Summer homework, need help

Split the integrand into partial fractions.

[tex]\dfrac{9x+2}{x^2+x-6} = \dfrac{9x+2}{(x-2)(x+3)} = \dfrac a{x-2} + \dfrac b{x+3}[/tex]

[tex]\implies 9x+2 = a(x+3) + b(x-2) = (a+b)x + (3a-2b)[/tex]

[tex]\implies \begin{cases}a+b=9 \\ 3a-2b=2\end{cases} \implies a=4,b=5[/tex]

Then we have

[tex]\displaystyle \int \frac{9x+2}{x^2+x-6} \, dx = 4 \int \frac{dx}{x-2} + 5 \int \frac{dx}{x+3} \\\\ = \boxed{4\ln|x-2| + 5\ln|x+3| + C}[/tex]

which follows from the result

[tex]\displaystyle \int \frac{dx}x = \ln|x|+C[/tex]

Answer:

one paperback = 0.6 pounds

one textbook = 3.6 pounds

Explanation:

Let the mass of one paperback be 'p' and one textbook be 't'.

Equation one:

sum of mass = total mass in box

Equation two:

make 't' subject

Insert this into equation one:

20p + 9(5.1 - 2.5p) = 44.4

20p + 45.9 - 22.5p = 44.4

20p - 22.5p = 44.4 - 45.9

-2.5p = -1.5

p = 0.6

The weight of 1 paperback is 0.6 pounds.

The weight of 1 textbook:

t = 5.1 - 2.5p

t = 5.1 - 2.5(0.6)

t = 3.6

The weight of 1 textbook is 3.6 pounds.

Answer:

7

Step-by-step explanation:

if the perimeter is 26

and x = 4+3

then x=7

Answer:

A. 7m

Step-by-step explanation:

Just add the 4m and 3m.

Answer:

-8

Step-by-step explanation:

3 + -4 - 7

3 - 4 - 7

-1 - 7

-8

Answer: -8

Step-by-step explanation:

3+(-4)-7

Whenever you have a +(- something), it ALWAYS becomes a -

So 3+(-4)= 3-4

Now we have:

3-4-7

PEMDAS states that you must do the subtraction  from left to right. So you start with the 3-4.

3-4-7

-1-7

-8

Whenever you have a negative number minus a number , the result will always be negative.

Hence, thats why the answer is -8

Answer: five times two times four plus three plus four

Step-by-step explanation:

5[2(4) + 3 +4]

whenever you have a number next to a bracket, like [ or ( ,it always means multiply. So thats how i know 5[2(4) means "five times two times four" as a verbal expression. The last part is "3+4" which translates to "three plus four"

I hope this is correct!!!

Answer:  No

Explanation:

Replace p with 2 and simplify

8 ≠ 3p + 2

8 ≠ 3(2) + 2

8 ≠ 6 + 2

8 ≠ 8

We get a false claim, so the original inequality 8 ≠ 3p + 2 is false when p = 2. Meaning that p = 2 is not a solution.

If the "not equal" sign was changed to an equal sign, then we would have a solution.

Answer:

no / false

Step-by-step explanation:

If we set the "p" in this equation to be equal to 2 (p = 2), we can test this inequality:

8 ≠ 3p + 2

8 ≠ 3(2) + 2

8 ≠ 6 + 2

8 ≠ 8

FALSE STATEMENT

so, p = 2 is not a solution to this inequality

(no)

hope this helps!!

{"≠" means the opposite of = [the two sides of the equation are not equal, which is not true for this situation] }

Answer:

Rose.

Step-by-step explanation:

21.147 may have the most numbers, but it is the smallest because there is a 1 in the tenths place

Answer:

-2

Step-by-step explanation:

if you divide 8 by -2 you get -4

Answer:

The solution of a number divides by 8 equals to 4.

Step-by-step explanation:

This statement does not match the condition discussed above.

Answer:

5 pennies = 1 nickel1 nickel = 5 pennies1 nickel + 5 pennies = 1 dime1 dime = 1 nickel + 5 pennies10 pennies = 1 dime1 dime = 10 pennies2 nickels = 1 dime1 dime = 2 nickels5 nickels = 1 quarter1 quarter = 5 nickels2 dimes + 1 nickel = 1 quarter1 quarter = 2 dimes + 1 nickel4 nickels + 5 pennies = 1 quarter1 quarter = 4 nickels + 5 pennies2 dimes + 5 pennies = 1 quarter1 quarter = 2 dimes + 5 pennies10 pennies + 3 nickels = 1 quarter1 quarter = 10 pennies + 3 nickels1 dime + 2 nickels + 5 pennies = 1 quarter1 quarter = 1 dime + 2 nickels + 5 pennies1 dime + 1 nickel + 10 pennies = 1 quarter1 quarter = 1 dime + 1 nickel + 10 pennies2 quarters = 1 half dollar1 half dollar = 2 quarters5 dimes = 1 half dollar1 half dollar = 5 dimes

5 nickels + 1 quarter = 1 half dollar1 half dollar = 5 nickels + 1 quarter3 dimes + 4 nickels = 1 half dollar1 half dollar = 3 dimes + 4 nickels4 dimes + 2 nickels = 1 half dollar1 half dollar = 4 dimes + 2 nickels1 quarter + 1 dime + 2 nickels + 5 pennies = 1 half dollar1 half dollar = 1 quarter + 1 dime + 2 nickels + 5 pennies2 half dollars = 1 one dollar coin1 one dollar coin = 2 half dollars5 dimes + 10 nickels = 1 one dollar coin1 one dollar coin = 5 dimes + 10 nickels1 one dollar bill = 1 one dollar coin1 one dollar coin = 1 one dollar bill4 quarters = 1 one dollar bill1 one dollar bill = 4 quarters3 quarters + 2 dimes + 1 nickel = 1 one dollar bill1 one dollar bill = 3 quarters + 2 dimes + 1 nickel10 dimes= 1 one dollar bill1 one dollar bill = 10 dimes1 quarter + 7 dimes + 1 nickel = 1 one dollar bill1 one dollar bill = 1 quarter + 7 dimes + 1 nickel2 quarters + 2 dimes + 5 nickels + 5 pennies = 1 one dollar bill

Step-by-step explanation:

This program simplifies our complex monetary system by familiarizing users with common combinations of coins and bills that are equivalent in value. Starting with five pennies equal one nickel, the program works up to equivalents for a twenty dollar bill.

Answer:

$1.05

Step-by-step explanation:

1 dime = 10 cents so 7 dimes = 70 cents
1 quarter = 25 cents

Therefore 10 cents + 7 dimes + 1 quarter = 10 + 70 + 25 = 105 cents = $1.05

Answer: G.

Step-by-step explanation:

The formula for a circle's circumference is C = 2[tex]\pi r[/tex]

r = radius

We know the rectangle ABCD has a perimeter of 72 cm.

The rectangle is divided into 6 perimeter sides: AP, PB, BC, CQ, QD, and DA.

If we divide 6 sides to the rectangle's perimeter, we can calculate the length of one side.

72 / 6 cm = 12 cm

A side of the perimeter of the rectangle ABCD is equal to 12 cm, which means PQ, the radius of the circle is equal to 12 cm.

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

radius = 12 cm

C = 2[tex]\pi[/tex] * 12 cm

C = 2 * 12 * Pi cm

C = 24[tex]\pi[/tex]

Answer = G.

Hope I Helped!

Answer:

24pi (G)

Step-by-step explanation:

This question might seem hard at first, but we know one crucial piece of information- line PQ- is the circle's radius. We also know that Q "fits perfectly" on line DC, and that angle QPB is a right angle. Since the line is straight and passes through THE MIDDLe of the rectangle, we can assume that line PQ divides the rectangle into two squares. Since squares have 4 corresponding sides, or sides with the same length, we can rewrite the equation as x+x+2x+2x, which is 6x = 72. Apply and find your answer.

EASIER EXPLANATION:

the radius is at a right angle, meaning it divides the rectangle into two squares.

It is stated that the perimeter of the rectangle is 72, meaning if we write it into an equation where x = short sides and y = long sides.

x+x+y+y = 72

However, the long sides really equal 2x, so we can rewrite the equation

x+x+2x+2x = 72

Simplify

X+x+x+x+x+x = 72

Simplify more

6x = 72

solve

x = 12

We also know that 2x is the dimeter, which is 24.

Apply to the circumference equation

C= Dpi

Since all our answeres are in pi form, we don't need to solve

ANSWER= 24

Answer:

7.25 cookies to each kids

Step-by-step explanation:

14.5 divided by 2

Answer:

c = 14.6

Step-by-step explanation:

[tex]\textrm {Applying the Pythagorean Theorem : }[/tex]

⇒ a² + b² = c²

[tex]\textrm {Here, we are given :}[/tex]

⇒ a = 4

⇒ b = 14

[tex]\textrm {Solving :}[/tex]

⇒ c² = 4² + 14²

⇒ c² = 16 + 196

⇒ c² = 212

⇒ c = √212

⇒ c = 14.6 [tex]\textrm {(nearest tenth)}[/tex]

Answer:

1. 96%

2. $6000

3. 176

4. 20%

Step-by-step explanation:

1. 1/5 of 80% is 16%. 80+16=96

2. 25% of 8000 is 2000. 8000-2000= 6000.

3. 10% increase of 200 is 20. 20+200=220. 20 percent of 220 is 44. 220-44=176

4. if you increase the original salary by 20%, then decreasing it by 20% of the new salary will give you the old salary.

Answer:

63,000

Step-by-step explanation:

Answer:

The zeros of a rational expression are the places where the numerator is zero:

4x = 0

x = 0

divide by 4

Answer: 8,230,472,011

Explanation:

billions: __8

millions: 230

thousands: 472

ones: 011

Answer:

8,230,472,011

Step-by-step explanation:

Answer:

$ 2155.62

Step-by-step explanation:

regular pay rate = 11.10

overtime pay rate = 1.8 * 11.10

142 *  $11.10        +         29 * ( 1.8 * $ 11.10)        =   $  2155.62

Answer:

-3.5 < 1.5 and |-3.5| > |1.5|

Answer:

7.0

Step-by-step explanation:

Answer:

0.8 < .85

Step-by-step explanation:

The left one shows   .80of the figure shaded

   the right one shows  .85 of the figure shaded

      I suppose you are to see that   .8  is less than .85

Answer:

x = √6 or - √6

Step-by-step explanation:

equation: -7x + 6 = x² - 7x

switch sides:

x² - 7x = -7x + 6

Add 7x to both sides,

x² - 7x + 7x = -7x + 7x + 6

x² = 6

For x² = f(a) the solution are x = √f(a), -√f(a)

x = √6 , x = - √6

Answer:

-7x + 6 = x² - 7x

-7x + 7x +6 - x² = 0

0 + 6 - x² = 0

-x² + 6 = 0

-x² = (-6)

x² = 6

x = ±√6

x =√6 or x = -√6

Answer: 1118

Step-by-step explanation:

plug in x and y into the equation

Answer:

Movie: 1:35pm

Soccer Game: 1:05pm

Concert: 1:50pm

Step-by-step explanation:

Movie:

Starting at 11:20am and ends in 2 hours and 15 minutes

hours : minutes

2 hours after 11am is 1pm

15 minutes after 20 is 35

so the movie will end at 1:35pm

Soccer Game:

Starting at 11:35am and ends in 1 hour and 30 minutes

hours : minutes

1 hour after 11am is 12pm

30 minutes after 35 is (65) 5 minute of the next hour (1 hour and 5 mins total)

so the soccer game will end at 1:05pm

Concert:

Starting at 12:15pm and ends in 1 hour and 35 minutes

hours : minutes

1 hour after 12pm is 1pm

35 minutes after 15 is 50

so the concert will end at 1:50pm

Answer:

1:35pm

Soccer Game: 1:05pm

Concert: 1:50pm

Step-by-step explanation:

Movie:

Starting at 11:20am and ends in 2 hours and 15 minutes

hours : minutes

2 hours after 11am is 1pm

15 minutes after 20 is 35

so the movie will end at 1:35pm

Soccer Game:

Starting at 11:35am and ends in 1 hour and 30 minutes

hours : minutes

1 hour after 11am is 12pm

30 minutes after 35 is (65) 5 minute of the next hour (1 hour and 5 mins total)

so the soccer game will end at 1:05pm

Concert:

Starting at 12:15pm and ends in 1 hour and 35 minutes

hours : minutes

1 hour after 12pm is 1pm

35 minutes after 15 is 50

so the concert will end at 1:50pm

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

4

Step-by-step explanation:

Since the question does not specify if you are rounding up or down, just round down to four from 4 1/6. 4 1/6 is closer to 4 than it is to 4 3/6 or 4 1/2.

Answer: I would say A or C bc they are similar but C seems more reasonable.

Step-by-step explanation:

Answer:

30%

Step-by-step explanation:

To express percentage as a fraction, the denominator must be 100.

Given ,

[tex]\frac{18/60}{60/60}\\= \frac{0.3}{1} \\= 0.3 * 100\\= 30%[/tex]

Answer:

1) Percent of skateboards that are longboards is 18÷60 or 30%

2) Number needed for equivalent ratio is 30 longboards

Step-by-step explanation:

1) Percentage= part divided by whole

18÷60 = 0.3

0.3 = 30%

2) Create a proportion, let x = # longboards needed for a equivalent ratio

(18÷60)=(x÷100)

x=30