Which statement shows how the product of (x + 7)2 demonstrates the closure property of multiplication?

x2 + 14x + 49 is a polynomial
x2 + 14x + 49 may or may not be a polynomial
x2 + 49 is a polynomial
x2 + 49 may or may not be a polynomial

Answer:

[tex]\left(-\dfrac{1}{2},\:-16\right)[/tex]

Step-by-step explanation:

The general equation of a parabola in polynomial form is
y = ax² + bx + c

where a, b, c are constants

If a is > 0, the parabola opens upward and the vertex is a minimum
If a < 0, the  the parabola opens downward and the vertex is a maximum

The vertex x value is given by the points
[tex]x_v = -b/2a\\[/tex]

The given parabola equation is
y = 4x² + 4x - 15

Since we have a = 4, b = 4
[tex]x_v = -b/2a = -{\dfrac{4}{2\cdot 4} = - \dfrac{4}{8} = - \dfrac{1}{2}[/tex]

To find the y value of the vertex, [tex]y_v[/tex] , plug this value into the parabola equation and solve for y

[tex]y_v=4\left(-\dfrac{1}{2}\right)^2+4\left(-\dfrac{1}{2}\right)-15\\\\= 4 \cdot \dfrac{1}{4} -2 - 15\\\\= 1 - 2 - 15\\\\= -16[/tex]

So the vertex is at [tex]\left(-\dfrac{1}{2},\:-16\right)[/tex] and is a minimum

The other number is 456.

Given that the product of two numbers is 155952, one number is 342, we need to find the other number.

So, let the other number be x,

Therefore, x × 342 = 155952

x = 155952 / 342

x = 456

Hence the other number is 456.

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When the expression √9x² is divided by √18y², we get result which is equal to x/2y.

To simplify the expression √9x²/√18y², we need to first simplify the square roots in the numerator and denominator.

√9x² = √(3²)(x²) = 3x

√18y² = √(2²)(3²)(y²) = 2(3y)

So, √9x²/√18y² can be written as:

(3x)/(2(3y))

We can simplify this expression by canceling out the common factor of 3 in the numerator and denominator:

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

Therefore, the simplified expression of √9x²/√18y² is x/2y.

In conclusion, the expression √9x²/√18y² can be simplified to x/2y by factoring out the common factors from the numerator and denominator, and then canceling out the common factor of 3.

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Answer:b

Step-by-step explanation:

Answer: 1/2   simplest form

Step-by-step explanation: 9 is half of 18 so the smallest fractions that is equivalent to 9/18 is 1/2.

Expanding the product, we can rewrite the expression as follows:

-5³*(-9y³ + 4y² + 3y) =  1,125y³ - 500y² - 375y

Here we have the following expression:

-5³*(-9y³ + 4y² + 3y)

To remove the parentheses, we need to expand the product, we know that:

-5³ = -125

Then we can rewrite the expression as:

-125(-9y³ + 4y² + 3y)

Now expand the product, we will get:

-125(-9y³ + 4y² + 3y) = 1,125y³ - 500y² - 375y

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The function does not have any x-intercepts since it is always positive. The graph of f(x) is a U-shaped curve opening upwards, with vertex at (1, 1) and no x-intercepts. Option (b) is the correct answer.

The given function f(x) = x^2 - 2x represents a parabola. The coefficient of x^2 is positive, indicating that the parabola opens upwards. The vertex of the parabola is at (1, 1), obtained by completing the square.

The x-coordinate of the vertex can be found by using the formula -b/2a, where a and b are the coefficients of x^2 and x respectively. The axis of symmetry is a vertical line passing through the vertex, which is x = 1 in this case.

The y-intercept can be found by setting x = 0, which gives f(0) = 0. Option (b) is the correct answer.

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The quotient written in scientific notation is:

[tex]1.69*10^{10}[/tex]

To do so, we can separate the quotients between the powers of 10 and the rational numbers, then we can rewrite the quotient as follows:

[tex]\frac{5.5*10^7}{3.25*10^{-3}} = \frac{5.5}{3.25}*\frac{10^7}{10^{-3}}[/tex]

Now solve these two:

[tex]\frac{5.5}{3.25}*\frac{10^7}{10^{-3}} = 1.69*10^{7 - (-3)} = 1.69*10^{10}[/tex]

That is the quotient between two numbers in scientific notation, expressed in scientific notation.

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D) No, there isn't enough information given for this question to determine if it's a parallelogram.

All sides of a parallelogram are equal, but it is not specified in this question if conterminous sides are equal. A parallelogram is a two-dimensional geometric shape with two sides that are comparable.

It's a four-sided polygon (also known as a quadrilateral) with comparable sides that are all the same length. The total of the girding angles of a parallelogram equals 180 degrees.

You must have learned about a variety of 2D shapes and sizes in figures, such as circles, places, blocks, rhombuses, and so on. Each of these categories has unique qualities. A parallelepiped is a three-dimensional shape having faces that are parallelograms.

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The set of positive integers less than 1000 that are:

a)Divisible by 7 are 142

b)Divisible by 7 but not by 11 are 130

c)Divisible by both 7 and 11 are 12

d)Divisible by either 7 or 11 are 220

e)Divisible by exactly one of 7 and 11 are 220

f)Divisible by neither 7 nor 11 are 780

g)Having distinct digits are 576

h)Having distinct digits and even are 337

We have,

A whole number that is greater than zero is known as positive integer

a)The positive numbers below 1000 that are divisible by 7 are 7, 14, 21, 28,..., 994.

Total terms: 994, divided by 7, plus (n-1)

There are 142 total terms below 1000 that are divisible by 7.

b) The numbers 77, 154, 231, 308, 385, 462, 539, 616, 693, 770, 847, and 924 are all divisible by both 7 and 11.

The total number of integers below 1000 that are divisible by 7 but not 11 therefore equals 142 - (total number of integers divisible by 7 and 11), which means that the total number of integers that fall into this category is 130.

c) The total amount of integers that can be divided by both 7 and 11 equals the total amount of integers that can be divided by 77.

There are 12 total integers below 1000 that can be divided by 77.

d) The total number of integers that can be divided by either 7 or 11 is equal to the sum of the numbers that can be divided by each of those numbers and the number that can be divided by 77.

The total number of integers below 1000 that are divisible by 11 is (11,22,33,...,990). 990 = 11 + (n-1) 11, which equals 90 integers.

Total integers that may be divided by both 7 and 11 are equal to 142 + 90 - 12 = 220.

e) The total number of integers that may be divided by either 7 or 11 perfectly is equal to 142 + 90 - 12 = 220 numbers.

f) The total number of integers that cannot be divided by either 7 or 11 is 1000 - (The total number of integers that can be divided by either 7 or 11), which is 1000 - 220 = 780 numbers.

g)Distinct digits from 1 to 100 = 100 - Total number of integers below 1000 with distinct digits = 1000 - (non-distinct digits) ( 11,22,33,44,55,66,77,88,99,100),

=> Unique digits from 1 to 100 equal 90.

=> The distinct numerals 101 to 200 equal 100. (101,110,111,112,113,114,115,116,117,118,119,121,122,131,133,141,144,151,155,161,166,171,177,181,188,191,199,200),

=> Unique digits from 101 to 200 are: 100 to 28, 72.

=> Unique numbers between 201 and 1000 = 72 x 8 = 576.

h)Different digits and even values equal to 337

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The perimeter and area of the square are; 24√2 units and 12 units² respectively

Given the coordinates of the midpoints of the four sides of a square are S(-4,11), Q(2,5), U(-4,-1), A (-10,5)

But since we have the midpoints of all the sides, we can assume they're equidistant from one another since the figure is a square.

SQ = √(x₂ - x₁)² + (y₂ - y₁)²

SQ = √(2 - (-4)² + (5 - 11)²

SQ = 6√2

Let's find QU

QU = √(-4 - 2)² + (-1 - 5)²

QU = 6√2

Let's find UA ;

UA = √(-10 - (-4))² - (5 - (-1)²

UA = 6√2

And the distance AS = 6√2

The perimeter of the square = 4 (6√2)

Perimeter = 24√2 units

The area of the square = l²

Area of the square = (6√2)²

Area of square = 12 units²

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The statement which this situation represent include the following: D. a relation only.

In Mathematics and Geometry, a function is a mathematical equation which is typically used for defining and representing the relationship that exists between two or more variables such as an ordered pair.

This ultimately implies that, all functions are used in mathematics to uniquely map an input variable (domain or independent values) to an output variable (range or dependent values).

Based on the graph shown above, we can reasonably infer and logically deduce that it represents a relation, but it does not represent a function because the input values (domain or independent values) are not uniquely mapped to the output values (range or dependent values).

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Complete Question:

Mrs. Anderton is giving a test in her third-period class. She has decided to record the amount of time that each student takes to finish the test (in minutes) and compare that to the grade each student receives on the test (out of 100). A plot of her results is below.

Which of the following does this situation represent?

A. both a relation and a function

B. a function only

C. neither a relation nor a function

D. a relation only

The number of open centers dave and sue are 12 and 14

We are given that;

Ratio= 3:1

Number of days= 16

Now,

If the manager shares the work out between Dave and Sue in the ratio 3:1, that means that for every 3 days that Dave opens the center, Sue opens it 1 day. So, a possible rota for the first 16 days of the month could look like this:

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6 Day 7 Day 8 Name Dave Dave Dave Sue Dave Dave Dave Sue Day 9 Day 10 Day 11 Day 12 Day 13 Day 14 Day 15 Day 16 Name Dave Dave Dave Sue Dave Dave Dave Sue

Therefore, by the given ratio the answer will be 12 and 14.

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When writing a proof, you should construct the first statement by copying the “prove” statement(s) from the original problem. The Option B is correct.

When constructing the first statement in a proof, it is important to begin with copying the “prove” statement(s) from the original problem. This involves writing the next statement based on the given or previously proven statements.

It is not helpful to write a justification for the first statement in the right column without considering its logical connection to the problem. By beginning with a logically connected statement, the proof can proceed in a clear and organized manner which leads to a valid conclusion.

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The value of missing probability is,

⇒ P (A or B) = 131/200

We have to given that;

P (A) = 9/20

P (B) = 1/4

P (A and B) = 9/200

Now, We know that;

P (A or B) = P (A) + P (B) - P (A and B)

P (A or B) = 9/20 + 1/4 - 9/200

P (A or B) = 9/20 + 5/20 - 9/200

P (A or B) = 14/20 - 9/200

P (A or B) = 140/200 - 9/200

P (A or B) = 131/200

Thus, The value of missing probability is,

⇒ P (A or B) = 131/200

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The zeros of the polynomial function are x = -1 and x = 5

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

y = x⁴ - 4x³ - 4x² - 4x - 5

To calculate the zeros of the polynomial function, we create a graph of the polynomial

The point where the graph intersect with the x-axis are the zeros of the polynomial function

using the above as a guide, we have the following:

Zeros: x = -1 and x = 5

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Answer:

54.55

Step-by-step explanation:

The value of m∠Q as shown in the right-angled triangle below is 62.59°.

The Formula used is:

m∠Q = cos⁻¹(s/r)........................ (1)

Where:

s = 29 m

r = 63 m

Now, Substitute these values into equation 1

m∠Q = cos⁻¹(29/63)

m∠Q = cos⁻¹(0.46)

m∠Q = 62.59°

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When a product's profits from sales equal its manufacturing costs, this is called the break-even point.

Since the break-even point is the point at which total costs and total revenues are equal, or "even," in economics, business, and specifically cost accounting.

Therefore, if opportunity costs were paid and capital received the expected return after adjusting for risk, there is no net loss or gain, and one has "broken even."

The break-even point is the point at which total cost and total revenue are equal in the realm of banking and economics.

The amount of units required to cover all costs is determined using the BEP analysis. Fixed and variable costs make up the overall cost in this case.

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The value of the fraction is x = 6 (option c).

In this problem, we are given an equation involving fractions:

27/9 = 18/x

To solve this equation, we can start by simplifying each fraction. Both 27 and 9 are divisible by 9, so we can simplify the left-hand fraction as follows:

3/1 = 18/x

Similarly, we can simplify the right-hand fraction by dividing both the numerator and denominator by 18:

3x = 18

x = 18/3 = 6

Therefore, the answer to this problem is option c. x = 6.

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The length of the hypotenuse in this right triangle is 2√(13) inches.

Now, in the given right triangle, we are given the lengths of the two legs, one measures 4 inches and the other measures 6 inches. We need to find the length of the hypotenuse. To do that, we can use the Pythagorean theorem.

The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. In other words, if we let a and b be the lengths of the legs, and c be the length of the hypotenuse, then:

c² = a² + b²

In this case, we have a = 4 and b = 6. So, we can plug these values into the formula and solve for c:

c² = 4² + 6² c² = 16 + 36 c² = 52

To find c, we take the square root of both sides:

c = √(52)

We can simplify this by factoring 52 into its prime factors: 52 = 2² x 13. Then we can take the square root of each factor:

c = √(2² x 13) c = 2√(13)

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The probability is 0.160, that a randomly selected student will be taller than 72 inches.

We have,

'Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.'

mean (μ) = 68 inches

Standard Deviation (σ) = 3

We know,

Z = mean/ standard deviation

From the normal distribution bell curve, we can see that the percentage of students taller than 72 inches = 14% + 2%

                                                 = 16%

The probability that a randomly selected student will be taller than 72 inches = 16/100

          = 4/25

          = 0.16

          = 16%

Hence, we can conclude, that the probability that a randomly selected student will be taller than 72 inches is 0.160

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The correct matching is given below:

Used to represent symmetrical objects: Half auxiliary view

Only the details of the inclined surface are projected and drawn in the auxiliary view: Partial auxiliary view

A single view projected from the primary auxiliary view to a plane that is inclined to all three principal planes: Secondary auxiliary view

A single view projected from a secondary or another tertiary auxiliary view: Tertiary auxiliary view

The half auxiliary view shows one-half of symmetrical objects while partial auxiliary views focus on inclined surface details.

Secondary auxiliary views offer extra angles by projecting from the primary view to an inclined plane. Tertiary auxiliary views expand on this by projecting from secondary/tertiary views to show details. Auxiliary views clarify technical drawings.

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The solution to the composite function f(a) + f(h) is f(a) + f(h) = a² - 5a + h² - 5h + 6

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

f(x) = x² - 5x + 3

Using the above as a guide, we have the following:

f(a) = a² - 5a + 3

f(h) = h² - 5h + 3

When these functions are added together, we have

f(a) + f(h) = a² - 5a + 3 + h² - 5h + 3

So, we have

f(a) + f(h) = a² - 5a + h² - 5h + 6

Hence, the solution is f(a) + f(h) = a² - 5a + h² - 5h + 6

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The exponential equations in the question indicates that solution for the equation are;

The solution to the system of equations y = f(x) and g(x) are (0, 7), and (2, 4). The solution of the system of equation f(x) = g(x) are 0 and 2

A system of equation is a set of equations that share the same variables.

The solution of the graphical equations are the points where the graph intersects the x-axis.

The solution are therefore; y = f(x) = 0 = 4(2)⁻ˣ + 3

4(2)⁻ˣ = -3

(2)⁻ˣ = -3/4

-x·ln(2) = ln(-3/4)

x = -ln(-3/4)/ln(2) (No real solution)

However, the solution of the system of equation is the points where the graphs of the equations intersect. The graph indicates that the solution points are (0, 7), and (2, 4)

Therefore, the x-values of the solution are; x = 0, and x = 2

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Step-by-step explanation:

There are 10% more boys than girls in a choir.

b = 1.1g

If there are 4 more boys than girls,

b = g + 4

Replace b with 1.1g

1.1g = g + 4

1.1g - g = 4

.1g = 40

g = 4/.1

g = 40 girls, then + 4 = 44 boys

If the diameter of a cylindrical water tank is 8ft, and its height is 6ft, the volume of the water tank is approximately 302 cubic feet.

To find the volume of the cylindrical water tank, we need to use the formula V = πr²h, where r is the radius of the base and h is the height of the cylinder. Since we are given the diameter of the tank, which is 8ft, we can find the radius by dividing it by 2. Thus, the radius of the tank is 4ft. The height is given as 6ft.

Substituting these values into the formula, we get:

V = π(4ft)²(6ft)

V = π(16ft²)(6ft)

V = 96π ft³

Now we can approximate this volume by using the value of π as 3.14 and rounding the answer to the nearest whole number.

V ≈ 96(3.14) = 302.4

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Answer:

A floor plan diagram would be useful for Linda to express her ideas to her client.

It will take Porter 2 hours to catch up to Mariam.

The answer to part B is y = 2.5 hours.

distance = rate x time

d = 40(t + 0.5) (since Mariam started driving half an hour earlier than Porter)

For Porter: distance = rate x time

d = 50t

Since they will meet at the same point, we can set these two equations equal to each other:

40(t + 0.5) = 50t

40t + 20 = 50t

20 = 10t

t = 2

Also, d = 40(t + 0.5)

d = 40(2 + 0.5)

d = 90

So Mariam will have driven 90 miles before Porter catches up to her, which means y = 2.5 (since she drives at a rate of 40 mph and it took 2.5 hours for her to drive 100 miles).

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