Some people advise that in very cold​ weather, you should keep the gas tank in your car more than half full. Irene​'s car had 5.5 gallons in the 14​-gallon tank on the coldest day of the year. Irene filled the tank with gas that cost ​$3.70 per gallon. How much did Irene spend on​ gas?

Problem 1

a) y = 8 and c) x = 2 are perpendicular lines to one another. The first is horizontal and the second is vertical.

The other two lines are not perpendicular because their slopes (1/8 and 8) do not multiply to -1. This rule only applies to lines that are neither horizontal nor vertical.

Answers: A and C.

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Problem 2

Equations b) y = (-1/2)x - 4 and c) y-4 = 2(x+3) are perpendicular. Equation B has a slope of -1/2, while equation C has a slope of 2. Those two values multiply to -1. One slope is the negative reciprocal of the other. It might help to think of 2 as 2/1.

The other two equations are not perpendicular to each other, nor are they perpendicular to B or C. Equation A has a slope of 0. Equation D has a slope of -2.

Answers: B and C

Answer:

[tex]\frac{(L x M)}{6}[/tex]

Step-by-step explanation:

The greatest common factor is the greatest number that will divide two values. We have two values L and M. Each has numbers which multiply together to give the number. The highest value or most in common they share is 6. This is the GCF.

The least common multiple is the smallest positive number which is a multiple of the two. This means both L and M divide into it evenly.

We know L x M is a multiple because L and M will be factors of it. But we don't know its the least.

As an example if L= 42 and M = 60, they have GCF 6. We can multiply them to find a multiple 42 x 60 = 2520 but we don't know this is the smallest or least multiple we can find. If we divide by the GCF, 2520/6=420. Interestingly, 42 x 10 =420 and 60 x 7 =420. This means 420 is the least common multiple.

We can multiply (L x M) and then divide by the GCF of L & M to find the least common multiple.

[tex]\frac{(L x M)}{6}[/tex]

Answer: the answer is 23

Step-by-step explanation: since you are trying to find the number of boxes, b, the first thing you do is isolate it by dividing 4b by 4 this eliminates the 4, and because you did it on one side you have to do it on the other so you work would look like this 4b/4=92/4 you equation would look like this when done b=23

To find the number of boxes Mr. Reed bought, we solve the equation 4b = 92. This involves dividing 92 by 4 which results in 23 boxes of markers.

The subject of this question is Mathematics, particularly algebra. We need to solve the equation 4b = 92, where 'b' represents the number of boxes Mr.Reed bought.

Step 1: Write down the equation: 4b = 92.

Step 2: We solve for 'b' by dividing each side of the equation by 4. This gives us: b = 92/4.

Step 3: Doing the division, we find that 'b' is 23. Therefore, Mr. Reed purchased 23 boxes of markers with $92.

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Answer: The price per pound is $18

1 feet is 12 inches.

We have 5 feet and 6 inches. First, let's convert the feet to inches. 5 times 12 is 60, so 5 feet is 60 inches.

Now add 60 inches to the 6 inches that we didn't mention. 60 plus 6 is 66. Thus, 5 feet and 6 inches is 66 inches.

Answer:

The answer is 66

Step-by-step explanation: 1 foot is 12 inches so you do 12 times 5 and get 60 and then add the next 6 inches... :)

Answer: [tex]\bold{(12x - 7 - i\sqrt{47})(12x - 7 + i\sqrt{47})=0}[/tex]

Step-by-step explanation:

[tex]\dfrac{21x^2-7x - 16}{3x^2-4}=5[/tex]

cross multiply:  21x² - 7x - 16 = 15x² - 20

set equal to 0:  6x² - 7x + 4 = 0

Use quadratic formula to find the roots:

a=6, b=-7, c=4

[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}[/tex]

   [tex]=\dfrac{-(-7) \pm \sqrt{(-7)^2-4(6)(4)}}{2(6)}[/tex]

   [tex]=\dfrac{7 \pm \sqrt{49-96}}{12}[/tex]

   [tex]=\dfrac{7 \pm \sqrt{-47}}{12}[/tex]

   [tex]=\dfrac{7 \pm i\sqrt{47}}{12}[/tex]

[tex]x_1 =\dfrac{7 + i\sqrt{47}}{12} \qquad >>\qquad (12x - 7 - i\sqrt{47})= 0[/tex]

[tex]x_2 =\dfrac{7 - i\sqrt{47}}{12} \qquad >>\qquad (12x - 7 + i\sqrt{47})= 0[/tex]

Answer:

The number of loaves sold

Step-by-step explanation:

Answer:

The domain is all real numbers. The range is {y|y ≤ 16}.

Step-by-step explanation:

The vertex of a parabola is given by

[tex](\frac{-b}{2a}, \frac{4ac-b^2}{4a})[/tex].

As a = -1, b = -2, c= 15 here, then the vertex is at (1,16).

As a is negative, it opens downward, so the range is  {y|y ≤ 16}.

Meanwhile, all parabolic functions have a domain of [tex]\mathbb{R}[/tex].

For each part A through D below, the idea is to find the common factor between the terms, which you'll then use the distributive property to pull out.

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

Part A

3x + 18 = 3(x+6)

Note how we pulled out a 3. If we distribute it back in, we end up with 3x+18 again. The other problems are done in a similar fashion

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Part B

2x - 14 = 2(x - 7)

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Part C

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

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Part D

9x - 15 = 3(3x - 5)

y = 2x + 2

for x = 0 → y = 2(0) + 2 = 0 + 2 = 2 → (0, 2)

for x = -1 → y = 2(-1) + 2 = -2 + 2 = 0 → (-1, 0)

y = x - 1

for x = 0 → y = 0 - 1 = -1 → (0, -1)

for x = 1 → y = 1 - 1 = 0 → (1, 0)

Look at the picture.

The complete statement is a division of long form ends with zeroes as remainders

We have the following statement -

A division of _____ ends?

The complete statement is -

A division of long division form ends with zeroes as remainders

Therefore, the complete statement is a division of long form ends with zeroes as remainders.

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Answer:

Option A is correct.

[tex]x = -6 \pm \sqrt{30}[/tex]

Explanation:

Given the expression: [tex]x^2+12x+6 = 0[/tex]

[tex]x^2+12x+6=0[/tex]  

Subtract 6 from both sides, we get

[tex]x^2+12x=-6[/tex]  

halve linear coefficient,then  square it, and add it to both sides

[tex]x^2+12x+36=30[/tex]

Now, the left side is a perfect square

[tex](x+6)^2=30[/tex]  

Now, take square root to both sides.

[tex]x+6=\sqrt{30}[/tex] 

Subtract 6 from both sides, we get;

[tex]x = -6 \pm \sqrt{30}[/tex]

So, the solutions are : [tex]x = -6 \pm \sqrt{30}[/tex]

Answer:

The correct answer is A

[tex]x=-6\pm \sqrt{30}[/tex]

Step-by-step explanation:

The given expression is

[tex]x^2+12x+6=0[/tex]

Add [tex]-6[/tex] to both sides

[tex]x^2+12x=-6[/tex]

Add [tex](\frac{12}{2} )^2=(6)^2[/tex] to both sides.

[tex]x^2+12x+(6)^2=-6+(6)^2[/tex]

We got a perfect square on the left hand side

[tex](x+6)^2=-6+36[/tex]

Simplify the left hand side to get,

[tex](x+6)^2=30[/tex]

Take square root of both sides

[tex](x+6)=\pm \sqrt{30}[/tex]

Solve for [tex]x[/tex].

[tex]x=-6\pm \sqrt{30}[/tex]

Answer:

Each pound of chocolate costs $7.30

Step-by-step explanation:

if 5 pounds of chocolate costs $36.50 then you could simply divide the $36.50 by 5 to calculate the cost of 1 pound of chocolate.

So, 36.50 ÷ 5 = 7.30

Each pound of chocolate costs $7.30

To find the cost of each pound of chocolate, you divide the total cost by the total number of pounds. Given a total cost of $36.50 for 5 pounds of chocolate, the resulting calculation is $36.50 ÷ 5 = $7.30. Thus, each pound costs $7.30.

If you have 5 pounds of chocolate that cost $36.50 in total, and you need to find the cost of each pound of chocolate, you can determine this by dividing the total cost by the number of pounds. This is similar to how in our reference material, to compute the cost of each piece of fruit, you divided the total expense by the quantity of fruit.

In this case, you need to divide the total cost, which is $36.50, by the quantity, which is 5 pounds. So the calculation is $36.50 ÷ 5 = $7.30. Therefore, each pound of chocolate costs $7.30.

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Expand to get 35x^3+49x^2-20x-28

Answer:

3x(3x + 2)

Step-by-step explanation:

Answer:

2,428

Step-by-step explanation:

(18 × 106) + (5 × 104)

      1908 + 520

= 2,428

I'm really sorry if this isn't what you meant... but if it is then... Hope this helps you! :)

Answer:

21/32 square inches.

Step-by-step explanation:

The area of a rectangle = length x width

The area of her picture = length x widht

= 7/8 x 3/4

= 21/32

The area of her picture is 21/32 square inches.

Yes, I agree the area of the picture is 21/32 square inches.

The area must be in square inches. So she need to specify it.

Thank you.

To find the area that is shaded red, you find the area of the rectangle and subtract it by the area of the triangle.

Area of a rectangle:

A = l × w             [ l = 11 in ; w = 6in ]    Plug these numbers into the equation

A = 11 · 6

A = 66 in²

Area of a triangle:

[tex]A=\frac{1}{2}bh[/tex]     [ b = 4 in ; h = 6 in ] Plug these #s into the equation

[tex]A = \frac{1}{2}(4)(6)[/tex]

[tex]A=\frac{24}{2}[/tex]

A = 12 in²

Area of rectangle - Area of triangle = Area of the shaded region

66 in² - 12 in ² = 54 in²

Your answer is B

The required red shaded region has the area of 54 in²

A figure bounded by 4 sides in which the opposite sides are equal and all the internal angles are 90 ° is called a rectangle.

A figure bounded by 3 sides and all the internal angles add up to 180 ° is called a triangle.

Area  = (1/2)(base)(height)

Area of the rectangle = (11 x 6) in² = 66 in²

Area of the right angled triangle = (1/2)(6 x 4)  in² = 12 in²

∴ Area of the red shaded region = (66 - 12)  in² = 54 in²

Option B is correct.

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Answer:

A. The equation has no solution

[tex](f-g)(x)=f(x)-g(x)\\\\\text{We have}\ f(x)=2x^2-5\ \text{and}\ g(x)=3x+3.\ \text{Substitute:}\\\\(f-g)(x)=(2x^2-5)-(3x+3)=2x^2-5-3x-3=2x^2-3x-8\\\\Answer:\ \boxed{(f-g)(x)=2x^2-3x-8}[/tex]

Answer:

The answer is B and E

Step-by-step explanation:

Julia runs 5 time and lifts 5 times in B. She also runs 10 times and lifts 10 times in E.

Answer:

True

Step-by-step explanation:

Each week the amount of radio active material is 100*(1/4)^x which is correct.

So at the end of 4 weeks she will have

amount = 100*(1/4)^x

amount = 100*(1/4)^4

amount = 100 * (1/256)

amount = 0.390625 grams after 4 weeks.

Answer:

Step-by-step explanation:

There is the answer.

Answer:

Let 5 consecutive no's be x,x+1,x+2,x+3,x+4

90 = x+ x+1+x+2+ x+3+x+4

90 = 5x+10

18 = x+2

x= 16

so smallest is 16

greatest = 16+4 = 20

sum = 16 +20 = 36

So to factor this expression, I'm going to be factoring by grouping. Firstly, what two terms have a sum of 4x and a product of -32x²? That's going to be 8x and -4x. Replace 4x with 8x - 4x:

[tex]x^2+8x-4x-32[/tex]

Now, factor x² + 8x and -4x - 32 separately. Make sure that they have the same quantity on the inside of the parentheses:

[tex]x(x+8)-4(x+8)[/tex]

Now you can rewrite the expression as:

[tex](x-4)(x+8)[/tex]

In short, the two binomial factors are (x - 4) and (x + 8).

Answer:

x-4 and x+8

Step-by-step explanation:

Factoring a quadratic equation of the form x^2+bx+c:

Divide b into two numbers p and q, so that p+q = b and p*q = c

8 + (-4) = 4 = b

8 * (-4) = -32 = c

x^2+8x-4x-32

Factor by grouping

(x^2+8x)+ (-4x-32) =

x*(x+8) + -4* (x+8) = (x-4)(x+8)

Answer:

B.) transitive property of equality

Step-by-step explanation:

x = –3 and –3 = z, then x = z.

Symmetric property of equality: if a = b then b = a

Transitive property of equality:  if a = b and b = c, then a = c

Closure property of multiplication:  the set is closed under multiplication

Closure property of addition:  the set is closed under addition

Answer:

72 / 50 = 36/25

x^16 / x^36  

= x^-20

Answer:

[tex]\frac{36}{25x^{20} }[/tex]

Step-by-step explanation:

In order to simplify this function, we have to divide by the maximum common divisor:

[tex]\frac{72x^{16} }{50x^{36} }\\ 72/2=36\\50/2=25\\\frac{36}{25} \\(x^{16} )(x^{-36})=x^{-20}=\frac{1}{x^{20} } \\\frac{36}{25x^{20} }[/tex]

By doing this you can simplify the function into the simplified form.

Answer:

y=5x+17

Step-by-step explanation:

perpendicular slope is 5

y-7=5(x+2) convert this equation into slope intercept and that's your answer

Answer:

Step-by-step explanation:

Please find attachment for step by step explanation.