7. The polynomial 2x2 + x – 15
can be written as
(2x – 5)(x + 3). At which
values does the graph of the
polynomial cross the x-axis?
A. x = 3,-5
B. x = , -3
C. x = -5,3
D. x = -3, 5

The quadrilateral given is Parallelogram.

Quadrilaterals are four sided polygons which also have four vertices and four angles.

Sum of all the interior angles of a quadrilateral is 360 degrees.

(a) The quadrilateral is sketched as shown in the graph below.

(b) We have to write the equation of four lines AB, BC, CD and AD in the form y = mx + b. m is slope and b is intercept along Y axis.

Coordinates of vertices are A(-5, 2), B(-2, 6), C(3, 5) and D(0,1).

Equation of line AB :

Slope = (6 - 2) / (-2 - -5) = 4/3

Equation in point slope form is

(y - 2) = 4/3(x - -5)

y - 2 = 4/3 x + 20/3

y = 4/3 x + 26/3

Equation of line BC :

Slope = (5 - 6) / (3 - -2) = -1/5

Equation in point slope form is,

(y - 6) = -1/5 (x - -2)

y - 6 = -1/5 x - 2/5

y = -1/5 x + 28/5

Equation of line CD :

Slope = (1 - 5) / (0 - 3) = -4/-3 = 4/3

Equation in point slope form is,

y - 5 = 4/3 (x - 3)

y - 5 = 4/3 x - 4

y = 4/3x + 1

Equation of line AD :

Slope = (1 - 2) / (0 - -5) = -1/5

Equation in point slope form is,

y - 1 = -1/5 (x - 0)

y - 1 = -1/5 x

y = -1/5 x + 1

(c) Opposite sides are having the same slope.

From the sketch, opposite sides are equal.

So quadrilateral is either parallelogram or rectangle.

But if the figure is rectangle, adjacent sides are perpendicular and therefore the product of their slope is -1.

But it is not the case here.

So it is parallelogram.

Hence the given figure is a parallelogram.

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Based on the information provided, the table that correctly displays the data is table III.

Note: The question is incomplete; below I attach the missing information:

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Answer:

50

Step-by-step explanation:

answer is 50

The sum of the series Σ(n = 1 to 4) n is 10.

We have,

The concept used to find the sum of the series Σ(n=1 to 4) n is called summation or addition.

In mathematics, summation is a way to express the total of a series of numbers.

The notation Σ (capital sigma) is used to represent summation.

It is followed by the index variable (in this case, n) which indicates the values being summed, and the range or condition under which the summation is performed (in this case, n=1 to 4).

The series Σ(n=1 to 4) n represents the sum of the numbers from 1 to 4.

The notation Σ (capital sigma) denotes the sum and the expression

(n = 1 to 4) indicates the range of values over which the sum is taken.

To find the sum, we add up all the numbers in the given range.

In this case, we have:

1 + 2 + 3 + 4 = 10.

Thus,

The sum of the series Σ(n = 1 to 4) n is 10.

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Taub earn $9.8 less because he earned $15.20 while Luke earned $25

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

Let y represent the amount of money earned by working for x hours.

Luke earning is given by:

y = 25x

Hence, luke earns $25 per hour

Taub earned $471.20 in 31 hours. Therefore:

y = kx

471.20 = 31k

k = 15.2

Taub earned $15.20 per hour.

Difference in earning = 25 - 15.2 = $9.8

Taub earn $9.8 less.

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Answer: x>5

If I Helped, Please Mark Me As Brainliest, Have A Great Day :D

Answer: x is greater than 5

Step-by-step explanation:

9(2(5)-9)-5 greater than 4

9(10-9)-5 greater than 4

9-5 greater than 4

4 greater than 4

So x MUST be greater than 5

Answer:

$27.10

Step-by-step explanation:

$542 x 0.05 = $27.10

The four basic properties of exponents are the negative exponent property, the product of powers property, the quotient of powers property, and the power of a power property.

The properties of exponents are a set of rules that allow us to simplify terms that contain exponents.

Negative exponent property states that when a negative exponent is present, the base and the exponent are switched and the sign of the exponent is changed. For example,  x-2 = 1/x2.

The product of powers property states that when two terms with the same base are multiplied, the exponents are added together. For example, x3 x4 = x7.

The quotient of powers property states that when two terms with the same base are divided, the exponents are subtracted. For example, x6/x2 = x4.

The power of a power property states that when a term with an exponent is raised to another power, the exponents are multiplied. For example, (x3)2 = x6.

These properties can be used to simplify expressions that contain exponents. For example, the expression (−2m−2????4) 3 can be simplified using the power of a power property by multiplying the exponents. The expression simplifies to −2m−6????12.

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Answer:

Step-by-step explanation:

a² + b² = c²

18² + b² = 30²

324 + b² = 900

b² = 576

b = 24

Answer: 24

Step-by-step explanation: you use the formula: a^2 + b^2 = c^2. If you drew a picture, it would form a triangle with 30 as the length of the hypotonuse, and 18 as one of the legs. This given, we would have a^2 + 18^2 = 30^2 (hypotonuse = c) Then, solve.

Answer: I think it’s A

Step-by-step explanation:

But go for it

The perimeter of this rectangle with the given vertices is equal to 18 units.

The area of this rectangle with the given vertices is equal to 20 square units.

Mathematically, the perimeter of a rectangle can be calculated by using this mathematical expression;

P = 2(L + W)

Where:

For the width, we would determine the distance between the vertices (-2, 2) and (3, 2)

Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]

Distance = √[(3 - (-2))² + (2 - 2)²]

Distance = √[(5² + 0²]

Distance = √25

Distance = 5 units.

For the length, we have:

Length = 4 units.

Perimeter of this rectangle, P = 2(5 + 4)

Perimeter of this rectangle, P = 18 units.

Mathematically, the area of a rectangle can be calculated by using this formula:

A = LW

A = 4 × 5

A = 20 square units.

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The reasonable PREDICTION of the number of visitors to the store 7 weeks after its opening is 93 visitors

Given the equation for the line of best fit expressed as y = 7.77x + 38.8

where:

y is the number of stores

x is the weeks after the store's grand opening.

To get the reasonable PREDICTION of the number of visitors to the store 7 weeks after its opening, we will substitute x = 7 into the equation to get y as shown:

y = 7.77(7) + 38.8

y = 54.39 + 38.8

y = 93.19

Hence the reasonable PREDICTION of the number of visitors to the store 7 weeks after its opening is 93 visitors

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I don't know how you want it solved but, I am giving u -2 I hope this helps

Answer:

7.52 seconds

Step-by-step explanation:

The height of the rocket, y in feet, is related to the time after launch, x in seconds, by the given equation:

\(y = -16x^2+110x+77\)

The rocket will hit the ground when its height is zero, so when y = 0.

Therefore, to find the time that the rocket will hit the ground, substitute y = 0 into the given equation and solve for x using the quadratic formula.

\(x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}\quad\textsf{when }\:ax^2+bx+c=0\)

For the given equation:

Substitute the values of a, b and c into the quadratic formula and solve for x:

\(x=\dfrac{-110 \pm \sqrt{110^2-4(-16)(77)}}{2(-16)}\)

\(x=\dfrac{-110 \pm \sqrt{12100+4928}}{-32}\)

\(x=\dfrac{110 \pm \sqrt{17028}}{32}\)

\(x=\dfrac{110 \pm 6\sqrt{473}}{32}\)

\(x=\dfrac{55\pm 3\sqrt{473}}{16}\)

Therefore, the two solutions for x are:

\(x=7.51535559...\)

\(x=-0.640355594...\)

As time cannot be negative, the only valid solution is:

\(x=7.51535559...\)

Therefore, the rocket will hit the ground at 7.52 seconds (to the nearest hundredth of a second) after its launch.

A sample size of 17 is required to construct a 90% confidence interval for a population proportion with an error of 0.2.

To determine the sample size required to construct a 90% confidence interval for a population proportion with an error of 0.2 (or 20%), we need to use the formula for sample size calculation in proportion estimation.

The formula for sample size in proportion estimation is:

n = (Z² * p * q) / E²

Where:

n = required sample size

Z = Z-score corresponding to the desired confidence level (90% confidence level corresponds to a Z-score of approximately 1.645)

p = estimated or assumed population proportion (since there is no knowledge about the population proportion, we can assume a conservative value of 0.5 to get the maximum sample size)

q = 1 - p (complement of p)

E = desired margin of error (0.2 or 20% in this case)

Substituting the values into the formula:

n = (1.645² * 0.5 * (1 - 0.5)) / 0.2²

n = (2.705 * 0.5 * 0.5) / 0.04

n = 0.67625 / 0.04

n ≈ 16.90625

Since the sample size must be a whole number, we round up the result to the nearest whole number:

n = 17

Therefore, a sample size of 17 is required to construct a 90% confidence interval for a population proportion with an error of 0.2.

It's important to note that this calculation assumes maximum variability in the population proportion (p = 0.5) to ensure a conservative estimate. If there is any information or prior knowledge available about the population proportion, it should be used to refine the sample size calculation.

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37.

Add all the distances .

3/4 + 1/2 + 2/3 + 3/4 = 8/3 miles

To add fractions you need equal bottom numbers

find the LCM ( Least common multiple of the denominators )

4 , 2 , 3 , 4 = LCM = 12

Multiply each fraction by the same numerator and denominator, to obtain 12 as a bottom number

(3/4 * 3/3) + (1/2 * 6/6) + (2/3 * 4/4) + (3/4 * 3/3)

9/12 + 6/12 + 8/12 + 9/12

Now that all fractions have the same denominator ( bottom number) you can add them.

Add the numerators ( top numbers ) and put 12 as a denominator.

(9 + 6 + 8 + 9 ) / 12 = 32/12

Simplify ( divide both numbers by 4 )

32/12 = 8/3

The volume of the solid generated by revolving the plane region y = 2 - x about the x-axis can be represented by the definite integral ∫[0,2] π(2 - x)² dx.

To find the volume using the shell method, we integrate along the x-axis. The height of each shell is given by the function y = 2 - x, and the radius of each shell is the distance from the axis of revolution (x-axis) to the corresponding x-value.

The limits of integration are from x = 0 to x = 2, which represent the x-values where the region intersects the x-axis. For each x-value within this interval, we calculate the corresponding height and radius.

∫[0,2] π(2 - x)² dx

= π ∫[0,2] (2 - x)² dx

= π ∫[0,2] (4 - 4x + x²) dx

= π [4x - 2x² + (1/3)x³] evaluated from 0 to 2

= π [(4(2) - 2(2)² + (1/3)(2)³) - (4(0) - 2(0)² + (1/3)(0)³)]

= π [(8 - 8 + (8/3)) - (0 - 0 + 0)]

= π [(8/3)]

= (8/3)π

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Answer:

3.5 and -3.5

Step-by-step explanation:

absolute value is the distance from zero to that number so 3.5 and -3.5 should be correct.

Answer:3.5 and -3.5

Step-by-step explanation:

n has absolute value marks, so whatever n is is positive. 3.5 and |-3.5| =3.5

The probability that a plain pencil from the first box and a color pencil from the second box are selected is 3/8.

The Probability in mathematics is the possibility of an event in time. In simple words, how many times that incident is happening in any given time interval.

Given:

A box contains 5 plain pencils and 5 pens.

A second box contains 3 color pencils and 1 crayon.

One item from each box is chosen at random.

The probability that a plain pencil from the first box and a color pencil from the second box are selected,

= 5/10 x 3/4

= 3/8

Therefore, the probability is 3/8.

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Answer:

-277.66

Step-by-step explanation:

130.6 + 147.06 = 277.66

-130.6 - 147.06 = -130.6 + (-147.06) = -277.66

Answer:

30 chocolate covered rasins

5 left over

Step-by-step explanation:

Step 1: 185 Divided by 6 and that gets you 30, and some left over.

Step 2: Do 6 x 30 and that gets 180

Step 3: Do 185 subtract 180 and then you get 5

Step 4: So 30 chocolate coverd raisins will go in each bag, and 5 will be left over.

Have a great day, Lord Bless :)

There are 27,720 different arrangements of red and yellow roses.

The total number of roses is 8 + 4 = 12. To find the number of different arrangements, we can use the formula for permutations, which is:

n! / (n - r)!

where n is the total number of objects and r is the number of objects we want to arrange.

In this case, we want to arrange all 12 roses, so n = 12. The number of red roses is 8, so r = 8. Therefore, the number of different arrangements of the roses is:

12! / (12 - 8)! = 12! / 4! = 27,720

So there are 27,720 different arrangements of the 8 red roses and 4 yellow roses.

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Answer:

1234

Step-by-step explanation:

The loan option with the lowest total value is the one with simple interest, which amounts to $57,247.50. Therefore, the small business owner would be better off choosing the loan with Simple interest, as it results in a lower overall cost compared to the other options.

Part A: To calculate the total value of the loan with simple interest, we use the formula: Total Value = Principal + (Principal * Rate * Time).

Here, the Principal (P) is $50,000, the Rate (R) is 4.35% or 0.0435, and the Time (T) is 3 years and 4 months, which is equivalent to 3.33 years.

Plugging the values into the formula, we have:

Total Value = $50,000 + ($50,000 * 0.0435 * 3.33)

Total Value ≈ $50,000 + $7247.5

Total Value ≈ $57,247.50

Part B: To calculate the total value of the loan with quarterly compounded interest, we use the formula: Total Value = Principal * (1 + (Rate / n))^(n * Time).

Here, n represents the number of compounding periods per year, which is 4 (quarterly compounding).

Plugging the values into the formula, we have:

Total Value = $50,000 * (1 + (0.0435 / 4))^(4 * 3.33)

Total Value ≈ $50,000 * (1.010875)^13.32

Total Value ≈ $50,000 * 1.156977

Total Value ≈ $57,848.85

Part C: To calculate the total value of the loan with continuously compounded interest, we use the formula: Total Value = Principal * e^(Rate * Time).

Here, e represents the mathematical constant approximately equal to 2.71828.

Plugging the values into the formula, we have:

Total Value = $50,000 * e^(0.0435 * 3.33)

Total Value ≈ $50,000 * e^(0.145005)

Total Value ≈ $50,000 * 1.15514

Total Value ≈ $57,757.00

Part D: Comparing the total values of the loans, we find that:

- The total value with simple interest is $57,247.50.

- The total value with quarterly compounded interest is $57,848.85.

- The total value with continuously compounded interest is $57,757.00.

Based on these calculations, the loan option with the lowest total value is the one with simple interest, which amounts to $57,247.50. Therefore, the small business owner would be better off choosing the loan with simple interest, as it results in a lower overall cost compared to the other options.

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The average of the 3 points A, B, and C is 1/3

We know that for a set of N values {x₁, x₂, ..., xₙ} the average is:

Average = (x₁ + ... + xₙ)/N

Assuming that all the weights are 1.

Here the values (y values) for the 3 points are:

A = -9

B = 2

C = 8

The average of these 3 points is:

average = (-9 + 2 + 8)/3

average = 1/3

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The equation of the secant line is y = 2x + 2.  The equation of the tangent line when x = -1 is y = -x - 1, in slope-intercept form.

(a) The equation of the secant line through the points where x has the given values can be found by calculating the slope between the two points and using the point-slope form of a line.

Let's calculate the slope first:

Slope (m) = (f(x2) - f(x1)) / (x2 - x1)

For x = -1 and x = 2:

f(-1) = \((-1)^2 + (-1)\) = 1 - 1 = 0

f(2) = \((2)^2 + 2\)= 4 + 2 = 6

Slope (m) = (f(2) - f(-1)) / (2 - (-1)) = (6 - 0) / (2 + 1) = 6 / 3 = 2

Now, we can use the point-slope form with either of the two given points (-1, 0) or (2, 6). Let's use the first point:

\(y - y_1 = m(x - x_1)\)

y - 0 = 2(x - (-1))

y = 2x + 2

Therefore, the equation of the secant line is y = 2x + 2.

(b) To find the equation of the tangent line when x has the first value, we need to calculate the derivative of the function and evaluate it at that point.

f(x) = \(x^2 + x\)

Taking the derivative of f(x) with respect to x:

f'(x) = 2x + 1

For x = -1:

f'(-1) = 2(-1) + 1 = -2 + 1 = -1

Using the point-slope form with the point (-1, f(-1)) = (-1, 0):

\(y - y_1 = m(x - x_1)\)

y - 0 = -1(x - (-1))

y = -x - 1

Therefore, the equation of the tangent line when x = -1 is y = -x - 1, in slope-intercept form.

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The complete question is:

For the given function, find (a) the equation of the secant line through the points where x has the given values and (b) the equation of the tangent line when x has the first value. y=f(x)=x^2+x; x=-1, x=2 (a) The equation of the secant line is y=______ (b) The equation of the tangent line is y=_____ type your answer in slope intercept form

To simplify 5+square root 7 over 6, you can start by rationalizing the denominator.

This means getting rid of any square roots or irrational numbers in the denominator. To do this, you can multiply both the numerator and denominator by the conjugate of the denominator, which is 6-sqrt(7). This gives you:

(5+sqrt(7))/6 * (6-sqrt(7))/(6-sqrt(7))
= (30-5sqrt(7)+6sqrt(7)-7)/(36-7)
= (23+sqrt(7))/29

So the simplified form of 5+square root 7 over 6 is (23+sqrt(7))/29.

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The slope of the line is undefined.

The equation of line in point-slope form passing through the points

(x₁ , y₁) and (x₂, y₂) with slope m is defined as;

⇒ y - y₁ = m (x - x₁)

Where, m = (y₂ - y₁) / (x₂ - x₁)

Given that;

Two points on the line are (-4, 6) and (-4, 1)

Now,

Since, The equation of line passes through the points (-4, 6) and (-4, 1)

So, We need to find the slope of the line.

Hence, Slope of the line is,

m = (y₂ - y₁) / (x₂ - x₁)

m = (1 - 6) / (-4 - (-3))

m = - 5 / 0

m = ∞

Thus, The slope of the line is undefined.

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The decision variable in this scenario is the model to be produced, which can be represented by the variables A, B, and C. The output variable is the cost of production for the next month.

To determine the model that should be produced to eliminate the cost for the next month, we need to analyze the cost of production for each model. The decision variable represents the choices available, which are models A, B, and C. Let's denote the decision variable as X, where X can take the values A, B, or C.

The output variable in this case is the cost of production for the next month. It is important to consider the costs associated with the raw materials, as well as other factors like delivery time and availability. To make an informed decision, we need to compare the costs associated with each model.

The decision can be made by evaluating the cost of production for each model based on the data provided in the table. By analyzing the cost for each model and considering other relevant factors, such as delivery time and availability of raw materials from the respective suppliers, we can determine which model should be produced to minimize the cost for the next month.

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