Solve for x: 2x − 2 > 4x + 6.
x < −4
x > −4
x < 4
x > 4

As an improper fraction, the simplified answer would be 9/7 after you divide both top and bottom by 10

------------------------

If you need a mixed number, then 9/7 converts to 1 & 2/7 because

9/7 = 1 remainder 2

If you had 9 cookies and 7 friends, then each friend gets 1 whole cookie, and there will be 2 left over.

Answer:

The answer would be 9/7 as improper, but if you want the mixed number it would be 2 2/7. Glad I could help let me know if I can do anything else

Step-by-step explanation:

Answer:

The answer is 1/6.

In each square yard, Norah would spread 1 / 6 ton of stone.

Given that,
Norah has 2/3 tons of stone to spread equally in 4 square yards, how many tons of stone will be spread in each square yard is ot be determined.

The ratio can be defined as the proportion of the fraction of one quantity towards others. e.g.- water in milk.

Here,
Quantity if Stone = 2/3 ton
Area = 4 square yards
Quantity per yard = [2/3] / 4= 1 / 6

Thus, in each square yard, Norah would spread 1 / 6 ton of stone.

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Answer:

B

Step-by-step explanation:

To get to to triangle Y'X'Z', you need to move triangle YXZ 3 units to the right (+3), and 1 unit down (-1). So (x+3,y-1)

Answer:

b

Step-by-step explanation:

Answer:

t = 56.67

Step-by-step explanation:

Remark

If you are given a rhombus, what you are being told is that all 4 sides are equal. So WX = XY

Equation

6t - 82 = 3t + 88                             Add 82 to both sides

Solution

Answer:

4 Dollars and 30 cents

Step-by-step explanation:

15.95 x 6 = 95.7

100-95.7= 4.30

Final answer:

Erin bought six shirts at $15.95 each, totaling $95.70. After paying with a $100 bill, she would receive $4.30 in change.

Explanation:

The question asks us to calculate the total cost of six shirts and then determine the change from a $100 bill. Erin bought six shirts that cost $15.95 each. To find the total cost, we multiply the price of one shirt by the number of shirts:

$15.95 × 6 = $95.70.

Next, we calculate the change Erin would receive if she paid with a $100 bill:

$100 - $95.70 = $4.30.

Therefore, Erin would receive $4.30 in change.

Answer:

2.5 is the answer

Step-by-step explanation:

7/2 = 2.5

You need to divide the no of bus rider with no of students

Answer:

3750 feet

Step-by-step explanation:

Given that Paulo begins at Stop 1 and then walks to Stop 2, then Stop 3, and then Stop 4. Then he walks to Stop 1 again.

Where stops are given by coordinates:

Stop 1 at (−2,1)

Stop 2 at (−2, −7) ​​

Stop 3 at (5,−7)

Stop 4 at (5, 1)

The path between each stop is a straight line. One unit on the coordinate grid equals 125 feet.

Now we need to find about what is the total distance Paulo walked.

So first we graph those points so that we can easily count the length of each side. then add each side to get the total length

length of rectangular path = 8+7+8+7=30

since one unit on the coordinate grid equals 125 feet. So to find the actual length we need to multiply 30 by 125 feet.

Hence final answer will be 125*30 = 3750 feet.

Answer:

10/14, 15/21

Step-by-step explanation:

WE are given a ratio 5/7

To find equivalent ratios it is sufficient to multiply both numerator and denominator by the same number

Let us take 2,3 for example.

When we multiply both numerator and denominator by 2, value does not change.

Hence we get equivalent fraction.

So 10/14 is one such fraction.

Next is multiply by 3

15/21 is another fraction.

Option: D is the correct answer.

  D.    The slope of is 3, and passes through O.

It is given that:

AB is dilated by a scale factor of 3 to form AB .

Also, the line AB pass through the origin.

So, if AB pass through (0,0) and some point (x,y) then the slope of line AB is:

[tex]Slope=\dfrac{y-0}{x-0}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3[/tex]

( Since, it is given the slope of AB is 3 )

Now , if AB is dilated to A'B' by a scale factor of 3 then

(0,0) → (0,0)

and

(x,y) → (3x,3y)

i.e. (0,0) and (3x,3y) will lie on A'B'.

Hence, the slope of line A'B' is given by:

[tex]Slope=\dfrac{3y-0}{3x-0}\\\\i.e.\\\\Slope=\dfrac{3y}{3x}\\\\i.e.\\\\Slope=\dfrac{y}{x}=3[/tex]

Hence, both have the same slope.

                The answer is :  Option: D

Answer:

Step-by-step explanation:

The center of the circle described by the equation x^2 + (y+4)^2 = 64 is at the point (0,-4), and the radius is 8.

In the context of a circle, the general equation form is (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is its radius. Looking at your given equation x^2 + (y+4)^2 = 64, it is in this general format.

Here, the value of a is 0 (as there is no number being subtracted from x) and b is -4 (the y coordinate has been shifted 4 units down). Therefore, the center of the circle is at point (0,-4).

For the radius, since r^2 = 64, the radius r will be the square root of 64 which is 8.

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Answer:

1225

Step-by-step explanation:

a loss of 20% represents 80% ( 100 - 20) of the cost price

100% represents the cost price

To find the cost price divide the selling price by 80 to find 1% and multiply by 100 to find cost price

cost price = [tex]\frac{980}{80}[/tex] × 100 = 1225

Final answer:

James cuts each of the three lasagnas into five equal parts, resulting in a total of 15 pieces of lasagna.

Explanation:

When James cuts each square lasagna into pieces that are each 1/5 of the lasagna, he's effectively dividing each whole lasagna into five equal parts. Since he has three whole lasagnas, each cut into 1/5-sized pieces, the total number of pieces he would end up with can be found by multiplying the number of pieces per lasagna by the number of lasagnas.

To calculate this, you multiply 5 (the number of pieces from one lasagna) by 3 (the number of lasagnas):

Multiply the number of pieces per lasagna (5) by the number of lasagnas (3).

5 pieces/lasagna × 3 lasagnas = 15 pieces

Thus, James cuts the lasagna into 15 pieces in total.

To write the slope-intercept form of a linear equation, we use the formula y = mx + b, where m represents the slope and b represents the y-intercept.

To write the slope-intercept form of a linear equation, we use the formula y = mx + b, where m represents the slope and b represents the y-intercept.

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Answer:

Each student would get 4 inches of ribbon

Step-by-step explanation:

Mrs. Barkley has 75 inches of ribbon and is splitting it between 18 students so you would divide 75 by 18. When you divide you get 4.166666... etc. So the answer would be 4

Each of the 18 students in Mrs. Barkley's class will receive 50 inches of ribbon when 75 feet of ribbon are divided equally among them.

The student has asked how many inches of ribbon each student will get if Mrs. Barkley has 75 feet of ribbon and splits it equally among 18 students. To solve this problem, we first need to convert feet to inches because there are 12 inches in a foot. Then we divide the total inches of ribbon by the number of students.

Total length of ribbon for each student= 75/18

The total length of ribbon for each student≈4.1667

So, each student will receive approximately 4.1667 feet of ribbon.

To find out how many inches this is, we'll convert this value to inches. Since 1 foot is equal to 12 inches, we can multiply the total length of the ribbon for each student by 12:

The total length of ribbon for each student (in inches)=4.1667×12

The total length of ribbon for each student (in inches)≈49.9999

Therefore, each student will receive approximately 50 inches of ribbon.

Answer:

4x - 3y = 36

Step-by-step explanation:

2/3x - 1/2y = 6

Multiply each side by 6 to get rid of the fractions

6*  (2/3x - 1/2y) = 6*6

Distribute the 6

12/3 x - 6/2y = 36

4x -3y = 36

We must find the difference between 3 1/12 and 2 1/3. So we can first subtract 3 from 2 and we earn 1 whole number. Next we must subtract  1/12 and 1/3. This is the same as 3/36-12/36, which is -9/36 or -1/4. Since we can't have -1/4 we must subtract 1/4 from 1 and earn 3/4 as our answer.

Hope this helps! <3

[tex]\sqrt[5]3+\sqrt{12}+\sqrt{32}=\sqrt[5]3+\sqrt{4\cdot3}+\sqrt{16\cdot2}=\sqrt[5]3+\sqrt4\cdot\sqrt3+\sqrt{16}\cdot\sqrt2\\\\=\boxed{\sqrt[5]3+2\sqrt3+4\sqrt2}[/tex]

Answer:

The labor fee is $14.25, each quart of oil costs $2.25.

Step-by-step explanation:

Let $x be thee price of each quart of oil and $y be a flat fee for labor.

1. If the oil change for one car required 5 quarts of oil, then these 5 quarts cost $5x and together with a flat fee for labor it cost $25.50. Thus,

5x+y=25.50.

2. If the oil change for another car required 7 quarts of oil, then these 7 quarts cost $7x and together with a flat fee for labor it cost $30.00. Thus,

7x+y=30.00.

3. Subtract from the second equation the first one, then

[tex]7x+y-(5x+y)=30.00-25.50,\\ \\7x+y-5x-y=4.50,\\ \\2x=4.50,\\ \\x=\$2.25.[/tex]

Substitute it into the first equation:

[tex]5\cdot 2.25+y=25.50,\\ \\y=25.50-11.25,\\ \\y=\$14.25.[/tex]

The labor fee is $14.25, each quart of oil costs $2.25.

The labor fee is $14.25 and the cost per quart of oil is $2.25.

To find the labor fee and cost per quart of oil, we can set up a system of equations using the given information. Let x represent the cost of each quart of oil and y represent the labor fee.

We have the equations:

5x + y = 25.50
7x + y = 30.00

We can solve this system of equations using substitution or elimination. Substituting y from the first equation into the second equation, we get:

7x + (25.50 - 5x) = 30.00

2x = 4.50

x = 2.25

Substituting x back into the first equation, we get:

5(2.25) + y = 25.50

11.25 + y = 25.50

y = 14.25

Therefore, the labor fee is $14.25 and the cost per quart of oil is $2.25.

Answer:

f(x) = -38

Step-by-step explanation:

well f(x) is the same thing as y so just write it as y so its easier to understand.

y = -2x -13

take the x value they give you which in this case is 5 and plug it in to the x in your equation.

y = -2(5) -13

now just use a calculator or something and find that

y = -25 - 13

and finally

y = -38

now just change y back to f(x) if needed

hope this helps :)

Final answer:

The probability of drawing a black pen first and then a red pen with replacement from a box of 10 pens is 20%.

Explanation:

To calculate the probability of drawing a black pen and then a red pen with replacement in a box that contains 10 pens, we should calculate the probability of each event separately and then multiply them since the events are independent.

There are 5 red pens, 4 black pens, and 1 blue pen, making a total of 10 pens. The probability of drawing a black pen is the number of black pens divided by the total number of pens: P(black) = 4/10 or 0.4.

Since the pen is replaced, the total stays the same. Therefore, the probability of then drawing a red pen is the number of red pens divided by the total number of pens: P(red) = 5/10 or 0.5.

To find the combined probability of both events happening in sequence (drawing a black pen and then a red pen), we multiply the two probabilities together: P(black and red) = P(black) × P(red) = 0.4 × 0.5 = 0.2 or 20%.

Answer:

Angle ABC is 22 degrees

Angle BAC is 68 degrees

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

Work Shown:

Because there are just 3 points, we can refer to "angle BAC" as "angle A" and "angle ABC" as "angle B". Focus on the middle letter of each three-letter sequence.

The three angles A, B, C add up to 180 degrees. This is true for any triangle.

A+B+C = 180

(6x+8) + (2x+2) + 90 = 180 ... substitution

6x+8 + 2x+2 + 90 = 180

8x+100 = 180

8x+100-100 = 180-100 ... subtract 100 from both sides

8x = 80

8x/8 = 80/8 ... divide both sides by 8

x = 10

If x = 10, then angle BAC is

angle BAC = 6x+8

angle BAC = 6*10+8

angle BAC = 60+8

angle BAC = 68

Use x = 10 to find angle ABC as well

angle ABC = 2x+2

angle ABC = 2*10+2

angle ABC = 20+2

angle ABC = 22

The three angles of this triangle are A = 68, B = 22, C = 90

As a check, the three angles must add to 180

A+B+C = 180

68+22+90 = 180

180 = 180

Answers are confirmed

Another thing to notice is that A+B = 90 meaning that A and B are complementary angles. A+B = 68+22 = 90.

Answer:

7.25252525

Step-by-step explanation:

Irrational numbers are numbers that never end, therefore 7.25 is an irrational number. also, none of the other ones are never ending

Answer:

Step-by-step explanation:

Unknown number be 'x'

X-2<9

An explanation of solving an inequality where the number is two less than a number less than 9.

An inequality can be written as: x - 2 < 9, where x is the number.

To solve the inequality:

Add 2 to both sides: x < 11

So, the solution to the inequality is: x < 11

Answer:

9r

Step-by-step explanation:

Simplify:

4r + 9r - 11r + 7r

13r - 11r + 7r

2r + 7r

9r

The answer to the given expression i.e. 4r + 9r - 11r + 7r is 9r.

Given that,

Based on the above information, the calculation is as follows:

= 4r + 9r - 11r + 7r

= 20r - 11r

= 9r

Therefore we can conclude that the answer to the given expression i.e. 4r + 9r - 11r + 7r is 9r.

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Answer: rotation 180 degrees counterclockwise about the origin

Step-by-step explanation: the formula for rotating 180 degrees is (x , y) = (-x , -y). thus, an example of point A is (2 , -4), and it results in being (-2, 4), and so forth for the following points.

Answer:

Reflection about the y axis, and then about the x- axis

Step-by-step explanation:

When reflecting an object about the y- axis, the x-coordinates are multiplied with -1.

When reflecting an object about the x-axis, the y-coordinates are multiplied with -.

When reflecting about both axes, both coordinates are multiplied by -1.

Now looking at the coordinates of the two triangles:

A(2, -4) → A'(-2, 4)

B(5, -5) → B'(-5, 1)

C(4, -5) → C'(-4, 5)

All of the coordinates are multiplied by -1.

[tex]-1.8w+3.96=(-0.36)(5w)+(-0.36)(11)\\\\=\boxed{-0.36(5w+11)}[/tex]

Answer:

If the python has the area x sq. ft, they all have the area [tex]\dfrac{5x}{2}+538\ sq. ft.[/tex]

Step-by-step explanation:

Let x sq. ft be the area the python has.

1. If the anaconda has 538 more square feet than the python, then the anaconda has (x+538) sq. ft.

2. If the python has twice as many square feet as the rattlesnake, then the rattlesnake has the area  [tex]\dfrac{x}{2}\ sq. ft.[/tex]

In total they have the area  

[tex]x+(x+538)+\dfrac{x}{2}=\dfrac{5x}{2}+538\ sq. ft.[/tex]

Answer:

It will take 10 hours.

Step-by-step explanation:

We know distance = rate * time

Sally's rate = 55

Jim's rate = 65

We want Jim to be 100 miles ahead of Sally

The time will always be the same.

d =Sally's distance

Sally

d = 55t

Jim

d+100 = 65 t

We know have 2 equations with 2 unknowns.  Substitute d= 55t into Jim's equations

55t + 100 = 65t

Subtract 55t from both sides.

55t-55t + 100 = 65t-55t

100 = 10t

divide each side by 10

100/10 = 10t/10

10 = t

Answer:

It will take exactly 10 hours

Step-by-step explanation:

Answer:

x = - 6 or x = 1

Step-by-step explanation:

given a quadratic equation in standard form : ax² + bx + c = 0 : a ≠ 0

then the equation can be solved using the quadratic formula

• x = ( - b ± [tex]\sqrt{b^2-4ac}[/tex]) / 2a

x² + 5x - 6 = 0 is in standard form

with a = 1, b = 5 and c = - 6

x = (- 5 ± [tex]\sqrt{5^2-(4(1)(-6)}[/tex]) / 2

  = (- 5 ± [tex]\sqrt{25+24}[/tex]) / 2

  = (- 5 ± [tex]\sqrt{49}[/tex]) / 2

x = [tex]\frac{-5-7}{2}[/tex] = [tex]\frac{-12}{2}[/tex] = - 6

or x = [tex]\frac{-5+7}{2}[/tex] = [tex]\frac{2}{2}[/tex] = 1

The solutions to the quadratic equation x² + 5x - 6 = 0 are x = 1 and x = -6.

To solve the quadratic equation x² + 5x - 6 = 0, Nathaniel used the quadratic formula.

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c correspond to the coefficients of the quadratic equation.

In this case, a = 1, b = 5, and c = -6.

Substituting these values into the quadratic formula, we get x = (-5 ± √(5² - 4(1)(-6))) / (2(1)).

Simplifying further, we have x = (-5 ± √(25 + 24)) / 2.

This yields two solutions: x = (-5 + √49) / 2 and x = (-5 - √49) / 2.

Simplifying the square root, we get x = (-5 + 7) / 2 and x = (-5 - 7) / 2.

Therefore, the solutions to the quadratic equation are x = 1 and x = -6.

Answer:

[tex](x-12)(x-4)[/tex]

Step-by-step explanation:

[tex]x^2 - 16x + 48[/tex]

In the given expression , the product is 48 and sum is -16

-4 times -12 gives us 48

-4 plus -12 gives us -16. So two factors are -4 and -12

Beak the middle term using factors

[tex]x^2 -4x-12x+48[/tex]

Group first two terms and last two terms

[tex](x^2 -4x)+(-12x+48)[/tex]

FActor out GCF from each group

[tex]x(x -4)-12(x-4)[/tex]

FActor out x-4 that is in common

[tex](x-12)(x-4)[/tex]