Solve the equation -2(y - 1) = 9.

[tex]1)\\p\%=\dfrac{p}{100}\\\\13\%=\dfrac{13}{100}=0.13\\\\13\%\ of\ 20\ is\ 0.13\cdot20=2.6\\\\2)\\\underbrace{7\cdot7\cdot7\cdot7\cdot7}_{5}=7^5\\\\3)\\Use:\\a^n\cdot a^m=a^{n+m}\\\\\dfrac{a^n}{a^m}=a^{n-m}\\\\12.\ 6^2\cdot6^{-4}=6^{2+(-4)}=6^{2-4}=6^{-2}\\\\13.\ 2^{-3}\cdot2^{-2}=2^{-3+(-2)}=2^{-5}\\\\14.\ \dfrac{4^4}{4^2}=4^{4-2}=4^2}\\\\15.\ \dfrac{8^3}{8^{-2}}=8^{3-(-2)}=8^{3+2}=8^5[/tex]

[tex]Domain:\\\\x+3\geq0\ \wedge\ 2x-1\geq0\\\\x\geq-3\ \wedge\ x\geq0.5\\\\D:x\in[0.5;\ \infty)[/tex]

[tex]\sqrt{x+3}-\sqrt{2x-1}=-2\qquad\text{square of both sides}\\\\(\sqrt{x+3}-\sqrt{2x-1})^2=(-2)^2\qquad\text{use}\ (a-b)^2=a^2-2ab+b^2\\\\(\sqrt{x+3})^2-2(\sqrt{x+3})(\sqrt{2x-1})+(\sqrt{2x-1})^2=4\qquad\text{use}\ (\sqrt{a})^2=a\\\\x+3-2\sqrt{(x+3)(2x-1)}+2x-1=4\qquad\text{combine like terms}\\\\3x+2-2\sqrt{(x+3)(2x-1)}=4\qquad\text{subtract 3x + 2 from both sides}\\\\-2\sqrt{(x+3)(2x-1)}=2-3x\qquad\text{square of both sides}\\\\\left(-2\sqrt{(x+3)(2x-1)}\right)^2=(2-3x)^2[/tex]

[tex]4(x+3)(2x-1)=2^2-2(2)(3x)+(3x)^2\qquad\text{use distributive property}\\\\(4x+12)(2x-1)=4-12x+9x^2\\\\(4x)(2x)+(4x)(-1)+(12)(2x)+(12)(-1)=4-12x+9x^2\\\\8x^2-4x+24x-12=4-12x+9x^2\\\\8x^2+20x-12=4-12x+9x^2\qquad\text{subtract }\ 9x^2\ \text{from both sides}\\\\-x^2+20x-12=4-12x\qquad\text{add 12 and}\ 12x\ \text{from both sides}\\\\-x^2+36x=16\qquad\text{change the signs}\\\\x^2-36x=-16\\\\x^2-2(x)(16)=-16\qquad\text{add}\ 16^2\ \text{to both sides}[/tex]

[tex]\underbrace{x^2-2(x)(16)+16^2}_{(a-b)^2=a^2-2ab+b^2}=16^2-16\\\\(x-16)^2=256-16\\\\(x-16)^2=240\iff x-16=\pm\sqrt{240}\\\\x-16=\pm\sqrt{16\cdot15}\\\\x-16=-\sqrt{16}\cdot\sqrt{15}\ \vee\ x-16=\sqrt{16}\cdot\sqrt{15}\\\\x-16=-4\sqrt{15}\ \vee\ x-16=4\sqrt{15}\qquad\text{add 16 to both sides}\\\\x=16-4\sqrt{15}\notin D\ \vee\ x=16+4\sqrt{15}\\\\\boxed{x=4(4+\sqrt{15})}[/tex]

Answer:

The unit rate is 0.14 cents per ounce.

Step-by-step explanation:

Divide 3.92 by 28 to find out how much the trail mix is per ounce.

The unit rate of Dmitri's trail mix purchase is $0.14 per ounce, calculated by dividing the total cost by the total weight.

To find the unit rate of Dmitri's trail mix purchase, we divide the total cost of the trail mix by the total weight of the trail mix. Dmitri bought 28 ounces of trail mix for $3.92, so we perform the following calculation:

Unit Rate = Total Cost / Total Weight

Unit Rate = $3.92 / 28 ounces

Unit Rate = $0.14 per ounce

Therefore, the unit rate is $0.14 per ounce. This means that for every ounce of trail mix, Dmitri paid $0.14.

Answer:

The answer is

n=5 3/5

Step-by-step explanation:

first collect the like terms:

2-1/2n=3n+16

then...

3n-1/2=16-2

==2 1/2n = 14

===n=5 3/5

Answer:

m <  −4/3

Step-by-step explanation:

−5(3m−2)>30

Simplify both sides of the inequality.

−15m+10>30

Subtract 10 from both sides.

−15m+10−10>30−10

−15m>20

Divide both sides by -15.

−15m/−15  >  20/−15

m<−4/3

[tex]-5(3m-2)>30\qquad\text{use distributive property}\\\\(-5)(3m)+(-5)(-2)>30\\\\-15m+10>30\qquad\text{subtract 10 from both sides}\\\\-15m>20\qquad\text{change the signs}\\\\15m<-20\qquad\text{divide both sides by 15}\\\\m<-\dfrac{20}{15}\qquad\text{simplify}\\\\m<-\dfrac{20:5}{15:5}\\\\\boxed{m<-\dfrac{4}{3}}[/tex]

Answer:

48 tickets

Step-by-step explanation:

I just had this question on a test and got it right! So this is how i did it:

if the advance price is $4, and you sell 40 tickets in advance, you do 40 times 4.

40 x 4 = 160

so you subtract the $160 from 400 and then that brings you $240 dollars left.

*these 240 dollars will be tickets bought at the door*

to determine the amount of tickets that need to be bought left, you need to do 240 divided by 5.

and that will give you a total of:

a least amount of 48 tickets

The least number of tickets the club needs to sell at the door to reach the president’s goal, 48.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, Tickets to a play cost $4 in advance and $5 at the door. The theater club president wants to raise at least $400 from the ticket sales. If the club sells 40 tickets in advance,

Since, the cost if advance ticket is $4 and they already sold 40,

Therefore, collected cost = 4 × 40 = $160

Now, cost to collect yet = 400 - 160 = $240

Cost of tickets at the door = $5

Therefore, tickets to be sold to meet the goal = 240/5 = 48

Hence, the least number of tickets the club needs to sell at the door to reach the president’s goal, 48.

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The inequality 20x ≤ 300 represents the number of 20-pound bags of soil a 300-pound capacity wheelbarrow can carry. Solving the inequality, we find x ≤ 15, meaning the wheelbarrow can carry up to 15 bags of soil without exceeding its weight limit.

To represent the problem as an inequality, let's say the number of bags of soil the wheelbarrow can carry is represented by x. Each bag of soil weighs 20 pounds, and the wheelbarrow can carry up to 300 pounds. So, the inequality would be 20x ≤ 300.

To solve the inequality, we divide both sides by 20: x ≤ 300/20. Therefore, x ≤ 15. This means the wheelbarrow can carry up to 15 bags of soil without exceeding its 300 pounds weight limit.

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A. They are not similar because their corresponding angles are not congruent.

Their angles are not the same.

The 1st triangle is a scalene triangle (a triangle that has 3 unequal sides and angles)

The 2nd triangle is an isosceles triangle (a triangle that has 2 congruent/equal sides and 2 congruent angles)

Answer:

Step-by-step explanation:

Answer:

6 units away from 0.

Step-by-step explanation:

when move to 6 you count the units.

Answer:

x = 11

Step-by-step explanation:

∠CAB = ∠DCA = 33° ( alternate angles )

∠ACB = 180 - 5x ( straight angle )

the sum of all 3 angles in a triangle = 180°, hence

33 + 180 - 5x + 2x = 180

- 3x + 213 = 180 ( subtract 213 from both sides )

- 3x = - 33 ( divide both sides by - 3 )

x = 11

Answer:

The answer would D.) 33.5 because 9.5+24 is 33.5 and since vertical distance is always an absolute value, it will never be a negative number.

The vertical distance between the top and bottom of the boat is calculated by summing the distances above and below the lake's surface, which total 33.5 feet, making option D correct.

To calculate this, we consider that the top deck of the boat is 9.5 feet above the surface of the lake, while the bottom of the boat is 24 feet below the surface. The total vertical distance would be the sum of these two values, as one needs to account for the entire distance the boat covers from top to bottom.

So, the calculation would be as follows: 9.5 feet + 24 feet = 33.5 feet. Therefore, the vertical distance between the top deck and the bottom of the boat is 33.5 feet. This makes option D the correct answer.

Answer:

The correct answer is option C , 4 + 9i

Step-by-step explanation:

A complex number is the one which has a real number and an imaginary number.

In all the example given , option C 4 + 9i has "i" which signifies the imaginary number which nothing but a negative square root.

Answer:

\\\90

Step-by-step explanation:

Answer:

61 inches

Step-by-step explanation:

took the test

Answer:

18 L

Step-by-step explanation:

(a) Millilitres shipped

There are 750 mL/bottle.

Vol. shipped = 24 × 750

Vol. shipped = 18 000 mL

=====

(b) Litres shipped

1 L = 1000 mL

Vol. shipped = 18 000 × 1/1000

Vol. shipped = 18 L

the answer is C) 2. the 8 is in the ones place, 2 is in the tenths, and 1 is in the hundreths.

Answer: h=14

Step-by-step explanation:

7h-5(3h-8)=-72

7h-15h+40=-72 > I distributed the -5(3h-8) to get rid of parenthesis

-8h+40=-72 > I combined the like terms 7h-15h

-8h=-112 > I subtracted 40 from both sides

h=14 > I divided -8 from both sides

The solution is h = 14.

Given: Equation

7h - 5(3h - 8) = -72

Now, we will solve the equation for the value of h.

⇒ 7h - 5(3h - 8) = -72

⇒ 7h - 15h + 40 = -72

⇒ 7h - 15h = -72 - 40

⇒ -8h = -112

Dividing both sides by -8, we get:

⇒ h = 14

Therefore, the solution of the given equation is h = 14.

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Answer:

The percent increase is 250 percent

Step-by-step explanation:

To find the percent increase we use the formula

percent increase = (new-original)/original * 100

                            = (35-10)/10 * 100

                              = 25/10 *100

                             250

The percent increase is 250 percent

There is a 250% increase.

Work is attached in the image provided.

Answer:

1/28

Step-by-step explanation:

think what two can be divided by it can only be divided by two

think if 56 can, it could so 2 divided by 2 is 1 and 56 divided by two is 28 so the answer is 1/28

Answer:

( [tex]\frac{11}{2}[/tex], 8)

Step-by-step explanation:

Find the midpoint using the midpoint formula

midpoint = [ [tex]\frac{1}{2}[/tex](3 + 8), [tex]\frac{1}{2}[/tex](2 + 14)] = ( [tex]\frac{11}{2}[/tex], 8)

Answer: (5.5, 8)

Step-by-step explanation:

We know that midpoint (x,y) of a line XY having points having points [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] is given by :-

[tex]x=\dfrac{x_1+x_2}{2}\ ;\ y=\dfrac{y_1+y_2}{2}[/tex]

Then similarly, the midpoint of AB with endpoints A(3,2) and B (8,14)  will be :_

[tex]x=\dfrac{3+8}{2}\ ;\ y=\dfrac{2+14}{2}\\\\\Rightarrow\ x=\dfrac{11}{2}\ ;\ y=\dfrac{16}{2}\\\\\Rightarrow\ x=5.5\ ;\ y=8[/tex]

Hence, the midpoint of AB with endpoints A(3,2) and B (8,14) = (5.5, 8)

Answer:

-88

Step-by-step explanation:

Let N(x) be the number of students at NMS for a certain number of years.

Let S(x) be the number of students at SMS for a certain number of years.

Let x be the number of years.

N(x)=1240-25x

S(x)=800-30x

When # of students is equal, N(x)=S(x). Therefore, we are looking for the value of x (# of years) when 1240-25x=800-30x

Subtract 1240 from each side

-25x=-440-30x

Add 30x

5x=-400

x=-88 years

Check your numbers.

Answer:

Marcia can make a total of 80 batches of soup

Step-by-step explanation:

400(total ounces)/5(ounces per batch)=80 batches

Answer:

80 batches of soup can Marcia .

Step-by-step explanation:

Given  : Marcia uses 5 ounces of chicken stock to make one batch of soup.She has a total of 400 ounces of chicken stock.

To find : How many batches of soup can Marcia make.

Solution : We have given

Marcia uses 5 ounces of chicken stock  =  1. batch of soup

Marcia uses 1 ounces of chicken stock = [tex]\frac{1}{5}[/tex].

Marcia uses 400 ounces of chicken stock =  [tex]\frac{400}{5}[/tex].

                                                                      = 80 batch of soup.

Therefore, 80 batches of soup can Marcia .

Answer:

10b + 5 is your answer

Step-by-step explanation:

Simplify the expression as much as possible. Combine terms with the same amount of variables.

6b + 4b = 10b

10b + 5

10b + 5 is your answer

~

Answer:

4. The mean and median age are most likely to be same for the students in Math 1.

Step-by-step explanation:

We have been given two box plots that show the ages of college students in different math courses. We are asked to choose the true statement about these box plots.

1. The median age of the students in math 1 is greater than the median age of the students in math 2.  

We can see from our given box plots that median age for both Math 1 and Math 2 is 19 that is represented by vertical middle line of box, therefore, 1st statement is not true.

2. The median age of the students in math 1 is less than the median age of the students in math 2.

Since median ages for students in Math 1 and Math 2 are same (19), therefore, 2nd statement is not true.

3. The mean and median age are most likely same for both sets of data.

We can see that box plot for ages of Math 1 students is symmetric, therefore, both mean and median will be same for Math 1 students.

The box plot representing ages of Math 2 students is skewed right as it has an outlier as 23, therefore, its mean age will be greater than median age.

Therefore, 3rd statement is not true either.

4. The mean and median age are most likely to be same for the students in Math 1.

We can see that box plot representing ages for Math 1 students is symmetric and its whiskers are equidistant from median. So both mean and median age are same that is 19, therefore, 4th statement is true.

Answer:

in shorter terms, the answer is d

Step-by-step explanation:

Answer:

Step-by-step explanation:

Where is line B?

Answer: 15 There would be 15 blue jays out of all the other birds

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Step-by-step explanation:

Answer:

Step-by-step explanation:

Its 4:7

The formula of a circumference is:

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

r - radius

or

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

d - diameter

We have d = 12cm. Substitute:

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

One-fourth of the circumference:

[tex]\dfrac{1}{4}C=\dfrac{1}{4}\cdot12\pi=3\pi\ cm\approx3\cdot3.14=9.42\ cm[/tex]

Hi there!

A valley farmer has 26 employees and he pays each of them $410 per week.

After paying them for one week he has $162 dollars left. We need to find how much money he had at first.

So the first step is to multiply $410 on 26 since he gives 410 dollars to each employee, which he has 26.

$410 · 26 = $10,660

So he had $10,660 before he paid the workers, but he still had $162 left. To find out his overall total of money he had we need to add $10,660 and $162 which will be $10,822.

The farmer had $10,822

Hope this helped!~

Answer:

     = 233.75

Step-by-step explanation:

To find the discount, we multiply the original price by the percent off

discount = 275* .15

               = 41.25

To get the sale price, take the original price and subtract the discount

sale price = 275-41.25

               = 233.75