A car rental agency rent 190 cars per day at a rate of $40 per day for each one dollar increase in rate five fewer cars are rented at what rate should the cars be rented to produce the maximum income?

9514 1404 393

Answer:

  x = 19

Step-by-step explanation:

The marked (consecutive interior) angles will be supplementary when the lines are parallel.

  (3x +10)° +(5x +18)° = 180°

  8x = 152 . . . . . . . . . . . . . . . divide by °, subtract 28

  x = 19 . . . . . . . . . . . divide by 8

Answer:

at least four times bigger

Answer:

Subtract 12 from the product of 5 and 3, then multiply by 8.

Answer:

y=-2x+10

Step-by-step explanation:

The y-int is 10, you can tell from the coordinate (0,10)

The slope would be -2 when you use the slope formula for both coordinates

hope this helps

With a monthly repayment of $809.49, the total interest on the car loan will be $5,569.67.

We assume that there are monthly repayments and compounding interest on the car loan.

With periodic repayments and compounding interest, the total interest paid on the car loan will be as shown by the car loan calculator.

Car loan = $43,000

Down payment = $0

Fixed Annual Percentage Rate (APR) = 4.9%

Loan term = 5 years

Car Loan Calculator with monthly Repayment:

Payment = $809.49/month

Interest Paid =$5,569.67

Total Paid = $48,569.67

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Answer:

2x^2 - 6x

Step-by-step explanation:

2x(x-3)

= 2x^2 - 6x

One second later, the distance between the two stones will change in a speed of 6.86 m/s

Distance can be defined as the length of change of position. When an object change from one position to another, the length between the points or position is known as distance.

If a dropped stone has a distance d = 4.9t²

Let us assumed that the time taken = 3 seconds

The distance d = 4.9 × 3² = 44.1 m

If another stone is dropped one second later, then the time t = 4 s

The distance = 4.9 × 4² = 78.4 m

One second later, the time = 5 seconds

The speed of change in distance = ( 78.4 - 44.1 )/ 5

The speed of change in distance = 34.3 / 5

The speed of change in distance = 6.86 m/s

Therefore, one second later, the distance between the two stones will change in 6.86 m/s

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Answer:

Step-by-step explanation:

12 months

Answer:

12 months b on edg

Step-by-step explanation:

edg 2022

Answer:

M=K*L

(K is the constant we use)

when L=35cm, M=80,

meaning K=80/0.35=228.571428571

so when L=0.3

we do 0.3*228.571428571=68.5714285713

rounded to 2dp= 68.57kg

9514 1404 393

Answer:

  50.38 kg

Step-by-step explanation:

The mass is proportional to the cube of edge length, So, if the edge length is decreased by a factor of 30/35 = 6/7, the mass is decreased by a factor of (6/7)³. That is, the smaller cube will have a mass of ...

  (80 kg)(6/7)³ ≈ 50.38 kg

__

If you want to write an equation, you can write the equation for the proportionality:

  M = kL³

  80 kg = k(0.35 m)³

  k = 80/0.35³ kg/m³

Then for the shorter length, we have ...

  M = k(0.3 m)³ = 80(0.3/0.35)³ kg = 80(6/7)³ kg ≈ 50.38 kg . . . . as above

Answer:

Simplifying radicals is the process of manipulating a radical expression into a simpler or alternate form. Generally speaking, it is the process of simplifying expressions applied to radicals.

Estimation (or estimating) is the process of finding an estimate, or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is derived from the best information available.

Step-by-step explanation:

The radical symbol represents the root of a number and is read as x radical n or the nth root of x.

The symbol " that expresses a number's root is known as radical, and it is read as x radical n or the nth root of x. The horizontal line that surrounds the number is known as the vinculum, and the number beneath it is known as the radicand. The index or degree is the number n written before the radical.

The process of transforming a radical expression into a simpler or alternate form is known as simplifying radicals. In general, it is the process of simplifying expressions that are applied to radicals.

Estimation (or estimating) is the process of determining an estimate, or approximation, which is a value that can be used for a specific purpose despite the fact that the input data may be incomplete, uncertain, or unstable. The value is still useful because it is based on the best available information.

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Step-by-step explanation:

for a quadratic equation

y = ax² + bx + c

the x value for the axis of symmetry is

x = -b/(2a)

in our case

y = 2x² - 4x + 5

a = 2

b = -4

x = - -4/4 = 4/4 = 1

x = 1 is the correct answer.

Answer:

Step-by-step explanation:

C=(10,-1)

D=(-6,3)

\(mid~point~x=\frac{10+(-6)}{2} =\frac{10-6}{2} =\frac{4}{2} =2\\y=\frac{-1+3}{2} =\frac{2}{2} =1\)

mid point=(2,1)

The midpoint of line segment CD is M = (2, 1).

We have,

To find the midpoint of the line segment CD, we can use the midpoint formula:

M = ((X₁ + X₂)/2, (Y₁ + Y₂)/2)

Given C = (10, -1) and D = (-6, 3), we can substitute the values into the formula:

M = ((10 + (-6))/2, (-1 + 3)/2)

= (4/2, 2/2)

= (2, 1)

Therefore,

The midpoint of line segment CD is M = (2, 1).

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Answer:

b. -1/6

Step-by-step explanation:

slope = (difference in y)/(difference in x)

slope = (1 - 0)/(-2 - 4) = 1/(-6) = -1/6

Answer:

m = -1/6 = B

Step-by-step explanation:

\(m = \frac{y_2-y_1}{x_2-x_1} \\ x_1=4\\ y_1=0\\ x_2=-2\\y_2=1.\\m = \frac{1-0}{-2-4} \\m = \frac{1}{-6}\)

Answer:

Below

Step-by-step explanation:

Line AB is of the form y = mx + b    where m is the slope = 2

 Line BC is perpendicular to this and will have slope - 1/m = - 1/2   and includes the point C (0,6)

 The point slope form of line BC will then be

     ( y-6) = - 1/2 ( x - 0)    which can be re-arranged to

       y = - 1/2x + 6     < ==== equation for line BC

The polynomial, f(x) = x² + 4·x - 1, has a value of -5 when x = -2

A polynomial consists of terms comprising of variables and numbers with positive integer indices with operations including additions, subtractions, multiplications.

The specified polynomial is f(x) = x² + 4·x - 1

The point at which the polynomial is evaluated is; x = -2

The value of the specified polynomial at x = -2 is therefore;

f(-2) = (2)² + 4 × (-2) - 1 = -5

The polynomial can also be evaluated by graphing polynomial and finding the point of intersection of the line x = -2 and the graph of the polynomial as follows;

The attached graph created with MS Excel, indicates that at the point x = -2 (represented by the point where the vertical line, x = -2, intersects the polynomial, x² + 4·x - 1) is the point where, f(x) = -5

The value of the polynomial, f(x) = x² + 4·x - 1, when x = -2 is -5.

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Using an algebraic equation to represent the word problem, the smallest integer is 1

This is a way of representing mathematical problems with words. To solve this, we have to use algebraic equations or expressions.

Let the integers be represented as

We can write an equation from the word problem given as

7 × (x + 2) = 15 + [x + (x + 4)]

7x + 14 = 15 + x + x + 4

7x + 14 = 15 + 2x + 4

collect like terms

7x - 2x = 15 - 14 + 4

5x = 5

Divide both sides by coefficient of x

5x / 5  = 5 / 5

x = 1

The smallest integer is 1

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Translation:

Find the smallest of three consecutive odd integers such that 7 times the middle integer is 15 more than the sum of the first and third integers

Answer:

The last table is the answer

Step-by-step explanation:

The last table has a constant slope of -3, hence it represents a linear function.

From the given table, we need to determine which of the table is a linear table.

Looking at the last table;

Slope = -4-(-2)/2-1
Slope = -4+1/1

Slope = -3

Since the last table has a constant slope of -3, hence it represents a linear function.

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Answer:

increases by 30

Step-by-step explanation: its right

12

Hope it helps!!!!!!!

Answer:

x = 5

Step-by-step explanation:

Let's solve your equation step-by-step.

4x+2=2(x+6)

Step 1: Simplify both sides of the equation.

4x+2=2(x+6)

4x+2=(2)(x)+(2)(6)(Distribute)

4x+2=2x+12

Step 2: Subtract 2x from both sides.

4x+2−2x=2x+12−2x

2x+2=12

Step 3: Subtract 2 from both sides.

2x+2−2=12−2

2x=10

Step 4: Divide both sides by 2.

\( \tt \: \frac{2x}{2} = \frac{10}{2} \)

Result:

x = 5

There are 4 cups of brown sugar are required for every 12 cups of white sugar.

A recipe calls for 2 cups of brown sugar for every 6 cups of white sugar. We can set up a proportion to find the relationship between the two quantities:

2 cups brown sugar / 6 cups white sugar = x cups brown sugar / 12 cups white sugar

To find the number of cups of brown sugar required for 12 cups of white sugar, we can cross-multiply and then solve for x:

2 cups brown sugar × 12 cups white sugar = 6 cups white sugar × x cups brown sugar

24 cups brown sugar = 6x cups brown sugar

x = 24/6

x = 4

So, 4 cups of brown sugar are required for every 12 cups of white sugar.

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Answer:

\(2x^{2} +3x\)

Step-by-step explanation:

g(2x+3)

x(2x+3)

2x^2+3x

The Value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC Therefore, AC is Congruent to c .

Since AC and BD bisect each other at O, we can say that AO = OC and BO = OD.

We need to prove that AC = CD.To do this, we can use the segment addition postulate which states that if a line segment is divided into two parts, the length of the whole segment is equal to the sum of the lengths of the two parts.

Let us draw a diagram to represent the given information:From the diagram, we can see that:AO + OB = AB (By segment addition postulate)OC + OD = CD (By segment addition postulate)AO = OC (Given)BO = OD (Given)

Now, we can substitute the values of AO and OC as well as BO and OD into the equations above:AO + OB = AB ⇒ OC + OB = AB (Substituting AO = OC)OC + OD = CDNow, we can add both equations:OC + OB + OC + OD = AB + CD ⇒ 2(OC + OD) = AB + CDWe know that OC = AO and OD = BO.

Therefore, we can write:2(AO + BO) = AB + CDSince AO = OC and BO = OD, we can write:2(OA + OD) = AB + CDNow, substituting AO = OC and BO = OD, we can write:2AC = AB + CD

Finally, we can substitute the value of CD from the second equation into the first equation:2AC = AB + OC + OD⇒ 2AC = AB + AB (By substituting OC = OA and OD = OB)⇒ 2AC = 2AB⇒ AC

Therefore, AC is congruent to c .

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If the radius is 3 cm, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm. The correct option is B.

The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.

We are given that the volume of the cylinder is 637 cm³ and the radius is 3 cm. Substituting these values into the formula, we get:

637 = π(3²)h

Simplifying:

637 = 9πh

h = 637 / (9π)

h ≈ 7.06

Thus, the height of the cylinder is approximately 7.06 cm, which is closest to option B, 7 cm.

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Answer:

Jason is taller than his brother

Step-by-step explanation:

Jason is taller and he is 0.5 meters taller than his brother.

A linear model is a mathematical model that describes a linear relationship between an independent variable and a dependent variable. This type of model is used in many fields, including statistics, economics, and machine learning, to explain relationships between variables, predict future outcomes, and analyze data.

Given that, Jason is 1.4 meters tall and his brother is 0.9 meter tall.

Here, difference in height = 1.4-0.9

= 0.5 meters

Therefore, Jason is taller and he is 0.5 meters taller than his brother.

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Answer:

1/7 or 0.14

Step-by-step explanation:

Answer:

0.14

Step-by-step explanation:

All I did was plug it into my calculator. If you don't have one, you can use your phone or computer. Both devices have calculators programmed in. This answer is not the exact answer; it is just the first two decimals.

Please let me know if you need more help. Hope this helps!

The total possible outcomes is 16, the probability that all children are males is 1/16, the probability of having all one gender is 1/8

1. The tree diagram for the sex of the children is as follows:

Child 1: M / F

Child 2: M / F

Child 3: M / F

Child 4: M / F

Possible Outcomes: MMMM, MMMF, MMFM, MFMF, FMFM, FMMF, FMFF, FFFF

There are 2 options for each child, so the total number of possible outcomes is 2 x 2 x 2 x 2 = 16.

2. The probability that all children are males is 1/2 x 1/2 x 1/2 x 1/2 = 1/16.

3. The probability of having all one gender of children is the sum of the probability of having all boys and the probability of having all girls. Each of these outcomes has a probability of 1/16, so the total probability is 1/16 + 1/16 = 1/8.

4. The easiest way to solve this problem is to find the probability of having no female children, and then subtract that from 1. The probability of having no female children is (1/2)^4 = 1/16, so the probability of having at least 2 female children is 1 - 1/16 - 1/16 = 7/8.

5. The tree diagram for flipping a coin, rolling a 6-sided die, flipping a coin, and rolling a 3-sided die is as follows:

C / H

/

1-6 1-3

\ /

H / T

The first branch represents the coin flip, the second branch represents the roll of the 6-sided die, the third branch represents the second coin flip, and the fourth branch represents the roll of the 3-sided die.

6. There are 2 options for the first coin flip, 6 options for the second branch, 2 options for the second coin flip, and 3 options for the fourth branch, so the total number of possible outcomes is 2 x 6 x 2 x 3 = 72.

7. The probability of getting only heads on both coin tosses is 1/2 x 1/2 = 1/4. Therefore, the probability of getting only heads on both coin tosses and any result on the dice is 1/4 x 1 = 1/4.

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Answer:

find the lcm of 22,36,and 42

Step-by-step explanation:

lcm of 22 = 11 x 2

lcm of 36 = 2 x 2 x 3 x 3

lcm of 42 = 2 x 3 x 7

so the lcm of three numbers are 11 x 2 x 2 x 2 x 3 x 3 2 x 3 x 7 = 1000

Answer:

2,772

Step-by-step explanation:

First we find the LCM (Least common multiple) of the given numbers.

2 | 22, 36, 42

2 | 11, 18, 21

3 | 11, 9, 21

3 | 11, 3, 7

7 | 11, 1, 7

11 | 11, 1. 1

| 1, 1, 1,

LCM of 22, 36, 42 = 2*2*3*3*7*11 = 2,772

Thus, the lowest number of four digits that can be divided by 22,36,and 42 is 2772.

Using a system of equations, the number of children and adults who attended the movies is as follows:

A system of equations is two or more equations solved concurrently.

A system of equations is also known as simultaneous equations.

The total number of people who went to the movies = 100

The unit cost of adult tickets = $4

The unit cost of children tickets = $2

The total sales = $276

Let the number of children who attended the movies = x

Let the number of adults who attended the movies = y

x + y = 100 ... Equation 1

2x + 4y = 276 ... Equation 2

Multiply Equation 1 by 2:

2x + 2y = 200 ... Equation 3

Subtraction Equation 3 from Equation 2:

2x + 4y = 276

-

2x + 2y = 200

2y = 76

y = 38

Substitute y = 19 in equation 1:

x + y = 100

x + 38 = 100

x = 62

Check in Equation 2:

2x + 4y = 276

2(62) + 4(38) = 276

124 + 152 = 276

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