0
The sum of three numbers is 10 The sum of twice the first number, 3 times the second number, and 4 times the third number is 27 The difference between 6 times
the first number and the second number is 35. Find the three numbers
first number
second number
third number

Answer:

14). 2nd quadrant

15). 1st quadrant

Step-by-step explanation:

14).Coordinates of a point → J(-8, -12)

    Coordinates of the new point J' after reflection of x-axis will follow the rule,

    (x, y) → (x, -y)

    Coordinates of J' → (-8, 12)

    Therefore, point J' will lie in 2nd quadrant.

15). Coordinates of a point → W(-6, 7)

    Rule for the rotation by 90°clockwise about the origin,

    (x, y) → (y, -x)

    Coordinates of point W → (-6, 7)

    Following this rule,

    W(-6, 7) → W'(7, 6)

    Therefore, point W' will lie in the first quadrant.

Answer:

18/8 = x/3

x = 6.75 inches (length)

Step-by-step explanation:

A larger rectangle has a length of 18 inches and width of 8 inches.

Inches /width = 18/8

So, for a rectangle that has a length of x inches and width of 3 inches the ratio is :

x/3

Solving for x:

18/8 = x/3

18/8 (3) =x

6.75 in= x

Feel free to ask for more if needed or if you did not understand something.

Given:

Sum of three consecutive integers is more than 62.

To find:

The inequality to represent the above  situation then solve your inequality.

Solution:

Let the three consecutive integers are [tex]x,x+1,x+2[/tex] respectively.

Sum of three consecutive integers is more than 62. So,

[tex]x+(x+1)+(x+2)>62[/tex]

[tex]3x+3>62[/tex]

Subtract 3 from both sides.

[tex]3x>62-3[/tex]

[tex]3x>59[/tex]

Divide both sides by 3.

[tex]x>\dfrac{59}{3}[/tex]

Therefore, the required inequality is [tex]x+(x+1)+(x+2)>62[/tex] and solution is [tex]x>\dfrac{59}{3}[/tex].

Answer:

If you have a quantity X of a substance, with a decay constant r, then the equation that tells you the amount of substance that you have, at a time t, is:

C(t) = X*e^(-r*t)

Now, we know that:

We have 2000g of substance A, and it has a decay constant of 0.03 (i assume that is in 1/year because the question asks in years)

And we have 3000 grams of substance B, with a decay constant of 0.05.

Then the equations for both of them will be:

Ca = 2000g*e^(-0.03*t)

Cb = 3000g*e^(-0.05*t)

Where t is in years.

We want to find the value of t such that Ca = Cb.

So we need to solve:

2000g*e^(-0.03*t) = 3000g*e^(-0.05*t)

e^(-0.03*t) = (3/2)e^(-0.05*t)

e^(-0.03*t)/e^(-0.05*t) = 3/2

e^(t*(0.05 - 0.03))  = 3/2

e^(t*0.02) = 3/2

Now we can apply Ln(x) to both sides, and get:

Ln(e^(t*0.02)) = Ln(3/2)

t*0.02 = Ln(3/2)

t = Ln(3/2)/0.02 = 20.3

Then after 20.3 years, both substances will have the same mass.

Answer:

Step-by-step explanation:

X=2.25

Ur welcome

Answer:

Step-by-step explanation:

4/9*x=1

x=9/4 The reciprocal of 4/9 is 9/4 and makes 1 whole.

**reciprocal is a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity

Answer:

Um finish the question but if its how much does he have left, its none.

Step-by-step explanation:

Didn't finish question and the reason why it's none well (-10), is because he had $200.000 than got 200=10 taken away.

Answer:

1716 ;

700 ;

1715 ;

658 ;

1254 ;

792

Step-by-step explanation:

Given that :

Number of members (n) = 13

a. How many ways can a group of seven be chosen to work on a project?

13C7:

Recall :

nCr = n! ÷ (n-r)! r!

13C7 = 13! ÷ (13 - 7)!7!

= 13! ÷ 6! 7!

(13*12*11*10*9*8*7!) ÷ 7! (6*5*4*3*2*1)

1235520 / 720

= 1716

b. Suppose seven team members are women and six are men.

Men = 6 ; women = 7

(i) How many groups of seven can be chosen that contain four women and three men?

(7C4) * (6C3)

Using calculator :

7C4 = 35

6C3 = 20

(35 * 20) = 700

(ii) How many groups of seven can be chosen that contain at least one man?

13C7 - 7C7

7C7 = only women

13C7 = 1716

7C7 = 1

1716 - 1 = 1715

(iii) How many groups of seven can be chosen that contain at most three women?

(6C4 * 7C3) + (6C5 * 7C2) + (6C6 * 7C1)

Using calculator :

(15 * 35) + (6 * 21) + (1 * 7)

525 + 126 + 7

= 658

c. Suppose two team members refuse to work together on projects. How many groups of seven can be chosen to work on a project?

(First in second out) + (second in first out) + (both out)

13 - 2 = 11

11C6 + 11C6 + 11C7

Using calculator :

462 + 462 + 330

= 1254

d. Suppose two team members insist on either working together or not at all on projects. How many groups of seven can be chosen to work on a project?

Number of ways with both in the group = 11C5

Number of ways with both out of the group = 11C7

11C5 + 11C7

462 + 330

= 792

Answer:

Therefore, Company B is offering the lowest price/lb at $12.73/lb.

So, Company A's price / lb = ($32.50/2.5lbs) = $13.00/lb

Step-by-step explanation:

To determine price per lb, divide dollar amount by lbs.

- Company A sells 2 1/2lbs (2.5lbs) for $32.50

- Company B sells 2 3/4lbs (2.75lbs) for $35.00

And, Company B's price / lb = ($35.00/2.75lbs) = $12.73/lb

Answer:

1) cos (140°-(50°+30°)) = 1/2

2)  [tex]sin255^{\circ}=\frac{-\sqrt{2}-\sqrt{6} }{\sqrt{4} }[/tex]

3)  [tex]cos150^{\circ}=-\frac{ \sqrt{3} }{2}[/tex]

4) ,  [tex]tan 240^{\circ}=\sqrt{3}[/tex]

Step-by-step explanation:

1) cos (140°-(50°+30°))

Solving:

cos (140°-(50°+30°))

=cos(140°-80°)

=cos(60°)

=1/2

So, cos (140°-(50°+30°)) = 1/2

2) sin 255°

We can write sin 255° as sin(180°+75°)

Solving sing formula sin(a+b)=sin(a)cos(y)+cos(x)sin(y)

[tex]sin(180^{\circ}+75^{\circ})\\=sin(180^{\circ})cos(75^{\circ})+cos(180^{\circ})sin(75^{\circ})\\=0(cos(75^{\circ}))+(-1)(\frac{\sqrt{2}+\sqrt{6} }{\sqrt{4} } )\\=0+(-1)(\frac{\sqrt{2}+\sqrt{6} }{\sqrt{4} } )\\\=\frac{-\sqrt{2}-\sqrt{6} }{\sqrt{4} }[/tex]

So, [tex]sin255^{\circ}=\frac{-\sqrt{2}-\sqrt{6} }{\sqrt{4} }[/tex]

3) cos 150°

We can solve this using the identity: cos(x)=sin(90°-x)

Solving:

cos 150°= sin(90°-150°)

=sin(-60°)

We know sin(-x)=-sin(x)

=-sin(60°)

=[tex]-\frac{ \sqrt{3} }{2}[/tex]

So, we get [tex]cos150^{\circ}=-\frac{ \sqrt{3} }{2}[/tex]

4) tan 240°

We know tan(180°+x)=tan(x)

tan 240° can be written as tan(180°+60°)

Using the above identity:

tan(180°+60°)=tan(60°) = [tex]\sqrt{3}[/tex]

So,  [tex]tan 240^{\circ}=\sqrt{3}[/tex]

Answer:

here ya go

Step-by-step explanation:

Answer:

20

Step-by-step explanation:

Because if 120 lasts 1/2 a year which is equivalent to 6 months you do 120 divided by 6 and get 20 hope this helps

Answer:

120/6 = 20 paper towels per month

Step-by-step explanation:

half a year is 6 months

120 divided by 6 is 20

Answer:

2. A 4√3

3. B -5/3

Step-by-step explanation:

Answer:

omg! mine is Kabal tooo

Step-by-step explanation: i love mortal combat lol

Answer:

Scorpion

I am a normie yes I know

Leave me alone

Step-by-step explanation:

Answer:

There are NO wholes in 1/8.

If it were 8/8, then it would be equal to 1 whole. Since it is only 1/8, there is non wholes.

I'll try! What's the link?

Answer:

Step-by-step explanation:

25

Answer:

6.4 laps

Step-by-step explanation:

Answer:

The correct answer is 120 students!

Step-by-step explanation:

There is a proportion you need to write down to solve it but i don’t know how to write it on here!

Answer:

9

Step-by-step explanation:

53/6 = 8 R5

One of the groups will have only 5 students because you can only have whole students, not parts of a student.

Answer:

Step-by-step explanation:

53/6= 8 5/6

The first 6 groups will have 8 students with 5 students remaining. They can have 5 groups with 9 students and 1 with 8 students

Answer:

y - 4 = 3(x + 2)

Step-by-step explanation:

y - y₁ = m(x - x₁)

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

y - 4 = 3(x + 2)

I need to see the other expressions

Answer:

90 i think if i did the math correct

Step-by-step explanation:

Answer:

90 inches

Step-by-step explanation:

12" in a foot so in order to convert 3' to inches after Walt apply it by 12. once you have that just the formula to find the perimeter.

3 × 12 = 36

the perimeter formula is: 2L + 2W = P

36 × 2 = 72 9 × 2 = 18

72 + 18 = 90

your answer should be 90 inches.

Answer:

5/4

Step-by-step explanation:

Lets suppose a quantity A that has a value of x

A = x

25% of A is = x/4

now adding this 25% to get 25% increase in the original value

A' = x+ x/4

    A' = 5x/4

    A' = 5*A/4

This means that , in order to increase the value by 25%  in a single step we must multiply the the original value by 5/4.

Answer:

It will cost $5.41

Step-by-step explanation:

You would take 5% of 5.15 since that is the price of the coffee with is about 0.26 cent than you add that to the cost of the coffee.

Answer:you got this:)

Step-by-step explanation:

Answer: $2.40

Step-by-step explanation:

$60.00 x .04 = $2.40

Answer:

2.40

Step-by-step explanation:

4% of 60.00 is 2.40

Answer:

100 litres

Step-by-step explanation:

Answer:

It is 100 liters

Step-by-step explanation:

I hope it helps lol

Answer:

1. Slope: [tex]m = \frac{4}{3}[/tex]

2. Distance: [tex]AB = 10[/tex]

3.  Midpoint: [tex]M = (5,7)[/tex]

4. Slope of perpendicular line: [tex]m_2 = -\frac{3}{4}[/tex]

Step-by-step explanation:

Given

[tex]A = (2,3)[/tex]

[tex]B = (8,11)[/tex]

Solving (1): Slope of AB

Slope (m) is calculated as follows:

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where:

[tex]A = (2,3)[/tex] --- [tex](x_1,y_1)[/tex]

[tex]B = (8,11)[/tex] --- [tex](x_2,y_2)[/tex]

So, we have:

[tex]m = \frac{11 - 3}{8 - 2}[/tex]

[tex]m = \frac{8}{6}[/tex]

[tex]m = \frac{4}{3}[/tex]

Solving (2): Length AB

This is solved by calculating the distance of AB using the following formula.

[tex]AB=\sqrt{(x_1-x_2)^2 + (y_1 - y_2)^2}[/tex]

Where:

[tex]A = (2,3)[/tex] --- [tex](x_1,y_1)[/tex]

[tex]B = (8,11)[/tex] --- [tex](x_2,y_2)[/tex]

So:

[tex]AB = \sqrt{(2-8)^2 + (3 - 11)^2}[/tex]

[tex]AB = \sqrt{(-6)^2 + (-8)^2}[/tex]

[tex]AB = \sqrt{36 + 64}[/tex]

[tex]AB = \sqrt{100}[/tex]

[tex]AB = 10[/tex]

Solving (3): Midpoint of AB.

Midpoint, M is calculated as follows:

[tex]M = \frac{1}{2}(x_1+x_2, y_1 + y_2)[/tex]

Where

[tex]A = (2,3)[/tex] --- [tex](x_1,y_1)[/tex]

[tex]B = (8,11)[/tex] --- [tex](x_2,y_2)[/tex]

So:

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

[tex]M = \frac{1}{2}(10,14)[/tex]

[tex]M = (5,7)[/tex]

Solving (4): Slope of line perpendicular to AB

The relationship between the slopes of two perpendicular lines is:

[tex]m_2 = -\frac{1}{m_1}[/tex]

Where

[tex]m_1[/tex] represents the slope of AB

[tex]m_1 = \frac{4}{3}[/tex]

So:

[tex]m_2 = -1/\frac{4}{3}[/tex]

[tex]m_2 = -1*\frac{3}{4}[/tex]

[tex]m_2 = -\frac{3}{4}[/tex]

Answer:

12.5 hours

Step-by-step explanation:

Answer:

it will take Lisa 12.5 hours

Step-by-step explanation:

first figure out how many minutes it takes her per apartment.

in 2.5 hours is 150 minutes so divide 150 by 6 = 25

So, it takes her 25 minutes per apartment.

next, find out how many minutes it takes her to clean 30 apartments by:

30* 25= 750 minutes for 30 partments

divide 750 by 60 to find out how many hours

12.5 hours.

Answer:

Step-by-step explanation:

8 fluid ounces in one cup

16 fluid ounces in a pint

2 feeders of 6 fluid ounces each

8 plus 16 plus 12

36, D