The short leg of a 90-45-45 triangle is 5. What is the long leg and the hypotenuse?

Answers

Answer 1

The long leg and the hypotenuse of the isosceles right triangle will be 7.07 units.

What is a Pythagoras theorem?

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The short leg of a 90-45-45 triangle is 5.

The right triangle is an isosceles right triangle. Then the two side will be same.

Then the long leg and the hypotenuse will be

H² = 5² + 5²

H² = 25 + 25

H² = 50

H = 7.07 units

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Related Questions

3. Multiply the polynomials (a² + 3a-7) and (2a²-a + 4). Simplify the answer. Show your work.
Answer:

Answers

Answer:

[tex]2a^{4} + 5a^{3} - 13a^{2} + 19a - 28[/tex]

Step-by-step explanation:


Drainpipe comes in lengths of 2.5 metres. A man wants to buy drainpipe to fit down
one side of his house from the ground to the gutter.
Estimate how many lengths he will need.
lengths

Answers

The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.

What is an equation?

An equation is an expression that shows the relationship between two or more numbers and variables.

Let us assume that the distance from the man side of the house to the gutter is 15 m, since the drainpipe comes in lengths of 2.5 m, hence:

Number of drainpipe needed = 15 m / 2.5 m = 6

The man would need 6 drainpipes with length of 2.5 meters each to fit the side of his house from the ground to the gutter.

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The required quantity of drainpipe is mathematically given as six.

L=6

What is the lengths he will need?

Generally, Let's say the distance from the male side of the house to the gutter is 15 meters. Since the length of the drainpipe typically comes in increments of 2.5 meters, we may reason as follows:

In conclusion, The required quantity of drainpipe is equal to 15 meters divided by 2.5 meters, which is equal to six.

L=15/2.5

L=6

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simplify 3 + [5n - (2-n)]

Answers

Answer:

6n+1

Step-by-step explanation:

Eliminate the parenthesis by changing the symbol of each term inside

3+[5n-2+n]

Eliminate the bracket and group similar terms

5n+n+3-2

Simplify terms

6n+1

has a slope of 2 and contains what point? y-3=2(x+4)

Answers

We know immediately that the line must pass through (-4, 3).

Mr.Baker is making a box using all of a 48-inch strip of oak. the box will be 14 inches wide. how long will the box be?

Answers

The length of the box made by Mr. Baker is 10-inch

Mr. Baker has strip of 48- inch long  oak, by this strip he is making the rectangle box of width 14-inch.

What is a rectangle?

The rectangle is 4 sided geometric shapes whose opposites are equal in lengths and all angles are about 90°.

As Mr. Baker has a strip that is 48-inch long and he made a rectangle box with it.

The width of the  box = 14 inches
now the length of the box = (total length of the strip - 2* width of the box)/2
length of the box = (48 - 2*14)/2
length of the box = 10 inches

Thus the Mr. Baker made the box which is 10 inches long.

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What is the slope of the line that passes through the points (6, 2) and (4, 10)? −4 −14 14 4

Answers

Answer:

-4

Step-by-step explanation:

The equation for slope is:

[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]

m: Slope

(6, 2) = [tex](x_1, y_1)[/tex]

(4, 10) = [tex](x_2, y_2)[/tex]

Substitute these values into the equation:

[tex]m=\frac{10-2}{4-6}=\frac{8}{-2}=-4[/tex]

Therefore the slope is -4.

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SOLVING

[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

What is the slope of the line that passes through the points? 2 points given

[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]

The formula used here, is [tex]\bf{\dfrac{y2-y1}{x2-x1}}[/tex].

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{\dfrac{10-2}{4-6}}[/tex] | subtract

[tex]\bf{\dfrac{8}{-2}}[/tex] | evaluate

[tex]\bf{-4}[/tex]

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

           [tex]\bf{=Slope\;-4}[/tex]

[tex]\boxed{\bf{aesthetic\not101}}[/tex]


The SAT is the most widely used test in the undergraduaté admissions process, Scores on the math portion of the SAT are believed to
be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire
is interested in estimating the mean math SAT scores of the incoming class with 95% confidence. How large a sample should she take
to ensure that the margin of error is below 20?
(You may find it useful to reference the z table. Round intermediate calculations to at
least 4 decimal places and "2" value to 3 decimal places. Round up your final answer to the nearest whole number.)

Answers

Using the z-distribution, it is found that she should take a sample of 97 scores to ensure that the margin of error is below 20.

What is a z-distribution confidence interval?

The confidence interval is:

[tex]\overline{x} \pm z\frac{\sigma}{\sqrt{n}}[/tex]

In which:

[tex]\overline{x}[/tex] is the sample mean.z is the critical value.n is the sample size.[tex]\sigma[/tex] is the standard deviation for the population.

The margin of error is given by:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800, hence by the Empirical Rule the standard deviation is given by:

[tex]6\sigma = 800 - 200[/tex]

[tex]\sigma = 100[/tex]

In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.

To ensure a margin of error of 20, we solve for n when M = 20, hence:

[tex]M = z\frac{\sigma}{\sqrt{n}}[/tex]

[tex]20 = 1.96\frac{100}{\sqrt{n}}[/tex]

[tex]20\sqrt{n} = 1.96 \times 100[/tex]

[tex]\sqrt{n} = 1.96 \times 5[/tex]

[tex](\sqrt{n})^2 = (1.96 \times 5)^2[/tex]

n = 96.04.

Rounding up, she should take a sample of 97 scores to ensure that the margin of error is below 20.

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Paulo is flying a kite as shown

in the right. Find the length of the kite string.

Answers

The length of the kite string is 50 ft

How to determine the length of the kite string?

The string and the kite form a right triangle.

So, the length can be calculated using Pythagoras theorem as follows:

c^2 = 30^2 + 40^2

This gives

c^2 = 2500

Take the square roots

c = 50

Hence, the length of the kite string is 50 ft

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10,000,000,000 is which power of ten? 21 -1 10 100

Answers

Answer:

10

Step-by-step explanation:

There are ten zeros therefore in standard form it is 1 x 10 to the power of 10 or [tex]10_{12}[/tex]

9x+9y=9. Solve for Y

Answers

Answer:

y = 1 - x

Step-by-step explanation:

9x + 9y = 9 ( divide through by 9 )

x + y = 1 ( subtract x from both sides )

y = 1 - x

Answer:

y = 1 - x

Step-by-step explanation:

9x + 9y = 9

First, take 9x to the right side.

9y = 9 - 9x

9y = 9 ( 1 - x )

Divide both sides by 9.

y = 1 - x

You must make 3 shots in a row to win the fairs basketball game. The hoop is uneven and the backboard curved. Only 5 players out of 100 win the game. What percentage of players do not win.

Answers

Answer:

95%

Step-by-step explanation:

5 player won, meaning 95 player didn't.

This means that 95% of the players didn't win.

what is the fraction 2500 of 3600

Answers

Answer:

25/36

Step-by-step explanation:

put 2500 over 3600 and you get 2500/3600 but you can simplify to get 25/36 but removing the 0's

100 students take a test. The mean score of the results is 88% with a standard deviation of 4%. Considering that the results were normally distributed, what is the median of the graph, what scores are within 2 standard deviations away, and how many student's scores would be within 1 standard deviation from the mean?

Answers

Using the Empirical Rule, it is found that:

Scores between 80% and 96% are within 2 standard deviations of the mean.68 scores are within one standard deviation of the mean.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

Approximately 68% of the measures are within 1 standard deviation of the mean.Approximately 95% of the measures are within 2 standard deviations of  the mean.Approximately 99.7% of the measures are within 3 standard deviations of the mean.

Considering the mean of 88% and the standard deviation of 4%, the scores that are within 2 standard deviations of the mean are:

88 - 2 x 4 = 80%.88 + 2 x 4 = 96%.

68% are within 1 standard deviation of the mean, hence, out of 100:

0.68 x 100% = 68 scores.

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which is the correct graph for the inequality

Answers

The correct answer is graph B

Rewrite the expression as a fraction.

Answers

4/15, 4 is being divided by 15 so it’s going to be over the number 15

Answer:

4/15

Step-by-step explanation:

in fractions, the number that goes on top is the dividend (the first number in the division problem) which is 4 in this case and the number that goes on the bottom of the fraction is the divisor, which is 15 in this case. therefore, the answer is 4/15.

Please help whilst I try to solve as well.

Answers

Answer:

Step-by-step explanation:

Answer:

420 cm³

Step-by-step explanation:

we find the volume as if it were a parallelepiped and we remove the volume of the missing part.

8 * 6 * 10 = 480 cm³

480 - 2 * 3 * 10 = 420cm³

please help me with this problem ! would appreciate it!!!

Answers

[tex]1) \text{ } 2^{1/2}=\sqrt{2}\\\\2) \text{ } 2^{2/3}=\sqrt[3]{2^{2}}\\\\3) \text{ } 3^{3/2}=\sqrt{3^{3}}\\\\4) \text{ } 3^{1/3}=\sqrt[3]{3}[/tex]

Answer: correct radical forms are:

[tex]2^\frac{1}{2} = \sqrt{2}[/tex]

[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]

[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]

[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]

Step-by-step explanation:

Radical form : If n is a positive integer that is greater than 1 and a is a real number then, [tex]\sqrt[n]{a} =a^\frac{1}{n}[/tex] where n is called the index, a is called the radicand, and the symbol √ is called the radical.

therefore,  

radical form of given values are :

[tex]2^\frac{1}{2} = \sqrt{2}[/tex]

[tex]2^\frac{2}{3} = \sqrt[3]{2}[/tex]

[tex]3^\frac{3}{2} = \sqrt[]{3^3}[/tex]

[tex]3^\frac{1}{3} = \sqrt[3]{3}[/tex]

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*30pts*What is the value of x in the triangle?

Answers

Answer:

A.4

Step-by-step explanation:

Using the sine rule

sin(α)/A equals sin(β)/B

From the question & inserting values,

sin(90°)/8 equals sin(30°)/x

∴x equals[tex]\frac{sin(30)}{sin(90)}[/tex]×8

∴x equals 4

You can learn more on the sine rule in case you get confused.

Answer:

A

Step-by-step explanation:

using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex] , then

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{x}{8}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2x = 8 ( divide both sides by 2 )

x = 4

Solve the formula d = rt for t

Answers

I’m not 100% but wouldn’t it be t = d/r

A cooler contains five​ colas, seven​ root beers, and four​ ginger ales.​ Three​ people grab a drink at random, one at a time. a) What is the probability that the first person grabs a cola, the second person grabs a ginger ale, and the third person grabs ​ b) What is the probability that the third person grabs a root beer given that the first two grabbed colas?

Answers

The probabilities are:

a) P = 0.024

b) P = 0.5

How to get the probabilities?

a) The probability that the first person grabs a cola is given by the quotient between the number of colas and the total number of drinks.

There are 5 colas, and 16 drinks in total, so the probability is:

P = 5/16

The second person needs to grab a ginger ale, now there are 15 drinks on the cooler (because one cola was taken) so this time the probability is:

Q = 4/15

Finally, the third person grabs (this is incomplete, I will assume that is another cola), this probability is:

Z = 4/14

The joint probability is:

prob = P*Q*Z = (5/16)*(4/15)*(4/14) = 0.024

b) If the two first persons grabed colas, then in the cooler we have:

3 colas, 7 root beers, and 4 ginger ales, for a total of 14 drinks.

Then the probability of grabbing a root beer is:

p = 7/14 = 1/2 = 0.5

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What’s the vertex of this graph??

Answers

Answer:

(4, -3)

Step-by-step explanation:

A vertex is just a point at which 2 lines going in different directions meet, hence (4, -3)

What is the surface area of the image below?

Answers

Answer:

Step-by-step explanation:

Comment

I'm going to assume that this is not a closed figure. The top is open like a water trough for horses.

There are 2 semicircular ends which add up to 1 whole circle.

There is 1 base area. The base area has a width of one of the semicircles. It has a length of 15 cm.

Solution

2 semi circles

r = d / 2

r = 20/2

r = 10

Area = pi r^2    This area is for 2 semicircles which = 1 circle.

Area = 3.14 * 10^2

Area = 3.14 * 100

Area =                                                  314

Trough

r = d / 2  

d= 20

r = 20/2

r= 10

w = 2*pi*r / 2

w = 2*3.14 *10/2

w = 31.4 cm

L = 15 cm

Area = 15 * 31.4

Area =                                                   471

Total Area =                                         785                              

Fig. R24 shows a flower vase whose circular base is parallel to its circular top.
Use the dimensions in the figure to calculate the curved surface area of the flower vase ​

Answers

Answer:

operant conditioning and schedules of reinforcement

35. Use the Change of Base Formula to evaluate logs 92. Then convert logs 92 to a logarithm in base 3. Round to the n
2.810; log3 55.2
2.810; log3 21.903
1.964, log3 55.2
4.522; log3 21.903

Answers

The answer is 1. 30b

What are the roots for the quadratic equation below?

3x^2+9x-2=0

Answers

Answer:

[tex]\sf{$a)$} \ x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]

Step-by-step explanation:

Quadratic formula: [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

Quadratic equation: ax² + bx + c = 0, where a ≠ 0

Given: 3x² + 9x - 2 = 0

⇒ a = 3, b = 9, c = -2

Substitute the given values into the formula and simplify:

[tex]x=\dfrac{-9\pm\sqrt{9^2-4(3)(-2)}}{2(3)}\\\\x=\dfrac{-9\pm\sqrt{81+24}}{6}\\\\x=\dfrac{-9\pm\sqrt{105}}{6}[/tex]

Therefore, the correct answer is A.

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Write an equation of the line that passes through a pair of points: On a coordinate plane, a line goes through (4, 1) and (5, 2). a. y = x + 3 c. y = -x + 2 b. y = x - 3 d. y = -x - 2 Please select the best answer from the choices provided A B C D

Answers

Answer:

b. y = x - 3

Step-by-step explanation:

The general form of the equation of the line is y = mx + c.

1) Find for m (gradient) using the following formula:

m = y2 - y1 / x2 - x1

Substitute the values into it and solve for m.

m = 2 - 1 / 5 - 4

m = 1 / 1

m = 1

2) Substitute into m of the y = mx + c.

y = 1x + c

3) Choose one the coordinates that the line goes through ((4, 1) or (5, 2)) to find c (y-intercept). I will choose (4, 1). Then, substitute your chosen coordinates into your newfound equation (y = 1x + c)

1 = 1(4) + c

1 = 4 + c

1 - 4 = c

-3 = c

Substitute -3 in place of c.

y = 1x - 3, which can be simplified to y = x - 3. Therefore, the correct choice is b.

What is the surface area of the cylinder below?

Answers

Answer:

Surface Area = 378.25

Step-by-step explanation:

Comment

It's not clear whether the figure has 0 1 or 2 lids. Since it is a cylinder, I will assume 2 lids like a can of soup.

Area lids

diameter = 11.4

radius = d/2

radius = 11.4/2

radius = 5.7

Area = pi * r^2

Area = (3.14 * 5.7^2) * 2 There are 2 lids.

Area =   102.01 yd^2

Area body

This is found by finding the circumference of the lid and multiplying by the height

Circumference

C = 2*pi*r

2*r = the diameter

2*r = 11.4

C = 3.14*11.4

C = 35.80

Area body

Area body = C* h

h = 7.8

Area body = 35.80 * 7.8

Area body = 279.24

Total Area = 102.01 + 279.24 = 378.25

Use the given sample data to find Q3.

49 52 52 52 74 67 55 55

Answers

The given sample data the Q3=61

We begin by ordering the data from smallest to largest.

Next, find the median of the data.

The data set has 8 values, so the two middle values are 52 and 55.

49 52 52 52 55 55 67 74

What is the formula for the median?

Median = (52 + 55) / 2

Median= 53.5

The third quartile (Q3) is the 25th percentile or the median of the upper half of the data.

To find the median of all the values that lie above 53.5.

Q3 = (55 + 67)/ 2

Therefore the Q3=61

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Which of the following points lies on the graph of the function y = 2*3^x? a. (1, 0) c. (3, 6) b. (2, 9) d. (0, 2) Please select the best answer from the choices provided A B C D

Answers

The point which lies on the graph of the given function is; Choice D; (0, 2).

Which of the following points lies on the graph of the function y = 2*3^x?

The point which lies on the graph of the given function; y = 2*3^x is it's y-intercept. The y-intercept which corresponds to the value of y when variable X is set to zero.

Hence, y = 2*3^0;

y = 2 ×1 = 2.

Hence, the point is; (0,2).

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I need help with my geometry proof homework from 2-3

Answers

Answer: Tbh i don’t know anything besides that all the angles are equal to another and you have to prove it. I would just say: “90 degrees = 90 degrees

Sorry mate I can’t help

Step-by-step explanation:

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