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2 years ago

A. 22.59 B. 14.34 C. 20.48 D. 10.70

Mathematics

1 answer:

REY [17]2 years ago

6 0

Answer:

B. 14.34

Step-by-step explanation:

The mnemonic SOH CAH TOA reminds you of the relationship between the side opposite the angle of interest and the hypotenuse:

Sin = Opposite/Hypotenuse

For the given triangle, this means ...

sin(35°) = b/25

b = 25·sin(35°)

b ≈ 14.34

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Ben, Tim, and Sam have to do a certain job. Ben can finish the job in 5 hours. Tim can finish the job in 6 hours. Sam can finish

Brut [27]

x is 7.5 hours

Step-by-step explanation:

Ben, Tim, and Sam have to do a certain job

Ben can finish the job in 5 hours
Tim can finish the job in 6 hours
Sam can finish the job in x hours
The three of them can finish the job in 2 hours if they work together

We need to find x

∵ Ben can finish the job in 5 hours

∴ The rate of Ben = $\frac{1}{5}$

∵ Tim can finish the job in 6 hours

∴ The rate of Tim = $\frac{1}{6}$

∵ Sam can finish the job in x hours

∴ The rate of Sam = $\frac{1}{x}$

They will working together to finish the job in two hours, that means the sum of their rate is equal to 1/2

∵ They can finish the job in 2 hours if they work together

∴ $\frac{1}{5}+\frac{1}{6}+\frac{1}{x}=\frac{1}{2}$

To add the fractions find the LCM for all denominators to make all fractions with same denominators

∵ The LCM of 5, 6 ans x is (5 × 6 × x) = 30 x,

- Divide it by each denominator to find the new numerators

∵ 30 x ÷ 5 = 6 x , 30 x ÷ 6 = 5 x , 30 x ÷ x = 30

- Change all the denominators to 30 x and then write the new

numerators of each fraction

∴ $\frac{6x}{30x}+\frac{5x}{30x}+\frac{30}{30x}=\frac{1}{2}$

Add the numerators and put the sum over 30 x

∵ $\frac{11x+30}{30x}=\frac{1}{2}$

- By using cross multiplication

∴ 2(11 x + 30) = 1(30 x)

- Simplify the both sides

∴ 22 x + 60 = 30 x

- Subtract 22 x from both sides

∴ 60 = 8 x

- Divide both sides by 8

∴ 7.5 = x

∴ The value of x is 7.5 hours

x is 7.5 hours

Learn more:

You can learn more about the word problems in brainly.com/question/10712420

#LearnwithBrainly

5 0

3 years ago

A fence is to be built to enclose a rectangular area of 450 square feet. The fence along three sides is to be made of material t

Mila [183]

Answer:

The short side is _15___ft and the long side is ___30___ ft.

Step-by-step explanation:

As fence is built in a rectangular area, so we can consider

Let

x be the length of the rectangle

y be width of the rectangle

Given area of rectangle is = 450 ft²

Formula for area of rectangle = Length x width

450 ft² = xy

Solve for y

y = 450/x

now according to given condition

three sides of the fence costs $5 per foot and for the fourth side costs$15 per foot.

We have two condition either the fourth side be x or y

So condition 1: Three sides =(x,y,x) 4-th side = y.

So we can write as 5x,5y,5x and 15 y

Cost C = 5x +5y+5x+15y

= 10x+ 5y+15y

= 5(2x+y) +15y----------------equation 1

= 10x +20y

Adding value of y 450/x

= 10x + 20(450/x)

= 10x + 9000/x

For minimum cost, we can consider the cost to be 0

0 = 10x + 9000/x

Dividing and multiplying by -x/x

0 = -10 +9000/x²

10 = 9000/x²

10x² = 9000/

x²= 900

x = 30

so y = 450/x = 450/30= 15 ft

so adding the values of x and y in equation 1 we will have

cost C= 5(2x+y) +15y----------------equation 1

cost is = 5(2(30)+15) +15(15)

= $600 is the cost

X= 30 y =15

So condition 2: Three sides =(y,x,y) 4-th side = x.

So we can write as 5y,5x,5y and 15 x

Cost C = 5y +5x+5y+15x

= 5x+ 10y+15x

= 5(x+2y) +15x----------------equation 2

= 20x +10y

Adding value of y= 450/x

= 20x + 10(450/x)

= 20x + 4500/x

For minimum cost, we can consider the cost to be 0

0 = 20x + 4500/x

Dividing and multiplying by -x/x

0 = -20 +4500/x²

20 = 4500/x²

20x² = 4500

x²= 4500/20= 225

x = 15

so y = 450/x = 450/15= 30 ft

so adding the values of x and y in equation 2 we will have

cost C= = 5(x+2y) +15x----------------equation 2

cost is = 5(15+2(30) +15(15)

= $600 is the cost

y= 30 x=15

so from both conditions satisfy the cost and the two sides are known as length and width

so dimension will be 15 ft by 30 ft

7 0

2 years ago

Find the missing angles for each problem, given that lines a and b are parallel (step by step)

marshall27 [118]

Answer:

1) 40°

2) 140°

3) 140°

5)40°

6)140°

7)140°

8)40°

Step-by-step explanation:

1 = 40 ° [Vertically Opposite angles are equal]

8 = 40 ° [Corresponding Angles are equal]

5 = 8 = 40° [Corresponding Angles are equal]

7 = 180° - 40° = 140° [Supplementary angles sum 180°]

6 = 140° [Vertically Opposite angles are equal]

2 = 140° [Corresponding Angles are equal]

3 = 140 ° [Vertically Opposite angles are equal]

3 0

3 years ago

Which relationships describe angles 1 and 2?

lozanna [386]

Complementary angles
Adjacent angles

Correct

7 0

2 years ago

Find the value of x and y

Ket [755]

A line has the angle of 180°

I'm going to assume that blurry number is a 35, but you can use this for any situation

180 - 35 = 145°

Angle x and y are the same

3 0

3 years ago