rewrite 1/2(x+3)(x+5) in standard form​

Answer:

A

[tex]F(x)=-\frac{1}{1500}(x+20)(x+5)(x-15)[/tex]

B

[tex]=> F(x)=-\frac{x^3}{1500}-\frac{x^2}{150}+\frac{11x}{60}+1[/tex]

Step-by-step explanation:

Function and its graphs

Part A

The graph shown in the image corresponds to a cubic function because of its classical infinite branches, three real roots and two extrema values

Part B

Knowing the value of the three roots x=-20, x=-5, and x=15 we can express the cubic function in factored form:

[tex]F(x)=C(x+20)(x+5)(x-15)[/tex]

The value of C will be determined by using any particular point from the graph. Let's use (0,1)

[tex]1=C(0+20)(0+5)(0-15)[/tex]

[tex]C=-\frac{1}{1500}[/tex]

Replacing, we find the factored form of the function

[tex]F(x)=-\frac{1}{1500}(x+20)(x+5)(x-15)[/tex]

The standard form demands to expand all the products and simplify

[tex]F(x)=-\frac{1}{1500}(x^3+10x^2-275x-1500)[/tex]

[tex]=> F(x)=-\frac{x^3}{1500}-\frac{x^2}{150}+\frac{11x}{60}+1[/tex]

To find out how much older the mother is than her daughter, we subtract the daughter's age (m/4) from the mother's age (m), resulting in the mother being three-fourths of her own age older than her daughter, which is 3m/4.

The question relates to a linear equation in the context of ages. If the mother is m years old, and she is four times as old as her daughter, then the daughter's age would be m/4 years old. To find out how much older the mother is than her daughter, we subtract the daughter's age from the mother's age, which gives us m - (m/4). Simplifying this, we get 3m/4, which means the mother is three-fourths of her own age older than her daughter.

Answer:

[tex]\left\{\begin{array}{l}x\ge 0\\ \\y\ge 0\\ \\x+y\ge 20\\ \\3.5x+5y\le 80\end{array}\right.[/tex]

Step-by-step explanation:

Let x be the number of small candles and y be the number of large candles.

Santhi needs to buy at least 20 candles, so

[tex]x+y\ge 20[/tex]

Small candles:

Cost of 1 small candle = $3.50

Cost of x small candles = $3.50x

Large candles:

Cost of 1 large candle = $5.00

Cost of y large candles = $5.00y

Total cost of all candles:

$3.50x + $5.00y

Thus,

[tex]3.5x+5y\le 80[/tex]

Using Desmos, plot the system of two inequalities:

[tex]\left\{\begin{array}{l}x+y\ge 20\\ \\3.5x+5y\le 80\end{array}\right.[/tex]

Answer:

63

Step-by-step explanation:

[(5.5+3)*7]+[(12/3)*2]-4.5

[8.5*7]+[4*2]-4.5

59.5+8-4.5

67.5-4.5

63

Answer:

1) The values of 'a' and 'b' are [tex]$ \frac{3}{4} $[/tex] and [tex]$ \frac{3}{4} $[/tex] respectively.

2) The values of 'a' and 'b' are '3' and '-3' respectively.

Step-by-step explanation:

1) Given: [tex]$ \frac{3x}{(x - 2)(3x + 2)} = \frac{a}{x - 2} + \frac{b}{3x + 2} $[/tex]

We solve this by partial fraction method.

Taking LCM in the RHS we get,

[tex]$ \frac{3x}{(x - 2)(3x + 2)} = \frac{a(3x + 2) + b(x - 2)}{(x - 2)(3x + 2)} $[/tex]

[tex]$ \implies 3x = a(3x + 2) + b(x - 2) $[/tex]

To find the value of 'a', substitute x = 2. This would make 'b' vanish leaving an equation with 'a'.

[tex]$ \therefore 3(2) = a(3.2 + 2) + b (2 - 2) \implies 6 = a(8) $[/tex]

[tex]$ \implies a = \frac{-2}{3} $[/tex]

Now, Substitute [tex]$ x = \frac{-2}{3} $[/tex] to solve for 'b'.

[tex]$ \implies 3(\frac{-2}{3}) = a (3.\frac{-2}{3} + 2) + b(\frac{-2}{3} -2) $[/tex]

[tex]$ \implies -2 = b \frac{-8}{3} $[/tex]

[tex]$ \implies b = \frac{3}{4} $[/tex]

Therefore, a = [tex]$ \frac{3}{4} $[/tex] and b = [tex]$ \frac{3}{4} $[/tex]

2) Given [tex]$ \frac{3}{x^2 - 5x + 6} = \frac{a}{x - 2} + \frac{b}{x - 3} $[/tex]

We follow the same procedure as (1).

Taking LCM we get

[tex]$ \frac{3}{x^2 - 5x + 6} = \frac{a (x - 3) + b(x - 2)}{(x^2 - 5x + 6)} $[/tex]

[tex]$ \implies 3 = a(x - 3) + b(x - 2) $[/tex]

Substituting x = 2, we get:

3 = a(-1) [tex]$ \implies a = -3 $[/tex]

Also, Substituting x = 3, we get:

3 = b(1)

[tex]$ \implies b = 1 $[/tex]

Therefore, the values of a and b are -1 and 1 respectively.

Answer:

19 and 20

Step-by-step explanation:

19^3 = 6859

20^3 = 8000

7201 is between the two numbers.

Answer: The answer is D

Answer:

Step-by-step explanation:

Hope this Helps ;)

Answer:488

Step-by-step explanation:

1464 divided by 3=488

Answer: 30

Step-by-step explanation:

rs + 2s when r = 8 and s = 3

8(3) + 2(3)

8 * 3 = 24

2 * 3 = 6

24 + 6 = 30

Answer:

30

Step-by-step explanation:

You first plug in the value of s and r into the equation.

(8)(3)+2(3)

Then you solve it.

24+6

30

So, the answer is 30.

Answer:

The maximum revenue that can be generated is $128.13

Step-by-step explanation:

we have

[tex]R(p)=-5.2p^{2}+65p-75[/tex]

where

R(p) represent the amount of revenue in dollars

p the product price

This is a vertical parabola open downward

The vertex represent a maximum

so

The y-coordinate of the vertex represent the maximum revenue that can be generated

Solve by graphing

using a graphing tool

Graph the quadratic equation

The vertex is the point (6.25,128.125)

see the attached figure

the y-coordinate of the vertex is 128.125

therefore

The maximum revenue that can be generated is $128.13

Final answer:

The solution to the inequality -2x ≤ -10 is found by dividing both sides by -2 and reversing the inequality sign, resulting in C) x ≥ 5.

Explanation:

The expression that represents the solution to -2x ≤ -10 is found by dividing both sides of the inequality by -2. When dividing by a negative number, we must reverse the inequality symbol. Thus, dividing both sides by -2 would give us x ≤ 5. However, since the inequality symbol was reversed, the correct solution is x ≥ 5.

Here are the steps broken down:

Starting with -2x ≤ -10.

Dividing both sides by -2 gives x ≥ 5.

Therefore, the correct answer is C) x ≥ 5.

Answer: Choice D) {6, 12}

============================================

Explanation:

The upside down U symbol means "set intersection". The intersection of two sets is the collection of all items that are in both sets at the same time.

In this case, only 6 and 12 are in both set A and set B at the same time, which is why choice D is the answer.

We can rule out choices A through C because 3 is not in set A (its only in set B).

Visually on a Venn Diagram, the intersection of the two sets will be shown as the overlapping region between the two circles A and B. So we'll have 6 and 12 in this overlapped region. The other values will go in their respective circles but not be in the overlapped region.

The intersection of sets A and B, denoted as A n B, includes only the elements that are present in both sets, which are 6 and 12. Therefore, A n B = {6,12}, which corresponds to option D of the provided choices.

The question asks for the intersection of sets A and B, which is denoted as A n B. Intersection means we look for elements that are common to both sets. In set A, we have {2,4,6,8,10,12}, and in set B, we have {3,6,9,12,15}. Therefore, the elements that are present in both sets are 6 and 12. Hence, A n B = {6,12}.

When comparing the answer choices provided, option D (A n B) = {6,12} is the correct answer because it lists exactly those numbers that are present in both set A and set B.

THe fraction is:

 X

----------

2X + 5

Decreases the numerator and denominator by 1, the fraction becomes 3/8.

So now the fraction looks like this:

X-1                   3

--------- =  -----------

2x +5-1            8

Cross multiplies:

8(x-1) = 3 ( 2x +5 -1)

8x - 8 = 3( 2x + 4)

8x - 8 = 6x + 12  <--- distributive right side

8x - 8 - 6x - 12 = 0 <--- everybody moves left,changing signs, to keep leading coefficient of x term positive

2x - 20 = 0 <-- combines like terms

2x = 20 <--- solves for x

x=10

So the fraction 10/25.

(10-1)/(25-1) = 9/24 = 3/8

The original equivalent value of the fraction is A = 19/43

An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.

Given data ,

Let's start by assigning variables to the numerator and denominator of the original fraction. Let x be the numerator and y be the denominator.

Then we can write:

y = 2x + 5 (since the denominator is five more than twice the numerator)

If both the numerator and denominator are decreased by 7, the new fraction can be written as (x-7)/(y-7), and we know that this is equal to 1/3:

(x-7)/(y-7) = 1/3

To solve for x and y, we can start by cross-multiplying to get:

3(x-7) = y-7

Next, we can substitute the expression for y that we derived earlier:

3(x-7) = 2x + 5 - 7

Simplifying this equation gives:

3x - 21 = 2x - 2

Bringing all the x terms to one side and all the constant terms to the other gives:

x = 19

Now that we know the value of x, we can substitute it back into our expression for y:

y = 2x + 5 = 43

Hence , the original fraction is x/y = 19/43

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Answer:

3x + 4y = 50

x + y = 15

Five 4-point questions

Step-by-step explanation:

Change x + y = 15 to determine what y equal

y = (-x) + 15

Plug it in the original equation using the substitution method

3x + 4(-x + 15) = 50

3x - 4x + 60 = 50

Combine like terms:

-x = -10, two negative signs equals a positive. x = 10

Plug 10 in for x in the equation x + y = 15

10 + y = 15

Subtract 10 from both sides

y = 5

Answer:

x=39, y = 5 and z = -4.

Step-by-step explanation:

x + y - 5z = 24

y + z = 1

z = -4

Plug z = -4 into the second equation:

y + -4 = 1

y = 5.

Now plug x = -4 and y = 5 into the first equation:

x + 5 - 5*4 = 24

x = 24 - 5 + 20

x = 39.

Answer:

[tex]1.2 \times 10^{10}[/tex] spents on housing for each year for the state.

Step-by-step explanation:

Given:

Population of State = 2000000

Average Citizen spends on housing = 6000

We need to find total spent on housing for the state.

For finding total spent on housing for state we need to multiply Population of state with average citizen spends on housing.

Total spent on housing for state = Population of State [tex]\times[/tex] Average Citizen spends on housing = [tex]2000000 \times 6000 = 12000000000[/tex]

Now expressing the above in scientific notation we get;

Total spent on housing for state = [tex]1.2 \times 10 ^{10}[/tex]

Final answer:

The total amount spent on housing for a state with a population of 2,000,000, where each spends $6,000 annually, is $12,000,000,000, which is expressed in scientific notation as[tex]$1.2 x 10^{10}.[/tex]

Explanation:

The question asks us to calculate the total amount spent on housing for a state with a population of 2,000,000, where the average citizen spends $6,000 on housing each year. To find the total, we multiply the average spending per citizen by the total number of citizens, which is 2,000,000 citizens times $6,000 per citizen. The calculation is:

2,000,000 x $6,000 = $12,000,000,000

To express this astronomical sum of money in scientific notation, we convert the standard form into a product of a number between 1 and 10 multiplied by a power of 10. So:

$12,000,000,000 = [tex]$1.2 x10^{10}[/tex]

Answer:

3+2i

Step-by-step explanation:

(3+2i)(1)

3+2i

Answer:

C = (5/9)(F-32)

Step-by-step explanation:

F = (9/5)C + 32    (subtract 32 from both sides)

F - 32 = (9/5)C     (multiply both sides by 5/9 and rearrange))

C = (5/9)(F-32)

F = 9/5·C + 32

5F = 9C + 32·5

9C = 5F - 5·32

9C = 5(F - 32)

C = 5(F - 32)/9

Answer:

Step-by-step explanation:

Use the Pythagorean theorem:

[tex]leg^2+leg^2=hypotenuse^2[/tex]

We have

[tex]leg=3,\ leg=x,\ hypotenuse=\sqrt{10}[/tex]

Substitute:

[tex]3^2+x^2=(\sqrt{10})^2[/tex]

[tex]9+x^2=10[/tex]             subtract 9 from both sides

[tex]9-9+x^2=10-9[/tex]

[tex]x^2=1\to x=\sqrt1\\\\x=1[/tex]

Answer:

51.5 therms of natural gas

Step-by-step explanation:

19.57/0.38= 51.5

Answer: 51.5 therms

Step-by-step explanation:

$0.38 per therm

amount of money paid/rate=therms used

19.57/0.38=51.5

Answer:

9 on edge

Step-by-step explanation:

point slope form: y-y1=m(x-x1)

coordinate (1,-7):

point y1--7

point x1=1

slope (m)=-23

input into equation:

y-(-7)=-23(x-1)

convert to slope intercept form:

-*-=+ so 7 becomes +7

y+7

distribute -23 in -23(x-1) using the rule: a(b+c)=ab+ac

-23x+23

refine

y+7=-23x+23

perform some inverse operations:

y+7=-23x+23

y+7=-23x+23-7

y=-23x+16

therefore, D. y+7=−23(x−1) equals y=-23x+16 in slope-intercept form

Required equation of the line is y+7 = −23(x−1).

So, Option four is the correct answer.

What is slope?

In mathematics, the slope of a line is the change in the y-coordinate relative to the change in the x-coordinate.

The net change in the y-coordinate is denoted by Δy and the net change in the x-coordinate by Δx.

Thus, the change in the y-coordinate with respect to the change in the x-coordinate is obtained as follows:

m = change in y/change in x = Δy/Δx

Where "m" is the slope of the line.

You can also specify the slope of the line

tan θ = Δy/Δx

So, tan θ is the slope of the line.

In general, the slope of a line gives its steepness and direction. The slope of a line between two points (x1,y1) and (x2,y2) is easily determined by finding the difference in the coordinates of the points. The slope is usually denoted by the letter "m".

Here given,a line, in point-slope form, that passes through (1, −7) and has a slope of −23.

We want to find what is an equation of a line which passes through (1, −7) and has a slope of −23 ?

We know, if a line passes through the point (a,b) and has slope m then equation of the line,

[tex](y - b) = m(x - a)[/tex]

Here,

[tex]a = 1 \\ b = - 7 \\ m = - 23[/tex]

So, required equation is

[tex](y -( - 7)) = ( - 23)(x - 1) \\ (y + 7) = ( - 23)(x - 1)[/tex]

Therefore,required equation of the line is y+7 = −23(x−1).

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Multiplication: (-2)(3) = -6

Division: (-2)/(3) = [tex]-\frac{2}{3}[/tex] or -0.67

Answer:

16

Step-by-step explanation:

Answer:b

Step-by-step explanation: because if you subtract 44,640 minus 43,200 which equal 1440

44,640-43,200=1,440

Answer: B) 1440

Step-by-step explanation:

March: 44,640 Minutes

April: 43,200 Minutes

Subtract 44,640-43,200=1440

Answer:

43:12

Step-by-step explanation:

Answer:

3 7/12 or 43/12

Step-by-step explanation:

It's just 86/24

Answer:

The Standard Form of the Equation is A. 2x - 5y = -15

Step-by-step explanation:

Given points: (-5, -1) and (10, -7).

Find the slope:

m = (y - y1)/(x - x1)

= -1 - (-7)/-5 - 10

= -1 + 7/-15

= 6/-15

m = -2/5

You already had the point slope form:

y - y1 = m(x - x1)

y - (-7) = -2/5(x - 10)

y + 7 = -2/5(x - 10)

The rest of the question is looking for the standard form of the equation:

Ax + By = C

Begin by solving the point slope form for y:

y + 7 = -2/5x + 20/5

y + 7 = -2/5x + 4

y = -2/5x - 3

Now, put the equation into the standard form:

y + 2/5x = -3

Multiply by 5, and place x first:

2x + 5y = -15, the Standard form of the Equation

Prove by setting x = 0 and finding the y intercept:

5y + 2(0) = -15

5y = -15

y = -3, giving the y intercept, when x = 0 as -3 or (0, -3)

Hope this helps!! Have an Awesome Day!!  :-)

Answer:

x=1y=3

Step-by-step explanation:

i just got it right

x=1 and y=3 are solutions of the system of equations

The given system of equations are

21x+7y=42 .....(1) and

-5x+5y=10....(2)

Multiply equation (1) with 5 and equation 2 with 7 to eliminate y

105x+35y=210..(3)

-35x+35y=70...(4)

Subtract equation 4 from 3

105x+35y+35x-35y=210-70

140x=140

Divide both sides by 140

x=1

Now plug in x value in equation 1

21+7y=42

7y=42-21

7y=21

Divide both sides by 7

y=3

Hence, the solutions of the system of equations are x=1 and y=3

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