the central angle of the arc of 75

Answer:

[tex]x=-\frac{1}{2},\frac{5}{2}[/tex]

Step-by-step explanation:

1) Split the second term in [tex]4{x}^{2}-8x-5[/tex]  into two terms.

1- Multiply the coefficient of the first term by the constant term.

[tex]4\times -5=-20[/tex] to -8 and multiply to -−20?

2 and −10

3 - Split -8x as the sum of 2x and -10x.

[tex]4x^2+2x-10x-5[/tex]

2)  Factor out common terms in the first two terms, then in the last two terms.

[tex]2x(2x+1)-5(2x+1)=0[/tex]

3) Factor out the common term [tex]2x+1[/tex].

[tex](2x+1)(2x-5)=0[/tex]

4) Solve for [tex]x[/tex].

1 - Ask: When will (2x+1)(2x-5) equal zero?

When 2x + 1 = 0 or 2x - 5 = 0

2 - Solve each of the 2 equations above.

[tex]x=-\frac{1}{2},\frac{5}{2}[/tex]

The equation that satisfies the data in the table is,

y = -4x - 4 [Option D]

Definition of an Equation:

An equation is defined as a mathematical assertion in which you use mathematical symbols to demonstrate the equality of two amounts. A combination of expressions with variables and constants on either side of the equality sign make up an equation.

The (x, y) coordinates from the given table are,

(-1,0), (0, -4), (1, -8)

Now, these points must satisfy the required equation.

Considering the first point (-1, 0), if we substitute these values of x and y coordinates in y=4x-4, the equality is no longer maintained.

Similarly, (-1,0) does not satisfy the second and third equations, that are, y = -x + 4 and y = x + 4, respectively, either.

Taking the fourth equation, y = -4x - 4

Putting x = -1 in this equation, we get,

y = -4(-1) - 4

y = 4 - 4

y = 0

Likewise, this equation satisfies the rest of the data in the table too.

Therefore, y = -4x - 4 is the required equation.

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Step-by-step explanation:

[tex] {2}^{4n} \times {2}^{2n} = 512[/tex]

[tex] {2}^{4n} \times {2}^{2n} = {2}^{9} [/tex]

[tex] {2}^{4n + 2n} = {2}^{9} [/tex]

[tex]6n = 9[/tex]

[tex]n = \frac{3}{2} [/tex]

The slope-intercept formula of the linear equation is:

[tex]y = \frac{3}{7}x + 7[/tex]

A linear function is modeled by:

y = mx + b

In which:

The y-intercept is of b = 7. The line also goes through point (0,-3), hence the slope is:

m = 3/7.

Thus the equation is:

[tex]y = \frac{3}{7}x + 7[/tex]

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Step-by-step explanation:

you multiply both sides by the same factor, so that the main message or information, the ratio, stays the same :

3:6 × 2/2 = 6:12

3:6 × 1/3 / 1/3 = 1:2

3:6 × 4/3 / 4/3 = 4:8

3:6 × 100/100 = 300:600

so, these are all equivalent ratios. and there are infinitely more, as you can see.

Answer:4

Step-by-step explanation: 32\8 = 4

Normal income: 25 $

Last week's income: 25 + 20: 45 $

% = Last week's/normal = 45/25 ×100 =180 %

Answer: 4

Step-by-step explanation:

yeh

The extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.

In the question, we are given a graph showing the bird population of a large lake and are asked the reason for the extreme drop between November and December most likely represent.

Birds migrate in order to shift from low-resource regions to high-resource areas or vice versa. The two main items sought after are food and places to build nests.

Thus, the fall in the graph for the number of birds between November and December represents the migration pattern of birds, in search of new resources.

Hence, the extreme drop in the graph for the number of birds between November and December MOST likely represents a reflection of the migratory nature of the birds at the lake, making option B the right choice.

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Answer: A reflection of the migratory nature of the birds at the lake.

A survey of 969 adult investors asked how often they tracked their portfolio. The probability that an adult investor tracks his or her portfolio daily is 0.238.

From the table it is clear that the number of responses daily by the adult investors is 231.

Probability is the ration of the number of possible value to the total value.

Here the number of daily response by the adult investors = 231

The total adult investors = 969

Hence, the The probability that an adult investor tracks his or her portfolio daily = 231/969 = 0.238.

Therefore, in the total number of 969 adult investors, the probability that the investors response daily is 0.238.

Disclaimer: The question is incomplete. The following is the correct question.

Question: Recently, the stock market took big swings up and down. A survey of 969 adult investors asked how often they tracked their portfolio. The table shows the investor responses. What is the probability that an adult investor tracks his or her portfolio daily

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See below for the interpretation of the graph

From the graph, the initial values of x and y are 0

As x increases, y decreases.

This means that the first statement is

Slope is calculated as:

[tex]m = \frac{y_2 - y_1}{x_2 -x_1}[/tex]

Using the graph values at the interval x =0 to x = 3, we have:

[tex]m = \frac{-3 - 0}{3 - 0}[/tex]

m = -1

This means that the second statement is

From the graph, y = -3, when x = 3

As x increases at this point, y increases.

This means that the third statement is

Using the graph values at the interval x = 3 to x = 5, we have:

[tex]m = \frac{3 + 3}{5 - 3}[/tex]

m = 3

This means that the fourth statement is

All y values at x = 0 to x = 4 are less than 0, while all y values at x = 4 to x = 8 are greater than 0

So, the last two statements are

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The height is changing by 0.5 each minute

The question implies that we calculate the slope of the table

From the table of values, we have the following points

(0, 150) and (1, 150.5)

The slope is then calculated as:

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

This gives

m = (150.5 - 150)/(1 - 0)

Evaluate

m = 0.5

Hence, the height is changing by 0.5 each minute

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The correct option is C. Isolating a variable in one of the equations.

The first step in solving a system of nonlinear equations by substitution is to isolate a variable in one of the equations.

A set of two or more equations in two or more variables that includes at least one nonlinear equation is referred to as a system of nonlinear equations.

The method to solve a system of nonlinear equations by substitution is-

The importance of systems of nonlinear equations are-

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The complete question is-

Which is most likely the first step in solving a system of nonlinear equations by substitution?

A. Substituting a number for one of the variables

B. Substituting one equation into the other equation

C. Isolating a variable in one of the equations

D. Taking the square root of both sides of one of the equations

Answer:

Isolating a variable in one of the equations.

Step-by-step explanation:

25,110.51 is the total amount accrued over the course of 4.5 years, principle plus interest, on a principal of 16,100.00.

We may employ the compound interest future value formula provided by:

[tex]A=P(1+r/n)^{nt}[/tex]

Where A is the final amount, P stands for the current value,

r=interest rate, n represents how many times interest is compounded annually, and t represents the number of years.

In this case,

P= 16100

r = 10%

t = 4 years and 6 months=4.5 years

n=4

So, A=[tex]16100(1+0.1/4)^{4*4.5}[/tex]

A= [tex]16100(1+0.025)^{18}[/tex]

A= 25110.51

So, 25,110.51 is the total amount accrued over the course of 4.5 years, principle plus interest, on a principal of 16,100.00 at a rate of 10 percent per year compounded four times each year.

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The average rate of change in weight is 3/8.

According to the statement

Weight of baby during birth = 3 kg

Weight of baby after 8 months = 6 kg

Average rate of change of in weight is calculated by

Average rate = Increased weight - Real weight / Time period

Average rate = 6-3 / 8

Average rate = 3/8

So, the average rate of change in weight is 3/8.

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Answer:

angle x equals 25

Step-by-step explanation:

130 + 25 = 155

180 - 155 = 25

Triangles always add up to 180°

Answer:

it is so easy the answer is 25

Step-by-step explanation:

The total sum of the traingle is 180 degree. So frist add both the numbers in the traingle and then subtract it by 180 degree

Answer:

I'm sorry mate for helping for nothing but i just need more points to post my question. I am really sorry.

The fraction based on the information given illustrated for each person.

Me: $14.89

Friend 1: $7.27

Friend 2: $25.67

Friend 3: $11.59

Total = $59.42

The fraction for each person will be:

Me: $14.89 = 14.89/59.42 = 0.25

Friend 1: $7.27 = 7.27/59.42 = 0.12

Friend 2: $25.67 = 25.67/59.42 = 0.32

Friend 3: $11.59 = 11.59/59.42 = 0.195

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Circumference = 10π in, Area = 25π in²

Circumference = 19 π in, Area = 90. 25 π in²

Area = 225 π in²

Circumference = 16π

It is important to note that the formula for area and circumference are;

Area = πr^2

Circumference = 2πr

For the first column, we have

radius = 5in

Substitute the values of the radius into the formula

Circumference = 2 × π × 5

Circumference = 10π in

The area;

Area = π × 5 × 5

Area = 25π in²

For the second column,

radius = 9. 5 in

Substitute the values of the radius into the formula

Circumference = 2 × π × 9. 5

Circumference = 19 π in

Area = π × 9. 5 × 9. 5

Area = 90. 25 π in²

For the third column

radius = 15in

Substitute the values of the radius into the formula

Area = π × 15 × 15

Area = 225 π in²

For the fourth column

radius = 8 in

Substitute the values of the radius into the formula

Circumference = 2 × π × 8

Circumference = 16π

From the solved solution, we can see that the shape is a circle.

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Answer: [tex]\theta=\frac{8}{3} \text{ radians}[/tex]

Step-by-step explanation:

[tex]8=3\theta\\\\\theta=\frac{8}{3} \text{ radians}[/tex]

The p value for the difference is 0.005.

According to the statement

we have given that the 74 of 100 urban residents favor the construction while only 70 of 125 suburban residents are in favor.

And we have  to find the difference between them in proportions.

So,

X1 = 74 represent the number of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

X2 = 70 represent the number of people suburban residents are in favor

N1  = 100 sample 1 selected

N2 = 125 sample 2 selected

AND

P1 = 0.74 represent the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant

And P2 = 0.56 represent the proportion of suburban residents are in favor And z would represent the statistic (variable of interest)  

Pv represent the value for the test (variable of interest)

Here we apply the Z test to find the difference then

Z = (0.74 - 0.56) / (0.64(1-0.64)(1/100+1/125) )^1/2

Now after solving

Z = 2.795.

Now The significance level provided is  ,and we can calculate the p value for this test.  

Since is a two tailed test the p value would be:  

P = (z>2,795)

P = 0.005.

So, The p value for the difference is 0.005.

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Answer:

21:14:8

Step-by-step explanation:

X:Y=3:2

Y:Z=7:4

X:Y=21:14

Y:Z=14:8

X:Y:Z=21:14:8

Answer:

[tex]x^2+7x-8-\frac{3}{x-7}[/tex]

Step-by-step explanation:

I think this question is a bit hard to explain by typing, so I'll add an image down below.  

I used long division for this question, and the final answer is: [tex]x^2+7x-8-\frac{3}{x-7}[/tex]

Answer: Choice C

Multiply both sides of the bottom equation by 2

Reason:

The y coefficient of the first equation is 2. For the other equation, that y coefficient is -1. We need these coefficients to be equal but opposite. One way to do this is to double everything in the bottom equation

The bottom equation 12x-y = 26 doubles to 24x - 2y = 52

At this point we have the equivalent system of

[tex]\begin{cases}4x+2y = 4\\24x-2y = 52\end{cases}[/tex]

And we can see that we have equal but opposite y coefficients (2 and -2). The y terms add to 0 since 2y + (-2y) = 0y = 0 meaning we've eliminated y.

The number of quarts of orange juice did Rebecca use is 7

Given that 28 glasses with orange juice are filled for a camp breakfast

Each glass holds 1 cup of juice

We need to find the number of quarts of orange juice did Rebecca use  

We know that a quarts has 4 cups

We need to calculate the quarts from 28 glasses  

Let the number of the quarts be x

So the equation formed is

4x = 28

Where x is number of quarts and 28 are the number of glasses

x = 7

Hence the number of quarts is 7

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Answer: (0, 16)

Step-by-step explanation:

y = mx + c

c is the y intercept

from the equation, c = 16

(it's not exactly mx but you don't need to solve for x)

As a rule of thumb, when each component is selected independently from the same population, the sampling distribution of the sample percentage may be estimated by a regular probability distribution.

Therefore the main solution is- from the identical group, each component is individually chosen.

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Rearranging the equation so q is the independent variable is; q = -1.6r

We are given the expression;

-7q + 12r = 3q - 4r

Since we want to make q the subject, let us rearrange the equation with variables having q on the left and others on the right side to get;

-7q - 3q = -4r - 12r

-10q = -16r

q = 16r/10

q = -1.6r

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Answer:

C. Radius or diameter must be known.

Step-by-step explanation:

The radius or diameter must be known so you can use the formula.

Hope this helps!