6) From a point on the ground 15 ft. From the base of a flagpole, the angle of elevation of the top of the pole measures 57°. How tall is the flagpole?

Answer:

B) cos Z = 15/17

Step-by-step explanation:

cos Z = 30/34 = 15/17

Answer:

1. 12

2. 31

3. 37

4. 87

Answer: 50 inches

Step-by-step explanation:

Answer:

PJ = 41.34

Step-by-step explanation:

P is incenter, three angles bisector meet

∠MJP ≅ ∠OJP

PM = PN = PO = 22   (radius: property of incenter)

∠JPM = 90 - ∠MJP = 90 - OJP = ∠JPO

ΔJPM ≅ ΔJPO   (ASA) or (SAS)

LM = JO

2x + 3 = 5x - 45

3x = 48

x = 16

JM = 35

PJ = √35²+22² = √1709 = 41.34

The value of PJ in triangle KJL is 41.32 units.

The point formed at the intersection of the three angle bisectors of a triangle; also the centre of the incircle.

Given that, P is incenter of the triangle KJL,

Considering the triangles ΔMJP and ΔOJP

PM = PO (property of incenter)

∠ JMP ≅ ∠ JOP

JP is common segment.

ΔJPM ≅ ΔJPO  (by SAS rule)

JM = JO  (CPCTC)

2x + 3 = 5x - 45

3x = 48

x = 16

JM = 35

Using the Pythagoras theorem,

PJ² = PM²+JM²

PJ = √35²+22² = √1709 = 41.34

Hence, The value of PJ in triangle KJL is 41.32 units.

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Answer:

8

total degree inside pentagon is (n - 2) x 180 = 540

180-62 = 118

180-66 = 114

180-77 = 103

180-59 = 121

118+114+103+121 = 456

540 - 456 = 84

84 + 12x = 180

12x = 180-84

x = 96/12

x = 8

The value of x in the given pentagon is 8.

Option D is the correct answer.

A pentagon is a polygon that has five sides and five angles.

The sides and angles of a pentagon are not all equal unless it is a regular pentagon.

A regular pentagon has five equal sides and five equal angles.

We have,

For a pentagon, n = 5, so we have:

total degree = (5 - 2) × 180 degrees

total degree = 3 × 180 degrees

total degree = 540 degrees

Now,

Each angle makes a straight angle.

So,

77 + a = 180

a = 180 - 77 = 103

59 + b = 180

b = 180 - 59 = 121

c + 66 = 180

c = 180 - 66 = 114

d + 62 = 180

d = 180 - 62 = 118

Now,

a + b + c + d + e = 540

103 + 121 + 114 + 118 + e = 540

e = 540 - 456

e = 84

Now,

12x + 84 = 180

So,

12x = 180 - 84

12x = 96

x = 8

Thus,

The value of x is 8.

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Answer:

the answer is y=30x

Step-by-step explanation:

however many inches times 30 is the consistent answer to the equation    

Answer:

y=30x

Step-by-step explanation:

We can start out by writing our slope-intercept form equation: y=mx+b. In this case, our y-intercept is 0, so we can write y=mx.

Let's find the slope. We can take the points (1,30) and (2,60). We can use the formula [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] to find our slope. Plug these values in, and we get [tex]\frac{60-30}{2-1}[/tex]. Evaluate this, and our slope is 30. So, our equation is y=30x.

Hope this helped!

Answer:

y= - 1/2(2)^(x)-2

Step-by-step explanation:

you could check on a graphing calculator

Answer:

12 .        18

    7 .             10

Step-by-step explanation:

Answer:

3/10 of people vacationed in another state.

Step-by-step explanation:

Because there are 60 people in total, the denominator has to be 60. The numerator then is going to be the amount of people that vacationed in another state. Simplify that fraction by 6, and you will get 3/10 as your answer.

Answer:

[tex]\frac{3}{10}[/tex]

Step-by-step explanation:

Since we want a fraction, we find the total number of people who vaccinated, then we find how many people vacationed in another state.

18+10+5+15+12=60, and 18 people vacationed in another state, we get

[tex]\frac{18}{60}[/tex], and we can divide top and bottom by 2, we simplify to [tex]\frac{3}{10}[/tex]

T/2π = √L/32

3.7 / 2 π = 0.588873289

0.588873289² =  L / 32

0.34677175 = L/32

0.34677175 x 32 = L

L = 11.096696 ft

11.0971

Answer:

35 cookie dough orders

Step-by-step explanation:

Juan and Rob are selling cookie dough for a school fundraiser. Juan has t cookie dough orders, and Rob has 40 cookie dough orders. They have a total of 75 cookie dough orders all together.

We have to calculate the number of cookie dough that Juan has.

The expression for the above question is given as:

t + 40 = 75

We collect like terms

t = 75 - 40

t = 35

Therefore, Juan has 35 cookie dough orders

Answer:

11 ft

Step-by-step explanation:

The formula for the area of a rectangle of length L and width W is

A = L * W.  

Represent the length, L, by 2W + 1 ("1 more than twice the width").  Then the area formula (above) becomes:

A = 55 ft^2 = (2W + 1)(W), which, when simplified, results in:

2W^2 + W - 55 = 0, whose coefficients are {2, 1, -55}.  Let's use the quadratic formula to solve this for W:

The discriminant, b^2 - 4ac, is 1^2 - 4(2)(-55), or 441.  The square root of 441 is 21.  Thus, the quadratic formula gives us:

        -1 ± 21

W = ------------- = (1/4)(-1 + 21), or W = 5 and W = -22/4 = -11/2

            2(2)

A measure of length can't be negative, so we reject W = -11/2 in favor of W = 5.

Then, according to the formula for L that we found earlier, L  = 2W + 1, or

L = 2(5) + 1, or L = 11.

Check:  Does L * W result in an area of 55 ft²?  Yes

The length dimension of the rectangle is 11 ft

Answer:

Growth

Step-by-step explanation:

y = 1/8 x

Step-by-step explanation:

9. 9x+1 + 9x+1 +88 =180

18x = 90

x = 5

Answer: 240 m

Step-by-step explanation:

Given

Football field measures [tex]100\ m\times 72\ m[/tex]

Another similar field of length

[tex]L=30\ m[/tex]

and width, say W is marked

So, their area must be the same

[tex]\Rightarrow 100\times 72=30\times W\\\\\Rightarrow W=\dfrac{7200}{30}=2540\ m[/tex]

The width of the football field is 41.7m

The football measures 100m by 72 m. The school football field is similar.

For similar rectangles, the corresponding sides have common ratios. Therefore, let's establish the proportion as follows:

cross multiply

3000 = 72w

divide both sides by 72

w = 3000 / 72

w = 41.6666666667

w = 41.7 m

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Answer:

She can get 10 pounds of steak and 10 pounds of chicken.

Step-by-step explanation:

As Jacie wants to have at least 20 pounds of meat, you can write the following  equation:

x+y=20, where

x refers to the pounds of steak

y refers to the pounds of chicken

Also, since the statement indicate that the steak is $8 per pound and chicken is $4 per pound and Jacie wants to spend at most 120 dollars on meat, you can write the following equation:

8x+4y=120

So, you have the following equations:

x+y=20 (1)

8x+4y=120 (2)

Now, you can solve for x in (1):

x=20-y (3)

Then, you can replace (3) in (2) and solve for y:

8(20-y)+4y=120

160-8y+4y=120

160-120=8y-4y

40=4y

y=40/4

y=10

Finally, you can relace the value of y in (3) to find x:

x=20-y

x=20-10

x=10

According to this, the answer is that she can get 10 pounds of steak and 10 pounds of chicken.

Answer:

In explanation below l

                                   v

Step-by-step explanation:

When a transversal cuts parallel lines, all of the acute angles formed are congruent, and all of the obtuse angles formed are congruent.  For example, ∠1, ∠4, ∠5, and ∠7 are all acute angles.

Answer:

$1483.52

Step-by-step explanation:

P=principle

Fn=total at the end of a given year(=n) (subscript)

I= interest in decimal

F=P(1+I)

at end of first year F1=P(1+I)

at end of second year F=F1(1+I)= P(1+I)(1+I)= P(1+I)^2

or in general Fn=P(1+I)^n

Well the distance from the two points is 15 so that means the midpoint in -10+7.5=-2.5. There you go! Have a nice day.

Answer:

I would use addition

Step-by-step explanation:

Since addition is the opposite of subtraction.

Answer:

Addition

Step-by-step explanation You would use addition because you can cancle out the numbers that way

Answer:

x = 4

Step-by-step explanation:

x + 6 +2x = 2x + 6 + 4

combine like terms:

3x + 6 = 2x + 6 + 4

add numbers:

3x + 6 = 2x + 10

subtract 6 on both sides:

3x + 6 - 6 = 2x + 10 - 6

3x = 2x + 4

subtract 2x from both sides:

3x - 2x = 2x - 2x + 4

x = 4

short explanation:

if you look at the equation, both sides have 6 and 2x which would cancel each other out. That would leave x = 4

Answer:

28 Pi

Step-by-step explanation:

circumference = 24(2)(π) = 48π

arc ABC = 360° - 150° = 210°

210/360(48π) = 28 Pi

Answer:

Step-by-step explanation:

Circumference

C = 2*pi * r

pi = 3.14

r = d / 2

r = 8/2

r = 4 feet

C = 3.14 * 2 * 4

C = 18.84 feet.

Area

pi = 3.14

r = d/2

r = 8/2

r = 4

Area = 3.14 * 4^2

Area = 3.14 * 16

Area = 50.24 ft^2