A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

A right triangle is shown. The lengths of the 2 sides are 10 feet and 3 feet. The angle opposite to side with length 3 feet is x.

What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

16.7°
17.5°
72.5°
73.3°

Answer:

2.5

Step-by-step explanation:

40 ounces = 2 12 pounds

So, 40 ounces = 4016 = 2 12 or 2.5 pounds.

Hope this helps and sorry if it doesn't

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The arrow is at a height of 48 ft after approx. 3 - √6 s and after 3 + √6 s.

To find the time it takes for the arrow to reach a height of 48 ft, we can use the formula for the height of the arrow:

s = v0t - 16t^2

Here, s represents the height of the arrow, v0 is the initial velocity, and t is the time.

Given that the initial velocity, v0, is 96 ft/s and the height, s, is 48 ft, we can set up the equation:

48 = 96t - 16t^2

Now, let's solve this equation to find the time it takes for the arrow to reach a height of 48 ft.

Rearranging the equation:

16t^2 - 96t + 48 = 0

Dividing the equation by 16 to simplify:

t^2 - 6*t + 3 = 0

We now have a quadratic equation in the form of at^2 + bt + c = 0, where a = 1, b = -6, and c = 3.

Using the quadratic formula:

t = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values:

t = (6 ± √((-6)^2 - 413)) / (2*1)

t = (6 ± √(36 - 12)) / 2

t = (6 ± √24) / 2

Simplifying the square root:

t = (6 ± 2√6) / 2

t = 3 ± √6

Therefore, the arrow reaches a height of 48 ft after approximately 3 + √6 seconds and 3 - √6 seconds.

In summary, the arrow takes approximately 3 + √6 seconds and 3 - √6 seconds to reach a height of 48 ft, assuming an initial velocity of 96 ft/s.

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Note the complete question is

The height of an arrow shot upward can be given by the formula s = v0*t - 16*t², where v0 is the initial velocity and t is time.How long does it take for the arrow to reach a height of 48 ft if it has an initial velocity of 96 ft/s?  

Solve (t-3)^2=6

The arrow is at a height of 48 ft after approx. ___ s and after ___ s.

Answer: the answer as a fraction is 14/5

Step-by-step explanation: in order to multiply a fraction and a whole number you have to make the whole number a fraction. You do this by putting the number over one because anything divided by one is still itself. So you get 2/5 x 7/1 then you multiply across the top so 2 x 7 is 14 then multiply the bottom 5 x 1 is 5 and get the fraction 14/5

does this help?

According to SAS congruent the △abc congruent △def. Thus using the given information, it can be prove.

What is congruent?

In geometry, two figures or objects are said to be congruent if their shapes and sizes match, or if one is the mirror image of the other.

There are four rules to prove congruency. They are SAS, AA, ASA, and SSS.

Given that ∠c ≅ ∠f

ab ≅ de

bc ≅ ef.

According to SAS rule, if two sides and one angle of a triangle is equal to two sides and one angle of another triangle, they the triangle are congruent.

Here two sides and one angle of △abc  is congruent of two sides and one angle of △def.

Therefore △abc congruent △def.

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With a pound of flour costing $12 and considering that there are 16 ounces in a pound, the cost per ounce is $0.75. Thus, for $3.30, you can purchase 4.4 ounces of flour.

To find out how many ounces of flour can be purchased for $3.30, we need to determine the cost of one ounce of flour.

Given that a pound of flour costs $12, we know that there are 16 ounces in a pound (since there are 16 ounces in 1 pound). So, the cost of one ounce of flour can be calculated as:

Cost of one ounce of flour = Cost of one pound of flour / Number of ounces in one pound

Cost of one ounce of flour = $12 / 16 ounces

Cost of one ounce of flour = $0.75

Therefore, the cost of one ounce of flour is $0.75.

To determine how many ounces of flour can be purchased for $3.30, we divide the total amount of money by the cost of one ounce of flour:

Number of ounces of flour = Total money / Cost of one ounce of flour

Number of ounces of flour = $3.30 / $0.75

Number of ounces of flour ≈ 4.4 ounce

Therefore, for $3.30, approximately 4.4 ounces of flour can be purchased.

In summary, with the given cost of $12 for a pound of flour, and knowing that there are 16 ounces in a pound, we find that one ounce of flour costs $0.75. Thus, for $3.30, approximately 4.4 ounces of flour can be purchased.

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Answer:

Not all lines have an x- and y-intercept. This line does not cross the x-axis. Similarly, the line x=2 is a vertical line which does not cross the y-axis.

Step-by-step explanation:

Answer:

No

Step-by-step explanation:

I am assuming you are talking about linear functions. When it comes to them, most of them have a y-intercept, and if they do, they are counted as functions. Linear functions must have some sort of slope, but because there is a special line that does not have a slope, then it is not a function. And since it does not have a slope, it also does not hit the y-axis. Usually, the equation is set to equal y, for example:

y = 1

But, a line that does not have a slope is equal to x, like:

x = 1

x = 1 is a completely vertical line that is parallel to the y-axis, which means it does not have a y-intercept.

To experiment this, you can try it in Desmos, which is a secure graphing website. I hope this helps you!

Tan(angle) = opposite/ adjacent

tan(42) = 67/x

x =67/tan(42)

X = 74.411

rounded to nearest tenth : x = 74.4

Answer: 22

Step-by-step explanation:

20 - 10/2 + 2 . 2

10/5 = 2

20 - 2 + 2 . 2

= 20 - 2 + 4  = 22

hope this helps

Answer:

Step-by-step explanation:

4x^2 - 5x + 3 + 2x - 7

4x^2 - 3x - 4

Answer:

5 ≤ L ≤ 35

Step-by-step explanation:

Let w represent the width of the rectangle.

The perimeter (P) of the rectangle is given by:

P = 2w + 2L

Where L is the length of the rectangle.

We know that w = 30 cm and that the perimeter is between 100 and 160 cm. We can now set up our compound inequality:

100 ≤ 2(30) + 2L ≤ 160

100 ≤ 90 + 2L ≤ 160

10 ≤ 2L ≤ 70

We can now divide both sides by 2 to solve for L:

5 ≤ L ≤ 35

Therefore, the compound inequality that represents the graph of a rectangle with a width of 30 centimeters and a perimeter of 100 centimeters to 160 centimeters is:  5 ≤ L ≤ 35

Answer:

0.125

Step-by-step explanation:

to get the reciprocal of a number we divide the number by 1

in this case it would be 1 divide by 8

1/8 = 0.125

Answer:

5

Step-by-step explanation:

12 x - 3y / 4 x - Z

=12×3-3×1/3÷4×3-5

=36-1/12-5

=35/7

=5

So the final answer is 5.

Answer:

{(x,y,z) : x = 1 - s - , y = s, z = t, s, t ∈ R}

Step-by-step explanation:

We will rearrange the linear equation for x + y + z = 1 that is

x + y + z = 1

x = 1 - y - z

Here there are three variables and one equation. So, there will be two parameters.

Let us assume parameters of s and t for free variables that is

y = s and

z = t

which lies

x = 1 - s - t

Therefore, the parametric representation will be

x = 1 - s - t

y = s

z = t

So, the answer set of the linear equation x + y + z = 1 is

{(x,y,z) : x = 1 - s - , y = s, z = t, s, t ∈ R}

Answer:

The campsites can be chosen in 5,765,760 different ways.

Step-by-step explanation:

Given that a group of campers is going to occupy 6 campsites at a campground, and there are 16 campsites from which to choose, to determine in how many ways the campsites can be chosen, the following calculation must be performed:

16 x 15 x 14 x 13 x 12 x 11 = X

240 x 182 x 132 = X

240 x 24,024 = X

5,765,760 = X

Therefore, the campsites can be chosen in 5,765,760 different ways.

Answer:

I think its B

Step-by-step explanation:

Its B because it is just an experiment to see what will happen and there are no better odds.

Answer:

maybe it's 10.because c is 10,b is 10,and so as s.

hence s is 10 also.

To find the distance above the ground at which the tack is, we need to calculate the vertical displacement of the front wheel when the tack was picked up.

First, let's determine the circumference of the front wheel. The circumference of a circle is given by the formula C = πd, where C is the circumference and d is the diameter. Given that the diameter is 26 inches, we can calculate the circumference:

C = π × 26

C ≈ 81.64 inches

This means that for every complete revolution of the wheel, Devon travels a distance of approximately 81.64 inches.

Next, we need to determine how many complete revolutions the front wheel made as Devon rolled another 100 feet (1200 inches). Since the circumference of the wheel is 81.64 inches, we can divide 1200 inches by 81.64 inches to find the number of revolutions:

1200 / 81.64 ≈ 14.68 revolutions

Now, we know that the tack was picked up after one full revolution. Therefore, out of the 14.68 revolutions, 13 complete revolutions have occurred. The tack is located at the point where the 14th revolution starts.

Since each revolution covers a distance equal to the circumference of the wheel, the vertical displacement of the tack is the height of the wheel, which is the radius of the wheel. The radius is half the diameter, so in this case, it is 26 / 2 = 13 inches.

Therefore, the tack is located 13 inches above the ground.

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The slope of the tangent line is:

a = (df(x1)/dx)

The slope of the normal one is:

a' = -1/(df(x1)/dx)

For any function y = f(x), we define the slope of the tangent line at the point x as the derivative evaluated in x.

So if we want to find the slope of the tangent line at the point (x1, y1), we just need to differentiate and evaluate in x1, then the slope will be given by:

df(x1)/dx

And the normal slope is the slope of the perpendicular line, two slopes are perpendicular if the product is -1, then:

a*(df(x1)/dx) = -1

a = -1/(df(x1)/dx)

Where df/dx reffers to the derivative of f(x).

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Answer:

13

Step-by-step explanation:

use distance formula \(d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\d= \sqrt{(7-2)^2+(7-(-5))^2} =13\)

Answer:

Let's assume that the total number of students in the school is "x". We can create a proportion to estimate how many students would choose the aquarium based on the given information:

Number of students who chose aquarium / Total number of students in the school = Percentage of students who chose aquarium / 100

We can plug in the values we know:

80 / x = p / 100

where "p" is the percentage of students who would choose the aquarium if the entire school were surveyed.

We can solve for "x" by cross-multiplying and simplifying:

8000 = px

x = 8000 / p

Now, we need to estimate the value of "p". We can do this by finding the average percentage of students who chose the aquarium, science center, planetarium, and farm:

(80 + 60 + 30 + 40) / x = (210 / x) = Average percentage of students who chose an attraction

This tells us that, on average, 210 out of every "x" students would choose one of the attractions. We can estimate that a similar percentage of the entire school would choose the aquarium:

p / 100 = 80 / 210

p = 38.1

So, we can estimate that approximately 38.1% of the students in the whole school would choose the aquarium. To find the estimated number of students who would choose the aquarium, we can plug in this value for "p" in our original proportion:

80 / x = 38.1 / 100

Cross-multiplying and solving for "x", we get:

x = 209.71

Rounding to the nearest whole number, we can estimate that approximately 210 students in the whole school would choose the aquarium.

Step-by-step explanation:

Answer:

The teacher surveyed a total of:

80 + 60 + 30 + 40 = 210 students.

If we assume that the sample of 210 students surveyed is representative of the entire population of 1000 students at Lake Middle School, we can use the relative frequency of students choosing the aquarium in the sample to estimate the number of students in the whole school who would choose the aquarium.

The relative frequency of students choosing the aquarium in the sample is:

80/210 = 0.38

This means that approximately 38% of the students in the sample chose the aquarium.

To estimate the number of students in the whole school who would choose the aquarium, we can multiply the relative frequency by the total number of students at the school:

0.38 x 1000 = 380

Therefore, the teacher can estimate that approximately 380 students out of 1000 at Lake Middle School would choose the aquarium for a field trip.

Answer:

$52

Step-by-step explanation:

first you find out what 60% of 130. all you need to do is put a decimal before the percent and multiply it with the cost, in this case 0.6 x 130, which results in 78. next you subtract the percentage result from the total cost to get your answer of $52.

The next number in the series would be 31 so the complete series is 101, 001, 66, 31.

The first thing we observe is that 101 equals 100 plus one. The second term, 001, equals 0 plus 1. Now consider the distinctions between consecutive terms:

101 - 001 = 100

001 - 66 = -65

When we look at the disparities (100, -65), we can see a pattern. The difference between 100 and 65 is a factor of 35. We can now apply this distinction to the final term in the series:

66 - 35 = 31

So the next number in the series is 31, completing the sequence: 101, 001, 66, 31.

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Answer:

FD is the shortest line

FG is the medium length line

GD is the longest line

Step-by-step explanation: THANK ME FOR MY SERVICES with 2% battery left

Answer:

its 8:9

Step-by-step explanation:

It would be 8 because you can see that the top row multiplies 16 by two in the exact spot where the missing number is.

its 56. please give brainliestStep-by-step explanation:

Answer:

It's A (4x^2-x) Got it on edge

Step-by-step explanation:

Answer:

The surface area is 125.66 \(cm^2\)

Hope this helps!