what is the coefficient for x2 -5x+6

Fractions

The values are  [tex]\frac{1}{4} , \frac{1}{8} , \frac{1}{81}[/tex]

Step-by-step explanation:

As we know the fractions whose numerators are 1 can be represented in exponents and vice versa provided that the power of the exponent is (-1) ,

like 1/a = a^(-1)  

[tex]\frac{1}{a}[/tex]  = [tex]a^{-1}[/tex]

so accordingly

a)

   4^(-1) or [tex]4^{-1}[/tex] can be represented exponentially as ¼ .

⇒   [tex]\frac{1}{4}[/tex]

Part b)

2^(-3)  or [tex]2^{-3}[/tex]

We can simplify the exponent so that the power should be equal to -1.

And, so [tex]2^{3}[/tex] = 8

So we can write the above the expression as 8^(-1)  or [tex]8^{-1}[/tex]

So the fraction corresponding to it is [tex]\frac{1}{8}[/tex].

⇒ [tex]\frac{1}{8}[/tex]

Part c)

3^(-4) now we  can simplify the exponent so that the power of the exponent is -1.

And thus , (3 ^4)^(-1) = 81^(-1)  = [tex]\frac{1}{81}[/tex]

So the fraction obtained is [tex]\frac{1}{81}[/tex].

⇒ [tex]\frac{1}{81}[/tex]

The values are  [tex]\frac{1}{4} , \frac{1}{8} , \frac{1}{81}[/tex]

Answer:

2161 miles

Step-by-step explanation:

The formula for the circumference of a circle is \pi d, where d represents the diameter. Therefore, if you divide the circumference of the moon by pi, you will get the diameter. 6790/pi is about 2161 miles. Hope this helps!

Final answer:

The diameter of the Moon is approximately 2161 miles when rounded to the nearest mile.

Explanation:

The circumference of the Moon is given as about 6,790 miles. To find the diameter, we use the formula for the circumference of a circle, C = πd, where C is the circumference and d is the diameter.

To solve for the diameter, the formula is rearranged to d = C / π. Using 3.14159 as an approximation for π, we calculate the diameter.

d = 6790 miles / 3.14159 ≈ 2160.98 miles

So, the diameter of the Moon is approximately 2161 miles when rounded to the nearest mile.

Answer:

4/10 or 40%

Step-by-step explanation:

4 black marbles out of 10 which equals to 4/10

Answer:

4/10 or 2/5

Step-by-step explanation:

Answer:

Volume of wood chips in the pickup truck is  [tex]70[/tex] cubic units.

Step-by-step explanation:

Given that,

The pickup truck rectangular bed with an area of [tex]35[/tex] square feet.

Height of wood chips is [tex]2[/tex] feet.

From the question,

The shape formed by combination of rectangular bed and wood chips is a cuboid shape.

So, Volume of cuboid is [tex]= l\times b\times h[/tex] cubic unit.

Then, Volume of wood chips [tex]=Area\times height[/tex]

                                                 [tex]= 35 \times 2=70[/tex] cubic units.

Therefore, Volume of wood chips in the pickup truck is  [tex]70[/tex] cubic units.

The volume of wood chips in Ernesto's pickup truck is calculated by multiplying the bed's area of 35 square feet by the height of 2 feet, resulting in a total volume of 70 cubic feet.

To determine the volume of wood chips that Ernesto's pickup truck can carry, we start with the given area of the rectangular bed, which is 35 square feet. Knowing the bed area and that Ernesto fills the bed to a height of 2 feet, we can calculate the volume by multiplying the area by the height.

Here is a step-by-step explanation:

Identify the area of the truck's bed: 35 square feet.

Identify the height to which the wood chips are filled: 2 feet.

Calculate the volume by multiplying the area by the height: Volume = area * height = 35 ft² * 2 ft.

Therefore, the volume of wood chips that the truck can carry is 70 cubic feet.

The point on the graph where N ' will be located after the reflection would be C. (-2, -3).

To find the image of point N (2, -3) after it is reflected across the y-axis, you need to change the sign of its x-coordinate while keeping the y-coordinate the same.

The reflection across the y-axis essentially involves switching the point's position horizontally.

So, for point N (2, -3), its image N' will have coordinates (-2, -3).

Therefore, the point that represents N' after the reflection across the y-axis is (-2, -3) on the graph.

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Answer:

20 side polygon: 180 x (20 -2)

Step-by-step explanation:

A n side polygon can be divided into n-2 triangles

each triangle has 180°

n-2 triangles have 180 x (n-2) degrees

To find the length and width, we use the provided information and the formulas for area and length. After determining the width is 7 feet, we find the length is 42 feet. Using these dimensions, the rectangle's perimeter is 98 feet.

Given the length of the rectangle is six times its width, we can denote this as L = 6W. The area of a rectangle is given by the formula Area = Length x Width or A = LW. Substituting L = 6W into our area formula gives A = 6W^2. We're given that the area is 294 square feet, so we set our formula equal to this: 6W^2 = 294. Solving this gives W = 7 ft.

Now, we substitute W = 7 ft back into our length formula, L = 6W, giving L = 42 ft. The perimeter of a rectangle is given by the formula Perimeter = 2(Length + Width) or P = 2(L + W), therefore P = 2(42 ft + 7 ft) = 98 ft.

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Option d. There are 8,568 possible starting lineups

The number of girls n, is given as 18 and the number of players, r is 5

To find the number of possible starting lineups from 18 girls when selecting 5 players, we can use the combination formula

[tex]C(n, r) = \dfrac{n!}{r! * (n - r)!}[/tex]

Substitute the values for n and r into the equation

[tex]C(18, 5) = \dfrac{18!}{5! * (18 - 5)!}[/tex]

[tex]C(18, 5) = \dfrac{18!}{5! * 13!}[/tex]

Expand

[tex]C(18, 5) = \dfrac{18 * 17 * 16 * 15 * 14 * 13!}{5! * 13!}[/tex]

[tex]C(18, 5) = \dfrac{18 * 17 * 16 * 15 * 14}{5!}[/tex]

[tex]C(18, 5) = \dfrac{18 * 17 * 16 * 15 * 14}{5 * 4 * 3 * 2 * 1}[/tex]

C(18, 5) = 1028160/120

C(18, 5) = 8568

Answer: i think is A or B

Step-by-step explanation:

[tex]y=\frac{2}{3} x+5[/tex]

Answer:

I know it is not A because I just tried the quiz but the other answer said either A or B so I am thinking it is B. I am very Sorry if I am wrong.

Answer: Quotient means when you divided a number by another number.

Our first number will be 48 and also in this problem lets have that second "number" be x.

So 48/x is the quotient.

The quotient of 48 and x represents the mathematical operation of 48 divided by x, where x cannot equal 0.

The phrase 'the quotient of 48 and x' represents a mathematical operation which refers to dividing 48 by a certain number (x). In mathematical terms, it would be written as 48/x. For example, if x were to equal 6, the quotient of 48 and 6 would be 8, since 48 divided by 6 equals 8. It is crucial to remember, however, that x cannot be 0, as division by zero is undefined in mathematics.

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Answer:

Option(B):  [tex]\(\dfrac{15}{108}\)[/tex]   is Correct Choice.

Explanation:

To find the probability that the next movie shown at Cinemania theater is an action movie, we can use the formula:

[tex]\[ \text{Probability} = \frac{\text{Number of action movies}}{\text{Total number of movies}} \][/tex]

Given that there were 15 action movies out of 108 total movies shown last year:

[tex]\[ \text{Probability} = \frac{15}{108} \][/tex]

So, the reasonable estimate of the probability that the next movie is an action movie is:

[tex]\[ \frac{15}{108} \][/tex]

Thus, the correct choice is:

(Choice B)  [tex]\(\dfrac{15}{108}\)[/tex]

Question:

The Cinemania theater showed 108 different movies last year. Of those, 15 movies were action movies.

Based on this data, what is a reasonable estimate of the probability that the next movie is an action movie?

Choose 1 answer:

(A) [tex]$\frac{108}{93}$[/tex]

(B) [tex]$\frac{15}{108}$[/tex]

(C) [tex]$\frac{15}{93}$[/tex]

(D)[tex]$\frac{93}{108}$[/tex]

The ratio of doors to tires on each of Jack's truck is 1:2.

Each truck has 2 doors and 4 tires.

So, the ratio of doors to tires is 2:4.

Simplifying this ratio gives us 1:2.

Answer:

y = -3, x = 9

Step-by-step explanation:

step 1) subtract 4y from both sides.

x + 4y - 4y = -3 - 4y

step 2) simplify

x = -3 - 4y

step 3) substitute x = -3 - 4y

-3 - 4y + 7y = -12

step 4)  Add similar elements: -4y + 7y = 3y

-3 - 4y + 7y = -12

step 5) Add 3 to both sides

-3 + 3y + 3 = -12 + 3

step 6) Simplify

3y = -9

step 7) Divide both sides by 3

3y/3 = -9/3

step 8) you now know y = -3

step 9) substitute y = -3 in for x = -3 - 4y

x = -3 - 4(-3)

step 10) negative times a negative equals a positive

x = -3 + 12

step 11) add -3 by 12 to get x = 9

step 12) you now have found the answer x = -3 and y = 9

The question involves solving a system of linear equations using the elimination method, resulting in the solution [tex]\(x = 9, y = -3\).[/tex]

The problem provided is a system of linear equations. Here's how to solve the system:

x + 4y = -3

x + 7y = -12

Subtract the first equation from the second:

[tex]\((x + 7y) - (x + 4y) = -12 - (-3)\)[/tex]

[tex]\(3y = -9\)[/tex]

Now, solve for y:

[tex]\(y = -3\)[/tex]

Substitute y back into the first equation to find x:

[tex]\(x + 4(-3) = -3\)[/tex]

[tex]\(x - 12 = -3\)[/tex]

[tex]\(x = 9\)[/tex]

So the solution is [tex]\(x = 9, y = -3\)[/tex].

The procedure used is known as the elimination method, which is a technique to solve simultaneous linear equations.

Cia collected the most money

Jen collected the least money.

Step-by-step explanation:

Let Jen collected money = x

Mark collected money = 23x

while Cia collected money = 212 (23x)

So, we can observe that Cia and Mark collected more money than Jen as Jen money is multiplied by 23 to make Mark's money and Mark's money is multiplied by 212 to get Cia's Money.

So, Cia collected the most money

Jen collected the least money.

Answer:

cai has the most

jen has the least money

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

Answer:

30% decrease

Step-by-step explanation:

Answer: 30%

Step-by-step explanation:

Exact value =125m

Another value =87.5m

To know the decrease

=125-87.5

=37.5

To get the percentage

37.5×100/125

=30%

Answer:

y=1/3x+5/3

Step-by-step explanation:

Slope intercept form: y=mx+b

Equation given info: y=1/3x+b

Point given: (-2,1)

New equation to solve for b: 1=1/3(-2)+b

1=1/3(-2)+b

1=-2/3+b

5/3=b

Final equation: y=1/3x+5/3

Answer:

You end up at Wcdonalds

Step-by-step explanation:

The reason why you would end up at Wcdonalds is pretty simple, but first we would have to answer why the character is starting on a bench. In most stories or games a story might start with a character on a bench for multiple reasons; the character was simply napping there, or was simply sitting down for a sip of coffee, but if a story started off as such it would't grab anyone's attention. So what does that imply, simple, the character is there because he/she got mugged and then got knocked out and was placed on the bench so the author could create a feeling of suspense in the story. At this point you might be wondering, what the heck am I talking about, what does this have to do with Wcdonalds and not "Mcdonalds" - the answer is simple. After the character (animal, human, alien, whatever) wakes up they supposedly move 6 units right and 3 units up, what does that imply, it suggest that the character is inputting a famous cheat code! And what does one do after entering the famous cheat code, Mr.GameAndWatchcode00021190, they teleport to Mcdonalds! Unluckily though, the consequences of being knocked out prior to the cheat code input has made the character see the M in Mcdonalds upside down, a W!

Anyways that's the answer to your question - You're Welcome

Mark lives 5,000 feet away from school and walks at a steady rate of 250 feet per minute, so it takes him 20 minutes to walk to school.

Step-by-Step Explanation

Mark lives 5,000 feet from school and walks at a steady rate of 250 feet per minute. To calculate the time it takes for Mark to walk to school, we divide the total distance by his speed:

Time = Distance \/ Speed

Time = 5,000 feet \/ 250 feet per minute

Time = 20 minutes

Thus, Mark takes 20 minutes to walk to school from his home.

Answer:

Trends:

In the graph or a table you easily can see trends in the data, for example, parts where if x increases also does y, or things like that.

Of course you, with some mathematical knowledge, also can notice those things when you have the equation, so this is a thing that the 3 have in common.

Range:

You usually can see the whole range (all the possible y values) of your equation by looking at the graph or the data set. And obviously, if you have the equation you can easily find the range of it.

If the radius is doubled, then the area of one base of a cylinder  quadrupled and the equation is:

[tex]\boxed{A_{b1}=4\pi r^2}[/tex]

The surface area of a solid is the total area of its outer surface. For a cylinder whose radius of its circular base is [tex]r[/tex], and height [tex]h[/tex], then the surface area (S) can be calculated as:

[tex]S=\text{Surface area of base 1}+\text{Surface area of base 2}+\text{Surface area of the side} \\ \\ S=A_{b1}+A_{b2}+A{s} \\ \\ S=\pi r^{2}+\pi r^{2}+2\pi rh \\ \\ S=2\pi r^{2}+2\pi rh \\ \\ \\ Because: \\ \\ \text{Surface area of base 1}=\text{Surface area of base 2} \\ \\ \\ Where: \\ \\ A_{b1}:\text{Surface area of base 1} \\ \\ A_{b2}:\text{Surface area of base 2} \\ \\ A_{s}:\text{Surface area of the side}[/tex]

So, if the radius is doubled then the area of one base is:

[tex]A_{b1}=\pi (2r)^{2} \\ \\ A_{b1}=\pi (4r^2) \\ \\ \boxed{A_{b1}=4\pi r^2}[/tex]

Answer:

The median, because the data distribution is skewed to the right

Step-by-step explanation:

If the longer part of the box is to the right (or above) the median, the data is said to be skewed right. If the longer part is to the left (or below) the median, the data is skewed left.  The data is skewed right.  The median would be a better estimate, because one or two numbers on the high end will cause the  numbers to be skewed to the right, and the mean to be high

Answer:

Last one:

The median, because the data distribution is skewed to the right

Step-by-step explanation:

Q1: 7.5

Q2: 8

Q3: 23

Q2 - Q1 = 8 - 7.5 = 0.5

Q3 - Q2 = 23 - 8 = 15

Since Q3 - Q2 > Q2 - Q1,

data is positively (right) skewed

Skeweness occurs because of outliers therefore mean is not a suitable option. Median will provide a better description of the centre

Answer:

1,1,2,3,5,8,13

Step-by-step explanation:

The unit form of 9/4 is 1/4 + 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4.

A unitary method is a mathematical way of obtaining the value of a single unit and then deriving any no. of given units by multiplying it with the single unit.

Given, We have to express 9 divided by 4 in unit form.

We know a unit fraction is when we have 1 in the numerator.

So, 9/4 = 9×(1/4).

= 1/4 + 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4+ 1/4.

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Answer:

[tex]\frac{3x^2}{x^2-6x-7}[/tex]

Step-by-step explanation:

The first step is to find the multiplied out numerator and denominator, and then to simplify if possible. For the numerator, 3x*x=3x^2. For the denominator, (x+1)(x-7)=x^2-6x-7. This gives a final fraction of [tex]\frac{3x^2}{x^2-6x-7}[/tex]. Hope this helps!

Answer:

Rachel has to drive for 5.789 seconds

Step-by-step explanation:

The equation that represents Rachel's remaining distance is:

[tex]D=-38t+220[/tex]

When Rachel completely escaped from the explosion, she has no distance to cover.

Hence D=0.

[tex] - 38t + 220 = 0[/tex]

[tex] - 38t = - 220[/tex]

Divide both sides by -38 to get:

[tex]t = \frac{ - 220}{ - 38} [/tex]

[tex]t = 5.789[/tex]

Rachel will cover 220m in approximately 6 seconds.

The total distance she has to drive is 220m

Rachel has to drive for approximately 6 seconds to reach her destination before the building explodes.

The given equation represents the relationship between Rachel's remaining distance (D) in meters and the time elapsed (t) in seconds.

The equation is:

D = -38t + 220

To find how long the distance Rachel has to drive, we need to find the value of D when she reaches her destination, which means D = 0 (since the distance remaining will be zero when she reaches the destination).

0 = -38t + 220

Now, solve for t:

38t = 220

t = 220 / 38

t ≈ 5.79 seconds

So, Rachel has to drive for approximately 6 seconds to reach her destination before the building explodes.

The total distance she has to drive is 220m.

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Answer:

The author helps persuade readers that math is fun by showing the number devil doing math in clever ways. The author also shows how Robert becomes less afraid of math. Readers can relate to this message and might be convinced to like math more themselves.

Step-by-step explanation:

sample response

Author helps persuade readers that math is fun by showing the number devil doing math in clever ways.

Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes.

The author helps persuade readers that math is fun by showing the number devil doing math in clever ways.

The author also shows how Robert becomes less afraid of math.

Readers can relate to this message and might be convinced to like math more themselves.

Hence,  author helps persuade readers that math is fun by showing the number devil doing math in clever ways.

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