prove that under any affine transformation, the ratio of parallel line segments is invariant, but the ratio of non-parallel line segments is not invariant

The equation y^2+4y represents a parabola that is open upward. The general form of a quadratic function is y = ax^2 + bx + c.

In this case, the coefficient of the x^2 term is 1, the coefficient of the x term is 4, and the constant term is 0.

This equation can be factored as y(y+4) = 0.

This equation is satisfied by y = 0 and y = -4.

Therefore, the solutions of y^2+4y = 0 are y = 0 and y = -4.

The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .

A polygon having three edges and three vertices is called a triangle. It is one of the fundamental geometric forms. Triangle ABC is the designation for a triangle with vertices A, B, and C. In Euclidean geometry, any three points that are not collinear produce a distinct triangle and a distinct plane.

The properties of a Triangle are :

The six types of triangles are: isosceles, equilateral, scalene, obtuse, acute, and right.

In triangle ΔABC

∠B = 44° and ∠C = 17°

So, The sum of angles of a triangle is 180°

Therefore,

∠A + ∠B + ∠C = 180°

⇒∠A + 44° + 17° = 180°

⇒∠A = 180° - 61°

⇒∠A = 119°

The value of ∠A in triangle ΔABC is 119° with ∠B = 44° and ∠C = 17° .

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The mathematical expression, for the given statement is 20g/3

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between.

Given is a statement, two-thirds times g times 10.

Converting into mathematical expression,

2/3 of g = 2g/3

And,

2/3 of g of 10

= 2g/3 × 10

= 20g / 3

Hence, the mathematical expression, for the given statement is 20g/3

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The required volume of concrete in cubic yards to make the sidewalk is 124.4444 yards³

The unitary method is a method in which you find the value of a unit and then the value of a required number of units.

Given here: Dimensions of the side walk 4 ft. 140 and 6 feet.

We know the volume of the rectangular cuboid side walk will be given by

V= 4×140×6

 =3360 ft³

Thus the volume of concrete that will be required to make the side walk is 3360 ft³

In yards³ we know

1 cubic foot= 0.037037 yards cube

∴  3360ft³=124.4444 yards³

Hence, The required volume of concrete in cubic yards to make the sidewalk is 124.4444 yards³

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Answer:

a. To find out how much more expensive Plugged Pipes is than Pete's Plumbing, we need to subtract Pete's Plumbing's cost from Plugged Pipes' cost. The expression for the difference in cost is:

(50x + 75) - (25x + 50) = 25x + 25

This is the simplified form of the expression that represents the difference in cost.

b. If they each work for 2 hours, we can substitute x = 2 into the expressions for their costs and compare the results:

Plugged Pipes: 50(2) + 75 = 125 dollars

Pete's Plumbing: 25(2) + 50 = 100 dollars

So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.

Step-by-step explanation:

Sure, here is a step-by-step explanation of how to find the difference in cost between Plugged Pipes and Pete's Plumbing for x hours of work:

To find out how much more expensive Plugged Pipes is for 2 hours of work we can substitute x = 2 into the expression for their costs and compare the results:

Plugged Pipes: 50(2) + 75 = 125 dollars

Pete's Plumbing: 25(2) + 50 = 100 dollars

So, Plugged Pipes is 25 dollars more expensive than Pete's Plumbing for 2 hours of work.

After taking the random sample, the following has the mean sample of (c) the sampling distribution of the sample mean.

A random sample is a group of people chosen at random, all with the same probability, from a larger group of people as mentionedinstatistics. It makes sure that the results you get from your sample should be close to what you would have gotten if you measured the entire population.

All units in the population have an equal chance of being chosen using the simplest random sample. Sampling should completely eliminate any signs of bias. Every person in the big population set has the same chance of being chosen because the people who make up the subset of the bigger group are selected at random.

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The answer to each part is given above.

Given are the functions as follows -

p(x) = - 5x + 5

q(x) = - 4x - 2

We can write -

(p о q)(5) = (- 5x + 5)(- 4x - 2)

(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2)

(p о q)(5) = 20x² + 10 - 20x - 10

(p о q)(5) = 20x² - 20x

(p о q)(5) = 20 x 25 - 20 x 5

(p о q)(5) = 500 - 100

(p о q)(5) = 400

(p о q)(5) = - 5x(- 4x - 2) + 5(- 4x - 2) = (q о p)(5) = 400

(q о p)(5) = 400

Therefore, the answer to each part is given above.

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The percentile of the top students will be 88%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The admissions index score is used to set eligibility standards intended to meet the goal of admitting the top 12% of high school students in the state.

The percentile of the top student is given as,

⇒ 100% - 12%

⇒ 88%

The percentile of the top students will be 88%.

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Answer:

737373

Step-by-step explanation:

You just add them together? Am I missing something?

(a) The probability of a failure given there are more than 1,000 wells in a geological formation is 0.1001.

(b) The probability of a failure given there are fewer than 500 wells in a geological formation is 0.0852.

(a) We have to determine the probability of a failure given there are more than 1,000 wells in a geological formation.

P(B∣A) = Total number of failed wells more than 1000 wells/Total number of wells with 1000 failed wells

P(B∣A) = (180 + 443 + 60)/(1685 + 3733 + 1403)

P(B∣A) = 683/6821

P(B∣A) = 0.1001

(b) We have to determine the probability of a failure given there are fewer than 500 wells in a geological formation.

P(B∣C) = Number of failed well/Number of failed wells with total less that 500 wells

P(B∣C) = (2 + 14 + 44 + 3)/(28 + 363 + 309 + 39)

P(B∣C) = 63/739

P(B∣C) = 0.0852

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The complete question is:

Consider the well failure data in the table below. Let A denote the event that the geological formation of a well has more than 1000 wells, let B denote the event that a well failed, and let C denote the event that the geological formation of a well has fewer than 500 wells.

(a) What is the probability of a failure given there are more than 1,000 wells in a geological formation? Round your answer to four decimal places (e.g. 98.7654). P(B∣A)=

(b) What is the probability of a failure given there are fewer than 500 wells in a geological formation? Round your answer to four decimal places (e.g. 98.7654). P(B∣C)=

Using a left-hand approximation means that we will use the left endpoint of each interval to approximate the area under the curve.

a) Using 4 boxes:

The interval from 0 to 2 can be divided into 4 equal parts, so each part has a length of 0.5.

The height of each box will be the value of y at the left endpoint of each interval.

The area of each box can be calculated as follows:

For the first box, the left endpoint is (0, 1) and the height is 2(0) + 1 = 1. The area is 0.5 * 1 = 0.5.

For the second box, the left endpoint is (0.5, 2) and the height is 2(0.5) + 1 = 2.5. The area is 0.5 * 2.5 = 1.25.

For the third box, the left endpoint is (1, 3) and the height is 2(1) + 1 = 3. The area is 0.5 * 3 = 1.5.

For the fourth box, the left endpoint is (1.5, 4) and the height is 2(1.5) + 1 = 4.5. The area is 0.5 * 4.5 = 2.25.

The total area is the sum of the areas of all the boxes, so the total area is 0.5 + 1.25 + 1.5 + 2.25 = 5.

b) Using 8 boxes:

The interval from 0 to 2 can be divided into 8 equal parts, so each part has a length of 0.25.

The height of each box will be the value of y at the left endpoint of each interval.

The area of each box can be calculated as follows:

For the first box, the left endpoint is (0, 1) and the height is 2(0) + 1 = 1. The area is 0.25 * 1 = 0.25.

For the second box, the left endpoint is (0.25, 2.5) and the height is 2(0.25) + 1 = 2.5. The area is 0.25 * 2.5 = 0.625.

For the third box, the left endpoint is (0.5, 3) and the height is 2(0.5) + 1 = 3. The area is 0.25 * 3 = 0.75.

And so on, for all 8 boxes.

The total area is the sum of the areas of all the boxes, so the total area is 0.25 + 0.625 + 0.75 + ... + 3.375 = 5.125.

So, the area between the x-axis and the curve y = 2x + 1 on the interval (0, 2) can be approximated as 5 or 5.125 depending on the number of boxes used.

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The measure of the length of u for the condition is  1560 inches (approx).

The law of sines specifies how many sides there are in a triangle and how their individual sine angles are equal. The sine law, sine rule, and sine formula are additional names for the sine law.

The side or unknown angle of an oblique triangle is found using the law of sine. Any triangle that is not a right triangle is referred to as an oblique triangle.

Given ΔTUV

t = 820 inches

∠U = 132°

∠V = 25°

and ∠T = 180 - 132 - 25

∠T = 23°

so according to the law of sines

[tex]\frac{SinT}{t} = \frac{SinU}{u}= \frac{SinV}{v}[/tex]

so u = t*(SinU/SinT)

u = 820(Sin132/sin23)

u = 820(1.9019)

u = 1559.58 inches = 1560 inches (approx)

Hence the value of u is 1560 inches (approx).

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Answer:

Let's call the original number of dollar bills Mother had "d". Each child received d/5 + 3 dollars.

Since each child received $14, we have:

d/5 + 3 = 14

Multiplying both sides by 5, we get:

d + 15 = 70

Subtracting 15 from both sides, we get:

d = 55

So, Mother had 55 dollar bills in her wallet.

Answer:

0.571428571

Step-by-step explanation:

To find the sum of two fractions with different denominators, a common denominator must be found.

In this case, the two in the denominator must be multiplied to make it 14.

14/2 = 7, so multiply 2 by 7 to get 14, and what you do to the bottom you must do to the top, so 1 * 7 = 7.

Now, your two fractions are 7/14 and 1/14. Add the numerators as the denominators are equal.

7+1 = 8

8/14 is the sum, which can be divided by 2 on the top and bottom to simplify.

8/2 = 4, and 14/2 = 7

4/7

Answer:

To find out how much it would cost Suzie to lay the flooring so it fully covers the floor of room, you need to know the area of the room's floor and the cost per square foot of the flooring.

If the flooring will cost $2 per square foot, and if the area of the room's floor is x square feet. Then the total cost will be $2x.

Without knowing the area of the room's floor, it is impossible to determine the cost of the flooring.

Answer: it would be B:log 5/log 7

Step-by-step explanation:

According to the problem Brad will need 28.27 feet of edging to enclose his flower garden.

Edging in math is a technique that involves finding the maximum or minimum value of a function. It is typically used to optimize or increase the performance of a particular solution. In other words, edging is a process by which a function is “reduced” to its most efficient form. For example, a function that is non-linear can be “edged” to become more linear, thereby increasing its efficiency. Additionally, edging can be used to identify certain features within a solution, such as local maximums or minimums. Edging is an important tool in math, and it can be used in a variety of different applications, from optimization to data analysis.

Brad will need 28.27 feet of edging to enclose his flower garden. This is because the circumference of a circle is equal to 2πr, where r is the radius. Therefore, the circumference of Brad's flower garden with a radius of 4.5 feet is 28.27 feet.

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Answer:

165 of the animals at the shelter are cats.

Step-by-step explanation:

If one-fourth of the animals at the shelter are cats and there are 660 animals at the shelter, to get the number of cats you divide the total number of animals by the percentage of cats.

660 / 4 = 165

Answer:

y = 5

Step-by-step explanation:

3y - 7 = 8  Add 7 to both sides

3y - 7 + 7 = 8 + 7

3y = 15  Divide both sides by 3

y = 5

Step-by-step explanation:

The y-intercept of a function can be found by looking at the point where the x-coordinate is 0. In this case, the y-intercept of the function is -3, as the point (0,-3) is on the graph.

The slope of a function can be found by looking at the change in y divided by the change in x between two points on the graph. In this case, we can use the points (0,-3) and (1,-1) to find the slope. The change in y is -1 - (-3) = 2 and the change in x is 1 - 0 = 1. So the slope is 2/1 = 2.

Therefore, the equation of the function can be written in slope-intercept form as y = mx + b, where m is the slope and b is the y-intercept. So the equation of the function is:

y = 2x - 3

It's the equation of a line that pass through (0,-3) and (1,-1) and (2,1) and (3,3) and (4,5)

Therefore , the solution of the given problem of slope comes out to be

line's equation is y =.1333 x + 1.55.

A line's steepness can be determined by looking at its slope. Slope is calculated mathematically as "rise over run" (change in y divided by change in x).If you look at the line from left to right, a line that is moving up will have a positive slope and a line that is moving down will have a negative slope.

Here,

Given : f(x) =4 +x

The line's "intercept" of the y-axis marks the location of the y-intercept. It also makes sense because a player with a 25 cm heel to toe measurement is about 1.55 metres tall. This is most likely.

Any line has the equation y=mx+b (m=slope, b=y-intercept).

Finding two spots on this line where it crosses will reveal the slope of the line. I'll use the numbers (25.5, 1.6) and (26.25,1.7).

=> (y(2)-y(1)) / (x(2)-x(1))

=> m 1.7 - 1.6 / 26.25 - 25.5

=>.1/.75 =.13333 is the formula to calculate the slope.

At roughly 1.55m, this line crosses the y-intercept.

This line's equation is y =.1333 x + 1.55.

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The measure of angle t is (d) 103 degrees

From the question, we have the following parameters that can be used in our computation:

The triangle

Using the law of cosines, we have the following equation:

t² = x² + y² - 2xy * cos(T)

Substitute the known values in the above equation, so, we have the following representation

44² = 32² + 24² - 2 * 24 * 32 * cos(T)

Evaluate the products and exponents

1936 = 1600 - 1536 * cos(T)

So, we have

cos(T) = -336/1536

Divide

cos(T) = -0.21875

Take the arccos of both sides

T = 103

Hence, the angle is 103 degrees

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Answer:

Below

Step-by-step explanation:

12/5  * 875 = R 2 100 000

to see how this works, set up a ratio

5 is to 875 000   as  12 is to x

5 / 875 000    = 12/x

x = 12/5 * 875 000

Answer:

R210,000

Step-by-step explanation:

875,00 : 5 days

x :12 days

cross multiply:

87500*12 = 1050000

5*x = 5x

divide:

1050000/5 = 210000

Step-by-step explanation:

115 its rhe reuth i rhibk lol

Answer:

To find the cost of a hot dog and hamburger, we can set up a system of equations based on the information given. For example, let x be the cost of a hot dog and y be the cost of a hamburger. Then we have:

4x + 7y = 68 (equation 1)

7x + 3y = 67 (equation 2)

We can use substitution or elimination methods to solve the system of equations.

Substitution method:

Solve equation 1 for y in terms of x: y = (68 - 4x)/7

Substitute this expression into equation 2: 7x + 3((68 - 4x)/7) = 67

Simplifying and solving for x: 7x + 3(68 - 4x)/7 = 67

7x + 204 - 12x = 469

-5x = -401

x = 80

Substitute x = 80 back into equation 1: 4(80) + 7y = 68

320 + 7y = 68

7y = -252

y = -36

Therefore, the cost of a hot dog is $80, and the price of a hamburger is $-36 (which is not possible, it could be a typo or mistake in the given information)

Step-by-step explanation:

Evaluating the composition of functions in x = 1 gives:

f(g(1)) = 28

Here we have the two functions:

f(x) = 4x

g(x) = 2x + 5

And we want to find to find the composition f(g(x)), we will get:

f(g(x)) = 4*g(x)

Replacing g(x) there we will get:

f(g(x)) = 4*(2x + 5)

         = 8x + 20

Now we can evaluate that in x = 1, then we will get:

f(g(1)) = 8*1 + 20 = 28

That is what we wanted to find.

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The solution to the function's operation of h(x) is -0.25x + 2.

A function connects an element x to an element f(x) also known as (y) in another set. The domain of a function refers to the x-values and the range of the function is the set of values of f(x)  i.e. (the y-values) that are produced by the values in the domain of the function, which is the set of values of x.

Given that:

f(x) = 0.25x - 2

h(x) -f(x)

We are going to simply replace the value of f(x) with h(x), i.e.

h(x) = -(0.25x - 2)

h(x) = -0.25x + 2

Therefore, we can conclude that the solution to the function's operation of h(x) is -0.25x + 2.

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The statement is false the expression √3x is equivalent to the expression x√3.

A mathematical operation such as subtraction, addition, multiplication, or division is used to combine terms into an expression. In a mathematical expression, the following terms are used:

let us check by an example put the value of x = 3

√3x = x√3.

and, √3 x 3  = 3√3

and, √9 ≠ 3√3

Here we can see that the two values are not equal.

Thus, the statement is false the expression √3x is equivalent to the expression x√3.

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If Rahul is 1.45 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 31.55 meters. He stands 26.7 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow.  the height of the tree is 9.43m.

Let x represent the height

x /1.45 = 31.55 -26.7

Cross multiply

x = 31.55 × 1.45 / 4.85

x = 45.7475 /4.85

x = 9.43

Therefore the height is 9.43.

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