A student wrote the expression: 2(5x + 3) what are two expressions that are equivalent to the student's expression

The evaluation of the algebraic fraction x+2x+1/x^2-25 is[tex]\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}[/tex]

The division of an algebraic expression can be carried out by using the long division method or expansion of the.

Given that:

[tex]\mathbf{\dfrac{x+2x+21}{x^2-25}}[/tex]

where:

By expanding the denominator, we have:

[tex]\mathbf{\dfrac{x+2x+21}{(x+5)(x-5)}}[/tex]

[tex]\mathbf{\dfrac{3x+21}{(x+5)(x-5)}}[/tex]

Creating a partial fraction from the denominator, we have:

[tex]\mathbf{\dfrac{3x+21}{(x+5)(x-5)} = \dfrac{a_o}{x+5} +\dfrac{a_1}{x-5}}[/tex]

Multiply the equation by the denominator, and we have:

[tex]\mathbf{\dfrac{(3x+21)(x+5)+(x-5)}{(x+5)(x-5)} = \dfrac{a_o(x+5)(x-5)}{x+5} +\dfrac{a_1(x+5)(x-5)}{x-5}}[/tex]

Simplifying, we have:

3x + 21 = a₀(x-5)+a₁(x+5)

Solve for the unknown parameter by plugging the real roots of the denominator: -5, 5

[tex]\mathbf{a_o =\dfrac{-3}{5}}[/tex]

[tex]\mathbf{a_1 =\dfrac{18}{5}}[/tex]

Replacing the solutions into the partial fractions parameters to obtain the final result, we have:

[tex]\mathbf{\dfrac{-(\dfrac{3}{5})}{x+5} +\dfrac{\dfrac{18}{5}}{x-5}}[/tex]

[tex]\mathbf{\implies -\dfrac{3}{5(x+5)} +\dfrac{18}{5(x-5)}}[/tex]

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Answer:

a.

Step-by-step explanation:

> is a symbol of inequality representing greater than

The required expression is given by 179.2 - 10.6d.

There were 179.2 gallons of water in the barrel and 10.6 gallons are used each day

Volume, is defined as the ratio of the mass of object to its density.

the volume of water in a rain barrel after "d"days
When there were 179.2 gallons of water in the barrel and 10.6 gallons are used each day.

since the amount of water is getting consumed day by day
therefore, the expression can be given as
  =  179.2 - 10.6d

Thus, the required expression is 179.2 - 10.6d.

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Answer:

b 12

Step-by-step explanation:

62=5x+2(opposite angle are equal)

5x=60

x=12

a. I and II only true statement.

b . ∠3  = 84°

c . m∠KJM = 138° and m∠KLM  = 59°

Therefore, i and ii are true for an isosceles trapezium.

∠2 ≅ ∠3

∠1 ≅ 96°

Therefore,

∠3  = 180 - 96

∠3  = 84°

m∠KJM = 180 - x - 14

5x - 2 = 180 - x - 14

5x - 2 = 180 - x  - 14

5x + x = 180 - 14 + 2

6x = 168

x = 168 /6

x = 28

m∠KJM = 5(28) - 2 = 138°

m∠KLM  = 180 - 10y + 29

3y + 14 = 180 - 10y + 29

3y + 10y = 180 + 29 - 14

13y = 195

y = 195 / 13

y = 15

m∠KLM  = 3(15) + 14

m∠KLM  = 45 + 14

m∠KLM  = 59°

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Answer:

C=0,12N-1,15

Step-by-step explanation:

Answer:

Step-by-step explanation So if you take that times 21 25 times two gives you X equals 250. So the answer is 2 50. And I use these equivalent fractions and then solve the proportion to come up with 2 50. Instead of doing a little aero trick you could have cross multiplied 200 times 1 25 and 100 times X.ion:

Answer:

Step-by-step explanation:

I had this exact question and I figured it out.

the answer is: P(police officer and chooses car)

In order to get this answer I did the P(police officer) X P(choosing car)

It ended up being 36/45 X 15/45. Which is equal to around .2666667.

Now you take the Intersection of police officer and chooses car and you divide it by 45. That value on the chart is 12.

lucky enough, the product of 36/45 and 15/45 is equal to 12/45.

So 0.8 X 0.33 = .26

.26 = .26

Answer:

answer is P(police officer and chooses car)

Step-by-step explanation:

the probability of P(policer officer) and P(choose a car) are independent probabilities ( they are not overlapping probabilities)

The parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3

This is a way of changing the position of an object on an xy-plane.

Given the parent function expressed as  y = (x + 2^)2

From the resulting image after translation, we can see that the parent. function shifted down by 2 units to produce x² and to the right by 3 units to produce y = x^2 + 3

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Answer:

5 × 5

Step-by-step explanation:

the area (A) of a square is calculated as

A = s² ( s is the side length ) , then

A = 5² = 5 × 5 = 25 in²

Angle is 90°

The sector is 1/4 th of circle

Area of sector

Triangle is right angled

Area

Area of unshaded region

Answer:

4.6 in²  (nearest tenth)

Step-by-step explanation:

To find the area of the unshaded region, subtract the area of ΔAGB from the area of sector AGB.

The measure of an arc is equal to its corresponding central angle measure.  Therefore, the central angle of sector AGB is 90°.

As the two sides of ΔAGB adjacent the central angle are the radii of the circle they are therefore equal in length ⇒ ∠GAB = ∠GBA.  

Therefore, ΔAGB is an isosceles triangle.

Area of triangle (using the Sine Rule):

[tex]\sf A=\dfrac{1}{2}ab \sin C[/tex]

(where a and b are the side lengths and C is the included angle)

Given:

[tex]\implies \sf Area\:of\:triangle=\dfrac{1}{2}(4)(4)\sin 90^{\circ}=8\:in^2[/tex]

Area of a sector of a circle

[tex]\textsf{A}=\left(\dfrac{\theta}{360^{\circ}}\right) \pi r^2[/tex]

[tex]\textsf{(where r is the radius and the angle }\theta \textsf{ is measured in degrees)}[/tex]

Substituting the given angle and radius:

[tex]\implies \textsf{A}=\left(\dfrac{90^{\circ}}{360^{\circ}}\right) \pi (4)^2=4\pi\:\: \sf in^2[/tex]

Area of the unshaded region:

[tex]\begin{aligned}\textsf{Area of unshaded region} & =\textsf{Area of sector} - \textsf{Area of triangle}\\& = 4 \pi - 8\\& = 4.566370614...\\ & = 4.6\:\sf in^2\:\:(nearest\:tenth)\end{aligned}[/tex]

The solution of the quadratic equation 8x² – 5x – 4 = 0 will be 1.085 and negative 0.460.

The solution of the equation means the value of the unknown or variable.

The quadratic equation is given below.

8x² – 5x – 4 = 0

Then we have

a = 8, b = -5, c = -4

Then the solutions will be

[tex]\rm x = \dfrac{-b\pm \sqrt{b^2 - 4ac}}{2a}\\\\\\\rm x = \dfrac{-(-5)\pm \sqrt{(-5)^2 - 4 * 8 * (-4)}}{2 * 8 }\\\\\\x = \dfrac{5 \pm 12.37}{16}\\\\\\x = \dfrac{5- 12.37}{16}, \dfrac{5 +12.37}{16}[/tex]

On further solving, we have

x = 1.085, -0.460

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Answer:

Step-by-step explanation:

Solution

I'm assuming you want this simplified. If not leave a note.

a(x + 1) - b(x + 1) - x - 1                     remove the brackets

ax + a - bx - b - x - 1                        gather like terms

ax - bx - x + a - b - 1

x(a - b - 1)  + (a - b - 1)                      Use the distributive property to simplify

Answer

(x + 1)(a - b - 1)

The common factor is (a - b - 1). That can be pulled out on either side of the isolated + sign

Linear programming which shows the best investment strategy for the client is Max Z=0.12I +0.09B and subject to constraints are :I+ B<=25000,

0.005 I +0.004B<=250.

Given maximum investment client can make is $55000, annual return= 9%, The investment advisor requires that at most $25,000 of the client's funds should be invested in the internet fund. The internet fund, which is the more risky of the two investment alternatives, has a risk rating of 5 per thousand dollars invested. the blue chip fund has a risk rating of 4 per thousand dollars invested.

We have to make a linear programming problem.

Let

I= Internet fund investment in thousands.

B=Blue chip fund  investment in thousands.

Objective function:

Max Z=0.12I+0.09B

subject to following constraints:

Investment amount: I+ B<=25000

Risk Rating: 5/100* I+4/100*B<=250 or 0.005 I +0.004B<=250

I,B>=0.

Hence the objective function is Max Z=0.12 I+ 0.09 B.

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The function is f(x) = -2x² + 2 if the function f(x) passes through the following points:(0,2), (1, 0), (-1,0)

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have:

The graph of a function f(x) passes through the following points: (0,2), (1, 0), (-1,0)

Let

f(x) = ax² + bx + c

Plug x = 0, and y = 2

c = 2 ...(1)

Plug x = 1 and y = 0

a + b + c = 0 ..(2)

Plug x = -1 and y = 0

a - b + c = 0  ...(3)

After solving (1), (2), and (3)

a = -2

b = 0

c = 2

f(x) = -2x² + 2

Thus, the function is f(x) = -2x² + 2 if the function f(x) passes through the following points:(0,2), (1, 0), (-1,0)

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Based on the game rules of randomly picking a card and multiplying it by the roll from a number cube, the following are true:

There are 6 sides to dice and 4 cards. The sample space is:

Dice             Card            Product        

1                 5                         5

1                 6                         6

1                 7                         7

1                 8                         8

2                 5                         10

2                 6                         12

2                 7                         14

2                 8                         16  

3                 5                         15

3                 6                         18

3                 7                         21

3                 8                         24

4                 5                         20

4                 6                         24

4                 7                         28

4                 8                         32

5                 5                         25

5                 6                         30

5                  7                         35

5                  8                         40

6                 5                         30                        

6                 6                         36

6                 7                         42

6                 8                         48

Frequency table

Product                     Frequency

5                                      1

6                                      1

7                                      1

8                                      1

10                                      1

12                                      1

14                                      1

16                                      1

15                                      1

18                                      1

21                                      1

24                                      2

20                                      1

28                                      1

30                                      2

32                                      1

25                                      1

35                                      1

40                                      1

36                                      1

42                                      1

48                                      1

Total                                24

The frequency table shows that to get 28 or more, a person will have a relative frequency of:

= 1 + 2 + 1 + 1 + 1 + 1 + 1 + 1

= 9

Probability is:

= 9 / 24

= 3/8

= 37.5%

The number of products required to win 25% of the time is:

= 25% x 24

= 6

To find the winning number, count down from the highest product 6 times to get 32.

The probability of getting 36 or higher is:

= ∑(Probabability of picking 36 and above numbers)

= 1 / 24 + 1/24 + 1/24 + 1/24

= 1 / 6

The probability of repeating this 4 times is:

= 1 / 6 x 1 / 6 x 1/ 6 x 1 / 6

= 1 / 1,296

= 0.0007716

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The mean and standard deviation in inches are 69.6063 inches and 2.83465 inches respectively. Computed using unit conversions.

Unit conversion is the process of converting a magnitude of the same nature from one unit to another using fixed constants.

The constant between centimeters and inches are as follows:

1 inch = 2.54 cm,

or, 1 cm = 1/2.54 inches = 0.3937 inches.

In the question, we are informed that in a report of the National Center for Health Statistics, the heights of 20-year-old men have a mean of 176.8 (cm) and a standard deviation of 7.2 cm.

We are asked to find the mean and standard deviation in inches.

To calculate the mean in inches:-

We know that 1 cm = 1/2.54 inches.

Therefore, the mean of 176.8 cm = 176.8/2.54 inches = 69.6063 inches.

To calculate the standard deviation in inches:-

We know that 1 cm = 1/2.54 inches.

Therefore, the standard deviation of 7.2 cm = 7.2/2.54 inches = 2.83465 inches.

Thus, the mean and standard deviation in inches are 69.6063 inches and 2.83465 inches respectively. Computed using unit conversions.

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Some of the questions that should be asked when evaluating rankings or other metrics that claim to demonstrate CSR are: option A, B, and C.

CSR is acronym for corporate social responsibility and it can be defined as an organization's (company's) obligation to act in a manner that benefits and adds significant value to the society and the people, usually as it conduct its business operations.

Some of the questions that should be asked when evaluating rankings or other metrics that claim to demonstrate CSR include the following:

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Complete Question:

What are some of the questions that you should ask when evaluating rankings or other metrics that claim to demonstrate CSR? (check all that apply)

A. What was the methodology used?

B. Who contributed to the study and how were they qualified to do so?

C. Do the findings seem to match what your common sense tells you?

D. Was the list published in print or online?

Answer:

$1,075

Step-by-step explanation:

Simple Intereat Formula:

A = P(1+rt)

where A is the final amount,

P is the principal(original amount invested)

r = annual interest rate

t = time in years

Given P = 1000

r = 2.5/100

t = 3 (Beginning of 4th year means the 4th year is not counted)

A = 1000(1+(0.025)(3))

= 1000(1.075)

=$1,075

Answer:

Step-by-step explanation:

[tex]L.H.S = 1^2+Sin^2A+Cos^2A+2SinA+2CosA+2SinACosA\\ \{(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ca\}\\ = 1 + (Sin^2A+Cos^2A) + 2SinA+2CosA+2SinACosA \\ \{Sin^2A+Cos^2A=1\}\\ = 1 + 1 + 2SinA+2CosA+2SinACosA \\ = 2(1 + SinA+CosA+SinACosA)\\ = 2(1^2 + (SinA+CosA).1+ SinACosA )\\ \{x^2+(a+b)x + ab = (x+a)(x+b)\} \quad here \quad x=1\\ = 2(1+SinA)(1+CosA).\\[/tex]

The value should be placed in the second column for the range 11 - 15 will be 4. Then the correct option is C.

The data is given below.

3, 12, 25, 2, 3, 6, 17, 17, 15, 13, 20, 12, 21, 18, 19.

Arrange the data in ascending order, then we have

2, 3, 3, 6, 12, 12, 13, 15, 17, 17, 18, 19, 20, 21, 25.

Then the frequency table will be

Range         Number of values

 1 - 5                      3

6 - 10                     1

11 - 15                    4

16 - 20                   5

21 - 25                   2

The value should be placed in the second column for the range 11 - 15 will be 4.

Then the correct option is C.

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The error in Amie's evaluation as described in the task content is; Amie should have multiplied 54 by Two-thirds.

Since it follows that the she needs the volume of the sphere in which case the radius of the sphere is half the height.

Hence we have;

V(sphere) = (4/3) πr² × h/2

V = (2/3) × πr²h

Where πr²h = Volume of the cylinder = 54cm

Hence, Amie should have multiplied 54 by Two-thirds.

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Answer:

9.375 miles

Step-by-step explanation:

1) Let's set up an equation.

2.60 + 1.50x = 17.60

1.50x = 17.60 - 2.60

1.60x = 15

x = 15/1.60

x = 9.375

No idea

Sorryyyyy

I dont know

Answer:

8. a , c

9. b

10. c

Answer:

no man you should reconsider the question again

try typing again i guess its wrong

Answer: exponential, f(x), divided by 4, 1,6

Step-by-step explanation:

△MNQ ≅ △PNQ by SAS congruence theorem.

If two triangles are congruent by the SAS congruence theorem, then they have two pairs of corresponding congruent sides and a pair of corresponding included sides that are congruent.

∠MNQ ≅ ∠PNQ [congruent angles formed by angle bisector]

Therefore, opposite sides to the angles, MQ and PQ would also be congruent.

Thus, MQ ≅ PQ

NQ ≅ NQ [reflexive property]

This means that both triangles have two pairs of corresponding congruent sides and a pair of corresponding included sides that are congruent.

Thus, △MNQ ≅ △PNQ by SAS congruence theorem.

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[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]

Billy thinks of a nonzero number. He multiplies it by 3. He gets...? 3 options given

[tex]\Large\maltese\underline{\textsf{This problem has been solved!}}[/tex]

This problem does not give us the information about the starting number (we can't read Billy's mind).

First, I'm going to assume that the number is positive

[tex]\bf{A\;positive\;number\;multiplied\;by\;-3;\;yields\;a\;negative}[/tex]

Next, I'll assume that Billy's number is a negative one.

[tex]\bf{The\;number\;is\;a\;positive\;one}[/tex].

[tex]\rule{300}{1.7}[/tex]

[tex]\bf{Result:}[/tex]

              [tex]\bf{=The\;answer\;could\;be\;either\;positive\;or\;negative.\;It\;depends\;on\;the\;sign}\\of\:the\:starting\:number.[/tex]