2x^2 + 108 = 42x NEED HELP SOLVING QUADRATIC EQUATION

Using a system of equations, Christine's investments in account one were $4,000 and in account two $16,000.

A system of equations refers to simultaneous equations.

Simultaneous equations are two or more equations solved concurrently.

Total investment in two accounts = $20,000

The simple interest rate for account one, x = 8%

The simple interest rate for account two, y = 10%

Total interest for a year = $1,920

Let account one = x and account two = y

x + y = 20,000 ... Equation 1

0.08x + 0.1y = 1,920 ... Equation 2

Multiply Equation 1 by 0.08

0.08x + 0.08y = 1,600 ... Equation 3

Subtract Equation 3 from Equation 2:

0.08x + 0.1y = 1,920

-

0.08x + 0.08y = 1,600

0.02y = 320

y = 16,000

= $16,000

In Equation 1, x + y = 20,000, Substitute y = 16,000:

x + 16,000 = 20,000

x = 4,000

= $4,000

Check:

From Equation 2:

0.08x + 0.1y = 1,920

0.08(4,000) + 0.1(16,000) = 1,920

320 + 1,600 = 1,920

Thus, using simultaneous equations, we can conclude that Christine invested $4,000 in the first account and $16,000 in the second account.

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Last year, Christine had $20,000 to invest. She invested some of it in an account that paid 8% simple interest per year, and she invested the rest in an account that paid 10% simple interest per year. After one year, she received a total of $1920 in interest. How much did she invest in each account?

First account:

Second account:

There are 72 different sums that can be obtained by rolling the die, spinning the spinner, and picking a card.

To determine the number of different sums possible, we need to consider the outcomes of rolling the die, spinning the spinner, and picking a card.

Let's analyze each component separately:

1. Rolling the die: The die has 6 sides, numbered 1 to 6. Therefore, there are 6 possible outcomes when rolling the die.

2. Spinning the spinner: The spinner has 6 sections labeled 1 to 6. Again, there are 6 possible outcomes when spinning the spinner.

3. Picking a card: The card has two options, either 6 or 7. Thus, there are 2 possible outcomes when picking a card.

To find the total number of different sums, we need to multiply the number of outcomes for each component. Therefore, the total number of different sums is obtained by multiplying 6 (die outcomes) by 6 (spinner outcomes) by 2 (card outcomes), resulting in 6 * 6 * 2 = 72 different possible sums.

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The number of yards, as a mixed number, will you drive until you reach this exit is 333 1/3 yards

The complete question is added as an attachment

From the attached figure, we have:

Exit = 1000 feet

From the question, we have

3 feet = 1 yard

So, the number of yards is

Number of yard =Exit/3 yards

This gives

Number of yard = 1000/3 yards

Evaluate the quotient

Number of yard = 333 1/3 yards

Hence, the number of yards, as a mixed number, will you drive until you reach this exit is 333 1/3 yards

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The probability is approximately 0.9544 or 95.44%.

To solve this problem, we need to calculate the z-scores for both values of interest and use a standard normal distribution table or calculator to find the probability.

The z-score for a score of 70 is:

z = (70 - 80) / 5 = -2

The z-score for a score of 90 is:

z = (90 - 80) / 5 = 2

Using a standard normal distribution table or calculator, we can find the probability that a randomly selected student scored between -2 and 2 on the standard normal distribution. This probability is approximately 0.9544.

However, we need to adjust this probability to account for the fact that the scores are not rounded. Since the distribution is continuous, we need to use the probability of the interval between 70 and 90, inclusive, which is:

P(70 ≤ X ≤ 90) = P(X ≤ 90) - P(X < 70)

where X is the random variable representing the exam score.

Using the z-scores we calculated earlier, we can find these probabilities as:

P(X ≤ 90) = P(Z ≤ 2) ≈ 0.9772

P(X < 70) = P(Z < -2) ≈ 0.0228

So, the probability of a randomly selected student scoring between 70 and 90 on the exam is:

P(70 ≤ X ≤ 90) = P(X ≤ 90) - P(X < 70) ≈ 0.9772 - 0.0228 = 0.9544

Therefore, the probability is approximately 0.9544 or 95.44%.

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By 15% percent does the population of weeds decrease each day given that the function representing the number of weeds is W(d)=1650(0.85)^d. This can be obtained by using the function representing the exponential decay.

Number of weeds is represented by the function,

W(d)=1650(0.85)^d

⇒ W(d)=1650(1 - 0.15)^d

Here, d = number of days since application

Function representing the exponential decay is,

⇒ A(r) = A(1 - r)^t

where,

A = Initial value

r = Percentage decay

t = duration

By comparing the given function and function representing the exponential decay,

r = 0.15 ≈ 15/100

Or r = 15%    

Therefore, population of weeds will decrease 15% each day.

Hence by 15% percent does the population of weeds decrease each day given that the function representing the number of weeds is W(d)=1650(0.85)^d.

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Answer:

Step-by-step explanation:

108cm3. Explanation: We are given the volume function: V=s3. The rate of change is found using the first derivative of this function.

Answer:

Step-by-step explanation:

The diagonal length of a right rectangular prism is given by the formula (l2 + w2 + h2) units. The length of the diagonal of this rectangular box is 5√2 cm.How do you find the length of a diagonal in a rectangular prism?Therefore, the equation for the diagonal length of a right rectangular prism is (l2+w2+h2), where l is the length, b is the breadth, and h is the height.

In rectangle , The width is 8 and the length is 37.

What is a rectangle ?

A rectangle is a sort of quadrilateral with parallel sides that are equal to one another and four vertices that are all 90 degrees apart. Because of this, it is also known as an equiangular quadrilateral.

                              The term "parallelogram" can also be used to describe a rectangle because the opposing sides are equal and parallel.

90 = 2(x + 5 + 4x)

90 = 2(5x + 5)

90 = 10x + 10

80 = 10x

x = 8

So the width is 8 and the length is 37.

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The complete question is -

The length of a rectangle is five inches more than four times it’s width. If the perimeter is 90 inches, find its dimensions

1. ∠1 and ∠3 are vertically angles

2. ∠8 and ∠7 are Same side interior .

when parallel lines are cut by a transversal line, angle relationships are formed such as corresponding angles, alternate interior angles, alternate exterior angles, linear angles, vertically opposite angles, same side exterior angles, same side interior angles etc.

Therefore, the angles can be established as follows:

Hence,

∠1 and ∠3 are vertically opposite angles.

Vertically opposite angles are congruent.

∠7 and ∠8 are Same side interior angles.

Same side interior angles are supplementary. That means they add up to 180 degrees.

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Answer:

0.2134

Step-by-step explanation:

Answer:

x=12

Step-by-step explanation:

We know that both triangles are congruent meaning corresponding parts are equal. We know that line LN=54 and that RT=LN meaning that RT also equals 54. With that information we can simply subtract 6 from 54 to get 48 then divide by 4 to get  12. Hope this helps!

The mean of the time taken by a mechanic to rebuild the transmission of 2005 Chevrolet Cavalie μ = 8.4 hours The standard deviation of the time taken by a mechanic to rebuild the transmission of 2005 Chevrolet Cavalier, σ = 1.8 hours.

The sample size, n = 40 We have to find the probability that their mean rebuild time exceeds 8.7 hours. We know that the sampling distribution of the sample means is normally distributed with the following mean and standard deviation.

We have to find the probability that the sample mean rebuild time exceeds 8.7 hours or Now we need to standardize the sample mean using the formula can be found using the z-score table or a calculator. Therefore, the probability that the mean rebuild time of 40 mechanics exceeds 8.7 hours is 0.1489.

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To find the matrix a of the rotation about the y-axis through an angle of π/2 counterclockwise as viewed from the positive y-axis, we can use the following formula:

a = [ cos(θ), 0, sin(θ) ] [ 0, 1, 0 ] [-sin(θ), 0, cos(θ) ] where θ is the angle of rotation.

In this case, θ = π/2, so we have: a = [ cos(π/2), 0, sin(π/2) ] [ 0, 1, 0 ] [-sin(π/2), 0, cos(π/2) ]

Simplifying this, we get: a = [ 0, 0, 1 ] [ 0, 1, 0 ] [-1, 0, 0 ]

Therefore, the matrix a of the rotation about the y-axis through an angle of π/2 counterclockwise as viewed from the positive y-axis is: a = [ 0, 0, 1 ] [ 0, 1, 0 ] [-1, 0, 0 ]

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Answer:

4/10=40%

Step-by-step explanation:

Step-by-step explanation:

6x² - 6x - 72 = 0

Using. Completing the squares method.

6x²/6 - 6x/6 = 72/6

x² - x = 12

Take the coefficient of x, halve and square and add to both sides.

(1/2)² = 1/4

( x + 1/4)² = 12 + 1/4

(x + 1/4)² = 48 + 1 /4

(x + 1/4)² = 49/4

x + 1/2 = 7/2

x = 7/2 ±1/2

x = 4 or x = 3

The head circumference of a newborn boy who marks the start of the 75th percentile is approximately 35.38 cm.

To find the head circumference of a newborn boy who marks the start of the 75th percentile, we need to first find the z-score corresponding to the 75th percentile using the standard normal distribution.

The z-score formula is

z = (x - μ) / σ

where x is the observed value, μ is the mean, and σ is the standard deviation.

To find the z-score that corresponds to the 75th percentile, we need to look up the z-score associated with a cumulative area of 0.75 under the standard normal distribution curve. This value can be found using a table or calculator and is approximately 0.674.

Now we can use the formula for the z-score to solve for the head circumference of a newborn boy at the 75th percentile

z = (x - μ) / σ

0.674 = (x - 34.5) / 1.3

0.674 × 1.3 = x - 34.5

0.8762 + 34.5 = x

x = 35.3762

x ≈ 35.38 cm

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Answer:

mold B

Step-by-step explanation:

The molds are of cylindrical shape. The volume of a cylinder is given by:

Volume = πr²h

where r is the radius and h is the height.

For mold A: diameter = 2 inches, hence radius = 1 inch. Height = 7 inches

volume = π(1²)7 = 7π in³

For mold B: diameter = 2 inches, hence radius = 1 inch. Height = 4 inches

volume = π(1²)4 = 4π in³

For mold C: diameter = 3 inches, hence radius = 1.5 inch. Height = 3 inches

volume = π(1.5²)3 = 6.75π in³

For mold C: diameter = 4 inches, hence radius = 1.5 inch. Height = 3 inches

volume = π(2²)3 = 12π in³

Therefore mold B has the smallest volume

Answer:

B

Step-by-step explanation:

A. y = -2x + 3 is the equation of the line in slope-intercept form.

What is the slope-intercept form of a line's equation?

Y = mx + b is the slope-intercept version of the equation.

b is the y-intercept.

The slope of the line is m.

Find the slope (m) as a result:

Slope (m) = y-fold change/x-fold change = -1/1 = -2

When a line crosses an axis, it is said to have a y-intercept (b) of 3.

Therefore, in y = mx + b, replace b with 3 and m with 2 to get y = -2x + 3.

As a result, A. y = -2x + 3 is the equation of the line in slope-intercept form.

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The perimeter of the triangle is 170 inches.

To solve for the perimeter, we first need to find the length of the perpendicular height. We can do this using the sine function:

sin(35°) = 46/x

x = 46/sin(35°) = 65 inches

Now that we know the length of the perpendicular height, we can find the length of the base of the triangle using the cosine function:

cos(35°) = 65/x

x = 65/cos(35°) = 75 inches

The perimeter of the triangle is the sum of the lengths of the three sides, so the perimeter is:

P = 65 + 75 + 30

= 170 inches

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The largest possible area for the rectangle is (64/9)√6, which corresponds to option (a).

To find the largest possible area for a rectangle with its base on the x-axis and upper vertices on the curve y = 8 - x^2, we will follow these steps:

1. Write down the area function: The area A of the rectangle can be expressed as A = x(8 - x^2) = 8x - x^3.
2. Find the critical points: To maximize the area, we need to find the critical points of the area function. To do this, we take the first derivative of A with respect to x and set it equal to 0.
  dA/dx = 8 - 3x^2 = 0
3. Solve for x: To find the critical points, we solve the equation from Step 2 for x:
  3x^2 = 8
  x^2 = 8/3
  x = ±√(8/3)
4. Determine which critical point maximizes the area: Since the area cannot be negative, only the positive value of x is relevant. Therefore, x = √(8/3).
5. Find the corresponding y-value: Now we plug the x-value back into the curve equation y = 8 - x^2 to find the y-value of the upper vertices:
  y = 8 - (√(8/3))^2 = 8 - 8/3 = 16/3
6. Calculate the maximum area: Finally, we multiply the base (x-value) by the height (y-value) to find the largest possible area for the rectangle:
  A_max = x * y = (√(8/3)) * (16/3) = (64/9)√6

So, the largest possible area for the rectangle is (64/9)√6, which corresponds to option (a).

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As a result, the quartile's value will be 52.5.

Data in math refers to numerical facts and values that are collected and organized for analysis. Data helps to answer questions, solve problems, and gain insights. It is used to perform calculations, draw conclusions, and make predictions. Data can be presented as tables, graphs, diagrams, and charts, and can be used to identify trends, compare different sets of information, and study cause-and-effect relationships.

Given information is:
56 32 48 52 51 53 48 38 35 42 40 46 54 50

If you organise the given data in ascending fashion first, you can retrieve the value of the top quartile.

32, 35, 38, 40, 42, 46, 48, 48, 50, 52, 53, 54, 56

48, 50, 52, 53, 54, and 56 are in the upper quartile.

The upper quartile value is expressed as:

=53+52/2

=105/2

=52.2

As a result, the upper quartile's value will be 52.5.

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Profitability index is 1.387. Thus, the correct option is (c) 1.387.

The formula for calculating the profitability index is:

P.I = PV of Future Cash Flows / Initial Investment

Where,

P.I is the profitability index

PV is the present value of future cash flows

The initial investment in the project is $30 million. The cash flow at the end of the first year is $2.85 million.

The present value of cash flows can be calculated using the formula:

PV = CF / (1 + r)ⁿ

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

n is the number of periods

For the first-year cash flow, n = 1, CF = $2.85 million, and r = 11%.

Substituting the values, we get:

PV = 2.85 / (1 + 0.11)¹ = $2.56 million

To calculate the present value of all future cash flows, we can use the formula:

PV = CF / (r - g)

Where,

PV is the present value of cash flows

CF is the cash flow in the given period

r is the discount rate

g is the constant growth rate

For the subsequent years, CF = $2.85 million, r = 11%, and g = 3.85%.

Substituting the values, we get:

PV = 2.85 / (0.11 - 0.0385) = $39.90 million

The total present value of cash flows is the sum of the present value of the first-year cash flow and the present value of all future cash flows.

PV of future cash flows = $39.90 million + $2.56 million = $42.46 million

Profitability index (P.I) = PV of future cash flows / Initial investment

= 42.46 / 30

= 1.387

Therefore, the correct option is (c) 1.387.

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Answer:

Find the volume of a concrete block that is 2.5 metres long,. 12 centimetres wide and. 10 centimetres high. Two of the dimensions, the width and height,

Answer:

480,000 cm3

Step-by-step explanation:

give crown please ( brainliest )

The length in feet of the pole is 13 ft.

The right-angled triangle's relationship between its three sides is explained by the Pythagoras theorem, commonly known as the Pythagorean theorem. The square of a triangle's hypotenuse is equal to the sum of its other two sides' squares, according to the Pythagoras theorem. Let's learn more about the Pythagoras theorem, its proofs, and its equations before moving on to cases that have been solved using the triangle and square Pythagoras theorem. The hypotenuse's square is equal to the sum of the squares of the other two sides if a triangle has a straight angle (90 degrees), according to the Pythagoras theorem. Keep in mind that BC² = AB² + AC² in the triangle ABC signifies this.

Use the Pythagorean relationship:

c²= a² + b²

= 5²  +  12²

= 25 + 144

= 169

c = 13

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Since the circle is circumscribed about an equilateral triangle, its center is also the center of the triangle.
So the radius of the circle is $r = 9$ units. The area of the circle is $\pi r^2 = \pi \cdot 9^2 = \boxed{81\pi}$ square units.

To find the area of the circumscribed circle around an equilateral triangle, we can follow these steps:
1. Calculate the height of the equilateral triangle.
2. Find the circumradius (radius of the circumscribed circle).
3. Calculate the area of the circle.
Step 1: Calculate the height of the equilateral triangle:
In an equilateral triangle, the height bisects one of the sides, creating two 30-60-90 right triangles. Let's call the height h.
Using the Pythagorean theorem on the 30-60-90 right triangle, we have:
(9/2)^2 + h^2 = 9^2
(81/4) + h^2 = 81
h^2 = 81 - (81/4)
h^2 = (243/4)
h = √(243/4) = √243/2
Step 2: Find the circumradius (R):
In an equilateral triangle, the circumradius (R) is related to the height (h) and the side length (s) by the formula:
R = (s/2) * (1 / sin(60°))
Since sin(60°) = √3 / 2,
R = (9/2) * (2 / √3) = (9/√3) * (√3/√3) = 3√3
Step 3: Calculate the area of the circle:
The area of the circumscribed circle can be found using the formula:
Area = πR^2
Area = π(3√3)^2
Area = π(27)
So, the area of the circumscribed circle is 27π square units.

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Answer:

107 hamburgers

Step-by-step explanation:

Let's call hamburgers A and cheese burgers B.

We know that A + B = 321

And that the number of cheeseburgers sold was two times the number of hamburgers sold which means ->  B = 2A

So A + 2A = 321

3A = 321

Now you need to divide both sides of the equation by 3 and you get:

A= 107

Answer:

x = 5/3

Step-by-step explanation:

4x= x + 5

3x=5

x = 5/3

Angela's use 6 cups of flour and Jaleel's use 19/3 cups of flour.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

The graph shows the relationship between the number of cups of flour and the number of cups of sugar in Angela's brownie recipe.

And, The table shows the same relationship for Jaleel's brownie recipe.

Hence, The equation for Angela's brownie recipe is,

Two points on graph are (4, 2) and (2, 1)

⇒ y - 2 = (2 - 1)/ (4 - 2) (x - 4)

⇒ y - 2 = 1/2 (x - 4)

⇒ y - 2 = 1/2x - 2

⇒ y = 1/2x

And, The equation for Jaleel's brownie recipe is,

Two points on graph are (3/2, 1) and (3, 2)

⇒ y - 1 = (2 - 1)/ (3 - 3/2) (x - 4)

⇒ y - 1 = 2/3 (x - 4)

⇒ y - 1 = 2/3x - 8/3

⇒ y = 2/3x - 8/3 + 1

⇒ y = 2/3x - 5/3

So, For Jaleel and Angela buy a 12-cup bag of sugar.

The equation for Angela's brownie recipe is,

⇒ y = 1/2x

⇒ y = 1/2 × 12

⇒ y = 6

The equation for Jaleel's brownie recipe is,

⇒ y = 2/3x - 5/3

⇒ y = 2/3 × 12 - 5/3

⇒ y = 19/3

Thus, Angela's use 6 cups of flour and Jaleel's use 19/3 cups of flour.

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Answer: a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.

Step-by-step explanation: the y-intercept is where the line meets the y line which in this case is -3. I used slope formula to find the m of the equation ( slope ) take a look at the attached image to see how I solved it.

Answer:

a graph of a line that passes through the points negative 1 comma 2 and 0 comma negative 3.

Step-by-step explanation: