Slope of the line passing through the points (-3,3) and (5,9)

Answer:

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

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:

223 hours

Step-by-step explanation:

Total hours worked by Lee = sum of all the hours worked

That’s

82 + 61 + 7 + 73 = 223 hours

Therefore, Lee worked 223 hours as manager for the local Pizza Hut

Lee Jenkins worked a total of 223 hours by adding the given values of 82, 61, 7, and 73 hours.

In this problem, we need to find out how many total hours did Lee work by summing up all the hours given in the problem. The hours worked as given in the problem are 82, 61, 7, and 73. To find the total hours worked, we simply add these values.

The addition becomes 82 + 61 + 7 + 73 = 223

Therefore, Lee Jenkins worked a total of 223 hours as a manager at a local Pizza Hut.

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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.

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:

Slope of the line = 1

Step-by-step explanation:

A line with two points, we are asked to find the slope

We are using the formula

m = (y_2 - y_1) /( x_2 - x_1)

We are provided with some points

( -9 , -9) ( -6 , -6)

x_1 = -9

y_1 = -9

x_2 = -6

y_2 = -6

Insert the values into the equation

m = (y_2 - y_1) / (x_2 - x_1)

m = ( -6 - (-9)) / ( -6 - (-9))

Hint: - * - = +

m =( -6 + 9) / ( -6 + 9)

= 3 / 3

= 1

Slope m = 1

Therefore, the slope of the line = 1

Answer:

Step-by-step explanation:

The figure appears to be drawn roughly to scale, so that fact can offer clues.

The triangles both have hypotenuses of 5. The only integer lengths for sides that will give a hypotenuse of 5 are side lengths 3 and 4. Right triangles with side lengths 3 and 4 will have an area of (1/2)(3)(4) = 6.

The rectangle at lower left will not have a side length of 3, so its width is 4. Since its area is 8 (width × height), the height of it must be 2. (The rectangle dimensions must be factors of 8.)

The vertical side of the left triangle is then 3. It appears to be divided so the upper segment (the side of the rectangle of area 6) is 1 and the lower segment (part of the right triangle vertical side) is 2.

Then the vertical side of the right triangle is 4, and its horizontal side (left half of the bottom of the upper rectangle) is 3.

Since the height of the upper rectangle is 1, its width must be 6. Then the little tab hanging down on the right must be 2 by 2 (for an area of 4).

Altogether, we have found the lengths to be as marked in the attachment.

___

Summary

The perimeter lengths, CW from the lower left vertical, are ...

  2, 5, 6, 3, 2, 2, 1, 5, 4 . . . . meters

The perimeter is their total: 30 m.

Step-by-step explanation:

[tex] m \angle \: a + 80 \degree = 180 \degree \\ (linear \: pair \: \angle s) \\ \therefore \: a = 180 \degree - 80 \degree \\ \huge \red { \boxed{\therefore \: a = 100 \degree}} \\ \\ \huge \purple { \boxed{m \angle \: b = 80 \degree }} \\ (corresponding \: \angle s) \\ \\ m \angle \: c=m \angle \: a \\ (vertical \: \angle s) \\\huge \orange { \boxed{ \therefore \: m \angle \: c = 100 \degree}}[/tex]

Answer:

  12

Step-by-step explanation:

Let d represent the number of dimes Lily saved. Then the value of her coins in cents is ...

  10d +100(16-d) = 520

  -90d +1600 = 520 . . . . . eliminate parentheses, collect terms

  -90d = -1080 . . . . . . . . . . subtract 1600

  d = -1080/-90 = 12 . . . . . divide by the coefficient of d

Lily has 12 ten-cent coins.

Answer:

None.

Step-by-step explanation:

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

Answer: none

Step-by-step explanation:

Answer:

It is on the x - axis

Step-by-step explanation:

Point (2, 0) lie on the x axis

Answer:

It is on the X axis

Step-by-step explanation:

The horizontal line is the x axis and the x coordinate is always given first (x, y) or in this case (2, 0)

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.

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:

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:

see the explanation

Step-by-step explanation:

we have

[tex]x^2+6x+y^2-16y=-9[/tex]

Convert the equation of the circle in center radius form

Group terms that contain the same variable

[tex](x^2+6x)+(y^2-16y)=-9[/tex]

Complete the square twice. Remember to balance the equation by adding the same constants to each side

[tex](x^2+6x+9)+(y^2-16y+64)=-9+9+64[/tex]

[tex](x^2+6x+9)+(y^2-16y+64)=64[/tex]

Rewrite as perfect squares

[tex](x+3)^2+(y-8)^2=8^2[/tex]

The center of the circle is (-3,8)

The radius of the circle is 8 units

Verify each statement

A. The center of the circle is (3,-8).

False

The center of the circle is (-3,8)

B. The circle is tangent to the x-axis

True

The circle is tangent to x=5 and x=-11 and is tangent to y=0 and y=16

Remember that y=0 is the x-axis

C. The circle has a radius of 64

False

The radius of the circle is 8 units

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:

[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]

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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Answer:

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

Example:  45 + 45 = 90 are complimentary

                60 + 30 = 90 are complimentary

The measure of ∠A is 137°.

Solution:

Given data:

Angle A = 43°

A quadrilateral inscribed in a circle is called cyclic quadrilateral.

∠A and ∠C are opposite angles in a cyclic quadrilateral.

In cyclic quadrilateral, opposite angles are supplementary.

⇒ m∠A + m∠C = 180°

⇒ 43° + m∠A = 180°

Subtract 43° from both sides of the equation, we get

⇒ m∠A = 137°

Hence the measure of ∠A is 137°.

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.

Each employees receive an amount of  $1976.25 / n

Explanation:

Amount of money that Philip has,(we can represent as  A) = $2000

Spends, (We can represent as s) = $23.75

Divides the rest equally among each employees.

Let the number of employees = n

To find the amount of money

Money left = A - s

                  = $2000 - $23.75

                  = $1976.25

Each employees receive = $1976.25 / n

Therefore ,Each employees receive an amount of  $1976.25 / n.

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%.

Answer:

Step-by-step explanation:152

You would need 152 points on game 3

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:

what is the question??

Answer:

x=8

Step-by-step explanation:

on edge

Answer:

8

Step-by-step explanation:

on edge

Answer:

-3, -9

Step-by-step explanation:

27  = 1*27     -1*-27

        3*9        -3*-9

We want it to add to -12

The only choice is -3+-9 = -12

The two numbers are -3, -9

The two numbers that multiply to 27 and add to -12 are -3 and -9.

The question is asking to find two numbers that multiply to give 27 and add to give -12. The fact that the product is positive and the sum is negative suggests that the two numbers in question are both negative because when two negative numbers are multiplied, the result is positive. To solve this, you need to think of the pairs of factors of 27, which are (1, 27) and (3, 9). Since we are looking for a sum of -12, the correct pair is (-3, -9) because -3 multiplied by -9 equals 27, and -3 plus -9 equals -12.