What is the length of the hypotenuse in simplified radical form?(Information needed - long leg is 13, short leg is 5, it is a right triangle)


A. √194
B. 2√97
C. 12
D. 13.93

Answer:

y = -3/2 x + 3

Step-by-step explanation:

If two lines' slopes multiply to get -1, they are perpendicular to each other.

In -6x+9y-12=0, find the slope by converting to slope-intercept form.

Isolate y:

-6x+9y-12=0

-6x+9y = 12

9y = 6x + 12

y = 6/9 x + 12/9

y = 2/3 x + 4/3

The slope in this line is 2/3.

To find the slope of a perpendicular line, find its negative reciprocal. The negative reciprocal is when you switch the top and bottoms numbers and multiply it by -1.

2/3 => -3/2

The slope of the perpendicular line is -3/2.

In -8x+2y-6=0, find the y-intercept by converting to slope-intercept form.

Isolate y:

-8x+2y-6=0

-8x + 2y = 6

2y = 8x + 6

y = 8/4 x + 6/2

y = 2x + 3

Slope-intercept form is y = mx + b, which b is the y-intercept.

The y-intercept is 3.

Substitute the slope and y-intercept values into the equation of a line in  slope-intercept form.

y = mx + b

y = -3/2 x + 3

Answer: It should be 3,500

Step-by-step explanation: If the number behind it is 5 or greater, then you round up, meaning the 3 would change to 4, but since it is lower than 2, it would stay the same (5) for it is closer to 3,500.

You compare fractions by seeing the denominator is the same and then you add them or multiply them or diving them and that is how you compare fractions.

It will take the snail 9.6 minutes to travel 24cm.

Step-by-step explanation:

Distance covered in 4 minutes = 10 cm

Ratio of distance to time = 10:4

New distance = 24cm

Let,

x be the time period

Ratio of new distance to time = 24:x

Using proportions;

Ratio of distance to time :: Ratio of new distance to time

[tex]10:4::24:x[/tex]

Product of mean = Product of extreme

[tex]24*4=10*x\\96=10x\\10x=96[/tex]

Dividing both sides by 10

[tex]\frac{10x}{10}=\frac{96}{10}\\x=9.6\ minutes[/tex]

It will take the snail 9.6 minutes to travel 24cm.

Keywords: ratio, proportion

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Box plots are useful for comparing the measure of variability in datasets. Specifically, they compare the interquartile range (IQR), which is the range covering the middle 50% of a dataset. This is represented by the box in the plot, and additional info like median and potential outliers are also shown.

In the field of statistics, box plots, also known as box and whisker plots, are useful for comparing the measure of variability in a data set. The specific measure of variability that can be compared using the box plots is called the interquartile range (IQR).

The IQR is the range within which the middle 50% of a dataset falls. It is calculated by subtracting the lower quartile (25th percentile) from the upper quartile (75th percentile). These quartiles are represented on a box plot by the edges of the box, which makes it easier to visually compare the variability of different datasets.Box plots also present additional information like median and potential outliers in the data.

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Is that it on the description? No question of nothing?

Answer:

10oz

Step-by-step explanation:

1 lb = 16 oz, so

(6*16 +4)-(5*16+10)

100-90=

10 oz

First, put both into just ounces. (1lb = 16oz)

6lb 4oz = 100oz.

5lb 10oz = 90oz.

Second, subtract.

100 - 90 = 10oz.

This is the answer. Note that 1lb = 16lb, so we can't put 10oz into pounds.

______

Hence, the answer is 10oz.

______

Best Regards,

Wolfyy :)

Answer:

-(7/8) is equivalent to -7/8

B) -7/8 is correct option

-7/8 is equivalent to -(7/8).

The multiplication or division of two negative number or sign will always give a positive numbeer or sign.

By cheking all options

1. -(7/-8)=7/8     as multiplication or division of two negative number or sign will always give a positive numbeer or sign.

2. -7/8=-(7/8)

3. -(-7/8)=7/8     as multiplication of two negative sign will always give a positive sign.

4. -7/-8=7/8       as division of two negative sign will always give a positive sign.

Therefore from above it is clear that -7/8 is equivalent to -(7/8).

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Answer:

Option B.) 45 units

Step-by-step explanation:

see the attached figure with letter to better understand the problem

step 1

Determine the coordinates of the corners of the rectangle

Let

A(4,5),B(1,8),C(14,21) and D(17,18)

step 2

we know that

The formula to calculate the perimeter of rectangle is equal to

[tex]P=2(AB+BC)[/tex]

the formula to calculate the distance between two points is equal to

[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]

Find the length side AB

[tex]A(4,5),B(1,8)[/tex]

substitute in the formula

[tex]d=\sqrt{(8-5)^{2}+(1-4)^{2}}[/tex]

[tex]d=\sqrt{(3)^{2}+(-3)^{2}}[/tex]

[tex]d_A_B=\sqrt{18}\ units[/tex]

Find the length side BC

[tex]B(1,8),C(14,21)[/tex]

substitute in the formula

[tex]d=\sqrt{(21-8)^{2}+(14-1)^{2}}[/tex]

[tex]d=\sqrt{(13)^{2}+(13)^{2}}[/tex]

[tex]d_B_C=\sqrt{338}\ units[/tex]

Find the perimeter

[tex]P=2(AB+BC)[/tex]

substitute the values

[tex]P=2(\sqrt{18}+\sqrt{338})[/tex]

[tex]P=45\ units[/tex]

Answer:

B) 45 units

Step-by-step explanation:

D = dx2 + dy2

W = (1-4)2 + (8-5)2

W = (-3)2 + (3)2 = 4.24264

L = (1-14)2 + (8-21)2

L = (-13)2 + (-13)2 = 18.38478

A = 2L+2W = 2(18.38478)+2(4.24264)= 45.3 units

Answer:

m = [tex]\frac{-2}{5}[/tex]

Step-by-step explanation:

2m + 1 = -3m - 1 (Given)

2m + 1 + 1 = -3m - 1 + 1 (Addition Property of Equality)

2m + 2 = -3m (Simplify)

2m - 2m + 2 = -3m - 2m (Subtraction Property of Equality)

2 = -5m (Simplify)

[tex]\frac{2}{-5} = \frac{-5m}{-5}[/tex] (Division Property of Equality)

[tex]\frac{-2}{5}[/tex] = m (Simplify)

m = [tex]\frac{-2}{5}[/tex] (Symmetric Property of Equality)

The answer is:

Work/explanation:

Combine like terms on each side:

[tex]\sf{2m+1=-3m-1}[/tex]

Make sure all terms that contain m are on the left side and all constant terms are on the right. Don't forget to use the opposite sign when moving terms from one side to the other one.

[tex]\sf{2m+3m=-1-1}[/tex]

[tex]\sf{5m=-2}[/tex]

Divide each side by 5

[tex]\sf{m=-\dfrac{2}{5}}[/tex]

Answer:

Sale price is $12 which is 80% of the regular price.

Step-by-step explanation:

A large two-topping Pizza is 20% off the regular price of $15.

Therefore, the sale price is [tex]15(1 - \frac{20}{100} ) = 15 \times 0.8 = 12[/tex] dollars. (Answer)

Now, let us assume that x% of regular price i.e. $15 is the sale price i.e. $12.

So, [tex]\frac{15 \times x}{100} = 12[/tex]

⇒ [tex]x = \frac{12 \times 100}{15}[/tex]

⇒ x = 80%  (Answer)

Answer:

15 regular price 20% discount ? sale price and the next answer is 0.8(15) and the sale price gone be 12.

Step-by-step explanation:

I did the I-ready Hope this helps.

0.8(15) answer 12 so thats how I know thats the sale price and they wanted to know what was the sale price. I did the I-ready..Now have a good day at school or whatever.

Answer:

The three 2-gallon cans of paint  is enough  to complete the job.

Step-by-step explanation:

Given:

It takes 2 1/8 gallons of paint to coat each door and 1 3/5 to coat all of shutters. He had three 2-gallon cans of paint.

Now, to find that is he have enough paint to complete the job.

Total gallons of paint he buys = 3 × 2 = 6 gallons.

Then, let the quantity used change to improper fraction from mixed:

[tex]2\frac{1}{8} =\frac{17}{8}[/tex] and [tex]1\frac{3}{5}=\frac{8}{5}[/tex].

Now, we add the quantity of paints used to paint doors and shutters:

[tex]\frac{17}{8}+\frac{8}{5}[/tex]

[tex]=\frac{85+64}{40}[/tex]

[tex]=\frac{149}{40}[/tex]

Now, subtracting quantity used from the total quantity:

[tex]6-\frac{149}{40}[/tex]

[tex]=\frac{240-149}{40}[/tex]

[tex]=\frac{91}{40}[/tex]

[tex]=2\frac{11}{40}[/tex]

So, after painting the two doors and several shutters from 3 cans of 2-gallon paint still 2 11/40 quantity of paint is remaining.

Therefore, the three 2-gallon cans of paint is enough to complete the job.

Answer:

The value of given expression for x = - 10  is - 81

Step-by-step explanation:

Given expression as :

3 [tex]\frac{4}{5}[/tex]x - 2 [tex]\frac{1}{2}[/tex]

Or, 3 +  [tex]\frac{4}{5}[/tex]x  - 2 -  [tex]\frac{1}{2}[/tex]

Or,  [tex]\frac{19}{5}[/tex]x -  [tex]\frac{5}{2}[/tex]

or,  [tex]\frac{38 x - 25}{5}[/tex]

Now for  x = - 10

[tex]\frac{38\times (- 10)  - 25}{5}[/tex]

Or, [tex]{38\times (- 2)  - 5}[/tex]

∴ - 76 - 5

Or, - 81

Hence The value of given expression for x = - 10  is - 81  Answer

Answer:

Parabola [tex]P^{2}[/tex] = 16A

Non-linear function.

Increasing function.

Step-by-step explanation:

Let a be the side length of a square ,

Then, Perimeter of square (P) = 4a

So, a can be written as a = [tex]\frac{P}{4}[/tex]

Area of square (A) = [tex]a^{2}[/tex] .

So, A = [tex]\frac{P^{2} }{4^{2} }[/tex]

        =  [tex]\frac{P^{2} }{16 }[/tex]

[tex]P^{2}[/tex] = 16A

It is the equation of parabola. (similar to [tex]y^{2}[/tex] = 4ax)

It is a non - linear function as square of Perimeter is related to Area , not directly Perimeter.

Also, it is a increasing function since as A increases P increases.

Final answer:

The function relating the area of a square to its perimeter is a quadratic function shown by the equation A = P²/16, which is graphed as a parabola. The graph is not linear, and it illustrates that as the perimeter increases, the area increases at an accelerating rate, hence it is always increasing.

Explanation:

To graph the function that relates the area of a square to its perimeter, first understand that the area A of a square is equal to the side length squared (s²), and the perimeter P is four times the side length (4s). These relationships can help us derive the function A = f(P). Here's how you would do it:

The graph of this function is not linear but a parabola opening upwards because it has the form of a quadratic equation A = P²/16. This means the graph will be an increasing curve as the perimeter increases, the area increases at an accelerating rate. It is important to note that the graph of this function is always increasing, and the rate of increase grows as the value of P increases

Answer:

c

Step-by-step explanation:

It is measured in the same unit as the original unit, so x will be 1.42x

Add the service charge as it is a constant addition, and we end up with:

y = 1.42x + 13.20

the correct equation representing the monthly water bill is:

[tex]\[ y = 1.42x + 13.20 \][/tex]

The correct option is (c).

Sure, let's break down the calculation step-by-step.

1. Monthly service charge: The monthly service charge is a fixed amount, which is $13.20.

2. Usage charge: The usage charge is $1.42 for every 100 cubic feet of water used. Since x represents the amount of water used in hundreds of cubic feet, the usage charge can be calculated as \(1.42x\).

3. Total monthly cost: To determine the total monthly cost \(y\), we add the monthly service charge to the usage charge. Therefore, the equation representing the total monthly bill is:

[tex]\[ y = \text{Monthly service charge} + \text{Usage charge} \][/tex]

[tex]\[ y = 13.20 + 1.42x \][/tex]

So, the correct equation representing the monthly water bill is:

[tex]\[ y = 1.42x + 13.20 \][/tex]

Therefore, the correct answer is option C.

Answer:

Step-by-step explanation:

So basically what you want to do is start with the distributive property.

-0.5(x+0.3) = 1.6x+0.9(x+4.8) would then equal -0.5x-0.15 = 1.6x+0.9x+4.32.

Then, add the matching terms on the right side (the x values) 1.6x+0.9x =2.5x

Your equation should the look like -0.5x-0.15 = 2.5x+4.32.

Next, add -0.5x to 2.5x giving you 3x

The equation will look like -0.15 = 3x+4.32

After that subtract 4.32 from -0.15 leaving you with -4.47=3x

Divide 3x from both sides

Your answer should be x= -1.49.

I hope this was helpful and not super confusing! Also if anything is incorrect let me know! :)

Answer:

1-  S < L

2-  Spending is less than the limit.

3- 30-3x [tex]\geq[/tex] 14

Step-by-step explanation:

Answer:

Step-by-step explanation:

answer is W = 7 and A = 43.

The rate of the plane in still air is 43 miles per hour and the rate of the wind is 7 miles per hour.

Given that, Togo flew his ultralight plane to a landing field 30 miles away.

The speed formula can be defined as the rate at which an object covers some distance. Speed can be measured as the distance travelled by a body in a given period of time. The SI unit of speed is m/s.

Let x represent the rate of the plane in still air.

Let y represent the rate of wind.

We know that, Distance = Speed × Time

Speed of flight with wind is x+y miles per hour

Speed of flight against wind is x-y miles per hour

With the wind, the flight took 3/5 hours.

Now, 30=3/5 (x+y)

50=x+y --------(I)

Returning against the wind, the flight took 5/6 hours.

30=5/6 (x-y)

36=x-y --------(II)

Add equation (I) and (II), we get

x+y+x-y=50+36

⇒ 2x=86

⇒ x=43 miles per hour

Substitute x=43 in equation (I), we get

43+y=50

⇒ y=7 miles per hour

Therefore, the rate of the plane in still air is 43 miles per hour and the rate of the wind is 7 miles per hour.

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Answer:

n=-19

Step-by-step explanation:

-37+n+37=-56+37

n=-19

Answer:

-37+n=-56

n= -56-(-37)

n= -19

Answer:

The probability that he will get a red gumdrop and a piece of butterscotch candy is 2/25

Step-by-step explanation:

The path to find the answer is to find the probability of both things happening  and then multiply them. First, there is 1 red gumdrop and 4 green gumdrops in a jar. There are 5 gumdrops total so the probability of choosing a red one is 1/5. Next, there are 2 pieces of butterscotch candy and 3 pieces of cinnamon candy in another jar. There are 5 pieces of candy total so the probability of choosing a piece of butterscotch candy is 2/5. Finally multiply the two probabilities: 1/5 * 2/5 = 2/25.

The probability that Craig will draw a red gumdrop from the first jar and a butterscotch candy from the second jar is 0.08 or 8%.

The subject of this problem is probability. Probability refers to the measure of the likelihood that an event will occur in a random experiment. In this specific problem, Craig randomly chooses one candy from each jar. We want to find the likelihood that Craig will choose one red gumdrop and one piece of butterscotch candy.

There are a total of 5 gumdrops in the first jar, with 1 being red. Thus, the probability of choosing a red gumdrop is 1/5. In the second jar, there are a total of 5 pieces of candy, with 2 being butterscotch. As such, the probability of choosing a butterscotch candy is 2/5.

To calculate the total probability, you multiply both probabilities, getting a final probability of (1/5) * (2/5) = 2/25 = 0.08. This means that there is an 8% chance that Craig will draw a red gumdrop and a butterscotch candy.

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Answer:

10(n-4)

Step-by-step explanation:

10n-40=10(n-4)

If this is what you were asked to find, then that's the answer. Because 10n-40 is just an expression, it's not something you can solve for it, since it's not an equation. So I simplified this expression for you by factoring.

Answer:

C. 45%

Step-by-step explanation:

Initial credit in his account = $750.00

Credit in his account after some purchases = $412.50

⇒Decrease in credit = $750.00 - $412.50

⇒Decrease in credit = $337.5

percentage decrease of amount of available credit = [tex]\frac{decrease\ in\ credit}{initial\ credit}[/tex]×100

                                    = [tex]\frac{337.50}{750.00}[/tex]×100

                                    = [tex]\frac{9}{20}[/tex]×100

                                    = 9×5

                                    = 45%

∴Percentage decrease of the amount of available credit in Dylan's account is 45%

Answer:

The graph that passes through (-3,-3), (-3,0) and (-3,3) does not represents linear function

Step-by-step explanation:

Mariko says that the graph that passes through (-3,-3), (-3,0) and (-3,3)

Now, the line joining (-3,-3) and (-3,0) has slope = [tex]\frac{-3 - 0}{- 3 -(- 3)} =[/tex] = ∞

Again, the line joining (-3, 0) and (-3,3) has slope = [tex]\frac{0 - 3}{- 3 -(- 3)} =[/tex] = ∞

Therefore, both the lines are parallel to y-axis and has a common point (-3,0). {Since, tan Ф = ∞, ⇒ Ф = 90°}

So, the graph that passes through (-3,-3), (-3,0) and (-3,3) does not represents linear function as the graph represents a vertical line parallel to y-axis. (Answer)

Answer:

2 days & 3 hours

Step-by-step explanation:

Answer: 6hrs

Step-by-step explanation:

Final answer:

The area of the rectangle is 12.8 square inches.

Explanation:

The area of a rectangle can be found by multiplying its length by its width. In this case, the length of the rectangle is 1.6 inches and the width is 8 inches. So, the formula for the area is:

Area = length x width

Substituting the given values, we get:

Area = 1.6 inches x 8 inches = 12.8 square inches

Answer:

Step-by-step explanation:

The formula of a surface area of a sphere:

[tex]SA=4\pi R^2[/tex]

R - radius

We have R = 30m.

Substitute:

[tex]SA=4\pi(30^2)=4\pi(900)=3600\pi\ m^2[/tex]

Answer:

{0 ≤ h ≤ 25}

Step-by-step explanation:

The domain of a function is the set of all values for independent variable for which the function must be defined.

Given: The amount earned by Hailey for one hour work =$9.50

She determines that her salary is modeled by the function .

Here h is the independent variable such that 's' is dependent on 'h'.

Since she never works more than 25 hours in a week.

Therefore, the maximum hours she will work = 25

Hence, the domain of this function in this situation is {0 ≤ h ≤ 25}, where h is number of hours she works.

Answer:

{0 ≤ h ≤ 25}

Step-by-step explanation:

The domain of a function is the set of all values for independent variable for which the function must be defined.

Given: The amount earned by Hailey for one hour work =$9.50

She determines that her salary is modeled by the function .

Here h is the independent variable such that 's' is dependent on 'h'.

Since she never works more than 25 hours in a week.

Therefore, the maximum hours she will work = 25

Hence, the domain of this function in this situation is {0 ≤ h ≤ 25}, where h is number of hours she works.

The factors are: x-5 and x+3

Step-by-step explanation:

Given

[tex]x^2-2x-15 = 0[/tex]

Simplifying

[tex]x^2-5x+3x-15 = 0\\x(x-5) + 3(x-5) = 0\\(x+3)(x-5) = 0[/tex]

Let us define the zero product property first

The zero product property states that

if ab=0 then either a=0 or b=0

So,

[tex]x+3 = 0\\x+3-3 = 0-3\\x = -3\\AND\\x-5 = 0\\x-5+5 = 0+5\\x = 5[/tex]

Hence,

the factors are: x-5 and x+3

Keywords: Factorization, Zero product property

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Answer:

39.5

Step-by-step explanation:

We put the numbers in order least to greatest and pick the middle one because that number is the median:

36, 38, 39, 39, 40, 47, 48, 51

Since 39 and 40 are tied for the median we go in between those two numbers, 39.5.  The answer is 39.5.

Answer:

A. Left by 4 units

Step-by-step explanation:

ƒ(x) = x²

It has a vertex at (0, 0), and the y-axis is the axis of symmetry

g(x) = x² + 8x + 16 = (x + 4)²

You have added 4 to the value of x, so you have shifted the graph four units to the left.

Thus, to make the graphs of ƒ(x) and g(x) coincide, you should shift ƒ(x) left by 4 units.

The diagram below shows ƒ(x) in red and g(x) in green.