How can I find the value of X in a circle?

\(7x +8y = 25 ~~~....(i)\\\\9x +10y = 35~~~ ....(ii)\\\\\text{Multiply equation (ii) by}~ \dfrac 79 ~ \text{and do (ii) - (i):}\\\\\dfrac 79 (9x +10y) - (7x +8y) = \dfrac 79 (35) - 25\\\\\\\implies 7x +\dfrac{70y}9 - 7x -8y = \dfrac{245}9 -25\\\\\\\implies - \dfrac{2y}9 = \dfrac{20}9\\\\\\\implies -2y =20\\\\\implies y =-10\\\\\text{Substitute}~ y = -10~ \text{in equation (i):}\\\\\\7x +8(-10) = 25\\\\\implies 7x = 25 +80\\\\\implies 7x = 105 \\\\\implies x =15\\\\\)

\(\\\text{Hence}~ (x,y) = (15,-10)\)

The equivalent fraction for the given fraction is 1/5.

Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.

The given fraction is 3/15.

The equivalent fraction is 3/15 =1/5

Therefore, the equivalent fraction for the given fraction is 1/5.

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Answer:

D. 3

Step-by-step explanation:

Answer:

61

Step-by-step explanation:

90 divided by 36 is 2.5 add 10 to the 90 then multiply 10 by 2.5 you get 25 then add 25 to 36 witch gives u 61.  90/36=2.5x10=25+36=61

/ is for division. Hope it helps.

Answer:

25/7 cannot be simplified, but it can be turned into the mixed number 3 4/7

Step-by-step explanation:

Multiply:

2(5/8) × -4(3/4)

⇛(80/8) × (-48/4)

⇛20 × (-6)

⇛-120. Ans.

The approximate length of one side of the tissue box which has a volume of about 90 cubic inches is 4.5 inches.

Volume of cube is the amount of quantity, which is obtained by it in the 3 dimensional space.

The volume of the cube can be given as,

\(V=a^3\)

Here, (a) is the side of the cube.

A tissue box, shaped like a cube, has a volume of about 90 cubic inches. Put the value of volume in above formula,

\(90=a^3\\a^3=90\\a=\sqrt[3]{90}\\a=4.48\\a\approx 4.5\rm\; in\)

Thus, the approximate length of one side of the tissue box which has a volume of about 90 cubic inches is 4.5 inches.

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Answer:

70 m and 60 m

Step-by-step explanation:

The formula for the area of a rectangle is length ⋅ width.

The area of the pasture of 4200 meters.

70 ⋅ 60 = 4200.

The formula for the perimeter of a rectangle is side + side + side + side.

The perimeter of the rectangle is 260 meters.

70 + 60 + 70 + 60 = 260.

Therefore, the length and width of this pasture are 70 meters and 60 meters.

Answer:

7/30

Step-by-step explanation:

1/6 = 1x5/6x5

    = 5/30

1/15= = 1x2/1x15

       =2/30

2/30 + 5/30 = 7/30

Answer:

the value of x that makes the equation true is x = 3.5.

Step-by-step explanation:

To find the value of x that makes the equation 18x + 5 - 3 = 65 true, we need to simplify the equation and solve for x.

Starting with the equation:

18x + 5 - 3 = 65

First, combine like terms:

18x + 2 = 65

Next, isolate the term with x by subtracting 2 from both sides:

18x = 65 - 2

18x = 63

Finally, divide both sides of the equation by 18 to solve for x:

x = 63 / 18

x = 3.5

Therefore, the value of x that makes the equation true is x = 3.5.

The answer is:

Steps & work :

First, I focus only on the left side.

Combine like terms:

\(\sf{18x+5-3=65}\)

\(\sf{18x+2=65}\)

Subtract 2 from each side:

\(\sf{18x=63}\)

Now, divide each side by 18:

\(\sf{x=\dfrac{63}{18}\)

Clearly, this fraction is not in its simplest terms, and we can divide the top and bottom by 9:

\(\sf{x=\dfrac{7}{2}}\)

\(\therefore\:\:\:\:\:\:\stackrel{\bf{answer}}{\boxed{\boxed{\tt{x=\frac{7}{2}}}}}}\)

a)The value of acceleration will be 4.8 m/s²

b)The total distance travelled is 505 m.

a) As all the movement happens along a straight line, we need to define an axis only, which we call x-axis, being the positive direction the one followed by the car.

We can choose to place our origin at the location where the motorcycle was stopped at the side of the road (assuming that it is the same point  for the car when it passes him), so our initial position is 0.

We can also choose our time origin to be the same as the instant that the motorcycle starts from rest, so t₀ = 0.

With these assumptions, and assuming also that the acceleration is constant, we can write two equations, one for the car (at constant speed) and the another one for the motorcycle, as follows:

xc = vx*t

xm= 1/2*a*t²

When the motorcycle passes the car, both distances traveled from the origin will be equal each other, i.e., xc = xm :

⇒ vx*t = 1/2*a*t²

We have as givens vx=35 m/s and t = 14.5 sec when both equations are equal each other.

⇒ 35 m/s* 14.5 s = 1/2*a*(14.5)²(s)²

Solving for a:

a = (2* 35 m/s) / 14.5 s = 4.8 m/s²

b) Replacing the value of a in the equation for xm, we have:

xm = 1/2*4.8 m/s²* (14.5)²s² = 505 m.

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The population in 10 years is equal to 3656 people.

We have given that

if a town with a population of 3000 grows by 2% per year,

We have to determine how large will the population be in 10 years.

A discrete group of people, animals, or things that can be identified by at least one common characteristic for the purposes of data collection and analysis.

To gather information about a large population, data is usually gathered from a sample.

3000 x 1.02^10 = 3656.98..

= 3656 people

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Answer:

2100 mg

Step-by-step explanation:

two can be multiplied by six to get 12 cleanly, so just multiply the amount for two tablets by six to get the amount for 12 tablets

350 x 6 = 2100 mg

Answer:

See answer and graph below

Step-by-step explanation:

∬Ry2x2+y2dA

=∫Ry.2x.2+y.2dA

=A(2y+4Ryx)+c

=∫Ry.2x.2+y.2dA

Integral of a constant ∫pdx=px

=(2x+2.2Ryx)A

=A(2y+4Ryx)

=A(2y+4Ryx)+c

The graph of y=A(2y+4Ryx)+c assuming A=1 and c=2

The evaluation of the double integral is \(\mathbf{ \dfrac{105}{2}\pi }\)

The double integral \(\mathbf{\int \int _R\ \dfrac{y^2}{x^2+y^2} \ dA}\), where R is the region that lies between

the circles \(\mathbf{x^2 +y^2 = 16 \ and \ x^2 + y^2 = 121}\).

Let consider x = rcosθ and y = rsinθ because x² + y² = r²;

Now, the double integral can be written in polar coordinates as:

\(\mathbf{\implies \int \int _R\ \dfrac{y^2}{x^2+y^2} \ dxdy}\)

\(\mathbf{\implies \int \int _R\ \dfrac{r^2 \ sin^2 \theta}{r^2} \ rdrd\theta}\)

\(\mathbf{\implies \int \int _R\ \ sin^2 \theta \ r \ drd\theta}\)

Thus, the integral becomes:

\(\mathbf{=\int^{2 \pi}_{0} sin^2 \theta d\theta \int ^{11}_{4} rdr }\)

∴

\(\mathbf{=\int^{2 \pi}_{0} \dfrac{1-cos 2 \theta }{2} \ \theta \ d\theta\dfrac{r}{2} \Big|^{11}_{4}dr }\)  

\(\mathbf{\implies \dfrac{1}{2} \Big[\theta - \dfrac{sin \ 2 \theta}{2}\Big]^{2 \pi}_{0} \ \times\Big[ \dfrac{11^2-4^2}{2}\Big]}\)

\(\mathbf{\implies \dfrac{\pi}{2} \times\Big[ 121-16\Big]}\)

\(\mathbf{\implies \dfrac{105}{2}\pi }\)

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1) Two different functions that could represent Davis' gross wages, where h is the number of hours Davis works per week, a(h) is his gross wages at the ice arena minus travel expenses, and d(h) is his gross wages from walking dogs are:

Function A: a(h) = 16.25h - 7.50

Function B: d(h) = 12.50h

2) If Davis works 1 hour, his gross pay at each job is:

    1 Hour      6 Hours

a) $16.25      $97.50

b) $12.50      $75

3) To find Davis' net pay after tax, the modified functions in question 1 are as follows:

Function A: a(h) = (16.25h - 7.50)(1 - 0.105)

Function B: d(h) = 12.50h(1 - 0.18)

4) The domain and range for each of these new functions are:

                          Domain                     Range

a) Function A    [1, 2, ... 7]           [7.83, 15.66, ... 54.81]

b) Function B    [1, 2, ... 12]         [10.25, 20.5, ... 123]

The domain refers to all the possible values of the independent (input) variables.

The range refers to the possible values of the dependent (output) values.

                                            Arena       Dog Walking

Pay rate per hour              $16.25           $12.50

Travel expense                  $7.50            $0

Maximum hours worked    7 hours          10 hours

Gross pay for one hour     $16.25        $12.50

Gross pay for 6 hours       $97.50         $75

After

Tax                                      10.5%           18%

After-tax factor                (1 - 0.105)       (1 - 0.18)

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Answer:

Step-by-step explanation:

Describe a functiDescribe a function that takes an input, adds 2, and then multiplies by 4on that takes aDescribe a function that takes an input, adds 2, and then multiplies by 4n inpDescribe a function that takes an input, adds 2, and then multiplies by 4ut, adds 2, and then multiplies by 4

Answer: 2x5x1, 1x10x1 (in any order) and any 3 multiples that make 10

Step-by-step explanation:

Answer:

There are multiple possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet. Here are some possible solutions:

A rectangular prism with dimensions of 1 ft x 2 ft x 5 ft (length x width x height) would have a volume of 10 cubic feet, since 1 x 2 x 5 = 10.

A rectangular prism with dimensions of 2 ft x 1 ft x 5 ft (length x width x height) would also have a volume of 10 cubic feet, since 2 x 1 x 5 = 10.

A rectangular prism with dimensions of 0.5 ft x 1 ft x 20 ft (length x width x height) would also have a volume of 10 cubic feet, since 0.5 x 1 x 20 = 10.

A rectangular prism with dimensions of 5 ft x 1 ft x 2 ft (length x width x height) would have a volume of 10 cubic feet, since 5 x 1 x 2 = 10.

There are infinitely many other possible sets of dimensions for a rectangular prism with a volume of 10 cubic feet.

==============================================

Work Shown:

F = future value

P = present value = 280

r = rate of inflation in decimal form = 0.08

t = elapsed time in years = 2

---------

F = P*(1+r)^t

F = 280*(1+0.08)^2

F = 326.592

F = 326.59

Answer:

221

Step-by-step explanation:

Interest goes up 5 dollar each year

Answer:

|-8|, |6|, |5|, |-1|

Step-by-step explanation:

Anything in an absolute value becomes positive, so this is what it becomes.

8, 6, 5, 1

Answer:-8|, |6|, |5|, |-1|

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

What we have to know is that when two triangles are similar their sides will always be proportional. So we will create a proportion that goes like this...\(\frac{\Delta1side}{\Delta1base} =\frac{\Delta2side}{\Delta2base}\) but since it doesn't tell us the exact value of triangle 1. We will have to add 3 and 12 to get 15 which is the base of the first triangle. Now we're ready to write the proportion.

\(\frac{4x}{15}=\frac{3x+1}{12}\)

Now we cross multiply and solve the equation...

\(48x=15(3x+1)\\48x=45x+15\\3x=15\\x=5\)

So the value of x is 5.

Answer:

slope = 3

Step-by-step explanation:

The slope of a line parallel to the given equation share the same slope. Note the slope intercept formula:

y = mx + b

y = (x , y)

m = slope

x = (x , y)

b = y-intercept

First, isolate the variable, y. Subtract 3x from both sides:

3x (-3x) - y = 1 (-3x)

-y = -3x + 1

Next, divide -1 from both sides:

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

y = 3x - 1

You are solving for the slope of a line parallel to the given equation. Since you are solving for parallel, the slope would be shared.

3 would be the slope of the line.

~

Answer:

B

Step-by-step explanation: