Which of the following is equal to the rational expression when X not equal -4 or 3?
x2 - 4x + 3
X^2+ X - 12

Mechanic A worked for 15 hours and mechanic B worked for 5 hours.

Step-by-step explanation:

Given,

Per hour charges of mechanic A = $95

Per hour charges of mechanic B = $75

Total hours worked = 20

Total amount charged = $1800

Let,

x represent the number of hours of mechanic A

y represent the number of hours of mechanic B

According to given statement;

x+y=20          Eqn 1

95x+75y=1800   Eqn 2

Multiplying Eqn 1 by 95

[tex]95(x+y=20)\\95x+95y=1900\ \ \ Eqn\ 3[/tex]

Subtracting Eqn 2 from Eqn 3

[tex](95x+95y)-(95x+75y)=1900-1800\\95x+95y-95x-75y=100\\20y=100[/tex]

Dividing both sides by 20

[tex]\frac{20y}{20}=\frac{100}{20}\\y=5[/tex]

Putting y=5 in Eqn 1

[tex]x+5=20\\x=20-5\\x=15[/tex]

Mechanic A worked for 15 hours and mechanic B worked for 5 hours.

Keywords: linear equation, elimination method

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The first mechanic worked for 15 hours while the second mechanic worked for 5 hours.

Let's denote the number of hours worked by the first mechanic as x and the number of hours worked by the second mechanic as y.

We know two things:

⇒ x + y = 20

⇒ 95x + 75y = 1800

⇒ y = 20 - x

⇒ 95x + 75(20 - x) = 1800

⇒ 95x + 1500 - 75x = 1800

⇒ 20x + 1500 = 1800

⇒ 20x = 300

⇒ x = 15

⇒ y = 20 - 15 = 5

Thus, the second mechanic worked for 5 hours.

Complete question:

Two mechanics worked on a car. The first mechanic charged $95 per hour, and the second mechanic charged $75  per hour. The mechanics worked for a combined total of 20 hours, and together they charged a total of $1800. How long did each mechanic work?

Answer:

The correct answer is D.  9 × 30 + 11 × 10; $380

Step-by-step explanation:

Let's write the correct equation to help Jonas to find out his earnings last week, this way:

Number of hours worked by Jonas last week = 40

Number of hours worked by Jonas last week as swim instructor = 10

Number of hours worked by Jonas last week as lifeguard = 30

Rate per hour as lifeguard = $ 9

Rate per hour as swim instructor = $ 11

Now, we can answer the question:

Total earnings last week = 30 * 9 + 10 * 11

Total earnings last week = 270 + 110 = $ 380

The correct answer is D.  9 × 30 + 11 × 10; $380

Answer:

The answer is D, short and simple.

Answer:

V = −1

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

3=−2v−v

3=−2v+−v

3=(−2v+−v)(Combine Like Terms)

3=−3v

3=−3v

Step 2: Flip the equation.

−3v=3

Step 3: Divide both sides by -3.

−3v  = 3

-3     -3

v=−1

Answer:

Subtract v from −2v.

Which equals −3v.

-3v = 3.

Step-by-step explanation:

v = -1.

-3 x -1 = 3.

3 = 3.

Therefore, v = -1.

Answer:

yes

Step-by-step explanation:

Given the 2 equations

y = [tex]\frac{3}{4}[/tex] x + 6 → (1)

y = - [tex]\frac{3}{4}[/tex] x + 5 → (2)

Substitute y = [tex]\frac{3}{4}[/tex] x + 6 into (2)

[tex]\frac{3}{4}[/tex] x + 6 = - [tex]\frac{3}{4}[/tex] x + 5 ( add [tex]\frac{3}{4}[/tex] to both sides )

[tex]\frac{3}{2}[/tex] x + 6 = 5 ( subtract 6 from both sides )

[tex]\frac{3}{2}[/tex] x = - 1 ( divide both sides by [tex]\frac{3}{2}[/tex] )

x = [tex]\frac{-1}{\frac{3}{2} }[/tex] = - [tex]\frac{2}{3}[/tex] ← one solution

Answer:

Y = 9

Step-by-step explanation:

2Y (with Y having a value of 9) would be equal to 2 x 9 which would give you 18

then you take the 18 and subtract 10x

which would give you 8x with the x not being relevant in your case (maybe)

To find the value of y in the equation 8 = 2y - 10x, rearrange the equation to isolate y. Divide both sides of the equation by 2, and the value of y is 4 + 5x.

To find the value of y, we need to isolate it on one side of the equation. First, let's rearrange the equation by moving the term with x to the other side:

8 + 10x = 2y

Next, let's divide both sides of the equation by 2 to solve for y:

(8 + 10x) / 2 = y

4 + 5x = y

So, the value of y is 4 + 5x.

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Answer: -12 b

Step-by-step explanation:i know this is the right answer bc i did the math

Answer: 1.95

Step-by-step explanation:

Multiply 15*13%

Answer:

Abswer is 1.95 thank you

Step-by-step explanation:

Answer:

At least 33 number of tickets can be sold in order to make a profit.

Step-by-step explanation:

Given:

A theater rents there space for $300 per night.

The company charges $9 per ticket.

Now, to find the least number of tickets that can be sold in order to make a profit.

Amount of rent per night = $300.

Charges of per ticket = $9.

So, to get the least number of tickets sold to get the profit we divide amount of rent per night by charges per ticket:

[tex]300\div9[/tex]

[tex]=33.33[/tex]

Thus, 33 tickets price is 33 × 9 = $297.

Therefore, at least 33 tickets can be sold in order to make a profit.

Without a clear graph or a well-defined inequality, it is not possible to determine which inequality is graphed. An inequality and its graph on the coordinate plane represent solutions to the inequality, such as regions to the right of a vertical line for x > 2.

The student has asked which inequality is graphed. Unfortunately, the provided information is insufficient to determine the inequality or the graph in question. Moreover, the data given appears to be disorganized or incorrectly transcribed, making it impossible to provide a specific answer. For a proper response, one would need either a clear description of the graph or the correct functional form of the inequality.

To demonstrate inequalities and their graphs, one might typically use coordinate axes where solutions to the inequality are represented by regions of the plane. For example, the inequality x > 2 would be represented graphically by a shaded region to the right of the line x = 2 on a number line, or in two dimensions, to the right of the vertical line x = 2.

If the student can provide a clear and accurate description of the graph or the inequality they are inquiring about, a more precise answer could be given.

Answer:

29 rows because if you do the math and divide 227 by 8 you will get 28 and a remainder so you would have to add an extra row

Answer:

soda:3.75      burger: 1.25

Step-by-step explanation:

Mafalda's save percentage improved by 0.153.

Solution:

Given that, Mafalda has a save percentage of 0.7380 so far this hockey season

Last season, her save percentage was 0.5850

To find: Percentage improved

To find improvement in Mafalda's save percentage we will subtract last season's save percentage from this season's save percentage.

From given,

Last season save percentage = 0.5850

This season save percentage = 0.7380

Percentage improved = This season save percentage - Last season save percentage

[tex]Percentage\ Improved = 0.7380-0.5850\\\\Percentage\ Improved =0.153[/tex]

Thus Mafalda's save percentage improved by 0.153.

Answer: 4 x + 13 y + 11

Step-by-step explanation:

Distribute:

=5+(2)(6y)+(2)(3)+4x+y

=5+12y+6+4x+y

Combine Like Terms:

=5+12y+6+4x+y

=(4x)+(12y+y)+(5+6)

=4x+13y+11

Answer:

=4x+13y+11

Answer: 7/8

Step-by-step explanation: This is a substitution problem, from the expression x + ³/₄, where x = ¹/₈, we now replace or substitute for x and then solve the expression fractionally, the expression now becomes

¹/₈ + ³/₄

Now , find the l. c. m. of the denominator 8 and 4

            1 + 6

        =  _____    

              8

          = 7/8

NOTE: To get 1 and 6, you find out how many times 8 can go in the l. c. m. and later multiplied the number of times by  the numerator which = 1.

And the number of times 4 can go in the l. c. m. (8) which is 2 times then multiplied by the numerator (3) = 6.

Adding 1 and 6 together gives 7/8.

Formula to find the slope:

m = y2-y1 / x2-x1

(4,3); (8,5)

m= 5-3 / 8-4

m = 2/4

m = 1/2

Therefore, the slope of the line that passes through these points is 1/2

Answer:

C. The difference of the medians is 4 times the interquartile range.

Step-by-step explanation:

The diagram show two box plots.

Mahoney's box plot:

Median [tex]=33[/tex]

Interquartile range [tex]=34-32=2[/tex]

Martin's box plot:

Median [tex]=41[/tex]

Interquartile range [tex]=42-40=2[/tex]

The interquartile ranges are the  same.

The difference of the medians [tex]=41-33=8[/tex]

Hence, the difference of the medians is 4 times the interquartile range.

There is no standard relationship stating that the difference of medians is a certain multiple of the interquartile range. The median and interquartile range measure different aspects of a dataset (central tendency and dispersion, respectively), so comparing them in this way is not universally applicable.

The question is asking about a theoretical relationship between the median and the interquartile range (IQR) in a set of data. However, in statistics, there's no standard relationship that states the difference of medians is a certain multiple of the interquartile range. The median is a measure of central tendency, or a 'middle' value of a dataset, while the interquartile range is a measure of dispersion, indicating the variability within the data. The difference between two medians or the comparison of a median to the interquartile range would be specific to a certain dataset, and it's not a universal relationship.

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Answer:

C) 4/55

Step-by-step explanation:

3/11-1/5=15/55-11/55=4/55

Answer:

40 grams of 40% sugar syrup

Step-by-step explanation:

It is 40g because you are adding 10g of sugar to 30g of syrup

It is 40 % syrup because you start out with 20% sugar in 30 g. That means the 1/5 of the syrup is sugar. That means that 6g is sugar. Then you add ten more grams of sugar. Now you have 16g of sugar in 40 grams of syrup.

Make equation to find percent

16/40=x/100

x=40

If you add 10 grams of sugar into 30 grams of 20 % sugar syrup, you will make 40 grams of 40% sugar syrup

A combination of sugar and water that is cooked over a low to medium heat setting, stirring contents until the sugar is fully dissolved and the mixture is clear. The mixture is then boiled for approximately one minute.

How to solve?

It is 40g because you are adding 10g of sugar to 30g of syrup

It is 40 % syrup because you start out with 20% sugar in 30 g. That means  1/5 of the syrup is sugar. That means that 6g is sugar. Then you add ten more grams of sugar. Now you have 16g of sugar in 40 grams of syrup.

Make an equation to find the percentage;

16/40=x/100

x=40.

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Incomplete Question the complete question with the figure is below

The triangles shown are similar.

What is the value of x?  

A.  12

B. 15

C. 20  

D. 13

Answer:

The correct option is B. 15

Therefore the value of x is

[tex]x=15\ unit[/tex]

Step-by-step explanation:

Given:

AB = 5

BC = 3

AC = 4

PQ = x

QR = 9

RP  = 12

ΔABC ~ ΔPQR

To Find:

x = ?

Solution:

ΔABC ~ ΔPQR       .................Given

If two triangles are similar then their sides are in proportion.  

[tex]\dfrac{AB}{PQ} =\dfrac{BC}{QR}=\dfrac{AC}{PR} \textrm{corresponding sides of similar triangles are in proportion}\\[/tex]  

Substituting the values we get

[tex]\dfrac{5}{x} =\dfrac{3}{9}\\\\x=\dfrac{45}{3}=15\ unit[/tex]

Therefore the value of x is

[tex]x=15\ unit[/tex]

Answer:            -12

Step-by-step explanation:

Answer:

-20+4=-16

-10-5=-15

=16/15

Final answer:

The rate of change between the points (5, -4) and (-10, -20) is found by calculating the slope, which is 16/15 or approximately 1.07.

Explanation:

To find the rate of change between two points, you can calculate the slope of the line that passes through them. The formula for the slope (Δy/Δx) is the difference in the y-coordinates divided by the difference in the x-coordinates of the two points.

Using the points (5, -4) and (-10, -20), we can substitute these into the slope formula:

Calculate the change in y (Δy): -20 - (-4) = -16.

Calculate the change in x (Δx): -10 - 5 = -15.

Divide the change in y by the change in x to find the slope: -16 / -15.

The slope of the line is therefore 16/15 or approximately 1.07.

Answer:

4 and 6

Step-by-step explanation:

4 + 6 = 10

4 x 6 = 24

Answer:

i have solved the question in the picture above. I used factorization to solve the quadratic equation I can also solve using quadratic formula or completing the square method if you want just comment below and I will solve it thank you

Final answer:

Maria and her sister's meal total cost is $13.60 before tip. With a 20% tip of $2.72 added, the total meal cost becomes $16.32.

Explanation:

First, we need to calculate the total cost of Maria and her sister's meal before tip. Each salad costs $5.40 and each drink costs $1.40. Given they both had a salad and a drink, we calculate the cost for each person as $5.40 + $1.40 = $6.80. Thus, for both Maria and her sister, the total cost of the meal is $6.80 x 2 = $13.60.

To calculate the total cost including a 20% tip, we first need to work out the amount of the tip. A 20% tip can be calculated by converting the percentage to a decimal (0.20) and multiplying it by the meal cost. So, the tip amount is 0.20 x $13.60 = $2.72.

Finally, to find the total cost of the meal including a 20% tip, we add the tip to the original meal cost: $13.60 + $2.72 = $16.32. Therefore, the total cost of the meal with a 20% tip is $16.32.

Answer:

3/4

Step-by-step explanation:

1/2 divided by 4/6= 1/2 divided by 2/3

We can use reciprocals.

1/2 divided by 2/3= 1/2*3/2=3/4

Answer:

 10c2 + 5c + 4

Step-by-step explanation:

Final answer:

To find the sum E + F, combine like polynomial terms: the result is 2c^2 + 5c + 4.

Explanation:

To find E + F, we need to perform polynomial addition by combining like terms. We're given that E = 6c² - 2c - 1 and F = -4c² + 7c + 5. Adding the coefficients of the terms with the same powers of c, we get:

Combining these results, we get: E + F = 2c² + 5c + 4

This polynomial represents the sum of the given polynomials, consolidating like terms to simplify the expression and facilitate further analysis.

Answer:

The amount of butter used by baker this month is 294 kilograms.

Step-by-step explanation:

The amount of butter used last month by the baker = 210 kilograms

Now, according to the question:

The amount of butter used this month

= Previous months's amount +  40% of previous month's usage

Calculating 40% of 210 kg:

[tex]\frac{40}{100} \times 210 = 84[/tex]

⇒40% of 210 kilograms  = 84 kilograms

⇒ The amount of butter used this month  

= 210 kg +  84 kg = 294 kg

Hence,the amount of butter used by baker this month is 294 kilograms.

The baker used 40% more butter this month than last month. To find this month's usage, calculate 40% of last month's usage (84 kilograms) and add it to last month's usage. The baker used 294 kilograms of butter this month.

To answer this question, we can first calculate how much 40% of the butter used last month is. 40% of 210 kilograms is 84 kilograms. This is the amount of butter the baker used additionally this month than the previous month. If we add this to the amount of butter that was used last month (210 kilograms), we get the total amount of butter used this month. 210 kilograms + 84 kilograms = 294 kilograms. So the baker used 294 kilograms of butter this month.

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Answer:

She put the negative sign for the 32 outside the parentheses

Step-by-step explanation:

in the formula the negitive is supposed to be inside the parentheses

The first error that Cara made was seen in the second step where she used "minus" (32) squared instead of "plus" (32).

Population variance (σ²) describes the way data points in a given population are distributed. It is the aggregate of the distances from each data set in the population towards the mean squared.

The population variance is a population parameter that is independent of research methodologies or sampling practices.

Mathematically, The correct calculation can be done by using the formula:

[tex]\mathbf{\sigma^2 = \dfrac{ \sum(x_i-\bar x)^2}{N}}[/tex]

[tex]\mathbf{\sigma^2 = \dfrac{ (87-78)^2 + (46-78)^2+ (90-78)^2+(78-78)^2+(89-78)^2}{5}}[/tex]

[tex]\mathbf{\sigma^2 = \dfrac{ (9)^2 + (-32)^2+ (12)^2+(0)^2+(11)^2}{5}}[/tex]  

We can now see that the minus 32 is supposed to be in the bracket.

[tex]\mathbf{\sigma^2 = \dfrac{81+1024+ 44+0+121}{5}}[/tex]

[tex]\mathbf{\sigma^2 = \dfrac{1270}{5}}[/tex]

[tex]\mathbf{\sigma^2 = 254}[/tex]

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Answer:

Step-by-step explanation:

G-8=25

+8. +8

G= 33

Answer:

-13 》-21

Step-by-step explanation:

The reason why is because -21 is further away from 0 than -13. Negative numbers are greater when they are closer to 0, and less when further away.

The inequality that compares these two temperatures is - 13°F > - 21°F so

Northway Alaska is warmer.

A numerical expression is a mathematical statement written in the form of numbers and unknown variables. We can form numerical expressions from statements.

Given, On a day in the month of February the temperature in Barrow Alaska is -21°F at the same time the temperature in Northway Alaska is -13°F.

We know 21 > 13 but - 13 > - 23.

Therefore the inequality that compares the temperature is - 13°F > - 21°F.

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