Find the surface area of the figure below

Answer:

x=1

Step-by-step explanation:

55+70=125

sum of angles in a triangle is 180 so

180-125=55

54x+1=55

x=1

Answer:

x=3

Step-by-step explanation:

- 3 on both sides

2x=6

divide by 2 on both sides

x=3

Answer:

x = 3

Step-by-step explanation:

[tex]2x+3=9[/tex]

Subtract 3.

[tex]2x=9-3\\2x=6[/tex]

Divide by 2.

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

Answer: Reduction

(0,0)

1/3

Step-by-step explanation:

Answer:

1-reduction

2-(0,0)

3-1/3

Step-by-step explanation:

Answer:

x=4, y=9.6

Step-by-step explanation:

Using Theorem of Intersecting Secant and Tangent

[tex]TP X TQ=TR^2[/tex]

[tex]9(9+12+x)=15^2\\9(21+x)=225\\189+9x=225\\9x=225-189\\9x=36\\x=4[/tex]

Next, we apply Theorem of Intersecting Chords

SV X VR=PV X VQ

5 X y = x X 12

Recall: x=4

5y=4 X 12

5y=48

y=48/5=9.6

Therefore: x=4, y=9.6

Answer: The answer is F

Step-by-step explanation:

Answer:

300 meters^2

Step-by-step explanation:

10 meters radius

10^2 x pi is about 100 x 3=300

Answer:

450

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

88%

Step-by-step explanation:

Answer:

after paying all expenses Ron will have $10 leftover each month.

Answer:

10 on edge

Step-by-step explanation:

Answer:

1. (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A))  = 1/8

2. θ = 30°

3. tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

from tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ) and sin²(θ) +  cos²(θ) = 1

4. tan10°·tan15°·tan75°·tan80°= 1 from;

sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]

cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]

5. x² + y² = a² + b² where x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ from;

cos²θ + sin²θ = 1

Step-by-step explanation:

1. Here we have 5·tan(A) = 5·sin(A)/cos(A) = 4

∴ 5·sin(A) = 4·cos(A)

Hence to find the value of (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) we have;

Substituting the value for 5·sin(A) = 4·cos(A) into the above equation in both the numerator and denominator we have;

(4·cos(A) - 3·cos(A)/(4·cos(A) + 4·cos(A)) = cos(A)/(8·cos(A)) = 1/8

Therefore, (5·sin(A) - 3·cos(A)/(4·cos(A) + 5·sin(A)) = 1/8

2. For the equation as follows, we have

[tex]\frac{sin \theta}{1 + cos \theta} + \frac{1 + cos \theta}{sin \theta} = 4[/tex] this gives

[tex]\frac{2sin (\theta/2) cos (\theta/2) }{2 cos^2 (\theta/2)} + \frac{2 cos^2 (\theta/2)}{2sin (\theta/2) cos (\theta/2) } = 4[/tex]

[tex]tan\frac{\theta}{2} + \frac{1}{tan\frac{\theta}{2} } = 4[/tex]

[tex]tan^2\frac{\theta}{2} + 1 = 4\times tan\frac{\theta}{2}[/tex]

[tex]tan^2\frac{\theta}{2} - 4\cdot tan\frac{\theta}{2} + 1 = 0[/tex]

We place;

[tex]tan\frac{\theta}{2} = x[/tex]

∴ x² - 4·x + 1 = 0

Factorizing we have

(x - (2 - √3))·(x - (2 + √3))

Therefore, tan(θ/2) = (2 - √3) or (2 + √3)

Solving, we have;

θ/2 = tan⁻¹(2 - √3) or tan⁻¹(2 + √3)

Which gives, θ/2 = 15° or 75°

Hence, θ = 30° or 150°

Since 0° < θ < 90°, therefore, θ = 30°

3. We have tan(θ) - cot(θ) = tan(θ) - 1/tan(θ)

Hence, tan(θ) - 1/tan(θ) = sin(θ)/cos(θ) - cos(θ)/sin(θ)

∴  tan(θ) - 1/tan(θ) = (sin²(θ) -  cos²(θ))/(cos(θ)×sin(θ))...........(1)

From sin²(θ) +  cos²(θ) = 1, we have;

cos²(θ) = 1 - sin²(θ), substituting the value of sin²(θ) in the equation (1) above, we have;

(sin²(θ) -  (1 - sin²(θ)))/(cos(θ)×sin(θ)) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

Therefore;

tan(θ) - cot(θ) = (2·sin²(θ) -1)/((cos(θ)×sin(θ))

4. tan10°·tan15°·tan75°·tan80°= 1

Here we have since;

sin(α)·sin(β) = 1/2[cos(α - β) - cos(α + β)]

cos(α)·cos(β) = 1/2[cos(α - β) + cos(α + β)]

Then;

tan 10°·tan15°·tan75°·tan80° = tan 10°·tan80°·tan15°·tan75°

tan 10°·tan80°·tan15°·tan75° = [tex]\frac{sin(10^{\circ})}{cos(10^{\circ})} \times \frac{sin(80^{\circ})}{cos(80^{\circ})} \times \frac{sin(15^{\circ})}{cos(15^{\circ})} \times \frac{sin(75^{\circ})}{cos(75^{\circ})}[/tex]

Which gives;

[tex]\frac{sin(10^{\circ}) \cdot sin(80^{\circ})}{cos(10^{\circ})\cdot cos(80^{\circ})} \times \frac{sin(15^{\circ}) \cdot sin(75^{\circ})}{cos(15^{\circ})\cdot cos(75^{\circ})}[/tex]

[tex]=\frac{1/2[cos(80 - 10) - cos(80 + 10)]}{1/2[cos(80 - 10) + cos(80 + 10)]} \times \frac{1/2[cos(75 - 15) - cos(75 + 15)]}{1/2[cos(75 - 15) + cos(75 + 15)]}[/tex]

[tex]=\frac{1/2[cos(70) - cos(90)]}{1/2[cos(70) + cos(90)]} \times \frac{1/2[cos(60) - cos(90)]}{1/2[cos(60) + cos(90)]}[/tex]

[tex]=\frac{[cos(70)]}{[cos(70) ]} \times \frac{[cos(60)]}{[cos(60) ]} =1[/tex]

5. If x = a·cosθ - b·sinθ and y = a·sinθ + b·cosθ

∴ x² + y² = (a·cosθ - b·sinθ)² + (a·sinθ + b·cosθ)²

= a²·cos²θ - 2·a·cosθ·b·sinθ +b²·sin²θ + a²·sin²θ + 2·a·sinθ·b·cosθ + b²·cos²θ

= a²·cos²θ + b²·sin²θ + a²·sin²θ + b²·cos²θ

= a²·cos²θ + b²·cos²θ + b²·sin²θ + a²·sin²θ

= (a² + b²)·cos²θ + (a² + b²)·sin²θ

= (a² + b²)·(cos²θ + sin²θ) since cos²θ + sin²θ = 1, we have

= (a² + b²)×1 = a² + b²

Answer:

16 units

Step-by-step explanation:

The y intercept is when the x value is 0

f(0) = 2(0)+8 = 8

The y intercept of f(x) is 8  

g(0) = -8

The y intercept of g(x)  is -8

The distance between f(0) and g(0)

8 - -8 = 8+8 = 16

Answer:

75

Step-by-step explanation:

87-12= 75

edg2020

Step-by-step explanation:

V = (12*4*5) + (2*3*5) + (5*3*5) + (12*4*5)

V = 240 + 30 + 75 + 240

V = 585 cm^3

Answer:

g+h+(j+k)

Step-by-step explanation:

(g+h)+j+k

(g+k)+j+h

(g+j)+h+k

(k+h)+j+h

(j+h)+g+k

Answer:

1 and 3

Step-by-step explanation:

dont mind me this needed to be longer wait still needs no be longer

Answer:

mean= 12.8

median=13

mode=there is no mode

Step-by-step explanation:

mean/average=14+10+12+15+ 13​=64/5=12.8

median=10,12,13,14,15=13

mode= is the number that repeats more often. = there is no mode

Answer:

She must buy 90 tiles for the cost to be the same at both stores

Step-by-step explanation:

Let x be the no. of tiles bought for the cost to be the same at both stores

Margo can purchase tile at a store for $0.89 per tile at shop 1

Cost of x tiles =0.89x

She rent a tile saw for $45.

So, total cost at Store 1 = 0.89x+45

At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile.

So, cost of 1 tile = 1.39

Cost of x tiles = 1.39x

ATQ

0.89x+45=1.39x

45=1.39x-0.89x

45=0.5x

[tex]\frac{45}{0.5}=x[/tex]

90=x

Hence She must buy 90 tiles for the cost to be the same at both stores

The beef price is $10.65

Onions price is $2.49

Potatoes are $3.29

Tomatoes are $8.45

Asparagus is $4.99

3.25 pounds of beef is          3.25 * 10.65 =  34.61

0.65 pounds of onions is      0.65 * 2.49   =  1.62

0.2 pounds of potatoes is     0.2 * 3.29     =  0.66

0.15 pounds of tomatoes is   0.15 * 8.45   =  1.27

0.33 pounds of asparagus is 0.33 * 4.99  =  1.65

Adding these up we get 34.61 + 1.62 + 0.66 + 1.27 + 1.65

This is equal to 39.81

A recipe is mixture of ingredients.

Divya will pay $39.81 for all the ingredients in the recipe.

The beef price is $10.65 per pound

So, price of 3.25 pounds of beef is ,  [tex]3.25 * 10.65 = 34.61[/tex]

Onions price is $2.49 per pound

So, price of 0.65 pounds of onions is,  [tex]0.65 * 2.49 = 1.62[/tex]

Potatoes are $3.29 per pound

So, price of 0.2 pounds of potatoes is ,  [tex]0.2 * 3.29 = 0.66[/tex]

Tomatoes price are $8.45 per pound.

So, price of 0.15 pounds of tomatoes is  , [tex]0.15 * 8.45 = 1.27[/tex]

Asparagus price is $4.99 per pound.

So, price 0.33 pounds of asparagus is , [tex]0.33 * 4.99 = 1.65[/tex]

Hence, total amount paid by Divya is,

             [tex]=34.61 + 1.62 + 0.66 + 1.27 + 1.65=39.81[/tex]

Thus, Divya will pay $39.81 for all the ingredients in the recipe.

Learn more:

https://brainly.com/question/18994792

Answer:

735.13268 units^2

Step-by-step explanation:

A=2πrh+2πr2=2·π·9·4+2·π·92≈735.13268

Answer:

Step-by-step explanation:

Let the price for children and adults package be represented with x and y respectively.

For the first week the sum of the package will be as follows:

3x+8y = 126

For the two weeks after:

6x+4y= 108

So, we will be having two equations

3x+8y = 126..... (1)

6x+4y= 108.......(2)

These are simultaneous equations

From equation 1

3x+8y = 126

3x = 126-8y

X = 126-8y/3 ............. (3)

Put equation 3 into 2

6 ( 126-8y)/3 +4y = 108

756-48y/3 +4y = 108

756-48y+12y/3 = 108

Cross multiplying

756-48y+12y= 108×3

756-48y+ 12y = 324

Collecting like terms

756-324 = 48y-12y

432= 36y

Divide both sides by 36

432/36 = 36y/36

y= 12

Substituting y into equation 1

3x+8= 126

3x+96=126

3x= 126-96

3x= 30

Divide both sides by 3

3x/3 = 30/3

x = 10

Hence for each of the packages for children and adults. It will be 10 and 12 respectively.

Answer:

The distance where the keys would drop from the base is 3.5m

Step-by-step explanation:

Height of the tower = 50m

Angle it makes to the ground = 86°

To solve this question, you have to understand that the tower isn't vertically upright and the height of the tower is different from the distance from the top of the tower to the ground.

The tower makes an angle 86° to the ground and that makes it not vertically straight because a vertically straight building is at 90° to the ground.

See attached document for better illustration.

The distance from where the keys drop to the base of the tower can be calculated using SOHCAHTOA

We have to use cosθ = adjacent / hypothenus

θ = 86°

Adjacent = ? = x

Hypothenus = 50m

Cos θ = x / hyp

Cos 86 = x / 50

X = 50 × cos 86

X = 50 × 0.06976

X = 3.488 = 3.5m

The distance where the keys would drop from the base of the tower is approximately 3.5m

Answer:

b = 4a

Step-by-step explanation:

Given

a = [tex]\frac{1}{4}[/tex] b

Multiply both sides by 4 to clear the fraction

4a = b

Answer:

Out side the circle

Step-by-step explanation:

This is because the center is 0 and if the point 6, square root seven is on the circle that mean that as far as the circle goes on each side.

Answer:

36

Step-by-step explanation:

Answer:

The surface area of the prism is 8/3ft²

Step-by-step explanation:

To calculate the surface area of the prism we have to use the following formula:

a = area

w = side = 2/3 ft

h = height = 2/3 ft

l = length = 2/3 ft

a = 2 * (w * h) + 2 * (w * l) + 2 * (h * l)

we replace the values that ​​we know        

v = 2 * (2/3 ft * 2/3 ft) + 2 * (2/3 ft * 2/3 ft) + 2 * (2/3 ft * 2/3 ft)

v = 2 * 4/9ft²  + 2 * 4/9ft²  + 2 * 4/9ft²

v = 8/9ft²  + 8/9ft²  + 8/9ft²

v = 24/9ft²

v = 8/3ft²

The surface area of the prism is 8/3ft²

Answer:

2⅔ ft²

Step-by-step explanation:

A cube has 6 square faces

6 × (⅔)²

6 × 4/9

8/3

2⅔

Answer:

If the product of two numbers is zero, there are two possibilities, namely;

1. One of the numbers is zero.

2. Both of the numbers are zero.

Step-by-step explanation:

As a rule in mathematics, when zero is used in multiplying any given whole number, the only result that would be obtained is zero.

Therefore,

1. If one of the numbers is zero, then the product of the two numbers is also zero. For example,

153, 000 * 0 = 0

2.  If both of the numbers are zero, then the product of the two numbers is zero. For example,

0 * 0 = 0.

So we can say that both can be true.

Answer:

Choose answers B and D

Step-by-step explanation:

Answer:

Choose answers B and D.

Step-by-step explanation:

Answer:

24

Step-by-step explanation:

Answer:

distance = sqrt((x2-x1)^2 + (y2-y1))

distance = sqrt((7-13)^2 + (10-2)^2)

distance = sqrt( -6^2 + 8^2)

distance = sqrt(36+64)

distance = 10

Step-by-step explanation:

Answer:

10 units

Step-by-step explanation:

d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]

d = [tex]\sqrt{(13 - 7)^2 + (2 - 10)^2}[/tex]

d = [tex]\sqrt{(6)^2 + (-8)^2}[/tex]

d = [tex]\sqrt{36 + 64}[/tex]

d = [tex]\sqrt{100}[/tex]

d = 10 units