(x-3)(3x-5) Expressed as a trinomial.

The graph to the inequality is added as an attachment

From the question, we have the following parameters that can be used in our computation:

2y+8x<4

5x+20 is greater than or equal to -10y

Express properly

2y+8x<4

5x+20 > -10y

Next, we make a plot of the system to determine the solution

The shaded area in the plot represent the solution to the inequality

In this case, the shaded area has a coordinate of (1.143, -2.571)

Hence, the solution is (1.143, -2.571)

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The correct quadratic equation that can be used to determine the thickness of the frame, x, is: 2x² + 10x - 7 = 0, Therefore Option B is the right answer

Here's how we can get this equation:

We are given that the mirror and frame together have an area of 7 square feet. The mirror itself has an area of 2 x 3 = 6 square feet. So, the area of the frame is 7 - 6 = 1 square foot.

Let's assume that the width of the frame is x feet. Then the overall width of the mirror and frame becomes 2 + 2x, and the overall length becomes 3 + 2x. The area of the mirror and frame can be expressed as:

(2 + 2x)(3 + 2x) = 6 + x(10 + 4x)

We know that this expression equals 7, so we can set it equal to 7 and obtain the quadratic equation:

2x² + 10x - 7 = 0

Therefore, the correct quadratic equation is 2x² + 10x - 7 = 0.

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Answer:

im him

Step-by-step explanation:

After cutting 9 pieces of ribbons, Diego made 14 pieces of wreaths with the remaining roll of ribbon.

For finding the pieces of wreaths we will first obtain the total meter required for 9 pieces of ribbon by multiplying 9 with 0.4 meter and then subtract it from the total meters of the roll of ribbons i.e., 12 meters and then divide the result with 0.6 meter.

Total meter required for 9 pieces of ribbon = 9x0.4 meter

                                                                        = 3.6 meters

Total meter of the roll of ribbon = 12 meters

Meter required per wreath = 0.6 meter per wreath

Meter of roll remaining for making wreaths = 12-3.6

                                                                        = 8.4 meters

Total number of wreath made from the remaining roll

= 8.4 meter / 0.6 meter

= 14 Wreaths

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Rounding off the 1004.8 into 3 significant figures will give 1000.

Since significant figures are established as digits, they are also known as significant digits. By counting all of the values beginning with the first non-zero digit on the left, it is possible to determine the number of significant digits.  

For example, the number of significant figures in 567 is 3.
The number of significant figures in 2.671 is 4.  

Here we have a number    

1004.8 need to be rounded off for 3 significant figures  

Since 4 is less than 5 then the resultant number = 1000  

[ 4 and 8 neglected since 4 < 5]

Therefore,

Rounding off the 1004.8 into 3 significant figures will give 1000.

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To buy down the quoted interest rate from 4.75% to 4.5% will cost Trystan and Kendall $4,800 after the down payment.

The down payment refers to the initial cash payment for the purchase of an item on mortgage.

The down payment is required by the financier to evaluate the buyer's financial readiness.

The cost of the new home = $300,000

Down payment = 20% or $60,000 ($300,000 x 20%)

Mortgage loan required = $240,000 ($300,000 - $60,000)

Bank quoted interest rate = 4.75%

Desired interest rate = 4.5%

Difference in interest rate = 0.25% (4.75% - 4.5%)

Rate of buy down of the quoted interest per point = 0.125%

The number of points to buy down the interest rate = 2 (0.25/0.125)

The cost of each point = 1% of $240,000 = $2,400

The total cost of 2 points = $4,800 ($2,400 x 2)

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Answer:

20(4+3)

Step-by-step explanation:

GCF of 80 and 60 = 20

20*4=80

20*3=60

20(4+3)

hope this helps! :)

The required we can save $13.86 annually by buying all your turkey at the discount store.

The equation model is defined as the model of the given situation in the form of an equation using variables and constants.

Here,
Let's call the price of turkey per pound at the supermarket "x". Then the price of turkey per pound at the discount store would be x - $0.99.

Since we consume 14 pounds of turkey annually, the cost of the turkey at the supermarket would be 14 × x dollars.

And the cost of the turkey at the discount store would be 14 × (x - $0.99) dollars.

Therefore, the amount you would save annually by buying all your turkey at the discount store is,

= 14 × x - 14 × (x - $0.99) = 14 × $0.99
= $13.86

So, we would save $13.86 annually by buying all your turkey at the discount store.

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Answer:

Part A: Slope (m) = -75

Part B:

Point-slope form --- y - 1350 = -75(x - 2)

Slope-intercept form --- y = -75x + 1500

Standard form --- 75x + 1y = 1500

Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').

Part D: The balance in the bank account after 5 days equals $1,125.

Step-by-step explanation:

(Pertaining to Part D --- Plugging in variables):

To find the answer to Part D, we must first take the function notation equation from Part C and plug in the appropriate variables needed to find the balance in the bank account after 5 days. So, we plug in '5' for g(x), which would give us g(5). For the other x found in the equation, we also correspondingly replace it with '5'. Our equation now appears as g(5) = -75(5) + 1500.

Finally, we must solve this equation using the order of operations, which simplifies our equation to g(5) = -375 + 1500. We can simplify this further by adding 1500 to -375, giving us the final answer for Part D of $1,125 being the balance in the bank account after 5 days.

Hope that helps!!

Answer:

Part A: Slope (m) = -75

Part B:

Point-slope form --- y - 1350 = -75(x - 2)

Slope-intercept form --- y = -75x + 1500

Standard form --- 75x + 1y = 1500

Part C: g(x) = -75x + 1500 (Just replace 'y' in y = mx + b with 'g(x)').

Part D: The balance in the bank account after 5 days equals $1,125.

The ratio of EP to PF is given as follows:

EP : PF = 2 : 7.

The ratio of EP to PF is obtained applying the proportions in the context of the problem.

Looking at the x-coordinates, we have that:

The ratio must necessarily be the same for the y-coordinates, hence the ratio is given as follows:

EP : PF = 4 : 14.

EP : PF = 2 : 7.

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Since the mode is the most frequently occurring data value so -

Option D : None of the alternatives is correct.

What is mode?

A mode is described as the value in a group of values that occurs more frequently. The value that appears the most frequently is called mode.

The distribution of the mean, median, and mode values will depend on how skewed the distribution is.

The total dependency of mean, median and mode of data is on the asymmetric form of the data.

As a result, mean or mode may be larger than or less than mode.

Therefore, the mode is neither large than mean or median and can never be larger than mean.

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According to the information, the value of the missing angle would be 206°, in a quadrilateral.

To calculate the value of the missing angle we must take into account that the angles of a quadrilateral must add up to 360°. On the other hand, the angles of a triangle must sum to 180°.

According to the previous information, if it is a triangle, then we must add the angles that we know and then subtract it from 180°.

On the other hand, if it is a quadrilateral we must add the angles and subtract them from 360°.

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The number that can each terms of the equation be multiplied by to eliminate the decimals before solving is 100

The equation is

5.6j + 0.12 = 4 + 1.1j

The equation is defined as the mathematical expression that shows the relationship between one expression and another expression with equal sign. The equation consist of mathematical operator like addition, subtraction, division and multiplication

The equation is

5.6j + 0.12 = 4 + 1.1j

Here three term has fractional part.

In 0.12 there are two digits after the decimal point to eliminate the decimal number we have to multiply the number with 100 .

Then the equation will become

560j + 12 = 400 + 110j

Therefore, the number is 100

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The given question is incomplete, the complete question is

Which number can each term of the equation be multiplied by to eliminate the decimals before solving?

5.6j + 0.12 = 4 + 1.1j

In a case whereby three numbers are in the ratio 2:3:5 and the sum of their cube is 34560 then the numbers are  12, 18, and 30.

The given Ratio of three numbers can be expressed as 2:3:5

Then we can represent the three numbers  as: 2x, 3x, and 5x.

We were given the Sum of their cubes as  34560

Thern we can cube them as 2x^3 + 3x^3 + 5x^3 =34560

The we will have 8x^3 + 27x^3 + 125x^3 =34560

Then we have 160x^3 = 34560

x^3 =34560/160

x= 6.

then we can find the values of the ratio as :

2x =( 2×6)

= 12

3x = (3×6 )

= 18

5x = (5×6 )

= 30

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Answer: 240 Grams.

Step-by-step explanation: First I need to find how many grams each bat eats, then multiply the 48 bats by each gram the bats eat. And you would get 240!

Answer:

Step-by-step explanation:

y = 2x:

This is an equation for a straight line in which "y" is proportional to "x" with a coefficient of 2. If you plot this line on a coordinate plane, it will have a slope of 2 and y-intercept of 0.

12 x 12:

This is a mathematical expression for finding the product of 12 and 12. The result is 144. In mathematical writing, it's usually written as "12 * 12 = 144".

Answer: The amount borrowed or deposited

Step-by-step explanation:

there isn't really an explanation, I just know the answer because I took a test with the exact same question and answer

Option C is correct, The difference between the future value and the amount of interest earned is the present value of money

percentage, a relative value indicating hundredth parts of any quantity.

The present value of money refers to the value of a future amount of money in today's dollars, based on a certain interest rate or discount rate.

It is the amount of money that would need to be invested today, at a given rate, to equal the future amount.

To calculate the present value of a future amount of money, we need to discount the future amount based on the interest rate or discount rate, which accounts for the time value of money

The difference between the future value and the amount of interest earned.

Hence, option C is correct, the difference between the future value and the amount of interest earned is the present value of money

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The solution to the system of linear equations associated with the reduced row-echelon form matrix is (0, 0). This indicates that both variables, x and y, have a value of zero.

The reduced row-echelon form of a matrix is the simplest way to represent the solution to a system of linear equations. In the case of a matrix with two rows and two columns, a solution is produced when the matrix is in its reduced row-echelon form. Specifically, for the given matrix, 0 0, the solution to the corresponding system of linear equations is (0, 0). This indicates that both variables, x and y, have a value of zero. This is because the reduced row-echelon form is the simplest way to represent the solution to a system of linear equations. In this form, all the leading entries are ones and all the other entries are zero. Since the matrix is 0 0, this indicates that the solution is (0, 0). This solution can be seen as an ordered pair, where the first value represents the solution for the x variable, and the second value represents the solution for the y variable. In this case, both values are zero, which means that the solution to the system of linear equations is (0, 0).

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The complete question is

The matrix 1 −1 ]5 0 0 ]0 is in reduced row-echelon form. Determine the solution of the corresponding system of linear equations. Write the solution as an ordered pair. For parametric solutions use either x = t or y = t as the parameter form matrix(0,0).

The type of sampling that Huw is using is called Convenience Sampling.

Explanation:

Convenience sampling is a non-probability sampling technique where the sample is selected based on ease of access and availability. In Huw's case, he is administering the questionnaire to people who happen to be in the town centre, which is convenient for him. The sample is not selected randomly, and therefore does not accurately represent the population as a whole. Convenience sampling is often used in quick, informal surveys where the researcher does not have the resources or time to conduct a more rigorous, randomized sampling method.

Area is the total space taken up by a flat (2-D) surface or shape. The area is always measured in square units.

To find the area of a parallelogram, we use this equation:

Now that we have this equation, we can apply it to each parallelogram.

Now, we can figure out which has the greatest area.

Therefore, the parallelogram that has the greatest area is 3, or III.

Answer:

III

Step-by-step explanation:

the area (A) of a parallelogram is calculated as

A = bh ( b is the base and h the perpendicular height )

I

A = 3 × 5 = 15 units²

II

A = 5 × 3 = 15 units²

III

A = 4 × 4 = 16 units²

IV

A = 4 × 3 = 12 units²

parallelogram III has the greatest area

Answer:

Step-by-step explanation: 22/7 is a rational number because it can be expressed as a ratio or fraction of two integers. The numerator (22) and denominator (7) are both integers, and the denominator is not equal to zero, so 22/7 is a well-defined fraction. Since every fraction represents a rational number, 22/7 is also a rational number

The measure of side AB of the triangle is given by equation AB = 3.5 cm

If two triangles' corresponding angles are congruent and their corresponding sides are proportional, they are said to be similar triangles. In other words, similar triangles have the same shape but may or may not be the same size. The triangles are congruent if their corresponding sides are also of identical length.

Corresponding sides of similar triangles are in the same ratio. The ratio of area of similar triangles is the same as the ratio of the square of any pair of their corresponding sides

Given data ,

Let the first triangle be represented as ΔACE

Let the second triangle be represented as ΔBCD

The measure of side AC = 14 cm

The measure of side EC = 84 cm

The measure of side ED = 21 cm

Now , ΔACE is similar to ΔBCD

So , corresponding sides of similar triangles are in the same ratio

Substituting the values in the equation , we get

AB / AC = ED / EC

AB / 14 = 21 / 84

Multiply by 14 on both sides of the equation , we get

AB = ( 1/4 ) 14

AB = 3.5 cm

Therefore , the value of AB is 3.5 cm

Hence , the measure of side AB of triangle is 3.5 cm

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The missing angle is approximately 108.5 degrees.

Law of sines is a trigonometric formula that relates the sides and angles of any triangle. Specifically, the law of sines states that the ratio of the length of a side of a triangle to the sine of the angle opposite that side is the same for all sides and angles in the triangle.

Using the law of sines:

sin(128°)/15 = sin(x)/12

Multiplying both sides by 12:

sin(x) = 12sin(128°)/15

Taking the inverse sine of both sides:

x = sin^-1(12sin(128°)/15)

x ≈ 108.5°

Therefore, the missing angle is approximately 108.5 degrees.

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a) Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))

b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.

Compound interest is a method of calculating interest on a principal amount that includes not only the initial principal but also the accumulated interest from previous periods.

a. The formula for periodic deposits, assuming a fixed interest rate and the same amount of deposit made at the end of each period, is:

Periodic Deposit = (A - P×(1 + r/n)ⁿᵗ) × (n / ((1 + r/n)ⁿᵗ - 1))

Where:

A = Financial goal

P = Initial deposit (assumed to be 0 in this case)

r = Annual interest rate (as a decimal)

n = Number of compounding periods per year

t = Time (in years)

Substituting the given values, we have:

Periodic Deposit = (210000 - 0*(1 + 0.035/12[tex])^{(12\times 13)}[/tex] * (12 / ((1 + 0.035/12[tex])^{(12\times 13)}[/tex] - 1))

= $543.15 (rounded to the nearest cent)

Therefore, the periodic deposit needed to reach the financial goal of $210000, with a 3.5% annual interest rate compounded monthly over 13 years, is $543.15 at the end of each month.

b. To determine how much of the financial goal comes from deposits and how much comes from interest, we can use the following formula for the future value of an annuity:

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

Where:

FV = Future value of the annuity (i.e., the financial goal)

P = Initial deposit

A = Periodic deposit

r, n, t = Same as before

Substituting the given values and solving for P, we have:

P = (210000 - 543.15 * (1 + 0.035/12[tex])^{(12\times 13)}[/tex] ) * (0.035/12) / ((1 + 0.035/12[tex])^{(12\times 13)}[/tex] - 1)

= $60305.24 (rounded to the nearest cent)

Therefore, the amount of the financial goal that comes from deposits is $60305.24, and the amount that comes from interest is $210000 - $60305.24 = $149694.76.

Hence,

a) Periodic Deposit = (A - P*(1 + r/n)ⁿᵗ) * (n / ((1 + r/n)ⁿᵗ - 1))

b) The amount of the financial goal that comes from deposits is $60305.24 and the amount that comes from interest is = $149694.76.

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The value of x is 80 degrees.

The correct answer is an option (A)

Consider the following figure.

Let us assume that the upper triangle be ABC and the lower triangle be NMC.

We can observe that both the triangles are isosceles triangles, because in both the triangles two sides are congruent.

Consider triangle ABC.

As the triangle is isosceles triangle, from the definition of  isosceles triangle ∠A = ∠B

So, ∠A = 65°

We know that the sum of all the angles of triangle is 180°

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠C = 180° - (65° + 65°)

⇒ ∠C = 180° - 130°

⇒ ∠C = 50°

We can observe that ∠ACB and ∠MCN are opposite angles.

So,  ∠MCN = 50°

Also, triangle MNC is also an isosceles triangle.

so, ∠C = ∠N

⇒∠N = 50°

We know that the sum of all the angles of triangle is 180°

⇒ ∠M + ∠N + ∠C = 180°

⇒ ∠M = 180° - (50° + 50°)

⇒ ∠M = 180° - 100°

⇒ ∠M = 80°

Therefore,  x = 80°

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Each wand costs $83, found by dividing the total cost of $498 by the total number of items, 6 (4 cloaks and 2 wands), resulting in $498 / 6 = $83.

To solve for the cost of each wand, we first need to determine the cost of each item (cloak and wand) that Harry bought. We can represent the cost of each item as "x". Since Harry bought 4 cloaks, the total cost of the cloaks is 4 * x. Similarly, since he bought 2 wands, the total cost of the wands is 2 * x.

The total cost of the cloaks and wands that Harry bought was $498, so we can write the equation: 4 * x + 2 * x = $498. This equation represents the total cost of the 4 cloaks plus the 2 wands, which must equal $498.

Next, we can simplify the equation by combining like terms: 4 * x + 2 * x = 6 * x = $498.

Finally, we can find the cost of each item by dividing both sides of the equation by 6: x = $498 / 6 = $83.

Therefore, each wand costs $83.

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Answer:

It is a function. You can identify when something is a function by finding whether plugging in any x value will result in one y value.

If he want to write an exponential function to represent the value of a $10,000 investment decreasing at 2% annually, then the multiplicative rate will be 0.98

The initial investment = $10000

decreasing percentage = 2%

Therefore, the second term will be the 98% of the first term

The first term = 10000

The second term = 10000 × 98/100

= 10000 × 0.98

= 9800

The common ratio is the ratio of the second term to the first term

The common ratio = second term / first term

= 9800 / 10000

= 0.98

Therefore, the multiplicative rate of change should Hal use in his function is 0.98

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If the functions be f(x) = 4x + 13 and g(x) = 10x − 2 then the expression (f + g)(x) be 4x + 11.

A function from a set X to a set Y in mathematics assigns each element of X exactly one element of Y. The set X is known as the function's domain, while the set Y is known as the function's codomain. Initially, functions were just an idealized representation of the relationship between two changing quantities.

Given f(x) = 4x + 13 and g(x) = 10x − 2

We must add both functions to reflect the amount of time it takes to travel east and west in order to calculate the round-trip time.

Let the equation be (f + g)(x) = f(x) + g(x)

substitute the values in the above equation, we get

= (4x + 13) + (10x − 2)

simplifying the above equation, we get

= 4x + 13 + 10x − 2

= 4x + 10x − 2 + 13

= 4x + 11

Therefore, the expression (f + g)(x) be 4x + 11.

The completed question is:

The function f(x) represents the time it takes an airplane to travel east. The function g(x) represents the time it takes an airplane to travel west. Given f(x) = 4x + 13 and g(x) = 10x − 2, solve for (f + g)(x) to determine the total roundtrip time.

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The solution of the system of linear equations y = 9x + 14 and y = 6x + 35 will be (7, 77).

An answer to a formula is any variable value that fulfills the equal outcomes, that is, it tends to make the Left Hand Side (LHS) and Right Hand Side (RHS) of the formula equal. To solve an equation, you must locate the feasible solution) to that formula.

The system of linear equations is given below.

y = 9x + 14                ....1

y = 6x + 35              ....2

From equations 1 and 2, then we have

9x + 14 = 6x + 35

3x = 21

x = 7

The value of 'y' is given as,

y = 6 (7) + 35

y = 42 + 35

y = 77

The solution of the system of linear equations y = 9x + 14 and y = 6x + 35 will be (7, 77).

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