Find the measurement of the angle indicated for the trapezoid.
*

Answer:

39

Step-by-step explanation:

1) Remove parentheses.

18 + 21

2) Simplify.

39

Thanks,
Eddie

Quick hint:

When there is a number and then a - sign outside the parenthesis and on the inside, then it creates a figure similar to the plus sign, that is when you just make it one.

Add the two numbers (both are always positive in this instance),

and there's your answer!

Answer:

a = 3

Hope this helps :)

Explanation and Check part below.

Step-by-step explanation:

1. Isolate the variable by doing the inverse operation which is in this case subtracting 2 on both sides of the equation.

a + 2 = 5

- 2 - 2

a = 3

Check:

1. Substitute a with the solution 3.

3 + 2 = 5

5 = 5 ✓

Rounding to an estimate, Sachin will have enough gas to go to both places before he runs out of gas.

An estimate is an equivalent numerical value obtained by rounding off.

The result of an estimate is not an exact value.  The value represents the nearest rounded value.

For instance, 75.9% can be estimated or rounded off to 76%.  32 minutes can be rounded off or approximated to ¹/₂ hour.

Driving distance before getting gas = 110 miles

The distance to his friend's house = 67 miles

The distance to his mom's house = 32 miles

The total distance to be covered on the available gas = 99 miles

Estimated distance to be covered = < 100 miles

Thus, using estimation, Sachin will still have more than 10 miles to drive before he gets gas.

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The line of reflection of the given congruent angles is the y-axis.

A line of reflection is defined as a line that lies in a position between two identical mirror images so that any point on one image is the same distance from the line as the same point on the other flipped image

Now, from the attached image, we see that the two given congruent triangles are; ΔAHJ and ΔADB

Now, we see that the coordinates are transformed as folllows;

D(5, 2) → H(-5, 2)

B(3, 0) → J(-3, 0)

Now, this type of transformation follows the transformation rule; (x, y) → (−x, y). This means it was reflected over the y-axis.

This the line of reflection of the given congruent angles is the y-axis.

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The length of time that it cost less to move good across town will be more than 2.36 hours.

From the information, ACME movers charges $59 plus $20 per hour to move household goods across town and Hank movers charges $45 per hour.

Let the number of hours be represented by h.

Therefore, the appropriate equation will be:

59 + 20h = 45h

Collect like terms

45h - 20h = 59

25h = 59

h = 59/25

h = 2.36 hours.

Therefore, the length of time that it cost less to move good across town will be more than 2.36 hours.

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ACME movers charges $59 plus $20 per hour to move household goods across town. Hank movers charges $45 per hour. For what length of time does it cost less to move good across town?

During an isosceles triangle two angles are identical, adding up to a total of 180, and its x value is 78.

Isosceles triangle: what is it?

In geometry, an isosceles triangle is one with at least two sides of equal length. There are two ways to define it: either as having precisely two sides of equal length or at least two sides of equal length, with the equilateral triangle being an exception to the second definition.

The aforementioned claim states that a triangle's total number of angles is 180.

the total of all angles in a triangle is 180.

⟹24+x+x=180

24+2x=180

12+x=90

x=90−12

x=78

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Answer:

10 분

Step-by-step explanation:

Answer:

The equation for this line is (P(x,y)----> P'(2h-x,2k-y), hence h=3 and k=1/2

Step-by-step explanation:

P(x,y)----> P'(2h-x,2k-y)

P(-4,-4)---->P'(8,5)

Now comparing the corresponding sides;

2h+4=8

2h=8-4

2h=4

h=2

Again,

2k-y=5

2k+4=5

2k=5-4

2k=1

k=1/2

Now, checking the answer:

P(-4,-4)----->P'{2*2-(-4),2*1/2-(-4)}

=P'(4+4,1+4)

=P'(8,5)

Step-by-step explanation:

a1 = 2

a2 = a1 + 9 = 2 + 9 = 11

a3 = a2 + 9 = 20

a4 = a3 + 9 = 29

a5 = a4 + 9 = 38

a6 = a5 + 9 = 47

It is true. For all rational numbers a and b, a−b = a + (−b).

Given that,
To determine whether the statement, "For all rational numbers a and b, a−b = a + (−b)." is true or false.

In mathematics, a rational number is a number that can be described as the result of a fraction of value or does not have face value.

Here,
= a + (-b)
Since in the parenthesis there is a negative value, when we open the parenthesis the sign of the arithmetic operator will change accordingly,
So,
= a - b
So, the condition is true for all rational numbers.

Thus, It is true. For all rational numbers a and b, a−b = a + (−b).

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The interval notation that expresses the statement is (-∝, 1]

The statement is given as:

The set of all numbers less than or equal to 1

The above can be represented as:

<= 1

Represent the set with variable x

So, we have

x <= 1

As an interval notation, we have (-∝, 1]

Hence, the interval notation that expresses the statement is (-∝, 1]

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Answer:

D. 27,468

Step-by-step explanation:

654

x42

--------

1,308

+26,160

---------

27,468

Answer:

A negative exponent flips the fraction and turns the exponent positive, and vice versa.

1/121 = 1/1211 = 121-1

As an example, 5-2 = 1/25, and 1/5-2 = 25.

The rate unit of the cost of the juice bought by Megan is  $1.28 per quart.

For the given question;

The price of 2-quart bottle of juice bought by Megan = $2.56.

For calculating the price of 1 bottle, simply divide the total cost by number of bottles.

Price of a single quart bottle = $2.56/2.

Price of a single quart bottle = $1.28 per quart.

Thus, the price of single quart bottle of juice is 1.28 per quart.

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42 bologna sandwiches were made

The ratio is given as

Cheese : Bologna : Peanut butter = 5 : 7 : 8

Also, we have

Total = 120 sandwiches

The number of bologna sandwiches made is calculated using

Bologna = bologna ratio/total ratio * 120

So, we have

Bologna = 7/(5 + 7 + 8) * 120

Evaluate

Bologna = 42

Hence, 42 bologna sandwiches were made

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Answer:3

Step-by-step explanation:

The value of the constant k such that the system has infinitely many solutions is; -2.

It follows from the task content that the system of equations given upon observation are multiples.

Hence, by multiplying the second equation by -2; we have;

-4x +6y = 4

-4x +6y = -2k

Hence, for the system to have infinitely many solutions; 4 = -2k.

Ultimately, k = -2 by dividing both sides of the equation above by -2.

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Answer: 87.96 km

Step-by-step explanation:

10.3% of 853.93km= 87.96 km

The approximate no . of miles Philip traveled are 4 . 98 * ( 10 ^ 5 ) miles .

Given : the circumference of earth 2.49 x ( 10^4 ) miles

To calculate :  the approximate number of miles Philip traveled

Philip  traveled 20 times

⇒ 20 * circumference of circle

⇒ 20 * [ 2.49 x ( 10^4 ) ]

  ( 2 * 2.49 ) * ( 10 ^ 5 )

= 4 . 98 * ( 10 ^ 5 )

Hence , the approximate no . of miles Philip traveled are 4 . 98 * ( 10 ^ 5 ) miles .

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Answer:

Step-by-step explanation:

Let the hours of actual work be x and total charge be y.

Total amount of charge is:

Total amount of charge is:

Since y is same for both companies, set the equation and solve for x:

a) A minimum of number of dogs that could have a mass of more than 24 kg is 6.

b) The maximum number of dogs that could have a mass of more than 18 kg is 20.

Rearrange the function using fundamental algebraic concepts to get the value of x when the derivative equals 0. This response gives the x-coordinate of the function's vertex, which is where the maximum or minimum will occur. To find the minimum or maximum, rewrite the solution into the original function.

The minimum of the values present in the interval 20 to 40 is 6

The maximum of the values present in the interval 20 to 40 is (12+6) = 18

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The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.

The catering cost was determined if the cost per person is R 225,00.​

The cost per person = 225,00 R

To calculate the cost per unit, add all of your fixed costs and all of your variable costs together and then divide this by the total amount of units you produced during that time period.

Let us assume,

Suppose you can find the cost for 50 people.

Then,

We can write,

Catering cost = x

x = 225,00 * 50

x = 1,125,000 R

Therefore,

The catering cost was determined if the cost per person is R225,00. then the cost of 50 people is equal to = 1,125,000 R.

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Answer:

400

Step-by-step explanation:

[tex]R(x)=\frac{2000x^2}{x^2+4}[/tex]

Since x represents the number of years since publication, the revenue at the end of the first year would be found by just plugging in 1 into the function.

[tex]R(1)=\frac{2000(1)^2}{(1)^2+4} \\\\R(1)=400[/tex]

As a result, 95% of the students had grade point averages ranging from 1.83 to 3.39.

A normal distribution is a data set design in which the majority of values cluster around the middle of the range and the remainder taper off symmetrically toward either end.

The normal distribution is also known as the bell curve because the probability density graph resembles a bell. It is also known as the Gaussian distribution, after German mathematician Carl Gauss, who described it initially.

A bell-curve distribution is a normal Distribution.

Let X be the grade point averages of undergraduate students at one university.

X ~ Normal Distribution(2.61,(0.39)2)

P(1.83 < X < 3.39)

= P(X < 3.39) - P(X < 1.83)

= P((X - μ)/σ < (3.39 - 2.61)/.39) - P(((X - μ)/σ)< (1.83 - 2.61)/039)

= P(z < 2) -P(z < -2)

= P(-2 < z < 2)

Thus, given a regular normal distribution (μ=0, σ =1), z is between 2 standard deviations away from the mean.

According to the Empirical Rule, 95% of the data obtained after a normal distribution is within two standard deviations of the mean.

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Step-by-step explanation:

Given that

To find

So, according to the question

we have,

We know that,

  Probability P(E) = [tex]\frac{possible\;events}{no.\;of\;events}[/tex]

There is,

possible event is 1, and no. of events are 5.

So, we can say that

   [tex]P(E) = \frac{1}{5}[/tex]

Answer:

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The area of the rectangle is 10x² - 13x - 3.

It should be noted that the area of a rectangle is the length multiplied by the width.

Here, the dimensions of a rectangle are 2x-3 and 5x+1.

The area will be:

= (2x - 3)(5x + 1)

= 10x² + 2x - 15x - 3

= 10x² - 13x - 3

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