a 12-ft ladder leans against a building so that the angle between the ground and the ladder is 74°. how high does the ladder reach on the building? (round your answer to the nearest foot.)

Answer:

24

Step-by-step explanation:

Since the diagram shows a right triangle and gives out some measurements of the sides, you can use the Pythagorean Theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to find the length of MP.

Given:

hypotenuse = 7  – because the radius is 7 units and it can be used as the hypotenuse

One side of the triangle = 4  – because the length of PO is 4 units and it can be used as one sides of the triangle

To Solve:

Since we know two values of the triangle, you can use the Pythagorean Theorem ([tex]a^{2}+b^{2}=c^{2}[/tex]) to find what the other value is. The variables c and b in the formula are already given, and we need to find what a is to find the length of MP. So, plug the given values of c and b into the formula:

[tex]a^{2}+4^{2}=7^{2}[/tex]

Simplify:

[tex]a^{2}+16=49[/tex]

Subtract 16 from both sides of equation:

[tex]a^{2}=33[/tex]

Do the square root of both sides to isolate the variable a:

[tex]\sqrt{a^{2}}=\sqrt{33}[/tex]

Evaluate:

[tex]a=\sqrt{33}[/tex]  Which simplifies to [tex]a= 5.744562646....[/tex] and round it to the nearest tenth to finally get [tex]a=5.7[/tex]

Answer: The length of MP is 5.7 units

If you look at the diagram in the question, you can see that the length of MN is twice the length of MP. So multiply the length of MP, which is 5.7, by 2:

5.7 · 2 = 11.4

Answer: The length of MN is 11.4 units

___________________________________________________________

Look at the first image below ↓

Description of the first image:

The first image shows a drawn image of the circle with labeled parts and measurements from the infomation given from the question.

The diameter is 26cm, which means that the radius is 13cm because the radius half of the diameter in a circle. The very top line is the surface of the water where it’s filled and it has a length of 20cm. Side b of the triangle is 10cm becuase it’s half the length of the the surface of the water bowl. The hypotenuse (side c) is 13cm because it’s the length of the radius. And side a is what what we need to find because it’s the distance between the surface of the water and the center of the bowl. But after when you find the length of side a, you need to add the length of the radius (which is 13cm) to the length of side a because that’s the rest of the length/depth of the water that’s filled in the bowl. The length of the radius is included with the depth of the water.

Total information given:

⇒ radius = 13cm  – because the radius is half of the diameter, and the diameter has a length of 26cm

⇒ length of the surface where the water’s filled = 20cm

⇒ hypotenuse (side c) = 13cm  – because it’s the length of the radius

⇒ side b = 10cm  – because it’s half the length of the surface where the water’s filled

To Solve

Since there is a right triangle shown in the image, you can use the Pythagorean Theorem  ([tex]a^{2}+b^{2}=c^{2}[/tex]) to find the missing length of side a. Plug the given values of c and b into the formula:

[tex]a^{2}+10^{2}=13^{2}[/tex]

Simplify:

[tex]a^{2}+100=169[/tex]

Subtract 100 from both sides of the equation:

[tex]a^{2}=69[/tex]

Do the square root of both sides to isolate the variable a:

[tex]\sqrt{a^{2}}=\sqrt{69}[/tex]

Evaluate:

[tex]a=\sqrt{69}[/tex]  Which simplifies to [tex]a= 8.30662386....[/tex]  and round it to the nearest tenth to finally get [tex]a[/tex] ≈ [tex]8.3[/tex]

This means that 8.3 is just the length of side a, which is the length between the surface of where the water’s filled and the center of the circle. But, now you need to add 13 to 8.3 to find the total depth of the water because the length of the radius is included with the depth of the water.

So,

13 + 8.3 = 21.3

Answer: The depth of the water is approximately 21.3 cm

Sorry for the very, VERY long explanation and the long solving process, but I really, really hope you understand and that this helps with your question! :)

Answer:

in step by step

Step-by-step explanation:

Distance problems are word problems that involve the distance an object will travel at a certain average rate for a given period of time.

The formula for distance problems is: distance = rate × time or d = r × t.

Things to watch out for:

Make sure that you change the units when necessary. For example, if the rate is given in miles per hour and the time is given in minutes then change the units appropriately.

It would be helpful to use a table to organize the information for distance problems. A table helps you to think about one number at a time instead being confused by the question.

Distance Problems: Given Total Time

Example:

John took a drive to town at an average rate of 40 mph. In the evening, he drove back at 30 mph. If he spent a total of 7 hours traveling, what is the distance traveled by John?

Solution:

Step 1: Set up a rtd table.

r

t

d

Case 1

Case 2

Step 2: Fill in the table with information given in the question.

John took a drive to town at an average rate of 40 mph. In the evening, he drove back at 30 mph. If he spent a total of 7 hours traveling, what is the distance traveled by John?

Let t = time to travel to town.

7 – t = time to return from town.

r

t

d

Case 1

40

t

Case 2

30

7 – t

Step 3: Fill in the values for d using the formula d = rt

r

t

d

Case 1

40

t

40t

Case 2

30

7 – t

30(7 – t)

Step 4: Since the distances traveled in both cases are the same, we get the equation:

40t = 30(7 – t)

Use distributive property

40t = 210 – 30t

Isolate variable t

40t + 30t = 210

70t = 210

210/70

Step 5: The distance traveled by John to town is

40t = 120

The distance traveled by John to go back is also 120

So, the total distance traveled by John is 240

Answer: The distance traveled by John is 240 miles.

Answer:

log₇t = ln t / ln 7

Step-by-step explanation:

Given:

log₇t

Computation:

We know that

logₐb = log b / log a

So,

log₇t = log t / log 7

= log₇t = ln t / ln 7

Answer:

202.5

Step-by-step explanation:

45x0.75=33.75

then do 6x33.75=202.5

Answer:

5/8

Step-by-step explanation:

Answer:

Convert to a decimal by dividing the numerator by the denominator.

0.046875. Then, change the decimal into a fraction which is 3/64ths

Answer:

The correct option is;

0.28

Step-by-step explanation:

The given parameters are;

The mean score for Michael, [tex]\bar x _1[/tex] = 150

The standard deviation, σ₁ = 30

The mean score for Alan,  [tex]\bar x _2[/tex] = 165

The standard deviation, σ₂ = 15

Taking n₁ = n₂ = 1

[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]

Taking μ₁ - μ₂ = 0

[tex]z=\dfrac{(150-165)}{\sqrt{\dfrac{30^{2} }{1}-\dfrac{15^{2}}{1}}} \approx -0.577[/tex]

The p-value for a z-score of -0.577 from the z-table is 0.28434

Therefore, the probability that Michael, with mean score, [tex]\bar x _1[/tex] = 150 will have a greater score than Alan, with a mean score of [tex]\bar x _2[/tex] = 165 is 0.28434 ≈ 0.28

Therefore, the correct option is 0.28

Answer:

The statements describe transformations performed in f(x) to create g(x) are:

a translation of 5 units up ⇒ c

a vertical stretch with a scale factor of 2 ⇒ d

Step-by-step explanation:

Let us use these rule to solve the question

∵ f(x) = x²

∵ g(x) is created from f(x) by some transformation

∵ g(x) = 2x² + 5

→ Substitute x² by f(x) in g(x)

∴ g(x) = 2f(x) + 5

→ Compare it with the rules above

∴ m = 2 and k = 5

→ That means f(x) is stretched vertically and translated up

∴ f(x) is stretched vertically by scal factor 2

∴ f(x) is translated 5 uints up

The statements describe transformations performed in f(x) to create g(x) are:

Answer:

A. 36 x 4 = ?

Answer:

a. 36 x 4

Step-by-step explanation:

If Justin has 4 times as many coins as Ella, who has 36 coins, he would have 144 coins.

Therefore, 36 x 4 = 144

Answer:

1/2x + 18 = 11 - 3x

Step-by-step explanation:

x = -2

Answer:

There are no like terms.

Step-by-step explanation:

Since your not factoring then will simply it

Let's simplify step-by-step.

2x+22

There are no like terms.

Answer:

65 + 0.20(65) = 65 + 13 = 78..they would have to sell 78 to get the bonus

Step-by-step explanation:

(65 - 60) / 65 = 5/65 = 0.0769 x 100 = 7.69 rounds to 7.7 % decrease compared to the 65 pizza's sold yesterday

Answer:

x = 18

Step-by-step explanation:

1: 1/2x - 7 = 1/3x - 4

2: 3/6x - 7 = 2/6x - 4

3: 3/6x = 2/6x + 3

4: 1/6x = 3

5: x = 18

Answer:

cf chocolate fudge

pbf peanut butter fudge

A) 7.50 cf + 7.00 pbf = $1,065

B) cf + pbf = 146

Multiplying equation B) by -7.50

B) -7.50cf -7.50pbf = -1,095 then adding equation A)

A) 7.50 cf + 7.00 pbf = $1,065

-.50pbf = -30

pbf = 60 pounds of Peanut butter fudge

cf = 146 -pbf = 86 pounds of peanut butter fudge

Double Check

86 + 60 = 146

7.50 * 86 + 7.00 * 60 = 1,065.00

Correct!!!

Step-by-step explanation:

The amount of carrots Joey has left according to the task content is; 1.8kg.

It follows from the task content that the quantity of carrots he has initially is; 3 kg.

On this note, upon adding 0.8 kilograms of carrots to a pot of vegetable soup, and grated 400 grams of carrots = 0.4kg, it follows that the quantity of carrot left is;

= 3 - 0.8 - 0.4 = 1.8kg.

Read more on subtraction;

https://brainly.com/question/220101

#SPJ1

Answer:

1st equation: -5x+y=-2

y= -2+5x

2nd equation: -3x+6y= -12

-3x+6(-2+5x)= -12

-3x-12+30x= -12

-3x+30x=0

27x=0

x=0

Answer:

B

Step-by-step explanation:

Answer:

im pretty sure b

Step-by-step explanation:

Answer:

76.25

Step-by-step ex planation:

Sorry if this isn't right, I haven't done inequalities in a while.

Answer:

20 percent

Step-by-step explanation:

Answer:

20%

Step-by-step explanation:

since 100% is a 200, half of them were circus clowns 200/2 = 100

so 100 persons are 50%

from these 100, only 60 graduated as rodeo clowns and 40 as memes

1 percent of 200 is 2, so 40/2=20%

answer : 0.0001982 in scientific notation = see picture

Answer:

The approximate 90% confidence interval is;

70,244 to 70,732

Step-by-step explanation:

Here, we want to calculate the approximate 90% C.I for the situation

Mathematically;

CI = mean ± (z * SD)/√n

From the question;

mean = 70,438

SD = 645.3

n = 30

we can get z from the CI table

90% CI is same as; 1.645 z-score

So , substituting these values;

CI = 70,438 ± ( 1.645 * 645.3)/√30

CI = 70,438 ± 194

So the CI = 70,438 -194 to 70,438 + 194

= 70,244 to 70,732

Answer:

B. 70,244 and 70,632

Please give me brainliest, I really need it.

Answer:

C. 5units

Step-by-step explanation:

Answer:

lllllllllllllllllllololollllll

Answer: 308

Step-by-step explanation:

SOLUTION STEPS

880×35%

Reduce the fraction  

[tex]\frac{35}{100}[/tex]

 to lowest terms by extracting and canceling out 5.

[tex]880*(\frac{7}{20} )[/tex]

Express [tex]880*(\frac{7}{20} )[/tex]

as a single fraction.

[tex]\frac{880*7}{20}[/tex]

Multiply 880 and 7 to get 6160.

[tex]\frac{6160}{20}[/tex]

Divide 6160 by 20 to get 308.

308