Find the mising reason in the proof.
Given: two parallel lines cut by a transversal, m26 = 3x, and m28 = 99°
Prove: x = 33
Proof:
Statements
1. m26 = 3x, m28 = 99°
2. m26 = m28
3. 3x = 99
4.と=33
9.
2
7
3
4
5
6
8
Reasons
Given
?
Substitution
Division Property

taking

Y=2x+3____(1)

Y=-3x+3____(2)

making take equation 1 and equate to 2 since y=2x+3

2x+3=-3x + 3

2x+3x=3-3

5x=0 so

substitute x=0 in equation(2)

y=-3(0)+3

y=3

Here are the correct matches to the expressions to their solutions.

The GCF of 28 and 60 is 4.

(-3/8)+(-5/8) = -4/4 = -1.

-1/6 DIVIDED BY 1/2 = -1/6 X 2 = -1/3.

The solution of 0.5 x = -1 is x = -2.

The solution of 1/2 m = 0 is m = 0.

-4 + 5/3 = -11/3.

-2 1/3 - 4 2/3 = -10/3.

4 is not a solution of -4 < x.

1. The GCF of 28 and 60 is 4.

The greatest common factor (GCF) of two numbers is the largest number that is a factor of both numbers. To find the GCF of 28 and 60, we can factor each number completely:

28 = 2 x 2 x 7

60 = 2 x 2 x 3 x 5

The factors that are common to both numbers are 2 and 2. The GCF of 28 and 60 is 2 x 2 = 4.

2. (-3/8)+(-5/8) = -1.

To add two fractions, we need to have a common denominator. The common denominator of 8/8 and 5/8 is 8. So, (-3/8)+(-5/8) = (-3 + (-5))/8 = -8/8 = -1.

3. -1/6 DIVIDED BY 1/2 = -1/3.

To divide by a fraction, we can multiply by the reciprocal of the fraction. The reciprocal of 1/2 is 2/1. So, -1/6 DIVIDED BY 1/2 = -1/6 x 2/1 = -2/6 = -1/3.

4. The solution of 0.5 x = -1 is x = -2.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate x by dividing both sides of the equation by 0.5. This gives us x = -1 / 0.5 = -2.

5. The solution of 1 m = 0 is m = 0.

To solve an equation, we can isolate the variable on one side of the equation and then solve for the variable. In this case, we can isolate m by dividing both sides of the equation by 1. This gives us m = 0 / 1 = 0.

6. -4 + 5/3 = -11/3.

To add a fraction and a whole number, we can convert the whole number to a fraction with the same denominator as the fraction. In this case, we can convert -4 to -4/3. So, -4 + 5/3 = -4/3 + 5/3 = -11/3.

7. -2 1/3 - 4 2/3 = -10/3.

To subtract two fractions, we need to have a common denominator. The common denominator of 1/3 and 2/3 is 3. So, -2 1/3 - 4 2/3 = (-2 + (-4))/3 = -6/3 = -10/3.

8. 4 is not a solution of -4 < x.

The inequality -4 < x means that x must be greater than -4. The number 4 is not greater than -4, so it is not a solution of the inequality.

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Answer:

Hi! The answer to your question is \(X = 3\)

Step-by-step explanation:

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Hope this helps!!

- Brooklynn Deka

Answer:

height = 5 cm

Step-by-step explanation:

a cube has congruent sides (s)

the volume (V) of a cube is calculated as

V = s³

given V = 125 , then

s³ = 125 ( take cube root of both sides )

\(\sqrt[3]{s^3}\) = \(\sqrt[3]{125}\) = \(\sqrt[3]{5^3}\)

s = 5

then height = 5 cm

Answer:

8/3 or 2 2/3

Step-by-step explanation:

Answer:

There are 55 sweets in total.

Step-by-step explanation:

The total number of sweets is t.

Henry, Brian and Colin share some sweets in the ratio 6:4:1.

This means that Henry earns \(\frac{6}{6+4+1} = \frac{6}{11}\) of the total(t).

Brian earns \(\frac{4}{11}\) of the total.

Colin earns \(\frac{1}{11}\) of the total

Henry gets 25 more sweets than Colin.

Henry earns \(\frac{6t}{11}\)

Colin earns \(\frac{t}{11}\)

So

\(\frac{6t}{11} = \frac{t}{11} + 25\)

Multiplying everything by 1

\(6t = t + 275\)

\(5t = 275\)

\(t = \frac{275}{5}\)

\(t = 55\)

There are 55 sweets in total.

Answer:

100km

Step-by-step explanation:

Answer:

100

Step-by-step explanation:

Notice that at x_0,

Therefore,

The answer is option C), g(x)=f(x)-2

Answer:

A ≈ 240.26

Step-by-step explanation:

Googs

Answer: 0

Explanation: Divide 2 and 11, and you get 2/11 and multiply that with 55 you get 10 and 10 - 10 equals 0! ^^

Answer:

The answer to this question your asking is b

Answer:

2x² + 5x + c = 0

For this quadratic equation to have one double root, the discriminant must equal 0.

5² - 4(2)(c) = 0

25 - 8c = 0

c = 25/8

2x² + 5x is not a perfect square because the coefficient of x², 2, is not a perfect square.

2x² + 5x is not a perfect square.

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The measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees

To find the measure of the angle to the nearest degree given trigonometric ratios, we can use inverse trigonometric functions.

Here are the steps to determine the angles:

a) sin A = 0.6018

Taking the inverse sine (arcsin) of both sides:

A = arcsin(0.6018)

Using a calculator, we find A ≈ 36 degrees (rounded to the nearest degree).

b) cos B = 0.9205

Taking the inverse cosine (arccos) of both sides:

B = arccos(0.9205)

Using a calculator, we find B ≈ 23 degrees (rounded to the nearest degree).

c) tan C = 0.0349

Taking the inverse tangent (arctan) of both sides:

C = arctan(0.0349)

Using a calculator, we find C ≈ 2 degrees (rounded to the nearest degree).

Therefore, the measures of the angles to the nearest degree are:

a) A ≈ 36 degrees

b) B ≈ 23 degrees

c) C ≈ 2 degrees.

Note: Trigonometric functions have periodicity, meaning there may be multiple angles with the same trigonometric ratio.

To determine the principal angle within a specific range, we use the inverse trigonometric functions.

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Answer:

20

Step-by-step explanation:

(15+35) * 0.4 = 50 * 0.4 = 20

The estimation of the numbers given as 0.87 × 310 will give 270.

You must approximate (eliminate or round off) the decimals to obtain whole numbers before you can use the whole numbers to find the product of two decimals using estimation.

A figure is discovered through estimation.

A value, amount, or size that rounds off to the nearest whole number is said to be approximating.

The estimation of the numbers given as 0.87 × 310 will give:

= 0.9 × 300

= 270.

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Complete Question

How large a sample is needed if we wish to be 96% confident that our sample proportion in Exercise 9.53 will be within 0.02 of the true fraction of the voting population?

Exercise 9.53

A. A random sample of 200 voters in a town is selected, and 114 are found to support an annexation suit. Find the 96% confidence interval for the fraction of the voting population favoring the suit.

B. What can we assert with 96% confidence about the possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57?

Answer:

The First question

                    \( n = 1879  \)

A

    The 96% confidence interval is  

                      \(0.51 <  p <  0.63 \)

B

   The possible size of our error if we estimate the fraction of voters favoring the annexation suit to be 0.57 is  

           \(E =    0.06 \)

Step-by-step explanation:

From the question we are told that

    The margin of error is  \(E = 0.02\)

     The sample size is  n =  200

     The number that supported the annexation suit is  k = 114

Considering the first question

Generally our sample in Exercise 9.53 is  \(\^ p = 0.57\)

From the question we are told the confidence level is  96% , hence the level of significance is    

      \(\alpha = (100 - 96 ) \%\)

=>   \(\alpha = 0.04\)

Generally from the normal distribution table the critical value  of  \(\frac{\alpha }{2}\) is  

   \(Z_{\frac{\alpha }{2} } =  1.751 \)

Generally the sample size is mathematically represented as  

    \(n = [\frac{Z_{\frac{\alpha }{2} }}{E} ]^2 * \^ p (1 - \^ p ) \)

=>  \(n = [\frac{1.751}{0.02 } ]^2 * \^ p (1 - \^ p ) \)

=>  \(n = [\frac{1.751}{0.02 } ]^2 * 0.57  (1 -0.57  ) \)

=>  \( n = 1879  \)

Considering question B

Generally the margin of error is mathematically represented as  

     \(E =  Z_{\frac{\alpha }{2} } * \sqrt{\frac{\^ p (1- \^ p)}{n} } \)

=>  \(E =    1.751 * \sqrt{\frac{ 0.57  (1- 0.57 )}{200} } \)

=>  \(E =    0.06 \)

Considering question A

Generally the sample proportion of the number that supported the annexation suit is mathematically represented as

        \(\^ p = \frac{114}{200}\)

=>      \(\^ p = 0.57\)

Generally 96% confidence interval is mathematically represented as  

      \(\^ p -E <  p <  \^ p +E\)

=>  \(0.57  - 0.06 <  p <  0.57  + 0.06 \)

=>  \(0.51 <  p <  0.63 \)

Answer:

x = 15

Step-by-step explanation:

the segment inside the triangle is an angle bisector and divides the side opposite the bisected angle into segments that are proportional to the other two sides, that is

\(\frac{x}{21-x}\) = \(\frac{25}{10}\) ( cross- multiply )

10x = 25(21 - x)

10x = 525 - 25x ( add 25x to both sides )

35x = 525 ( divide both sides by 35 )

x = 15

Answer:The area of the parking lot is length * width. If the width of the parking lot is 8 yards, the area of the parking lot can be represented by the inequality:

Area <= 80

length * 8 <= 80

To get the possible lengths of the parking lot we need to divide both sides by 8:

length <= 10

Therefore, the inequality that describes the possible lengths of the parking lot (in yards) is:

length <= 10 yards

The possible lengths of the parking lot is any value less than or equal to 10 yards.

Step-by-step explanation:

-a2b²c²(a+b-c) =

Use distributive rule

a•(b+c) = ab + ac

Then

-a^2b^2c^2 •a= -a^3•b^2•c^2

-a^2b^2c^2 •b = -a^2•b^3•c^2

-a^2b^2c^2 •(-c)= a^2•b^2•c^3

Step-by-step explanation:

Step 1- convert 25% into a decimal

Step 2- Multiply 34,400.00 x 0.25

            Which should give you $8600.00

Step 3- Then subtract 34,400.00 from 8600.00

              Which will give you $25800.0

The The thing to remember is Multiply with the discount then subtract your answer from the original price of the item.

Hope This Helps !!

Answer:

A B D

The sum of the function and its additive inverse is 0.

The function and its additive inverse have symmetry over the x-axis.

The product of the function and its multiplicative inverse is 1.

Step-by-step explanation:

Answer:

The correct answers are:

A, B, and D.

Step-by-step explanation:

Edge 2020

Answer:

  (c)  8 jars

Step-by-step explanation:

You want to know the number of 1.25 quart jars that can be filled from a 2.5 gallon container.

The number of jars can be found from ...

  (2.5 gal) × (4 qt/gal) × (1 jar)/(1.25 qt) = (2.5·4/1.25) jars = 8 jars

Lorraine can fill 8 jars from the 2.5 gallon pot.

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Step-by-step explanation:

the area of a triangle is

baseline × height / 2

so, we only have to sum all 6 triangles and the base area :

6 × 6×8/2 + 93.5 = 36×4 + 93.5 = 144 + 93.5 =

= 237.5 in²

Answer:

a. Population -  1. the 52 water draws

b. Sample -  4. 7/52 lead measurements

c. Parameter -   2. 7 micrograms per deciliter

d. Statistic -  3. 5 micrograms per deciliter

Step-by-step explanation:

If the value is from a population, it is a parameter.

Otherwise, if the value is from a sample, it is a statistic.

A population is an entire group of people, or of something, while a sample is a small number of observations from this group.

In this question:

The entire population is the measures drawn from the 52 points in the city's system.

In the entire system, the average is no more than 7 micrograms per deciliter. This is a value from the entire population, so this is a parameter.

To found the average of 5 micrograms, she took 7 of these measurements. So the 7 measurements are the sample and the average os 5 micrograms is a statistic.

So the correct matching is:

a. Population -  1. the 52 water draws

b. Sample -  4. 7/52 lead measurements

c. Parameter -   2. 7 micrograms per deciliter

d. Statistic -  3. 5 micrograms per deciliter

The transformation from the graph of f(x) = x to the graph of g(x) = (1/9)·x -2, is a rotation and a translation. The correct option is therefore;

The transformation are a rotation and a translation

A translation transformation is a transformation in which there is a displacement of all points on the preimage figure in a specified direction.

The transformation from f(x) = x to f(x) = (1/9)·x - 2, includes a slope reduction by a factor of (1/9), or rotating the graph of f(x) = x in the clockwise direction, and a translation of 2 units downwards, such that the y-intercept changes from 0 in the parent function, f(x) = x to -2 in the specified function f(x) = (1/9)·x - 2, therefore, the translation includes a rotation clockwise and a translation downwards by two units

The correct option is the second option; The transformation are a rotation and a translation

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