What are the roots of the equation x2 – 10x + 21 = 0?

The given statement is true because it is the definition of nonlinear optimization.

it is the branch of mathematics with deals with the basic mathematical operators called arithmetic operators are addition, division, multiplication and subtraction.

Here,

The nonlinear optimization problem is an optimization problem in which at least one term in the objective function or a constraint is nonlinear, is true, Since its the basic definition of nonlinear optimization.

Thus, the given statement is true.

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Answer:

True

Step-by-step explanation:

I'm assuming this is a true or false question, and so the answer is true. Because two negatives (-) equal a positive. So, 45,000 - (-800) actually is 45,00 + 800 because there was as subtraction sign and a negative sign.

Answer:

Step-by-step explanation:

45,000-(-800)=45,800

45,000-(-800) does =45,800

The measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.

An angle that has a measure that is less than 90 degrees is classified as an acute angle.

Given the diagram below, the angle that is formed by rays AO and CO is angle AOC. The instrument shows that angle AOC is exactly 30 degrees.

30 degrees is less than 90 degrees and can therefore be termed an acute angle.

Therefore, the measure of angle AOC is 30 degrees. Angle AOC is classified as an acute angle.

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Answer:

x=3

Step-by-step explanation:

4x-2x+6=-7+5x+4

2x+6=-7+5x+4

2x+6-6=5x-3-6

2x=5x-9

-3x=-9

x=3

Using linear function concepts, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.

A linear function is modeled by:

y = mx + b

In which:

From the table, we have that:

Thus, the graph of the Celsius-Fahrenheit relationship is linear with an intercept of 32 and slope of 1.8.

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x= 29 which is Friday of that Month.

As 1st February 2008 is Friday

By adding 7 to the date we will get the next Friday Date of that month

i.e., 1 + 7= 8

i.e., 8 is Friday

Again if we will add 7 in 8 then we will get another Friday

so by adding again i.e., 8 + 7= 15 which is again Friday

Then 15 + 7 = 22 which is Friday.

adding again we will reach final to final answer 22+ 7 = 29 which is Friday

after adding 29 with 7 we will get 36 and as we know there are only 30/31 days in a month.

So, by adding 7 to the date we will reach the next week.

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[tex]\angle DAE \cong \angle DCF[/tex]

by CPCTC.

Answer:

k = x^3+y^3+z^3

Step-by-step explanation:

Solve for k by simplifying both sides of the equation, then isolating the variable.

Hope this helps.

The average rate of change for the function will be 234.

It is the average amount by which the function is modified per unit throughout that time period. It is calculated using the gradient of the line linking the interval's ends on the graph that represents the function. The average rate of change of the function is given as,

Average rate = [f(x₂) - f(x₁)] / [x₂ - x₁]

The function is given below.

f(x) = 3ˣ + 17

The value of the function at x = 3 will be

f(x) = 3³ + 17

f(x) = 27 + 17

f(x) = 44

The value of the function at x = 6 will be

f(x) = 3⁶ + 17

f(x) = 729 + 17

f(x) = 746

Then the average rate of change for the function will be

Average rate = [746 - 44] / [6 - 3]

Average rate = 702 / 3

Average rate = 234

The average rate of change for the function will be 234.

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By the concept of Permutations and Combinations, we get:

Number of ways to distribute 5 dollar bills among three children = 21

and

Number of ways to distribute 5 dollar bills such that each child gets at least one dollar = 6

Given:

To find: (A) number of ways to distribute the dollar bills among the children

(B) number of ways to do the same if each child gets at least a dollar.

Finding:

By using the formula: [tex]\binom{n+r-1}{r-1}[/tex],

Number of ways to distribute 5 dollar bills among three children = [tex]\binom{5+3-1}{3-1} = \binom{7}{2}= \frac{7\times6}{2}[/tex] = 21 ways.

Similarly, upon modifying the above formula as: [tex]\binom{n-1}{r-1}[/tex],

Number of ways to distribute 5 dollar bills such that each child gets at least one dollar is =

[tex]\binom{5-1}{3-1}= \binom{4}{2}=\frac{4\times3}{2}[/tex] = 6 ways.

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Answer:

[tex]\mathrm{Focus:\;\;} \left(-\frac{5}{3},\:2\right)[/tex]

[tex]\mathrm{Directrix:\;\;}x=-\frac{1}{3}[/tex]

Step-by-step explanation:

The standard equation for a parabola is

[tex]4p\left(x-h\right)=\left(y-k\right)^2[/tex]

with vertex at (h, k) and a focal length of |p|

[tex]\mathrm{Rewrite}\:x=-\frac{3}{8}\left(y-2\right)^2-1\:\mathrm{in\:the\:standard\:form}[/tex]:

[tex]\mathrm{Add\:}1\mathrm{\:to\:both\:sides}[/tex]

[tex]x+1=-\frac{3}{8}\left(y-2\right)^2-1+1[/tex] or

[tex]x+1=-\frac{3}{8}\left(y-2\right)^2[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}-\frac{3}{8}[/tex]
[tex]\frac{x+1}{-\frac{3}{8}}=\frac{-\frac{3}{8}\left(y-2\right)^2}{-\frac{3}{8}}[/tex]

[tex]\mathrm{Simplify}[/tex]
[tex]-\frac{8x}{3}-\frac{8}{3}=\left(y-2\right)^2[/tex]

[tex]\mathrm{Factor\:}-\frac{8}{3}[/tex]
[tex]\left(-\frac{8}{3}\right)\left(x+\frac{-\frac{8}{3}}{-\frac{8}{3}}\right)=\left(y-2\right)^2[/tex]

[tex]\mathrm{Simplify}[/tex]
[tex]\left(-\frac{8}{3}\right)\left(x+1\right)=\left(y-2\right)^2[/tex]

[tex]\mathrm{Factor\:}4[/tex]
[tex]4\cdot \frac{-\frac{8}{3}}{4}\left(x+1\right)=\left(y-2\right)^2[/tex]

[tex]\mathrm{Simplify}[/tex]
[tex]4\left(-\frac{2}{3}\right)\left(x+1\right)=\left(y-2\right)^2[/tex]

[tex]\mathrm{We\; can\; rewrite\:this\;as}[/tex]
[tex]4\left(-\frac{2}{3}\right)\left(x-\left(-1\right)\right)=\left(y-2\right)^2[/tex]

Comparing this with the standard form we get
[tex]\left(h,\:k\right)=\left(-1,\:2\right)[/tex]
[tex]\:p=-\frac{2}{3}[/tex]

The parabola is symmetric around the x-axis.

The focus lies a distance [tex]p[/tex] from the center [tex]\left(-1,\:2\right)[/tex] along the x axis

So focus is at
[tex]\left(-1+p,\:2\right)[/tex] [tex]=\left(-1+\left(-\frac{2}{3}\right),\:2\right)[/tex] [tex]=\bold{ \left(-\frac{5}{3},\:2\right)}[/tex]

The parabola is symmetric around the x-axis and so the directrix is a line parallel to the y-axis at a distance -p from the center

[tex]x=-1-p[/tex]

[tex]x=-1-\left(-\frac{2}{3}\right) = \bold{-\frac{1}{3}}[/tex]

Answer: Total number of employees are employed by the store = 15 employees.

Step-by-step explanation:

The ratio of Full time employees to Not Full time employees would be 1 to 4.

Let, Full time employees F =1      

Not Full time employees N =4

We can write:

                                F/N = ¼

Cross multiply to get:

                                 N=4F

If 5 more Full time employees were hired, then the ratio would be 2 to 3.

This would be mean there are no (F+5) Full time employees.

Also there are still Not Full time employees.

We can write:

                             (F+5) / N = 2/3

Cross multiply to get:

                              3(F+5) =2N

Expand to get:

                               3F+15=2N

Replace N with 4F to get:      

                               3F+15=2(4F)

Solve to get:

                              3F+15=8F

                              15=8F-3F

                              15=5F

                                F=3

So, there are presently 3 Full time employees.

How many employees does the store have?

Since           F=3,

we can use the equation N=4F

To help find the value of N Replace F with 3 to get:

                              N = 4(3)

Solve to get:

                               N=12

So, Full time employees F=3    

Not Full time employees N=12

Then, Total number of employees = F+N

                                                         = 3+12

                                                         = 15.

Hence, Total number of employees = 15 employees.

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The objective observations are so important to science because they are helpful in removing bias.

Objective observations are simply the direct observation recorded by an observer. It does not contain any personal interpretation by the observer. So it can be considered as a bias less observation.

In a scientific study, objective observations are equal to facts. An objective observer will not have a predetermined mind. So that observation will not contain prejudice. That is why it is not biased. So an objective observation helps in removing bias. So they are important in Science.

The opposite of objective observation is subjective observation. In a subjective observation, there is a chance of personal interpretations.

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Answer:

2 [tex]\frac{1}{10}[/tex]

Step-by-step explanation:

.10

change it to 10/100

reduce by 10

1/10

Answer: 2 1/10

Step-by-step explanation:

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there is 1 number to the right of the decimal point, place the decimal number over 10^1(10). Next, add the whole number to the left of the decimal.

2 1/10

Answer:

Geometric.

Step-by-step explanation:

For example

2, 4, 8, 16

where the common ratio is 4/2 = 8/4 = 16/8 = 2.

Answer:

184

Step-by-step explanation:

Answer:

A - Domain - [0,9] , Range - [0,3] , It represents a function because it passes the (vertical line test).

B - (0,0)

C - I'm not sure about this question but, If i would guess, (0,0) (9,3).

Step-by-step explanation:

For question C i think It means maximum and minimum points on the graph.

Im sorry if you get any of it wrong.

Answer: See below

Step-by-step explanation:

1) For the first question, we have to multiply the width by the length to find the area of the whole rectangle:

(4x-4)(x+1)= 4x^2 -4

2) For the second question, we have to multiply the width by the length to find the area of the shaded area in the rectangle:

(2x+2)(x-1)= 2x^2-2

3) The total area of the unshaded part of the whole triangle equals the area of the whole rectangle minus the shaded area:

4x^2-4 - 2x^2 -2 = 2x^2 - 6

At Maryland, the mean number of points per player per game is greater than the median number of points per player per game. The mean number of points per player per game is the same at all 3 schools.

Given that in Baylor's University that there are 6 players who each score 12 points per game, and 6 players who each score 0 points per game.

The scores are 0, 0, 0, 0, 0, 0, 12, 12, 12, 12, 12, 12.

Mean = Sum/Count = 72/12 = 6.

Median is the average between the nth  and (n+1)th  term.

(0+ 12)/2 = 6

In Maryland university 1 player scores 58 points per game, 1 player scores 14 points per game, and the rest of the 10 score 0 points per game,

58, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Mean = Sum/Count = 72/12 = 6.

Median is 0

In Dartmouth, university, 4 players score 5 points per game, 4 players score 6 points per game, 4 players score 7 points per game.

The scores are

5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7

Mean = Sum/Count = 72/12 = 6

Median =(6+6)/2= 6

​

At Maryland, the mean number of points per player per game is greater than the median number of points per player per game.

The mean number of points per player per game is the same at all 3 schools.

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Answer:

When i24 is increased by 25% the answer is 30

A translation along the directed line segment NB then a reflection over the vertical line about B so sequence A is correct therefore option (A) will be correct.

Transformation is rearranging a graph by a given rule it could be either increment of coordinate or decrement or reflection.

Reflection is a mirror image of a graph about any axis.

If we reflect any graph about y = x then the coordinate will interchange it that (x,y) → (y,x).

Given the triangle MNO and ABC

Now,

If we translate MNO along the directed line segment NB and reflect over B then M will coincide with A and N with B and O with C.

In sequence B if we reflect on MO then M will not coincide with A and it will not form a triangle ABC.

Hence "A translation along the directed line segment NB then a reflection over the vertical line about B".

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The given question has missed an image, incomplete question is given in the image,

Answer:

28x-4

Step-by-step explanation:

Given

length (l)= 9x-4

Breadth (b) = 5x+2

Now

Perimeter (P) = 2(l+b)

=2(9x-4+5x+2)

=2(14x-2)

=28x-4

Answer:

z divided by 4 is 12

48 divided by 4 is 12

In a poll conducted by a certain research​ center, 1046 adults were called after their telephone numbers were randomly generated by a​ computer, and were able to correctly identify the random sampling.

Each sample has an equal chance of being chosen as part of the sampling technique known as random sampling. A randomly selected sample is intended to be a fair representation of the entire population.

In statistics, a simple random sample is a subset of people chosen at random from a larger group, all of whom were chosen with the same probability. It is a procedure for randomly choosing a sample.

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Step-by-step explanation:

[tex] \frac{46}{62} \times 100 = 74.19 percent \\ 100 - 74.19 = 25.81 \: percent \\ her \: loss \: was \: 25.81 \: percent[/tex]

Answer: 4/9 es racional - cualquier fracción adecuada x/y es un número racional. Expresado como un decimal, esto es igual a 0.4 recurrente (es decir, 0.44444...)

Step-by-step explanation: ¡Espero que esto ayude!

El número 4/9 es un número racional. Es una razón, o fracción, formada por dos números enteros, 4 y 9.

Answer:

v < 2

Step-by-step explanation:

To solve this problem, start by adding 12 to each side of the inequality, to clear the -12 from the left side. 10 + (-12) is 2, so your answer is v < 2.

Hope this helps! Let me know if you have any confusion!

Answer:

good luck broooooooooooo

Answer:

-1

Step-by-step explanation:

→ -4 + (6/2)

→ -4 +3 = -1

So, the answer is -1.

Answer:

42.5

Step-by-step explanation:

You have to multiply 7 times 5 equals 35. Then you multiply 7 times 2 which is 14 plus 3 equals 5. So you have 175 as the first number. Then you put a 0 under that number. You multiply 5 times 1 which is 5 and 2 times 1 which is 2. Now you have 250 as your second number.

Add 175 plus 250 which is 425 but you have to put the decimal between 2 and 5. Now you have 42.5

Hope that helps

When the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.

The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]

The general equation of the circle is [tex]x^{2} +y^{2}+2gx+2fy+c=0[/tex]

Where (-g,-f) is the coordinates of the circle

The equation of the circle = [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex]

Divide the equation by 2

[tex]x^{2} +y^{2}-6x+4y-12=0[/tex]

Compare the equation with general form

2g= -6

g= -3

2f= 4

f= 2

The center of the circle (-g,-f) = (3,-2)

The radius of the circle = [tex]\sqrt{g^{2}+f^{2}-c }[/tex]

Substitute the values in the equation

r= [tex]\sqrt{(-3)^{2}+2^{2}- (-24) }[/tex]

[tex]=\sqrt{9+4+24} \\=\sqrt{37}[/tex]

=6.08 units

Hence, when the equation of the circle is [tex]2x^{2} +2y^{2}-12x+8y-24=0[/tex], then the center of the circle is (3,-2) and the radius of the circle is 6.08 units.

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