When the following expression is written in simplest form, what is the coefficient of the variable term?

-2.5y + 8y - 10.5y

5.5
0
-21
-5

Answer:

6y^2+43

Step-by-step explanation:

6y^2+(19+15)

Answer:

(2y+3)(3y+5)

Step-by-step explanation:

6y^2+19y+15

Factor the expression by grouping. First, the expression needs to be rewritten as 6y^2+ay+by+15. To find a and b, set up a system to be solved.

a+b=19

ab=6×15=90

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 90.

1,90

2,45

3,30

5,18

6,15

9,10

Calculate the sum for each pair.

1+90=91

2+45=47

3+30=33

5+18=23

6+15=21

9+10=19

The solution is the pair that gives sum 19.

a=9

b=10

Rewrite 6y^2+19y+15 as (6y^2+9y)+(10y+15).

(6y^2+9y)+(10y+15)

Factor out 3y in the first and 5 in the second group.

3y(2y+3)+5(2y+3)

Factor out common term 2y+3 by using distributive property.

(2y+3)(3y+5)

Answer:

22% decrease

Step-by-step explanation:

(1100-900)/900 = .22

Answer:

\( |6| = | - 6| \)

Step-by-step explanation:

\( |6| = | - 6| \\ 6 = - ( - 6) \\ 6 = 6\)

Answer:

The first table; the first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 16, 8, 4, 2.

Step-by-step explanation:

Exponential decay means that the graph or table is exponentially decreasing. Meaning, if you went from point 4 to 1, you would see an exponential increase. Other tables show other forms of functions, such as quadratic, or linear. To find out which rate it is decaying by, ask yourself, at 0, what is the y output? You can then divide the output of 0 by 1, and so on. If it is decaying at a consistent rate, then you know it is exponential. If you do not need to divide, but know it is decaying at a rate of two, it is linear. If it does not divide the first time smoothly, it is quadratic. It could also be a number of things.

I hope this helps you. We studied this quite a while ago, and I do not remember the equation at the tip of my tongue, and I do not want to give you wrong information. Have a great rest of your day!

Answer:

the 1s options

1 16

2 8

3 4

4 2

Step-by-step explanation:

The line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1, 1), and the line segment from (1,1) to (0,1) is equal to 2/5.

What is integral?

The value obtained after integrating or adding the terms of a function that is divided into an infinite number of terms is generally referred to as an integral value.

To evaluate the line integral using Green's theorem, we need to find a vector field F = (P, Q) such that ∇ × F = Qₓ - Pᵧ, where Qₓ represents the partial derivative of Q with respect to x, and Pᵧ represents the partial derivative of P with respect to y.

Let's consider F = (P, Q) = (x²y², xy).

Now, let's calculate the partial derivatives:

Qₓ = ∂Q/∂x = ∂(xy)/∂x = y

Pᵧ = ∂P/∂y = ∂(x²y²)/∂y = 2x²y

The curl of F is given by ∇ × F = Qₓ - Pᵧ = y - 2x²y = (1 - 2x²)y.

Now, let's find the line integral using Green's theorem:

∫[C] (Pdx + Qdy) = ∫∫[R] (1 - 2x²)y dA,

where [R] represents the region enclosed by the curve C.

To evaluate the line integral, we need to parameterize the curve C.

The arc of the parabola y = x² from (0, 0) to (1, 1) can be parameterized as r(t) = (t, t²) for t ∈ [0, 1].

The line segment from (1, 1) to (0, 1) can be parameterized as r(t) = (1 - t, 1) for t ∈ [0, 1].

Using these parameterizations, the region R is bounded by the curves r(t) = (t, t²) and r(t) = (1 - t, 1).

Now, let's calculate the line integral:

∫∫[R] (1 - 2x²)y dA = ∫[0,1] ∫[t²,1] (1 - 2t²)y dy dx + ∫[0,1] ∫[0,t²] (1 - 2t²)y dy dx.

Integrating with respect to y first:

∫[0,1] [(1 - 2t²)(1 - t²) - (1 - 2t²)t²] dt.

Simplifying:

∫[0,1] [1 - 3t² + 2t⁴] dt.

Integrating with respect to t:

[t - t³ + (2/5)t⁵]_[0,1] = 1 - 1 + (2/5) = 2/5.

Therefore, the line integral ∫[C] (Pdx + Qdy) over the given curve C consisting of the arc of the parabola y = x² from (0,0) to (1,1), and the line segment from (1,1) to (0,1) is equal to 2/5.

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Answer:

1.{2,8}

Step-by-step explanation:

that's my answer

Answer :

1. { 2, 8 }

x² - 10x + 16 = 0

x² - 2x - 8x + 16 = 0

x ( x - 2 ) - 8 ( x - 2 ) = 0

( x - 2 ) ( x - 8 ) = 0

x - 2 = 0

x = 2

x - 8 = 0

x = 8

Therefore,

the solution to the equation x² - 10x + 16 = 0 is { 2, 8 }.

Answer:

53

Step-by-step explanation:

In statistical experiments, each time the experiment is repeated, a different outcome may occur. The correct answer is C.

Statistical experiments involve random processes, such as the random selection of individuals from a population, the random assignment of subjects to groups, or the random measurement of a variable.

The outcome of a statistical experiment is influenced by chance and is inherently uncertain, so it is not possible to guarantee that the same outcome will occur every time the experiment is repeated. Different outcomes may occur, even if the experimental conditions are kept constant, due to the random nature of the processes involved.

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Answer:

9

Step-by-step explanation:

i can not really tell what letters are on the picture but i think it is 9

John will clean the house for 5/2 = 2.5 hours.

What is quadratic equation?

The polynomial equation whose highest degree is two is called a quadratic equation or sometimes just quadratics. It is expressed in the form of:

ax² + bx + c = 0

where x is the unknown variable and a, b and c are the constant terms.

Given, that John cleans the house 2 hours more than Jane.

Let x be the time taken by the Jane and x +2 be the time taken by John.

Total they work for 2 hours 24 minutes

first we will convert minutes into hours, 24/60

= 2.4 hours

Let time taken by John = 1/x+2

time taken by Jane = x

1/x + 1/(x+2) = 2.4

Taking lcm,

x+x+2 = 2.4(x)(x+2)

2x +2 = 2.4\(x^{2}\) +4.8x

2.4x\(x^{2}\)+2.8x -2 = 0

On solving it,

x = \(\frac{b-\sqrt{b^{2-4ac} } }{2a}\)

x = 1/2 and x = -5/3

only x = 1/2 is possible value.

Time taken by John = 1+1/2

=5/2

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A figure has a surface area of 496 m². If the dimensions are doubled by half, the surface area of the new figure is 124 m².

Firstly, we will assume it being a rectangle then calculate the new area using the formula and then we will put the values of original figure into new figure.

Assume we're working with a rectangle. We know that the area equals the length (l) multiplied by the width (w).

A = l x w

If we divide the dimensions in half, we get A = (1 / 2)l x (1 / 2)w.

A = (1 / 4) × (l  x w)

As a result, the new surface area would be one-quarter of the original:

\(A_{original}\) = 496 m²

\(A_{new}\) = (1/4) × \(A_{original}\)

\(A_{new}\) = (1 / 4) × (496)

\(A_{new}\) = 124 m²

As a result, the new area would be 124 m².

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The equivalent expressions are given as follows:

The general format of the exponential expression is given as follows:

\(a^{\frac{n}{m}}\)

To obtain the radical form, we have that:

Hence the radical form of the exponential expression is given as follows:

\(a^{\frac{n}{m}} = \sqrt[m]{a^n}\)

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Answer: -3, 9√, pi, 49√

Step-by-step explanation:

Having the check beside a number, ex: 49√, shows that something squared, in other words multiplied by itself, equals this. In this example it would be 7. For, 7*7=49. For 9√ it would be 3. Pi is 3.14. Listing these out we have:

-3, 3.14, 3, 7. Let's order this...

-3 is the least, then 3, then 3.14 (slightly bigger than 3), lastly, 7.

Answer:

k is the option that makes sense

Answer:

The factored form is,

\((4a^2+2a+1)(4a^2-2a-1)\)

Step-by-step explanation:

We have,

\(16a^4-4a^2-4a-1\\factoring,\\We\ can \ write \ 16a^4 \ as \ (4a^2)^2\\Also,\\then we have,\\(4a^2)^2-(4a^2+4a+1)\\Now, 4a^2 + 4a + 1 \ is \ a \ perfect \ square,\\4a^2 + 4a + 1 = (2a)^2 + 2(2a) + 1\\= (2a + 1)^2\\so, we \ have,\\(4a^2)^2 - (2a + 1)^2\\\)

Using the difference of square formula,

\(x^2 - y^2 = (x+y)(x-y)\\with,\\x = 4a^2,\\y = 2a+1,\\we \ get,\\(4a^2+2a+1)(4a^2-2a-1)\)

Which is the factored form,

If an interval estimate is said to be constructed at the 90 confidence level, the confidence coefficient would be 0.9.

Confidence level:

Confidence level means the proportion or frequency of acceptable confidence intervals that contain the true value of the unknown parameter.

For example,

A 0% confidence level means you have no faith at all that if you repeated the survey that you would get the same results.

Confidence Coefficient:

Confidence coefficient states the confidence level stated as a proportion, rather than as a percentage.

For example, if you had a confidence level of 99%, the confidence coefficient would be .99.

Given,

Here we know that the confidence level is 90%, now we have to find the confidence coefficient of it.

Based on the definition,

The confidence coefficient for 90% confidence level is 0.9.

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Answer:

p=8^9

Step-by-step explanation:

The following statements are true:

Segment DEF is parallel to ABC

The line segment  AB is parallel to DE

Line FC is parallel to AD

the line that is skewed to DE is BC

One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.

The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)

Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;

DEF is parallel to ABC

CADF is parallel to CBEF

For the lines, the lines that are parallel to each other are:

AD is parallel to BE

AB is parallel to DE

FC is parallel to AD

Skew lines are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC

The missing image is attached with the answer below.

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Answer:

2.4

Step-by-step explanation:

all you have to do is divide 12 by 5

Answer:

198/0.33= 600

Step-by-step explanation:

Answer:

distribute 3 into the parenthesis

The answers that describe the quadrilateral DEFG area rectangle and parallelogram.

The correct answer choice is option A and B.

A quadrilateral is a parallelogram, which has opposite sides that are congruent and parallel.

Quadrilateral DEFG

if line DE || FG,

line EF // GD,

DF = EG and

diagonals DF and EG are perpendicular,

then, the quadrilateral is a parallelogram

Hence, the quadrilateral DEFG is a rectangle and parallelogram.

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To perform a two-sample t procedure, we need to determine the degrees of freedom. In this case, we have two simple random samples drawn from a normal population, with sample sizes of 75 and 25.

The degrees of freedom for a two-sample t procedure can be calculated using the formula:
df = (n1 - 1) + (n2 - 1)
where n1 and n2 represent the sample sizes of the two groups.

For this example, we have a sample size of 75 for one group and 25 for the other. Plugging these values into the formula, we get:
df = (75 - 1) + (25 - 1)
  = 74 + 24
  = 98
Therefore, the degree of freedom for this two-sample t procedure is 98.

In summary, when two simple random samples of size 75 and 25 are drawn from a normal population, we can use 98 degrees of freedom to perform a two-sample t procedure.

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This circular swimming pool has 4595  ft³ of water in it.

According to what is said, the depth grows linearly from 2 feet at the south end to 7 feet at the north end and remains constant along east-west lines.

The given data in the question-

Diameter of  circular swimming Pool; d = 30 ft

Radius r = d/2 = 30/2 = 15 ft

The average depth is given as;

avg (h) = (4 + 9)/2

avg (h) = 6.5 ft

Formula for circular area is;

A = πr²

Put the values;

A = π × 15²

A = 225π

Formula for circular volume is;

Volume = Area × depth

Volume = 225π × 6.5

Volume = 4594.57 ft³

Rounding to a whole number;

Volume =  4595 ft³

Thus, this circular swimming pool has 4595  ft³ of water in it.

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Answer:

8sin(2x).

Step-by-step explanation:

2sin(x)cos(x) = sin(2x)

So 16sin(x)cos(x)

= 8* 2sin(x)cos(x)

= 8sin(2x).

Answer:

| x-3| >1:

x>4 or x<2

| 2x+5 | >0.5 :

x > −2.25 or x < −2.75

| 0.2x+3.5 | > 1.7:

x > −9 or x < −26

| x+3 | <1:

x < −2 and x > −4

| 2x+5 | <0.5

x < −2.25 and x > −2.75

| 0.2x+6 | <0.15

x < −29.25 and x > −30.75

| x+5 | >-1

x > −6 or x < −4

| 2x+3 | <-1

No solutions.

| 0.7x +5 | >6.7

x>2.428571 or x<−16.714286

if they are similar triangles this means that the relation between the segments RP-FH and GF-RQ

so the first relation is:

so the secon relation will be:

So the solution is numeral B)

Answer:

1/p⁵

Step-by-step explanation:

Answer:

\( V = \pi r^2 h\)

And for this case the value for the height is \( h = 10.7 in\) the diameter is provided \( D = 2r = 8.1 in\) so then the radius is given by:

\( r = \frac{D}{2}=\frac{8.1 in}{2}= 4.05 in\)

Then we can find the volume with the first formula and replacing we got:

\( V = \pi (4.05in)^2 (10.7 in)= 551.4 in ^3\)

The final answer for this case would be 551.4 cubic inches

Step-by-step explanation:

The volume for a right circular cone is given by this formula:

\( V = \pi r^2 h\)

And for this case the value for the height is \( h = 10.7 in\) the diameter is provided \( D = 2r = 8.1 in\) so then the radius is given by:

\( r = \frac{D}{2}=\frac{8.1 in}{2}= 4.05 in\)

Then we can find the volume with the first formula and replacing we got:

\( V = \pi (4.05in)^2 (10.7 in)= 551.4 in ^3\)

The final answer for this case would be 551.4 cubic inches

Answer V:183.8^3 previous answer is wrong