Find the surface area of the prism. Write your answer as a fraction or mixed number.

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:

C

Step-by-step explanation:

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:

8.66 meters

Step-by-step explanation:

Assuming that the building is completely straight, a right angle is formed and therefore a right triangle.

Thanks to this we can calculate the height at which the ladder reaches the wall using the Pythagorean theorem, this height being one of the legs.

We have to:

c ^ 2 = a ^ 2 + b ^ 2

c = 10

a = 5

replacing

b ^ 2 = 10 ^ 2 - 5 ^ 2

b ^ 2 = 75

b = 8.66

that is to say that the height at which the ladder reaches the wall is 8.66 meters

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:

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:

88%

Step-by-step explanation:

Answer:

50.32 I think

Step-by-step explanation:

52,13+50,32=102.45

Answer:

A=2x^2+5x

Step-by-step explanation:

length of frame = 2x+5

width of frame = x

A=lw

A=(2x+5)x

A=2x^2+5x

Answer:

450

Step-by-step explanation:

Answer:

the correct answer is 9

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

Answer:

X=25

Step-by-step explanation:

Since these 2 angles are vertically opposite angles so they are equal. (rule)

75°=(4x-25°)

75° + 25° = 4x

100=4x

X=100/4 = 25

___________

Hope this helps...

Answer:

Tim has $50. 15+15=30-35=5

Tim has $5 left

Answer:

a

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

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

Answer:

Step-by-step explanation:

Guven two prime numbers to be 31/x and 71/x, if their sum is 10 as given;

3x + 71/x = 10 then to find the value of x, the following steps must be taken;

Step 1

Find the LCM of the given equation;

3x + 71/x = 10

[tex]\frac{3x^{2}+71 }{x} =10\\[/tex]

Step 2:

Cross multiplying;

[tex]3x^{2} +71=10x\\3x^{2} -10x+71 =0\\[/tex]

Using the general formula to get the value of x;

x = -b±√b²-4ac/2a

a=3, b=-10, c=71

= 10±√(-10)²-4(3)(71)/2(3)

= 10±√100-852/6

= 10±√-752/6

= 10±27.4i/6

= 10+27.4i/6 or 10-27.4i/6

x = 5/3+27.4i/6 or 5/3-27.4i/6

Since the values of x are real values then, our answer will be the real part of the complex number gotten.

x = 5/3

==========================================================

Explanation:

The center is at (0,2). So (h,k) = (0,2) leads to h = 0 and k = 2.

The radius is 2 units, meaning r = 2.

Plug h = 0, k = 2, r = 2 into the formula below and simplify

[tex](x-h)^2 + (y-k)^2 = r^2\\\\(x-0)^2 + (y-2)^2 = 2^2\\\\x^2 + (y-2)^2 = 4[/tex]

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

creo que la respuesta el 10 minutos, porque dice "horas" pero no dice a cuantas horas equivale :)      espero que te aya adudado auque sea un poquito

Answer:

Choose answers B and D

Step-by-step explanation:

Answer:

Choose answers B and D.

Step-by-step explanation:

Answer:

In the books of Wirtz, the selling party, the required entries are

Debit Accounts receivable $780

Credit Revenue $780

Being entries to recognize sales revenue on account

Debit Cost of sales $470

Credit Inventory  $470

Being entries to recognize the cost of items sold

In the books of Cha Company

Debit Inventory $780

Credit Accounts payable  $780

Being entries to record cost of inventory purchased

Step-by-step explanation:

When a company makes a sale, the effect of such sale is dual in the books of the company being that the company would first recognize revenue and then recognize the cost of items sold.

To recognize revenue,

Debit Cash/Accounts receivable

Credit Revenue

To record the cost of the item sold

Debit Cost of sales

Credit Inventory

For the party that makes the purchase

Debit Inventory

Credit Cash/Accounts payable

Answer:45

Step-by-step explanation:

Sin^-1= 5÷7

Answer:

h ≈ 2.64ft

Step-by-step explanation:

A = 2πrh + 2πr2

h= A /2πr﹣r = 240 /2·π·5﹣5 ≈ 2.63944ft

Kono Dio Da!!

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:

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

Answer:

10 on edge

Step-by-step explanation:

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:

-0.954(rounded)

Step-by-step explanation:

first write it in number form

√2(3)-√27

the exact form will be 3√2-3√27 = -0.954(rounded)

Answer:

BGC

Step-by-step explanation:

They are both on a straight line and add up to 180 degrees.

Answer: Reduction

(0,0)

1/3

Step-by-step explanation:

Answer:

1-reduction

2-(0,0)

3-1/3

Step-by-step explanation: