A point P lies on the line with
equation y = -2x + 3. If the x-value
of the point is 3, what is the y-value?​

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:

3+2i

Step-by-step explanation:

(3+2i)(1)

3+2i

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:

No Solution.

Step-by-step explanation:

-(6x-5)=-6x+13

-6x+5=-6x+13

-6x-(-6x)+5=13

-6x+6x+5=13

0+5=13

5=13

Answer:

Exact form : x=-1/3

Decimal form : x=-0.3 (line over the 3!!!)

Step-by-step explanation: Isolate the variable by divinding each side by factors that don't contain the variable.

Hope this helps you out! ☺

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]

Answer:

2462.4 square inches

Step-by-step explanation:

To find the length of the longer wall use the following ratio and solve for x.

x/36= 4.75/ 2.5

x= 68.4

Area of a rectangle = l(w)

68.4(36)= 2462.4 square inches

The area of the wall is the product of its dimension.

The area of the actual wall is  2462.4 square inches

The scale is given as:

[tex]\mathbf{Scale = 4.75 : 2.5}[/tex]

The shorter side of the actual wall is 36 inches.

So, we have:

[tex]\mathbf{Long : 36= 4.75 : 2.5}[/tex]

Express as fractions:

[tex]\mathbf{\frac{Long }{36}= \frac{4.75 }{ 2.5}}[/tex]

Multiply both sides by 36

[tex]\mathbf{Long= 36 \times \frac{4.75 }{ 2.5}}[/tex]

[tex]\mathbf{Long= 68.4}[/tex]

So, we have:

[tex]\mathbf{Long= 68.4}[/tex]

[tex]\mathbf{Short= 36}[/tex]

The area is then calculated as:

[tex]\mathbf{Area = 68.4 \times 36}[/tex]

[tex]\mathbf{Area = 2462.4in^2}[/tex]

Hence, the area of the actual wall is  2462.4 square inches

Read more about areas at:

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The weight of crate when it has 19 bricks is 165 pounds

Given that, A crate with 20 bricks weighs 167 pounds.  

When the same crate has 32 bricks, it weighs 191 pounds.  

Now, let the weight of each brick be "m" pounds and weight of the crate be 'n" pounds.

Then, when crate has 20 bricks

Total weight = weight of bricks + weight of crate

[tex]167 \text { pounds }=\text { number of bricks } \times \text { weight of each brick }+\text { weight of crate }[/tex]

[tex]167=20 \times m+n[/tex]

20m + n = 167 ----- eqn (1)

Now, when crate has 32 bricks

Total weight = weight of bricks + weight of crate

[tex]191 \text { pounds }=\text { number of bricks } \times \text { weight of each brick + weight of crate }[/tex]

[tex]191=32 \times m+n[/tex]

32m + n = 191 ----- eqn (2)

Now, subtract (1) from (2)

32m + n = 191

20m + n = 167

(-) ----------------

12m + 0 = 24

m = 2

Then, from eqn (1)  

20(2) + n = 167  

40 + n = 167  

n = 167 – 40 = 127

Now, when the box has 19 bricks

Total weight = 19 bricks x 2 pounds per brick + 127 pounds of crate

[tex]\text { Total weight }=19 \times 2+127=38+127=165[/tex]

Hence, the weight of crate when it has 19 bricks is 165 pounds.

Answer:

1.5 miles per hour

Step-by-step explanation:

9 (1/6) = 1.5

Answer:

1.5 miles per hour

Step-by-step explanation:

In the attached file

Answer:

Area = 12 ft²

Step-by-step explanation:

Convert values to feet

12 inches = 1 foot

48 / 12 = 4 feet

36 / 12 = 3 feet

Area = l x w = 3 x 4 = 12 ft²

Answer: The answer is 1,728 in. squared

Step-by-step explanation:

All you do is multiply 48 by 36 because in order to get area,you multiply base and height.

Answer: The answer is D

Answer:

Step-by-step explanation:

Hope this Helps ;)

Answer: 1. 210 meters per second .

2.  756  kilometers per hour.

Step-by-step explanation:

Given : The formula [tex]S(d)=\sqrt{9.8d}[/tex] to calculate the estimated speed, in meters per second of a tsunami.

1. If the disturbance occurred at an ocean depth of 4,500 meters.

Then put d= 4500 in the above formula , we get

[tex]S(d)=\sqrt{9.8\times4500}[/tex]

[tex]S(d)=\sqrt{44100}=\sqrt{21\times21\times10\times10}\\\\=\sqrt{210^2}=210[/tex]

Hence, if the disturbance occurred at an ocean depth of 4,500 meters , the estimated speed would be 210 meters per second .

Also, A meter per second is equal to 3.6 kilometers per hour.

i.e. 1 meter per second = 3.6 kilometers per hour

Then by unitary method ,

210 meters per second  =[tex]3.6\times210[/tex] kilometers per hour

=756  kilometers per hour.

Answer:

43:12

Step-by-step explanation:

Answer:

3 7/12 or 43/12

Step-by-step explanation:

It's just 86/24

Answer:

see explanation

Step-by-step explanation:

Since l and m are parallel lines, then

11x - 47 = 6x - 2 ( corresponding angles )

Solve this equation for x

Subtract 6x from both sides

5x - 47 = - 2 ( add 47 to both sides )

5x = 45 ( divide both sides by 5 )

x = 9

The correct choices B, C, and D all represent the equation that Conner scored 25% more points than Max, using algebraic terms to demonstrate this proportional increase. Choices B and C show the total score as a multiple of Max's score, while D adds an extra 25% to Max's score.

The problem presented is an algebraic representation of a proportional relationship. Given that Conner scored 25% more points than Max, we can express this relationship in different but equivalent equations. Choices B, C, and D effectively communicate that Conner's score, c, is increased by 25% more than Max's score, m.

Choice B is written as c = (1 + 0.25)m, which represents a 100% (which is 1 in decimal form) of Max's score plus an additional 25%. Choice C simplifies this to c = 1.25m, which is another way to represent a 25% increase on Max's score. Choice D is expressed as c = m + 0.25m which sums Max's score with another 25% of it. Each of these equations correctly translates the scenario into a mathematical expression.

Good evening ,

Answer:

15x⁷y⁵.

Step-by-step explanation:

5x³y²×3x⁴y³ = (5×3)(x³x⁴)(y²y³) = 15x⁷y⁵.

:)

Answer:

2/6, 3/9, 4/12 ...

Step-by-step explanation:

We can find equivalent fractions to 1/3 by multiplying the numerator, or top number, and the denominator, or bottom number, by the same factor.

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:70

Step-by-step explanation:

You do the inverse operation which would be subtraction and multiplication. You add the 6 to the 8 and you get 14. Then you would multiply 14 by 5 to get 70. Hope this helps :D

Answer:

Step-by-step explanation:

Answer:

413 minutes of long distance calls

Step-by-step explanation:

$80.00 - $18.00 = $62.00

$62.00/$0.15 = 413.33

Answer:

The length of the first banner = 8 ft

The length of the second banner = 12  ft

The length of the third banner  = 16 ft

Step-by-step explanation:

The total length of the banner material = 36 ft

Now, let us assume the length of the first banner  = k ft

So, the length of the second banner  = First banner + 4 ft = ( k + 4) ft

The length of the third banner = Second banner  + 4 ft  = [( k + 4) + 4]  ft

Now, according to the question:

The length of ( First  + Second + Third) banner  = 36 ft

⇒ (k) + (k +4) + (k + 8)  = 36

or, 3 k = 36 - 12= 24

or, k = 24/3  = 8

⇒ k = 8 ft

So, the length of the first banner = k = 8 ft

The length of the second banner = k + 4 = 8 + 4 = 12  ft

The length of the third banner = k + 4 + 4  = 8 + 8 =  16 ft

Answer:

A

Step-by-step explanation:

Answer: 11

Step-by-step explanation: The factors of 88 are 1,2,4,8,11,22,44,88; The factors of 121 are 1,11,121.

Final answer:

To find the greatest common factor (GCF) of 88 and 121, determine the common factors through their prime factorizations, which results in 11 as the GCF.

Explanation:

The greatest common factor (GCF) of 88 and 121 can be found by determining the largest number that can evenly divide both numbers. To find the GCF:

Answer:

27

Step-by-step explanation:

Substitute x = 3 into the expression

2(3)² + 3(3) = 2(9) + 9 = 18 + 9 = 27

Answer:

13

Step-by-step explanation:

2×2=4+3(3)=4+9=13

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:

The velocity is the speed in a given direction hence the units are the same as that of speed, m/s. Thus the answer is 30 m/s.

Step-by-step explanation:

I do not understand the second option.

Answer:

14/70 or 1/5

Step-by-step explanation:

Final answer:

Carlo has read 14 out of 70 books about George Washington.

Explanation:

To find the fraction of the books about George Washington that Carlo has read, we need to divide the number of books Carlo has read by the total number of books about George Washington in the library.

Carlo has read 14 books and there are 70 books about George Washington, so the fraction of books Carlo has read is 14/70.

Answer:

18 pieces are needed

Step-by-step explanation:

Edgings are put all around the rectangular flower garden. So we need to know the perimeter (sum of all sides) of the rectangle. The formula is:

Perimeter of Rectangle = 2(Length + Width)

Given,

Length = 15

Width = 12

So,

Perimeter = 2(Length + Width)

Perimeter = 2(15 + 12)

Perimeter = 2(27)

Perimeter = 54

So, we need to cover 54 feet. Each edging is 3 feet in length, so 54 feet will be covered by:

54/3 = 18 edgings

Answer:

20 full people

Step-by-step explanation:

100-65=35

35/1.16= 30.1724

30.1724/1.5=20.1149

You can't feed a .1149 of a person so 20 people

Given the maximum budget and cost per pound, the largest turkey you can purchase is approximately 30.17 pounds. This will feed about 20 guests, considering each person consumes 1.5 pounds of turkey.

The subject of this question is mathematics, specifically, problem-solving involving budgets and limits. Given that the maximum budget for this dinner is $100 and the fixed costs total to $65, we're left with $35 for the turkey. Each pound of turkey is priced at $1.16.

By dividing the remaining amount of money (which is $35) by the cost per pound of turkey (which is $1.16), we compute the total pounds of turkey we can afford. That is, $35 / $1.16 = approximately 30.17 pounds.

Each guest requires 1.5 pounds of turkey, so we now calculate how many guests can be fed by this amount of turkey. We do this by dividing the total pounds of turkey (30.17 pounds) by the amount required per guest (1.5 pounds), which gives us 30.17 / 1.5 = approximately 20.11. Since you can't invite a fraction of a person, the largest size turkey you can afford can feed about 20 people.

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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.

Question is Incomplete, Complete question is given below.

When mack babysits, he charges $12 an hour plus bus fare. The amount mack is paid depends on the number of hours he babysits.

1. If mack babysits for 1 hour and the bus fare is $2.50, how much will mack be paid?

2. If mack babysits for 4 hours and the bus fare is $2.50, how much will mack be paid?

Answer:

1. Total Amount mack will be paid for 1 hour is $14.50.

2. Total Amount mack will be paid for 4 hours is $50.50.

Step-by-step explanation:

Given:

Charges of mack for 1 hour = $12

bus fare = $2.50

We will fist find for part 1.

1) Given:

Number of Hours= 1

Charges of mack for 1 hour = $12

bus fare = $2.50

we need to find the amount he get paid for it can be calculated by Multiplying Charges of mack for 1 hour with number of hours and then adding bus fare

Total amount he will get paid = Charges of mack for 1 hour × Number of Hours + Bus fare = [tex]\$12\times 1 +\$2.50= \$14.50[/tex]

Hence, Total Amount mack will be paid for 1 hour is $14.50.

Now we will find for part 2.

2) Given:

Number of Hours= 4

Charges of mack for 1 hour = $12

bus fare = $2.50

we need to find the amount he get paid for it can be calculated by Multiplying Charges of mack for 4 hour with number of hours and then adding bus fare

Total amount he will get paid = Charges of mack for 1 hour × Number of Hours + Bus fare = [tex]\$12\times 4 +\$2.50= \$50.50[/tex]

Hence, Total Amount mack will be paid for 4 hour is $14.50.