Write the equation of the line that passes through the given points.

(0,- 4) and (2,3)

The equation of the line is( )​

Answer:

The height of the building is 21.38 m

Step-by-step explanation:

Trigonometric Ratios

The ratios of the sides of a right triangle are called trigonometric ratios.

The image attached shows the measures and angles provided in the problem. The first angle of elevation is y=22°, the man walks B=20 m and finds the new angle of elevation is x=33°.

It's required to find the height of the building H.

The tangent ratio relates the opposite side with the adjacent side of a given angle. Applying it to the larger triangle:

[tex]\displaystyle \tan y=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]

[tex]\displaystyle \tan 22^\circ=\frac{H}{D+B}[/tex]

Multiplying by D+B:

[tex]\tan 22^\circ(D+B)=H[/tex]

Dividing by tan 22°

[tex]\displaystyle D+B=\frac{H}{\tan 22^\circ}[/tex]

Subtracting B:

[tex]\displaystyle D=\frac{H}{\tan 22^\circ}-B\qquad\qquad[1][/tex]

Applying to the smaller triangle:

[tex]\displaystyle \tan 33^\circ=\frac{H}{D}[/tex]

Multiplying by D:

[tex]\tan 33^\circ D=H[/tex]

Substituting from [1]:

[tex]\displaystyle \tan 33^\circ \left(\frac{H}{\tan 22^\circ}-B\right)=H[/tex]

Substituting values:

[tex]\displaystyle 0.6494 \left(\frac{H}{0.4040}-20\right)=H[/tex]

Operating:

[tex]1.6074H-12.988=H[/tex]

[tex]1.6074H-H=12.988[/tex]

[tex]0.6074H=12.988[/tex]

[tex]H = 12.988/0.6074[/tex]

H = 21.38 m

The height of the building is 21.38 m

Answer:

Step-by-step explanation:

It would be easier to just show you.

Because we're using variables, I'm going to plug in a random set of numbers to stand for x and y.

(x+y)^2

(2+4)^2=36

vs.

x^2+y^2

2^2+4^2=20

The difference is because, following the order of operations, in the first situation you must first take care of what is in the parenthesis, which means you add x and y together-then you multiply that combined number by the 2nd power. Whereas in the second situation, you multiply x and y by the 2nd power separately, and then add the product of that together. So opposite order. In the first situation you add, then multiply. In the second, you multiply then add.

Answer:

Step-by-step explanation:

[tex] \frac{5(x + 6) - 15(2 - x)}{3x - 1} = 10 \\ [/tex]

[tex] = > 5(x + 6) - 15(2 - x) = 10(3x - 1)[/tex]

[tex]5x + 30 - 30 + 15x = 30x - 10[/tex]

[tex] = > 20x = 30x - 10 \\ = > 20x - 30x = - 10 \\ = > - 10x = - 10 \\ = > x = 1[/tex]

hope it helps:)

Answer:

TU = 8.4

Step-by-step explanation:

The geometric figure consists of the following segments;

1) 4 parallel lines, WS, YR, XQ, and, VP

2) Three transversals, VW, PS, and, TU

The given parameters are;

PQ = QR = RS

Therefore, given that the transversal, PS, makes equal intercept with the 4 given parallel lines, by equal intercept theorem, the transversal TU will make equal intercepts with the given parallel lines

Therefore;

TX = 2.8 = XZ = ZU

From which we have, by segment addition postulate;

TU = TX + XZ + ZU

∴ TU = 2.8 + 2.8 + 2.8 = 8.4

TU = 8.4.

Answer:

12 x 3 = 36

Step-by-step explanation:

This is a Multiplication problem Because the Factory can produce 12 shoelaces in 3 minutes so take 12 and multiply it by 3 and your answer is  36. So the factory made 36 shoelaces in that time.

Answer:

12*3=36

Step-by-step explanation:

8/5 = 1 3/5

(5 x 1 = 5 + 3 = 8, to get 8/5)

13/12 = 1 1/12 (12 x 1 = 12 + 1 = 13, to get 13/12)

Hope this helped! :D

Answer:

50

Step-by-step explanation:

Answer:

For instance, there's the basic formula that the area of a triangle is half the base times the height. This formula only works, of course, when you know what the height of the triangle is. ... That is to say, the area of a triangle is half the product of two sides times the sine of the included angle.

Step-by-step explanation:

Answer:

A - 105

Step-by-step explanation:

since the two measurements are supplements, you do x+82+x+112=180. then you get x=-7. then you do 112-7=105

Answer:

105°

Step-by-step explanation:

A line equals 180, so take the two expressions and set them equal to 180:

x+82+x+112=180

simplify:

2x+194=180

2x=-14

x=-7

now plug the x value into the bolded expression

x+112

-7+112 = 105°

Answer:

[tex]\sqrt{109}[/tex]

Step-by-step explanation:

using pythagorean theorem

height:3

length=10

a^2+b^2=c^2

a=height=3

b=length=10

9+100=c^2

c=[tex]\sqrt{109}[/tex]

Answer:

it would be only one solution

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

35% off of $8.00 is equal to $5.20

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Answer:

The value of n is 5

Step-by-step explanation:

Here, we want to get the value of n

To get this, we will need to use the appropriate trigonometric identity

As we can see, n represents the opposite as it the side that faces the angle given

m is the hypotenuse as it is the side that faces the right angle

The last side is called the adjacent

The trigonometric identity we want to use is that which connects the opposite to the adjacent

The appropriate trigonometric identity to use in this case is the tan

Thus;

Mathematically, the tan is the ratio of the opposite to the adjacent

hence;

tan 30 = n/ 5 √3

n = 5 √3 * 1/ √3

n = 5

a) The two points that should be used to find the equation are given as follows: (6,9) and (10,13).

b) The slope of the linear model is of 1.

c) The point-slope form of the linear model is given as follows: y - 9 = (x - 6).

d) The slope-intercept form of the equation you wrote in part (c) is given as follows: y = x + 3.

e) The least squares regression line is given as follows: y = 1.028x + 2.271.

The slope-intercept definition of a linear function is given as follows:

y = mx + b.

In which:

Two points from the line are defined as follows:

(6,9) and (10,13).

These points were chosen as they have the least residual, that is, these points are the closest to the line of best fit.

Given two points, the slope is calculated as the change in y divided by the change in x, hence:

m = (13 - 9)/(10 - 6) = 1.

Considering point (6,9), the point-slope equation is given as follows:

y - 9 = (x - 6).

Hence the slope-intercept definition of the linear function is given as follows:

y - 9 = x - 6

y = x + 3.

The points from the scatter plot are given as follows:

(1,2), (2,6), (5,6), (6,9), (7,11), (9,10), (10,13).

Inserting these points into a linear regression calculator, the regression line is given as follows:

y = 1.028x + 2.271.

More can be learned about linear functions at https://brainly.com/question/24808124

#SPJ1

Answer:

I believe the answer is A and D.

Answer:

y=4/3x+7/3

Step-by-step explanation:

I don't know if this is right.

Answer:

5 pounds of potatoes is $3.75 1 pound is .75 cents

Step-by-step explanation:

Answer:

$8.75

Step-by-step explanation:

Set up a proportion where x is the cost of a bottle with 250 vitamins:

[tex]\frac{150}{5.25}[/tex] = [tex]\frac{250}{x}[/tex]

Cross multiply and solve for x

150x = 1312.5

x = 8.75

So, it will cost $8.75 for a bottle with 250 vitamins

Answer:

V = hπr^2

V = 5 X π X 15^2

V = 3534.29173

V = 3534.2 cubic feet

The equation that can be used to find the volume V of the swimming pool is πr²h

The swimming pool is circular and has a diameter of 30 feet and a depth of 5 feet.

This simply means the swimming pool follows the shape of a cylinder. The

two bases are circular and has a height of 5 feet.

Therefore, the volume of the swimming pool in cubic feet is the volume of a cylinder.

volume = πr²h

where

r = radius = 30 / 2 = 15 feet

h = 5 feet

volume = 3.14159 × 15² × 5 = 3.14159 × 225 × 5 = 3534.28875 = 3534.3 ft³

learn more about cylinders here: https://brainly.com/question/20766511?referrer=searchResults

Answer: 6.25 cm

Step-by-step explanation:

Area of parallelogram [tex]A=base\times height[/tex]

Using base as AB and height as DE

[tex]Area=8\times 5[/tex]

Now, using base BC and height as DF

[tex]Area=6.4\times x[/tex]

Equating area

[tex]8\times5=6.4\times x\\x=6.25\ cm[/tex]

Answer:

10th number in the sequence is 786432

n = 4

Step-by-step explanation:

Multiply the following number by 4 (starting at #4) until you reach the 10th number in the sequence

Answer:2 3/ 8

Step-by-step explanation: 5 1/8 - 2 3/4

                                            = 41/ 8  - 11/4

                                          = 41/8 - 22/8

                                           =19/8

                                        =2 3/ 8

Change to improper fraction .Then make the denominator the same ,make both denominator to 8 . Now you have 41/8 and 22/8 ,you can subtract it and it gives you 19/8.Lastly you make the improper fraction to mixed  numbers which is 2 3/ 8 .

Answer:

Well when simplified your answer would be

-8-32g

Step-by-step explanation:

So distribute -4 to each number in the parentheses

-4*2= -8

-4*8g= -32g

Now the answer is

-8-32g

Answer: -5 and 5

Step-by-step explanation:

-5 plus 5 added has a sum of 0

WHAT IS THAT ? THX

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Answer:

6 onuces per serving

Step-by-step explanation:

Answer: 7) No   8) No

Step-by-step explanation:

According to the Pythagoras theorem of the right triangle,

Square of largest side = Sum of square of other two sides.

8) Given sides: 5cm, 12cm, 14cm

Here, Largest sides = 14 cm

[tex]5^2+12^2=25+144=169\neq14^2 \ \ \ [14^2=196][/tex]

These sides do not represent a right triangle.

7) Given sides:  9m, 4m, 5m

Largest side = 9 m

[tex]4^2+5^2=16+25=49\neq 9^2 \ \ \ \ \ [9^2=81][/tex]

These sides do not represent a right triangle.

Answer:

w = 7 inches

Step-by-step explanation:

length = n

width = n/2

Perimeter = 2n + 2(n/2)

42 = 2n + n

42 = 3n

n = 14

width = 14/2 = 7

Answer:

last option is the answer

Step-by-step explanation:

the answer cannot be the two middle options because you can see the y-intercept is 2 so the equation must end with that

now you have to determine if the slope of the line is -5 or -1

you can find the slope by selecting two points on the line; for example, (0,2) and (1,1) and using formula:  difference of y-values       2 - 1  

                                              difference of x-values        0 - 1

the slope is -1