In Exercises 19-22, are AC and DF parallel? Explain
your reasoning.
19.
21.
A
57° B
D
D
123⁰
E
CF
62⁰
A B 62°
E
с
F
20.
22.
A B
D
A
143⁰
D
37°
65°
E
115°
E
с
B C
65°
F

The total amount in the account after interest will be about $4525.63 .

In the fields of finance and economics, interest is the additional sum that is paid by a borrower or deposit-taking financial institution to a lender or depositor at a certain rate (the amount borrowed).

Interest when the principal is $4000 , time is 5 years and rate is 2.5%.

We know that from compound interest:

Amount = principal (1 + rate)ⁿ

Therefore

Amount = 4000 (1 +0.025)⁵

Amount = $4525.6328...

Amount ≈ $4525.63

Therefore adding interest the sum would be worth $657.51

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Answer:

30 feet

Step-by-step explanation:

i used a ruler, mm side. 1 mm = 1 foot

draw a horizontal line.

draw a vertical line 28mm high

use a protractor to find a line that connects to the base and top of vertical line.

measure said line

Answer:

Step-by-step explanation:

\text{sin }\color{purple}{71}=\frac{\color{green}{\text{opposite}}}{\color{#EB0000}{\text{hypotenuse}}}=\frac{\color{green}{28}}{\color{#EB0000}{x}}

sin 71=

hypotenuse

opposite

​

=

x

28

​

\text{sin }71=

sin 71=

\,\,\frac{28}{x}

x

28

​

\frac{\text{sin }71}{1}=

1

sin 71

​

=

\,\,\frac{28}{x}

x

28

​

x\text{ sin }71=

x sin 71=

\,\,28

28

Cross multiply.

\frac{x\text{ sin }71}{\text{ sin }71}=

sin 71

x sin 71

​

=

\,\,\frac{28}{\text{ sin }71}

sin 71

28

​

Divide both sides by sin 71

x=\frac{28}{\text{ sin }71}=29.613379...\approx29.61

x=

sin 71

28

​

=29.613379...≈29.61

The value of y-coordinate from the given information is 36.

Given that, the water level rises 12 centimeters every 7 minutes and you record the data point of ​(21​, y).

The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.

According to the question the water rises 12 cm every 7 minutes. Taking x to represent the time in minutes and y to represent the rise in cm then, find the rise y in time x as;

7 minutes = 12 cm

1 minute

(1×12)/7 = 12/7

Hence in 1 minute, the rise is 12/7 cm

Thus in 11 minutes, the rise will be ;

21  × 12/7 = 3 × 12 = 36 cm

So, (x, y) will be (21, 36)

Therefore, the value of y-coordinate from the given information is 36.

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Using the sum of angles, we know that the value of 'x' is 14°.

What is the sum of the angles of a triangle?

Some of the angles of a triangle are the property of triangle states that the sum of interior angles of a triangle is 180°.

Given angles are 47, 103, 3x-12:

Therefore, using the sum of angles, we know that the value of 'x' is 14°.

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Answer:

Answer down below!

Step-by-step explanation:

The best way to find the slope of the line is first find a point that rests on the line on an exact point. This exact point is (-1,0)

Then, once you find that point, continue to use rise/run to find the slope.

In this case, it goes up one, and over one

So, your slope would be 1/1 or just 1.

(NOTE: IF YOU CONTINUE TO KEEP GOING ONE UP AND ONE OVER, IT WILL STILL GIVE YOU THE SAME SLOPE, BUT YOU WILL HAVE TO DO MORE WORK!!)

The translation from AB to A’B’ is (x, y) → (x + 9, y + 2).

Given:

The coordinates of A(preimage) are (-5,1).

The coordinates of A'(image) are (4,3).

From the coordinates of the translated image, A'B' we can determine the transformations.

The translation applied to the point (-5,1) are (x, y) → (x + 9, y + 2).

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Answer:

Option 2

Step-by-step explanation:

Even though there is a hole at x=2, the graph still approaches 3 from both sides. (We only consider the behavior around the point, not the point itself)

1. The frequency table will be:

Physics - Not in algebra = 9

Not in physics (Algebra) = 24

Not in physics (Not in algebra) = 2

Total (Not in physics) = 26

Total = 11

2. The students are enrolled in either algebra or physics is B. 38.

It was found that 29 are taking algebra, 14 are taking physics, and 5 are enrolled in both.

Not in physics for algebra = 24

Not in physics = 2

The Total for the value will be:

= 24 + 2= 26

The students enrolled in either will be:

= Algebra + Physics - Both

= 29 + 14 - 5

= 43 - 5

= 38

This illustrates the concept of addition and subtraction of numbers.

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Answer:

Its B. 38

Step-by-step explanation:

Hope this helps :)

By definition. a Translation is a transformation in which a figure is moved a fixed distance in a fixed direction.

The Image is the figure obtained after the transformation and the Pre-Image is the original figure.

In this case, you know that the figure shown in the picture must be translated 5 units up. Therefore, the rule for this transformation is:

You can identify that the marked point on the Pre-Image has the following coordinates:

Therefore, applying the rule for this transformation, you get that the coordinates of the marked point in the final figure, are:

The answer is:

Coordinates of the marked point in the original figure:

Coordinates of the marked point in the final figure:

Answer:

2700 kg

Step-by-step explanation:

54 × 50 kg = 2700 kg

Answer:

262.20

Step-by-step explanation: she originally payed for 10%=.10

2,622x.10=262.2

A woman purchased 12 little frames and 10 large frames.

We create an algebraic equation in this question.

An algebraic equation is a mathematical statement that makes two expressions equal to one another.

In most circumstances, an algebraic equation consists of a variable, coefficients, and constants.

According to question, the equation will be

Let x = large frame

     y = small frame

x + y = 22                                     ---(1)

10x + 5y = 160                             ---(2)

Now, solve the eq(1) and eq(2),

we get, x = 10

     and, y = 12

If you want to cross-check you can do like that,

large frame price = $10

and, x = 10 (means 10 large frames women bought)

so the price will be = $ 10 * 10

                                = $100

Now, for the small frame price = $5

and, y = 12 (means 10 large frames women bought)

so the price will be = 12 * $5

                              = $60

Now total price is given = $160

and if we add both the prices of large and small frames = $100 + $60

we get, same as total price =  $160                                                                                              

Therefore, we can say that woman bought 10 large frames and 12 small frames.

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Answer:

[tex]y=-\frac{1}{3} x - 6[/tex]

Step-by-step explanation:

3x+9y=-54

9y=-3x-54

y=-1/3x-6

:] good luck

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{x}{3} - 6[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given equation is :

[tex]\qquad\displaystyle \tt \rightarrow \: 3x + 9y = - 54[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 9y = - 54 - 3x[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{ - 54}{9} - \frac{3x}{9} [/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{x}{3} - 6[/tex]

And this the equation of same line in its slope intercept form, where slope (m) = -1/3 and y - intercept = -6

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

8 divided by 2

Step-by-step explanation:

Answer: Two out of three concert-goers prefer country music.

Step-by-step explanation:

Toby is interviewing country music concert participants, and therefore isn't getting a diverse spread of interviewees and isn't getting accurate data.

The equation of line which is parallel and the line perpendicular to the given line passing through the given point as y = 2x + 7; (0, 1) is y = (-1/2)x + 1.

What is perpendicular line?

The definition of a perpendicular line in geometry is a pair of lines that meet or intersect at right angles (90°). The Latin word "perpendicularis," which denotes a plumb line, is where the word "perpendicular" first appeared.

[tex](y-1) = -\frac{1}{2} (x-0)[/tex]The equation of the line given in the question is:

y = 2x+7

On comparing with the equation y = mx + a

where, m is slope

we get slope of the line as m = 2.

Since the line we have to find is parallel to given line, they have equal slope.

Now, we know that the equation of perpendicular line is given by:

[tex](y-y_1) = -\frac{1}{m} (x-x_1)[/tex]

given points are (0,2) which is represented by (x1,y1)

On putting the value in the equation, we get

[tex](y - 1) = -\frac{1}{2}(x-0)[/tex]

After simplifying it we get the final equation as:

[tex]y = -\frac{1}{2} x + 1[/tex]

Above equation is the equation of line which is parallel and the line perpendicular to the given line passing through the given point as y = 2x + 7; (0, 1).

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The number of positive pairs that satisfy the given linear function is given by: 161.

We have to look at the graph of the function relative to the x-axis, more specifically if the function is above or below the x-axis, as follows:

In the context of this problem, the function is defined as follows:

4x + 12y = 640.

Which is a linear function, as both x and y have exponents of 1. The ordered pairs on the function are the values above the line. With integer numbers, that is, numbers that have no decimal parts, from the graph of the function given at the end of the answer, the values of x for which the function is positive is given by:

0 ≤ x ≤ 160.

Containing 161 values of x. Since this represents a function, each of the 161 values of x is associated to a value of y, meaning that there are 161 positive integer pairs (x,y) that satisfy the equation 4x + 12y = 640.

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Answer:

y=3x+3

Step-by-step explanation:

Use rise/run

Answer:

y=-9x+5

Step-by-step explanation:

Answer: 8

Step-by-step explanation:

found slope

Kindly check below.

1) Examining the expressions inside the tiles, we can tell that:

2) Based on this we can tell the following relationship of equivalence:

consequently, the time and a half rate will be 33 dollars per hour according to the query.

A higher rate of pay known as "time and a half" is normally only applied to hours that are over 40 in a workweek or that are worked extra.

Companies have different overtime pay practices, with time and a half as a typical rate.

Simply said, it means that for each hour performed within the time and a half window, the employee will receive payment in addition to their regular hourly rate of one half of that amount.

Time and a Half Rate = Hourly Rate * 1.5

According to the given question:

Time and a half rate =22$*1-1/2

   =22$*1.5

   =33$ per hour

Therefore, According to the question given the Time and a pay half rate will

be 33$ per hour.

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y = -6x -25 is equation of slope intercept .

What exactly does slope intercept mean?

 The equation is  y = -6x + 8

     compare with equation y=mx+b

  slope m = -6

Use the point-slope method

y = -6x + 8    

point P(-1,-4)  point given (x1,y1)

y-y1=m(x-x1)  point-slope form

y - ( -1 ) = -6 ( x - (-4))

y + 1 = -6 ( x + 4 )

y + 1 = -6x - 24

y = -6x -25

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Line segments DA and BE are parallel to FC.

We need to find all the segments parallel to FC.

Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.

From the given figure, FC parallel to DA and FC parallel to BE.

Therefore, line segments DA and BE are parallel to FC.

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The possible values of k such that the quadratic equation has real distinct roots are 1 / 2 and 2.

In this problem we find the case of a quadratic equation, of which the values of a variable k must be found such that the polynomial have real distinct roots. This can be done by using the discriminant of the quadratic formula, which is defined below:

For a · x² + b · x + c = 0, the discriminant is:

b² - 4 · a · c > 0

Then, if we know that a = k - 1, b = 2 and c = 2 · k - 3, then the possible values of k are:

2² - 4 · (k - 1) · (2 · k - 3) > 0

4 - (4 · k - 4) · (2 · k - 3) > 0

4 - (8 · k² - 8 · k - 12 · k + 12) > 0

8 · k² - 20 · k + 8 > 0

Whose form form is shown below:

8 · (k² - (20 / 8) · k + 1) = 0

8 · (k² - (5 / 2) · k + 1) = 0

8 · (k - 2) · (k - 1 / 2) = 0

The possible values of k are 1 / 2 and 2.

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Answer:

2x-5< 14 is the answer

Step-by-step explanation:

Answer:

2x-5<14

I hope this helps!

Answer:

10.57

Step-by-step explanation:

44+400=444

(4+62)-24=

66-24=42

444/42=10.57

The students will earn $82.5 if they sell all the bottles of liquid soap.

The formula of the unitary method is to find the value of a single unit and then multiply the value of a single unit to the number of units to get the necessary value.

Given that,

Total amount of liquid soap prepared by the students for a craft fair =

97.5 ounces

Weight of each bottle in which students poured the soap = 6.5 ounces

Let us first calculate the number of bottles, each contains 6.5 ounces of soap from 97.5 ounces of soap.

So, Number of bottles = [tex]\frac{97.5}{6.5}[/tex] = 15

It means, 15 bottles are prepared which contains 6.5 ounces of soap from 97.5 ounces of soap.

The amount at which each bottle is sold = $5.50

The total amount earned by selling all the bottles of liquid soap = 15×$5.50 = $82.5

Hence, The students will earn $82.5 if they sell all the bottles of liquid soap.

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If Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove faster because the speed of the Mr. Giordano greater than Mr. Baras

Total distance traveled by the Mr. Giordano = 4.5 miles

The time taken = 5 minutes

Speed = Distance / Time

Speed = 4.5/5

= 0.9 miles per minutes

Total distance traveled by the Mr. Baras = 6.3 miles

The time taken = 8 minutes

Speed = Distance / Time

Speed = 6.3/8

= 0.78 miles per minutes

Hence, if Mr. Giordano's drove 4.5 miles in 5 minutes and Mr. Baras drove 6.3 miles in 8 minutes, then the Mr. Giordano drove faster because the speed of the Mr. Giordano greater than Mr. Baras

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Answer:

b

Step-by-step explanation:

using the rule of exponents

[tex]a^{m}[/tex] × [tex]a^{n}[/tex] = [tex]a^{(m+n)}[/tex] , then

[tex]5^{3}[/tex] × [tex]5^{4}[/tex]

=[tex]5^{(3+4)}[/tex]

= [tex]5^{7}[/tex]