A right triangle has a side with length 12 in and a hypotenuse with length 20 in. find the length of the second leg (in inches). (round to the nearest hundredth if needed)

Answers

Answer 1

if the second leg is x so
x² = b² - a²
x² = (20)² - (12)² = 256
x = 16 in

Related Questions

The graph of f(x)=x^2 has been shifted into the form f(x)=(x-h)^2+k

What is the value of h?:
A. 1
B. -1
C. -3
D. 3

Answers

The answer is D because if you look at the graph the order pairs are (3,3). I substitute h for 3 and substitute k for 3. That's why D is the answer.

Answer:

D. 3

Step-by-step explanation:

Here h represents the horizontal shift. In the given graph, the graph shifted 3 units to the right from the origin.

Therefore, h = 3.

Answer: D. 3

Hope this will helpful.

Thank you.

Given: QR = 59; RT = 59 Prove: QR = RT StatementsReason 1. QR = 59; RT = 591. Given 2. 59 = RT2. Symmetric Property of Equality 3. QR = RT3. Which property listed below is the final reason in the proof.

Answers

Statement 3 is QR=RT. This can be validified by the reason of Transitive Property of Equality. This property is applied when the situation is if a=c and b=c, then a=b. The same is true for QR=59 and RT=59, then QR=RT.

Answer:

By using transitive property

QR=RT

Step-by-step explanation:

Given

QR=59

RT=59

To prove that QR=RT

1. Statement QR=59; RT=59

Reason : Given in the question.

2. Statement: 59=RT

Reason: By using symmetric property of equality .

Symmteric property is that property of equality

ab=bc

Then ,

bc=ac

3. Statement: QR=RT

Reason: By using transitive property of equality.

Transitive property : If ac=bc

and bc=ca

Then , ab=ca

Hence proved.

A rectangle is 13 centimeters longer than it is wide. Its perimeter is 226 centimeters. What are the length and width?

Answers

let width be x
let length be x+13
perimeter=2*(L+W)
226=2*(x+x+13)
226=2*(2x+13)
226=4x+26
subtract 26 from each sides
200=4x
x=50, which is the width
length=63

Write the following fractions as decimals 2/10,3/100

Answers

2/10 or 1/2 = .5 you would divide 2 by 2 and 10 divided by 2 (whatever you multiply or divide by on the top you must do on the bottom)
2/10=.50
3/100=.03 (divide 3 by 10=.03)

Answers:

A. .2

B. .03

C. .093

D. .1456

Have a blessed day ☺️

#23 please!!! Thanks

Answers

[tex]\text{gcf}(x^2y^2,xy^3)=xy^2\\\\ xy^2=45\\ [/tex]

45|3
15|3
5|5
1

[tex]xy^2=3^2\cdot5[/tex]

Since x and y are both positive integers, then there's only one possible solution to the above - [tex]x=5,y=3[/tex]

So E.

Let h = (v0^2)/4.9 sin(theta)cos(theta) model the horizontal distance in meters traveled by a projectile? If the initial velocity is 52 meters/second, which equation would you use to find the angle needed to travel 200 meters?
A) 275.92sin(2Theta)=200
B) 551.84sin(2Theta)=200
C) 200sin(2 Theta)=200
D)10.61sin(2THeta)=100

Answers

The horizontal distance traveled by the projectile is given as
[tex]d= \frac{V_{0}^{2}}{4.9} sin\theta cos\theta[/tex]
where
V₀ = initial velocity, m/s

Note that
sin(2θ) = 2sinθ cosθ

Therefore, the horizontal distance traveled is
[tex]d= \frac{V_{0}^{2}}{4.9} ( \frac{sin(2\theta)}{2} )= \frac{V_{0}^{2}}{9.8} sin(2\theta)[/tex]

Because V₀ = 52 m/s, in order to travel a horizontal distance of 200 m, the correct equation to determine θ is
(52²/9.8) sin(2θ) = 200
or
275.92 sin(2θ) = 200

Answer: A

Answer:

A) 275.92sin(2Theta)=200

a p e x

How to draw exactly two planes intersect the third plane does not intersect the other two?

Answers

Lay two of the planes exactly on top of each other (this makes them intersect an infinite number of times) and then lay one plane parallel above or below the other two.

how much money will you have if you started with $1000 and put it in an account that earned 5% every year for 15 years

Answers

The interest equation is A = P(1 + r)^t. We can plug in the known information to get A = 1,000(1 + 0.05)^15. Next, we can add the 1 and the 0.05 to get A = 1,000(1.05)^15. Finally, we can take 1.05 to the power of 15 and multiply by 1,000 to get an answer of $2,078.93.

Hope this helps!

what is another name for the set of all x-values from its graph

Answers

For functions, it's solutions.

Another way to say it is the zeros

The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period. What is a cosine function that models this reaction?
f(t) = −30 cos (pi/3) t + 20

f(t) = −60 cos (pi/3) t + 30

f(t) = 30 cos (6t) + 20

f(t) = 60 cos (6t) + 30

Answers

maximum amount of cos is 1 and it's minimum is -1 so the answer should be something you put 1 and -1 (without attaining to cos itself) find -10 and 50
so it's the first one or the third one
(period)T=2pi/a
6=2pi/a
a=pi/3
the first one is the answer

Answer:

Option 1 - [tex]f(t)=-30 sin(\frac{\pi}{3}t)+20[/tex]

Step-by-step explanation:

Given : The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius. The temperature is at its lowest point when t = 0, and the reaction completes 1 cycle during a 6-hour period.

To find : What is a cosine function that models this reaction?

Solution :

General form of cosine function is [tex]f(x)=A cos(Bx)+C[/tex]

Where A is the amplitude

[tex]B=\frac{2\pi}{\text{Period}}[/tex]

C is the midline

Now, We have given

The temperature of a chemical reaction ranges between −10 degrees Celsius and 50 degrees Celsius.

A is the average of temperature,

i.e, [tex]A=\frac{-10-50}{2}=-30[/tex]

Period of 1 cycle is 6 hour

So, [tex]B=\frac{2\pi}{6}=\frac{\pi}{3}[/tex]

The temperature is at its lowest point when t = 0 and we know lowest point is -10

So, [tex]f(t)=A\cos t+C[/tex]

[tex]-10=-30\cos 0+C[/tex]

[tex]C=20[/tex]

Substituting the values we get,

The cosine function is [tex]f(t)=-30 sin(\frac{\pi}{3}t)+20[/tex]

Therefore, Option 1 is correct.

What is the simplified form of 30 times x to the sixth power over 14 times y to the fifth power times the fraction 7 times y-squared over 6 times x to the fourth power ?

Answers

If we convert the given in its mathematical form, we have,

(30x⁶/14y⁵)(7y²/6x⁴)
It can be observed that the numerator of the first and the denominator of the second have a common factor of 6x⁴. Also, the denominator of the first and the numerator of the second expression have a common factor of 7y².

((6x⁴)(5x²)/(7y²)(2y³))(7y²/6x⁴)

Cancellation of the common terms will give us an answer of,

5x²/2y³

Therefore, the simplified version of the involved operation is 5x²/2y³.

solve the inequality 9x-11 > 4x +12

Answers

You need to get x by itself. So add 11 to both sides. Then you get 9x>4x+23. Subtract 4x from both sides. The new inequality you get is 5x>23. Then, divide each side by 5. You get x>4.6. The answer is x>4.6. Hope this helps! ;)

A square is inscribed in the circle. A point in the figure is selected at random. Find the probability that the point will be in the part that is NOT shaded.

Answers

Ok
Probability (the point will be on unshaded part) = area of unshaded part / area of the circle.

= pi r^2 - s^2
-------------- where r = radius of circle and s = length of the side of the square.
pi r^2

To find the probability of selecting an unshaded area within a circle where a square is inscribed, one must calculate the areas of the shaded and unshaded regions and use these areas to determine the ratio representing the probability.

The question seeks to determine the probability that a randomly selected point within a figure that includes both a circle and a square will be in the unshaded area. To solve this problem, we would typically need to calculate the area of the shaded and unshaded regions and then use these areas to determine the probability. When calculating probability in a geometric context, the ratio of the area of the desired region to the area of the entire space (in this case, the circle) gives the probability of randomly selecting a point in that region.

Similarly, if the question pertained to the probability of selecting a chord shorter than the side of an inscribed equilateral triangle, we would consider the probability distribution of chord lengths within the circle. This problem involves understanding that selecting a chord at random equates to selecting its midpoint at random. If the midpoint lies within a certain area, the chord will be shorter than the triangle's side.

When dealing with probability questions like the one about Times Square visitors, the random variable would typically represent the characteristic we're interested in, such as being a visitor versus a resident. In evaluating probabilities, graphical methods, such as shading areas on a graph, can be useful to visually represent and calculate the likelihood of a specific range of outcomes.

Ariel has a plastic ice cream cone in her food playset. The ice cream cone is a half-sphere sitting on top of a cone. What is the approximate volume of the toy ice cream cone? Use 3.14 for ππ .

Answers

the approximate volume of the toy ice cream cone is around [tex]$ \frac{32}{3}π $[/tex]cubic inches, considering the half-sphere as[tex]$ \frac{16}{3}π $[/tex] and the cone as [tex]$ \frac{16}{3}π $.[/tex]

let's calculate the approximate volume of the toy ice cream cone step by step.

First, we need to determine the volume of the half-sphere, which is the ice cream part.

The formula for the volume of a sphere is:

[tex]\[ V_{\text{sphere}} = \frac{4}{3}πr^3 \][/tex]

But since we only have a half-sphere, we'll divide the result by 2.

Now, we need to find the radius ((r)) of the half-sphere. We can do this by measuring the radius of the ice cream cone's base.

Let's say the radius of the ice cream cone's base is (r = 2) inches.

Substituting the value of (r) into the formula:

[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{4}{3}π(2)^3 \][/tex]

[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{4}{3}π(8) \][/tex]

[tex]\[ V_{\text{half-sphere}} = \frac{1}{2} \times \frac{32}{3}π \][/tex]

[tex]\[ V_{\text{half-sphere}} = \frac{16}{3}π \][/tex]

Now, let's find the volume of the cone part.

The formula for the volume of a cone is:

[tex]\[ V_{\text{cone}} = \frac{1}{3}πr^2h \][/tex]

Where (h) is the height of the cone.

Let's say the height of the cone is (h = 4) inches.

Substituting the values into the formula:

[tex]\[ V_{\text{cone}} = \frac{1}{3}π(2)^2(4) \][/tex]

[tex]\[ V_{\text{cone}} = \frac{1}{3}π(16) \][/tex]

[tex]\[ V_{\text{cone}} = \frac{16}{3}π \][/tex]

Now, to find the total volume of the ice cream cone, we'll add the volumes of the half-sphere and the cone together:

[tex]\[ V_{\text{total}} = V_{\text{half-sphere}} + V_{\text{cone}} \][/tex]

[tex]\[ V_{\text{total}} = \frac{16}{3}π + \frac{16}{3}π \][/tex]

[tex]\[ V_{\text{total}} = \frac{32}{3}π \][/tex]

So, the approximate volume of the toy ice cream cone is [tex]$ \frac{32}{3}π $[/tex]cubic inches.

The Empire State Building is just over 1,450 feet tall. In anticipation of visiting this landmark on your vacation, you create a model of it using blocks.
a. Suppose you are making a model where one block represents 2 feet. About how many blocks tall is your model of the Empire State Building? What is the scale factor?

Answers

You have two given data available here: the actual height of the Empire State Building measuring 1,450 feet, and the height of the block measuring 2 feet. To find how many blocks stacked together would make up 1,450 feet, just divide 1,450 by 2.

Number of blocks=1,450 feet * (1 block/2 feet)
Number of blocks = 725 blocks

Therefore, you would use a model requiring 725 blocks. The scale factor for the model is 1 block per two feet.

Answer:

725, 1 per every 2 ft.

Step-by-step explanation:

It gives the actual height for the building, 1,450, and it says one block is two feet. Divide 1,450 by 2 and you'd get 725. And we already know dat one block is two feet so it's 1:2

(why did I start singing ``You Reposted in the Wrong Hero Academia?`` UwUz)

Order of operation:3[10-(27 divided by 9)] sorry I don't have the division sign

Answers

PEMDAS (parenthesis, exponents, multiply, divide, add, subtract)

first you do parthesis (27/9) = 3
then you subtract from 10 [10-3] = 7
then multiply 3 (this is last because it is outside the parenthesis and [ ].
7 x 3 = 21

21 is your answer

hope this helps

What is the slope of the line that contains the points (-4,2) and (6,-3)

Answers

(-4,2)(6,-3)
slope = (-3 - 2) / (6 - (-4) = -5/10 = 1/2 <=

Is the relationship between the variables in the table a direct variation, an inverse variation, or neither? If it is a direct or inverse variation, write a function to model it.

Answers

direct variation is y = kx where k is a constant
k = y/x
test some of the values in table :-

y/x = -17/9 and -1/11 - not equal so not direct

For indirect yx will be a constant :=

yx = 9*-17 , 11*-1 - s it not indirect variation.

Answer is neither

The graph of F(x) can be compressrd vertically and shifted to the right to produce the graph of G(x). If F(x) = x^3, which of the following could be the equation of g(x)?
A.) G(x) = 1/2(x-6)^3
B.) G(x) = 2(x-6)^3
C.) G(x) = 2(x+6)^3
D.) G(x) = 1/2(x+6)^3

Answers

It is option A. A vertical compression means that the function is only a "fraction" of its original height, hence the fractional coefficient.

REMEMBER, movement along the x-axis is always the OPPOSITE of what you think. So left = + and right = -

So (x-6) actually means a shift 6 units to the right. (NOT left like you would naturally think)

The figure below is a square pyramid. Which of the following could not be a cross section in the figure?

Square
Rectangle that is not a square
Trapezoid
Isosceles triangle

Answers

if you run a plane like in the picture below, I don't think you could get an isosceles triangle, namely, a triangle with two equal sides.

Answer:

A rectangle that is not a square is the actual answer.

what is the slope of the line that passes through (1,4) and (1,-3)?

A. 7
B. -7
C. undefined
D. 0

Answers

Use formula of a slope.

M = y2 - y1 / x2 - x1
= -3 - 4 / 1 - 1
= -7 / 0
= undefined.

Therefore the answer is C.

The first point is (1,4) which means (x1,y1) = (1,4). So,
x1 = 1
y1 = 4

The second point is (1,-3) meaning that (x2,y2) = (1,-3). So,
x2 = 1
y2 = -3

Now use the slope formula. Plug in those four values mentioned above

m = (y2 - y1)/(x2 - x1)
m = (-3 - 4)/(1 - 1)
m = -7/0

This is where we run into issues. The denominator is 0. We CANNOT divide by zero. So the result is undefined.

Your calculator may say "UND" for "Undefined", it might say "NaN" for "Not a Number", or it might produce some other type of error.

Answer: Choice C) undefined

Note: if you draw a line through the two given points, the line is completely vertical

The results of a study indicate that the mean weight of adult skunks in an area is between 4.3 kg and 4.9 kg. What is the study’s margin of error?

Answers

Since we are given the range of the area, the margin of error can be calculated by firstly calculating the difference of the range and dividing by 2. This is expressed in this formula:

Margin of error = ± (Upper range – Lower range) / 2

Margin of error = ± (4.9 kg – 4.3 kg) /2

Margin of error = ± 0.3 kg

Find the arc length of a central angle of pi/4 in a circle whose radius is 8 inches

A) pi/32 in
B) 2pi in
C) 360 in
D) 60 in

Answers

The formula of the arc is:

Arc Length = 2πR.(C°/360°), where R is the radius, C°(in degrees) is the central angle of the arc:

We are given:
R = 8 in
Central angle = π/4 ≈ (180°/4) = 45°
Length of the arc= 2π x 8 x (45°/360°) →16π(1/8) :

Length of the arc = 2π in (answer B)

The arc length of a central angle of π/4 in a circle whose radius is 8 inches is 2π inches. Therefore, option B is the correct answer.

What is arc length of a circle?

The arc length is defined as the interspace between the two points along a section of a curve. An arc of a circle is any part of the circumference. The angle subtended by an arc at any point is the angle formed between the two line segments joining the center to the end-points of the arc.

The formula to find the arc length of a circle is θ/360° ×2πr.

Given that, θ=π/4 =180/4 = 45° and radius = 8 inches.

Now, arc length = 45°/360° ×2×3.14×8

= 1/8×2×3.14×8

= 6.28 inches or 2π inches

Therefore, option B is the correct answer.

Learn more about the arc length of a circle here:

https://brainly.com/question/1577784.

#SPJ3

#12 with work please

Answers

[tex]\bf \textit{let's say, the angle is }\theta \textit{ so then }cos^{-1}\left( \frac{2}{3} \right)=\theta \\\\\\ \textit{this means }cos(\theta )=\cfrac{2}{3}\cfrac{\leftarrow adjacent}{\leftarrow hypotenuse}\impliedby \textit{now, let's find the \underline{opposite}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases}[/tex]

[tex]\bf \pm\sqrt{3^2-2^2}=b\implies \pm\sqrt{9-4}=b\implies\boxed{ \pm\sqrt{5}=b}\\\\ -------------------------------\\\\ cos^{-1}\left( \frac{2}{3} \right)=\theta \implies sin\left[ cos^{-1}\left( \frac{2}{3} \right) \right]\implies sin(\theta ) \\\\\\ sin(\theta )=\cfrac{\pm\sqrt{5}}{3}\cfrac{\leftarrow opposite}{\leftarrow hypotenuse}[/tex]

it doesn't say the angle is in a certain quadrant, thus the +/- versions of it are both valid.

The length of a rectangle is 9 feet longer than the width. if the perimeter is 78 feet, find the length and width of the rectangle.

Answers

Length - l

Width - w

Given,

Perimeter = 78 ft

2(l + w) = 78

l + w = 39

l = 39 - w

Given,

l = 9 + w

39 - w = 9 + w

2w = 30

--- w = 15

--- l = 39 -w = 39 - 15 = 24

Therefore, the length of the rectangle is 24 ft and width is 15 ft.

Larry mixed 15 grams of salt with 210 grams of a 5% salt solution in water. What is the percent of salt in his new solution?

Answers

When the concentration of a solution is expressed in weight percentages, that is just equal to the mass of solute over the mass of the total solution. For a solution weighing 210 grams, 5% of it is salt. That is equal to

210*0.05= 10.5 g salt

The rest of the amount, determined by difference, is the amount of solvent which is water.

water = 210-10.5 = 199.5 g salt

To solve for the new concentration, you add up 15 g to the already existing 10.5 g of salt in the solution. The water, on the other hand, remains constant.

Concentration = (15+10.5)/(210+15) = 0.1133 or 11.33%

If the circumference of a circle is 24, and the angle measure of an arc is 120o, which is the length of the arc?

Answers

The best way to solve this problem is to use proportions. That said, a circle's given arc length is proportional to the angle measure of that arc. So, 120degrees out of 360degrees total is one third (1/3) of the circle. Therefore, the arc length will be one third of the circle's circumference (24 • 1/3) which is 8.

The arc length is 8.

Kim's softball team is playing in the championship game. they are losing by a score of 171717 to 666. there are 444 innings to go. kim wants to know how many runs her team needs per inning to win the game if the other team does not score. (each run is worth 111 point.)

Answers

they are losing by a score of 17 to 6....4 innings to go...each run equals 1 point........so they are losing by (17 - 6) = 11 points, which means 11 runs behind. So they would need 11 to tie...but 12 to win. 12 runs in 4 innings = 12/4 = 4 runs per inning.

answer is : 4 runs per inning to win

The Sugar Sweet Company will choose from two companies to transport its sugar to market. The first company charges $2510 to rent trucks plus an additional fee of $125.25 for each ton of sugar. The second company does not charge to rent trucks but charges $250.75 for each ton of sugar.
For what amount of sugar do the two companies charge the same?
What is the cost when the two companies charge the same?

Answers

2510 + 125.25s = 250.75s
2510 = 250.75s - 125.25s
2510 = 125.50s
2510 / 125.50 = 20 = s.......they charge the same at 20 tons of sugar

they will both cost : 250.75(20) = $ 5015

The two companies charge the same when transporting 20 tons of sugar, for $5015 for transporting that amount.

To determine what amount of sugar the two companies charge the same, we should set up an equation where both companies' cost functions are equal. For the first company, the cost function is C1 = 2510 + 125.25x, where x is the number of tons of sugar. For the second company, the cost function is C2 = 250.75x. To find the point at which C1 equals C2, we solve for x:

2510 + 125.25x = 250.75x

Subtract 125.25x from both sides:

2510 = (250.75 - 125.25)x

2510 = 125.5x

Divide both sides by 125.5:

x = 2510 / 125.5

x = 20 tons

Therefore, the two companies charge the same for transporting 20 tons of sugar. To find the cost when they charge the same, substitute x into one of the cost functions:

C1 = 2510 + 125.25(20) = 2510 + 2505 = $5015

Thus, the cost when the two companies charge the same is $5015 for 20 tons of sugar.

Find the volume of each figure to the nearest tenth. Show your work. please

Answers

Sphere volume: [tex] \frac{4}{3} \pi r^3[/tex]

[tex] \frac{4}{3} \pi 6^3 [/tex]

[tex] \frac{4}{3}*216 \pi [/tex]

[tex]288 \pi [/tex]

V = 288π = 288*3,14 = 904,3 m³

Cone volume: [tex] \frac{ \pi r^2h}{3} [/tex]

We don't have the height, so we should find it firstly.

Watch the triangle "inside" the cone. It is a right triangle. The apothem is the hypothenuse and the radius is the shortest leg.

Apply Pitagora.

h (longest leg) = √13²-5² = √169-25 = √144 = 12 m

V = [tex] \frac{ 5^2*12 \pi}{3} [/tex]

[tex] \frac{25*12* \pi }{3} [/tex]

[tex] \frac{300 \pi }{3} [/tex]

(300*3,14)/3 = 942/3 = 314 m³

Parallelepiped volume: a*b*h

a = 11, b = 5, h = 6

V = 11*5*6 = 330 cm³

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