Factor this trinomial x^2+8x+12

62 + 35 = 97

62 represents the people who think the education helped them grow personally

35 represents the people who somewhat believe it helps them develope specific skills in the work place.

93 in total were interviewed for the "helping them grow personally" question

84 in total for the question that talkings about helping the people develop specific skills and knowlege

93 + 84 = 177

If 97 of those people believe the college degree was useful personally and somewhat useful for learning specific skills, we have to find what is 97 of 177 as a percentage.

54.802259887 rounded is 54.8%

Which means 54.8% of college graduates believe their education was useful for helping them grow personally but not useful for developing specific skills.

the general formula of a parabola is

we can replace the the points to find a,b and c

First (0,4)

Then (-5,1.5) and c=4

Answer:

The first one is a function but the second one is not.

Step-by-step explanation:

Using the vertical line test, we can check if the graphs are a function or not. Every vertical line can only touch a graph once in order for the function to pass the Vertical Line Test. If a graph passes the Vertical Line Test, it's the graph of a function. The first one has no points intersecting each other if you draw a vertical line for each point. However, if you draw vertical lines for the second graph, the points vertically intersect each other, making it not a function.

[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{2}{3} x + 9[/tex]

____________________________________

[tex] \large \tt Solution \: : [/tex]

The given equation is :

[tex]\qquad\displaystyle \tt \rightarrow \: 8x + 12y = 108[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: 12y = 108 - 8x[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = \frac{108}{12} - \frac{8}{12} x[/tex]

[tex]\qquad\displaystyle \tt \rightarrow \: y = - \frac{2}{3} x + 9[/tex]

That's the required equation, with slope (m) = -2/3 and y - intercept = 9

Answered by : ❝ AǫᴜᴀWɪᴢ ❞

Answer:

n + 4

Step-by-step explanation:

n is being used to describe the position of a term.

We can see that the sequence is increasing linearly by 1.

Since the position of the next term is increasing linearly by 1, all we have to do is look at the first term and subtract 1 from it to get our constant (4).

An equation to think about this better would be

n + C = S

C is the constant we are solving for.

We know n = 1.

S is the number corresponding in the sequence with n.

1 + C = 5

Subtract 1 from both sides to isolate C.

C = 4

1 + 4 = 5  Checks out

n + 4

You don't need to include the equals sign because the problem asks for an expression which doesn't contain an equals sign unlike an equation.

The value of the card in 2005 is $15.49.

A mathematical equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

When he retired in 1999 his card was worth $7.81 but the value has increased by $1.28 each year since then.

Therefore, the value of the card in 2005 will be:

y = 7.81 + 1.28x

where x = number of years

From 1999 to 2005 is 6 years. This will be:

= 7.81 + 1.28x

= 7.81 + 1.28(6)

= 7.81 + 7.68

= 15.49

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Answer: 1 angle is 144° and the other angle is 36°

Step-by-step explanation:

To find the smaller angle you would do:

1. x+4x=180

2. 5x=180

3. x=36

Then for the larger angle it would be 36×4=144

Chester made 9 sales and Vickie made 16 sales this week

Base salary of Vickie = $70

Vickie's commission per sale = $24

Base salary of Chester = $142

Chester's commission per sale = $9

Both people earned the same amount this week. Let x represent the number of sales made by Vickie, then sales made by Chester is x+7

Formulating the equation we get:

Base salary of Vickie + Vickie's commission per sale*Number of sales = Base salary of Chester + Chester's commission per sale*Number of sales

= 70 + 24x = 142 + 9(x+7)

70+24x = 142+9x+63

70+24x = 205+9x

15x = 135

x = 9

Chester sales = 9

Vickies sales = 9+7 = 16

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The false statement about the statement is (a) If you subtract 6 from b, it will be less than or equal to a.

From the question, the inequality is given as

y > x - 6

The ordered pair is given as

(a, b)

The above ordered pair implies that

(x, y) = (a, b)

So, we have

x = a and y = b

This means that

b > a - 6

Subtract 6 from both sides

b - 6 > a - 6 - 6

Evaluate

b - 6 > a - 12

Using the above as a guide, we cannot determine the direct relationship between variables a and b.

However, it is false that b is less than a

Hence, the false statement is (a)

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Complete question

The ordered pair (a,b) satisfies the inequality y > x - 6

Which statement is NOT true?

A. If you subtract 6 from b, it will be less than or equal to a.

B. If you add 6 to a, it will be greater than b.

C. a is greater than b.

D. If you add 6 to a, it will be less than b.

The explicit formula and the recursive formula are aₙ₋₁ +  200 and the rest is mentioned below.

A formula can be either recursive or explicit. The main difference between Recursive and Explicit is that Recursive formula gives the value of a specific term based on the previous term while Explicit formula gives the value of a specific term based on the position.

Given : a₁ =  -26, a₂ = 174, a₃ = 374, a₄= 574

The common difference that is d can be found out by

thus d = a₂ - a₁ = 174 -(- 26 ) = 174 + 26 = 200

And this is same for all the numbers of this particular sequence.

Thus aₙ = aₙ₋₁ + d

            = aₙ₋₁ +  200

Recursive formula :  aₙ₋₁ + d

That is the following sequence will have a common difference of 200 and the next 5th, 6th, 7th and nth term is going to be .

774 , 974 ... etc

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The approximate diameter of the circle is 5.77 cm

Given that :

area of circle = 28.3 cm²

How is Area of circle is calculated ?

Area of circle is calculated using formula :

A= πr²

where "π" represents 3.14 and r is radius. So now, according to given information,

Where Pi = 3.14

Hence,

A= πr²

Substitution the value of A in above formula :

28.3 = πr²

28.3 = 3.14r²

r² =28.3/3.14

r² =8.323

√r²=√8.323

r = 2.885

r = 2.885 cm Approximately.

d = 2r

d = 5.77 Approximately.

Therefore, the diameter of the circle is 5.77 cm

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Least possible value of m and n are 6 and 10.

Given a perfect square is an integer that is also square of an integer.

The given m and n are positive integers such that mn > 15.

To find out the least possible value of mn;

As given 15mn is a perfect square.

[tex]\sqrt{15mn}[/tex] is to be an integer.

[tex]\sqrt{15mn} = \sqrt{5*3*m*n}[/tex]

Now, insert m = 3, n = 5;

⇒ [tex]\sqrt{5*3*m*n} = \sqrt{5^2* 3^2} = 15[/tex]

but it is mn < 15.

So, assume m = 3 * 2, n = 5 * 2;

⇒ [tex]\sqrt{5*3*m*n} = \sqrt{5*3*3*2*5*2} = \sqrt{5^2*3^2*2^2} = 30[/tex]

30 it is an integer.

As we solved that the least possible value of m and n are 6 and 10.  

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Answer:f(x)=x8−8x6+19x4−12x3+14x2−8x+9=x8−8x6+16x4+3x4−12x3+12x2+2x2−8x+8+1

which allows us to rewrite f(x) as

f(x)=x4(x2−4)2+3x2(x−2)2+2(x−2)2+1

The first three terms are clearly non-negative, and each reaches their minimum of 0 at x=2 (the first term also has a minimum at x=−2). Thus, the minimum of f(x) must be 1.

This can't really be generalized. (I mean, you can apply the approach generally, but it won't generally give you such a convenient result.) I'm not sure I would have looked for this decomposition of f(x) except for the presence of the question.

Step-by-step explanation:

Answer: 62.752

Step-by-step explanation: 78.44$ - 20% = 62.752

The solution of the given inequality would be x = 4. the graph of the given inequality is attached below.

If the equation or inequality contains variable terms, then there might be some values of those variables for which that equation or inequality might be true. Such values are called solution to that equation or inequality. Set of such values is called solution set to the considered equation or inequality.

Given the inequality as |8x−8|≤24.

For solving the given expression,

|8x−8|≤24

We can consider the expression as;

8x−8 = 24

8x = 24 + 8

8x = 32

x = 32/8

x = 4

Hence, the solution of the given inequality would be x = 4.

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Answer:

  x = 4

Step-by-step explanation:

You want the equation of a line that goes through point (4, 0) and has an undefined slope.

The slope of a line is the ratio of "rise" to "run." When the "run" is zero, the ratio involves division by zero, which results in the value "undefined." That is, a line with undefined slope has a "run" of zero, meaning it is a vertical line.

The equation for a vertical line is ...

  x = c . . . . . where c is some constant

We want the line to go through a point that has x-coordinate = 4, so that constant must be 4.

The equation is x = 4.

Answer:

23.01

Step-by-step explanation:

743.22-312.29-36.7-6.26

=387.97

410.98-387.97

=23.01

He has mowed the law before he makes a total of Dollar 300, The number of times he has to mow a lawn is 10

Joe mows a lawn, for which he charges = $ 30

Some one-time cleanup work, for which he is paid = $ 60

According to the question:

He has to mow the lawn before he makes a total of Dollar300

Number of times he has to mow a lawn =   300 /  30

The number of times he has to mow a lawn = is 10

He has mowed the law before he makes a total of Dollar 300, 10 times.

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Through hypothesis testing, it can be explained that Type I error occurs when the allergist determines that the percentage of the population who are allergic to some cheese products is at least 30% when it is actually less than 30%. Similarly, Type II error occurs when the allergist assumes that the percentage of the population who are allergic to certain cheese products is less than 30% when it is actually at least 30%

There are two possible outcomes for hypothesis testing, which leads to two different sorts of conclusion-related errors. This is due to the possibility that the estimated value of the measure and the inference made about the population measure from the samples could diverge.

Let's say an allergist wants to investigate the claim that at least 30% of the population has a cheese allergy.

Let p represent the actual percentage of the population that were allergic to certain cheese products.

The following is how the hypotheses are put forth:

[tex]H_{0}:p < 0.3\\H_{a}:p\geq 0.3[/tex]

The two types of errors that can be committed by the allergist can be described as below:

(a) Type I error:

When the null hypothesis is assumed to be true when it is actually false, type I error arises.

When an allergist determines that the percentage of the population who are allergic to some cheese products is at least 30% when it is actually less than 30%, type I mistake has been committed.

(b) Type II error:

When the null hypothesis is unsuccessfully rejected even when it is false, type II error has occurred.

When an allergist assumes that the percentage of the population who are allergic to certain cheese products is less than 30% when it is actually at least 30%, type II error has occurred.

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slope of the rode is 0.015.

What is slope of line ?

Slope of line is the angle made by the line from positive x-axis in anticlockwise direction, it also denoted the steepness of the line.

The point with coordinate having same slope as with given coordinates can be plotted on the same line.

Here, it is given that :

When driving up a certain hill, we rise 15 feet for every 1000 feet that is :

for 15 feet up = 1000 feet forward

Now,

slope = upward distance / horizontal distance covered

slope = 15/1000

slope = 0.015

slope is a unitless quantity.

Therefore, slope of the rode is 0.015.

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Ratio compares the number of shaded to the total number of sections is 1/2

Given- diagram

Find- ratio of shaded sections to total number of section

Shaded sections =4

total sections =8

Hence, Shaded sections: total sections.

= 4: 8

=4/8

=1/2

Hence,

1/2

A solid's cross section is a plane figure formed when the solid intersects another plane. As a result, the cross section of an object is an infinitesimal "slice" of a solid, and it can vary depending on how the slicing plane is oriented.

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Answer:

y=-1/4x-6

Step-by-step explanation:

it hit -6 on the y axis

And it is jumpin by 4 going down

So -4 is the x axis

The amount Patricia paid as fees on on the account last year was $226.25

What makes up the total cost for Patricia?

Patricia pays a fixed monthly maintenance fee of $17 for every month last year, which means that the total annual maintenance fee last year is the monthly maintenance fee multiplied by 12 months, whereas, the annual check-writing fee is the check-writing fee per check multiplied by the number of checks issued last year.

total annual maintenance fee=monthly maintenance fee *12

monthly maintenance fee=$17

total annual maintenance fee=$17*12

total annual maintenance fee=$204.00

annual check-writing fee= check-writing fee per check*number of checks

annual check-writing fee=$0.05*445

annual check-writing fee=$22.25

total fees paid by Patricia last year=$204.00+$22.25

total fees paid by Patricia last year=$226.25

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Answer: 20% of 25 is more than 25% of 16 if that is the question

I hope that is the question-

20% of 25 > 25% of 16

The answer is 3/10

Explanation:

= 3/4 x 2/5

= 3/4 x 2/5

= 3/2 x 1/5

= 3 x 1 / 2 x 5

= 3 / 2 x 5

= 3/10

The explicit formula which correctly represents the progression represented by the recursive formula above is; a(n) = 8 + 15(n - 1).

It follows from the complete task content that the explicit formula which correctly represents the progression described by the recursive formula; an = an-1 + 15 be determined.

Therefore, by observation of the recursive formula; it follows that the progression is arithmetic with a common difference, d = 15.

Also, since the first term; a₁ = 8, the required explicit formula is;

a(n) = 8 + 15(n - 1).

This follows from the general explicit formula of arithmetic progressions; a(n) = a₁ + (n - 1)d.

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Answer:

g = 2

Step-by-step explanation:

11- (15g - 13) = - 6 ( subtract 11 from both sides )

- (15g - 13) = - 17 ( multiply both sides by - 1 )

15g - 13 = 17 ( add 13 to both sides )

15g = 30 ( divide both sides by 15 )

g = 2

Given:

percent of dividend = 6%

percent of interest = 9%

Total annual interest = $ 660

Let the amount invested in both stocks be x and y.

Annual interest on 6% dividend gives:

Annual interest on 9% interest rate:

The total annual interest is $ 660. We can write:

We are given that Nelson divided his investment in half. This implies:

Substituting, we have:

Divide both sides by 0.15:

Hence, the amount Nelson has invested:

Answer:

Nelson has $4400 invested in each investment

The rule of the compounded interest is

A is the new amount

P is the initial amount

r is the interest rate in decimal

n is the number of periods per year

t is the number of years

Since the initial amount is $1100, then

P = 1100

Since the interest rate is 5.5%, then

r = 0.055

Since the interest is compounded monthly, then

n = 12

Since the time is 2 years, then

t = 2

Substitute them in the rule above to find A

Lydia's return after 2 years is $1227.60 to the nearest cent