The table below shows values for x and y. If y varies directly as x, what is the constant of variation?
x y
0 0
1 -9
2 -18
3 -27




-9

0

3

9

Answer:

48

Let me know if this was right :)                                                

[tex]x^2=40^2+9^2\\x^2=1600+81\\x^2=1681\\x=\sqrt{1681}=41[/tex]

To solve this you must use Pythagorean theorem:

[tex]a^{2} +b^{2} =c^{2}[/tex]

a and b are the legs (the sides that form a perpendicular/right angle)

c is the hypotenuse (the side opposite the right angle)

In this case...

a = 9

b = 40

c = x

^^^Plug these numbers into the theorem

[tex]9^{2} +40^{2} =x^{2}[/tex]

simplify

81 + 1600 = [tex]x^{2}[/tex]

1681 = [tex]x^{2}[/tex]

To remove the square from x take the square root of both sides to get you...

41 = x  

Hope this helped!

~Just a girl in love with Shawn Mendes

The key  property of the absolute value parent function is:

        C. It’s vertex is at the origin.

The absolute value parent function is given by:

                  [tex]f(x)=|x|[/tex]

i.e. the graph of the function lie in the first and second quadrant.

Answer:

(arranged from top to bottom)

System #3, where x=6

System #1, where x=4

System #7, where x=3

System #5, where x=2

System #2, where x=1

Step-by-step explanation:

System #1: x=4

[tex]2x+y=10\\x-3y=-2[/tex]

To solve, start by isolating your first equation for y.

[tex]2x+y=10\\y=-2x+10[/tex]

Now, plug this value of y into your second equation.

[tex]x-3(-2x+10)=-2\\x+6x-30=-2\\7x=28\\x=4[/tex]

System #2: x=1

[tex]x+2y=5\\2x+y=4[/tex]

Isolate your second equation for y.

[tex]2x+y=4\\y=-2x+4[/tex]

Plug this value of y into your first equation.

[tex]x+2(-2x+4)=5\\x+(-4x)+8=5\\x-4x+8=5\\-3x=-3\\x=1[/tex]

System #3: x=6

[tex]5x+y=33\\x=18-4y[/tex]

Isolate your first equation for y.

[tex]5x+y=33\\y=-5x+33[/tex]

Plug this value of y into your second equation.

[tex]x=18-4(-5x+33)\\x=18+20x-132\\-19x=-114\\x=6[/tex]

System #4: all real numbers (not included in your diagram)

[tex]y=13-2x\\8x+4y=52[/tex]

Plug your value of y into your second equation.

[tex]8x+4(13-2x)=52\\8x+52-8x=52\\0=0[/tex]

all real numbers are solutions

System #5: x=2

[tex]x+3y=5\\6x-y=11[/tex]

Isolate your second equation for y.

[tex]6x-y=11\\-y=-6x+11\\y=6x-11[/tex]

Plug in your value of y to your first equation.

[tex]x+3(6x-11)=5\\x+18x-33=5\\19x=38\\x=2[/tex]

System #6: no solution (not included in your diagram)

[tex]2x+y=10\\-6x-3y=-2[/tex]

Isolate your first equation for y.

[tex]2x+y=10\\y=-2x+10[/tex]

Plug your value of y into your second equation.

[tex]-6x-3(-2x+10)=-2\\-6x+6x-30=-2\\-30=-2[/tex]

no solution

System #7: x=3

[tex]y=10+x\\2x+3y=45[/tex]

Plug your value of y into your second equation.

[tex]2x+3(10+x)=45\\2x+30+3x=45\\5x=15\\x=3[/tex]

Answer:

range=u ± 3.09 sd

Step-by-step explanation:

Given:

mean, u= 26.8 mpg

standard deviation, sd=72 mpg

% contained in interval = 99.8%

the interval for 99.8% of the values of a normal distribution is given by

mean ± 3.09 standard deviation= u ± 3.09 sd

                                                      =26.8  ± 3.09(72)

                                                      =26.8 ± 222.48

                                                      = 249.28 , -195.68

range=u ± 3.09 sd = 249.28 , -195.68 !

Answer:

See below.

Step-by-step explanation:

Compare our equation with one  standard form of a circle:

x^2 + y^2 = r^2    where r = the radius.

So x^2 + y^2 = 9 is the equation of a circle with it's center at the origin and it's radius is 3 units.

x^2 + y^2 = 0 is not a circle because r = 0  ( a radius of 0). A circle of radius 0 is really a point!!

The value of the radius of a circle  must be positive  so it cannot have a radius of -3.

Answer

[tex]x ^{2} + {y}^{2} = r^{2} [/tex]

since all the terms are squared so there can be a negative number

but in number line

...... -4,-3,-2,-1,0,1,2,3.......

as we know negative sign indicates only the direction so -3 means in which coordinates will it lie.

.

.

.

[tex] {x}^{2} + {y}^{2} = 9[/tex]

it means the origin is (0,0) and radius 3

Answer:

[tex]\sin(x)=\frac{\sqrt{95}}{12}=0.8122[/tex]

[tex]\cos(x)=\frac{7}{12} \approx .5833[/tex]  

[tex]\tan(x)=\frac{\sqrt{95}}{7} \approx 1.3924[/tex]  

[tex]x=\sin^{-1}(\frac{\sqrt{95}}{12}) \approx 54.3147[/tex] degrees.

I don't know what you want to round to but I can tell you are rounding...

Step-by-step explanation:

Soh Cah Toa is the acronym we will use to help us solve this.

This says sine is opposite over hypotenuse.

It also says cosine is adjacent over hypotenuse.

And finally tangent is opposite over adjacent.

Note:  Opposite and adjacent can change depending on how you are looking at the triangle, like which angle you are referring to.

Let's look at x:

The side that is opposite, not touching, the angle whose measurement is x, is the side that has measurement [tex]\sqrt{95} \approx 9.7[/tex].

I see you already found this measurement. This is really good.  I might use the exact value for now and round at the end.

The side that is the hypotenuse no matter the angle you are referencing is always going to be opposite the angle whose measurement is 90 degrees. It is also the longest side (since it is opposite the largest angle).  This side has measurement 12.

The hypotenuse will be one of the sides touching your angle you are referencing.  The other side that is touching your angle is the adjacent side.  This side has measurement 7.

Anyways let's plug into the definitions we had above:

[tex]\sin(x)=\frac{\sqrt{95}}{12}[/tex]  (O/H)

[tex]\cos(x)=\frac{7}{12}[/tex]   (A/H)

[tex]\tan(x)=\frac{\sqrt{95}}{7}[/tex]   (O/A)

Now we can solve anyone of these for x.

Take your pick.

[tex]\sin(x)=\frac{\sqrt{95}}{12}[/tex]

[tex]x=\sin^{-1}(\frac{\sqrt{95}}{12})[/tex]

[tex]x=54.3147[/tex] degrees.  

Answer:

17.167 rounded

Step-by-step explanation:

17+(1/6)

17+0,166

17.167

well, firstly convert the mixed fraction to improper fraction, and then simply divide the numerator by the denominator and round as needed.

[tex]\bf \stackrel{mixed}{17\frac{1}{6}}\implies \cfrac{17\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{103}{6}}~\hfill \stackrel{\textit{to a decimal}~\hfill }{103\div 6 = 17.166\overline{6}}\implies \stackrel{\textit{rounded up}}{17.167}[/tex]

Answer:

380 cubic feet of air

Step-by-step explanation:

Volume = height * width * length.

So

Volume = 10 * 2 * 19 = 380 cubic feet of air

Answer:

[tex]380\text{ ft}^3[/tex]

Step-by-step explanation:

We have been that a classroom is 19 ft long 2 ft wide and 10 feet high. We are asked to find the number of cubic feet of air in the room​.

To find the number of cubic feet of air in the room​, we will find the volume of the given room by multiplying all of its side as:

[tex]\text{Volume of the room}=\text{19 ft}\times \text{2 ft}\times\text{10 ft}[/tex]

[tex]\text{Volume of the room}=380\text{ ft}^3[/tex]

Therefore, there are 380 cubic feet of air in the room.  

[tex]xy=\log_{5\sqrt5}{125}\cdot\log_{2\sqrt2}64\\\\xy=\dfrac{\log_5125}{\log_5 5\sqrt5}\cdot\dfrac{\log_264}{\log_22\sqrt2}\\\\xy=\dfrac{3}{\log_55^{\tfrac{3}{2}}}\cdot\dfrac{6}{\log_22^{\tfrac{3}{2}}}\\\\xy=\dfrac{3}{\dfrac{3}{2}}\cdot\dfrac{6}{\dfrac{3}{2}}\\\\xy=3\cdot\dfrac{2}{3}\cdot6\cdot\dfrac{3}{2}\\\\xy=18[/tex]

Answer:

The product of x and y is 8.

Step-by-step explanation:

It is given that

[tex]x=\log_{5\sqrt{5}}\left(125\right)[/tex]

[tex]y=\log_{2\sqrt{2}}\left(64\right)[/tex]

We need to find the product of x and y.

[tex]x\cdot y=\log_{5\sqrt{5}}\left(125\right)\cdot\log_{2\sqrt{2}}\left(64\right)[/tex]

It can be written as

[tex]xy=\log_{5\sqrt{5}}\left(5\sqrt{5}\right)^2\cdot\log_{2\sqrt{2}}\left(2\sqrt{2}\right)^4[/tex]

Using the properties of logarithm, we get

[tex]xy=2\cdot 4[/tex]                    [tex][\because log_aa^x=x][/tex]

[tex]xy=8[/tex]

Therefore the product of x and y is 8.

Answer:

15/56

Step-by-step explanation:

You just multiply 3/7 by 5/8 to get 15/56. Since you cannot simplify it more, that is the fraction of boys in mrs.jones class compared to the whole sixth grade class

Answer:

15/56

Step-by-step explanation:

Let the total number of students be x

Number of boys=[tex]\frac{3}{7}[/tex] of x

Number of boys in Mrs jones' class= [tex]\frac{3}{7}[/tex]of[tex]\frac{5}{8}[/tex]

Fraction of number of boys of Mrs jones' class to total class strength=[tex]\frac{15x/56}{x}[/tex]

Hence, the fraction is[tex]\frac{15}{56}[/tex]

a) 600340

b) 600300

c) 600000

Answer:

A=$538.82

Step-by-step explanation:

We're going to use the compounded interest formula:

A=P(1+r/n)^n*t

Where,

A = the future value of the investment/loan, including interest

P = the principal investment amount (the initial deposit or loan amount)

r = the annual interest rate (decimal)

n = the number of times that interest is compounded per unit t

t = t is the amount of time at which you're checking how much it's worth (yrs)

Using this information, we can use:

A=500(1+0.025/4)^3*4

A=500(1+0.00625)^12

A=500(1.00625)^12

A=500(1.07763259886)

A=538.82

A=$538.82....

Answer:

3x -5

Step-by-step explanation:

(4x – 12) + (–x + 7)

= 4x – 12 –x + 7

= 3x -5 (answer)

Answer:

3x-5

Step-by-step explanation:

(4x – 12) + (–x + 7)

Open the parenthesis

=4x-12-x+7

Solve the like terms:

=3x-5

The answer is 3x-5

20% of 50 is found by multiplying the base (50) by the decimal equivalent of the percent (0.2). The calculation yields an amount of 10, which indicates that 20% of 50 is 10.

Calculating percents involves using the basic equation that relates the percent, the base (also called 'whole' or 'total'), and the amount (or 'part'). The equation can be represented as percent = (amount/base)  imes 100. To find what is 20% of 50, we use this equation, where the percent is known (20%) and the base is known (50), but the amount is what we are looking for.

First, let's convert the percent to a decimal to make the calculation easier: 20% = 20/100 = 0.2. Then, we multiply the base (50) by the decimal form of the percent (0.2): 50 x 0.2 = 10. So, 20% of 50 is 10.

Therefore, the correct representation relating the Percent, Amount, and Base in this problem is option A) Percent=20%, Amount=50, Base=unknown, since we're calculating the amount based on the known percent and base.

Answer:

C.) percent= 20%, Amount=unknown, Base =50

Step-by-step explanation:

20% is the percent

50 is the amount

20% of 50 is the unknown. This is the amount.

20% of 50 = 0.2 × 50 = 10

Answer:

option B

Step-by-step explanation:

Given:

per day late costs= 1.50

Purchase price= 9.99

A round trip cab ride to the video store will cost = 10

5 day late cost= 5(1.50)

                       = 7.50

Payment after 5 day late= 5 day late cost + Purchase price

                                       = 7.50 + 9.99

                                       = 17.49

If she gets a cab, then total payment= 10 + 7.50

                                                             = 17.50

Hence both costs almost the same, option B is true

b.

It would cost about the same to keep or return the movie. Susan should keep it!

Answer:

x=2

Step-by-step explanation:

Vertical lines have the same x value all the time.  It is of the form x=

Their slope is undefined

The line passes through the point (2,4) and the x value is 2

x=2

Answer:

Step-by-step explanation:

-3*j = -3j

(-3)(-1) = 3

Answer

-3j + 3 Notice the sign change. Be careful about that when signs are used with the distributive property.

Answer:

7(a + 2b)(a² - 2ab + 4b²)

Step-by-step explanation:

Given

7a³ + 56b³ ← factor out 7 from each term

= 7(a³ + 8b³) ← sum of cubes which factors in general as

a³ + b³ = (a + b)(a² - ab + b²)

8b³ = (2b)³ ⇒ b = 2b

a³ + 8b³ = (a + 2b)(a² - 2ab + (2b)²) = (a + 2b)(a² - 2ab + 4b²)

Hence

7a³ + 56b³ = 7(a + 2b)(a² - 2ab + 4b²) ← in factored form

[tex]\huge\text{Hey there!}[/tex]

[tex]\huge\text{Note}\rightarrow[/tex] [tex]\leq \& \geq \ = \huge\text{closed circle}\\ < \& > = \huge\text{(o)(p)(e)(n)(e)(d) circle}[/tex]

[tex]\huge\text{So, we know that A or C could be our answer}.[/tex]

[tex]\huge\text{Eliminate option B and D}[/tex]

→ [tex]\huge\text{Find the absolute value of the problem}[/tex]

→ [tex]\huge\text{You can now know that  it could be:}[/tex]  

[tex]\huge\text{x}\large\huge{\ >}\huge\text{ 10 or x }< \huge\text{ -10}[/tex]

→ [tex]\huge\text{Possible answer \#1: x }>\huge\text{10}\\\\\huge\text{Possible answer \#2: x}<\huge\text{ -10}[/tex]

→ [tex]\boxed{\boxed{\huge\text{Answer: C}}}[/tex]  

[tex]\huge\text{Option A. would be too small}[/tex] [tex]\huge\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

C

Step-by-step explanation:

MEAN:4+7+11+11+16+17=66÷6=11

MEDIAN:11+11=22÷2=11

MODE=11

Answer:

The correct answer is option C

4,7,11,11,16,17

mean = mode = median = 11

Step-by-step explanation:

Check option A

10,10,12,12,13,13

Mean = 12, mode = 12,13 , 14 and median = 12

Check option B

2,3,4,4,5,7

Mean = 4.15, mode = 4 and median = 4

Check option C

4,7,11,11,16,17

Mean = 11, mode = 11 and median = 11

Check option D

1,2,3,3,5,6

Mean = 3.33, mode =3 and median = 3

The correct answer is option C

4,7,11,11,16,17

mean = median = mode = 11

Answer:

Polygon ABCDE = 50 units

Polygon FGHIJ = 23.4 units

Polygon KLMNO = 19.24 units

Polygon UVWXY = 38 units

Step-by-step explanation:

In order to find the perimeter, we have to find lengths of all sides of given points

The distance formula will be used to find the lengths

[tex]d = \sqrt{(x_2-x_1)^{2}+(y_2-y_1)^{2} }[/tex]

where (x_1,y_1) are coordinates of first point and (x_2,y_2) are coordinates of second point)

So,

For A(1,1), B(6,13), C(8,13), D(16,-2) and E(1, -2)

AB = 13 units

BC = 2 units

CD = 17 units

DE = 15 units

EA = 3 units

Perimeter of polygon ABCDE = 13+2+17+15+3 = 50 units

For F(14,-10), G(16,-10), H(19,-6), I(14,-2) and J(11,-6)

FG = 2 units

GH = 5 units

HI = 6.40 units

IJ = 5 units

JF = 5 units

Perimeter of polygon FGHIJ = 2+5+6.40+5+5 = 23.4 units

For K(4,2), L(8,2), M(12,5), N(6,5) and O(4,4)

KL = 4 units

LM = 5 units

MN = 6 units

NO = 2.24 units

OK = 2 units

Perimeter of polygon KLMNO = 4+5+6+2.24+2 = 19.24 units

For P(7,2), Q(12,2), R(12,6), S(7,10) and T(4,6)

PQ= 5 units

QR= 4 units

RS=6.40 units

ST= 5 units

TP = 5 units

Perimeter of polygon PQRST = 5+4+6.40+5+5 = 25.40 units

For U(4,-1), V(12, -1), W(20,-7), X(8, -7) and Y(4,-4)

UV = 8 units

VW = 10 units

WX = 12 units

XY = 5 units

YU = 3 units

Perimeter of polygon UVWXY = 8+10+12+5+3 = 38 units

Answer:

lol i need help with the same question

Step-by-step explanation:

Roger, with a batting average of 0.250, recorded 60 successful hits from a total of 240 attempts. Therefore, he failed to get a hit 180 times.

In this question, we are dealing with Roger's batting average and his performance. A batting average of 0.250 means that for every 4 at-bats, Roger gets a hit on average 1 time. So, if he has been at bat a total of 240 times, we can expect that he got hits 0.250 times out of these at-bats. So to calculate the number of successful hits, we multiple 240 by 0.250 which equals 60. Therefore, Roger has hit the ball 60 times. To find out how many times he failed to get hits, we subtract his hits from his total tries. So, 240 - 60 = 180. Therefore, Roger failed to get a hit 180 times.

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Answer:

Step-by-step explanation:

The correct answer would be -18

To solve this, you would substitute x with the x value, which in this case is -2

That would make it so f(x)= 9(-2)

9*-2=-18

Therefore f(x)=-18

Note that f(x) is another way to write y, therefore...

y = 9x

To solve for this plug -2 in for x in this equation like so...

y = 9 * -2

When a positive number is being multiplied with a negative number the answer will be negative.

y = -18

C. is the answer (assuming that you meant to write -18 instead of 1 18)

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

Mary = 24

Chau = 15

David = 48

Step-by-step explanation:

The formula is

Mary + Chau + David = 87

And we know that

Chau = Mary - 9

David = Mary * 2

So when we fill this in

Mary + Mary - 9 + Mary * 2 = 87

4Mary - 9 = 87

4Mary = 96

Mary = 24

Chau = Mary - 9 = 15

David = Mary * 2 = 48

Final answer:

The problem is solved using basic algebra, yielding Chau has $15, Mary has $24, and David has $48, all adding up to the total amount of $87.

Explanation:

The question involves a three-person word problem focusing on algebraic relationships and equation solving. Mary, Chau, and David have a total of $87 in their wallets. Mary has $9 more than Chau, and David has twice what Mary has. To find out how much each person has, we'll let 'c' represent the amount that Chau has.

Accordingly, Mary has c + $9, and David has 2(c + $9). Together, they have a total of c + (c + $9) + 2(c + $9) = $87. Simplifying this, we get 4c + $27 = $87. Subtracting $27 from both sides gives us 4c = $60. Dividing both sides by 4, we find that Chau has $15.

Now, since Mary has $9 more than Chau, Mary has $24 ($15 + $9). David, having twice what Mary has, possesses $48 (2 x $24). These amounts add up to the total of $87.

Answer:

B. (3, 0), (0, -6)

Step-by-step explanation:

Plug 0 in for each variable one at a time, and you will get both intercepts.

Answer:

I think it would be 11:1.

Step-by-step explanation:

360,000 / 30,000 = 12

11/12 of the yearly budget was used on other costs

1/12 of the yearly budget was used for leasing office

space.

Answer:

Step-by-step explanation:

Okay so I may be wrong BUT since it's asking for the other costs, I'm assuming we're subtracting the $30,000 from the $360,000 first. Therefore the original ratio would be 30,000: 330,000 which is simplified to 1:11 ($ on office space: $ on other costs)

Answer: P(red): 1/2

P(red or black):3/4

Step-by-step explanation: Count the total number of marbles. There are 8. Since there are 4 red marbles out of the 8, put this into a fraction. It will be 4/8, but simplify to 1/2. The P(red) is 1/2.

Since there are 4 red marbles and 2 black marbles, add them. There are 6 out of the 8 marbles. The fraction is 6/8 simplify to 3/4. The P(red or black) is 3/4.

The probability of choosing a red marble from the box is 0.5 and the probability for choosing either a red or black marble is 0.75.

The subject of this question refers to calculating probabilities which is a concept in Mathematics, specifically in the scope of Statistics. To calculate the probability of an event, we need to know the total amount of outcomes and the amount of favorable outcomes. In the context of the question, these outcomes are represented by marbles.

First, we need to add the total number of marbles, which is 4 red + 2 black + 2 green = 8 marbles in total.

To find the probability of picking a red marble, we divide the number of red marbles by the total number of marbles. Hence, P(red) = 4/8 or 0.5.

To find the probability of picking a red or black marble, we add the number of red and black marbles and divide by the total number of marbles. Hence, P (red or black) = (4 red + 2 black) / 8 total = 6/8 or 0.75.

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[tex]2(n-5)\geq2n+10\\2n-10\geq2n+10\\-10\geq 10\\n\in\emptyset[/tex]

Answer:

[tex]\3.11\ ounces[/tex]

Step-by-step explanation:

we know that

To find the number of ounces of food each turtle will receive, divide the total ounces of food by the total number of turtles

so

[tex]\frac{84}{27}=3.11\ ounces[/tex]

Answer: 3.1

Step-by-step explanation: which is 3.1 with the line on top!