A person is standing exactly 36 ft from a telephone pole. There is a 30° angle of elevation from the ground to the top of the pole. A person is standing 36 feet from the base of a telephone pole. A line is drawn from the top of the telephone pole to the person to form a right triangle. The angle at the person is 30 degrees. What is the height of the pole? 12 ft 12 StartRoot 3 EndRoot ft 18 ft 18 StartRoot 2 EndRoot ft

Answer:  a = 11.24    B = 75.5°       C = 53.5°

Step-by-step explanation:

Use Law of Cosines to find a: a² = b² + c² - 2bc · cos A

Given: b = 14, c = 6, A = 51°

a² = (14)² + (6)² - 2(14)(6) · cos 51°

a² = 196 + 36 - 168 · cos 51°

a² = 232 - 105.72

a² = 126.27

a = 11.24

Use Law of Sines to find B: [tex]\dfrac{\sin A}{a}=\dfrac{\sin B}{b}[/tex]

Given: A = 51°, a = 11.24, b = 14

[tex]\dfrac{\sin 51^o}{11.24}=\dfrac{\sin B}{14}\\\\\\\dfrac{14\sin51^o}{11.24}=\sin B\\\\\\\sin^{-1}\bigg(\dfrac{14\sin51^o}{11.24}\bigg)=B\\\\\\75.5^0=B[/tex]

Use Triangle Sum Theorem to find C: A + B + C = 180°

Given: A = 51°, B = 75.5°

51° + 75.5° + C = 180°

126.5° + C = 180°

             C = 53.5°

Answer:

Diameter=12 inches

Step-by-step explanation:

Given:

x^{2}+y^{2}-2x-4y-31=0

Using completing the square

x^2 - 2x + 1 + y^2 - 4y + 4 = 31+1+4

(x-1)^2 + (y-2)^2 = 36

Rewrite in the form

(x-h)^2+(y-k)^2=r^2

We have,

(x-1)^2+(y-2)^2=6^2

radius = 6

Diameter =radius ×2

=6 × 2

diameter = 12 inches

Answer:

18581.16

Step-by-step explanation:

The area of each of the shale can be calculated as

distance between each point = x

The area of the regular Dodecahedron

A = [tex]\sqrt[3]{25+10\sqrt{5} } a^{2}[/tex]

where a = number of edges = 30

hence the area of the regular dodecaheron = 18581.16

Answer: this not correct ,because in the expression it is not clear , the numbers are neither exactly rounded to nearest tens or tenths.

Step-by-step explanation:

Our total add is

= 7.95 + 8.11 + 78.5 + 8.05 + 79.4 + 0.815

When we spherical it up to nearest tens

7.95 = 8.00

8.11 = 8.00

78.5 = 79

8.05 = 8.00

79.4 = 79.0

0.815 = 1

when we estimate the rational numbers with an extra operation once done,our results is

= eight + eight + eighty + eight + eighty + zero.8 = 184.8, isn't correct ,because within the expression it's not clear , the numbers area unit neither precisely rounded to nearest tens or tenths.

for example ,79.4 once rounded to nearest tens = seventy nine,but within the expression eighty (80) is written,which isn't correct.

Similarly,when rounded to nearest tens, 0.815 = 1, however within the expression 0.8 is written,which is wrong.

Similarly,when rounded to nearest tens ,78.5 = 79 , however within the expression eighty ( 80 ), is written,which is wrong

Answer:2.the answer is 189,250pages

Step-by-step explanation:

1L=1000ml

3.785=?3785

1ml=50pages

3785ml=?

The answer is 189,250

Answer:

Hey there!

5. f(4) is 3. f(3) is 2. Thus, f[f(4)]=2

6. g(2) is 3. g(3) is 1. g[g(2)]=1

Hope this helps :)

Answer:

140°

Step-by-step explanation:

[tex] \because m\widehat{BG} = 360\degree - m\widehat{GCB} \\

\therefore m\widehat{BG} = 360\degree - 300\degree \\

\therefore m\widehat{BG} = 60\degree \\

\because m\widehat{BGD} = m\widehat{BG}

+m\widehat{GD}\\

\therefore m\widehat{BGD} = 80\degree+60\degree\\

\therefore m\widehat{BGD} = 140\degree\\

\because m\angle BAD = m\widehat{BGD} \\

\huge\purple {\boxed {\therefore m\angle BAD =140\degree}} [/tex]

Answer:

10.5 m²

Step-by-step explanation:

Given:

∆ with 2 side lengths, 4.7m, 6.1m, and an included angle, 47°.

Required:

Area of the triangle

SOLUTION:

Area of such triangle that has 2 known sides and an included angle between them is given as ½*a*b*sin(θ).

Where,

a = 4.7 m

b = 6.1 m

θ = 47°

Area = ½*4.7*6.1*sin(47)

Area = 10.5 m² (to the nearest tenth)

Answer:

:

"(100 + 3) (100 + 7)

Now, by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = 3 , b = 7

= (100)² + (3+7)*100 + (3*7)

= 10000 + 1000 + 21

= 11021

.

(110 - 7) (110 - 3)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = (-7) , b = (-3)

= (110)² + { (-7) + (-3) }*110 + {(-7)*(-3)}

= 12100 + (-10)*110 + 21

= 21200 - 1100 + 21

= 11021

.

➖➖➖➖➖➖➖➖➖➖

.

(90 + 5) (90 + 6)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 90 , a = 5 , b = 6

= (90)² + (5+6)*90 + (5*6)

= 8100 + 990 + 30

= 9120

.

(100 - 5) (100 - 4)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = (-5) , b = (-4)

= (100)² + { (-5) + (-4) }*100 + 20

= 10000 + (-9)*100 + 20

= 10000 - 9000 + 20

= 10020 - 900

= 9120

.

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.

(100 + 4) (100 - 4)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 100 , a = 4 , b = (-4)

= (100)² + { 4 + (-4) }*100 + 4*(-4)

= 10000 + (4 - 4)*100 - 16

= 10000 + 0*100 - 16

= 10000 - 16

= 9984

.

(90 + 14) (90 + 6)

by using identity

(x + a) (x + b) = x² + (a+b)*x + ab

So,

x = 90 , a = 14 , b = 6

= (90)² + (14 + 6)*90 + (14*6)

= 8100 + 20*90 + 84

= 8100 + 1800 + 84

= 9984"

This answer was in another question

This answer was given by BloomingBud

Step-by-step explanation:

Answer:

1) 9120 2) 11021

Step-by-step explanation:

95 * 96 = (100-5)(100-4) = 10000 - 500 - 400 + 20 = 9120

103 * 107 = (100+3)(100+7) = 10000 + 300 + 700 + 21 = 11021

Answer:

Answer is A

Step-by-step explanation:

Hope it helps

Answer:

Step-by-step explanation:

tim has an after school delivery service that he provides for several small retailers in town. he uses his bicycle and charges $1.25 for a delivery made within 1 1/2 miles, $1.70 for a delivery of at least 1 1/2 miles but less than 1 3/4 miles. $2.15 for a delivery of at least 1 3/4 miles but less than 2 miles, and so on. if tim raised his rates by 10%, what would he be paid to deliver a package 3 1/8 miles.

Answer:

From the question asked the cost of additional 1/4 mile (1 3/4 - 1 1/2) is $0.45 ($1.7 - $1.25). If the rate is increased by 10% (0.1), the new price for an additional 1/4 mile would be 1.1 (1 + 0.1) × 0.45 = $0.495.

Tim new charge rate are as follows:

$1.25 for a delivery made within 1 1/2 miles

$1.745 for a delivery of at least 1 1/2 miles but less than 1 3/4

$2.24 or a delivery of at least 1 3/4 miles but less than 2

$2.735 or a delivery of at least 2 miles but less than 2 1/4

$3.23 or a delivery of at least 2 1/4 miles but less than 2 1/2

$3.725 or a delivery of at least 2 1/2 miles but less than 2 3/4

$4.22 or a delivery of at least 2 3/4 miles but less than 3

$4.715 or a delivery of at least 3 miles but less than 3 1/4

Since 3 1/8 is within 3 miles and 3 1/4 miles, Tim would charge $4.715 to deliver a package 3 1/8 miles.

Answer:

[tex]-3(2 + 4k) + 7(2k)[/tex] = [tex]2k - 6[/tex] or [tex]2(k - 3)[/tex]

Step-by-step explanation:

The question seem incomplete; however, the given parameter is assumed as

[tex]-3(2 + 4k) + 7(2k)[/tex]

Required

Simplify

[tex]-3(2 + 4k) + 7(2k)[/tex]

Start by opening the brackets

[tex]-3*2 -3* 4k + 7*2k[/tex]

[tex]-6 -12k +14k[/tex]

Collect Like Terms

[tex]-6 -12k +14k[/tex]

[tex]-6 + 2k[/tex]

Reorder the above expression

[tex]2k - 6[/tex]

The answer can be further simplified as

[tex]2(k - 3)[/tex]

Hence;

[tex]-3(2 + 4k) + 7(2k)[/tex] = [tex]2k - 6[/tex] or [tex]2(k - 3)[/tex]

It's an example of rotation symmetry, if the image appears unchanged. If the rotation symmetry exists there is a one centre point around which an image appears unchanged.

Answer:

It's an example of rotation symmetry, if the image appears unchanged. If the rotation symmetry exists there is a one centre point around which an image appears unchanged.

Answer:

200 cubic centimeters is the answer :)

Step-by-step explanation:

Answer:

- 0.93

Step-by-step explanation:

0.93 has an absolute value of  0.93 and is positive, so its opposite would be negative with the same absolute value.

The opposite number of 0.93 is -0.93.

The number that produces zero when added to an is known as the additive inverse of a number, or a, in mathematics. This number is also referred to as the opposite number. In another word, oppositely positioned numbers on the number line are called opposite number.

Hence, opposite number of a positive number is a negative number and opposite number of the negative number is a positive number.

For an example, the opposite number of +7 is -7 because +7 + ( -7) = 0.

The opposite number of -0.5 is 0.5 because (-0.5) +0.5 = 0.

In this question, the given number is +0.93.

Let the opposite number of +0.93 is x.

Then it can be written that:

+0.93 + x = 0

⇒ x = 0 -0.93

⇒ x = -0.93

Hence,  the opposite number of 0.93 is -0.93.

Learn more about opposite numbers here:

https://brainly.com/question/28492868

#SPJ3

Answer/Step-by-step Explanation:

Given, [tex]\frac{3}{4}*-4\frac{2}{9}[/tex]

Ivy solves this problem by writing each number as a fraction and then multiplies as shown below:

[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}* -\frac{38}{9} [/tex]

[tex] = \frac{3}{4}*-\frac{38}{9} = -\frac{3*38}{4*9} = -\frac{1*19}{2*3}[/tex]

[tex]= -\frac{19}{6}[/tex]

Fabian solves this problem by writing the mixed number as a sum and applies the distributive method of multiplication as shown below:

[tex] \frac{3}{4}*-4\frac{2}{9} = \frac{3}{4}(-4 + -\frac{2}{9}) [/tex]

[tex] = \frac{3}{4}*-4 + \frac{3}{4}*-\frac{2}{9} [/tex]

[tex] = -\frac{3}{1} + \frac{1}{2}*-\frac{1}{3} [/tex]

[tex] = -3 + (-\frac{1}{6}) [/tex]

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

Answer:

If X ≤ 1, these side lengths has no sense.

Step-by-step explanation:

We can factored the expression X² + 4X - 5 in a expression in the form:

(X+a) (X+b)

Where a*b = -5 and a+b = 4

That means a could be 5 and b = -1:

(X+5) (X-1)

The side lenghts of the rectangle will not have any sense if ≤ 0. With the factored expression:

(X+5) ≤ 0 ;  If X ≤ -5, these side lengths has no sense.

Also:

(X-1) ≤ 0; If X ≤ 1, these side lengths has no sense.

Both expressions are resumed in:

Answer:

x can be any integer greater than 12.

Step-by-step explanation:

x + x + 1 + x + 2 > 40

3x + 3 > 40

3x > 37

x > 12 1/3

x can be any integer greater than 12.

Answer:

answer hoga 3/2 ok.....

Answer: 3/2

Step-by-step explanation:

Answer:

No. he need 64 more

Step-by-step explanation:

Answer:

|BC| = 9.4 m

Step-by-step explanation:

Angle bxy = angle abc (reason, corresponding angles)

Angle ayx = angle acb ( reason , corresponding angles)

So angle abc= 62°

Angle acb = 51°

Angle acb + and + bac = 180 (reason, sum of angles in a triangle)

Anlge bac = 180-62-51

Angle bac= 180-113

Angle back = 67°

Using sine formula

|BC| /sin 67 = 9/sin 62

|BC| = sin 67 *9/sin62

|BC| = 9.4 m

Answer:

D

Step-by-step explanation:

just compare the augmented matrix to the possible answers and you will see it the option D

Answer:

  c)  x/h

Step-by-step explanation:

The rate of filling is 1 tank per h hours, or 1/h tanks per hour. Then in x hours, the amount of filling will be ...

  (x hours)(1/h tanks/hour) = x/h tanks

The part of the tank filled in x hours is x/h.

Answer:

[tex]\huge\boxed{-35}[/tex]

Step-by-step explanation:

(-20) + (-15)    [ +(-) = - ]

=> -20-15

=> -35

Answer:

-35

Step-by-step explanation:

a negative plus a negative = negative

negative plus a positive = positive or negative (it depends on which is larger)

negative * negative =  positive

negative * positive= negative

negative-negative= negative

use keep change change

i.e., 8-6 -> 8+-6

change the sign of the middle and the sign of the second term.

Answer:

$2.

Step-by-step explanation:

This is because the base price is $12, which means the constant is 12. The toppings are the only things you can add to the pizza, so the price of each additional topping is the slope of the pizza's cost. The slope is 2 dollars.

Hope this helps!

Answer:

2

Step-by-step explanation:

If we were to write a linear equation in slope-intercept form (y = mx + b where m = slope and b = y-intercept) of this situation, it would be y = 2x + 12 where y is the price and x is the number of toppings. This is because the price for every topping is 2x but the base price doesn't change, therefore it's a constant so it would be + 12. In this case, since m = slope, the slope is 2.

Answer:

d = 55.5  

x = 1

c = 11

m = [tex]\frac{1}{122}[/tex]

k = [tex]\frac{a}{(c + 5)}[/tex]

Step-by-step explanation:

Sorry, the formatting is slightly hard to understand, but I think this is what you meant.

Q1.

[tex]\frac{1}{6}[/tex]d - 8 = [tex]\frac{5}{8}[/tex] x 2

Step 1. Simplify.

[tex]\frac{5}{8}[/tex] x 2 = [tex]\frac{5}{8}[/tex] x [tex]\frac{2}{1}[/tex] = [tex]\frac{10}{8}[/tex]

Step 2. Cancel out the negative 8.

[tex]\frac{1}{6}[/tex]d - 8 = [tex]\frac{10}{8}[/tex]

+ 8 to both sides (do the opposite: [tex]\frac{1}{6}[/tex]d is subtracting 8 right now, but to cancel that out, we will do the opposite of subtraction, i.e. addition)

[tex]\frac{1}{6}[/tex]d = [tex]\frac{10}{8}[/tex] + 8

Step 3. Simplify.

[tex]\frac{10}{8}[/tex] + 8 = [tex]\frac{10}{8}[/tex] + [tex]\frac{8}{1}[/tex] = [tex]\frac{10}{8}[/tex] + [tex]\frac{64}{8}[/tex] = [tex]\frac{74}{8}[/tex] = [tex]\frac{37}{4}[/tex]

Step 4. Cancel out the [tex]\frac{1}{6}[/tex].

[tex]\frac{1}{6}[/tex]d = [tex]\frac{37}{4}[/tex]

÷ [tex]\frac{1}{6}[/tex] from both sides (do the opposite: d is multiplied by [tex]\frac{1}{6}[/tex] right now, but to cancel that out, we will do the opposite of multiplication, i.e. division)

÷ [tex]\frac{1}{6}[/tex] = x 6

So....

x 6 to both sides

d = [tex]\frac{37}{4}[/tex] x  6 = [tex]\frac{37}{4}[/tex] x [tex]\frac{6}{1}[/tex] = [tex]\frac{222}{4}[/tex] = [tex]\frac{111}{2}[/tex] = 55.5

Step 5. Write down your answer.

d = 55.5

Q2.

3x - 4 + 5x = 10 - 2x × 3

Step 1. Simplify

3x - 4 + 5x = 3x + 5x - 4 = 8x - 4

10 - 2x × 3 = 10 - (2x × 3) = 10 - 6x

Step 2. Cancel out the negative 6x

8x - 4 = 10 - 6x

+ 6x to both sides (do the opposite - you're probably tired of reading this now - right now it's 10 subtract 6x, but the opposite of subtraction is addition)

14x - 4 = 10

Step 3. Cancel out the negative 4

14x - 4 = 10

+ 4 to both sides (right now it's 14x subtract 4, but the opposite of subtraction is addition)

14x = 14

Step 4. Divide by 14

14x = 14

÷ 14 from both sides (out of the [14 × x] we only want the [x], so we cancel out the [× 14])

x = 1

Step 5. Write down your answer.

x = 1

Q3.

7(c - 3) = 14 × 4

Step 1. Expand the brackets

7(c - 3) = (7 x c) - (7 x 3) = 7c - 21

Step 2. Simplify

14 x 4 = 56

Step 3. Cancel out the negative 21

7c - 21 = 56

+ 21

7c = 56 + 21

7c = 77

Step 4. Cancel out the ×7

7c = 77

÷ 7

c = 77 ÷ 7

c = 11

Step 5. Write down your answer.

c = 11

Q4.

11([tex]\frac{m}{22}[/tex] + [tex]\frac{3}{44}[/tex]) = 87m + m × 5

Step 1. Expand the brackets

11([tex]\frac{m}{22}[/tex] + [tex]\frac{3}{44}[/tex]) = (11 x [tex]\frac{m}{22}[/tex]) + (11 x [tex]\frac{3}{44}[/tex]) = ([tex]\frac{11}{1}[/tex] x [tex]\frac{m}{22}[/tex]) + ([tex]\frac{11}{1}[/tex] x [tex]\frac{3}{44}[/tex]) = [tex]\frac{11m}{22}[/tex] + [tex]\frac{33}{44}[/tex] = [tex]\frac{m}{2}[/tex] + [tex]\frac{3}{4}[/tex]

Step 2. Simplify.

87m + m x 5 = 87m + 5m = 92m

Step 3. Cancel out the add [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] + [tex]\frac{3}{4}[/tex] = 92m

- [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = 92m - [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = [tex]\frac{92m}{1}[/tex] - [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = [tex]\frac{368m}{4}[/tex] - [tex]\frac{3}{4}[/tex]

[tex]\frac{m}{2}[/tex] = [tex]\frac{368m - 3}{4}[/tex]

Step 4. Cancel out the ÷ 4

[tex]\frac{m}{2}[/tex] = [tex]\frac{368m - 3}{4}[/tex]

x 4

2m = 368m - 3

Step 5. Cancel out the 368m

2m = 368m - 3

- 368m

-366m = - 3

Step 6. Cancel out the × -366

-366m = -3

÷ -366

m = [tex]\frac{-3}{-366}[/tex]

m = [tex]\frac{1}{122}[/tex]

Step 7. Write down your answer.

m = [tex]\frac{1}{122}[/tex]

Q5.

ck + 5k = a

Step 1. Factorise

ck + 5k = (c × k) + (5 × k) = (c + 5) x k = k(c + 5)

Step 2. Cancel out the × (c + 5)

k(c + 5) = a

÷ (c + 5)

k = a ÷ (c + 5)

k = [tex]\frac{a}{(c + 5)}[/tex]

Answer:

82 degrees

Step-by-step explanation:

Measure of arc ABC = 86*2 = 172 degrees.

Measure of arc DC = 360 - (145+172) = 360-317 = 43 degrees.

Measure of arc BCD = 121+43 = 164 degrees.

Measure of angle A = 164/2 = 82 degrees

Answer:

T'(-1, -3)

U'(-8, -3)

V'(-9, -10)

W(1, -10)

Step-by-step explanation:

For each point, draw a segment from it to the line y = -x and perpendicular to the line, and extend it the same distance to the other side of the line.

T'(-1, -3)

U'(-8, -3)

V'(-9, -10)

W(1, -10)

Answer:

12x^2 -21x -6

Step-by-step explanation:

(3x-6)(4x+1)

FOIL

first 3x*4x= 12x^2

outer 3x*1 = 3x

inner -6*4x = -24x

last  -6*1 = -6

Add them together

12x^2 +3x -24x -6

Combine like terms

12x^2 -21x -6