Complete each function table.
1. Input (v)
0
*+6
Output (y)
3

Ann's age after h years is 2h

Bill's age after h years is 3h

Charles' age after h years is 8 + h

The sum of their ages after h years is 6h + 8

Step-by-step explanation:

The given is:

Anne is currently h years old

Bill is currently 2h years old

Charles is currently eight years old

We need to find an expression for each person’s age after h years and then find an expression for the sum of their ages after h years

∵ Ann is h years old now

∵ Her age after h years = her age now + h

∴ Her age after h years = h + h

∴ Her age after h years = 2h

Ann's age after h years is 2h

∵ Bill is 2h years old now

∵ His age after h years = his age now + h

∴ His age after h years = 2h + h

∴ His age after h years = 3h

Bill's age after h years is 3h

∵ Charles is 8 years old now

∵ His age after h years = his age now + h

∴ His age after h years = 8 + h

∴ His age after h years = 8 + h

Charles' age after h years is 8 + h

Add their ages after h years

∵ The sum of their ages after 8 years = 2h + 3h + 8 + h

- Add like terms

∴ The sum of their ages after 8 years = (2h + 3h + h ) + 8

∴ The sum of their ages after 8 years = 6h + b

The sum of their ages after h years is 6h + 8

Learn more:

You can learn more about word problems in brainly.com/question/10557938

#LearnwithBrainly

Anne, Bill, and Charles's ages after h years will be 2h, 3h, and h+8, respectively. The sum of their ages after h years is 6h + 8.

The question asks for expressions that represent each person's age after h years and for the sum of their ages after h years. Currently, Anne is h years old, Bill is 2h years old, and Charles is eight years old.

After h years have passed:

Now, to find the expression for the sum of their ages after h years, we add the expressions together:

Sum of their ages = Anne's age after h years + Bill's age after h years + Charles's age after h years
= 2h + 3h + (h + 8)
= 6h + 8.

Final answer:

To double the area of the rectangular garden, the dimensions should increase by 5 meters.

Explanation:

To double the area of the rectangular garden, we need to find the increase in dimensions that will result in double the original area. The original dimensions are 5m by 7m, so the original area is 5m x 7m = 35 square meters. To double this area, the new area should be 35 square meters x 2 = 70 square meters. Let's assume the increase in dimensions is 'x'. The new dimensions will be (5m + x) by (7m + x). We can set up the equation:

(5m + x)(7m + x) = 70 square meters

Expanding and simplifying the equation, we get:

35m + 5x + 7x + x^2 = 70 square meters

Combining like terms, we have:

x^2 + 12x + 35 = 70 square meters

Next, we rearrange the equation into standard form:

x^2 + 12x + 35 - 70 = 0

Simplifying further, we get:

x^2 + 12x - 35 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula. Factoring the equation gives us:

(x + 7)(x - 5) = 0

Setting each factor equal to zero, we have:

x + 7 = 0 or x - 5 = 0

Solving for 'x', we get:

x = -7 or x = 5

Since a negative value doesn't make sense in this context, we can conclude that the dimensions should increase by 5 meters.

Answer:

c = 1.4

d = 8

Step-by-step explanation:

In a 45-45-90 triangle, the legs are equal and the hypotenuse is √2 times that.

2 = c √2

c = 2 / √2

c = 1.4

In a 30-60-90 triangle, the hypotenuse is 2 times the short side, and the long side is √3 times the short side.

d = 2 × 4

d = 8

Answer:

Jamie: His inequality would look like this:  25x >= 600

Stella: Her inequality would look like this: 15y >= 600

Her limitations would be listed as: y=40

Yep. Stella has plenty of money by baking 40 pies; $600.

We can back that up by breaking this down. So. We know that it cost $600 to pay upfront and Jamie makes $25 per car he washes. Stella would make $15 for every pie she baked. So simply, let x represent the number of cars Jamie washes. Let y represent the number of pies Stella makes. Easy.

Since the cost for washing one car is $25

Now, in order to sign up for the trip, money obtained from car washing must be greater than or equal to $600. We know that. Now, lets see their profit margins.

Since the cost for making one pie is $15

Therefore, the cost of making y pies is 15y.

Now, in order to sign up for the trip, money obtained from pie making must be greater than or equal to $600 so with that being the case... 15y>=600

We all know the maximum number of pies that Stella can make is 40. So, the value of can't exceed 40 and must be less than or equal to 40. So.... y<=40

Bam.

In order to sign up for the trip, Stella's total earning must be at least $600. So, is the minimum condition for signing up for the trip. Now, let us solve the above equation for . So our end project looks like this: 15y = 600 y = 600/15 = 40

The minimum number of pies required for signing up for the trip is 40 and luckily that's the maximum supply Stella has for pies. Therefore, she can sign up for the trip by making all the 40 pies and earning a total of 600 dollars.

Step-by-step explanation:

Answer:

760 mm

Step-by-step explanation:

Answer:

3 friends

Step-by-step explanation:

The mean age is 27 so 3 friends are above that age.

The average age of the friends is 27. Only two of the friends, both aged 31, are older than the average age.

To find out how many of the friends are older than the average age, we need to first find the arithmetic mean of the ages. We do this by adding up all the ages and dividing by the number of ages. So, (20+31+28+31+25)/5 = 27. Once we have the average, we can see that the ages of 31 and 31 are larger than the average of 27. Therefore, there are 2 friends whose ages are older than the average.

https://brainly.com/question/27193544

#SPJ2

Answer:

$717336

Step-by-step explanation:

The total of monthly payments for a 3-year loan is $22317.12.

So, the total amount has to pay back in 3 years is $(22317.12 × 12 × 3) = $803416.32.

Let the amount of money that was originally borrowed is $x and the given APR is 4%.

Then we can write, [tex]x(1 + \frac{4 \times 3}{100}) = 803416.32[/tex]

⇒ 1.12x = 803416.32

⇒ x = $717336 (answer)

Answer:

The minimal number for the objective function P =20x+16y is: 780

The value of x then is: 15

and the value of y then is : 30

Step-by-step explanation:

We are given a system of inequalities as:

y is less than or equal to 2x

i.e.          y ≤ 2x--------(1)

x + y is greater than or equal to 45

i.e.      x+y ≥ 45  ------------(2)    

and    x is less than or equal to 30.    

i.e.               x ≤ 30 -----------(3)    

On plotting these inequalities we get the boundary points as:

        (15,30) , (30,60) and (30,15)    

( Since, the optimal solution always exist at the boundary point )

The optimal function is given by:

 Minimize  P = 20x+16y

Hence, at (15,30) we get:

P= 780

at (30,60) we get:

 P= 1560

at (30,15) we get:

P= 840

This  means that the minimal value of the function is 780

and the value exist at (15,30)

Answer:

1 ¹/₉ hours

Step-by-step explanation:

Let's say L is Larry's speed, C is Curly's speed, and M is Moe's speed.

1 = 2 (L + C)

1 = 1 ⅔ (C + M)

1 = 1 (L + C + M)

Solve the system of equations.  First, simplify the equations:

1 = 2L + 2C

3 = 5C + 5M

1 = L + C + M

Double the third equation and subtract the first equation from it:

2 = 2L + 2C + 2M

1 = 2L + 2C

1 = 2M

M = 1/2

Plugging into the second and third equations, we get:

C = 1/10

L = 2/5

Therefore, the time it takes Larry and Moe together is:

1 = t (L + M)

t = 1 / (L + M)

t = 1 / (2/5 + 1/2)

t = 1 / (4/10 + 5/10)

t = 1 / (9/10)

t = 10/9

t = 1 ¹/₉ hours

It takes them 1 ¹/₉ hours, or 1 hour 6 minutes 40 seconds.

Larry and Moe would take 5/3 hours, or 1 hour and 40 minutes, to build a bookcase together, based on the rates of building individually and in different pairs.

Larry and Curly together build a bookcase in 2 hours. This means that together they have a rate of 0.5 bookcases per hour, since 1 divided by 2 is 0.5. Similarly, Curly and Moe together can build one in 1 2/3 hours, which is the same as 5/3 hours. Therefore, their collective rate is 3/5 bookcases per hour. Larry, Curly, and Moe together can build a bookcase in 1 hour, which means their combined rate is 1 bookcase per hour.

Let's denote the rates of work for Larry, Curly, and Moe as L, C, and M respectively. When working together the sum of their rates equates to the rate at which they finish the job together. Hence:

L + C = 0.5 (Larry and Curly's rate)

C + M = 3/5 (Curly and Moe's rate)

L + C + M = 1 (Larry, Curly, and Moe's rate)

Using the first two equations, we can solve for L and M by substituting the values into the third equation:

L + 3/5 = 1

L = 1 - 3/5 = 2/5

C + 0.5 = 1

C = 1 - 0.5 = 0.5

Now we know that Larry's rate is 2/5 bookcase per hour, and Curly's rate is 0.5 bookcase per hour. We can use Curly's rate to find Moe's rate:

C + M = 3/5

0.5 + M = 3/5

M = 3/5 - 0.5 = 1/5

Larry and Moe's combined rate is L + M = 2/5 + 1/5 = 3/5 bookcases per hour.

To find the time it takes for Larry and Moe to build one bookcase together, we take the reciprocal of their combined rate:

Time = 1 / (L + M) = 1 / (3/5) = 5/3 hours, which is equal to 1 hour and 40 minutes.

How to distribute  2.5(-y + 2)

= (2.5 * -y) + (2.5 * 2)

= -2.5y + 5

Distributive Property is when you multiply different addends from a sum then add them.

______

Best Regards,

Wolfyy :)

Answer: 45

Step-by-step explanation: To divide this start with finding how many times 585 goes into 13 which is 0. I put a picture for you to look at.

25x+35y=405 and y= x+3 can be used to determine the number of bottles of soda and number of bottles of juice purchased where, x represents the number of soda bottles and y represents the number of juice bottles.

Step-by-step explanation:

Given,

Sugar contained by each soda bottle = 25 grams

Sugar contained by each juice bottle = 35 grams

Let,

x be the number of soda bottles.

y be the number of juice bottles.

According to given statement;

25x+35y=405   Eqn 1

y= x+3   Eqn 2

25x+35y=405 and y= x+3 can be used to determine the number of bottles of soda and number of bottles of juice purchased where, x represents the number of soda bottles and y represents the number of juice bottles.

Keywords: Linear equation, substitution method

Learn more about linear equations at:

#LearnwithBrainly

Answer:

[tex]\frac{17}{26}[/tex]

Step-by-step explanation:

In probability

"AND" means to multiply, and

"OR" means to add

Here, we want probability getting a red card OR a 10 OR a queen. So we find each individual probabilities and ADD.

In a standard deck, there is 52 cards.

P(Red):

half the cards are red and half are black, so there are 52/2 = 26 red cards

Hence

P(Red) = 26/52 = 1/2

P(10):

There are 4 suits with each one having 1 "10" card, so there are FOUR 10s in a deck. So,

P(10) = 4/52 = 1/13

P(Queen):

There are 4 suits with each one having 1 Queen. So in 4 suits, there are a total of 4 Queens. So,

P(Queen) = 4/52 = 1/13

P(Red, or, 10, or, Queen) = 1/2 + 1/13 + 1/13 = [tex]\frac{17}{26}[/tex]

Answer:

[tex]\frac{2}{7}[/tex]

Step-by-step explanation:

The possibility of the event A occurring is given by the formula:

[tex]\boxed{P(A)= \frac{\text{number of favourable outcomes in A}}{\text{total possible outcomes}}}[/tex]

Since the event that we are looking for (favourable event) is choosing a girl with glasses, the number of favourable outcomes is the number of girls with glasses in the class.

Number of favourable outcomes= 4

Total possible outcomes

= total number of students in the class

= 10 +4

= 14

Thus, P(girl with glasses)

= [tex]\frac{4}{14}[/tex]

= [tex]\bf{\frac{2}{7} }[/tex]

Additional:

For more questions on probability, do check out the following!

Answer:

B

Step-by-step explanation:

If you use the method of rise over run, you find the slope to be -2, and the y intercept is given.

y = 2x+8 is the slope-intercept equation of the line. Option D is correct.

From figure two points (0,8), (6, -4). equation of the line to be determine.

Equation of the line is y = mx +c where m = slope and c = y intercept.

Here
Equation of the line = [tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
y - 8 = 8+4/0+6(x-0)
y - 8 = 2(x)
y = 2x + 8

Thus, y = 2x+8 is the slope-intercept equation of the line.

Learn more about equation of line here:
https://brainly.com/question/21511618

#SPJ2

Answer:

8.76/24.3= 0.36

16.95/32.6= 0.519 round up to make 0.52

Step-by-step explanation:

8.76/24.3= 0.36

16.95/32.6= 0.519

Answer: The answer is (9+2) - 4

Step-by-step explanation:

Final answer:

The correct numerical expression that translates the phrase "4 less than the sum of 9 and 2" is Option A: 9 + 2 - 4, which calculates the sum of 9 and 2, then subtracts 4.

Explanation:

The question asks which numerical expression correctly translates the phrase "4 less than the sum of 9 and 2." To solve this, you first need to find the sum of 9 and 2, and then subtract 4 from it. The sum of 9 and 2 is 11, so subtracting 4 from this sum would give us 7. The correct numerical expression for this operation is 9 + 2 - 4.

Therefore, as per the above explaination, the correct answer is Option A: 9 + 2 - 4 which results in 7.

it's 94.20967742 if you simplify it you will get 94.21

5,841 divided by 62 equals 94 with a remainder of 13. You can find this using long division, where 62 goes into 584 (from 5,841) nine times and then into 261 (the remainder with the next digit) four times.

To find the result of 5,841 divided by 62, we can use long division. Let's break down the problem step by step:

To express this as a decimal, we could continue the division process by adding a decimal point and zeros to the dividend, but that is not requested in this problem.

Answer:

y = - 3

Step-by-step explanation:

To find the value of y, substitute x = 3 into the equation, that is

y = - 2(3) + 3 = - 6 + 3 = - 3

Answer:

C) 6 inches

Step-by-step explanation:

Given function:

[tex]Y=1.3x-0.8[/tex]

The function compares plant height in inches to the age of plant in weeks.

So, we can say

[tex]Y[/tex] represents height of plant in inches.

[tex]x[/tex] represents age of the plant in weeks.

In order to predict the height of the plant in 5 weeks, we will plugin [tex]x=5[/tex] in the given function and evaluate [tex]Y[/tex]

⇒ [tex]Y=1.3(5)-0.8[/tex]

⇒ [tex]Y=6.5-0.8[/tex]

⇒ [tex]Y=5.7[/tex] inches

Thus the approximate height of plant in 5 weeks would be [tex]\approx 6[/tex] inches

Answer:

C: 6

Step-by-step explanation:

[tex]f = 30000 - (2000 \times m)[/tex] is an equation to represent the height of the airplane in feet above the ground f(x) in relationship to time in minutes x

Step-by-step explanation:

As given that the plane is at 30000 feet above the grounds. And starts descending at the rate of 2000 feet/ min  

So, let us consider the below,

H= height in feet above ground

r = rate of descent

m = minutes

So, now frame the required equation format with the given data as follows,

                           [tex]H = 30000 - (2000 \times m)[/tex]

Answer: 6 columns.

Step-by-step explanation:

24 ÷ 4 = 6

Answer:

6

Step-by-step explanation:

24 divided by 4 = 6

Answer:

Step-by-step explanation:

The correct answer is x = 3

The value of x in the equilateral triangle is 3 units.

A triangle is a three-sided closed-plane figure formed by joining three noncolinear points. Based on the side property triangles are of three types they are Equilateral triangle, Scalene triangle, and Isosceles triangle.

We know the perimeter of any planer figure except a circle is the sum of the lengths of all the sides and we also know that an equilateral triangle has equal sides and equal angles.

∴ We can equate any of the two sides of the given equilateral triangle.

So, 5x = 6x - 3.

5x - 6x = - 3.

- x = - 3.

x = 3.

learn more about triangles here :

https://brainly.com/question/2773823

#SPJ2

Answer:

$12.09

Step-by-step explanation:

formula Y = KX

where; y = $24.18

            x = 2 books

            k = constant proportionality

Step 1. Do the equation based on the data given

$24.18 = k 2

Step 2. Divide 2 on both sides to eliminate integer on the right side

$24.18 / 2 = k2/2

Answer ;

k = $12.09 dollar in relate to number of books

Answer:

[tex]a_{n}[/tex] = 8[tex](-3)^{n-1}[/tex]

Step-by-step explanation:

The n th term of a geometric sequence is

[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]

where a is the first term and r the common ratio

Here a = 8 and r = - 24 ÷ 8 = - 3, thus

[tex]a_{n}[/tex] = 8[tex](-3)^{n-1}[/tex]

Answer:

Rs 2163.20.

Step-by-step explanation:

The formula for this is

A = P(1 + r)^t     where P is the amount invested, r = the rate (as a decimal) and t = the number of years.

So for rs 2000 we have:

A = 2000(1 + 0.04)^2 = Rs 2163.20

Answer:

36 hours - 6,300

24 hours - 4,200

In 36 hours, 6300 quarts of ice cream could be made. The rate per day would be 6300 quarts per day.

350 quarts of ice cream are made in 2 hours. To find out how many quarts could be made in 36 hours, we can set up a proportion: 350 quarts / 2 hours = x quarts / 36 hours. Solving for x gives us 6300 quarts in 36 hours. To find the rate per day, we divide the total quarts made in 36 hours by the number of days: 6300 quarts / 1 day = 6300 quarts per day.

Answer: ABC is isosceles

Step-by-step explanation:

The coordinate of points given are:

A(1,-4)

B(-1, -2 )

C ( -2 , -5 )

For ABC to be isosceles , then AB must be equal to BC or AB = AC

The next thing to do  is to find the value of AB , BC and AC using the formula for finding distance between two points which is given by:

D = [tex]\sqrt{(x_{2}-x_{1})  ^{2}+(y_{2}-y_{1})  ^{2}}[/tex]

Calculating AB first , we have

[tex]\sqrt{(-1-1)^{2}+(-2+4)^{2}  }[/tex]

= [tex]\sqrt{4+4}[/tex]

=[tex]\sqrt{8}[/tex]

Therefore:

AB = [tex]\sqrt{8}[/tex]

Calculating BC , we have :

D = [tex]\sqrt{(x_{2}-x_{1})  ^{2}+(y_{2}-y_{1})  ^{2}}[/tex]

D = [tex]\sqrt{(-2+1)^{2}+(-5+2)^{2}  }[/tex]

D = [tex]\sqrt{10}[/tex]

Therefore:

BC = [tex]\sqrt{10}[/tex]

Calculating AC , we have :

D = [tex]\sqrt{(x_{2}-x_{1})  ^{2}+(y_{2}-y_{1})  ^{2}}[/tex]

D = [tex]\sqrt{(-2-1)^{2}+(-5+4)^{2}  }[/tex]

D = [tex]\sqrt{10}[/tex]

Therefore:

AC = [tex]\sqrt{10}[/tex]

Since AC = BC then triangle ABC is isosceles

Practice Analytic Geometry

1. Find the midpoint of the line segment defined by the points: (sqrt 2, 0) and (0, -sqrt 2)

Answer is ((sqrt 2)/2, (-sqrt2)/2)

2. Find the distance of the line segment joining the two points: (5,4) and (-2,1)

Answer is sqrt 58

3. Find the distance of the line segment joining the two points: (1/2, -5/2) and (-4/3, -1/6)

Answer is (sqrt 317)/6

4. Given triangle ABC with vertices at A (1,-4), B (-1, -2), and C (-2,-5), prove or disprove that triangle ABC is an isosceles

Answer triangle ABC is isosceles since AB = sqrt 8, BC = sqrt 10, and AC = sqrt 10

Answer:

70 people

Step-by-step explanation:

Final answer:

The total number of employees at the company is calculated using the given ratio of men to women, 2 to 3, along with the information that there are 42 women. By converting the ratio into actual numbers, we find that there are 28 men and 42 women, totaling 70 employees.

Explanation:

The question asks about the total number of employees in a company given the ratio of men to women and the number of women. To find the answer, we will use the ratio of men to women, which is 2 to 3, and the information that there are 42 women working for the company.

Answer:

For the given expression [tex]x^3 = 135[/tex] , the value of x = 5.13

Step-by-step explanation:

Here, the given expression is : [tex]x^3 = 135[/tex]

Now, to solve this given equation,we need to find the suitable value for x.

Solving for x , we get:

[tex]x^3 = 135[/tex]

Taking cube roots both sides, we get:

[tex]\sqrt[3]{(x)^3}  = \sqrt[3]{135} \\\implies (x)^{3 \times \frac{1}{3}}   =  (135)^{\frac{1}{3}} \\[/tex]

But, 135 = 5.13 x 5.13 x 5.13

[tex]\implies 135   =  (5.13)^3\\\implies x^{3 \times \frac{1}{3}} =  (5.13)^{3 \times \frac{1}{3}}\\\implies x  = 5.13[/tex]

Hence, for the given expression [tex]x^3 = 135[/tex], the value of  x = 5.13

Answer:

the other answer was a bit confusing so, 135 divided by 3 is 45, so, x=45

135 divided by 45 is 3 lol.

Step-by-step explanation: