Analyze the diagram below and complete the instructions that follow.
10
6
B.
'C С
8
Find sin ZA
A 3
5
B. 4
C 1

By using the corresponding angles theorem we can see that (6x - 5)° and (x - 25)° are supplementary angles, so they add up to 180°.

This means that:

(6x - 5) + (x - 25) = 180

7x - 30 = 180

7x = 210

x = 30

If you want to find the exact values of the angles, just plug x = 30 into the angle values! :)

Answer:

x=19°

Step-by-step explanation:

Line n and l form a right angle. We know that because line m and l are parallel to each other and line n crosses through them as a vertical line.

Right angles always add up to 90°.

So, Angle 1 add Angle 2 equals 90°.

4x+9+x-14=90°

Collect the like terms:

Like terms are terms with the same variables and powers.

4x+x=5x

9-14= -5

Form an equation:

5x-5=90°

Do inverse operations to isolate x.

90+5=95°

95÷5=19° (We divide by 5 because, in algebra, when a number is next to a letter, it means times, so we have to do the opposite and divide).

So, x=19°

Hope this helps :)

Answer:

C.

Step-by-step explanation:

212/4 = 53, so 53/1, or 53 miles are driven every hour.

Answer: [tex]a=\sqrt{60}[/tex]

Step-by-step explanation:

To solve for a, we want to use Pythagorean Theorem as provided int eh problem. a and 2 are the legs while 8 is the hypotenuse.

[tex]a^2+2^2=8^2[/tex]           [exponent]

[tex]a^2+4=64[/tex]            [subtract both sides by 4]

[tex]a^2=60[/tex]                  [square root both sides]

[tex]a=\sqrt{60}[/tex]

Now we know that [tex]a=\sqrt{60}[/tex].

Answer:

let the sides be 25x,12x and 5x ......then

25x+12x+5x=540

45x=540

x=25

sides are 25×12=300

12×12=144

5×12=60

we can find area by herons formula

the students took math and physics = 55

Answer:

30

Step-by-step explanation:

First, we can say that because the men do 1/3 of the work in 20 days,

for 10 men:

20 days = 1/3 total work

Because we need the house built in 30 days, and 20 days have already passed, we only have 30-20=10 days left. Furthermore, 20/2=10, so in our equation of 20 days = 1/3 total work, we can divide both sides by 2 to get

10 days = 1/6 total work

The amount of work we need to get done in 10 days is (all of it) - (1/3 of total work) = 1 - 1/3 = 2/3 = 4/6

Since 10 men can do 1/6 of the work in 10 days, 10*4 =40 men can do 1/6 * 4 = 4/6 of the work in 10 days. This is the amount of work that needs to get done. Therefore, the contractor needs 40 (total workers) - 10 (current workers) = 30 new workers to finish the remaining work in due time

Answer:

12:05 pm

Step-by-step explanation:

Let z be the number of hours, from 11:00 am, when Jimmy would catch up with John. The time that Jimmy will have to drive to catch up with John is z - 1/4 as he started a quarter of an hour late. When Jimmy would catch up with John, they would have traveled the same distance. Hence

50 z = 65 (z - 1/4)

Solve for t

50z = 65z - 65/4

z = 65/60 = 1.083 hours = 1 hour and 5 minutes

Jim will catch up with John at

11:00 am + 1 hour 5 minutes = 12:05 pm

Answer From Gauth Math

Answer:

160π in²

Step-by-step explanation:

The formula for the surface area of a cylinder is: A = 2πrh + 2πr²

From here we can plug in what we know (r = 4, h = 16):

A = 2π(4)(16) + 2π(4²)

A = 128π + 32π

A = 160π in²

The surface area of a cylinder is 160π in².

The surface area of a cylinder is also called the total surface area of the cylinder.

Suppose that:

Radius of the considered cylinder = 'r' units

Height of the considered cylinder = 'h' units

The formula for the surface area of a cylinder is:

A = 2πrh + 2πr²

From here we can plug in what we know that,

(r = 4, h = 16):

A = 2π(4)(16) + 2π(4²)

A = 128π + 32π

A = 160π in²

Hence, the surface area of a cylinder is 160π in².

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Answer:

1g - 50 = p(g)

Step-by-step explanation:

The profit function is,

⇒ p(g) = g - 50

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Betty sets up a lemonade stand and charges $1 per glass.

It cost her $50 to set up the stand.

And, We have to find the function gives the profit, p, she makes by selling g glasses of lemonade.

Now, The number of glasses of lemonade sold = g,  

And, A profit, p by function p(g)

Setup cost = $50

Since, Charges for 1 glass  = 1 $

Hence, Charges for g glasses = 1.g  = $g

Here, The cost = $50  

Hence, Profit  = $g - 50

⇒ p(g)  =  g - 50  

Therefore, The profit function is,

⇒ p(g) = g - 50

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Answer:

x = 7.75       y = -0.125

Step-by-step explanation:

3x + 2y = 23                         1/2x - y = 4

2(1/2x - y) = (4)2                   1x - 2y = 8

    3x + 2y = 23

+   1x - 2y = 8

4x = 31

x = 7.75

3(7.75) + 2y = 23

23.25 + 2y = 23

2y = -0.25

y = -0.125

Answer:

the number is 2.45

Step-by-step explanation:

let the original number = n

[tex]\frac{n^4}{n/2} = \frac{2n^4}{n} = 2n^3\\\\2n^3 + \frac{141}{2} = 100\\\\4n^3 + 141= 200\\\\4n^3 = 200 - 141\\\\4n^3 = 59\\\\n^3 = \frac{59}{4} \\\\n^3 = 14.75\\\\n = \sqrt[3]{14.75} \\\\n = 2.45[/tex]

Therefore, the number is 2.45

Answer: x = -3

[tex]2x+6=0\\\\2x=-6\\\\x=\frac{-6}{2} =-3[/tex]

Answer:

x= -3

Step-by-step explanation:

Solve the equation:

2x +6 = 0

We have isolate 'x'.

First subtract 6 from both sides

2x = 0-6

2x = -6

Divide each side by 2

x = -6/2

x = -3

The transformation that maps the pre-image to the image is given as follows:

Dilation.

The four types of transformation listed in this problem cause these following changes:

From the image, we get that the side lengths were doubled, while the angle measures remained constant, meaning that the transformation is a dilation and the first option is the correct option.

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Answer:

dilation

Step-by-step explanation:

took the test

Answer:

MO, NO, MN

Step-by-step explanation:

First, we can identify this triangle as a right triangle, as given by the square next to the O. Next, we know that a right angle is equal to 90 degrees, and the sum of the angles of a triangle is equal to 180 degrees.

Therefore,

∠M + ∠O + ∠N (the angles of the triangle) = 180

49 + 90 + ∠N = 180

139 + ∠N = 180

subtract both sides by 139 to isolate the variable

∠N = 41

Therefore, ∠N is 41 degrees.

In a triangle, given the angles, we know that the side opposite the smallest angle is the side with the smallest length and so on.

Our angle lengths are

41, 49, and 90 degrees in order.

Therefore, the side opposite the largest angle (90 degrees, or ∠O) is the longest side. This is MN. Similarly, ∠N is the smallest angle, and the side opposite of that (MO) is the shortest side. This leaves NO to be in the middle

When a line is rotated, it is rotated about a fixed point to its new position. Line AB must turn 180 degrees about point A to coincide with line AE.

The complete question is that we determine the angle which AB will turn to, about point A to align with AE (see attachment for the figure)

Line AB and AE form a straight line. This means that the angle between these two lines on either side of point A is [tex]180^o[/tex]

So for line AB to coincides with line AE, the line AB must turn 180 degrees about point A.

Hence, option (B) is correct.

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Answer:

b, c, d

Step-by-step explanation:

Answer:

0.04

Step-by-step explanation:

2 / 50 is the same as 1 / 25.

1 / 25 = 0.04

Answer:

0.04

Step-by-step explanation:

Answer:

0.8716 = 87.16% probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

Step-by-step explanation:

For each customer, there are only two possible outcomes. Either they order a nonalcoholic beverage, or they order an alcoholic beverage. The probability of a customer ordering a nonalcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.

[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]

And p is the probability of X happening.

At a Noodle & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 0.43.

This means that [tex]p = 0.43[/tex]

Find the probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

This is:

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]

In which

[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]

[tex]P(X = 0) = C_{7,0}.(0.43)^{0}.(0.57)^{7} = 0.0195[/tex]

[tex]P(X = 1) = C_{7,1}.(0.43)^{1}.(0.57)^{6} = 0.1032[/tex]

[tex]P(X = 2) = C_{7,2}.(0.43)^{2}.(0.57)^{5} = 0.2336[/tex]

[tex]P(X = 3) = C_{7,3}.(0.43)^{3}.(0.57)^{4} = 0.2937[/tex]

[tex]P(X = 4) = C_{7,4}.(0.43)^{4}.(0.57)^{3} = 0.2216[/tex]

Then

[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0195 + 0.1032 + 0.2336 + 0.2937 + 0.2216 = 0.8716[/tex]

0.8716 = 87.16% probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.

Answer:

(x-5)(x+2)(x+4)

Step-by-step explanation:

I just did It

Answer:

PR = 39 cm

Step-by-step explanation:

Using Pythagoras' identity in the right triangle

PR² + PQ² = QR² , that is

PR² + 80² = 89²

PR² + 6400 = 7921 ( subtract 6400 from both sides )

PR² = 1521 ( take the square root of both sides )

PR = [tex]\sqrt{1521}[/tex] = 39

Answer:

[tex]PR=39[/tex]

Step-by-step explanation:

The triangle (PQR) is a right triangle. This means the triangle has a (90) degree angle, such is indicated by the box around one of the angles in the triangle. One of the properties of the sides of a right triangle is the Pythagorean theorem. The Pythagorean theorem states the following:

[tex]a^2+b^2=c^2[/tex]

Where (a) and (b) are the legs of the right triangle, or the sides adjacent to the right angle. (c) is the side opposite the right angle of the triangle triangle, in other words, the hypotenuse. Substitute the respective legs into the formula for the Pythagorean theorem and solve for the unknown,

[tex]a^2+b^2=c^2[/tex]

Substitute,

[tex]a^2+b^2=c^2[/tex]

[tex]PQ^2+PR^2=QR^2[/tex]

[tex]80^2+PR^2=89^2\\[/tex]

Simplify,

[tex]80^2+PR^2=89^2\\[/tex]

[tex]6400+PR^2=7921[/tex]

Inverse operations,

[tex]6400+PR^2=7921[/tex]

[tex]PR^2=1521\\\\PR=39[/tex]

Answer:

Here is the sample space, its size is 4*3 = 12:

Answer:

According to your question :-

four marbles :-

cubes numbered as :-

_______________________

outcomes :-

At black ..

At blue ..

At yellow ..

At red ..

________________________

Size ...

4 X 3 = 12 size,,

hopes its helps you.

Answer:

[tex]{ \sf{ {(x - 2)}^{2} + {(y + 8)}^{2} = 4}}[/tex]

Answer:

Center is (2, -8) and radius =2

h = 2 and k = -8

Filling in this equation:

(x -h)² + (y -k)² = radius²  we get:

(x - 2)^2 + (y--8)^2 = 2^2 which equals

(x-2)^2 + (y +8)^2 = 4

Source: http://www.1728.org/circleqn.htm

Step-by-step explanation:

The fractional amount of banana Mrs. Vacarro's toddler ate is 2/5.

A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

For the given situation,

Mrs. Vacarro sliced a banana into 5 pieces.

Number of slices she gave to her toddler = 4/5

Number of slices left after her toddler had finished eating = 2/5

Thus number of slices toddler ate,

⇒ [tex]\frac{4}{5} -\frac{2}{5}[/tex]

⇒ [tex]\frac{4-2}{5}[/tex]

⇒ [tex]\frac{2}{5}[/tex]

Hence we can conclude that the fractional amount of banana Mrs. Vacarro's toddler ate is 2/5.

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not possible because the area of a square is always a square of it's length and a square cannot be a prime number

Answer:

No

Step-by-step explanation:

Because the area of a square is always a square of its length and a square can't be prime.

Answer:

y = 3x + 7

Step-by-step explanation:

When lines are parallel, the slope is the same but the y-intercept is not

The blue line is the graph for y = 3x + 2

The slope for the line is 3/1

So the slope for the line containing (-2,1) should be 3/1

I plotted (-2,1) and used the Rise/Sun (3/1) to find a point on the y-axis, the teal point.

I graphed the line in yellow

In y=mx + b, b = 7, and mx = 3x

So the equation is y = 3x + 7

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

Answer: c

Step-by-step explanation:

c is the same and it is the correct answer

Answer:

x = -1/2

Step-by-step explanation:

4x^2 + 4x + 1 = 0

Factor

(2x+1)(2x+1) =0

Using the zero product property

2x+1 = 0 2x+1 =0

2x = -1  2x=-1

x = -1/2   x = -1/2

Answer:

1861÷1250

Step-by-step explanation:

This is the simplified version

Answer:

see explanation

Step-by-step explanation:

(1)

x - (9x - 10) + 11 = 12x + 3(- 2x + [tex]\frac{1}{3}[/tex] ) ← distribute parenthesis on both sides

x - 9x + 10 + 11 = 12x - 6x + 1 ← collect like terms on both sides

- 8x + 21 = 6x + 1 ( subtract 6x from both sides )

- 14x + 21 = 1 ( subtract 21 from both sides )

- 14x = - 20 ( divide both sides by - 14 )

x = [tex]\frac{-20}{-14}[/tex] = [tex]\frac{10}{7}[/tex]

(3)

- 4x - 2(8x + 1) = - (- 2x - 10) ← distribute parenthesis on both sides

- 4x - 16x - 2 = 2x + 10

- 20x - 2 = 2x + 10 ( subtract 2x from both sides )

- 22x - 2 = 10 ( add 2 to both sides )

- 22x = 12 ( divide both sides by - 22 )

x = [tex]\frac{12}{-22}[/tex] = - [tex]\frac{6}{11}[/tex]

(7)

8(2x + 9) = 56 ( divide both sides by 8 )

2x + 9 = 7 ( subtract 9 from both sides )

2x = - 2 ( divide both sides by 2 )

x = - 1