A brace for a shelf has the shape of a right triangle. Its hypotenuse is 8 inches long and the two legs are equal in length. How long are the legs of the triangle?

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Answer 1

since it's a right triangle

[tex]\bf \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ -------\\ c=8\\ b=a \end{cases}\implies 8^2=a^2+a^2 \\\\\\ 64=2a^2\implies \cfrac{64}{2}=a^2\implies 32=a^2\implies \sqrt{32}=a \\\\\\ \sqrt{16\cdot 2}=a\implies \sqrt{4^2\cdot 2}=a\implies 4\sqrt{2}=a[/tex]

Related Questions

Keeping in mind that a functions rate of change is measure of how fast the function is increasing or decreasing what does the slope of a linear function indicate?

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When a linear function is graphed, a line will drawn on the plot. If we analyze this, this means that the two variables are related by a constant of proportionality. That constant is called the slope. Since the slope is constant, that means that the rate of change is also constant. It would only differ if the rate is increasing or decreasing. It would be increasing if its magnitude is positive which will be graphed as a diagonal to the right. Otherwise, it is decreasing whose magnitude is negative which will be graphed as a diagonal to the left.

Answer: A linear function is represented as a straight line. The slope of the line gives the function’s rate of change.

Step-by-step explanation: Plato sample answer

a car dealership has 55 cars and 11 vans.what is the ratio of cars to vans? wriiten as a fraction in simplest form?

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55/1 ratio is 5 to 1 or 5/1. 55 divided by 11 is 5 and 11 divided by 11 is 1, so the ratio is 5 to 1.

A rug is shaped like a rectangle who's per Perimeter there's 192 feet the length is five times longer with find the length and the width

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P = Perimeter = 2(length) + 2(width). Let the width be x; then if the length is 5 times longer than the width, the length is 5x.

Plug these values into the Perimeter equation P = 2(length) + 2(width):

P = 2(5x) + 2(x), or P = 12x, and this is known to have the value 192 units. Solve for the width, x:

(192 units) = 12x gives us x = 16 units. Then the length is 5(16 units) = 80 units.

Check: Does 2(80 units) + 2(16 units) = 192 units? If so, then our width (16) and length (80) are correct.

Evaluate the limit, if it exists. (if an answer does not exist, enter dne.) lim h→0 (5 + h)−1 − 5−1 h

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[tex]\displaystyle\lim_{h\to0}\frac{(5+h)^{-1}-5^{-1}}h=\lim_{h\to0}\frac{\frac5{5(5+h)}-\frac{5+h}{5(5+h)}}h[/tex]
[tex]\displaystyle=-\lim_{h\to0}\frac h{5(5+h)h}[/tex]
[tex]\displaystyle=-\lim_{h\to0}\frac1{5(5+h)}=-\frac1{25}[/tex]

Alternatively, recall that if [tex]f(x)=\dfrac1x[/tex], then [tex]f'(x)=-\dfrac1{x^2}[/tex], and so

[tex]f'(5)=\displaystyle\lim_{x\to5}\frac{\frac1x-\frac15}{x-5}[/tex]

Take [tex]h=x-5[/tex], so that [tex]x=h+5[/tex], and we have the original limit. So the limit is equivalent to the value of [tex]f'(5)[/tex], i.e.

[tex]f'(5)=-\dfrac1{5^2}=-\dfrac1{25}[/tex]

A medical plan requires a patient to pay a $25.00 copay plus 20% of all charges incurred for a medical procedure. If the average bill for a patient is between $200 and $800, find the range of the original bill.

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Let the original bill be [tex]x[/tex], then the final bill after the charges been added are [tex]1.2x+25[/tex], where [tex]1.2[/tex] is the increase in the bill by 0.2 (100%+20% = 120% = 1.2)

The range of the original bill is
200 < [tex]1.2x+25[/tex] < 800, subtract each term by 25
175 < [tex]1.2x[/tex] < 775, divide each term by [tex]1.2[/tex]
145.83 < [tex]x[/tex] < 645.83

Hence, the range of the original bill is between $145.83 and $645.83

a triangular prism has height of 10cm and a base area of 12cm. a rectangular prism has height of 10cm and base dimensions of 3 cm and 4 cm. do the solids have the same volume?

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check the picture below.

notice, the base area of the rectangular prism is just 3x4.

A small company repairs home computers. In the past 200 days, it has been quite busy, taking in and repairing 2 computers on 52 of those days; 3 computers on 84 of those days; 4 computers on 40 of those days; and 5 computers on 24 of those days. Build a probability distribution for the number of computers repaired on any given day, show it is a valid distribution, and calculate its mean and variance.

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The probability distribution is shown in the table below

The value of [tex]x[/tex]: 2, 3, 4, and 5 shows the number of computers repaired and [tex]P(X=x)[/tex] shows the probability

Mean = (2×0.26×) + (3×0.42) + (4×0.2) + (5×0.12)
Mean = 0.52+1.26+0.80+0.6
Mean = 3.18

Variance = [(2²×0.26)+(3²×0.42)+(4²×0.2)+(5²×0.12)] - (3.18)²
Variance = 0.9076

Your employer offers you a choice of wage scales: a monthly salary of $2800 plus commission of 8% of sales or a salary of $3300 plus a 6% commission. At what sales level would the options yield the same salary?

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2800 + 0.08s = 3300 + 0.06s
0.08s = 0.06s = 3300 - 2800
0.02s = 500
s = 500 / 0.02
s = 25,000 <==

At the 25,000 salary scale, the options yield will be the same salary the answer is 25,000.

What is percentage?

It's the ratio of two integers stated as a fraction of a hundred parts. It is a metric for comparing two sets of data, and it is expressed as a percentage using the percent symbol.

We have:

Your employer offers you a choice of wage scales:

A monthly salary of $2800 plus a commission of 8% of sales or

A salary of $3300 plus a 6% commission.

First choice of wage scale:

= 2800 + 0.08s

Second choice of wage scale:

= 3300 + 0.06s

2800 + 0.08s = 3300 + 0.06s

0.08s - 0.06s = 3300 - 2800

0.02s = 500

s = 25,000

Thus, at the 25,000 salary scale, the options yield will be the same salary the answer is 25,000.

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The course for a walkathon is 6 miles long. If Chloe wants to walk 50 miles during the walkathon, how many times must she walk the course?

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she should walk the course about 8 or 9 times

divide 50 by 6

50/6 = 8.333

so she has to walk it 8.33 times

round answer as needed.

What statement regarding the diagram is true?

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I believe the second one right, because if I remember two opposite angles of an outside angle = the outside angle.

Evaluate the integral. (3 + 1/4 u^4 − 2/3 u^9) du

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(3 + 1/4 u^4 − 2/3 u^9) du

What is the height of a cylinder with a volume of 315 pi cubic meters and a radius of 6 meters? 8.75 meters 12.25 meters 26.25 meters 52.5 meters

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check the picture below.

simplify away.

Since this cylinder has a radius of 6 meters, its height is equal to 8.75 meters.

Given the following data:

Radius of cylinder = 6 m.

Volume of cylinder = 315π m.

How to calculate the height of this cylinder?

Mathematically, the volume of a cylinder is calculated by using this formula:

V = πr²h

Where:

h is the height.r is the radius.

Substituting the given parameters into the formula, we have;

315π = π × 6² × h

315π = 36πh

h = 315/36

Height, h = 8.75 meters.

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Two identical twins can only be distinguished by the characteristic that one always tells the truth and the other always lies. One twin tells you of a lucky number pair: "When I multiply my first lucky number by 3 and my second lucky number by 6, the addition of the resulting numbers produce a sum of 12. When I add my first lucky number and twice my second lucky number, the sum is 5." Which twin is talking? How do you know?

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To get a sum of 12, you know that the lucky numbers must be pretty small. The first lucky number is 2, multiplied by 3 gets us 6. The second lucky number is 1, multiplied by 6 gets us 6. 6 + 6 = 12.
The solve the next problem, the second lucky number (1) twice is 2. When added to the first lucky number, the sum is 4. This is tricky, because if the first lucky number was multiplied by 2 and added to the second lucky number, the sum would be 5.
In this case, the twin that lies is talking.

A(-3, 9) and B(5, 9) are the endpoints of the diameter of a circle. Use these points to find the standard equation of the circle.

Answers

check the picture below.

notice the midpoint of the diameter segment, is just 1,9.

also, recall the radius is half the diameter, notice how long the radius is, just 4 units.

[tex]\bf \textit{equation of a circle}\\\\ (x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2 \qquad \begin{array}{lllll} center\ (&{{ h}},&{{ k}})\qquad radius=&{{ r}}\\ &1&9&4 \end{array} [/tex]

The axis of symmetry for a quadratic equation can be found using the formula x =-b/2a , where a and b are coefficients in the quadratic equation and x represents the values along a vertical line on the coordinate plane. When the equation is solved for a, such that b is the numerator of the resulting fraction, what is the denominator of the fraction?

2x

–2x

1/2x

–1/2x

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if x = -b/2a, then 2a = -b / x so a = -b / 2x or a = b / -2x

So the denominator is -2x because it has to take the minus sign that the numerator refused to take ;-)

The answer is B on edgen.

PLEASE help me...Suck at math. find the following using the given triangle.

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To find the perimeter just add the sides

5+5+6 = 16

To find the area, you need to use the following formula

[tex] area = \frac{1}{2}bh[/tex]
we know b but we need to find the height. We can find the heigh by using pythagorean theorem [tex]a^2 + b^2 = c^2[/tex]

height = [tex] a^2 + 3^2 = 5^2 [/tex]
[tex] a^2 + 9 = 25 [/tex]
[tex] a^2 = 25 - 9[/tex]
[tex] a^2 = 16 [/tex]
[tex] a = \sqrt{16} = 4 [/tex]
h = height = 4

[tex] area = \frac{1}{2}\times 6\times 4 = 12cm^2[/tex]

Cost:

6.00 per cm^2 = 6.00 x 12 = $72.00 dollars

check the picture below.

what's the cost? well is $6 per square foot, what area did you get? well, say you got A, so the cost is just A * 6.

Atmospheric pressure decreases by about 11.8% for every 1000 meters you climb. The pressure at sea level is 1013 millibars (a unit of pressure). Construct an exponential model to represent the atmospheric pressure at a given altitude in thousands of meters. Use your model to determine the atmospheric pressure at an altitude of 4000 meters.
(Express your answer in millibars rounded correctly to the nearest tenth.)

Answers

at sea level, the pressure is 1013, that's when the altitude is at 0, sea level, let's see

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1 - r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\to &1013\\ I=\textit{initial amount}\\ r=rate\to 11.8\%\to \frac{11.8}{100}\to &0.118\\ t=\textit{meters climbed}\to &0\\ p=period\to &1000 \end{cases} \\\\\\ 1013=I(1-0.118)^{\frac{0}{1000}}\implies 1013=I\cdot 1\implies 1013=I[/tex]

so, the inital amount is 1013, when t = 0,

[tex]\bf \textit{Periodic Exponential Decay}\\\\ A=I(1- r)^{\frac{t}{p}}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &1013\\ r=rate\to 11.8\%\to \frac{11.8}{100}\to &0.118\\ t=\textit{meters climbed}\to &t\\ p=period\to &1000 \end{cases} \\\\\\ A=1013(1-0.118)^{\frac{t}{1000}}\implies A=1013(0.882)^{\frac{t}{1000}}[/tex]

now, to check the atmospheric pressure at 4000, simply set t = 4000, to get A.

Why does a calculator return an error when trying to find inverse sine of 1.055?

Answers

Sin(x) is a function bounded between -1 and 1. A value greater than 1 or smaller than -1 (-1.1, for instance) does not correspond to any real angle.

It then returns error

Answer:

1.055 is outside the domain of the sine function.

Step-by-step explanation:

When we are taking the inverse sine, we are finding an angle that gives a value of 1.055.

The sine function NEVER gives a value greater than 1 or less than -1. The domain of the sine function is between -1 and 1, inclusive.

So wanting to know which angle gives a sine value of 1.055 is futile. Sine can never be greater than 1.

That's why the calculator gives an error, because 1.055 is outside the domain of the sine function.

A math teacher gave her class two tests. 76% of the class passed the first test. 58% of the class passed both tests. What is the approximate probability that a student who passed the second test, given that he passed the first test.

Answers

P(test 2 | test 1) = P(test 2∩test 1) ÷ P(test 1)
P(test 2 | test 1) = 0.58 ÷ 0.76
P(test 2 | test 1) = 0.76 ≈ rounded to two decimal places

write each fraction as a sum or difference
2m-5/9

Answers

This is a fraction that has a linear expression as the numerator and a constant number in denominator.
So we can simply divide each term of numerator by denominator because we can write [tex] \frac{a+b}{c} = \frac{a}{c}+ \frac{b}{c} [/tex]
So we can write given fraction as
[tex] \frac{2m-5}{9} = \frac{2m}{9} - \frac{5}{9} [/tex] which is expressed as a difference.

How many four-digit even numbers are possible if the leftmost digit cannot be zero

Answers

Final answer:

There are 4500 four-digit even numbers possible when the leftmost digit cannot be a zero.

Explanation:

The question is about finding out the number of four-digit even numbers possible given that the first or leftmost digit cannot be a zero. In a four-digit even number, the last digit (rightmost) should be an even number, i.e., 0, 2, 4, 6, or 8. Hence, there are 5 possibilities for the last digit.

Next, since the leftmost digit cannot be a zero, it leaves us with 9 possibilities (1-9). Lastly, the middle two digits can be any digit from 0 to 9, so there are 10 possibilities each for the second and third digits.

Therefore, the total number of four-digit even numbers under the given conditions is found by multiplying these possibilities: 9 (for the first digit) * 10 (for the second digit) * 10 (for the third digit) * 5 (for the last digit) = 4500.

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Final answer:

To find the number of four-digit even numbers where the leftmost digit cannot be zero, there are 9000 possibilities.

Explanation:

To find the number of four-digit even numbers where the leftmost digit cannot be zero, we need to consider the following:

Choose the digit for the leftmost position (excluding zero). This can be done in 9 ways.Choose the digits for the other three positions (including zero for even numbers) in 10 ways each (0-9).

By multiplying the number of choices for each position, we get the total number of four-digit even numbers without leading zeros: 9 * 10 * 10 * 10 = 9000.

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What is the probability that a fair die never comes up an even number when it is rolled six times? (note: enter the value of probability in decimal format and round it to three decimal places.)?

Answers

Let us compute first the probability of ending up an odd number when rolling a dice. A dice has faces with numbers 1 up to 6. The odd numbers within that is 3 (1, 3 and 5). Therefore, each dice has a probability of 3/6 or 1/2. Then, you use the repeated trials formula:

Probability = n!/r!(n-r)! * p^r * q^(n-r), where n is the number of tries (n=6), r is the number tries where you get an even number (r=0), p is the probability of having an even face and q is the probability of having an odd face.

Probability = 6!/0!(6!) * (1/2)^0 * (1/2)^6
Probability = 1/64

Therefore, the probability is 1/64 or 1.56%.

What's the answer to the equation;
√2y+3=11

Answers

y=59 that should be the correct answer

The answer should be Y=32 should be it

Matthew currently has enough money to buy 45 toy cars. If the cost of each car was 10 cents less, Matthew could buy 5 more cars. How much money does Matthew have to spend on toy cars?

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x=price per toy car
45x = money Matt has
45x =50(x-.1)
45x =50x -5
5 =5x
x=$1
45x= $45
the cost of each car is $1

Drag the tiles to the correct boxes to complete the pairs. A team of 10 players is to be selected from a class of 6 girls and 7 boys. Match each scenario to its probability.

Answers

What tiles??? it doesn't make much sense

Answer:

Here you go!

Step-by-step explanation:

how many miles can you drive with 13.2 gallons of gasoline

Answers

286.44 I multiplied the numbers together

This depends on how large your car is and how fast you drive.
Certain cars burn more gasoline than others. You also may burn more or less gasoline depending on your speed. Slower speeds burn less, whereas faster speeds burn more.

Mike is taking a social studies test. mike was only able to finish 1/6 of the test in 1/2 an hour. How long will it take him to finish the test.

Answers

1/6 = 1/2 hr

2/6 = 1 hr

6/6-1/6 = 5/6 left of the test

2/6 + 2/6 = 4/6 = 2 hours

4/6 + 1/6 = 2 + 1/2 = 2 1/2

so 2 1/2 more hours

Translate this sentence into an equation; 14 less than Julie's score is 62. Use the variable m to represent Julie's score.

Answers

First, when we hear "less than" we should think of subtraction. Since Julie's score is represented by m, 14 less than her score would be the same as m-14 because we need to use subtraction. Then since 14 less than her score is equal to 62, we can set m-14 equal to 62 to get our final answer which is m-14=62.

I hope this helps!

To solve problems like these, we must break it down for each term.

"14 less than Julie's score"
This implies that we are going to have 14 less than the variable that represents Julie's score (which in this case, is m).

m-14

"is 62"
"Is" is almost always used as a way of saying "=," and 62 is the value that it equals.

m-14=62

Using the reasoning above, we can see that an equation to represent this scenario is m-14=62.

The total ages of 2 buildings is 201 years. if one building is twice as old as the other, what are the ages of 2 buildings?

Answers

Answer: 67 years and 134 years

In this case, you are given the buildings sum ages ( building A ages+ building B ages = 201 years) and the building ratio ( Building A ages= 2x Building B ages).
To answer the question, you simply need to insert the second equation into the first. It would be:

building A ages + building B ages= 201
2x building B ages + building B ages= 201
building B ages= 67 years.

Then building A ages= 2x 67 years= 134 years.

The ages of the two buildings are 67 and 134 years. This is found by setting up an algebraic equation where the sum of their ages is 201, and one is twice as old as the other.

Finding the Ages of Two Buildings

If the total ages of two buildings is 201 years and one building is twice as old as the other, then we can express the ages of the buildings using algebra. Let's denote the age of the younger building as y years. The older building is twice as old, so its age would be 2y years. The equation based on their total ages would be:

y + 2y = 201 years

Solving this equation:

Combine like terms: 3y = 201.

Divide both sides by 3 to isolate y: y = 201 / 3.

Calculate the exact value: y = 67 years.

So, the younger building is 67 years old, and the older building, being twice as old, is 134 years old.

A bus traveled on a level road for 4 hours at an average speed of 20 miles per hour faster than it traveled on a winding road. The time spent on the winding road was 5 hours. Find the average speed on the level road if the entire trip was 449 miles.

Answers

To solve this problem, we must recall that the formula for velocity assuming linear motion:

v = d / t

Where,

v = velocity

d = distance

t = time

For condition 1: bus travelling on a level road

v1 = d1 / t1

(v2 + 20) = (449 – d2) / 4 --->1

For condition 2: bus travelling on a winding road

v2 = d2 / t2

v2 = d2 / 5 --->2

Combining equations 1 and 2:

(d2 / 5) + 20 = (449 – d2) / 4

0.8 d2 + 80 = 449 – d2

1.8 d2 = 369

d2 = 205 miles

Using equation 2, find for v2:

v2 = 205 / 5

v2 = 41 mph

Since v1 = v2 + 20

v1 = 41 + 20

v1 = 61 mph

Therefore the average speed on the level road is 61 mph.

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A brace for a shelf has the shape of a right triangle. Its hypotenuse is 8 inches long and the two legs are equal in length. How long are the legs of the​ triangle?

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A brace for a shelf has the shape of a right triangle. Its hypotenuse is 8 inches long and the two legs are equal in length. How long are the legs of the triangle?