which of the following is a polynomial expression a. 2^x + x + 3 b. x^2 + 2x + 7 or c. 1/x + 1/x2 + 1/x3 ( btw the ^2 means it’s squared ) please answer

It is -1, at least thats what i got i hope this helped

The slope of a line can be found, given two points, as follows:

[tex]P_{1}(-5.5,6.1) \\ \\ P_{2}(-2.5,3.1) \\ \\ m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}} \\ \\ m=\frac{3.1-6.1}{-2.5-(-5.5)}=-1[/tex]

So this slope tells us the direction of a line and represents the vertical change divided by the horizontal change.

d because 0.7 is larger than 0.007

Remark

On the right, the deposits will build up and the river will have trouble depositing more material and still follow the path it is on. Eventually the river will want to take a short cut across the narrowest part or the neck.

Usually during flooding the water will cut across the narrowest part and an oxbow lake is formed. I think you are intended to answer B, but 50 years may not be enough time in which case D is the answer.

If you have notes on this event, find out what they say. I will choose B, but if you agree don't be surprised if it is D.

As written, the inequality has a negative coefficient for the variable n. It can be convenient to add the opposite of the right side of the inequality to both sides, so the comparison is to zero:

... 25 +3(4n -3) > 0

... 25 + 12n -9 > 0 . . . . . . eliminate parentheses using the distributive property

... 12n + 16 > 0 . . . . . . . . . collect terms

... n + 4/3 > 0 . . . . . . . . . . divide by 12*

... n > -4/3 . . . . . . . . . . . . add the opposite of the constant (first of answer choices)

_____

6w -8 ≥ 22 . . . . . . . given

6w ≥ 30 . . . . . . . . . add 8

w ≥ 5 . . . . . . . . . . . .divide by 6* (second of answer choices)

_____

* When solving inequalities, solution can proceed in the same way it does for solving equations, with one exception. When multiplying or dividing by a negative number, the direction of the comparison changes. Consider the inequality

... 1 < 2

Now, see what happens when we multiply by -1:

... -1 > -2

You may note that we were always dividing by a positive number in the solutions above. That is intentional. In other words, we specifically chose the solution method for problem 3 so that we would avoid dividing by a negative number.

For quadratics, these formulas are used mainly for factoring.

Your equation can be written as ...

... 2(x² +2x -3) = 0

You factor this by looking for factors of -3 (c=x1·x2) that add to give +2 (b=-(x1+x2)). These are {-1, +3}, so the factorization is ...

... 2(x -1)(x +3) = 0

The roots are then 1 and -3, which sum to -b = -2.

(You will note that the numbers used in the binomial factors are the opposites of the roots x1 and x2 in the Viete's Formulas. That is how we can look for them to sum to "b", rather than "-b".)

The slope of y = -x is m = -1.  Thus, starting with the slope-intercept form y = mx + b, we substitute -1 for m, 8 for x and 2 for y, to determine the vaue of b:

2 = -1(8) + b, or 10 = b.  Then the equation of the line parallel to y = -x and passing thru (8,2) is:

y = -x + 10.

co·ef·fi·cient

ˌkōəˈfiSHənt/Submit

noun

1.

MATHEMATICS

a numerical or constant quantity placed before and multiplying the variable in an algebraic expression (e.g., 4 in 4x y).

So your answer is 3

3 because the number 3 in 3x is a coefficient and the x is the variable.

hope that helps :)

Answer:

 So the water level of pond reduces by 8.16 centimeter over 25.5 days.

Explanation:

 Average change in pond's water level = -0.32 centimeter.

 Duration considered for taking the average of change in pond's water level = 25.5 days.

 Total change in the pond's water level = -0.32*25.5 = -8.16 centimeter

So the water level of pond reduces by 8.16 centimeter over 25.5 days.

The only factorial expression that is shown properly evaluated is that of selection A.

_____

If you number the terms starting from 0 on the left, you find that 20 is term #3 on the row that has 6 as term #1. In combination notation, this would be

... 6C3 or C(6, 3)

It is computed as

... 6!/(3!·(6-3)!) = 6·5·4/(3·2·1) = 20

Answer:

(-2.5, ∞)

Step-by-step explanation:

You can add the opposite of the right side.

5.1(3 +2.2x) +14.25 +6(1.7x +4) > 0

15.3 +11.22x +14.25 + 10.2x +24 > 0 . . . eliminate parentheses

21.42x +53.55 > 0 . . . . . . . . . . . . . . . . . . collect terms

x + 2.5 > 0 . . . . . . . . . . . . . . . . . . . . . . . . .divide by the coefficient of x

x > -2.5 . . . . . . add the opposite of the constant

(- 2.5, ∞ )

distribute parenthesis on both sides of inequality and simplify

15.3 + 11.2x > - 14.25 - 10.2x - 24

15.3 + 11.2x > - 38.25 - 10.2x ( add 10.2x to both sides )

15.3 + 21.42x > - 38.25 ( subtract 15.3 from both sides )

21.42x > - 53.55 ( divide both sides by 21.42 )

x > - 2.5

solution x ∈ (- 2.5, ∞ )

Answer:

286.1 people per mile^2

Step-by-step explanation:

there are 11.69 million people in ohio

and ohio is 44,825 mi^2

so if you do 11.69 million / 44,825 = 268.1

Population density is calculated by dividing the population of an area by its size. The actual population density of Ohio can vary from estimates due to factors like population changes and migration. Researchers use various methods to calculate population size and density, especially for large areas.

The subject of this question deals with population density, which in the context of geography, refers to the number of people per unit of area. To calculate the population density of Ohio, you would need to first find the actual area of Ohio, and then find the actual population of Ohio. Once you have these two pieces of information, you can calculate the population density by dividing the population by the area. The difference between your initial estimate and the actual population density could be due to various factors, such as fluctuations in population size, migration patterns, or changes in the area's ">demographic data.

Population size can often be estimated using life tables, but this can be a complex process. A straightforward way to estimate population size is to count all the inhabitants in a certain area. However, for large areas like Ohio, this isn't always feasible, which is why researchers often use other methods or statistics to make these estimations. Understanding how population densities are calculated and how they can vary is important in fields like urban planning, sociology, and environmental science.

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We have a rectangular garden. The length of the garden is 7 feet longer than its width.

Lets say the width of the garden is 'x' feet. So, the length of the garden must be [tex](x+7)[/tex] feet.

Length [tex]=(x+7)[/tex] feet

Width [tex]=x[/tex] feet

We have been given that the perimeter of the garden is 186 feet.

Now as we know that the perimeter of the rectangle is:

[tex]2(length+width)[/tex]

Plugging the values of length and width in the equation, we get:

Perimeter [tex]= 2((x+7)+x)=2(2x+7)=4x+14[/tex]

We know that perimeter of the garden is equal to 186 feet,

So,

[tex]186=4x+14[/tex]

Solving for 'x' we get:

[tex]4x+14=186[/tex]

[tex]4x=186-14=172[/tex]

[tex]x=\frac{172}{4} =43[/tex]

We had assumed that the width of the garden is 'x' feet and now that we have the value of 'x'. We can say that:

The width of the rectangular garden is 43 feet.

The width of the garden is found by using the perimeter formula for a rectangle and the given information that the length is 7 feet longer than the width. Solving the resulting equation gives a width of 43 feet.

To find the width of the garden, we use the fact that the perimeter (P) of a rectangle is given by the formula P = 2l + 2w, where l is the length and w is the width. We are told that the length is 7 feet longer than the width, so we can express the length as w + 7. Substituting the given perimeter of 186 feet, we set up the equation as follows: 186 = 2(w + 7) + 2w. Simplifying further, we get 186 = 4w + 14. Subtracting 14 from both sides gives us 172 = 4w and dividing both sides by 4, we find w = 43. Therefore, the width of the garden is 43 feet.

Answer: The answer is 40

Step-by-step explanation:

Answer:

1/8

Step-by-step explanation:

The relations can be written as ...

... blue = (3/5)×shirt

... sale = (5/8)×blue

... medium = (1/3)×sale

Substituting, we get

... medium = (1/3)×((5/8)×((3/5)×shirt)) = (1·5·3)/(3·8·5) × shirt = (1/8)×shirt

_____

1/8 of the shirts in the shop are medium blue T-shirts on sale.

Answer:

[tex]12a^{3}-15a^{2}+36a[/tex]

Step-by-step explanation:

To solve this problem you must apply the procccedure shown below:

1. You have the following expression:

[tex]3a(4a^{2}-5a+12)[/tex]

2. Then, you must apply the Distributive property. In other words, you need to multiply [tex]3a[/tex] by each term inside the parentheses.

3. You need to remember the properties of exponents. When you have equal base, you only need to multiply the coefficients, write the base and add the exponents. Therefore, you have:

[tex]3a(4a^{2}-5a+12)=12a^{(2+1)}-15a^{(1+1)}+36a=12a^{3}-15a^{2}+36a[/tex]

Answer:

The answer will be 3.55

Step-by-step explanation:

Answer:

3.55

Step-by-step explanation:

26.30 - 22.75 = 3.55

So, you got it right.

[tex]Echy[/tex]

We need to find the unit price of each box.

So, a box that weighs 30 Oz costs $4.50.

lets say that 30 Oz box is named box 1. We can use unitary method to find out the unit price of box 1.

Unitary method is a process to find the value of a single unit.

Now,

30 Oz costs $4.50

therefore, 1 Oz should cost:

[tex]\frac{4.50}{30} =0.15[/tex] dollars

So, the unit price of box 1 is $0.15.

Now, lets say the 20 Oz box is named box 2. Again we can use unitary method to find out the unit price of box 2.

Now,

20 Oz box costs $3.60

therefore, 1 Oz should cost:

[tex]\frac{3.60}{20} =0.18[/tex] dollars

So, the unit price of box 2 is $0.18.

- 3, - 9.6 and - 22.8

to generate the first, fourth and tenth term substitute n = 1, 4, 10 into the rule

a(1) = - 3 + 0 = - 3

a(4) = - 3 - 6.6 = - 9.6

a(10) = - 3 - 19.8 = - 22.8

Angle 1 is in the northwest corner of the intersection of lines. Other (corresponding) angles that are in the northwest corner are ∠5, ∠9, and ∠13.

The appropriate choice is ...

... ∠5 and ∠13

- a³m³

each term inside the parenthesis is raised to the power of 3

note that (- 1 )³ = - 1, thus

(-am)³ = - a³m³

The equation of a parallel line will have the same x-term, but a different constant (y-intercept). The required value can be found by putting the given point values in to the equation to see what it needs to be.

... y = 5x + ___

... 8 = 5·4 + ___

... 8 - 20 = -12 = ___

Your equation is ...

... y = 5x -12

m∠3 + m<6 = 180

Given: m∠6 = 75°

so

m<3 + 75°= 180°

m<3 = 105°

Answer:

Here is the answer! Hope I helped! Have a nice day! Really helpful for k12 users! And sorry I am late!!!!

Step-by-step explanation:

Answer:

x intercept is the point (0.3, 0)

Step-by-step explanation:

Just read it off the graph The line passes through the horizontal x axis halfway between 0.2 and 0.4  which is  0.3. Here x = 0.3 and y = 0.

the x-intercept is the point where the line crosses the x- axis.

From the graph this is where x = 0.3 or (o.3, 0 )

Answer:

B. 120

Step-by-step explanation:

2cos x + 1 = 0

2 cos x = -1

cos x = -1/2

x = cos^1(-1/2)

(cos inverse (-1/2))

x = 120°

Short answer: you don't.

The linear term in the numerator of the integral means the form shown is not applicable. Rather, you perform the integration using partial fraction expansion.

[tex]\displaystyle\int{\frac{5x+1}{25x^2+60x-13}}\,dx=\int{\frac{5x+1}{(5x-1)(5x+13)}}\,dx\\\\=\frac{1}{35}\int{\frac{5}{5x-1}}\,dx+\frac{6}{35}\int{\frac{5}{5x+13}}\,dx[/tex]

The integral is ...

... (1/35)ln|5x-1| +(6/35)ln|5x+13| +C

_____

If the numerator of your integral were a constant, then the fractions multiplying the separate partial fraction integrals would have the same magnitude and opposite signs. You would end with the difference of logarithms, which could be expressed as the log of a ratio as shown in your problem statement.

c = 2b

a = [tex]2\sqrt{3}[/tex]

b = ?

Use Pythagorean equality:

[tex]c^2 = a^2 + b^2\\b^2 = c^2 - a^2\\b^2 = 4b^2 - 12\\b^2 = 4\\[/tex]

b can be only positive so the solution is b=2

Answer:

B. (2a +3b)(4a -c)

Step-by-step explanation:

Group the terms pairwise, then factor each pair.

... (8a² -2ac) +(12ab -3bc)

2a is a common factor in the first pair of terms; 3b is a common factor in the second pair of terms. We can factor those out.

... = 2a(4a -c) +3b(4a -c)

Then we see that (4a-c) is a common factor in the result. We can factor that out.

... = (2a +3b)(4a -c) . . . . matches selection B

Answer:

The equation that can be used to solve for a is 1 = a(0=1)²-3.

Explanation:

In this case, I would model the parabola in vertex form.  Vertex form is y = a(x-h)²+k, where (h,k) is the vertex of the parabola.  Using the information from the question, we can plug in values to get 1 = a(0+1)²-3.  (This could be simplified as 1 = a(1)²-3 ⇒ 1 = a-3 ⇒ a = 4, but we are only interested in finding the equation that can solve for a.)

Answer:

The correct answer is A, 1 = a(0 + 1)^2 – 3

Step-by-step explanation:

The verified guy made a typo, putting = instead of + :P

Adam will be 14, and it is 8 more than 6.

We have given that,

Adam is three years younger than twice bobs age. in 5 years Adams's age will be 8 years more than bobs age.

We have to determine the what are their 2 ages.

The age of majority is the age when children legally become adults.

Adam is 9 years old and Bob is 6.

Twice Bob’s age is 12, and three years younger than that is 9.

If Adam is 9 now then in five years, Adam will be 14, which is 8 more than 6.

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