If P(x)=6x^3=13x^2+x-2, and P(-2)=0, then the factorization of P(x) is

Answer:

53%

Step-by-step explanation:

subtract 6.5 - 4.25 = 2.25

then divide 2.25/4.25 = .529

times answer by 100 = 53% rounded

Answer: 53% increase

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

Work Shown:

A = old value = 4.25

B = new value = 6.50

C = percent change

C = 100*(B-A)/A

C = 100*(6.50 - 4.25)/4.25

C = 52.94%

C = 53%

------------

notes:

The positive C value indicates we have a percent increase. If C was negative, then we'd have a percent decrease.

The formula shown above for C is basically having us compute the difference in price (B-A) and then we divide that difference over the original price A. This computes the decimal form of the answer. The "100*" tacked out front will convert from decimal to percent form.

If you took 52.94% of the original price 4.25, then you would get 0.5294*4.25 = 2.24995 which rounds to 2.25; this is the amount the price increases so we add this to 4.25 and we get 4.25+2.25 = 6.50 which is the new share price.

Answer:

The consecutive even numbers are -42, -44, -46

Step-by-step explanation:

As the numbers are consecutive even integers,

Let,

The first number is "x"

The second number is "x+2"

The third number is "x+4"

According to the equation,

x + (x+2) + (x+4) = -132

As the sum is -132. Now we break the parenthesis by using the addition rule.

or, x + x + 2 + x + 4 = -132

or, 3x + 6 = -132

or, 3x = -132 - 6 (side change)

or, 3x = -138

or, x = -138/3 (interchange)

or, x = -46

Therefore, the first number is -46

The second number is -46+2 = -44

And the third number is -46+4 = -42

The consecutive even numbers are -42, -44, -46

Answer:

x = 25.33333333

Step-by-step explanation:

x  =  4

76 12

Cross multiply:

x * 12 = 76 * 4

Simplifying

x * 12 = 76 * 4

Reorder the terms for easier multiplication:

12x = 76 * 4

Multiply 76 * 4

12x = 304

Solving

12x = 304

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Divide each side by '12'.

x = 25.33333333

Simplifying

x = 25.33333333

1140

Step-by-step explanation:

Answer:

x=1, y=1. (1, 1). The answer is D).

Step-by-step explanation:

3x-5y=-2

4x-7y=-3

--------------

4(3x-5y)=4(-2)

-3(4x-7y)=-3(-3)

------------------------

12x-20y=-8

-12x+21y=9

--------------------

y=1

3x-5(1)=-2

3x-5=-2

3x=-2+5

3x=3

x=3/3

x=1

Answer:

not direct variation

Step-by-step explanation:

The equation for x and y in direct variation is

y = kx ← k is the constant of variation

y = [tex]\frac{5}{x}[/tex] is not in this form, thus not direct variation.

The equation for x and y varying inversely is

y = [tex]\frac{k}{x}[/tex] ← k is the constant of variation

y = [tex]\frac{5}{x}[/tex] is in this form and represents inverse variation

Answer:

11/15

Step-by-step explanation:

To answer this, add (combine) 1/3 and 2/5.

First we must rewrite these fractions with the same denominator, the LCD.

The LCD here is obtained by multiplying the denominators 3 and 5 together, obtaining 15.

Thus, 1/3 + 2/5 becomes 5/15 + 6/15, which, in turn, is 11/15.

The fraction of the total inventory that is children’s or women’s clothing

is 11/15.

Answer:

169/100

Step-by-step explanation:

93 + 76/100 = 169/100

Answer: 169/100

Step-by-step explanation:

Answer:4.6

Step-by-step explanation:

28/6

Answer:

168/35 points per minute

Step-by-step explanation:

5 5/6=35/6

28/(35/6)=(28/1)(6/35)=168/35

13 Degrees Celsius, or 55.4 degrees Fahrenheit.

-2 + 15 = 13. To find your answer in Fahrenheit, just do (Celsius here) x 9/5 + 32.

The new temperature value if an initial temperature value of - 2°C rises by 15°C will be 13°C

Using the addition operation :

Final temperature = Initial temperature + Final temperature

Final temperature = (-2°C + 15°C) = 13°C

Therefore, the final temperature is 13°C

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Answer:

2.5

Step-by-step explanation:

56(t+1/2)=70 t

56T + 28= 70T

28=70T-56T

28=14

2=T

s=T+ 1/2

S=2+ 1/2

S=2.5 hours

Tina traveled for 2 hours at a speed of 70 miles per hour, covering a distance of 140 miles.

Stephanie traveled for 2.5 hours at a speed of 56 miles per hour, also covering a distance of 140 miles.

The distance traveled by a vehicle is given by the formula: distance = speed × time.

For Stephanie:

Distance_stephanie = Speed_stephanie × Time_stephanie

Distance_stephanie = 56 × (t + 0.5)

For Tina:

Distance_tina = Speed_tina × Time_tina

Distance_tina = 70 × t

Since both Stephanie and Tina are traveling the same route, the distances they travel should be equal:

Distance_stephanie = Distance_tina

Substitute the expressions for distances:

56 × (t + 0.5) = 70 × t

Now solve for "t":

56t + 28 = 70t

28 = 14t

t = 28 / 14

t = 2

So, Tina traveled for 2 hours.

Now we can find the distance traveled by both Stephanie and Tina:

Distance_tina = 70 × t

Distance_tina = 70 × 2

Distance_tina = 140 miles

Distance_stephanie = 56 × (t + 0.5)

Distance_stephanie = 56 × (2 + 0.5)

Distance_stephanie = 56 × 2.5

Distance_stephanie = 140 miles

Both Stephanie and Tina traveled a distance of 140 miles.

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Answer:

The diameter of the pizza is 12 inches

Step-by-step explanation:

Given:

Circumference of a pizza = 38 inches

To Find:

The Diameter of the pizza =?

Solution:

Circumference:

The distance around the edge of a circle (or any curvy shape). It is a type of perimeter.

We know that the shape of the pizza is circle.

So the given circumference is circumference of a circle.

Now,

Circumference of the circle(pizza)=[tex]2\pi r[/tex]

where r is the radius of the circle

circumference of the pizza =38

Thus

[tex]2\pi r= 38[/tex]

[tex]\pi r=\frac{38}{2}[/tex]

[tex]\pi r=19[/tex]

[tex]r=\frac{19}{3.14}[/tex]

r=6.050 inches

Now,

Diameter = [tex]2\times r[/tex]

Diameter = [tex]2\times 6.05[/tex]

Diameter=12.1 inches

Rounding to the nearest tenth

Diameter=12 inches

Final answer:

To find the diameter of a pizza with a circumference of about 38 inches, we apply the formula C = πD, leading to a calculation of 38 / 3.14, which results in approximately 12.1 inches.

Explanation:

The question is about finding the diameter of a pizza given its circumference, which is approximately 38 inches. To calculate the diameter from the circumference, we use the formula C = πD, where C is the circumference and D is the diameter. Since π (Pi) is approximately 3.14, we rearrange the formula to find the diameter: D = C / π. Thus, substituting the given value of C = 38 inches, we get D = 38 / 3.14, which is approximately 12.1 inches.

It will take 4 years for these trees to be the same height

Step-by-step explanation:

A gardener is planting two types of trees:

Type A is 6 feet tall and grows at a rate of 12 inches per year

Type B is 2 feet tall and grows at a rate of 24 inches per year

We need to find exactly how many years it will take for these trees to be the same height

Assume that it will take x years for these trees to be the same height

Type A:

∵ The initial height of the tree is 6 feet

∵ 1 foot = 12 inches

∴ 6 feet = 6 × 12 = 72 inches

∴ The initial height of the tree is 72 inches

∵ It grows at a rate of 12 inches per year

∵ The number of years is x

∴ The height of the tree in x years = 72 + 12 x

Type B:

∵ The initial height of the tree is 2 feet

∴ 2 feet = 2 × 12 = 24 inches

∴ The initial height of the tree is 24 inches

∵ It grows at a rate of 24 inches per year

∵ The number of years is x

∴ The height of the tree in x years = 24 + 24 x

Equate The heights of the two types

∴ 72 + 12 x = 24 + 24 x

- Subtract 2 from both sides

∴ 48 + 12 x = 24 x

- Subtract 12 x from both sides

∴ 48 = 12 x

- Divide both sides by 12

∴ x = 4

It will take 4 years for these trees to be the same height

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The price of jacket was $24.54

Step-by-step explanation:

Let,

Cost of jacket = x

Cost of pair of shoes = y

According to given statement;

x+y=52.95   Eqn 1

x = y-3.87    Eqn 2

Putting value of x from Eqn 2 in Eqn 1

[tex](y-3.87)+y=52.95\\y-3.87+y=52.95\\2y=52.95+3.87\\2y=56.82\\[/tex]

Dividing both sides by 2

[tex]\frac{2y}{2}=\frac{56.82}{2}\\y=28.41[/tex]

Putting y=28.41 in Eqn 2,

[tex]x=28.41-3.87\\x=24.54[/tex]

The price of jacket was $24.54

Keywords: linear equation, division

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Final answer:

The price of the jacket is $24.54, calculated by first finding the price of the shoes from the total cost and the price difference between the jacket and shoes, and then subtracting the difference from the price of the shoes.

Explanation:

The question at hand involves finding the price of a jacket given the total cost of the jacket and a pair of shoes and the relationship between their prices. Let's denote the price of the jacket as J and the price of the shoes as S. According to the information provided, we have the following two equations:

J + S = $52.95 (The total cost of both items)

J = S - $3.87 (The jacket costs $3.87 less than the shoes)

We can substitute the second equation into the first to find the price of the shoes:

(S - $3.87) + S = $52.95

2S - $3.87 = $52.95

2S = $52.95 + $3.87

2S = $56.82

S = $56.82 / 2

S = $28.41

Now we can find the price of the jacket by substituting the price of the shoes back into the second equation:

J = $28.41 - $3.87

J = $24.54

Therefore, the price of the jacket is $24.54.

Answer: 10

Step-by-step explanation:

Answer:

The answer would be ten.

Step-by-step explanation:

I plugged it into my TI-84 plus calculator.

Answer:

The number of adult tickets sold was 300 and that of child's ticket sold is 900.

Step-by-step explanation:

Let us assume that the ticket sales at Wednesday's game are x number adult and y number child's tickets.

Therefore, as per given conditions, we can write, y = 3x .......... (1)

Again, each adult ticket cost $20 and each child's ticket costs $10 and there was a $15000 ticket sale.

So, 20x + 10y = 15000

⇒ 2x + y = 1500 ......... (2)

Now, solving equations (1) and (2) we get,

2x + 3x = 1500

⇒ 5x = 1500

⇒ x = 300 and y = 3x = 900

Therefore, the number of adult tickets sold was 300 and that of child's ticket sold is 900. (Answer)

Answer:

8

Step-by-step explanation:

Answer:

Step-by-step explanation:

1. 1 7/9

2. 22

3. 8

4. 64

5. 16

Answer:

Cube root of 16

Step-by-step explanation:

Place 2 inside of the square root and 3 outside and 4 inside

Here's how it looks:

[tex]\sqrt[3]{2} ^{4}[/tex]

then you can quadruple root the 2 which gives you 16 and 16 doesn't simplify any further into a cube root so your answer is the cube root of 16

Answer:

(b) The statement :  It is greater for Group B than Group A is correct.

Step-by-step explanation:

Here, the given question is INCOMPLETE.

Two groups of students were asked how far they lived from their school. The table below shows the distances in miles

Group A (distance in miles) 1 1.5 3.03 3.2 2.8 1.5 1.8 2.5 2.2

Group B (distance in miles) 2 2.5 3.23 1.3 1.8 2.4 3 1.5 1.8

Which statement best compares the mean distances for the two groups?

It is equal for Group A and Group B.

It is greater for Group B than Group A.

Its value for Group A is double the value for Group B.

Its value for Group B is double the value for Group A.

Answer:

Now,here the  calculating the mean as calculated by the group A.

[tex]\textrm{Mean}  = \frac{\textrm{Sum of Obseravtion}}{\textrm{ Number of Observation}}[/tex]

Mean as calculated by Group A  = [tex]\frac{\textrm{1 +  1.5 +3 +3.2+ 2.8+ 1.5 +1.8+ 2.5 +2.2}}{\textrm{ Number of Observation}} = \frac{19.5}{9}  =2.16[/tex]

So, mean by Group A  = 2.16

Now, calculating the mean as calculated by the group B.

[tex]\textrm{Mean}  = \frac{\textrm{Sum of Obseravtion}}{\textrm{ Number of Observation}}[/tex]

Mean as calculated by Group B  = [tex]\frac{\textrm{2 + 2.5 +3.23 +1.3 + 1.8+ 2.4 +3 +1.5 +1.8}}{\textrm{ Number of Observation}} = \frac{14.93}{9}  =2.48[/tex]

So, mean by Group B  = 2.17

Hence, the statement :  It is greater for Group B than Group A is correct.

Answer:

The correct answer is B. It is greater for Group B than Group A.

Step-by-step explanation:

The values are not equal and the difference just isn't enough for it to be any of the other answers making B the right option.

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Answer:

60.42

Step-by-step explanation:

tan40 = opposite/adjascent

tan40 =x/72

x=72tan40

x = 72 * 0.8391

x = 60.42

Answer:

There are 44 yellow slabs.

Step-by-step explanation:

Multiply 1/5 x 55. This gives you 11. 55 - 11 = 44.

The number of yellow slabs in a garden patio is 44.

Given that, a garden patio is covered with grey slabs and yellow slabs 1/5 of the slabs are grey.

The ratio is defined as the comparison of two quantities of the same units that indicates how much of one quantity is present in the other quantity.

The ratio of grey to yellow slabs are 1:4.

There are 55 slabs in total.

Number of grey slabs =1/5 ×55

= 11

So, the number of yellow slabs

= 55-11

= 44

Therefore, the number of yellow slabs in a garden patio is 44.

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With 2.5 litres of water, it can be estimated that you can make 400 grams of pasta.

The question is asking how many grams of pasta could be made with 2.5 litres (or 2500 ml) of water. According to the initial ratio, 500 ml of water is used to make 80 grams of pasta.

To find out how many grams of pasta can be made with 2.5 liters of water, you first need to find the pasta-to-water ratio which is 80 grams pasta to 500 ml water, or 0.16 grams/ml. You then multiply this ratio by the total amount of water you have:

0.16 grams/ml * 2500 ml = 400 grams of pasta.

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Answer:

[tex]\displaystyle 79°[/tex]

Step-by-step explanation:

The m∠x is 79°, according to the Alternate Exterior Angles Theorem.

I am joyous to assist you anytime.

* That does NOT look like an acute angle because 79° is considered an acute angle, since it is less than 90°.

Answer:

4x+3−9x= 3-5x

5+3.2n−6−4.8n= -1.6n-1

2y−5(y−3)= -3y-15

−1/2(8b+3)+3b= -1b-1.5

Step-by-step explanation:

Add the numbers with the variables.

4x-9x= -5x

Then add the rest of the equation to it.

3-5x

Again, add the numbers with the variables and simplify the others.

3.2n- 4.8n= -1.6n

5-6= -1

That leads to....

-1.6n-1

Distribute the 5 into the parenthesis.

2y-5y- 15

Now, subtract the variables.

-3y-15

Distribute into the parenthesis.

-4b+(-1.5)+ 3b

Add the variables together.

-1b-1.5

Answer:

131040

Step-by-step explanation:

10*9*8*7*26

=131040

Final answer:

To calculate the unique student numbers possible, multiply the number of options for each character position: 10 x 9 x 8 x 7 for the digits and multiply by 26 for the final letter, yielding 131,040 unique numbers.

Explanation:

The question asks us to calculate how many unique student numbers are possible with a specific format: the first four characters must be single-digit numbers with no repeat, and the last character must be a letter.

To find the total number of unique student numbers, we multiply the possibilities for each position. For the first position, we have 10 choices (0-9), for the second position 9 choices (excluding the first digit chosen), for the third position 8 choices, and for the fourth position 7 choices. This can be calculated using factorial notation as 10 x 9 x 8 x 7. The last character is a letter and since there are 26 letters in the English alphabet, we have 26 choices for the last character. The total number of combinations is hence 10 x 9 x 8 x 7 x 26, which equals 131,040.

Answer:

m = - 1

Step-by-step explanation:

Given

[tex]\frac{15m+3}{2}[/tex] = - 6

Multiply both sides by 2 to clear the fraction

15m + 3 = - 12 ( subtract 3 from both sides )

15m = - 15 ( divide both sides by 15 )

m = - 1

[tex]\text{Solve:}\\\\\frac{15m+3}{2}=-6\\\\\text{Multiply both sides by 2}\\\\15m+3=-12\\\\\text{Subtract 3 from both sides}\\\\15m=-15\\\\\text{Divide both sides by 15}\\\\\boxed{m=-1}[/tex]

Answer:

[tex]8\div9\times3\div16+1\div12=\frac{1}{4}[/tex]

Step-by-step explanation:

Given operation:

[tex]8\div9\times3\div16+1\div12[/tex]

Using PEDMAS to evaluate the order of operations.

First division:

[tex]=\frac{8}{9}\times\frac{3}{16}+\frac{1}{12}[/tex]

Next multiplication:

[tex]=\frac{1}{6}+\frac{1}{12}[/tex]

Then addition:

taking LCD of [tex]6\ and\ 12=12[/tex]

[tex]=\frac{2}{12}+\frac{1}{12}[/tex]

[tex]=\frac{3}{12}[/tex]

reducing to simplest fraction by division of both numbers by GCF.

[tex]=\frac{3\div3}{12\div3}=\frac{1}{4}[/tex]

Answer:

20.1%.

Step-by-step explanation:

(735 - 612 = 123 ft.

% error = (123/612) * 100

= 20.1%.

Answer:

1. Ox-intercept is -4; y-intercept is 8.

2. Ox-intercept is 16; v-intercept is 20.

Step-by-step explanation:

1. -10x + 5y = 40

Recall the equation of line in slope - intercept form :

y = mx + c , where m is the slope and c is the y - intercept

Writing the given equation in this form,we have:

-10x + 5y = 40

5y = 10x + 40

y = 10/5 x + 40/5

y = 2x + 8

comparing with y = mx +c , then y - intercept is 8 , the x - intercept is the point at which y = 0 , substituting y = 0 into the equation , we have

0 = 2x + 8

2x = -8

x = -8/2

x = -4

2. Following the same procedure:

y = -5x/4 + 20

y - intercept = 20

x - intercept = 16

Answer:

jo mamma

Step-by-step explanation: