A ladder is leaning against a building and makes 42° angle with the ground. The top of the ladder reaches 30 feet up on the building. What is the length of the ladder?

Answers

Answer 1

Here we have a right triangle with hypotenuse h, which is to be found. The top of the ladder is 30 feet above the ground, and that distance is opposite the 42 degree angle mentioned. Use the sine function to determine the hypotenuse, h:

sin 42 deg = opp / hyp, or hyp*sin 42 deg = 30 ft. Then hyp = (30 ft)(sin 42), which in turn equals hyp = (30 ft) / (0.669) = 44.8 feet (answer)

Answer 2

The length of the ladder will be 44.8 feet.

What is a right-angle triangle?

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The connection between the lengths and angles of a triangular shape is the subject of trigonometry.

A ladder is leaning against a building and makes a 42° angle with the ground.

The top of the ladder reaches 30 feet up on the building.

Let the length of the ladder be L.

Then the length of the ladder is given by the sine of angle 42°.

sin 42° = 30 / L

L = 30 / sin 42°

L = 30 / 0.699

L = 44.8 feet

The length of the ladder will be 44.8 feet.

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Related Questions

Out of 28 students in a class, 7 have blue eyes. What is the probability a student picked at random from the class does NOT have blue eyes?

A) 1/4

B) 3/4

C) 1/7

D) 6/7

Answers

3/4 because 1/4 of the class has blue eyes, so the other 3/4 don't.

there are 28 total and 7 have blue eyes meaning the probability of picking so.eone with blue eyes is
[tex] \frac{7}{28} = \frac{1}{4} [/tex]
so the probability of pi king someone without blue eyes is the entire sample minus the probability of blue eyes so
[tex]1 - \frac{1}{4} = \frac{4}{4} - \frac{1}{4} = \frac{3}{4} [/tex]
so there is 75% chance of picking someone without blue eyes.

if u like my answer please rate as brainliest! thx

PLZ HELP 20 POINTS!

What is7√2 in simplest radical form?

Answers

9.8 I think... I hope this helps in any way

What is the simplified form of the equation 3/5n-4/5=1/5n ?

A- n=-1
B- n=2
C- n =5/3
D- n=5/2

Answers

3/5=.6
4/5=.8
1/5=.2
The answer is n=-1

Answer:

B. n = 2

Step-by-step explanation:

Given equation,

[tex]\frac{3}{5}n-\frac{4}{5}=\frac{1}{5}n[/tex]

[tex]\frac{3n-4}{5}=\frac{n}{5}[/tex]

[tex]3n-4=n[/tex]

Subtracting n on both sides,

[tex]3n - 4 - n = n - n[/tex]

[tex]2n - 4 = 0[/tex]

Adding 4 on both sides,

[tex]2n=4[/tex]

Divide both sides by 2,

[tex]n=2[/tex]

Hence, OPTION B is correct.

What is the mode of the given data set? 65, 45, 79, 56, 63, 45, 71, 69, 65, 53, 45

Answers

The mode of that data set is 45.

45
line them up from least to greatest an find the number that repeats the most
45 repeats 3 times

I need help... i don't really understand this...

In 2000, the circulation of a local newspaper was 3,250. In 2001, its circulation was 3,640. In 2002, the circulation was 4,100. a. Find the percent of increase in the newspaper’s circulation from 2000 to 2001 and from 2001 to 2002. b. Which period had a higher percent of increase, 2000 to 2001, or 2001 to 2002?

Answers

The formula for percentage change is:

(New number - Original number) / Original number × 100 = Percentage change

(3640-3250)/3250 x 100 =
(390)/3250 x 100 =
.12 x 100 = 12%

(4100-3640)/3640 x 100 =
(460)/3640 x 100 =
.1263736264 x 100 = ~ 12.6%

2001 to 2002 had a higher percent of increase.

The percent of increase in the newspaper’s circulation from 2000 to 2001 and from 2001 to 2002 is 12% and 12.6% respectively

Given:

2000 = 3,250

2001 = 3,640

2002 = 4,100

Percentage change2000 to 2001 = (Difference in change) / old value × 100

= (3,640 - 3,250) / 3,250 × 100

= 390 / 3,250 × 100

= 0.12 × 100

= 12%

Percentage change 2001 to 2002 = (Difference in change) / old value × 100

= (4,100 - 3,640) / 3,640 × 100

= 460 / 3,640 × 100

= 0.126373626373626 × 100

= 12.63736263736263%

Approximately,

12.6%

Therefore, the period which had a higher percent of increase is 2001 to 2002

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which is a table of values for y = x - 12

Answers

we have that
y=x-12
so

for x=-5
y=-5-12----> y=-17

for x=-8
y=-8-12----> y=-20

for x=-7
y=-7-12----> y=-19

the answer is
x y
-5 -17
-8 -20
-7 -19

Answer:

The second one

Step-by-step explanation:

-5 -17

-8 -20

-7 -19

HELP ASAP!! I have my Algebra EOC tomorrow and I need help on this question. Please explain!!! 30 POINTS

Answers

figuring it out now.. one minute :)

10 point! Please Help! ASAP!!

How many more cubic inches of juice will cup B hold than cup A when both are completely full? Round your answer to the nearest tenth.

A 8.8 cubic inches
B 10.1 cubic inches
C 14.7 cubic inches
D 22.3 cubic inches

Answers

The answer for the given equation is C

Find the volume of each cup.

Volume of cup A = [tex] \frac{1}{3} \pi r^{2} h[/tex]

V = [tex] \frac{1}{3} (3.14)(1)^2(4)[/tex]
V = [tex]4.187[/tex]

Volume of cup B = [tex] \pi r^2h[/tex]

V = [tex](3.14)(1)^2(6)[/tex]
V = [tex]18.84[/tex]

Now subtract the volume of cup A from cup B.

18.84 - 4.187 = 14.653

cup B will hold 14.7 cubic inches more juice than cup A.

The answer is C.

Hope this helps :)

4. Rosa plays games at a fair. She can buy 8 game tokens for $ 1. Each game cost 2 tokens. How many games can she play with 120 tokens? Write a rule and complete the table.

Please help with the bottom one too

Answers

Answer:

60 tokens and the rule is the number of tokens divided by 2

20 cups of oats and the number of cups of raisins times 2

Final answer:

Rosa can play a total of 60 games with 120 tokens.

Explanation:

To determine the number of games Rosa can play with 120 tokens, we need to divide the total number of tokens by the number of tokens required to play a game. Since each game costs 2 tokens, we divide 120 by 2. This gives us the number of games Rosa can play, which is 60.

We can also write a rule to calculate the number of games Rosa can play. Let G represent the number of games, and T represent the number of tokens. The rule would be: G = T ÷ 2. We can substitute T with 120 to find G: G = 120 ÷ 2 = 60.

Here is a table that shows the number of games Rosa can play for different numbers of tokens:

Number of Tokens
Number of Games

2
1

4
2

6
3

8
4

10
5

...
...

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A circle has an area of 78.5 square inches. What is the diameter of the circle?

Answers

We have to know the formula to finding the area of a circle. Since the area is clearly rounded, we can use 3.14 for pi.
R^2•3.14=78.5
Let’s divide both sides by 3.14.
R^2=25
5•5
5
So the radius is 5. The diameter is double the radius. The diameter of the circle is 10.

Final answer:

To determine the diameter of a circle with an area of 78.5 square inches, we solve for the radius using the area formula (A = πr²). We find the radius to be 5 inches, and since the diameter is twice the radius, the diameter is 10 inches.

Explanation:

The student has asked how to determine the diameter of a circle if the area is known to be 78.5 square inches. To find the diameter, we first need to calculate the radius using the area formula for a circle, which is A = πr², or area equals pi times the radius squared. Pi (π) is approximately 3.14159, but for most calculations, we can use 3.14 for simplicity.

To solve for the radius, we rearrange the formula to r² = A / π. Plugging in the given area of 78.5 square inches:

r² = 78.5 / 3.14 = 25

Next, we take the square root of both sides to find the radius: r = √25 = 5 inches.

Now that we have the radius, we can determine the diameter by multiplying the radius by 2, as the diameter is twice the length of the radius. Thus, the diameter of the circle is 10 inches.

6 grade math plz help

Answers

A. Lily made $75.36 more than Layla.
B. She is incorrect.

A. First find out how many cupcakes each made. To do so, you multiply 8 by 60 to find how many minutes are in those 8 hours, then divide by the number of minutes it took for each batch.
Next you'd multiply the answer you get by the number of cupcakes in each batch, to get how many they made total.
After that, you find how many each of them sold.
Then, you multiply how many they sold, by how much each costed.
Finally, you subtract the smaller value from the larger value to find the difference, and who made the most money.

Lily: First, 8*60 = 480. Divide 480 by 10 (how long each batch took) to get 48. Multiply 48 by 7 to get how many cupcakes she made (336).
Next, divide 336 by 3, to get 112, then multiply by 2 to find how many she sold (2/3 of 336 = 224).
Then, multiply 224 by $1.29 to find how much she made ($288.96).

Layla: First, 8*60 = 480 and divide 480 by 12 (again, how long each batch took) to get 40.
Multiply 40 by 8 (cupcakes per batch) to get 320.
Divide 320 by 4 to get 80, then multiply 80 by 3 to get how many she sold (240).
Multiply $0.89 by 240 to get her total ($213.60).
Finally, subtract Layla's total from Lily's total to find out how much more Lily made.

B. Since Layla made 240 cupcakes, and she thinks selling each for a dollar will make her total larger than Lily's, multiply $1.00 by 240, to get $240.00, thus proving her hypothesis was incorrect.

I hope this helps!

Which point is a solution to the system of equations graphed below?

Answers

I would say, "6.5, 5."

A giant pencil, in the shape of a cylinder, has a length of 36 inches and a diameter of 6 inches. On top, it has a cone-shaped tip with a height of 4 inches. What is the volume of the pencil terms of pi?

Answers

r=3
Vcyl.=36(9π)=324π
Vcone=4(9π)=36π
V pencil=324π+36π=360π

Mary and her dad shared one dozen brownies 2/6 of them have nuts which dad doesn't eat how many brownies did dad not eat because they had nuts

Answers

He did not eat 4 of the brownies. This is because 2/6 is equivalent to 4/12. That means he couldn't have eaten 4 of them. Hope that helps!!

“Dad”couldn’t eat 4 since 2/6 is equivalent to 4/12 and the problem states that Mary had cooked a dozen brownies so overall he couldn’t eat 4 brownies

HURRY BRAINLIEST ALREADY TAKEN BUT WOULDN'T IT BE NICE TO KNOW YOU HELPED SOMEONE? :)
Is this right? Problem attached

Answers

The distance between Angela's house and the gas station, is the distance between the points (4,3) and (10,8). To find that distance, we are going to use the distance formula: [tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]

From our two points we can infer that [tex]x_1=4[/tex], [tex]y_1=3[/tex], [tex]x_2=10[/tex], and [tex]y_2=8[/tex]. So lets replace those values in our ditance formula:
[tex]d= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2} [/tex]
[tex]d= \sqrt{(10-4)^2+(8-3)^2} [/tex]
[tex]d= \sqrt{(6)^2+(5)^2}[/tex]
[tex]d= \sqrt{36+25}[/tex]
[tex]d= \sqrt{61} [/tex]

We can conclude that the gas station is [tex] \sqrt{61} [/tex] units, which is approximately 7.8 units, from her house.

how much green ooze was carried all??

Answers

There is 4 1/2 cups of green ooze

Answer:

[tex]5[/tex] cups.

Step-by-step explanation:

We have been given a line plot, which represents the cups of green ooze. We are asked to find the total number of cups.

To find the total number of cups, we will add all the given quantities as shown below:

[tex]2\times\frac{1}{4}+2\times\frac{3}{8}+2\times\frac{1}{2}+3\times\frac{5}{8}+\frac{7}{8}[/tex]

[tex]\frac{2\times1}{4}+\frac{2\times3}{8}+\frac{2\times1}{2}+\frac{3\times5}{8}+\frac{7}{8}[/tex]

[tex]\frac{2}{4}+\frac{6}{8}+\frac{2}{2}+\frac{15}{8}+\frac{7}{8}[/tex]

Make a common denominator:

[tex]\frac{2\times2}{4\times2}+\frac{6}{8}+\frac{2\times 4}{2\times 4}+\frac{15}{8}+\frac{7}{8}[/tex]

[tex]\frac{4}{8}+\frac{6}{8}+\frac{8}{8}+\frac{15}{8}+\frac{7}{8}[/tex]

Add numerators:

[tex]\frac{4+6+8+15+7}{8}[/tex]

[tex]\frac{40}{8}[/tex]

[tex]5[/tex]

Therefore, there are [tex]5[/tex] cups of green ooze in all.

PLEASE HELP ME 19 POINTS What is the perimeter of quadrilateral MNOP ?
16 units
18 units
22 units
36 units

Answers

The answer is 22. Add the 2 dudes of 6 to get 12. Use Pythagorean theorem to get 5 as each diagonal side. So 10 plus 12=22.

The value of the perimeter of quadrilateral MNOP is,

= 22 units

What is mean by Rectangle?

A rectangle is a two dimension figure with 4 sides, 4 corners and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other.

We have to given that;

A quadrilateral MNOP is shown in figure.

M = (- 2, 2)

N = (2, 5)

O = (8, 5)

P = (4, 2)

Now, We can formulate;

MP = 6 units

PO = √(8 - 4)² + (5 - 2)²

PO = √ 25

PO = 5

Thus, The value of the perimeter of quadrilateral MNOP is,

= 2 (MP + PO)

= 2 (6 + 5)

= 2 x 11

= 22 units

So, The value of the perimeter of quadrilateral MNOP is,

= 22 units

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URGENTAbel uses a probability simulator to roll a six-sided number cube 100 times and to flip a coin 100 times. The results of the experiment are shown below: Number on the Cube
Number of Times Rolled
1 l 12
2 l 18
3 l 30
4 l 22
5 l 10
6 l 8
Heads:34 Tails:66
Using Abel's simulation, what is the probability of rolling a 2 on the number cube and the coin landing on tails?
84/10,000
1,188/10,000
18/100
66/100

Answers

The running of the simulation serves to give us an approximate probability of each of the outcomes, so in this case, P(Tails)=66/100 and P(2)=18/100.
The probability of two independent things occurring can be written as P(A)*P(B).
Therefore, the probability of a 2 and tails is (66/100)*(18/100)=0.1188= 1188/10000

The running back for the Bulldogs football team carried the ball 3 times for a total loss of 6 3/4 yards. Find the average change in field position on each run. Enter the average change as a simplified mixed number.

Answers

-6 3\4 / 3 = -2 1/4
Average of -2 1/4 yards per play

Final answer:

The average change in field position per run is -2 1/4 yards. This is found by dividing the total yardage lost (6 3/4 yards) by the number of runs (3).

Explanation:

The subject of this problem is calculating the average. In this case, we are looking for the average yardage lost by the running back on each run. The running back for the Bulldogs football team has carried the ball 3 times for a total loss of 6 3/4 yards.

To find the average change in field position on each run, divide the total loss by the number of runs:

Convert the mixed number 6 3/4 to an improper fraction. This gives us 27/4. Divide the numerator (27) by the denominator (4). This gives us -6.75. Divide -6.75 by 3 (the number of runs). This gives us -2.25. Convert -2.25 to a mixed number, which gives us -2 1/4.

Therefore, -2 1/4 yards is the average change in field position on each run.

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HELP ME PLEASE!!!!!!

The body of a 154-pound person contains approximately 2 X 10^-1 milligrams of gold and 6 X 10^1 milligrams of aluminum. Based on this information, the number of milligrams of aluminum in the body is how many times the number of milligrams of gold in the body?

Answers

The number of milligrams of aluminium in the body is 300 times the number of milligrams of gold in the body.

Given amount of gold is = g = [tex]2 * 10^{-1}[/tex] mg.

Given amount of aluminium is = a = [tex]6*10^1[/tex] mg.

Let the number of milligrams of aluminium in the body is "k" times the number of milligrams of gold in the body.

So, a = kg

[tex]k=\frac{a}{g}\\k=\frac{6\cdot10^{1}}{2\cdot10^{-1}}\\k=300[/tex]

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Final answer:

The body of a 154-pound person contains approximately 300 times more milligrams of aluminum than milligrams of gold. This is found by dividing the amount of aluminum (60 milligrams) by the amount of gold (0.2 milligrams).

Explanation:

To find out how many times the number of milligrams of aluminum is compared to that of gold in a 154-pound human body, we need to divide the amount of aluminum by the amount of gold. The problem states that there are 2 X 10^-1 milligrams of gold and 6 X 10^1 milligrams of aluminum. If we simplify these expressions, we get 0.2 milligrams of gold and 60 milligrams of aluminum.

Next step is to divide the number of milligrams of aluminum by the number of milligrams of gold. Hence, 60 ÷ 0.2 gives us 300.

Therefore, the body of a 154-pound person contains approximately 300 times more aluminum than gold.

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The volume of a cube can be found using the equation V = s³, where V is the volume and s is the measure of one side of the cube. Match the equation for how to solve for the side length of a cube to its description. Drag the equation into the box to match the description.A cube has a volume of 756 in³.

Answers

If the Volume of the cube is 756in³, then
756in³ = s³ now just take the cube root of each side of the equation.
[tex] \sqrt[3]{756} = \sqrt[3]{ s^{3} } [/tex]
so the new equation to solve for 's' is:
[tex]s= \sqrt[3]{756} [/tex]

Answer:

Step-by-step explanation:

Simplify the expression

Answers

Notice that we have a difference of squares in the numerator of our expression. In the denominator we have a quadratic expression of the form [tex]ax^2+bx+c[/tex]. So we can factor both numerator and denominator and cancel common terms:
[tex] \frac{w^2-9}{w^2-4w-21}= \frac{w^2-3^2}{(w+3)(w-7)} = \frac{(w+3)(w-3)}{(w+3)(w-7)}= \frac{w-3}{w-7} [/tex]

We can conclude that the correct answer is the fourth one: [tex]\frac{w-3}{w-7}[/tex]

Solve and graph on number line.
a-1 > -9

Answers

I’m not sure if this is helpful at all, but I put it in a math app called photomath, and the picture attached is what I got, a>8

1)you can use any side as the__ of a triangle.
2)An ___ is a region blinded by an arc and the two radii to the arcs endpoints.
3)the distance from the center to a vertex is the ___ of a regular polygon.
4)two arcs of a circle with exactly one point in common are ___.

9) A triangle has legs measuring 5ft and 12ft, and hypotenuse measuring 13ft. What is the area?

13) is the picture above.

17) what is the area of a regular hexagon with a perimeter of 240cm?

I have more questions but will post separately because they are all pictures!!!!

Answers

Answers:
(1) Base
(2) Sector of a circle
(3) Radius
(4) Adjacent arcs
(9) 30
(13) 256 ft^2
(17) 4156.92 cm^2

Explanations:
(1) It's a common convention that you can choose any side of a triangle as a base, but in specific cases like in the right-angled triangle, the base should always be the adjacent leg with which the 90 degree angle is made. In other words, in the case of right-angled triangle, the two legs of a triangle must be perpendicular to one another (meaning make 90 degrees angle). But in general triangles you can choose any side as a base of a triangle.

(2) The image is attached below. As you can see that a sector of a circle is actually the region which is shaded. Two radii that meet at the end points of an arc yield a region within a circle know as "sector". Hence the correct fill in the blank is the "sector of a circle."

(3) The radius of a regular polygon is the distance from the center to any vertex. It is the same for each and every vertex. The radius is also the radius of the polygon's circumcircle, which is the circle that passes through every vertex. In this role, it is sometimes called the circumradius. Hence the correct answer is "radius."

(4) Adjacent arcs in simple words are the arc that lie next to each other. They have one point in common being next to each other. Hence the correct answer is adjacent arcs. One interesting fact is that a circle is made up of very large number of adjacent arcs.

(9) As the hypotenuse is mentioned, it means that it is a right-angled triangle; therefore:

Area of a right angled triangle = 1/2 * base * height
Area of a right angled triangle = 1/2 * 5* 12 = 30 ft^2

(13) The picture consists of FOUR right-angled triangles (making a parallelogram) therefore the area would be:
Area = 4 * 1/2 * base * height
Area = 4 * 1/2 * 12.8* 10 = 256 ft^2

(17) The general formula for the area of a polygon is:
Area = [tex] \frac{3 \sqrt{3} a^2 }{2} [/tex]

Where P = perimeter = 6a (hexagon)
=> a = P/6

Plug in the values
Area = [tex]\frac{ \sqrt{3} P^2 }{24} = \frac{ \sqrt{3} (240)^2 }{24} = 4156.92 cm^2[/tex]

The base of a pryramid can be any polygon how many faces does a pentagonal pyramid have ? Describe the shapes of the faces 22 points plz help give a good answer

Answers

The pentagonal pyramid will have 6 faces: 5 triangular and 1 pentagonal. We know what one face is - the pentagonal base. Since a pentagon has five edges, and the other triangular faces extend from these edges to the point of the pyramid, there must be 5 other sides. I have also attached images of this pyramid both regular and flattened out so you can picture what it looks like.

A pentagonal pyramid has six faces: one pentagonal base and five triangular lateral faces. Each side of the pentagonal base connects to the apex forming five triangular faces. The total number of faces is six.

A pyramid is a three-dimensional geometric shape with a polygon as its base and triangular faces that meet at a single point called the apex.

A pentagonal pyramid has a base in the shape of a pentagon.

The total number of faces in a pentagonal pyramid equals the number of sides on the base (5) plus one more for the base itself, giving a total of six faces.

Thus, a pentagonal pyramid consists of six faces - one pentagonal base and five triangular lateral faces.

The sum of two numbers is 55. One number is 4 times as large as the other. What are the numbers? PLEASE HELP

Answers

11 and 44 because 44 is 4 times as much bigger than 11

Answer:

44 and 11

Step-by-step explanation:

A malt shop used one-fourth of a box of waffle cones every day they were open. How many days would 2 whole boxes last them

Answers

It would last them 8 days

8 open business days.

If f(x) = x2 and g(x) = 1 over 2x + 3 , find g(f(-1)).

Answers

f(x)=x^2
g(x)=1/(2x+3)
g(f(-1))=?

x=-1→f(-1)=(-1)^2→f(-1)=1
g(f(-1))=g(1)=1/[2(1)+3]=1/(2+3)→g(f(-1))=1/5

Answer: Third option 1/5

a parking garage charges $2.00 for the first hour and $0.50 for each fraction of an hour thereafter. Which statement describes the relationship between the parking fee and the amount of time a person parks in the garage? A. the parking fee depends on the amount of time a person uses the garage B. The amount of time a person uses the garage depends on the parking fee C. the parking fee and the amount of time a person uses the garage are independent D. the relationship cannot be determined

Answers

The answer is A. The parking fee depends on the amount of time a person is parked

What is the simplified form of square root 64x^16?
A. 8x^4
B. 8x^8
C. 32x^4
D. 32x^8

Answers

[tex] \sqrt{64x^{16} } [/tex]
We know that the root of 64 is 8 and the root of 16 is 4.
= [tex]8x^{4} [/tex]

The simplified form of [tex] \sqrt{64x^{16} } [/tex] is [tex]8x^{4} [/tex].

Other Questions

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