Which quadrilateral has one, and only one, line of symmetry?
rectangle square isosceles trapezoid or parallelogram? ​

Answer:

D

Step-by-step explanation:

The parabola of m(x) is thinner than the parabola of f(x) since 4 times 2 squared is 16 while 2 squared is 4

Answer:

x = 5/6

Step-by-step explanation:

Combine multiplied terms into a single fraction, Multiply by 1, Find common denominator, Combine fractions with common denominator, Multiply all terms by the same value to eliminate fraction denominators, Cancel multiplied terms that are in the denominator, DistributeMultiply the numbers, Subtract  from both sides, and then Simplify the expression.

Answer:

a is true

x=72

Step-by-step explanation:

4/6 doesnt make sense. where did they get the denominator 6 from, it wasnt in the problem

b is false

Answer:

I think 241.6 is you answer

Step-by-step explanation:

I hope I helped! to get the answer first you have to convert 5/8 into a whole number but 5/8 can never be a whole number so make it a decimal which equals to 0.625 then divide 151 / 0.625 and you should get 241.6 as your answer

density = 693.79 kg/[tex]m^3[/tex] (approx)

The density of the block of wood can be calculated using the formula:

density = mass / volume

To find the volume of the block of wood, we need to multiply its length, width, and height:

volume = length x width x height

volume = 6.0 cm x 4.2 cm x 8.6 cm

volume = 217.08 cm^3

We need to convert the volume to cubic meters and the mass to kilograms to use the density of glass, which is typically given in kg/m^3:

volume = 217.08 cm^3 = 0.00021708 m^3

mass = 150.5 g = 0.1505 kg

Now we can calculate the density of the block of wood:

density = mass / volume

density = 0.1505 kg / 0.00021708 [tex]m^3[/tex]

density = 693.79 kg/[tex]m^3[/tex] (approx)

Keep in mind that the density of wood varies depending on its moisture content and type, but it is typically lower than that of glass, which is between 2500 and 3000 kg/[tex]m^3[/tex].

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The angle of elevation is the angle between the horizontal line of sight and an upward direction to an object or point.

The angle of elevation is often used in trigonometry and geometry to solve problems involving distances and heights.

1) Cos x = 16/27

x = Cos-1(16/27)

= 54 degrees

2)Sin x = 4/19

x = Sin-1(4/19)

x = 12 degrees

3) Tan 34 = x/8

x = 8 Tan 34

= 5 feet

4) Tan 61 = 166/5.5 + x

1.8(5.5 + x) = 166

9.9 + 1.8x = 166

x = 87 feet

Height of the statue = 5.5 + 87 = 92.5 feet

5) Tan 46 = x/35

x = 35tan 46

x = 36 feet

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The second row and second column's frequency, C. 81, is a marginal frequency (the column total for the second column).

The frequency distribution statistics method identifies the frequency with which a given value or variety of values exists in a data set. The process is dividing the data into intervals, or "bins," and counting a number of values that fall within every bin.

A graph, such as a statistic or a frequency polygon, can be used to show the frequency distribution. The table displays the categories or intervals as well as the frequency or count for each interval.

The y-axis on the graph represents frequencies, while the x-axis represents intervals. The bars or polygons on the graph reflect the count or % of data within every interval.

given

The totals for each row and column make up the marginal frequencies in the table.

The frequencies for each category in the first variable are represented by the row totals, while the frequencies in the second variable are represented by the column totals.

In order to choose a marginal frequency from the available options:

A. The frequency of 23, which is not a marginal frequency, is in the first row and first column.

B. 46 is not a marginal frequency; it is the frequency in the first row and second column.

The second row and second column's frequency, C. 81, is a marginal frequency (the column total for the second column).

D. A marginal frequency is represented by the frequency in the second row and third column (the column total for the third column).

Options C and D therefore have negligible frequencies.

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The segments KM and JN are parallel because the ratio LK : KJ = LM : MN are equivalent

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

The triangle

To determining whether KM || JN, we make use of the following ratio

LK : KJ = LM : MN

Substitute the known values in the above equation, so, we have the following representation

8 : 5 = 12 : 7.5

Express as fraction

5/8 = 7.5/12

Simplify

So, we have

0.625 = 0.625

This means that KM || JN

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Answer:The probability that a shopper buys shoes and a book is 0.015

Step-by-step explanation:

Answer:

Step-by-step explanation:

Find the surface area of a cylinder with a height of 7in and a bass radius of 2in. Use the value 3.14 for π, , and do not do any rounding.

A=2πrh+2πr2=2·π·2·7+2·π·2²=

not rounded 113.09734  

Rounded 113.1

At a rate οf 160 cm per minute, the surface area is changing.

A twο-dimensiοnal figure's area is the amοunt οf space it takes up. In οther terms, it is the amοunt that cοunts the number οf unit squares that span a clοsed figure's surface.

One can calculate a shape's area by cοmparing it tο squares οf a specific size. The Internatiοnal System οf Units' standard unit οf area is the square metre (abbreviated as m2), which measures the surface area οf a square with sides that are οne metre lοng (SI).

Surface Area οf Sphere (S)= 4πr²-------(1)]

Given: dr/dt =  2 cm/minute, r= 10 cm

Differentiating bοth sides with respect tο 't', we get

dS/dt = 4π * 2*r*  dr/dt

dS/dt = 4π * 2*10*  2 =  160π   cm/minute

The surface area is changing at the rate οf   160π   cm/minute

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Answer:

[tex]4x^2[/tex]+8x-21

Step-by-step explanation:

First foil 2x to 2x to get [tex]4x^{2}[/tex].
Then, foil 2x to 7 to get 14x.
Then, foil -3 to 2x to get -6x.
Then, foil -3 to 7 to get -21.
After doing all of that, you will get [tex]4x^2[/tex]+14x-6x-21.
Simplify it, so your final answer is [tex]4x^2[/tex]+8x-21

Let's break down the problem into steps to solve it:

Calculate the interest for the first 2 years:

The formula for compound interest is A = P(1 + r/n)^(nt), where A is the final amount, P is the principal, r is the annual interest rate, n is the number of times the interest is compounded per year, and t is the time period in years.

In this case, P = Rs 45,000, r = 10%, n = 1 (compounded annually), and t = 2 years.

So, A = 45000(1 + 0.1/1)^(1x2) = Rs 59,049

Therefore, the interest for the first 2 years is Rs 59,049 - Rs 45,000 = Rs 14,049

Calculate the remaining principal:

Ram paid one third of the principal at the end of 2 years, which is (1/3) x Rs 45,000 = Rs 15,000.

So, the remaining principal after 2 years is Rs 45,000 - Rs 15,000 = Rs 30,000

Calculate the interest for the next 2 years:

Since Ram paid off the remaining principal and interest at the same rate at the end of the next 2 years, the interest rate will still be 10%.

So, the interest for the next 2 years will be:

A = 30,000(1 + 0.1/1)^(1x2) = Rs 39,690

Therefore, the interest for the next 2 years is Rs 39,690 - Rs 30,000 = Rs 9,690

Calculate the total amount Ram paid at the end of 4 years:

To clear his debt, Ram paid the remaining principal (Rs 30,000) and the interest for the next 2 years (Rs 9,690).

So, the total amount he paid at the end of 4 years is Rs 30,000 + Rs 9,690 = Rs 39,690.

Therefore, Ram paid Rs 39,690 at last to clear his debt.

An equation for a circle with centre (-15, 3√7) and an area of 2π in standard form is (x + 15)² + (y - 3√7)² = 2.

In Mathematics and Geometry, the standard form of the equation of a circle is represented by the following mathematical equation;

(x - h)² + (y - k)² = r²

Where:

For the radius, we have:

Area of a circle = πr²

2π = πr²

r = √2

By substituting the given parameters into the equation of a circle formula, we have the following;

(x - h)² + (y - k)² = r²

(x - (-15))² + (y - 3√7)² = (√2)²

(x + 15)² + (y - 3√7)² = 2.

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Answer:

C. 3 x 4

There's not really a way to explain it. If you still have questions, I would recommend asking your teacher or someone you can trust.

The quadratic function representing the area of ​​the photo and the frame is A(x) =  1.7x²+ 16.2x + 36

When calculating a rectangle's area, we multiply the length by the width of the rectangle.

Area of rectangle = length × breadth

To represent the  photo and frame area, we need to add the photo area  to the frame area. Since the frame is 3 inches wide on all sides, the photo dimensions are reduced by 6 inches in both  length and  width. Therefore the length of the photo with the frame is (x 6) inches and the width is (1.7 x 6) inches. Thus, the area of ​​the photo and the frame can be represented by a quadratic function:

A(x) = (x 6) (1.7 x 6)

Expanding this expression, we get:

A(x) =  1.7x² + 16.2x + 36

So the quadratic function representing the area of ​​the photo and the frame is A(x) =  1.7x²+ 16.2x + 36

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The answer of the given question based on inequality is (1) D , (2) B . (3) A , (4) C

A number line is a visual representation of the real numbers in a linear format. It is a straight line that is divided into equal segments or intervals, each of which represents a specific value on the number scale.

Number lines are usually oriented horizontally, with negative numbers to the left of zero and positive numbers to the right of zero. The distance between each point on the line is usually consistent, which means that the scale is evenly spaced.

For the first inequality, 7x/9 > -14/3, we can start by multiplying both sides by 9 to eliminate the fraction:

7x > -42

x > -6

So the solution to this inequality is x > -6, which means that all values of x greater than -6 satisfy the inequality.

For the second inequality, -75x/4 > 225/2, we can start by multiplying both sides by -4 to eliminate the fraction and flip the inequality:

75x < -450

x < -6

However, we need to remember to flip the inequality back since we multiplied both sides by a negative number:

x > 6

So the solution to this inequality is x > 6, which means that all values of x greater than 6 satisfy the inequality.

For the third inequality, x/4 <= -3/2, we can start by multiplying both sides by 4 to eliminate the fraction:

x <= -6

So the solution to this inequality is x <= -6, which means that all values of x less than or equal to -6 satisfy the inequality.

For the fourth inequality, 2x/3 > -16/3, we can start by multiplying both sides by 3 to eliminate the fraction:

2x > -16

x > -8

So the solution to this inequality is x > -8, which means that all values of x greater than -8 satisfy the inequality.

Now, let's match each inequality to the number line that represents its solution:

The first inequality, 7x/9 > -14/3, corresponds to the number line with an open circle at -6 and an arrow pointing to the right, indicating that all values of x greater than -6 satisfy the inequality.

The second inequality, -75x/4 > 225/2, corresponds to the number line with an open circle at 6 and an arrow pointing to the left, indicating that all values of x less than 6 satisfy the inequality.

The third inequality, x/4 <= -3/2, corresponds to the number line with a closed circle at -6 and an arrow pointing to the left, indicating that all values of x less than or equal to -6 satisfy the inequality.

The fourth inequality, 2x/3 > -16/3, corresponds to the number line with an open circle at -8 and an arrow pointing to the right, indicating that all values of x greater than -8 satisfy the inequality.

So the correct pairs are:

7x/9 > -14/3: ( )-------------●--->

-75x/4 > 225/2: <---●-------------( )

x/4 <= -3/2: [ ●]--------------<--

2x/3 > -16/3: ( )-------------●--->

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The area of the sector OPR is approximately 5.20 cm².

What is an area?

First, we need to find the length of PR. Since O is the center of the circle, we know that OP and OR are both 6 cm long (the radius of the circle). By the triangle inequality, we have:

PR < OP + OR = 6 + 6 = 12

Since QR = 14, we have:

PR > QR - OP - OR = 14 - 6 - 6 = 2

Therefore, 2 cm < PR < 12 cm.

Next, we can use the formula for the area of a sector of a circle:

A = (θ/360)πr²

where A is the area of the sector, θ is the central angle of the sector (in degrees), and r is the radius of the circle.

To find the central angle θ, we can use the law of cosines:

(PR)² = (OP)² + (OR)² - 2(OP)(OR)cos(θ)

Substituting in the known values, we get:

(PR)² = 6² + 6² - 2(6)(6)cos(θ)

(PR)² = 72 - 72cos(θ)

cos(θ) = (72 - (PR)²)/72

Using the known values, we have:

cos(θ) = (72 - (PR)²)/72 = (72 - x²)/72

where x is the length of PR.

Since OPQ is a triangle, we know its area:

25 = (1/2) base × height

25 = (1/2) QR × OP

25 = (1/2) (14) × 6

25 = 42

Therefore, the height of triangle OPQ is:

height = (2)(25)/QR = (2)(25)/14 = 25/7

The height of the triangle is also the distance from O to the line PQ, which is also the distance from O to the chord PR. Therefore, the area of sector OPR can be calculated as follows:

A = (θ/360)πr² = (θ/360)π(6)²

A = (θ/360)(36π) = (θ/10)π

where θ is the central angle of the sector in degrees. To find θ, we can use the formula:

sin(θ/2) = (PR/2)/r = x/6

Substituting in the known values, we get:

sin(θ/2) = x/6

θ/2 = [tex]sin^{-1}[/tex](x/6)

θ = 2[tex]sin^{-1}[/tex](x/6)

Finally, substituting this value of θ into the formula for the area of the sector, we get:

A = (θ/10)π = [2[tex]sin^{-1}[/tex](x/6)]/10 * π

To find the value of x that gives the area of the sector, we can use trial and error or a numerical solver. Using a calculator, we find that x ≈ 5.5 cm gives an area of the sector of:

A ≈ 5.20 cm²

Therefore, the area of the sector OPR is approximately 5.20 cm².

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The marginal cost is the derivative of the cost function.

Option C is the correct answer.

Marginal cost is the additional cost incurred by a firm or producer when producing one more unit of a good or service.

It is the cost of producing an additional unit of output.

We have,

Marginal cost is a concept in economics that describes the additional cost of producing one additional unit of output.

It is calculated as the derivative of the total cost function with respect to the quantity produced.

In other words, if the total cost function is represented as C(q), where q is the quantity of output produced, then the marginal cost (MC) function is given by:

MC(q) = dC(q) / dq

The derivative represents the rate of change of the cost function with respect to the quantity produced, which gives the additional cost of producing one more unit of output.

For example, if a company produces 100 units of a product at a total cost of $1000, and then produces 101 units of the same product at a total cost of $1020, the marginal cost of producing the 101st unit is $20, which is the difference in cost between producing 100 units and producing 101 units.

Thus,

The marginal cost is the derivative of the cost function.

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The complete question.

Complete the following sentence.

The marginal cost is the derivative of the ________ function.

A) Utility.

B Income.

C) Cost.

D Demand.

Answer: 430.00

Step-by-step explanation:

So.

3x^2-2x+3.

Replace x with 7

(3·7)^2-(2·7)+3

Multiply within the parenthesis

21^2-14+3

Take care of exponent

441-14+3

Solve the rest.

430

If you did it right, you would get 430 as the end result.

Happy Solving

Therefore, the equation of the circle that passes through the point (2, -5) and has its center at (4,0) is.[tex](x - 4)^2 + y^2= 29[/tex].

A circle is a closed, two-dimensional geometric shape that consists of all points in a plane that are equidistant from a fixed point called the center. It can also be defined as the set of all points in a plane that are at a given distance (called the radius) from the center point. The circumference of a circle is the distance around its outer boundary, and the diameter is the distance across the center of the circle. Circles have several important properties and are used extensively in mathematics, science, and engineering.

To find the equation of a circle, we need to know the coordinates of its center and its radius. We are given the center of the circle, which is (4,0). To find the radius, we can use the distance formula between the center and the point on the circle (2, -5):

[tex]radius = \sqrt{[(4 - 2)^2 + (0 - (-5))^2]}[/tex]

[tex]= \sqrt{[2^2 + 5^2]}[/tex]

[tex]= \sqrt{29}[/tex]

So the equation of the circle can be written in the standard form as:

[tex](x - h)^2 + (y - k)^2 = r^2[/tex]

where (h, k) is the center of the circle and r is its radius.

Substituting the values we found, we get:

[tex](x - 4)^2 + (y - 0)^2 = (\sqrt{29})^2[/tex]

Simplifying, we get:

[tex](x - 4)^2 + y^2 = 29[/tex]

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Answer:

1,469 [tex]m^{2}[/tex]

Step-by-step explanation:

The volume of a rectangular prism is given by the following:

V = Bh, where B is the area of the base and h is the height.

In this problem, we are given that the volume is 23,504 [tex]m^{3}[/tex] and the height is 16 m.

23,504 [tex]m^{3}[/tex] = B × 16 [tex]m[/tex]

Dividing both sides by 16, we get:

B = 23,504 [tex]m^{3}[/tex]  / 16 [tex]m[/tex] = 1,469 [tex]m^{2}[/tex]

Therefore, the value of B, the area of the base, is approximately 1,469 [tex]m^{2}[/tex].

the closest answer choice to this value is 372.32 yd2.

How to solve the question?

The given shape is a trapezoid, where the two parallel sides are the base and the top, and the height is the perpendicular distance between them. We can divide this trapezoid into a rectangle and a right triangle, as shown below:

 A (bottom     B (bottom

 left vertex)   right vertex)

We can find the length of the top side by adding the portions given on each side of the perpendicular, as follows:

top side = 6.4 yards + 14.9 yards = 21.3 yards (same as the base)

The area of the rectangle (ABCD) is the product of the base (21.3 yards) and the height (12.8 yards):

area of rectangle = 21.3 yards * 12.8 yards = 272.64 square yards

The area of the right triangle (BCD) is half the product of the height (12.8 yards) and the difference between the base and the top (21.3 yards - 6.4 yards = 14.9 yards):

area of triangle = 0.5 * 12.8 yards * 14.9 yards = 95.36 square yards

Therefore, the total area of the figure is the sum of the area of the rectangle and the area of the triangle:

total area = 272.64 square yards + 95.36 square yards = 368 square yards

Therefore, the closest answer choice to this value is 372.32 yd2.

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The function f(x) = 3x² - 3x has absolute extrema at (-1, -5/2)

To find the absolute extrema of the function f(x) = x³ - 3/2x² on the closed interval [-1, 2], we need to first find the critical points of the function in the interval and evaluate the function at those points as well as at the endpoints of the interval.

To find the critical points, we need to find where the derivative of the function is equal to zero or does not exist. The derivative of f(x) is:

f'(x) = 3x² - 3x

Setting f'(x) = 0, we get:

3x² - 3x = 0

3x(x - 1) = 0

x = 0 or x = 1

We also need to check if there are any values of x where the derivative does not exist. However, since the derivative is a polynomial function, it exists for all real values of x.

The absolute extrema is at (-1, -5/2)

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Option B is the correct option for the total area of the shape which is approximate 8049 ft².

An isosceles triangle is a polygon with three sides, where two of the sides have equal length.

Suppose the equal sides of Isosceles triangle is 'a',

so we can say that by Isosceles triangle rule: 70 = a√2

or side of Isosceles triangle (a) = 35√2 ft         (by Pythagoras theorem)

Area of isosceles triangle (A₁) = [tex]\frac{1}{2}[/tex] × (Side of Isosceles triangle)²

                                                 = [tex]\frac{1}{2}[/tex] × (35√2)² = 1225 ft²

Area of two square (A₂) =  2 × a × a

                                       = 2 × 35√2 × 35√2  = 4900 ft²

Area of quadrant circle (A₃) = (πr²)/4

                                              = 3.14 × (35√2)² × (1/4) = 1923.25 ft²

Total area of the shape = A₁ + A₂ + A₃

                                       = 1225 + 4900 + 1923.25 = 8048.25 ft²

Therefore, the total area of the shape is approximate 8049 ft²

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The probability that at most 20 freshmen out of 85 plan to major in STEM is approximately 0.2420.

What is probability?

Probability is a measure of the likelihood or chance of an event occurring. It is a number between 0 and 1, with 0 representing an impossible event and 1 representing a certain event. The probability of an event is calculated by dividing the number of ways the event can occur by the total number of possible outcomes.

We can use the normal distribution to find probabilities related to STEM majors.

Let X be the number of freshmen out of 85 who plan to major in a STEM discipline. We are given that p = 0.27 is the proportion of freshmen who plan to major in STEM.

Then, X follows a binomial distribution with parameters n = 85 and p = 0.27.

The mean of the distribution is given by μ = np = 85 × 0.27 = 22.95.

The standard deviation of the distribution is given by σ = sqrt(np(1-p)) = sqrt(85 × 0.27 × 0.73) ≈ 4.27.

To find the probability that at most 20 freshmen plan to major in STEM, we can use the normal approximation to the binomial distribution:

P(X ≤ 20) ≈ P(Z ≤ (20 - 22.95) / 4.27) ≈ P(Z ≤ -0.697)

Using a standard normal distribution table or calculator, we find that P(Z ≤ -0.697) ≈ 0.2420.

Therefore, the probability that at most 20 freshmen out of 85 plan to major in STEM is approximately 0.2420.

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The line of fit y = -4.2x + 100 shows a negative correlation between the distance traveled and the remaining charge on the battery of the motorized wheelchair.

The slope of the line is -4.2, which means that for every one unit increase in distance traveled, the remaining charge on the battery decreases by 4.2 units.

The y-intercept of the line is 100, which means that when the distance traveled is zero, the remaining charge on the battery is 100.

The line of fit can be used to make predictions about the remaining charge on the battery for a given distance traveled.

Based on the scatter plot, we can see that there is a negative correlation between the distance traveled and the remaining charge on the battery. As the distance traveled increases, the remaining charge on the battery decreases.

Overall, the line of fit provides a way to estimate the remaining charge on the battery for a given distance traveled based on the data shown in the scatter plot.

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