It takes 313131 employees and \$7500$7500dollar sign, 7500 to build a car, and it takes 191919 employees and \$4300$4300dollar sign, 4300 to build a motorcycle.
Genghis Motors wants to spend more than \$84000$84000dollar sign, 84000 to build cars and motorbikes using at most 706706706 employees.
Let CCC denote the number of cars they build and MMM the number of motorbikes they build.

Answer:

Restrictions: x ≠ 0, 3

The value of x is equal to 5.

General Formulas and Concepts:

Pre-Algebra

Algebra I

Equality Properties

Terms/Coefficients

Domain

Step-by-step explanation:

Step 1: Define

Identify given.

[tex]\displaystyle \frac{2}{x - 3} = \frac{5}{x}[/tex]

Step 2: Examine

Since we have an x - 3 and x in the denominator, we must make sure the denominator cannot equal 0, or that would get us an undefined answer. Therefore, our restrictions are that x ≠ 0, 3.

Step 3: Solve for x

Since 5 is not equal to 0 or 3, it can be our solution.

∴ we have found the value of x from the given rational function.

---

Topic: Algebra I

Option A: 7/16 of a foot is the right answer

Step-by-step explanation:

Given

Length of Braden's Jump = [tex]9\frac{5}{16} = \frac{149}{16}[/tex] feet

Length of Jordan's Jump = [tex]8\frac{7}{8} = \frac{71}{8}[/tex]

In order to find how much farther Braden jumped than Jordan

[tex]=\frac{149}{16} - \frac{71}{8}\\=\frac{149-142}{16}\\=\frac{7}{16}[/tex]

Braden jumped 7/16 feet farther than Jordan

Hence,

Option A: 7/16 of a foot is the right answer

Keywords: Fractions, measurements

Learn more about fractions at:

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Final answer:

By converting Jordan's jump to sixteenths and subtracting it from Braden's, we determine that Braden jumped 9/16 of a foot farther than Jordan. The correct answer is option B.

Explanation:

The question involves finding out how much farther Braden jumped than Jordan. To solve this, we subtract Jordan's jump length from Braden's jump length. Braden jumped 9 5/16 feet, and Jordan jumped 8 7/8 feet.

First, we need to find a common denominator to subtract the fractions. The common denominator for 16 and 8 is 16. Convert Jordan's jump to sixteenths: 8 7/8 equals 8 14/16.

Now, subtract Jordan's jump from Braden's: 9 5/16 - 8 14/16 = 1 - 9/16. Braden jumped 9/16 of a foot farther than Jordan.

So the correct answer is option B. 9/16 of a foot.

Final answer:

Min will need a total of 700 bookmarks for the pages where the digits in the thousands and units places add up to 7, since there are 700 four-digit page numbers meeting the criteria.

Explanation:

To determine the number of bookmarks Min needs for the pages where the digits in the thousands and units place add up to 7, we will consider all four-digit numbers that meet this criterion. This involves taking the sum of the thousands and units digits, which can equal 7 in the following ways: 1+6, 2+5, 3+4, 4+3, 5+2, 6+1, and 7+0. Considering that for every combination of thousands and units digits, there are 10 possibilities for the hundreds digit and 10 possibilities for the tens digit, we can calculate the total number of eligible page numbers.

For 1+6 or 6+1, the number of possibilities is 2 (the two combinations) multiplied by 100 (since there are 10 choices for each of the two remaining digits), giving us 200 options.

For 2+5 or 5+2, we have another 200 options.

For 3+4 or 4+3, we get another 200 options.

For 7+0, we would only have 100 options, as there is only one combination.

Summing these up, we find Min will need 700 bookmarks: 200 + 200 + 200 + 100 = 700.

Answer:

[tex]2(x - 3)\: >\: \frac{1}{14}[/tex]

Step-by-step explanation:

The difference of x and 3 is given as:

x-3

Twice the difference of x and 3 becomes:

2(x-3)

The reciprocal of 14 is

[tex] \frac{1}{14} [/tex]

Twice the difference of x and 3 is greater than the reciprocal of 14 then becomes

[tex]2(x - 3)\: >\: \frac{1}{14} [/tex]

Answer:

4

Step-by-step explanation:

2x-7=-2x+9

2x-(-2x)-7=9

2x+2x-7=9

4x-7=9

4x=9+7

4x=16

x=16/4

x=4

Answer:

perp. : 1/3= m

y + 8 = 1/3(x -4): answer is c

y + 24/3 = (1/3)x - 4/3

y = (1/3)x - 28/3

Step-by-step explanation:

answer is c

To find the equation of a line perpendicular to y = -3x + 11 that passes through the point (4, -8), we first calculate the negative reciprocal of the original line's slope, which is 1/3. Then we apply this slope and the given point to the point-slope form equation to obtain y + 8 = (1/3)(x - 4).

The student has asked for an equation in point-slope form for a line that is perpendicular to y = -3x + 11 and passes through the point (4, -8). Firstly, we identify the slope of the given line, which is -3.

As we need a perpendicular line, we find the negative reciprocal of this slope, which is 1/3 (since the slope of perpendicular lines are negative reciprocals of each other). Now, using the point-slope form formula, y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope, we plug in our values to get:

y - (-8) = (1/3)(x - 4)

This simplifies to:

y + 8 = (1/3)(x - 4)

Which is the equation of the line perpendicular to y = -3x + 11 that passes through the point (4, -8) in point-slope form.

Answer:

  they have the same value (0)

Step-by-step explanation:

Cosine is an even function, meaning that cos(x) = cos(-x). When x=90°, we have ...

  cos(90°) = cos(-90°)

Both values happen to be zero.

The relationship between cos(90°) and cos(-90°) is that they both equal 0.

The relationship between cos(90°) and cos(-90°) can be explained using the unit circle. In the unit circle, the cosine function represents the x-coordinate of the point on the circle corresponding to the given angle.

For cos(90°), the x-coordinate is 0, which means the cosine value is 0.

For cos(-90°), the x-coordinate is also 0, so the cosine value is also 0. Therefore, cos(90°) = cos(-90°) = 0.

The answer for the above mentioned problem is JL = 12.5

Step by step explanation:

Given:

JM = 8

KM = 6

To Find:

JL = ?

Formula to be used:

[tex]KM^2[/tex] = JM x ML

In order to find " JL" we must first find "ML",

[tex]KM^2[/tex] = JM x ML

         [tex]6^2[/tex] = 8 x ML

         36 = 8 x ML

         36/8 = ML

         ML = 4.5

Now JL = 4.5+8

             = 12.5

Thus the value of JL = 12.5

[tex]\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{45}{4}\\\\\frac{\text{Distance of tamar}}{\text{Distance of melkon}} = \frac{4}{45}[/tex]

Solution:

Given that,

Tamar travels 8/9 miles to the grocery store

Melkon travels 10 miles to the grocery store

Therefore,

[tex]Tamar = \frac{8}{9}\ miles\\\\Melkon = 10\ miles[/tex]

[tex]\text{ Distance of melkon : Distance of tamar } = 10 : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } = \frac{10 \times 9}{1 \times 9} : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } = \frac{90}{9} : \frac{8}{9}\\\\\text{ Distance of melkon : Distance of tamar } =90 : 8\\\\In\ fraction\ form\\\\\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{90}{8}\\\\In\ simplest\ form\\\\\frac{\text{Distance of melkon}}{\text{Distance of tamar}} = \frac{45}{4}[/tex]

[tex]\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : 10\\\\\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : \frac{10 \times 9}{1 \times 9}\\\\\text{ Distance of tamar : Distance of melkon } = \frac{8}{9} : \frac{90}{9}\\\\\text{ Distance of tamar : Distance of melkon } = 8 : 90\\\\In\ fraction\ form\\\\\frac{\text{Distance of tamar}}{\text{distance of melkon}} = \frac{8}{90}\\\\\frac{\text{Distance of tamar}}{\text{distance of melkon}} = \frac{4}{45}[/tex]

Thus the required are found

Answer:

F. y= -[tex]\frac{1}{3\\}[/tex]x

Step-by-step explanation:

A proportional relationship between x and y exists if it can be expressed in the form y/x=k or y=kx. From the choices listed, F. y= -[tex]\frac{1}{3\\}[/tex]x is the only equation expressed in this form.

The correct option is J. [tex]\( y = 2x - 4 \).[/tex]

To determine which equation represents a proportional relationship between [tex]\( x \)[/tex] and [tex]\( y \)[/tex], we need to look for an equation where [tex]\( y \)[/tex] is a constant multiple of [tex]\( x \)[/tex], and passes through the origin (0,0). A proportional relationship can be expressed in the form [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.

Let's analyse each option:

F. [tex]\( y = -\frac{1}{3}x \)[/tex]

This equation represents a proportional relationship with a constant of proportionality [tex]\( k = -\frac{1}{3} \)[/tex].

G. [tex]\( y = -x + 1 \)[/tex]

This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is 1).

H. [tex]\( y = \frac{3}{2}x + \frac{3}{2} \)[/tex]

This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is [tex]\( \frac{3}{2} \))[/tex].

J. [tex]\( y = 2x - 4 \)[/tex]

This equation does not represent a proportional relationship because it does not pass through the origin (the y-intercept is -4).

Step-by-step explanation:

Given , a line passes through the points (1,-3) and (3,1)

The equation of line which passes through the points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is

[tex]y - y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]

Here [tex]x_1 = 1 , y_1= -3[/tex]     and      [tex]x_2 = 3 , y_2= 1[/tex]

The required equation of the line is

[tex]y+3=\frac{1+3}{3-1} (x-1)[/tex]

[tex]\Leftrightarrow y +3 =2(x-1)[/tex]

[tex]\Leftrightarrow y =2x-2-3[/tex]

[tex]\Leftrightarrow y =2x-5[/tex]

8.

Given, y varies directly with x and y=24 when x=8

Therefore,

[tex]y\propto x[/tex]

[tex]\Rightarrow y = kx[/tex].........(1)

y = 24 when x=8

[tex]\therefore 24 = 8k[/tex]

[tex]\Rightarrow k =3[/tex]

Equation (1) becomes

y= 3x

So, when x=10

y=3×10

⇒y=30

To calculate a 20% tip and round up, multiply the bill by 0.2, then round to the nearest 10 cents.

To calculate a 20% tip, first, determine the total bill amount. Then, multiply the bill amount by 0.2 to find 20% of the bill. Finally, round up to the nearest multiple of 5 or 10 cents. Since Kadisha always rounds up, she should round up to the nearest 10 cents.

If the total bill is $50, to calculate a 20% tip, we multiply $50 by 0.2 to get $10, which is 20% of the bill. Then, we round up to the nearest 10 cents, making the tip $10.00.

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Answer:

.97 cents

Step-by-step explanation:

3.88 divided by 4 = .97

Answer:

97¢

Step-by-step explanation:

If 4 liters cost $3.88, then divide 4 into 3.88

Answer:

C) Consistent and Dependent.

Step-by-step explanation:

As the system has at least ONE solution. Both lines lie over each other, which makes them dependent.

The system, therefore, is consistent and dependent.

Answer:

$63

Step-by-step explanation:

30% of 90 is 27

90-27=63

The value of B = [tex]\dfrac{2S-NA}{N}[/tex]

Step-by-step explanation:

The given equation,

[tex]S=\dfrac{N}{2}(A+B)[/tex]

To find, the value of B in terms of S, N and A = ?

∴ [tex]S=\dfrac{N}{2}(A+B)[/tex]

By crossmultiplication, we get

⇒ N(A + B) = 2S

⇒ NA + NB = 2S

⇒ NB = 2S  - NA

⇒ B = [tex]\dfrac{2S-NA}{N}[/tex]

∴ The value of B = [tex]\dfrac{2S-NA}{N}[/tex]

Answer:

207.24 inches

Step-by-step explanation:

The formula for circumference is C=[tex]2[/tex][tex]\pi r[/tex]

Apply the formula here

r = 33

[tex]\pi[/tex]=3.14

C=2*3.14*33 = 207.24

Apply units!

207.24 inches

Check the picture below.

The measure of arc CD of circle A will be 90°. Then the correct option is A.

Let r be the radius of the sector and θ be the angle subtended by the sector at the center. Then the arc length of the sector of the circle will be

Arc = (θ/2π) 2πr

In circle A, arc CD is congruent to arc BD. And we know that the Line segment CAD is the diameter of the circle. Then the equation is given as,

arc CD = arc BD                           ....1

arc CD + arc BD = 180°                ....2

From equations 1 and 2, then we have

arc CD + arc CD = 180°

2 arc CD = 180°

arc CD = 90°

The measure of arc CD of circle A will be 90°. Then the correct option is A.

More about the arc length of the sector link is given below.

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Final answer:

The negative solution to the equation x² - 3x - 4 = 0 is x = -1.

Explanation:

The difference of the square of a number and 4 is equal to 3 times that number. To find the negative solution, let's represent the number as x.

The equation becomes x2 - 4 = 3x.

Rearranging the equation, we get x2 - 3x - 4 = 0.

To find the negative solution, we can use the quadratic formula: x = (-b - √(b2 - 4ac)) / (2a).

For our equation, a = 1, b = -3, and c = -4. Plugging these values into the quadratic formula, we get x = (-(-3) - √((-3)2 - 4(1)(-4))) / (2(1)).

Simplifying further, we get x = (3 - √(9 + 16)) / 2, which simplifies to x = (3 - √25) / 2.

The square root of 25 is 5, so x = (3 - 5) / 2, which equals -1.

Therefore, the negative solution to the equation is x = -1.

Answer:  5 (x + 2y - 3)

Step-by-step explanation:

Answer:

Step-by-step explanation: so, u would do 80 times 30 which equals 2400. Then u would divide 2,400 by 4 which gives u ur answer which is 60ft long! :)

Answer:

if im right its 110ft

Step-by-step explanation:

Answer:

First Option

Step-by-step explanation:

An exponent is how many times you multiply a number by its self, in this case, that's 5 times

Answer:

[tex] \frac{32}{243} \\ [/tex]

Step-by-step explanation:

[tex] = ( { \frac{2}{3})}^{5} \\ \\ = \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} \times \frac{2}{3} [/tex]

Answer:

The measure of each interior angle of the dodecagon is 150 degrees.

Step-by-step explanation:

(n - 2) x 180 = 1800       Use the equation to find the number of sides

n - 2 = 10                        Divide by 180 on both sides

  + 2  + 2                        Add 2 to both sides

n = 12

Take the sum of the interior angles divided by the number of sides to find the measure of each angle

1800/12 = 150 degrees for each angles of the dodecagon.

It will take Luis 12240 seconds to complete the project.

12240 seconds are 204 minutes when converted.

Step-by-step explanation:

Given,

Time taken to paint 1 square foot = 45 seconds

Time taken for 272 square feet = 45*272

Time taken for 272 square feet = 12240 seconds

We know that;

60 seconds = 1 minute

Therefore;

We will divide the total seconds by 60 to convert them into minutes.

12240 seconds = [tex]\frac{12240}{60} = 204\ minutes[/tex]

It will take Luis 12240 seconds to complete the project.

12240 seconds are 204 minutes when converted.

Keywords: conversion, multiplication

Learn more about multiplication at:

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Answer:

  [tex]10+\dfrac{x}{6}[/tex]

Step-by-step explanation:

The wording, "the sum of A and B" translates to the math formula A+B.

The wording, "the quotient of A and B" translates to the math formula A/B.

Then "the sum of 10 and the quotient of x and 6" will translate to the math formula ...

  [tex]\boxed{10+\dfrac{x}{6}}[/tex]

Answer: 15/24

Step-by-step explanation: 6x4=24 which is the denominator and 5x3=15 which is the numerator

Answer:

15/24

Step-by-step explanation:

Answer:-2+5

Step-by-step explanation:

So basically you do simple math and you need to know that the highest number goes on the right

So basically for each one there is

3-1 that makes 2

-2+5 creates 3 because it’s a negative so you must cancel the negative out and your left with three after

And with that mind set in mind with having to cancel the negative out with the positive

4+(-2) is basically 4-2 and that makes 2

And the last one is a little bit tricky because of all the negatives involved and with this one you need to know that to negatives make a positive

So it’s -4-(-2) so because of the minus and the negative two being negatives right next to each other they cancel each other out to make the equation basically -4+2 which would ultimately make -2

So all the answers are

3-1=2

-2+5=3

4+(-2)=2

-4-(-2)=-2

And out of all those we know 3 is the highest number there so therefore it would make it the one farthest to the right on a number line when solved.