Two cars got an oil change at the same auto shop. The shop charges customers for each quart of oil plus a flat fee for labor. The oil change for one car required 5 quarts of oil and cost $24.80. The oil change for the other car required 7 quarts of oil and cost $29.30. How much is the labor fee and how much is each quart of oil?

Question 3

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Explanation:

Note how in choice A we have repeated x values

x = 3 pairs up with y = 4 and y = 5 at the same time.

The input x = 3 must only pair up with one output only if we want a function to happen.

If you plotted the points (3,4) and (3,5), it is possible to draw a vertical line through them. So this fails the vertical line test.

The other answer choices do not have repeated x values, so they are all functions.

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

Question 4

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If you plotted choice A and choice D on an xy coordinate system, you should see straight lines forming.

2x+3y = 10 turns into y = (-2/3)x+10/3 which is y = mx+b form.

Choice D's equation is equivalent to y = 0x+18, so its slope here is 0, making it a flat horizontal line.

Choice B does not count as an answer because while it is a linear vertical line, it is not a function for similar reasons back in question 3. The fact that x = 16 pairs up with infinitely many y values is what makes this not be a function.

Choice C is not a linear equation. Instead it is a quadratic equation because the largest exponent is 2.

Step-by-step explanation:

so to find out how long you would first do 60-30 as this is how many extra minutes they workout. the answer is 30.

then you would divide 30 by 2 that makes 15 as there is 2 people then you would add 15 to 30 and you get 45

45mins on treadmill

freehand=60-45=15

60-30=30

30÷2=15

15+30=45

60-45=15

part A:

freehand=f

treadmill=t

x=y+30

that is what i believe the eqation is

D.1998-2000

Step-by-step explanation:

Deflation describes the drop of prices for goods and services leading to slowing down of economic growth.During economic uncertainty, prices of goods and services can get very low causing the inflation rate to go lower than zero.CPI index shows inflation when it rises over a short period of time.CPI declines to mean deflation where there is a steady decrease in prices of goods and services.

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Answer:

n-21=31

Step-by-step explanation:

Just read it carefully, it is worded weirdly, but just think about it.

Answer:

52

Step-by-step explanation:

n-21=31

n=31+21

n=52

Final answer:

The weight of each bag of equal weight is 1 17/20 kg and the weight of the third bag is 1 41/20 kg.

Explanation:

Let's assume the weight of each bag of equal weight is x kg. According to the question, the third bag is heavier than each of the equal bags by 1 1/5 kg, which can be written as 6/5 kg.

So, the weight of the third bag is x + 6/5 kg.

Now, we can set up an equation based on the given information:

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

Simplifying the equation, we get:

3x + 6/5 = 27/4

Now, we can solve for x by multiplying both sides of the equation by 5 to get rid of the fraction:

15x + 6 = 135/4

15x = 135/4 - 6

15x = 135/4 - 24/4

15x = 111/4

Now, divide both sides of the equation by 15 to solve for x:

x = (111/4) / 15 = 111/60 = 37/20 = 1 17/20

Hence, the weight of each bag of equal weight is 1 17/20 kg and the weight of the third bag is 1 17/20 + 6/5 = 1 17/20 + 24/20 = 1 41/20 kg.

Answer:

6 seconds

Step-by-step explanation:

1/12 mile * 5280 feet/mile = 440 feet per train

50 miles/hour * 1/3600 hr/sec * 5280 ft/mile = 73 1/3 ft/second

one train has to travel 440 feet to pass the other train

440 feet * 1/(73 1/3) sec/ft = 6 seconds

The time it will take for the two trains to pass each other's rear car is 6 seconds.

The speed is the distance covered by an object at a particular time. Therefore, it is the ratio of distance and time.

[tex]\rm{Speed = \dfrac{Distance}{Time}[/tex]

Two passenger trains travelling in opposite directions meet and pass each other. Each train is 1/12 miles long and is traveling 50 mph.

Therefore, the total distance that the two train needs to cover is twice the size of a train.

Distance = 2 × 1/12miles = 1/6 miles

Also, the relative speed of the two trains moving in opposite directions is,

Speed = 50 mph + 50 mph = 100 mph

Now, the time that the two trains need to cover the entire distance is,

Time = (1/6 miles)/ 100mph = 1/600 hours

Converting the time to seconds,

Time = 1/600 hours × 3600 = 6 seconds

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Answer:

67000*.15=10,050

Step-by-step explanation:

The required down payment would be the amount of $10,050.

The percentage is defined as a ratio expressed as a fraction of 100.

Anna wants to buy a house for $67,000.

She will need a down payment of 15%.

We have to determine the evaluation of 15% of $67,000.

⇒ 15% of 67,000

15%  is expressed as 15/100 in fractional form

⇒ (15/100)(67,000)

15/100  is expressed as 0.15 in decimal form

⇒ (0.15)(67,000)

Apply the multiplication operation, and we get

⇒ 10,050

Therefore, the down payment would be $10,050.

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The width of rectangle is [tex]2\frac{1}{4}\ cm[/tex] and length is [tex]5\frac{5}{12}\ cm[/tex]

Step-by-step explanation:

Let,

Width of rectangle = w

Length of rectangle = w+[tex]3\frac{1}{6}=w+\frac{19}{6}[/tex]

Perimeter of rectangle = [tex]15\frac{1}{3}=\frac{46}{3}\ cm[/tex]

Perimeter of rectangle = 2(Length + Width)

[tex]2(w+\frac{19}{6}+w)=\frac{46}{3}\\2(2w+\frac{19}{6})=\frac{46}{3}\\4w+\frac{19}{3}=\frac{46}{3}[/tex]

Subtracting [tex]\frac{19}{3}[/tex] from both sides

[tex]4w+\frac{19}{3}-\frac{19}{3}=\frac{46}{3}-\frac{19}{3}\\4w=\frac{46-19}{3}\\4w=\frac{27}{3}\\4w=9[/tex]

Dividing both sides by 4

[tex]\frac{4w}{4}=\frac{9}{4}\\w=\frac{9}{4}[/tex]

Therefore,

Width of rectangle = w = [tex]\frac{9}{4}=2\frac{1}{4}[/tex] cm

Length of rectangle = [tex]w+\frac{19}{6}=\frac{9}{4}+\frac{19}{6}=\frac{27+38}{12}=\frac{65}{12}=5\frac{5}{12}\ cm[/tex]

The width of rectangle is [tex]2\frac{1}{4}\ cm[/tex] and length is [tex]5\frac{5}{12}\ cm[/tex]

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Answer:

(x-8)/10

Step-by-step explanation:

-------

(X - 8)/10 or (8 -X)/10

The unknown number can be given as X

The difference between the number and 8 can be given as 8 -X or X - 8

The dividing it by 10 will give (x-8)/10 or (8-x)/10 depending on the value of the unknown number X

Answer:

To solve this inequality you need to get m by itself

3m+10<30 (First subtract 10 from each side)

3m<20 (10-10=0, 30-10=20) (Then divide each side by 3)

m< 20/3 or 6.666666

So your answer is any that is less than 6.66666

Your answer would be 5

5

Hope this helps ;)

how many consecutive odd integers are there, or else I can't help you

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

Work Shown:

x = some integer

2x = even integer

2x+1 = odd integer

(2x+1)+2 = 2x+3 = odd integer just after 2x+1

The integers 2x+1 and 2x+3 add to 36

(2x+1)+(2x+3) = 36

2x+2x+1+3 = 36

4x+4 = 36

4x+4-4 = 36-4 ... subtract 4 from both sides

4x = 32

4x/4 = 32/4 .... divide both sides by 4

x = 8

With x = 8, we can say

2x+1 = 2*8+1 = 17 is the first odd integer

2x+3 = 2*8+3 = 19 is the next odd integer

17+19 = 36, so the answer is confirmed

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A non-algebraic way to get the answer is to divide 36 in half to get 18

Then try odd integers around 18, so 19+21 = 40 but thats too high

then maybe try 15+17 = 32, thats too low

17+19 = 36 is right on the money

The 3 inside angles need to equal 180.

Subtract E from 180 to find the sum of the other two angles:

180 - 104 = 76

Now because EF ≅ DE , angle D and F would be the same so divide 76 by 2

Angle D = 38

Answer:

[tex]\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right][/tex]

Step-by-step explanation:

In the first equality

[tex]5\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right] =\dfrac{2}{5}m\times \left[\begin{array}{cc}-1&2\\4&8\end{array}\right],[/tex]

the matrices in both parts are the saem. The equality will be true if the same matrices are multiplied by the same numbers, so

[tex]5=\dfrac{2}{5}m\Rightarrow m=5\times \dfrac{5}{2}=\dfrac{25}{2}[/tex]

For the second equality

[tex](H+[1\ 4\ -2])+[3\ 2\ -6]=[-2\ 3\ -1]+([1\ 4\ -2]+[3\ 2\ -6]),[/tex]

if [tex]H=[-2\ 3\ -1][/tex], then this equality represents the assotiative property of matrix addition.

Hence,

[tex]m\times H=\dfrac{25}{2}\times [-2\ 3\ -1]=\left[\begin{array}{ccc}-25&\dfrac{75}{2}&-\dfrac{25}{2}\end{array}\right][/tex]

Answer:

Step-by-step explanation:

5x+2y=9.......(1)

x+y= -3.........(2)

Making y as subject bin (2)

y = -3 - x

Substituting in (1)

5x + 2(-3 - x) = 9

5x - 6 - 2x = 9

3x = 9 + 6

3x = 15

x = 15/3

x = 5

And y = -3 - x

y = -3 - 5

y = -8

Answer:

The solution for the system of linear equations is x = 5, y = -8

Step-by-step explanation:

Let's solve the system of linear equations by substitution:

5x + 2y = 9

x + y = -3

Solving for x in the 1st equation, this way:

5x + 2y = 9

5x = 9 - 2y

x = (9 - 2y)/5

Substituting x in the 2nd equation:

x + y = -3

(9 - 2y)/5 + y = -3

9 - 2y + 5y = - 15 (Multiplying by 5 at both sides)

3y = - 15 - 9

y = -24/3

y = - 8

Substituting y in the 1st equation:

5x + 2y = 9

5x + 2 * - 8 = 9

5x - 16 = 9

5x = 25

x = 25/5 = 5

The solution for the system of linear equations is x = 5, y = -8

Answer:

The answer is 2

Step-by-step explanation:

4 + (-2) = 2

Answer:

2

Step-by-step explanation:

Given the expression : a + (-b)

where a = 4 and b = 2

Therefore: a + (-b) = 4 + (-2)

=4 - 2

= 2

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

Work Shown:

3(x+9)-2

3*x+3*9 - 2 ..... distribute

3x+27-2 .... multiply

3x+25 .... combine like terms

Answer:3x+25

Step-by-step explanation:

it had to be b cuz now all quadrilateral have straight sides

4. take 110-80/4-2, this gives you 30/2, which is then 15. Therefore it is 15 dollars per hour

Answer:

The nth term of the given arithmetic sequence is [tex]a_n=-17+(n-1)9[/tex]

Step-by-step explanation:

Given sequence is -17,-8,1,...

To find the nth term of the given sequence :

Let  [tex]a_1=-17,a_2=-8,a_3=1,...[/tex]

To find the common difference d :

[tex]d=a_2-a_1[/tex]

[tex]=-8-(-17)[/tex]

[tex]=-8+17[/tex]

Therefore d=9

[tex]d=a_3-a_2[/tex]

[tex]=1-(-8)[/tex]

[tex]=1+8[/tex]

Therefore d=9

The common difference d is 9

Therefore the given sequence is an arithmetic sequence

The nth term of an arithmetic sequence is given below

[tex]a_n=a_1+(n-1)d[/tex]

Substitute [tex]a_1=-17[/tex] and d=9 in the above equation we get

[tex]a_n=-17+(n-1)9[/tex]

Therefore the nth term of the given arithmetic sequence is [tex]a_n=-17+(n-1)9[/tex]

The formula for the nth term of the sequence -17, -8, 1 is a_n = 9n - 26, where n is the position of the term in the sequence.

The sequence provided is -17, -8, 1, which suggests that there is a common difference between terms since it is an arithmetic sequence. To find the nth term of an arithmetic sequence, we use the formula a_n = a_1 + (n - 1)d, where a_n is the nth term, a_1 is the first term, and d is the common difference. In this case, the common difference is 9 (since -8 - (-17) = 9).

So, using the formula for the nth term of an arithmetic sequence:

Our formula becomes a_n = -17 + (n - 1) × 9. Simplifying this:

a_n = -17 + 9n - 9

a_n = 9n - 26

Therefore, the formula for the nth term of the given sequence is a_n = 9n - 26.

The quotient is [tex]\frac{3(y-5)}{2}[/tex]

Explanation:

The expression is [tex]\frac{2 y^{2}-6 y-20}{4 y+12} \div \frac{y^{2}+5 y+6}{3 y^{2}+18 y+27}[/tex]

Now, reciprocal the term [tex]\frac{y^{2}+5 y+6}{3 y^{2}+18 y+27}[/tex] and convert ÷ to ×

[tex]\frac{2 y^{2}-6 y-20}{4 y+12} \times \frac{3 y^{2}+18 y+27}{y^{2}+5 y+6}[/tex]

Taking the common terms out, we get,

[tex]\frac{2\left(y^{2}-3 y-10\right)}{4(y+3)} \times \frac{3\left(y^{2}+6 y+9\right)}{y^{2}+5 y+6}[/tex]

Factorizing each numerator and denominator, we get,

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

Multiplying the terms, we have,

[tex]\frac{6(y-5)(y+2)(y+3)^{2}}{4(y+3)^{2}(y+2)}[/tex]

Cancelling the common factors, we get,

[tex]\frac{3(y-5)}{2}[/tex]

Thus, the quotient is [tex]\frac{3(y-5)}{2}[/tex]

Answer:

B

Step-by-step explanation:

On edge 2021

The quotient of 26,208 divided by 42 is 624. This is a straightforward division problem that can often be solved using a calculator or through long division by hand.

To find the quotient of 26,208 divided by 42, you need to perform a division operation. When you divide 26,208 by 42, you'll find that the answer is 624 without any remainder. This is a straightforward division problem that can often be solved using a calculator or through long division by hand.

she drinks 9/2 ounces of water in 1 hour

Step-by-step explanation:

On average, the person drinks 1/2 of a 6-ounce glass of water in 2/3 hour.

First of all, we have to rewrite the amount of water in a single fraction: we have

[tex]\frac{1}{2}\cdot 6 = \frac{6}{2}=3[/tex]

This means that the person drinks 3 ounces of water every 2/3 hours.

In order to find how much water she drinks in one hour, we use the following proportion:

[tex]\frac{3}{2/3}=\frac{x}{1}[/tex]

where

x is the amount of water she drinks in one hour.

Solving the equation for x,

[tex]x=\frac{3\cdot 1}{2/3}=\frac{3\cdot 1 \cdot 3}{2}=\frac{9}{2}[/tex]

Therefore, she drinks 9/2 ounces of water in 1 hour.

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Answer:

∠CIS.

Step-by-step explanation:

This angle is opposite from the smallest side. Therefore, according to the triangle inequality, it is the smallest angle.

The smallest angle that the angular momentum vector can make with the z-axis for an electron with quantum number l=2 is found using the magnetic quantum numbers. For m₁=+2, the angle would be the smallest, approaching 0 degrees.

The question pertains to the calculation of the smallest angle that the angular momentum vector ℓ can make with the z-axis given the quantum number l for an electron. To find this, we use the concept of quantized angular momentum in quantum mechanics.

For an electron with a quantum number l=2, it can have multiple magnetic quantum numbers m₁, ranging from -l to +l. Therefore, for l=2, m₁ can be -2, -1, 0, 1, or 2. Each of these values corresponds to a different angle with the z-axis.

The smallest angle corresponds to the maximum value of m₁, which is 2 in this case. The formula cos 0 = Lz/L uses the magnetic quantum number m₁ and the total angular momentum to calculate the cosine of the angle. For m₁=+1, the value of cos 0 would be 0.707, using the provided ratios and simplifying the formulas given. This corresponds to an angle whose cosine is 0.707, which through the inverse cosine function can be determined to be approximately 45 degrees. However, for m₁=+2, the angle would be even smaller, approaching 0 degrees as the z-component of angular momentum becomes maximally aligned with the z-axis.

Answer:

Step-by-step explanation:

[tex]\left\{\begin{array}{ccc}x-3y=15\\3x-9y=45\end{array}\right\\\\\text{Divide both sides of the second equation by 3}\\\\\dfrac{3x}{3}-\dfrac{9y}{3}=\dfrac{45}{3}\\\\x-3y=15\\\\\text{We received the same equation as the first.}\\\\\bold{CONCLUSION}\\\\\text{The system of equations has infinitely many solutions.}[/tex]

[tex]\left\{\begin{array}{ccc}a_1x+b_1y=c_1\\a_2x+b_2x=c_2\end{array}\right\\\\\text{If}\ a_1=a_2,\ b_2=b_2,\ c_1=c_2,\ \text{then the system of equations}\\\text{ has infinitely many solutions}\\\\\text{If}\ a_1=a_2,\ b_1=b_2,\ c_1\neq c_2,\ \text{then the system of equations}\\\text{has no solutions}\\\\\text{Other the system of equations has one solution.}[/tex]

Answer:

I think the answer is C

Step-by-step explanation:

from looking at the graph and how the lins intercept

Answer:

C is the correct answer.

Step-by-step explanation:

Answer:

10 weeks

Step-by-step explanation:

Answer: 26 weeks

Step-by-step explanation:

This is an example of an arithmetic sequence.

The first term = 3.5

common difference = 0.5

Using the formula for calculating the nth term of an arithmetic sequence :

[tex]t_{n}[/tex] = a + (n - 1 ) d

Therefore :

16.5 = 3.5 + ( n - 1 ) x 0.5

16. 5 = 3.5 + 0.5n - 0.5

16.5 = 3 + 0.5n

16.5 - 3 = 0.5n

13.5 = 0.5n

n = 13.5/0.5

n = 27

Therefore , it will take the cat (n-1)  weeks to weigh 16.5 ounce, which will be 27 - 1 = 26

check:

3.5 + 26 ( 0.5)

= 3.5 + 13

= 16.5

Answer:

C none of the above

Step-by-step explanation:

x + z + y

is not going to be equal to x + y - z

Its like saying 10 + 5 - 4 = 11

To 10 + 5 + 4, they are not going to be equal

Answer:

C none of the above

Step-by-step explanation:

Answer:

{-6, -5, -4, -3, -2, -1}.

Step-by-step explanation:

The set contains the integer -6  ( because of the ≤ )  but not 0 because of the < 0.

Answer:

  13/10

Step-by-step explanation:

13/10 = 1.30 is a number between 1.25 and 1.50.