ∪ B = {1,2,3,4,5,6,7,8,9,10}

LHS = (A ∪ B)' = {11,12,13,14,15}

A' = {7,8,9,10,11,12,13,14,15}

B' = {1,2,3,4,5,11,12,13,14,15}

RHS = A' ∩ B' = {7,8,9,10,11,12,13,14,15} ∩  {1,2,3,4,5,11,12,13,14,15} = {11,12,13,14,15}

As we can observe from above,

LHS = RHS

Hence, the statement that for two sets A and B, (A ∪ B)' = A' ∩ B' is true.

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Answer:

[tex]100 < 112 < 121[/tex]

[tex] \sqrt{100} < \sqrt{112} < \sqrt{121} [/tex]

[tex]10 < \sqrt{112} < 11[/tex]

A and C are the desired numbers.

Zeros of a Polynomial

When a polynomial has a zero at x = a, then its graph 'touches' or 'crosses' the x-axis. If the zero has an even multiplicity (2, 4, 6, etc.), the graph 'bounces' off the x-axis.

We can see the graph crosses the x-axis 4 times and no bouncing occurs, so each zero has a multiplicity of 1.

From left to right, the zeros are:

x = -4 with a multiplicity of 1.

x = -2 with a multiplicity of 1.

x = 1 with a multiplicity of 1.

x = 3 with a multiplicity of 1.

For the function f(x) = x + 2, the value of x when f(x) = 1, gives x = -1

An equation is an expression that shows the relationship between two or more numbers and variables.

Equations are classified based on degree (value of highest exponents) as linear, quadratic, cubic and so on. Variables can be dependent or independent. Dependent variables depend on other variable while an independent variable do not depend.

Given that:

f(x) = x + 2

When f(x) = 1, substituting:

1 = x + 2

x = -1

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The amount that will be made by the local festival given the expression m=2p - 0.75p - 50 is 225.

From the information, at the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each.

The expression given was illustrated as:

m=2p - 0.75p - 50

Therefore since we are given the value of p as 220. This will be:

m=2p - 0.75p - 50

m = 2(220) - 0.75(220) - 50

m = 440 - 165 - 50

m = 440 - 215

m = 225

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At the local hot air balloon festival, the Ma & Pa Ice Cream Trucks sells ice cream pops, which cost them $0.75 each, but are sold for $2 each. They also paid $50 to the festival's organizers for a vendor permit. Use the expression m=2p - 0.75p - 50 to answer the following questions.

Find the profit when the number of the ice cream pops represented by p is 220.

For purposes of description, lines, planes, and points are crucial in geometry. The correct answer is as follows:

A. 9 points (Points - M, N, O, P, Q, R, S, T, U)

B. 3 lines (Lines - MO, PQ, RS)

C. 2 planes (Planes - K and L)

D. (P, N, Q) , (M, N, O), (R, N, S)

E. (M, P, S, T)

F. M, O

G. N

H. S

I. Horizontal plane

J. Line D

Collinearity in geometry is the quality of a set of points being on a single line. Collinear points are a group of points that share this characteristic. The phrase has been used more broadly to refer to aligned objects, i.e., things that are "in a line" or "in a row."

The subject of geometry involves points, planes, and lines. A plane is a flat surface that can be either horizontal or vertical, whereas a line is a straight path that links two locations.

Understanding the offered figure and interpreting each question in light of the terminologies in it are necessary in order to answer the questions. As an illustration, collinear points are those that can be joined by a straight line, but non-collinear points cannot be connected by a straight line.

The correct answers is as follows:

A. 9 points (Points - M, N, O, P, Q, R, S, T, U)

B. 3 lines (Lines - MO, PQ, RS)

C. 2 planes (Planes - K and L)

D. (P, N, Q) , (M, N, O), (R, N, S)

E. (M, P, S, T)

F. M, O

G. N

H. S

I. Horizontal plane

J. Line D

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Answer:

Step-by-step explanation:

A. 9 points (Points - M, N, O, P, Q, R, S, T, U)B. 3 lines (Lines - MO, PQ, RS)C. 2 planes (Planes - K and L)D. (P, N, Q) , (M, N, O), (R, N, S)E. (M, P, S, T)F. M, OG. NH. SI. Horizontal planeJ. Line D