Find the area of the trapezoid.
10.5 cm
9.28 cm
21.1 cm
[ ? ] cm2
Enter the exact answer. Do not round.

Answer: \(x^{10}+10x^8y+40x^6y^2+80x^4y^3+80x^2y^4+32y^5\)

Step-by-step explanation:

\(\mathrm{Apply\:binomial\:theorem}:\quad \left(a+b\right)^n=\sum _{i=0}^n\binom{n}{i}a^{\left(n-i\right)}b^i\)

\(a=x^2,\:\:b=2y\)

\(=\sum _{i=0}^5\binom{5}{i}\left(x^2\right)^{\left(5-i\right)}\left(2y\right)^i\)\(=\frac{5!}{0!\left(5-0\right)!}\left(x^2\right)^5\left(2y\right)^0+\frac{5!}{1!\left(5-1\right)!}\left(x^2\right)^4\left(2y\right)^1+\frac{5!}{2!\left(5-2\right)!}\left(x^2\right)^3\left(2y\right)^2+\frac{5!}{3!\left(5-3\right)!}\left(x^2\right)^2\left(2y\right)^3+\frac{5!}{4!\left(5-4\right)!}\left(x^2\right)^1\left(2y\right)^4+\frac{5!}{5!\left(5-5\right)!}\left(x^2\right)^0\left(2y\right)^5\)

simplify all =  \(x^{10}+10x^8y+40x^6y^2+80x^4y^3+80x^2y^4+32y^5\)

The product of (a + 3) and (-2a^2 + 15a + 6b^2) is -2a^3 + 9a^2 + 6ab^2 + 45a + 18b^2.

To find the product of (a + 3) and (-2a^2 + 15a + 6b^2), we can use the distributive property of multiplication over addition.

(a + 3) * (-2a^2 + 15a + 6b^2) can be expanded as follows:

(a + 3) * (-2a^2 + 15a + 6b^2) = a * (-2a^2 + 15a + 6b^2) + 3 * (-2a^2 + 15a + 6b^2)

Now, let's distribute the multiplication:

= -2a^3 + 15a^2 + 6ab^2 + 3 * (-2a^2) + 3 * 15a + 3 * 6b^2

Simplifying further:

= -2a^3 + 15a^2 + 6ab^2 - 6a^2 + 45a + 18b^2

Combining like terms:

= -2a^3 + 9a^2 + 6ab^2 + 45a + 18b^2

Therefore, the product of (a + 3) and (-2a^2 + 15a + 6b^2) is -2a^3 + 9a^2 + 6ab^2 + 45a + 18b^2.

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The algorithm justifies the answer of 3/5 as the fraction each person gets.

Representation of the fractions on the second row:

From what you described, two of the loaves were divided into thirds.

This means each person receives one third, and there is one third remaining. Then, this remaining third from the second loaf was further divided into fifths.

Therefore, each person receives one fifth from this remaining third.

So, the representation of the fractions on the second row would be:

Each person receives 1/3 (one third) from the two loaves.

Each person receives 1/5 (one fifth) from the remaining third.

Algorithm/Abstract strategy to justify the 3/5 found as the answer:

To find the final answer of 3/5, we can follow the steps you provided:

Divide two loaves into thirds, giving each person 1/3.

Divide the remaining third from the second loaf into fifths, giving each person 1/5.

Combining the fractions, each person has 1/3 + 1/5.

To add these fractions, we need to find a common denominator. In this case, the least common multiple (LCM) of 3 and 5 is 15. We can convert 1/3 and 1/5 to have a denominator of 15:

1/3 = 5/15 (multiplying numerator and denominator by 5)

1/5 = 3/15 (multiplying numerator and denominator by 3)

Now, we can add the fractions:

5/15 + 3/15 = 8/15

Therefore, each person receives 8/15 of a loaf.

Simplifying this fraction, we get 3/5.

Hence, the algorithm justifies the answer of 3/5 as the fraction each person gets.

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Hi!

So you have your problem:

(1 + 4a) + (5 + 3x)

What you'll want to do first is rearrange the problem:

(4a + 1) + (3x + 5)

Then, you'll eliminate the parenthesis:

4a + 1 + 3x + 5

Now you add all 'like terms' together:

4a + 6 + 3x

Last, is you rearrange again:

4a + 3x + 6

Hope this helped!

Have a nice day :)

Answer:

15x+35

Step-by-step explanation:

5(3x+7)=5(3x)+5(7)

          =15x+35

Answer:

15x + 35

Step-by-step explanation:

5(3x + 7)

5(3x) + 5(7), by the distributive propoerty of equality

15x + 7

Answer:

B.The coefficient of determination measures the percent of variation explained by the multiple regression model.

Step-by-step explanation:

The answer to this question is option b because the coefficient of variation R² gives a measure of the variability that is ending y values or the dependent variables which can be explained in a multiple linear regression.

In simpler words, it is the percentage of proportion of variation in the dependent variable that can be predicted using the explanatory variables.

The tip of the minute hand on a clock travels a distance of 4π inches in 15 minutes.

The distance traveled by the tip of a minute hand on a clock can be calculated using the circumference formula.

The circumference of a circle is given by the formula:

C = 2πr C is the circumference, π is pi (approximately 3.14159) and r is the radius.

The distance from the center of the clock to the tip of the minute hand is the radius is 8 centimeters.

The circumference of the circle traced by the tip of the minute hand is:

\(\text{C} = 2\pi \text{r}\)

\(= 2\pi (8)\)

\(= 16\pi \ \text{centimeters}\)

Since the minute hand travels the full circumference of the circle in 60 minutes, in 15 minutes it will cover 15/60 = 1/4 of the circumference.

The distance traveled by the tip of the minute hand in 15 minutes is:

\(\text{Distance} = \huge \text(\dfrac{1}{4}\huge \text) \times C\)

\(= \huge \text(\dfrac{1}{4}\huge \text) \times (16\pi)\)

\(= 4\pi \ \text{centimeters}\)

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Answer:

4π cm ≈ 12.6 cm

Step-by-step explanation:

The clock can be modelled as a circle, where the radius (r) is equal to the length of the minute hand:  r = 8 cm.

A clock face is divided into 12 equal sectors (numbered 1 to 12).

It takes 60 minutes for the minute hand to complete one revolution of the clock. Therefore, each sector represents the passing of 5 minutes.

This means that 15 minutes equals 3 sectors, which is a quarter of the circle.

To find the distance the tip of the minute hand travels in 15 minutes, we need to find a quarter of the circumference of a circle with radius 8 cm.

The formula for the circumference of the circle is C = 2πr, where r is the radius. Therefore, the equation to find the distance the tip of the minute hand travelled in 15 minutes is:

\(\sf Distance=\dfrac{2 \cdot \pi \cdot 8}{4}\)

Simplifying, we get:

\(\sf Distance=\dfrac{16 \cdot \pi}{4}\)

\(\sf Distance=4 \pi\)

Therefore, the minute hand will travel 4π cm or approximately 12.6 cm (to the nearest tenth) in 15 minutes.

Answer:

Step-by-step explanation:

A cone with a diameter of 16 centimeters has a volume of 320π cubic centimeters, the height of the cone is 15 cm.

A cone should be emptied at a time after being filled with water. The cylinder is filled to a third with each cone. Since there are three of them, the cylinder will be filled. As a result, the volume of a cone is equal to one-third of the volume of a cylinder.

Cone volume is calculated using the method V=1/3πhr².

Given that,

diameter(d) = 16 cm

radius (r) = d/2 = 8 cm

volume = 320π cubic centimeters

πr²h/3 = 320π

or, [π × (8)² × h]/3 = 320π

or,  h = (3 × 320)/(8)²

or, h = 15 cm

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Hello!

y = 88° (opposite are equal)

z = 180° - 128° = 52° (straight angle = 180°)

x = 180° - 140° = 40° (straight angle = 180°)

Answer:

x=40°

y=88°

z=52°

Step-by-step explanation:

Solution Given:

x+140°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for x.

x=180°-140°

x=40°

\(\hrulefill\)

y°=88°

Since the vertically opposite angle is equal.

therefore, y=88°

\(\hrulefill\)

z+128°=180°

Since the sum of the angle of a linear pair or straight line is 180°.

solving for z.

z=180°-128°

z=52°

Answer:

the first and second

Step-by-step explanation:

Answer:

Step-by-step explanation:

The triangles are similar because they have two sides and the angle between them (EFG) respectively equals, and it’s evident the factor between the two triangles is 2. So EG=2CB=2*8=16

Answer:

the value of EG is 20.

Step-by-step explanation:

3×4 = 12, AB and EF is similar but the value of AB is multiplied by 4 to become 12 for EF.

similarly, 4×4 = 16, BC and FG is similar but the value of BC is multiplied by 4 to become 16 for FG..

In this way, AC and EG are also similar so 5×4 = 20.

All the values are multiplied by 4 ...

Answer:

13.5x + 5 feet is the perimeter of the rectangle.

Step-by-step explanation:

Given: the width of a rectangle is 4.25x - 2.5 feet and its length is 2.5x + 5 feet. Find the perimeter of the rectangle.

First, the formula to finding the perimeter of a rectangle is 2(l+w).

Put in the length and width in the formula:

2(4.25x - 2.5 + 2.5x + 5)

Then simplify the expression in the parenthesis:

2(4.25x - 2.5 + 2.5x + 5)

2(4.25x+2.5x - 2.5+5)

2(6.75x + 2.5)

Then solve:

2(6.75x + 2.5)

2 * 6.75x + 2 * 2.5

= 13.5x + 5 feet is the perimeter of the rectangle.

Answer:

\(\boxed{\mathtt{Perimeter = 13.50x+5}}\)

Step-by-step explanation:

\(\textsf{We are asked for the perimeter of the rectangle.}\)

\(\textsf{The Perimeter is simply the sum of the edges of a shape.}\)

\(\textsf{Because there's 4 sides to a Rectangle, we consider the Length and Width twice.}\)

\(\mathtt{Perimeter = Length + Length + Width + Width}\)

\(\textsf{Let's begin solving for the Perimeter.}\)

\(\large\underline{\textsf{Substitute:}}\)

\(\mathtt{Perimeter = 2(2.5x+5) + 2(4.25x-2.5)}\)

\(\large\underline{\textsf{Multiply:}}\)

\(\mathtt{Perimeter = 5x+10 + 8.50x-5}\)

\(\large\underline{\textsf{Combine Like Terms:}}\)

\(\boxed{\mathtt{Perimeter = 13.50x+5}}\)

Answer:

5 units of vertical distance

Step-by-step explanation:

just count

The area of the shaded portion in the equilateral triangle with sides 6 is 9√3 - 36π.

To find the area of the shaded portion in the equilateral triangle, we need to determine the area of the three arcs and subtract it from the area of the equilateral triangle.

First, let's find the area of one arc. Each arc has a radius equal to the length of the side of the equilateral triangle, which is 6. The formula for the area of a sector is A = (θ/360)πr², where θ is the central angle in degrees.

In an equilateral triangle, each interior angle measures 60 degrees, so the central angle of the arc is 120 degrees (360 degrees divided by 3). Plugging these values into the formula, we get A_arc = (120/360)π(6)² = (1/3)π(6)² = 12π.

Since there are three identical arcs, the total area of the arcs is 3 times the area of one arc, which is 3(12π) = 36π.

Now, let's find the area of the equilateral triangle. The formula for the area of an equilateral triangle is A_triangle = (√3/4)s², where s is the length of a side.

Plugging in the value of the side length, we have A_triangle = (√3/4)(6)² = (√3/4)(36) = 9√3.

Finally, we subtract the area of the arcs from the area of the equilateral triangle to find the shaded portion's area: A_shaded = A_triangle - A_arc = 9√3 - 36π.

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Answer:

It will take for Brian 7.14 years.

Step-by-step explanation:

I=PRT

4,000=8,000*7/100*T

4,000=560T (then you divide 560 from both sides.)

T=7.14

Answer:

B

Step-by-step explanation:

b is correct

Answer:

89, 178, 267, 356, 445, 534, 623, 712, 801, 890 and so on

x=2;

y= 5.

Method to use: Substitution.

In this case we are going to solve Eq. 2 for x:

\(-4x + 4 y = 12\\ \\-4x+4y-4y=12-4y\\ \\-4x=12-4y\\ \\x=\frac{12-4y}{-4} \\ \\x=-\frac{12-4y}{4}\\ \\x=-(\frac{12}{4}-\frac{4y}{4} )\\ \\x=-(3-y)\\ \\x=-3+y\\ \\x=y-3\)

\(12(y-3) - 7 y = -11\\ \\12y-36-7y=-11\\ \\5y-36=-11\\ \\5y=25\\ \\y=\frac{25}{5} \\ \\y=5\)

\(-4x + 4(5) = 12\\ \\-4x+20=12\\ \\-4x=-8\\ \\x=\frac{-8}{-4}\\ \\ x=2\)

x=2;

y= 5.

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Answer:

Step-by-step explanation:

where is the picture?

Answer:

you need a picture lol

Step-by-step explanation:

Answer:

-1 is the correct answer

Step-by-step explanation:

Move that many points on the number line

The position of B on number line is at - 1.

Number line is a horizontal line where numbers are marked at equal intervals one after another form smaller to greater.

Given that;

Point A is shown on the the number line below.

And, Another point, B , is to be placed on the number line and will be 2 1/2 unit from point A.

Now,

Since, The position of Point A = 1 1/2

And, Another point, B , is to be placed on the number line and will be 2 1/2 unit from point A.

So, The point B = 1 1/2 + (-2 1/2)

                        = 3/2 - 5/2

                        = - 2/2

                        = - 1

Thus, The position of point B = - 1

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Answer:

Step-by-step explanation:

The numbers for the faculty members are

select: 83, 58, 64, 26, 47, 68, 29, 4, 78

23 comma 80 comma 37 comma 65 comma 54 comma 64 comma 70 comma 56 comma 9.

​(Use a comma to separate answers as​ needed.)

​(b) The president uses technology to produce the following random numbers.

Determine the numbers for faculty members who will be included in the sample.

After answering the presented questiοn, we can cοnclude that The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape

An equatiοn in mathematics is a statement that states the equality οf twο expressiοns. An equatiοn is made up οf twο sides that are separated by an algebraic equatiοn (=). Fοr example, the argument "2x + 3 = 9" asserts that the phrase "2x Plus 3" equals the value "9." The purpοse οf equatiοn sοlving is tο determine the value οr values οf the variable(s) that will allοw the equatiοn tο be true.

The fοrmula tο find the area and perimeter οf a twο-dimensiοnal shape depends οn the type οf shape. Here are sοme cοmmοn fοrmulas:

1. Rectangle:

• Area: A = length x width

• Perimeter: P = 2(length + width)

2. Square:

• Area: A = side x side (οr A = side²)

• Perimeter: P = 4 x side

3. Circle:

• Area: A = π x radius²

• Circumference (perimeter): C = 2π x radius (οr C = π x diameter)

4. Triangle:

• Area: A = (base x height) / 2

• Perimeter: P = side1 + side2 + side3

5. Trapezοid:

• Area: A = ((base1 + base2) x height) / 2

• Perimeter: P = side1 + side2 + side3 + side4

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la suma de los angulos internos es de 540°

Answer:

Step-by-step explanation:

To differentiate the function y = x^4 - x, we will use the power rule of differentiation. The power rule states that if f(x) = x^n, then the derivative of f(x) is f'(x) = nx^(n-1).

So, for y = x^4 - x, we can find the derivative as follows:

y' = 4x^3 - 1

So, the derivative of the function y = x^4 - x is y' = 4x^3 - 1.

The equation matches the function provided in the graph is: y = sin(x + π/2)

The sine function is defined as the function which is sinusoidal in nature, and it has a domain of all real numbers and lies between the [a, a] where a is the amplitude of the function.

We are told that a graph of a trigonometric function is given:

We know that:

y = sinx has a sinusoidal graph

Based on the graph, we can apply a transformation to get the required function.

Applying transformation:

x → x + π/2

The sine function will shift left side by π/2 unit

The equation of the function becomes:

y = sin(x + π/2)

The equation of the function shown in the graph is y = sin(x + π/2)

Thus, the equation matches the function provided in the graph is y = sin(x + π/2)

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Answer:

Line A

Step-by-step explanation:

It has a lower slope of 3/4

Answer:

6x^2*y^2

Step-by-step explanation:

to find greatest factor:

find the biggest thing they have in common

example:

xy+xe+xz all have x in common so you can facor out x like x(y+e+z)

6x^2 y^3 +18x^3 y^3 + 36x^3 y^2

-they are all divible by 6

=6 (x^2 y^3 +3x^3 y^3 + 6x^3 y^2)

-all have at least x^2

=6x^2 (y^3 +3x y^3 + 6x y^2)

-all have at least y^2

=6x^2 y^2 (y +3xy +6x)

greatest common factor is 6x^2*y^2

Answer: 150 degrees

Step-by-step explanation: 10+ 20 = 30

180-30 = 150 degrees.