Rational Equations

- It takes one worker 12 hours to complete a specific job. If two workers do the same job, it takes them 6 hours to finish the job. How long would it take 6 workers to do the same job?

It will take ____ hours.

9514 1404 393

Answer:

  x = 7

Step-by-step explanation:

Using Cramer's rule, the value of x is ...

  [tex]x=\dfrac{\left|\begin{array}{cc}2&3\\22&-2\end{array}\right|}{\left|\begin{array}{cc}-1&3\\4&-2\end{array}\right|}[/tex]

  x = ((2)(-2) -(22)(3))/((-1)(-2) -(4)(3)) = (-4-66)/(2-12) = -70/-10

  x = 7

Answer:

You just have to put it into Geogebra Classic. It's a great help for this kind of stuff

Answer: 50in²

Step-by-step explanation:

The area of the ice cream cone will be equal to 50.13 square inches.

The space occupied by any two-dimensional figure in a plane is called the area. The space occupied by the semicircle in a two-dimensional plane is called the area of the semicircle.

The space occupied by the triangle in a two-dimensional plane is called the area of the triangle.

Given that the diameter of the semicircle is 6 inches and the height of the triangle is 12 inches.

The area of the cone will be calculated as,

A = Area of semicircle + Area of triangle

A = (1/2)πr² + (1/2) x B x H

A = (1/2) π (3)² + (1/2) x 12 x 6

A = 14.137 + 36

A = 50.13 square inch

Therefore, the area of the ice cream cone will be equal to 50.13 square inches.

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The required amount of potassium-42 left after 62.0 hours is 26.5 grams.

Given that,
Potassium-42 has a half-life of 12.4 hours. How much of an 848-gram sample of potassium-42 will be left after 62.0 hours is to be determined.

The half-life of the element is defined as the time span in which the element grows or decays half of its whole composition of growth and decay.

Here,
Amount left of the potassium after 62 hours is given as,
A = 848 [1 / 2 ] ⁶²/¹²°⁴
A = 26.5 gram

Thus, the required amount of potassium-42 left after 62.0 hours is 26.5 grams.

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Answer:

see explanation

Step-by-step explanation:

so, when a=-3, c is -20. now, to find b when a is -3, plug a (which is -3) into the equation b=4a-5 to get b=-17. so b=-17, c=-20. b is obviously larger (remember the negative sign)

when c is 21, a is 5. plug numbers in to get b=15.

when a is 6, there is no clear value for c, so i'd guess undefined. b however is 19

we can plot the line and the points, for problem 4 and all points above the line means that c is greater than b, and when below it's less than. doing this we get when a is 12, when a is 0, and when a is 5. hope this was clear

Answer:

Not a function

Step-by-step explanation:

The reason the ordered pairs are not a function is because there is no real equation that can get the correct x and y for each. Along with 3 being a x-value twice, which is also a key sign that it's not a function.

Answer:

I would use chase bank, checking account. they have really good over draft protection.

Answer:

L = 8yd

Step-by-step explanation:

Volume of a rectangular prism = L × W × H

L×5¾yd×2½yd = 115 yd³

14⅜L = 115

L = 115 ÷ 14⅜

L= 8

Answer:

Slope of the line represented by the table is 2.5.

Step-by-step explanation:

For a linear function,

Slope of the line passing through two points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by,

Slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

Therefore, slope of the line passing through (0, 12) and (-2, 7) will be,

Slope = [tex]\frac{12-7}{0-(-2)}[/tex]

          = [tex]\frac{5}{2}[/tex]

          = 2.5

Therefore, slope of the line represented by the table is 2.5.

Answer:

The answer for x is 18

Step-by-step explanation:

You may realize that we have not yet discussed the distance around a very important geometric shape: a circle! The distance around a circle has a special name called the circumference. To find the circumference of a circle, we use this formula: C = 2πr

In this formula, π is pronounced “pi,” and is defined as the circumference of a circle divided by its diameter:  

π

=

C

d

. We usually replace π with the approximation 3.14. The letter r represents the radius of the circle.

Let’s see where the formula for circumference comes from. Figure 4 shows a generic circle with radius r.

Answer:

Step-by-step explanation:

An expression is a sort of equation but without any number after the equal to sign

so 2x-7 would be an expression but 3x would not be a expression

3x is just a term

2+7 would also not be an expression because this can be simplified into 9 which is not a expression

2x-7=14 is not a expression cuz it has the equal to sign

-14 is not a expression because its a single number

Answer:18/25 1/5 14/25

Step-by-step explanation:

The probability we have to choose 18/25 1/5 14/25.

Ms. Florina buys a bag of different-colored rubber bands. She randomly selects a rubber.

band, records the color, and returns it to the bag. She does this a total of 50 times.

and selects 8 red, 18 blue, 10 green, and 14 yellow rubber bands.

Based on this information, what is the probability that Ms. Florina will select a blue rubber

band, return it to the bag and then select a green rubber band

Click the arrows to choose an answer from each menu.

It is expressed as, Probability of an event P(E) = (Number of favorable outcomes) ÷ (Sample space).

Based on the given information, the probability that Ms. Florina will select a blue rubber band is,

Therefore the probability we have to choose 18/25 1/5 14/25.

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Answer:

10

Step-by-step explanation:

First, you would subtract 100-70 to get 30

Then, you would do 30/3 to learn that you could still buy 10 packs of Oreos with the remaining money.

Answer:

(E). only (a) and (c)

Step-by-step explanation:

H0 : p1 - p2 = 0

H1 : p1 - p2 ≠ 0

To indicate that difference exists between the two treatments, then we must reject the null and confidence interval must show that the difference between the two treatment is significant.

In other to use confidence interval to test for significance ; Intervals which do not contain 0 implies that difference exists and hence, the difference is significant.

The interval Given by : (-0.279, -0.035) is significant as the interval does not contain 0.

The interval Given by : (0.279, 0.035) is significant as the interval does not contain 0.

The interval Given by : (-0.279, 0.035) is not significant as the interval contains 0.

Answer: 4697

Step-by-step explanation:

x + y = 11 ......... i

x² + y² = 325 ........ ii

From equation i

x + y = 11

Therefore, x = 11 - y....... iii

Put equation iii into equation ii

x² + y² = 325

(11 - y)² + y² = 325

(11 - y)(11 - y) + y² = 325

121 - 11y - 11y + y² + y² = 325

121 - 22y + 2y² = 325

121 - 325 - 22y + 2y² = 0

2y² - 22y -204 = 0

2y² - 34y + 12y - 204 = 0

2y(y - 17) + 12(y - 17) = 0

(y - 17) = 0

y = 0 + 17

y = 17

Since x + y = 11

x + 17 = 11

x = 11 - 17

x = -6

Therefore, x³ + y³

= (-6)³ + (17)³

= -216 + 4913

= 4697

Here, as the tangents are given above in variable length with radius of the circle as r = 4.4 cm, we get as

since the sides opposite to the equal angles are always equal we get as,

x-2 = 2x-10

===> -2 +10 = 2x-x

==> 8 = x

hence the measurement of the Tangents is,

putting x = 8

2(8)-10 ==> 16-10 ==> 6 cm

length of each tangent is 6 cm.

Answer:

8

Step-by-step explanation:

2x - 10 = x - 2

2x - x = - 2 + 10

x = 8

Answer:

The answer is 4m-1

Step-by-step explanation:

Answer:

2 + m -1 + m

Step-by-step explanation:

Answer:

14x+21x if thats an option

Step-by-step explanation:

where are the answer choices?

Answer:

Step-by-step explanation:

To complete the given table we will substitute the output value to calculate the input value.

Given function is,

y = 2x + 4

For output value, y = 18

18 = 2x + 4

2x = 18 - 4

x = 7

For output value, y = 22

22 = 2x + 4

2x = 22 - 4

x = 9

For output value, y = 34

34 = 2x + 4

2x = 34 - 4

2x = 30

x = 15

Therefore, table will be,

       Input (x)                 y = 2x + 4                output

          7                                                              18

          9                                                             22

         15                                                             34

Answer:

6,500

Step-by-step explanation:

Answer:

6500

Step-by-step explanation:

3900 divided by 3 is 1300 which is the cost of 1 shirt, so 1300 times 5 is 6500

Answer:

282.7 in³

Step-by-step explanation:

The solid is a cylinder

Volume of the cylinder = πr²h

Where,

radius (r) = 3 in.

height (h) = 10 in

Volume = π*3²*10

= π*9*10

= π*90

= 282.743339 ≈ 282.7 in³ (nearest tenth)

Answer:

Step-by-step explanation:

Givens

Let the smallest integer = x - 1    (You'll see why in a moment).

Let the middle integer = x

Let the largest ingeger = x + 1

Equation

x - 1 + x + x + 1 = 255

Solution

Combine like terms on the left.

3x - 1 + 1 = 255

3x = 255                      Divide by 3

3x/3 = 255/3

x = 85

So the smallest number is  84

The middle number is        85

The largest number is        86

Total                                  255

Do you see why I made the smallest number x - 1?

It is because the -1 and the plus 1 cancel out.

Please realize the question says consecutive integers. It does not say consecutive odd or consecutive even integers.

Answer:

Volume of cubical tank = 0.278 yard³ (Approx.)

Step-by-step explanation:

Given:

Length of tank = 1/2 yard

Width of tank = 1/6 yard

Height of tank = 1/3 yard

Find:

Volume of cubical tank

Computation;

⇒ Volume of cubic block = (length)(width)(height)

⇒ Volume of cubical tank = (1/2)(1/6)(1/3)

⇒ Volume of cubical tank = 1/36 yard³

Volume of cubical tank = 0.278 yard³ (Approx.)

Answer: 1/36

Step-by-step explanation: This is the plato answer

Answer:

(x+3), (y+9)

Step-by-step explanation:

Adding to x with translate the figure right (subtracting will translate it left), and adding to y will translate it up (subtracting will translate it down).

To get from a point on [tex]y[/tex] to the corresponding point on [tex]y_{1}[/tex], you would move 3 to the right and 9 up, so it would be (x+3), (y+9)

Answer:

(a+b) (a-b) =a^2 - b^2

In this question a=2, b=square root of 5

So 2*2=4 square root of 5 times square root of 5 is 5

4-5=-1

Answer:

I believe the answer is -1.

Step-by-step explanation:

So I distributed,

2 x 2 = 4

[tex]-\sqrt{5}[/tex] x 2 = [tex]-2\sqrt{5}[/tex]

[tex]\sqrt{5}[/tex] x 2 = [tex]2\sqrt{5}[/tex]

[tex]\sqrt{5}[/tex] x [tex]-\sqrt{5}[/tex] = -5

4 [tex]-2\sqrt{5}[/tex] + [tex]2\sqrt{5}[/tex] - 5 = ?

the radicals cancel out and 4 -5 = -1

Answer:

11.5

Step-by-step explanation:

x=8 & y=23

then

x=4 is half so you divide by 2

so half of 23 would be 11.5. If you are rounding then it would be 12

Answer:

[tex]\tan(30) = \frac{\sqrt 3}{3}[/tex]

[tex]\tan(60) = \sqrt 3[/tex]

Step-by-step explanation:

Given

The attached triangle

Required

Find [tex]\tan(30)[/tex] and [tex]\tan(60)[/tex]

The tangent of an angle is calculated as:

[tex]\tan(\theta) = \frac{Opposite}{Adjacent}[/tex]

So, we have:

[tex]\tan(30) = \frac{b}{a}[/tex]

This gives:

[tex]\tan(30) = \frac{3}{3\sqrt 3}[/tex]

3 cancels out

[tex]\tan(30) = \frac{1}{\sqrt 3}[/tex]

Rationalize

[tex]\tan(30) = \frac{1}{\sqrt 3} * \frac{\sqrt 3}{\sqrt 3}[/tex]

[tex]\tan(30) = \frac{\sqrt 3}{3}[/tex]

Similarly;

[tex]\tan(60) = \frac{a}{b}[/tex]

This gives:

[tex]\tan(60) = \frac{3\sqrt 3}{3}[/tex]

3 cancels out

[tex]\tan(60) = \sqrt 3[/tex]

Answer:

[tex] slope \: (m) = \frac{2}{5} \\ \\ y - intercept \: (b) = \frac{1}{5} [/tex]

Step-by-step explanation:

[tex]5y = 2x + 1 \\ \\ \therefore y = \frac{2x + 1}{5} \\ \\\therefore y = \frac{2}{5} x + \frac{1}{5} \\ \\ equating \: it \: with \\ \\ y = mx + b \: we \: find : \\ \\ slope \: (m) = \frac{2}{5} \\ \\ y - intercept \: (b) = \frac{1}{5} [/tex]

Answer:

Critical value ≈ 1.299

Step-by-step explanation:

number of Kidney transplant ( n )  = 49

Determine the critical value for the test

the sample mean = ∑ failure time / n  = 1252.28 / 49 = 25.56

next we determine the standard deviation of the sample

s = [tex]\sqrt{1/(n-1)(xi -X ) ^2}[/tex] = 17.3126

standard error = s / √n  = 17.3126 / 7 = 2.4732

Given  a significance level of 0.1

df (degree of freedom ) = n -1 = 49 - 1 = 48

∝ = 0.1

critical value = 1.299 ( using excel function ; =T.INV(0.90,48) )

Answer:

Piston

Step-by-step explanation:

Because i took the test       ..................................