Peter left his home in Chicago and drove to a town a few hours away. On the way there, he drove 40 mph due to traffic, but on the way back home, he drove 60 mph. What was his average speed?

Answer:

3 and -4

Step-by-step explanation:

First, you write out each statement as an equation:

x + y = -1

2x + 4y = -10

Next, rewrite one equation so only x is on one side of the equation, and plug it into the other equation, and solve for y:

x = -y - 1

2 (-y - 1) + 4y = -10

-2y - 2 + 4y = -10

2y = -8

y = -4

Plug the found value for y into the original equation and solve for x:

x + y = -1

x - 4 = -1

x = 3

Plug both values into the second equation to check your work:

2x + 4y = -10

2(3) + 4(-4) = -10

6 - 16 = -10

-10 = -10

Final answer:

The two numbers in question are 3 and -4. These values are obtained by solving a system of equations derived from the given conditions.

Explanation:

The sum of two numbers is -1. When twice the first number and four times the second number are added, it equals -10. To find these two numbers, we can set up a system of equations.

Step 1: Establish equations

Let the first number be x and the second number be y. According to the problem, we have:

x + y = -1 (Equation 1)

2x + 4y = -10 (Equation 2)

Step 2: Solve the system

A simple method to solve these equations follows. First, multiply Equation 1 by -2 to get:

-2x - 2y = 2 (Multiply Equation 1 by -2)

Add this new equation to Equation 2:

(2x + 4y) + (-2x - 2y) = -10 + 2

2y = -8

y = -4

Now substitute y = -4 back into Equation 1 to find x:

x + (-4) = -1

x = -1 + 4

x = 3

Therefore, the two numbers are 3 and -4.

Answer:

x=8

Step-by-step explanation:

on edge

Answer:

8

Step-by-step explanation:

on edge

Answer:

[tex] \frac{2}{5} = \frac{30}{x} \\ 2x = 30 \times 5 \\ \frac{2x}{2} = \frac{150}{2} \\ x = 75 {m}^{2} [/tex]

Answer:

$1600 is the full budget

Step-by-step explanation:

1200/3=400

400x4=1600

Answer:

$1600

Step-by-step explanation:

1200 is 3/4 of the budget, so just divide 1200 by 3/4.

Step-by-step explanation:

Two points on the line are (1,4) and(-4,-4)

slope of the line =

[tex] \frac{ y2 - y1}{x2 - x1} [/tex]

[tex] \frac{ - 4 - 4}{ - 4 - 1} [/tex]

[tex] \frac{ - 8}{ - 5} [/tex]

[tex] \frac{8}{5} [/tex]

Answer:

14.75 days

Step-by-step explanation:

number of pages she reads a day :

384/8 = 48

remaining of the book

1056-348= 708

708/48= 14.75 days

Answer:

9

Step-by-step explanation:

3^2 = 9

Answer:

f(2) = 9

Step-by-step explanation:

Step 1:  Substitute 2 for x in the function

f(x) = 3^x

f(2) = 3^2

f(2) = 3*3

f(2) = 9

Answer:  f(2) = 9

Answer:

B) 37.68 ft

Step-by-step explanation:

The diameter is 12 because the square's side is 12. The circumference is diameter * pi. 12 * 3.14 = 37.68.

Hope I Helped

Answer:

[tex]y=-\frac{3}{4}x-\frac{3}{2}[/tex]

or

[tex]y=-0.75x-1.5[/tex]

Step-by-step explanation:

step 1

Find the equation of the line in point slope form

[tex]y-y1=m(x-x1)[/tex]

we have

[tex]m=-\frac{3}{4} \\point\ (-6,3)[/tex]

substitute

[tex]y-3=-\frac{3}{4}(x+6)[/tex]

step 2

Convert to slope intercept form

[tex]y=mx+b[/tex]

we have

[tex]y-3=-\frac{3}{4}(x+6)[/tex]

Isolate the variable y

[tex]y-3=-\frac{3}{4}x-\frac{9}{2}[/tex]

[tex]y=-\frac{3}{4}x-\frac{9}{2}+3[/tex]

[tex]y=-\frac{3}{4}x-\frac{3}{2}[/tex]

Answer:

89

Step-by-step explanation:

92 = (90 + 98 + 96+ 94 + 85 + x )/6

92*6 = 90 + 98 + 96+ 94 + 85 + x

552 - (90 + 98 + 96+ 94 + 85) = x

x = 89

Answer: X/6 -24 = -5

Step-by-step explanation:

The value of x = 11 and y = 11√3.

Solution:

The triangle is right triangle.

θ = 30° and hypotenuse = 22

The value of sin 30° = [tex]\frac{1}{2}[/tex]

The value of cos 30° = [tex]\frac{\sqrt{3} }{2}[/tex]

Using trigonometric formulas,

[tex]$\sin\theta=\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]

[tex]$\sin30^\circ=\frac{x}{\text{22}}[/tex]

[tex]$\frac{1}{2} =\frac{x}{\text{22}}[/tex]

Do cross multiplication, we get

22 = 2x

Switch the sides

2x = 22

Divide by 2, we get

x = 11

[tex]$\cos\theta=\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]

[tex]$\cos30^\circ=\frac{y}{\text{22}}[/tex]

[tex]$\frac{\sqrt{3} }{2} =\frac{y}{\text{22}}[/tex]

Do cross multiplication, we get

[tex]22\sqrt 3 = 2y[/tex]

Switch the sides

[tex]2y=22\sqrt 3[/tex]

Divide by 2, we get

[tex]y= 11\sqrt3[/tex]

Hence the value of x = 11 and y = 11√3.

Answer:

68

Step-by-step explanation:

fg(-2) is equal to f(g(-2)). g(-2)=-6. f(-6)=68

Answer:

g(-2)= 5(-2) + 4 = -10 + 4= -6

f(-6) = 8 - 10(-6)= 8 + 60 = 68

Step-by-step explanation:

Answer:

Step-by-step explanation:

The value of a is -6, and the value of b is 48.

To solve the equation a(3x-8) = b - 18x for the values of a and b, we need to distribute the 'a' to both terms inside the parentheses and then compare coefficients from both sides of the equation.

Firstly, we distribute:

Now, since the equation should hold true for all values of 'x', the coefficients of 'x' on both sides must be equal, and the constant terms should also be equal. We can set up two separate equations as follows:

Solving these two equations, we find that:

So, the value of a is -6, and the value of b is 48.

Answer:

533 sq in

Step-by-step explanation:

13x29=377. that is the area of the rectangle.

then, the side of the triangle will be 13+11= 24in

area of a triangle is bxh/2 so 13x24 is 312 then divided by 2 is 156.

Add the two areas together 377+156 to get 533.

Answer:

533 sq inch

Step-by-step explanation:

Area for rectangle is Length time with

29x13 = 377

area of triangle is base time hieght / 2

24 x 13 = 312 / 2 =156

add them

A = $ 1,721.28

A = P + I where

P (principal) = $ 1,500.00

I (interest) = $ 221.28

With daily compounding, $1500 at 7% annual interest for 2 years yields approximately $1721.79. Compound interest accelerates growth.

To find the balance after 2 years with daily compounding interest, we'll use the formula for compound interest:

[tex]\[A = P\left(1 + \frac{r}{n}\right)^{nt}\][/tex]

Where:

[tex]- \(A\) is the amount of money accumulated after \(t\) years, including interest.- \(P\) is the principal amount (the initial amount of money).- \(r\) is the annual interest rate (in decimal).- \(n\) is the number of times that interest is compounded per unit \(t\).- \(t\) is the time the money is invested for, in years.[/tex]

Given:

[tex]- Principal \(P = $1500\)\\- Annual interest rate \(r = 7\% = 0.07\) (in decimal)\\- Compounded daily, so \(n = 365\) (days in a year)- Time \(t = 2\) years[/tex]

Let's calculate the balance  [tex]\(A\):[/tex]

[tex]\[A = 1500\left(1 + \frac{0.07}{365}\right)^{365 \times 2}\]\[A \approx 1500\left(1 + \frac{0.07}{365}\right)^{730}\]Now, let's compute the value:\[A \approx 1500 \times (1 + 0.0001917808)^{730}\]\[A \approx 1500 \times (1.0001917808)^{730}\]\[A \approx 1500 \times 1.15183587\]\[A \approx 1727.7538\][/tex]

The corrected calculation gives a balance of approximately $1727.75. This is very close to the initial answer of $1727.67. The slight discrepancy could arise from rounding differences or calculation precision. However, it seems the correct answer is indeed very close to $1727.67, as initially calculated.

To earn $17.00 per hour at a rate of $0.48 per mile, the truck driver needs to drive approximately 35 miles per hour.

To calculate the number of miles the truck driver must travel to earn $17.00 per hour at a rate of $0.48 per mile, one would set up a math problem to solve for the unknown variable, which in this case is the number of miles. We can accomplish this by dividing the desired total wage by the wage earned per mile.

Therefore: 17 ÷ 0.48 = 35.42. Since we cannot have fraction of miles and we must round up or down, we round to the nearest whole number as per the question's instructions, the truck driver must drive approximately 35 miles in one hour to earn $17.00.

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Martha's percent error in estimating the number of marbles in the jar is 21.57%, calculated by finding the difference between her estimate and the actual amount, dividing by the actual amount, and then multiplying by 100.

Explanation:

To calculate Martha's percent error in estimating the number of marbles in a jar, we first determine the difference between the estimated amount and the actual amount.

Actual number of marbles: 102

Estimated number of marbles: 80

Difference: 102 - 80 = 22

Next, we use this difference to find the percent error by dividing the difference by the actual number and then multiplying the result by 100 to get a percentage:

Percent Error = (Difference / Actual number) × 100

Percent Error = (22 / 102) × 100

Percent Error = 0.2157 × 100

Percent Error = 21.57%

Thus, Martha's percent error in her estimation of the number of marbles is 21.57%.

In this high school-level mathematics combinatorics question, the total number of different sets of answers for a quiz comprised of two true-false questions and four multiple-choice questions (each with three options) is 324.

The subject of this question is combinatorics, a branch of mathematics concerning the study of counting, both as a means and an end in obtaining results, and certain properties of finite structures. Considering first the true-false questions, for each question there are 2 possible answers - true or false. So, for two questions, it would be 2x2 which equals 4 possibilities. Now, moving onto the multiple-choice questions, each with three choices (let's say A, B or C), for four such questions it would be 3x3x3x3 which equals 81 possibilities. To find the total possible answer combinations, multiply the results together: 4 (from true/false) x 81 (from multiple choice) = 324. Therefore, there are 324 different sets of answers for this quiz.

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To calculate the number of different sets of answers for a quiz with two true-false questions and four multiple-choice questions, you multiply the possibilities for each question type together, resulting in 324 different sets of answers.

To find the number of different sets of answers for a quiz with two true-false questions and four multiple-choice questions with three choices each, we need to consider the principle of counting. For each true-false question, there are 2 possible answers (True or False). For each multiple-choice question, there are 3 possible answers. To find the total number of different sets of answers, we multiply the number of possible answers for each question together.

For the true-false questions: 2 × 2 = 4 possible combinations.

For the multiple-choice questions: 3 × 3 × 3 × 3 = 81 possible combinations.

Therefore, the total number of different sets of answers is:

4 (from the true-false questions) × 81 (from the multiple-choice questions) = 324 different sets of answers.

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Answer:

d

Step-by-step explanation:

Answer:

$1050

Step-by-step explanation:

The show price will be 25% of $840 and the result added to $840.

Therefore

25% of $840

25% /100% x $840

0.25 x $840

$210

Show price = $840 + $210

= $1050

The show price will be $1050

Final answer:

The show price of the most expensive item after the 25% markup will be $1050.

Explanation:

To determine the show price, we need to calculate a 25% markup on the original price of $840. This markup represents the additional amount added to the original price to determine the final selling price.

To calculate the markup amount, we multiply $840 by 0.25. This gives us $210, which represents the 25% of the original price.

Next, we add the markup amount to the original price. $840 plus $210 equals $1050. This means that the final show price of the most expensive item, after applying a 25% markup, will be $1050.

Therefore, the show price of the most expensive item after the 25% markup will be $1050.

Answer:

what is the question??

Answer:

Complementary angles are two angles that add up to 90 degrees.

Example:  45 + 45 = 90 are complimentary

                60 + 30 = 90 are complimentary

A system of two linear equations in two unknowns have: 4 possible solutions (One, two, Infinitely many and No solutions).The correct options are options C, D, E, F.

One Solution (C): If the two lines intersect at a single point, the system has a unique solution.

Two Solutions (D): This is not a typical outcome for a system of two linear equations in two unknowns. Usually, there is either one solution, no solution, or infinitely many solutions. However, it's worth noting that technically, if the two equations represent the same line, every point on that line is a solution, and you could argue for "two solutions" in that sense.

Infinitely Many Solutions (E): If the two lines are coincident (overlapping), there are infinitely many points of intersection, resulting in infinitely many solutions.

No Solution (F): If the two lines are parallel and distinct, they will never intersect, indicating no solution.

So, C, D, E, and F are correct outcomes

Complete and correct question:

How many possible solutions can a system of two linear equations in two unknowns have? Select all that apply.

A. Four

B. Three

C. One

D. Two

E. Infinitely many solutions

F. No solution

Answer:

D

Step-by-step explanation:

By the graph, males had the highest weight, females stopped around 90 kg, males went well over that.  Males did weigh more on average, being around 70, with the females around 50-60

Answer:

d

Step-by-step explanation:

Answer:

None.

Step-by-step explanation:

You cannot deduce any segments  to be parallel with the given information.

Answer: none

Step-by-step explanation:

Final answer:

The equation 1/9 + x = 1/2 is solved by finding a common denominator and subtracting the fractions, which results in x = 7/18.

Explanation:

To solve the equation 1/9 + x = 1/2, we need to find the value of x.

First, we'll align the equation to isolate x:

Next, we must have a common denominator to subtract the fractions. The least common denominator (LCD) for 9 and 2 is 18. We convert both fractions to have this common denominator:

Now we subtract the numerators:

Thus, the value of x is 7/18.