What is an equation of the line that passes through the points (-7, 3) and (5, 3)?

The complete proof using the AAS congruence postulate and CPCTC is explained below to show that QT ≅  SR.

When two angles of a triangle, and one of its side that is nonincluded are congruent to corresponding two angles and a nonincluded side in the another triangle, then both triangles are congruent by the AAS congruence postulate.

If two triangles are congruent, then all its corresponding parts are also congruent to each other based on the CPCTC theorem.

Below is the two-column proof that proves that side QT is congruent to side SR.

Statement                                     Reasons                                    

1. ∠R ≅ ∠T, QT ≅ SR                    1. Given

2. ∠TQS ≅ ∠RSQ                         2. Alternate interior angles

3. QS ≅ QS                                   3. Reflexive property

4. ΔTQS ≅ ΔRSQ                          4. AAS

5. QT ≅  SR                                   5. CPCTC

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[tex]{ \bold{ \sqrt[3]{V}}} [/tex]

Step-by-step explanation:

[tex]{ \green{ \sf{V = s³}}}[/tex]

Cube on both sides, then

[tex]{ \green{ \sf{s = \sqrt[3]{V}}}} [/tex]

The identification process of direct proportion, inverse proportion and partitive proportion is show below.

Proportion is comparison of things or magnitudes in terms of size, amount.

In direct proportion, when one quantity increase or decreases, the another quantity will also increase or decrease in the same ratio.

In inverse proportion, When one quantity increases, the another quantity decreases and vise versa.

Partitive proportion is when the division of a quantity into two or more equal or unequal parts.

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Answer:

h = 289 feet

Step-by-step explanation:

Comment

You need two givens to use in the formula to solve for the third.

Formula

v = sqrt(2*g*h)

Givens

V = 136 ft/s

g = 32 ft/s^2

h = ?

Solution

v = sqrt(2*g*h)                  Put the givens into the formula.

136 = sqrt(2* 32 * h)         Square both sides

136^2 = sqrt(2*32*h)^2   Expand

18496 = 64* h                  Divide by 64

18496/64 = 64*h/64  

289 feet = h

So the object must fall 289 feet before it reaches 136 m/s

Yes the miles driven and the amount of gasoline used can be said to have a causation as well as a correlation.

The strength and direction of a relationship between two or more variables are described by the statistical measure of correlation, which is given as a number. However, a correlation between two variables does not necessarily imply that a change in one variable is the reason for a change in the values of the other.

There is a causal relationship between the two occurrences, which means that causation shows that one event is the outcome of the occurrence of the other event. This concept is also known as cause and effect.

When the amount of gasoline is small, it would cause the miles covered to be just a few miles. Or if there is no gas, then no mile would be covered.

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Considering the definition of an inequality, the maximum number of people who can go to the amusement park is 4.

An inequality is the existing inequality between two algebraic expressions, connected through the signs:

An inequality contains one or more unknown values, in addition to certain known data.

Solving an inequality consists of finding all the values ​​of the unknown for which the inequality relation holds.

In this case, you know that:

Being "x" the maximum number of people who can go to the amusement park, the inequality that expresses the previous relationship is

10.50 + 23.50x ≤ 110

Solving:

23.50x ≤ 110 - 10.50

23.50x ≤ 99.50

x ≤ 99.50÷ 23.50

x ≤ 4.23

Finally, the maximum number of people  is 4.

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Answer:

x = 4, 2

Step-by-step explanation:

Answer:

The second option.

Step-by-step explanation:

We can figure this out by going down each option and checking if it works and is arranged from least to greatest.

The first option provides the numbers -3.5, -1/4, 2, 1/3 in that order.

This does not work because 1/3 is less than 1 which is less than 2. 1/3 should come before 2.

The second option provides the numbers -3.5, -1/4, 1/3, 2.

This option does work, because -3.5 is less than -1/4, -1/4 is less than 1/3 because it is negative, and 1/3 is less than 2.

If we look at this on a number line, the numbers that are smaller will appear farther to the left on the number line.

Answer: 0=1620=162

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The number of cells cut into two by the diagonal of the rectangle, found by using Pythagorean theorem, are approximately 51 cells

Pythagorean theorem can be expressed as the square of the hypotenuse side of a right triangle is equal to the sum of the square of the legs of the triangle.

The dimensions of the rectangle = 60 units by 40 units

The dimensions of each grid = 1 unit by 1 unit

The vertices of the rectangle are (0, 0), (60, 0), (60, 40), (0, 40)

The slope of the diagonal is therefore;

m = 40/(60) = 2/3

The equation of the line is; y - 0 = 2/3·(x - 0) = 2/3·x

y = 2/3·x
The number of cells in the diagonal is found using Pythagorean theorem as follows as follows;

Length the diagonal, l = √(60² + 40²) ≈ 72.1

Length of the diagonal of a unit = √(1 + 1) =√2

Number of units in the diagonal, n = 72.1/√(2) ≈ 51 units

The number of cells  cut into two ≈ 51 cells

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Answer:

The result is 2 hours

Hope this helped!

The p-value of the distribution of population standard deviation of 33.17 texts per day is 0.9435

The test statistic's "p-value" measures how likely it is that future results will be at least as extreme as the one your sample yielded. You must understand that the null hypothesis is the underlying presumption to compute this probability.

The parameters are as follows:

The sample mean ([tex]\bar x[/tex]) = 118.4

The population standard deviation ([tex]\sigma[/tex]) = 33.17

The sample size (n) = 30

Calculate the z-score first.

[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }[/tex]

according to the entire question, x = 128

So, we have:

[tex]z = \bold{ \frac{x - \bar x}{\frac{\sigma}{\sqrt{n} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{\sqrt{30} } } }\\\\z = \bold{ \frac{9.6}{\frac{33.17}{5.477 } } }\\\\z = \bold{ \frac{9.6}{ 6.056} }\\\\z = 1.5852[/tex]

As determined by the z table of probability, p = 0.9435395

or p = 0.9435 (approx.)

Consequently, the distribution's p-value is 0.9435.

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Option D is the right choice.

It is discovered through the use of conditional probability that there is a 0.4 = 40% chance that it will stop working in less than 2 years.

Conditional probability is a term used in probability theory to describe the likelihood that one event will follow another given the occurrence of another event.

Conditional Probability:
P (B / A) = P (A∩B) / P (A)

Here:

P(B / A) is the likelihood that event B will occur in the absence of event A.

P (A∩B) is the likelihood that both A and B will occur.

P(A) denotes the likelihood that A will occur.

As per the question:

Event A: Delivery was harmed.

Event B: Fails to function after less than two years.

P (A) = 0.1 due to the probability of being damaged during delivery being 0.1.

P (A∩B) = 0.04 because there is a 0.04 likelihood that it will be damaged during the delivery and stop working.

The likelihood under the condition is:

P (B / A) = P (A∩B) / P (A) = 0.04 / 0.1 = 0.4

0.4 = 40% chance that it will stop working in under two years.

Therefore, option D is correct.

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Answer:

Step-by-step explanation:

Expand: 36e^2+12e-48=e

Subtract e from both sides 36e^2+11e-48=0

Using the quadratic formula, e=(-11+-sqrt7033)/72

Answer: I think its B: x=-4

Step-by-step explanation:

The reduced fraction is 6/7 using GCF method.

What is GCF method?

The largest number, which is the factor of two or more number is called the Greatest Common Factor (GCF). It is the largest number (factor) that divide them resulting in a Natural number. Once all the factors of the number are found, there are few factors which are common in both. The largest number that is found in the common factors is called the greatest common factor. The GCF is also known as the Highest Common Factor (HCF)

Given,

the fraction = 24/28.

the factors of 24  = 2×2×2×3

The factors of 28 = 2×2×7

The gcf is 2 × 2 = 4

divide the denominator and numerator by 4

24 ÷ 4 = 6

28÷ 4 = 7

We get,

the fraction = 6/7.

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1. 3x + 9 = -4.5x + 20 ; This is true for one value of x.

2. 9(x + 3) = 9x + 12 ; This is true for no values of x.

3. 4(2x + 3) = 12 + 8x ; True for any values of x.

Given,

The equations;

1. 3x + 9 = -4.5x + 20

2. 9(x + 3) = 9x + 12

3. 4(2x + 3) = 12 + 8x

We have to find whether each equation is true for all, one or no values of x.

Here,

1. 3x + 9 = -4.5x + 20

Solve for x;

3x + 4.5x = 20 - 9

7.5x = 11

x = 11/7.5

x = 1.47

Then,

This is true for one value of x.

2. 9(x + 3) = 9x + 12

Solve using distributive property;

9x + 27 = 9x + 12

9x - 9x = 12 - 27

0 = -15

This is true for no values of x.

3. 4(2x + 3) = 12 + 8x

Use distributive property and solve;

8x + 12 = 12 + 8x

8x - 8x = 12 - 12

0 = 0

True for any values of x.

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The system of linear equations which is used to find number of 7 -inch plates ,x and 12- inch plates y is

x+y = 15 ---(1)

7x+12y = 144 ---(2)

In the given question we have following informations,

total number of plates in kitchen cabinet = 15

diameter of each plate either 7-inch or 12-inch.

let the number of plates in kitchen cabinet with Diameter 7-inch = x

and number of plates in kitchen cabinet with Diameter 12-inch = y

the diameter of all 15 plates combined = 144 inches

from the above details we can make a system of linear equations for two variables say x and y

x + y = 15 -----(1)

7x + 12y = 144 ---(2)

equation (1), (2) made the required system of equations.

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The Probability that someone holds b.s. degree if it is known that he or she earns more than $100,000 is 0.75.

Considering the values given in the question,

P(earns more than $100000 without college education) = 0.2

P(earns more than $100000 with a B.S. or higher degree) = 0.6

P(Has a B.S. degree) = 0.5

P(earns more than $100000) = P(earns more than $100000 | without college education) × P(without college education) + P(earns more than $100000 | with a B.S. or higher degree) × P(has a B.S. degree)

= 0.2 × (1 - 0.5) + 0.6 × 0.5

= 0.4

P(at least a B.S. degree | earns more than $100,000) = P(earns more than $100000 | with a B.S. or higher degree) × P(has a B.S. degree) / P(earns more than $100000)

= 0.6 × 0.5 / 0.4

= 0.75

Therefore, If a person's income above $100,000 is known, there is a 0.75  probability that they have at least a b.s. degree.

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Answer:

x = 1, -1

x = 6i, -6i

Answer:

1, -1, 6i, -6i

Step-by-step explanation:

An equation to determine the original price of the lawnmower discounted at 9% to $1,517.74 is B. y = 0.91x.

An equation summarizes a mathematical statement that equates two or more mathematical expressions.

Equations operate with values, numbers, and variables, using the equation symbol (=) and mathematical operands to establish the equality of values.

Discount offered = 9%

Amount paid for a lawnmower = $1,517.74

Original price = x

Discounted price, y = 0.91x

Y = 0.91x

1,517.74 = 0.91x

x = 1,667.85

Thus, the original price of the lawnmower is determined by Equation B.

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Answer:

four tablespoons to make 6 cups of popcorn.

Step-by-step explanation:

1.5 is nine Equals 2.25 x. And then divide both sides by 2.25. That gives you four tablespoons to make 6 cups of popcorn.

Answer:

y = x - 3

Step-by-step explanation:

y - y1 = m( x - x1 )

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

y + 2 = x - 1

y = x - 3

Using the exterior angles theorem, the measures of the named angles are:

m∠PQR = 51°

m∠PRQ = 96°

Based on the exterior angles theorem, the measure of the exterior angle of a triangle has an angle degree that is equal to sum of the interior angles of the triangle.

Therefore, the following equation would be set to find the value of x:

33 + 10x + 1 = 17x - 1

34 + 10x = 17x - 1

Combine like terms

34 + 1 = 17x - 10x

35 = 7x

35/7 = 7x/7

5 = x

x = 5

m∠PQR = 10x + 1 = 10(5) + 1 = 51°

m∠PRQ = 180 - (17x - 1) = 180 - (17(5) - 1) = 96°

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The numeric values for the population function are given as follows:

To obtain the numeric value of a function or of an expression, each instance of the input variable in the function or in the expression is replaced by the value at which we want to find the numeric value.

The function giving the population after t years is defined as follows:

[tex]P(t) = \frac{340}{1 + 6e^{-0.45t}}[/tex]

The initial population is the numeric value at t = 0, that is, the lone instance of t is replaced by zero, hence:

[tex]P(0) = \frac{340}{1 + 6e^{-0.45(0)}} = \frac{340}{7} = 49[/tex]

After eight years, the population is given by the numeric value at t = 8, hence:

[tex]P(8) = \frac{340}{1 + 6e^{-0.45(8)}} = 292[/tex]

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The correct selling price of the item has being solved as $20.04 The error that the manager has made is $12.04

Given that there is a markup, the item that is being sold for 12 dollars would be affected by the percentage of the mark up.

This mark up is a 67% markup

This would be solved as

12$ + 67% of 12$

= $12 + 8.04

= $20.04

Hence the correct selling price is $20.04

Next we would have to find the likely error that the manager has made

= $20.04- ​$8

= $12.04

The likely error of the manager is $12.04

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Answer:

1.5

Step-by-step explanation:

3÷2=1.5

The dimensions of the rectangle that will allow for the most economical fence to be built is 50 feet and 25 feet in length and width respectively.

Given in the question,

Area = 1250 ft²

The three sides cost $3 per foot, and the fourth side costs $9 per foot.

Let x and y be the length and width of the rectangle.

Because the area is 1250 ft², therefore

xy = 1250, or

y = 1250/x            

Case 1: Three sides are (x,y,x) and the 4-th side is y.

The cost is

C = 3(2x +y) + 9y

  = 6x + 12y

  = 6x + 12(1250/x)

  = 6x + 15000/x

For C to be minimum, C' = 0. That is

6 - 15000/x² = 0

x² = 15000/6

x =  50 ft, y = 1250/50 = 25 ft

C = 6(50) + 15000/(50²) = $600

Case 2: Three sides are (y,x,y) and the 4-th side is x.

The cost is

C = 3(x + 2y) + 9x

   = 12x + 6y

   = 12x + 6(1250/x)

   = 12x + 7500/x

For C to be minimum, C' = 0.

12 - 7500/x² = 0

x² = 7500/12 = 625

x = 25 ft, y = 50ft

C = 12(25) + 7500/25 = $600

Thus, the Dimensions will be 25 feet and 50 feet.

Question:

A fence is to be built to enclose a rectangular area of 1250 square feet. the fence along three sides is to be made of material that costs ​$3 per foot. the material for the fourth side costs ​$9 per foot. find the dimensions of the rectangle that will allow for the most economical fence to be built.

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The GCF of the number given as 45 and 27 is 9 and the factored expression is 9(5 - 3)

From the question, we have the following statement

The greatest common factor of 45 and 27

Rewrite the given expression as follows

This is represented using

45 and 27

Factor out 3 from the expression

So, we have the following representation

15 and 9 => Factored 3

Factor out 3 from the expression

So, we have the following representation

5 and 3 => Factored 3 * 3

So, we have

Factored = 3 * 3 = 9

This represents the GCF

So, the GCF is 9

In (a), we have

5 and 3 => Factored 3 * 3

This means that

45 - 27 = 3 * 3(5 - 3)

Evaluate the product

45 - 27 = 9(5 - 3)

Hence, the factored expression is 9(5 - 3)

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