A van travels 240 miles on 20 gallons of gas. How far does it travel per gallon? Carlos installed 24 wooden cabinets in 8 days. On the average, how many cabinets did he install each day? Which is a better buy—100 sheets of binder paper at $2.50, or 150 sheets at $3.50? Julie is trying to choose between two packs of cookies. Pack A has 36 cookies for $5.90. Pack B has 24 cookies for $4.10. Which pack has cheaper cookies? Anita is offered two summer jobs. One is in retail and pays $500 for a 40-hour work week. The other job is at a restaurant and pays $12 an hour. Which job has a higher hourly rate?

Answer:

Correct choice is C.

Step-by-step explanation:

The conic section is represented by equation

[tex]11x^2-2y^2 + 66x-16y + 45 = 0.[/tex]

First, simplify this equation:

[tex](11x^2+66x)+(-2y^2-16y) + 45 = 0,\\ \\11(x^2+6x)-2(y^2+8y)+45=0,\\ \\11(x^2+6x+9-9)-2(y^2+8y+16-16)+45=0,\\ \\11((x+3)^2-9)-2((y+4)^2-16)+45=0,\\ \\11(x+3)^2-2(y+4)^2-99+32+45=0,\\ \\11(x+3)^2-2(y+4)^2=22,\\ \\\dfrac{(x+3)^2}{2}-\dfrac{(y+4)^2}{11}=1.[/tex]

This is the equation of hyperbola with center at point (-3,-4), real semiaxis [tex]a=\sqrt{2}[/tex] and imaginary semiaxis [tex]b=\sqrt{11}.[/tex] Then the distance from the center to the focus is

[tex]c=\sqrt{a^2+b^2}=\sqrt{(\sqrt{2})^2+(\sqrt{11})^2}=\sqrt{2+11}=\sqrt{13}.[/tex]

Then foci are placed at points [tex](-3-\sqrt{13},-4),\ (-3+\sqrt{13},-4).[/tex]

Thus, correct choice is C.

Answer:

the answer is c

Step-by-step explanation:

I looked it up and found if on a trust worthy website.

Answer:

11

Step-by-step explanation:

Since Farmer Tim has one of each coin, 50+20+10+5=85 cents are accounted for, leaving 395 - 85 = 310 cents for the remaining coins. We can try minimizing the number of coins that add up to 310 cents by using as many large denominations as possible.

The largest denomination is 50 cents, so we can take six 50 cent coins, which add up to 6 times 50 = 300 cents. We then can take one 10 cent coin. Thus, we have a combination of seven coins that up to 310 cents.

Therefore, the smallest number of coins that Farmer Tim could have is 4 + 7 = 11.

Answer:

B

Step-by-step explanation:

Put the second y into the first equation

3x + y = 10                           substitute for y

3x + 6x + 1 = 10                    Combine like terms on the left

9x + 1 = 10                             Subtract 1 from both sides

9x = 10 - 1                              Combine the right.

9x = 9                                    Divide by 9

x = 9/9                                   Divide

x = 1

The answer is right there. Only B is possible

y = 6x + 1

y = 6(1) + 1

y = 6 + 1

y = 7

Answer B

Let us assume that it is 1/8 lb packages of fudge.

So, the question is how many 1/8 lbs of fudge can be sold from 7 pounds of fudge

Answer:

Total amount of fudge = 7 pounds

Portions of division = 1/8 pounds

So, number of packages that can be made from 7 pounds are =

[tex]\frac{7}{\frac{1}{8}}[/tex]

= [tex]7\times8=56[/tex]

Hence, 56 packages of 1/8 lbs each can be made from 7 pounds fudge.

Answer:

23 buns

Step-by-step explanation:

The dog ate 5 buns.

The Owen gave the dog 18 more buns

5+18 = 23

The simplified expression for (m+13)-(p+25) is m - p - 12.

To simplify the expression (m+13)-(p+25), we can distribute the negative sign to both terms inside the parentheses:

[tex]\[m + 13 - p - 25.\][/tex]

Next, combine like terms by grouping the variables (m and -p) and the constants (13 and -25):

[tex]\[m - p + 13 - 25.\][/tex]

Now, simplify the constants:

[tex]\[m - p - 12.\][/tex]

So, the final answer is m - p - 12. This expression represents the simplified form of the given algebraic expression.

In the original expression, (m+13)-(p+25), we subtracted the entire quantity (p+25) from (m+13). Distributing the negative sign, we subtracted p and 25 individually. Combining like terms involved combining the variables (m - p) and constants (13 - 25). The final result is m - p - 12, where m and p are coefficients of the respective variables, and 12 is the simplified constant term.

In summary, the expression (m+13)-(p+25) simplifies to m - p - 12 by applying the principles of combining like terms and distributing the negative sign. This simplified form is a more concise representation of the original expression.

Answer:

2 1/2 ft

Step-by-step explanation:

Area is given by the formula

A = l*w

We know the area is 8 1/2  

Changing this to an improper fraction  8 1/2 = (2*8 +1)/2 = 17/2

The width is 3 2/5  as an improper fraction  = (5*3+2)/5 = 17/5

A = l*w

17/2 = l* 17/5

Multiply each side by 5/17

17/2 * 5/17 = l* 17/5 * 5/17

5/2 = l

2 1/2 = l

Answer:

Step-by-step explanation:

First find 2 points on the line.  To do this you will need to substitute numbers in for x and y.  Do this by first putting 0 in for x to find the value of y:

9(0) + 4y = -36

0 + 4y = -36       =  4y = -36   =        y = -36 ÷ 4 = -9     y= -9

(0,-9)

Now that we have that point substitute 0 in for y.

9x + 4(0) = -36

9x + 0 = -36   =    9x = -36     =    x = -36  ÷ 9    x = -4

(-4,0)

After you have your two points decide which on you want to be (x1,y1) and which you want to be (x2,y2).  It doesn't matter which one you choose.  You will then plug in your numbers into the slope formula:

       y2 - y1           -9 - 0         -9           The slope is - 9/4

       x2 - x1            0 - 4          -4            

In a parallelogram, opposite angles are the same.

Because you are given angle C is 70 degrees, angle R is also 70 degrees.

An exterior angle of a triangle is equal to the sum of the two opposite inside angles.

Angle KSO is an exterior angle to the triangle made from ORS,

So angle KSO would equal the sum of angle O and angle R.

Angle KSO = 65 + 70 = 135 degrees.

The answer is D you move the decimal over 1 then add 2 0

Answer:

D

Step-by-step explanation:

Answer:

The ratio is 1:3

Step-by-step explanation:

People can do this in different ways.

Firstly, set some variables for cydlinder A:

Diameter = 18

Height = 1

Radius = 18 ÷ 2 = 9

Area of a cylinder is [tex]\pi r^{2} h[/tex]

Plug values in:

[tex]\pi 9^{2} 1[/tex] = 81π

Diameter = 18 ÷ 3 = 6

Height = 1 * 3 = 3

Radius = 6 ÷ 2 = 3

[tex]\pi3^{2}3  = 27\pi[/tex]

Cylinder b is 3 times less than cylinder a:

81π ÷ 27π = 3

So that means three lots of cylinder b is equal to one of cylinder a.

Meaning the ration is 1:3

Answer:

The correct option is C. 5,400

Step-by-step explanation:

Consider the provided number.

[tex]5.4\cdot 10^3[/tex]

If the exponent of 10 is a positive number then you need to move the decimal point right as much as the exponent value.

If the exponent of 10 is a negative number then you need to move the decimal point left as much as the exponent value.

Now consider the provided number.

[tex]5.4\cdot 10^3[/tex]

Here the power of 10 is positive, so move the decimal point right as shown.

[tex]5400[/tex]

Hence, the correct option is C. 5,400

Answer:

A factor of 24 is a number that can be multilied by another number (normally whole (not fraction or decimal) numbers) so a factor must be less than the number any multiple of 2 greater than 24 will work so just any even number greater than 24 exg 26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60, and so on.

Step-by-step explanation:

Not all multiples of a number are its factors. In the case of the number 24, only the multiples that can divide evenly into 24, which include 1, 2, 3, 4, 6, 8, 12, and 24, can be considered its factors. Higher multiples like 48, 72 or 96 are not factors as they do not divide into 24.

In mathematics, the multiples of a number are obtained by multiplying that number by any integer. The factors of a number, on the other hand, are the numbers that you can evenly divide into that number. Therefore, for the number 24, its multiples include 24, 48, 72, 96, and so on.

However, not all multiples of 24 are factors of 24. A factor must divide into 24 with no remainder, which isn't the case with greater multiples of 24. For instance, 48, 72, 96 etc. are multiples of 24, but they are not factors of 24 because they cannot divide evenly into 24.

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Answer:

[tex]\frac{25}{4}[/tex]

Step-by-step explanation:

You have to use Order of Operations so you MUST multiply first  which gave me [tex]\frac{2}{25}[/tex] and in order to divide that you must make it a reciprocal and that's how I got the answer

Divide by a fraction means the same as multiply by its reciprocal.

[tex]\dfrac{1}{2}\div\dfrac{1}{5}\times\dfrac{2}{5}=\dfrac{1}{2}\times\dfrac{5}{1}\times\dfrac{2}{5}\\\\=\dfrac{1}{\not2_1}\times\dfrac{5}{1}\times\dfrac{\not2^1}{5}=\dfrac{1}{1}\times\dfrac{\not5^1}{1}\times\dfrac{1}{\not5_1}=1\times1\times1=1\\\\Answer:\ \boxed{\dfrac{1}{2}\div\dfrac{1}{5}\times\dfrac{2}{5}=1}[/tex]

Answer:

The answer is 7 if you round 6.5

Step-by-step explanation:

1/5(-22.38 - 10.12)

1/5 (-32.5)

= -6.5

Answer:

25/w = l

Step-by-step explanation:

We know that the formula for the area of a rectangle is

A = l*w

We know the area is 25

Substituting this into the equation

25 = l*w

We are to solve for l, by dividing each side by w

25/w = lw/w

25/w = l

To find the length (L) of a rectangle when the area (A) is 25 square inches, you use the formula L = A/W, substituting A with 25 and W with the given width.

To solve for the length (L) of a rectangle with a known area (A), you first need the formula for a rectangle's area, which is A = L × W, where L is the length and W is the width of the rectangle. Given that the area (A) is 25 square inches and the area formula has been incorrectly stated as A = 2LW, we should correct it to A = LW.

If you have a specific width (W), you can rearrange the formula to solve for L by dividing both sides by W, resulting in L = A/W.

Using an example, if we know the width (W) is 5 inches, we could substitute into the formula:

L = A/W

L = 25 in2/5 in = 5 in

Therefore, the length (L) of the rectangle would be 5 inches.

[tex]2x+4\geq24\qquad\text{subtract 4 from both sides}\\\\2x\geq20\qquad\text{divide both sides by 2}\\\\\boxed{x\geq10\to x\in[10;\ \infty)}[/tex]

Answer:

The box plot will have its left tail longer than the right tail becuase a few exceptionally low prices make the distribution skewed to the left.                                              

Step-by-step explanation:

As seen in the attached file, the box plot has its left tail longer than the right tail because of the exceptionally low prices that is :$2

Firstly arranging the data in increasing order:

$2,$2,$25,$25,$26,$26,$27,$27,$28,$28,$30

Median of the data = 26 (since there are odd numbers)

Lower quartile (Q1) = 25

Upper quartile (Q2) = 26

By plotting the box plot we conclude that the left tail is longer than the right tail.

Answer:

The Answer is C. The box plot will have its left tail longer than the right tail because a few exceptionally low prices make the distribution skewed to the left.

Hope This Helps?

check the picture below.

so red line of BD is perpendicular to AC, hmmmm let's firstly find the slope of AC, bearing in mind that perpendicular lines have negative reciprocal slopes.

[tex]\bf A(\stackrel{x_1}{-4}~,~\stackrel{y_1}{-2})\qquad C(\stackrel{x_2}{18}~,~\stackrel{y_2}{-8}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{-8-(-2)}{18-(-4)}\implies \cfrac{-8+2}{18+4} \\\\\\ \cfrac{-6}{22}\implies -\cfrac{3}{11} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]

[tex]\bf \stackrel{\textit{perpendicular lines have \underline{negative reciprocal} slopes}} {\stackrel{slope}{-\cfrac{3}{11}}\qquad \qquad \qquad \stackrel{reciprocal}{-\cfrac{11}{3}}\qquad \stackrel{negative~reciprocal}{\cfrac{11}{3}}}\impliedby \textit{BD's slope}[/tex]

so we're really looking  for the equation of a line whose slope is 11/3 and runs through B(4,4).  Keeping in mind that

standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

[tex]\bf B(\stackrel{x_1}{4}~,~\stackrel{y_1}{4})~\hspace{10em} slope = m\implies \cfrac{11}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-4=\cfrac{11}{3}(x-4)[/tex]

[tex]\bf \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}\textit{ to do away with the denominators}}{3(y-4)=3\left( \cfrac{11}{3}(x-4) \right)\implies 3y-12=11(x-4)} \\\\\\ 3y-12=11x-44\implies 3y=11x-32 \\\\\\ -11x+3y=-32\implies \blacktriangleright 11x - 3y= 32\blacktriangleleft[/tex]

Final answer:

The equation for the altitude passing through point B(4,4) is in standard form as 11x - 3y = 32. This was found by calculating the slope of AC, finding the perpendicular slope, and then applying it with point B to find the equation of the line.

Explanation:

To find the equation of the altitude that passes through point B(4,4) of the triangle ABC with vertices A(-4,-2), B(4,4), and C(18,-8), we need to determine the slope of line AC and then find the perpendicular slope that passes through B.

Firstly, we calculate the slope of AC:

The slope of the altitude will be the negative reciprocal of the slope of AC because the altitude is perpendicular to AC. Hence,

Now we use the point-slope form of the equation of a line using point B:

Rewriting in standard form (Ax + By = C), we get:

So, the standard form of the equation of the altitude passing through point B is 11x - 3y = 32.

Answer:

x=72 and the exterior angle is 154

Step-by-step explanation:

We will call the unknown angle in the triangle y.  Angle y and the angle (2x +10) form a straight line so they make 180 degrees.

y + 2x+10 =180

Solve for y by subtracting 2x+10 from each side.

y + 2x+10 - (2x+10) =180 - (2x+10)

y = 180-2x-10

y = 170-2x

The three angles of a triangle add to 180 degrees

x+ y+ 82 = 180

x+ (170-2x)+82 = 180

Combine like terms

-x +252=180

Subtract 252 from each side

-x+252-252 = 180-252

-x = -72

Multiply each side by -1

-1*-x = -72*-1

x=72

The exterior angle is 2x+10.  Substitute x=72 into the equation.

2(72)+10

144+10

154

Answer: x=72 and the exterior angle is 154

Step-by-step explanation:

We will call the unknown angle in the triangle y.  Angle y and the angle (2x +10) form a straight line so they make 180 degrees.y + 2x+10 =180Solve for y by subtracting 2x+10 from each side.y + 2x+10 - (2x+10) =180 - (2x+10)y = 180-2x-10y = 170-2xThe three angles of a triangle add to 180 degreesx+ y+ 82 = 180x+ (170-2x)+82 = 180Combine like terms-x +252=180Subtract 252 from each side-x+252-252 = 180-252-x = -72Multiply each side by -1-1*-x = -72*-1x=72The exterior angle is 2x+10.  Substitute x=72 into the equation.2(72)+10144+10154

The subset of real numbers that the number 1/3 belongs is to the rational numbers. These numbers  is a number that can be written as a ratio. The numerator and the denominator of the fraction are both integers.

Step-by-step explanation:

[tex]\dfrac{1}{3}[/tex]   belongs to the subset "Rational number( [tex]\mathbb Q[/tex] )" of Real numbers [tex]\mathbb R[/tex].

Or

[tex]\dfrac{1}{3} \in \mathbb{Q} \subset \mathbb R[/tex]

To find in which subset of real numbers does  [tex]\dfrac{1}{3}[/tex]   belong.

In technical terms, there can be infinite subsets of real numbers in which  [tex]\dfrac{1}{3}[/tex]  can belong to.

But, the set of real numbers is divided into some special subsets viz. rational numbers. irrational numbers, integers, non integers etc..

Since the given number is expressed in the form of  [tex]\dfrac{m}{n}[/tex] which are called rational numbers, thus given number  [tex]\dfrac{1}{3}[/tex] belongs to rational numbers.

The set of rational numbers is denoted by [tex]\mathbb Q[/tex]

The set of real numbers is denoted by [tex]\mathbb R[/tex].

Thus, we can express our result symbolically as:

[tex]\dfrac{1}{3} \in \mathbb{Q} \subset \mathbb R[/tex]

Learn more about rational numbers here:

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Answer:

The equation of the line would be y = 5/4x - 4

Step-by-step explanation:

To find the equation of any line, start by finding the slope using the slope formula.

m(slope) = (y2 - y1)/(x2 - x1)

m = (-4 - 1)/(0 - 4)

m = -5/-4

m = 5/4

Now that we have the slope, use that and either point to get the equation of the line

y - y1 = m(x - x1)

y + 4 = 5/4(x - 0)

y + 4 = 5/4x

y = 5/4x - 4

The equation of the line would be y = (5/4) x - 4. Hence, option B is correct.

An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

To find the equation of any line, start by finding the slope using the slope formula.

m(slope) = (y₂ - y₁)/(x₂ - x₁)

m = (-4 - 1)/(0 - 4)

m = -5/-4

m = 5/4

Now that we have the slope, use that and either point to get the equation of the line.

y - y₁ = m(x - x1)

y + 4 = 5/4(x - 0)

y + 4 = 5/4x

y = 5/4x - 4

Hence, option B is correct.

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Answer:

125 liters of gasoline

Step-by-step explanation:

176/88 = 2

250 / 2 = 125

Answer:

8x¹²y³

Step-by-step explanation:

Answer:

The answer would be x=2

Step-by-step explanation:

Answer: 3 days

Step-by-step explanation: It would take 3 days for seven hens to 7 lay eggs because each hen lays an egg each day.

1 hen/1 egg = 3 days

7 hens/7 days = 14 eggs

7 hens/3 days = 7 eggs

Answer:

3 days

Step-by-step explanation:

Three hens lay 3 eggs in 3 days

We have to find the days in which 7 hens lay 7 eggs

Hen/egg=[tex]\frac{3}{3}[/tex]

Hen/egg=1

Using unitary method

1 hen lays 1 egg in 3 days

1 hen lays in 1 day =[tex]\frac{1}{3}[/tex]eggs

7 hens lay 7/3 eggs in 1 day

7 hens lay 1 egg=[tex]\frac{3}{7}[/tex]days

7 hens lay 7 eggs=[tex]\frac{3}{7}\times 7[/tex]

7 hens lay 7 eggs=3 days

Hence, 7 hens lay 7 eggs in 3 days

Answer:

x=15

Step-by-step explanation:

Answer:

x=15

Step-by-step explanation:

Lets start solving the equation line by line,

2/5(5+x)=8

For solving such type of question one must know the BODMAS Rule.

Where,

B= Bracket  

O=Orders

D=Division

M=Multiplication

A=Addition

S=Subtraction

and its very important to remember the priority of each operation, as you need to solve it as per their Priorities.

Bracket first, Orders second, Division and so on....

So now lets start with the given equation,

2/5(5+x)=8

As per the BODMAS we have to first start with brackets,

2/5(5+x)=8

2/5*5+2/5*x=8 First Step

2+2/5*x=8

2/5*x=8-2

2/5*x=6

2x=30

so x=15.

This is a very common Traditional Method  to solve such problems but their are other ways too.

Lets see one by one how NIco, Erik, Raj sandra and Aditi is trying to solve this question by their methods.

Lets analyze the method used by Nico first,

Nico has smartly multiplied both the sides of the equation with 5/2 so that the problem becomes easy to solve in further steps,

2/5(5+x)=8

5/2*2/5(5+x)=8*5/2

5+x=20

so x=15.

smart answer in a few steps.

Now let's analyze the answer by  Aditi,

2/5(5+x)=8

5/2*(5)+5/2=(5/2)8

The second step of Aditi is incorrect as it doesn't make any sense.

Now lets analyze the answer by Erik,

2/5(5+x)=8

2/5(5+x)-5=8-5

this will also yields a correct answer but subtracting 5 from both side doesn't seems to be a optimum way to solve and it will add more steps before getting the answer.

Raj has again using a smart way to solve the equation,

2/5(5+x)=8

1/2*2/5(5+x)=8*1/2

This will also gives correct answer in a few steps.

Sandra is using a traditional way to solve the question and it will also give correct result.

So, we can say that except Aditi all will get the correct answer.

and if we compare then Nico and Raj will get the answer in few steps.

I hope this will help you.

Answer:

2 solutions

Step-by-step explanation:

Since the equations are not equal, they provide two solutions. Negative numbers provide no solutions. If they are equal to zero, they have one solution.

Answer:

Eliphat is right, 2

Step-by-step explanation: