What is the length of the hypotenuse?

What Is The Length Of The Hypotenuse?

Answers

Answer 1

Answer:

Step-by-step explanation:

First things first, let's explain what a right triangle is. The definition is very simple and might even seem obvious for those who already know it: a right-angled triangle is a triangle where one and only one of the angles is exactly 90°. The other two angles will clearly be smaller than the right angle because the sum of all angles in a triangle is always 180°. In a right angled triangle the sides are defined in a special way. The side opposing the right angle is always the biggest in the triangle and receives the name of "hypotenuse". The other two sides are called catheti. The hypotenuse is opposite the right angle and can be solved by using the Pythagorean theorem. In a right triangle with cathetus a and b and with hypotenuse c, Pythagoras' theorem states that: a² + b² = c².

To solve for c, take the square root of both sides to get c = √(b²+a²). This extension of the Pythagorean theorem can be considered as a "hypotenuse formula".

Steps to solve:

[tex]c=\sqrt{a^{2} +b^{2} } \\c=\sqrt{1.3^{2} +6.1^{2} } \\c=\sqrt{1.69+37.21} \\c=\sqrt{38.9} \\c=6.236986[/tex]


Related Questions

Helppppp I really need this asap

Answers

Answer:

gago putangina mo bold

panget

Graph the set {x | -7 < x < - 1} on the number line. Then, write the set using interval notation. Thank you!

Answers

To graph this on a number line, we'll have open holes at -7 and -1. Then shade between those open holes to complete the graph. The open holes tell the reader "do not include the endpoint". The x values span from -7 to -1, excluding both endpoints. Use of filled in holes, or closed endpoints, will signal that we include the endpoint.  

The answer in interval notation is (-7, -1) which unfortunately looks identical to ordered pair notation. The parenthesis tell the reader to exclude the endpoints. If you wanted to include the endpoint, then use a square bracket instead.

Summary:Graph: Plot two open holes at -7 and -1, then shade in betweenInterval notation:  (-7, -1)

If a = {6 6 4 7 -4 4 -6 9 -3} and B= {1 5 -8 9 -5 -8 9 -5 2}, find 3a +9B Matrix operations

Answers

Answer:

[tex]3A+9B=\begin{bmatrix} 27 & 63 & -60 \\\\ 102 & -57 & -60\\\\ 63 & -18 & 9 \end{bmatrix}[/tex]

Step-by-step explanation

[tex]A=\begin{bmatrix} 6 & 6 & 4\\\\7 & -4 & 4\\\\ -6 & 9 & -3\end{bmatrix}\: and \: B=\begin{bmatrix}1 & 5 & -8\\\\ 9 & -5 & -8\\\\ 9 & -5 & 2\end{bmatrix}[/tex]

[tex]\rightarrow 3A=3\begin{bmatrix} 6 & 6 & 4\\\\7 & -4 & 4\\\\ -6 & 9 & -3\end{bmatrix},\: \: 9B =9\begin{bmatrix}1 & 5 & -8\\\\ 9 & -5 & -8\\\\ 9 & -5 & 2\end{bmatrix}[/tex]

[tex]\rightarrow 3A=\begin{bmatrix} 3*6 & 3*6 & 3*4\\\\3*7 & 3(-4) & 3*4\\\\ 3(-6) & 3*9 & 3(-3)\end{bmatrix},\:\: 9B =\begin{bmatrix}9*1 &9* 5 &9( -8)\\\\ 9*9 & 9(-5) & 9(-8)\\\\ 9*9 & 9(-5) & 9*2\end{bmatrix}[/tex]

[tex]\rightarrow 3A=\begin{bmatrix} 18 & 18 & 12 \\\\ 21 & -12 & 12\\\\ -18 & 27 & -9\end{bmatrix},\:\: 9B =\begin{bmatrix} 9 & 45 & -72 \\\\ 81 & -45 & -72\\\\ 81 & -45 & 18\end{bmatrix}[/tex]

[tex]\rightarrow 3A+9B=\begin{bmatrix}18+9 & 18+45 & 12+(-72) \\\\ 21+81 & -12 +(-45) & 12+(-72)\\\\ -18+81 & 27+(-45) & -9+18 \end{bmatrix}[/tex]

[tex]\rightarrow 3A+9B=\begin{bmatrix} 18+9 & 18+45 & 12-72 \\\\ 21+81 & -12 -45 & 12-72\\\\ -18+81 & 27-45 & -9+18 \end{bmatrix}[/tex]

[tex]\rightarrow \purple{\bold{3A+9B=\begin{bmatrix} 27 & 63 & -60 \\\\ 102 & -57 & -60\\\\ 63 & -18 & 9 \end{bmatrix}}}[/tex]

Anthony's Muffin Shop recently sold 4 blackberry muffins and 6 other muffins. Considering this data, how many of the next 20 muffins sold would you expect to be blackberry muffins?

Answers

Answer:

there should be 8 blackberry muffins

Answer:

8 Black berry muffins

Step-by-step explanation:

Trust me

The 95 % confidence interval (use z*) is:
____ to ____
(to 3 decimals)

Answers

Using the z-distribution, it is found that the 95% confidence interval is given by:

[tex]\overline{x} - 1.96\frac{\sigma}{\sqrt{n}}[/tex] to [tex]\overline{x} + 1.96\frac{\sigma}{\sqrt{n}}[/tex]

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.

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.

Hence, the interval is:

[tex]\overline{x} - 1.96\frac{\sigma}{\sqrt{n}}[/tex] to [tex]\overline{x} + 1.96\frac{\sigma}{\sqrt{n}}[/tex]

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Find the slope of a line parallel to -3x+7y=-15

Answers

Answer:

[tex] \boxed{\rm \: Slope = 3/7 \: x}[/tex]

Step-by-step explanation:

Given :

3x+7y=-15

To Find:

The slope

Solution:

Well,to find out the slope of the line here, we'll need to re-write the fully solved equation into slope - intercept form.

[tex] \boxed{ \rm \: y = mx = b}[/tex]

Here,

m = slopeb = y - intercept.

[Add 3x to both sides to the original equation:]

[tex] \rm \: 7y = - 15 + 3x[/tex]

Divide each term in this equation by 7:

[tex] \cfrac{7y}{7} = \cfrac{ - 15}{7} + \cfrac{3x}{7} [/tex][tex] \rm \: y = \cfrac{ - 15}{7} + \cfrac{3x}{7} [/tex]

Now rewrite this equation into slope-intercept form.

[tex]y = mx + b[/tex]

Plug values.

[tex]y = \cfrac{3x}{7} - \cfrac{15}{7} = \cfrac{3}{7} x - \cfrac{15}{7} [/tex]

> So , y - intercept is 15/7> Slope m is 3/7 x.

Hence,we can conclude:

The slope of the line parallel to -3x+7y=-15 is 3/7 x.

[tex] \rule{225pt}{2pt}[/tex]

Determine whether the function x2 = –y – 2 is quadratic or not. Explain.

Answers

Answer:

Yes, it is.

Step-by-step explanation:

A quadratic function always has [tex]x^{2}[/tex] [tex]x[/tex]≠0

The function x² = -y - 2 is a quadratic function.

What is a Function?

A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. The German mathematician Peter Dirichlet initially offered the contemporary definition of function in 1837: A variable y is said to be a function of the independent variable x if there is a relationship between them such that whenever a numerical value is assigned to x, there is a rule that determines a specific value of y.

As per the given data:

The function is x² = -y - 2

Rearranging the function:

y = x² - 2

A quadratic function is always of the form:

y = ax² + bx + c, where a, b and c are real numbers with a not equal to 0.

We can write y = x² - 2 as:

y = x² + 0(x) - 2, here a = 1, b = 0, c = -2

Hence, the function x² = -y - 2 is a quadratic function.

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A nickel has a diameter of 21.21 millimeters. What is the area of the face of a nickel? Use 3.14 for π . Round to the nearest hundredth if necessary.

Answers

The area of the face of a nickel 353.14 [tex]mm^{2}[/tex] (nearest hundredth)

What is Area of Circle?

The area of a circle is the amount of space enclosed within the boundary of a circle. The region within the boundary of the circle is the area occupied by the circle.

As the surface of nickel is in shape of 2-D circle.

radius of circle = [tex]\frac{21.21}{2}[/tex] = 10.605 mm

Area of circle= [tex]\pi r^{2}[/tex]

                      = 3.14* 21.21*21.21

                      = 353.143 [tex]mm^{2}[/tex]

                      = 353.14 [tex]mm^{2}[/tex] (nearest hundredth)

Thus, the area of the face of a nickel 353.14 [tex]mm^{2}[/tex] (nearest hundredth)

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Fill in the blank




…………………..

Answers

So uhh I’m so sorry to tell you but I don’t know how to do math myself and I just need points so I’m answering this.. but I’m sure If you just cheat off a smart person in your class you’ll be fine. If you need any tips on how to cheat lmk I’ll gladly help

Answer:

See below ~

Step-by-step explanation:

Q2

x - 7 > 10x - 7 + 7 > 10 + 7x > 17

Q3

3x ≤ 213x/3 ≤ 21/3x ≤ 7

Q4

5a - 2 < 185a - 2 + 2 < 18 + 25a < 205a/5 < 20/5a < 4

Q5

2t + 8 ≥ -4(t + 1)2t + 8 ≥ -4t - 46t ≥ 126t/6 ≥ 12/6t ≥ 2

WILL MARK BRAINLIEST 50 POINTS
Ben tracked the attendance in his class over a period of time and recorded the data in a frequency table.
Create a dot plot for the data in the table. Hover over each number on the number line. Then click and drag up to create the dots

Answers

The data recorded by Ben shows the attendance log of his classmates over a given period of time.

What is a Dot Plot?

This refers to a simple chart that resembles a histogram that is used to represent small data.

Hence, we can see that because Ben tracked the attendance of the class over a given time period with the frequency on a frequency table, a sample of a dot plot has been provided below,

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in standard form for properties of exponents

Answers

Answer:

1 / 64

Step-by-step explanation:

(2^2)^-3

apply exponent rule: (a^b)^c = a^(bc)     a ≥ 0

2^((2) - 3)

((2) - 3) = -6

2^-6

apply exponent rule: a^-b = 1 / a^b

2^-6 = 1 / 2^6

2^6 = 64

1 / 64

Let me know if you have any questions !

Bob's living room floor is a rectangle that measures 9 feet by 12 feet. What is the diagonal distance, in feet, across the floor? A. 13 B. 15 C. 16 D. 21​

Answers

Answer:

B

Step-by-step explanation:

here, we can use the pythagorean theorem. more info here: https://en.wikipedia.org/wiki/Pythagorean_theorem

formula: a^2+b^2=c^2

so we can apply the formula by doing this:

9^2+12^2=c^2

81+144=c^2

81+144=225

c=√225

c=15

solved

Find equation of the straight line that passes through the point (-1,1) and is perpendicular to 2y = 3x +2

Answers

Answer:

3y = -2x + 1

Step-by-step explanation:

Equation of given line is 2y = 3x + 2

==> y = (2/2)x + 1

Slope = 3/2

Slope of perpendicular line is negative of reciprocal of given line ie slope = -2/3

So equation of perpendicular line is of the form

y = (-2/3)x + c where c is a constant

Given that this passes thru x= -1, y =1 we can substitute these values in the above to get

1  =  (-2/3)(-1) + c
This yields 1 = (2/3) + c or c = 1-2/3 = 1/3

So the equation of the perpendicular line is

y = (-2/3)x + 1/3

3y = -2x + 1

Jenny is putting 11 books in a row on her bookshelf. She will put one of the books, The Iliad, in the first spot. She will put another of the books, The Odyssey, in the last spot. In how many ways can she put the books on the shelf?

Answers

i believe the answer is there are
39,916,800 ways she can put the books on the shelf

What’s the Square root of 13.33

Answers

Answer:

3.65102725271

Step-by-step explanation:

click on the picture and please help this is due in 1 hour!

Answers

Answer:

4.7 Pounds

Step-by-step explanation:

[tex]14 \div 3≈4.6[/tex]

(Note: This symbol (≈) that looks like a squiggled equal sign means an approximate amount)

Adriano loves anime and collect toys from his fav series. Each month he gains 4 toys. If Adriano has 3 toys when he start collecting, how many dose he have in 4 months.

Answers

Answer:

19 toys

Step-by-step explanation:

102 I hope this helps you person

The First National Bank of Wilson has 700 checking account customers. A recent sample of 50 of these customers showed 29 have a Visa card with the bank.

a. What is the margin of error for a 95% confidence interval for the population proportion? (Round your answer to 3 decimal places.)

b. What is the 95% confidence interval for the population proportion?

Answers

The margin of error is 0.137 and the confidence interval for the population proportion is (0.443, 0.717).

What is the margin of error(MOE)?

It is defined as an error that provides an estimate of the percentage of errors in real statistical data.

The formula for finding the MOE:

[tex]\rm MOE = Z\times \dfrac{s}{\sqrt{n}}[/tex]

Where   Z is the z-score at the confidence interval

            s is the standard deviation

            n is the number of samples.

We have:

n = 50, X = 29,

Estimate point p = 29/50 = 0.58

q = 1-p = 1-0.58 = 0.42

Z at 0.05/2 (95% confidence interval) = 1.96

[tex]\rm MOE = 1.96\sqrt{\dfrac{0.58\times0.42}{50}}[/tex]

After calculating:

MOE = 0.137

Confidence interval will be: (p - MOE, p+MOE)

= (0.58-0.137, 0.58+0.137)

= (0.443, 0.717)

Thus, the margin of error is 0.137 and the confidence interval for the population proportion is (0.443, 0.717).

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what is the slope of the line that passes thought the points (4,-6) and (-2,3)? write your answer on simplest form.​

Answers

Step-by-step explanation:

[tex] \frac{y - y0}{x - x0} \\ \frac{ - 6 - 3}{ 4 + 2} \\ - \frac{9}{6} = - \frac{3}{2} = 1.5[/tex]

Please help! 5th-grade math!

Answers

It is a quadrilateral, parallelogram, and a rhombus

Answer:

quadrilateral, parallelogram, and rhombus.

Step-by-step explanation:

All quadrilaterals have 4 sides, all parallelograms have 2 sets of parallel sides, and a rhombus has diagonals that bisect each other perpendicularly.

On a​ map, 1 inch equals 25 miles. Two cities are 3 inches apart on the map. What is the actual distance between the​ cities?

Answers

Answer:

75 Miles apart

Step-by-step explanation:

I = inches on a map

I=25

3I=75

75 miles apart

1. If the line 4x - 9y = 0 is tangent in the first quadrant to the graph of y = x³ + c, what is the value of c? 2. Find a formula for the nth derivative of y=+ 1-x 3. Let f(x)=2. Then find a) Critical number(s) of f b) Monotonic intervals (increasing and decreasing intervals) of f c) The intervals on which f(x) is concave up and concave down d) Inflection points of f e) Sketch the graph of f(x) 4. Evaluate f (*¹-2x+¹) dx. please do it ​

Answers

Answer:

Acount is a great place to work for a loved ones like you a few months

Bell sells pies each week at the farmers market. She spends $65 on materials and charges $10 per pie. She hopes to make a profit of at least $15 per hour. What constraints might bell want to set?

Answers

Answer:

43.33

Step-by-step explanation:

You will start out by putting 65 in time 10 divide by 15 and that will give you your answer  

Answer:

43.33

Step-by-step explanation:

You will start out by putting 65 in time 10 divide by 15 and that will give you your answer  

A doctor claims that the mean number of hours of sleep that seniors in high school get per night differs from the mean number of hours of sleep college seniors get per night. To investigate, he selects a random sample of 50 high school seniors from all high schools in his county. He also selects a random sample of 50 seniors from the colleges in his county. He constructs a 95% confidence interval for the true mean difference in the number of hours of sleep for seniors in high school and seniors in college. The resulting interval is (0.57, 1.25). Based upon the interval, can the doctor conclude that mean number of hours of sleep that seniors in high school get per night differs from the mean number of hours of sleep college seniors get per night?

yes because 1 is in the confidence interval
yes because 0 is not in the confidence interval
no because 1 is in the confidence interval
no because 0 is not in the confidence interval

Answers

Considering the given confidence interval, the correct option regarding the conclusion of the hypotheses test is given by:

yes, because 0 is not in the confidence interval.

What are the hypotheses tested?

At the null hypotheses, it is tested if the difference is equals to zero, that is:

[tex]H_0: \mu = 0[/tex].

At the alternative hypotheses, it is tested if it is different, hence:

[tex]H_1: \mu \neq 0[/tex].

The confidence interval is (0.57, 1.25). Since it does not contain 0, there is enough evidence that the difference is different of 0, hence the correct option is given by:

yes, because 0 is not in the confidence interval

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Kate has a box of red nibbon and bhie ribbons The ratio of red ribbons to total ribbons is 5 14 Choose all the statements that are true about Katie's box of ribbons

(A The ratio of total ribbons to blue ribbons is
14:9

(B. The ratio of red ribbons to blue ribbons is 9:5


(C. The ratio of total ribbons to red ribbons is 14:5

(D. There must be 9 more blue ribbons than red ribbons

(E. The ratio of blue ribbons to red ribbons is 9,5​

Answers

D and C.

You already stated the total ratio is 14:5 so that gives you the answer of choice C.

And 5+9=14 so that gives you the answer of choice D.

When the core of a reactor overheated, what happened at Chernobyl?
A. Power was cut off to Europe for six months
B. Radiation was released across Europe
C. The power station exploded killing many
D. Though it overheated, no negative impacts occurred

Answers

Answer: D

On April 26, 1986, the Number Four RBMK reactor at the nuclear power plant at Chernobyl, Ukraine, went out of control during a test at low-power, leading to an explosion and fire that demolished the reactor building and released large amounts of radiation into the atmosphere. When the core of a reactor overheated, what happened at Chernoby Though it overheated, no negative impacts occurred

Step-by-step explanation:

Tins of paint are filled at the rate of 2m3 per minute.
How many 750 ml tins of paint can be filled in 1 hour?

Answers

Answer:

  160,000 tins

Step-by-step explanation:

To find the number of tins, divide the fill rate by the volume per tin.

__

  (2·(1000 L)/min)×(60 min)/(1 h)/(0.75 L/tin) = 160,000 tin/h

160,000 tins of paint can be filled in 1 hour.

_____

Additional comment

That's one tin every 22.5 milliseconds. It would be a feat of engineering to move that volume without splashing.

There are 60 minutes per hour. There are 1000 liters per cubic meter.

Which is the graph of linear inequality 2y > x – 2?

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the right of the line is shaded.

On a coordinate plane, a solid straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the right of the line is shaded.

Answers

On a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.

How to graph inequality?

Inequality of a graph is represented with the greater then(<), less then(>) or with the other inequity signs. The inequality line on the graph is represented with the dotted lines.

The given linear inequality is,

[tex]2y > x - 2[/tex]

Solve it further,

[tex]2y > x - 2\\2y-x > - 2[/tex]

Change the inequality with changing the sign of it,

[tex]x-2y < 2[/tex]

The inequality equation is graphed, which can be shown in the image provided below. In this graphed equation,

The inequality is shaded with dotted line.As the equation is linear. Thus, in the graph, a straight line is plotted.The sign in of greater than. Thus, the left of the line is shaded.

Thus, on a coordinate plane, a dashed straight line has a positive slope and goes through (negative 4, negative 3), (0, negative 1), and (2, 0). Everything to the left of the line is shaded.

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please help asap giving brainiest and lots of points! this is an easy math/ engineering question if you dont know theres online calculators just pls help!

The initial velocity of a projectile is 57 m/sec, and the firing angle is 22°. Calculate the horizontal distance.
a 230 meters
b 330 meters
c 430 meters
d 130 meters

Answers

Answer:

a 230 metera 230 metersa 230 metersa 230 metersa 230 metersa 230 meters

Gertrude climbs a 8-meter tower to ride a straight water slide. The
slide is 33 meters. After landing in the splash pool, how far does she
walk to get back to the base of the tower? Provide an answer accurate
to the nearest tenth.
33 m
8 m
walk
label required

Answers

Answer:

Hello,

11.2 is your answer!

Let's Beginnn.... READ EXPLANATION!!! ITS ALWAYS HELPS... TRUST MEEEEEEEEEEE!!!!

Step-by-step explanation:

Okay so this is clearly a pythagorean theorem question....

Imagine a ladder on a wall..... its kinda like a triangle.....

with that said... lets begin the math... A^2 + B^2 = C^2

The problem itself gives us c and a.

We have to solve for b.

33^2 - 8^2= b^2

1089 - 64 = 1025 = b^2

notice that we found b^2 but we are looking for b

so we have to take the square root....

√1025= 11.18

it says round to nearest tenth.... sooooo

11.2 is your answer!

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