Leyton Buy bags of popcorn bags of pretzels for a party. A bag of popcorn costs $ 2 . A bag of pretzels cost three. Leyton spends $24 for bags in all

Answer:  240 liters

=======================================================

Work Shown:

x = capacity of barrel in liters

This value of x is some positive real number. It represents the most amount of water the barrel can hold.

The problem states that the barrel is 2/3 full to start with. This means, we start off with (2/3)x liters of water. Then we subtract off 60 of them to get to 5/12 full, meaning we have (5/12)x liters left.

We can form this equation

(2/3)x - 60 = (5/12)x

Multiply both sides by 12 to clear out the fractions

(2/3)x - 60 = (5/12)x

12*( (2/3)x - 60 ) = 12*(5/12)x

12*(2/3)x - 12*60 = 12*(5/12)x

8x - 720 = 5x

From here we solve for x

8x - 5x = 720

3x = 720

x = 720/3

x = 240

The barrel's full capacity is 240 liters

--------------------------

Check:

2/3 of 240 = (2/3)*240 = 160

The barrel starts off with 160 liters of water inside.

We then use 60 of them to be left with 160-60 = 100 liters

Note how 100/240 = (5*20)/(12*20) = 5/12, showing that 100 liters out of 240 total reduces to the fraction 5/12. In other words, when we say "5/12 full" we mean 100 liters full. This helps confirm we have the right answer.

Answer

$7.82

Step-by-step explanation:

12 hrs=$93.84

1 hr= 93.84/12

1 hr=$7.82

Let's take this problem step by step:

To find the ordered pair of the system:

⇒ must set both equations equal to each other

    ⇒ and solve for 'x'

Let's solve:

 \(x^2-2x+3=-2x+19\\x^2-2x+2x+3-19=0\\x^2-16=0\\(x+4)(x-4)=0\)

Let's find the x-values:

   \((x-4)=0\\x=4\\\\(x+4)=0\\x=-4\)

Let's find f(x)'s value for each 'x':

 \(x=4\\f(4)=-2(4)+19=-8+19=11\\\\x=-4\\f(-4)=-2(-4)+19=8+19=27\)

Answer: (4, 11), (-4,27)

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Answer:

9120(b)

Step-by-step explanation:

95×96

(90+5)×(90+6)

(90×90)+(5+6) (90)+(5)(6)

(90) square+(5+6) (90)+(5)(6)

I am using identity 4

=8100+990+30=9120

Answer:

\(x = 8\)

Step-by-step solution:

2D dimensions give us this equation when it comes to parallelograms like these:

\( \frac{area}{height} = side\)

In this case, x is side. So now you do 104/13=x, so x=8.

Given:

Given a triangle.

Required:

To find the remote interior angles of angle 1.

Explanation:

Remote interior angles are angles that don't share a vertex or corner of a triangle with the exterior angle.

Here the remote interior angles of angle 1 are

Final Answer:

Option C and F are correct.

Answer:

7x

Step-by-step explanation:

(8x+5)- (x+5)

8x+5-x-5

8x -x(1x)

7x

Answer:

30 square inches

Step-by-step explanation:

The table of values for the composition (f o g)(x) for polynomial functions f(x) and g(x) is:

x (f o g)(x)

-2 7

-1 4

0 3

1 4

2 7

To find the values of (f o g)(x), we need to substitute the values of g(x) into f(x). The composition (f o g)(x) means that we first apply g(x) to x, and then apply f(x) to the result.

Using the table of values for g(x):

x g(x)

-2 4

-1 1

0 0

1 1

2 4

We substitute these values into f(x):

x f(x)

0 3

1 4

2 5

3 6

4 7

Calculating (f o g)(x):

For x = -2:

(f o g)(-2) = f(g(-2)) = f(4) = 7

For x = -1:

(f o g)(-1) = f(g(-1)) = f(1) = 4

For x = 0:

(f o g)(0) = f(g(0)) = f(0) = 3

For x = 1:

(f o g)(1) = f(g(1)) = f(1) = 4

For x = 2:

(f o g)(2) = f(g(2)) = f(4) = 7

Completing the table of values for (f o g)(x):

x (f o g)(x)

-2 7

-1 4

0 3

1 4

2 7

Therefore, the completed table of values for (f o g)(x) is as shown above.

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The value of "a" is approximately 1.83 given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive.

We are given that the absolute value of the difference between the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive. We need to find the value of "a".

Let the two roots of the equation be r1 and r2, where r1 is not equal to r2. Then, we have:

|r1 - r2| = √(61) / 3

The sum of the roots of the quadratic equation is given by r1 + r2 = -5 / a, and the product of the roots is given by r1 × r2 = -3 / a.

We can express the difference between the roots in terms of the sum and product of the roots as follows:

r1 - r2 = √((r1 + r2)² - 4r1r2)

Substituting the expressions we obtained earlier, we have:

r1 - r2 = √(((-5 / a)²) + (4 × (3 / a)))

Simplifying, we get:

r1 - r2 = √((25 / a²) + (12 / a))

Taking the absolute value of both sides, we get:

|r1 - r2| = √((25 / a²) + (12 / a))

Comparing this with the given expression |r1 - r2| = √(61) / 3, we get:

√((25 / a²) + (12 / a)) = √(61) / 3

Squaring both sides and simplifying, we get:

25 / a² + 12 / a - 61 / 9 = 0

Multiplying both sides by 9a², we get:

225 + 108a - 61a² = 0

Solving this quadratic equation for "a", we get:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61)

Since "a" must be positive, we take the positive root:

a = (108 + √(108² + 4 × 61 × 225)) / (2 × 61) ≈ 1.83

Therefore, the value of "a" is approximately 1.83.

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The question is -

Given that the absolute value of the difference of the two roots of the quadratic equation "ax squared plus 5x minus 3 equals 0" is the square root of 61 divided by 3, and "a" is positive, what is the value of "a"?

Answer:

(1, -6)

Step-by-step explanation:

After reflecting over y axis: (1, 6)

After reflecting (1, 6) over x axis: (1, -6)

I think you made a typo in your question. I think you meant "x-axis" instead of "r-axis"

The couple needs to invest $9,060.52 per year to have enough money to send their daughter to university.  The couple needs to invest an additional $1,322.18 per year if they wait one year to start saving for their daughter's university education.

a. The amount of money the couple needs to invest each year can be calculated using the present value of annuity formula. The future value of the university cost after 10 years can be calculated by compounding the current cost for 10 years at an annual inflation rate of 5.6%.

Then, the present value of this future cost can be found by discounting it back to the present using the effective annual interest rate of 6.75%. Finally, this present value can be divided by the present value of an annuity factor for 9 years (one year before the university starts) at an effective annual interest rate of 6.75%.

Using these calculations, the couple needs to invest $9,060.52 per year to have enough money to send their daughter to university.

b. If the couple waits for one year, they will have nine years to save for their daughter's university education. This means they will have one less year to invest, so they will need to invest more each year to have enough money for their daughter's university education.

The additional amount they need to invest can be found by subtracting the present value of an annuity of $9,060.52 for 9 years from the present value of an annuity of $9,060.52 for 8 years.

Using these calculations, the couple needs to invest an additional $1,322.18 per year if they wait one year to start saving for their daughter's university education.

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The linear equation that passes through the points (14, 15) and (20, 24) crosses the y-axis at y = -6.

A general linear equation can be written as:

y = m*x + b

Where m is the slope and b is the y-intercept.

If the line passes through two points (x₁, y₁) and (x₂, y₂), then the slope can be written as:

m = (y₂ - y₁)/(x₂ - x₁).

In this case the line passes through (14, 15) and (20, 24) so the slope is:

m = (24 - 15)/(20 - 14) = 9/6 = 3/2

y = (3/2)*x + b

To find the y-intercept we can replace the values of one of the points, like (14, 15)

15 = (3/2)*14 + b

15 = 3*7 + b

15 = 21 + b

15 - 21 = b

-6 = b

The y-intercept is -6.

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Answer:

2/3

Step-by-step explanation:

i graphed it on desmos lol

It is one of the most fundamental curvilinear geometric shapes, a cylinder has historically been thought of as a three-dimensional solid. It is considered a prism with a circle as its base in basic geometry.

the area of mathematics that focuses on the characteristics and connections between points, lines, surfaces, solids, and their higher dimensional equivalents.

We can find the solution this way,

The volume of water in the Cylinder before marbles were dropped in =

The volume of water in the Cylinder After marbles were dropped in -

Volume of marbles

So, we can write it as,

Volume of water before = Volume of water after - Volume of Marbles

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The probability of choosing an integer at random from the first 100 positive integers that is exactly divisible by 7 is 7/50.

The probability of choosing an integer from the first 100 positive integers that is exactly divisible by 7 can be calculated by determining the number of integers in the range that are divisible by 7 and dividing it by the total number of integers in the range.

To find the number of integers between 1 and 100 that are divisible by 7, we need to find the largest multiple of 7 that is less than or equal to 100.

By dividing 100 by 7, we get 14 with a remainder of 2. This means that the largest multiple of 7 less than or equal to 100 is 14 * 7 = 98.

So, there are 14 integers between 1 and 100 that are divisible by 7 (7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, 98).

Now, we can calculate the probability by dividing the number of integers divisible by 7 (14) by the total number of integers in the range (100).

Probability = Number of favorable outcomes / Total number of outcomes

Probability = 14 / 100

Simplifying the fraction, we get:

Probability = 7 / 50

Therefore, the probability of choosing an integer at random from the first 100 positive integers that is exactly divisible by 7 is 7/50.

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Answer:

6 inches

Step-by-step explanation:

The width is generally the smaller number unless it is landscape instead of portrait

Answer:

x ≈ 1051.368672

Step-by-step explanation for #3:

\(tan(\frac{x}{12}) =24\)          Use tangent function because it relates to the opposite and adjacent sides of the triangle.

\(tan^{-1}(tan(\frac{x}{12}))=tan^{-1}(24)\)

\(\frac{x}{12} = tan^{-1}(24)\)

\(x = 12[tan^{-1}(24)]\)

x ≈ 1051.368672

If you have any more questions, feel free to ask and I'll answer them in the comments section under this answer. Please consider marking my answer as Brainliest, because it really helps me out.

Thanks!

Easy, the dot coordinate at y is -4, and so you find the c in ax² + bx + c that has -4.

Answer:

n=0

Step-by-step explanation:

-10n + 24 + 24n = -6n + 24 is the equation you are given

The first thing I did was combine like terms (-10n and 24n)

I should look like this... 14n+24=-6n+24

The second thing I did was add the 6n to 14n. Remember when you switch the sides of a number/letter in an equation the sign in front of it needs to change.

It should look like this... 20n+24=24

The third thing I did was take 24 and 24 and subtract them. You will get 0.

It should look like this... 20n=0

The last thing to do is divide 0 and 20. That will equal 0!

It should look like this... n=0

I hoped I helped. If you have any more question about his problem let me know! Good Luck. God Bless. Stay Safe. Max Larson

The equation of the line is y = 2x + 8 that is parallel to the given line y = 2x + 2 and passes through the point (−3, 2)

An equation is an expression that shows the relationship between two or more numbers and variables.

The equation of a straight line is:

y = mx + b

Where m is the rate of change and b is the y intercept.

Two lines are parallel if they have the same slope.

Let us assume that the line is parallel to y = 2x + 2 and passes through the point (−3, 2).

The slope of the line y = 2x + 2 is 2, Since it is parallel, the slope is also 2. hence:

y - y₁ = m(x - x₁)

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

y - 2 = 2(x + 3)

y = 2x + 8

The equation of the line is y = 2x + 8

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An equation of the line that is parallel to the given line and passes through the point (−3, 2) is: 4x + 3y = -6.

Mathematically, the slope of any straight line can be calculated by using this formula;

Slope, m = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope, m = (y₂ - y₁)/(x₂ - x₁)

By critically observing the graph (see attachment), we can logically deduce that the line passes through the following points:

Points (x, y) = (3, -1)

Points (x, y) = (0, 3)

Substituting the given parameters into the formula, we have;

Slope, m = (3 + 1)/(0 - 3)

Slope, m = 4/-3

Slope, m = -4/3.

In Geometry, two (2) lines are parallel under the following conditions:

m₁ = m₂ ⇒ -4/3 = -4/3

Note: m represents the slope.

At point (-3, 2), an equation of the other line can be calculated by using the point-slope form:

y - y₁ = m(x - x₁)

Where:

Substituting the given points into the formula, we have;

y - y₁ = m(x - x₁)

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

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

y - 2 = -4x/3 - 4

y - 2 = -4x/3 - 4 + 2

y = -4x/3 - 2

Multiplying all through by 3, we have:

3y = -4x - 6

Rearranging the equation, we have:

4x + 3y = -6

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Average waiting time for FCFS: 8.75

Average waiting time for SJF: 4.75

To solve this scheduling problem using FCFS (First-Come, First-Served) and SJF (Shortest Job First) algorithms, let's go step by step:

Schedule order for FCFS:

The FCFS algorithm schedules processes based on their arrival time. So, the schedule order for FCFS is as follows:

Pl -> P2 -> P3 -> P4

Average waiting time for FCFS:

To compute the average waiting time for FCFS, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P2 | 3 | 10 | 3

P3 | 4 | 6 | 13

P4 | 5 | 1 | 19

Average waiting time = (0 + 3 + 13 + 19) / 4 = 8.75

Therefore, the average waiting time for FCFS is 8.75.

Schedule order for SJF:

The SJF algorithm schedules processes based on their running time. The process with the shortest running time gets executed first. If multiple processes have the same running time, the process with the earliest arrival time is selected first. The schedule order for SJF is as follows:

Pl -> P4 -> P3 -> P2

Average waiting time for SJF:

To compute the average waiting time for SJF, we need to calculate the waiting time for each process and then take the average.

Process | Arrival Time | Running Time | Waiting Time

Pl | 0 | 3 | 0

P4 | 5 | 1 | 3

P3 | 4 | 6 | 6

P2 | 3 | 10 | 10

Average waiting time = (0 + 3 + 6 + 10) / 4 = 4.75

Therefore, the average waiting time for SJF is 4.75.

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If you make annual payments of $1400 for 8 years at a 6% interest rate compounded annually, the total amount accumulated over the 8-year period would be approximately $12,350.

To explain further, when you make annual payments of $1400 for 8 years, you are essentially depositing $1400 into an account each year. The interest rate of 6% compounded annually means that the interest is added to the account balance once a year.

To calculate the total amount accumulated, you can use the formula for the future value of an ordinary annuity:

FV = P * ((1 + r)^n - 1) / r

where FV is the future value, P is the payment amount, r is the interest rate per compounding period (in this case, 6% or 0.06), and n is the number of compounding periods (in this case, 8 years).

Plugging in the values, we have:

FV = $1400 * ((1 + 0.06)^8 - 1) / 0.06

≈ $12,350

Therefore, the total amount accumulated over the 8-year period would be approximately $12,350.

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Answer:

9

Step-by-step explanation:

The answer of the given question based on the right angle triangle is , the height of the light pole to the nearest tenth of a foot is 9.3 feet.

A right-angled triangle, also known as a right triangle, is a triangle that has one angle equal to 90 degrees. The side opposite right angle is called hypotenuse, and other two sides is called legs. The leg opposite to a particular acute angle is known as the opposite side, and the leg adjacent to it is known as the adjacent side.

The Pythagorean theorem is a fundamental theorem that applies to all right-angled triangles. It states that square of hypotenuse of right-angled triangle is equal to sum of squares of its two legs

To determine the height of the light pole, we can use similar triangles.

Let's call height of light pole be  "x". Then we have:

(height of stop sign) / (length of stop sign's shadow) = (height of light pole)/(length of light pole's shadow)

Substituting the given values, we have:

8/12 = x/14

Simplifying this equation, we get:

x = (8/12) * 14 = 9.33 feet

Therefore, the height of the light pole to the nearest tenth of a foot is 9.3 feet.

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Therefore , it means if an equation have 2 roots , it means it is a quadratic function .

The outcome of multiplying a number by itself produces the original number, which is the square root of that number. Squares and square roots are a few of examples of exponents. Try to visualize nine. Furthermore, this can be written as 3x3.

Here,

A quadratic function is one where an equation has two roots.

A quadratic function's two roots are equal if D=0.

D (discriminant) = 0 such that b24ac = 0 is needed in order for the roots of a polynomial function to be equal.

As a result, if an equation has two roots, a quadratic function is what it is.

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Answer:

1/3x^11

Step-by-step explanation:

1/3x^11 is the answer

Answer:

Step-by-step explanation:

a= v/t, where v is the speed and t is the time

a=8/4= 2 m/s^2

The value of both domain and range of this exponential function is (−∞,∞).

y = 2x-9

The domain of the function can be defined as all real numbers except the ones where the expression is undefined. In the case of 2x-9, there is no real number for which this expression is undefined. Therefore, a domain of this exponential function is (−∞,∞).

The range of the function is defined as the set of all valid y values. In this case, all real numbers are valid values of y. Therefore, the range of this exponential function is (−∞,∞).

Therefore, domain of y = 2x-9 is (−∞,∞) and range is also (−∞,∞).

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