What is the fully factored form of the expression 45x²y2 + 18x3

Answer:  462 cm^3

Step-by-step explanation:

formula for triangular prisms:

0.5*b*h = V

b or base = 6*6 cm

h or height = 7 cm

7 * 6 * 6 * 0.5 = 126

V or Volume of triangular prism is 126 cm^3.

formula for rectangular prisms:

b * h = V

b or base = 8*6 cm

h or height = 7 cm

8 * 6 * 7 = 336

V or Volume for rectangular prism is 336 cm^3.

Total Volume of Composite Figure = sum of both Volumes

336 + 126 = 462 cm^3.

[tex]v = a \times b \times h \times \frac{1}{2} [/tex]

[tex]v = 6 \times 6 \times 7 \times \frac{1}{2} [/tex]

[tex]v = 126 \: {cm}^{3} [/tex]

[tex]v = whl[/tex]

[tex]v = 7 \times 8 \times 6[/tex]

[tex]v = 336 \: {cm}^{3} [/tex]

[tex]v = 126 + 336[/tex]

[tex]v = 462 \: {cm}^{3} [/tex]

Answer:

160 cm^2.

Step-by-step explanation:

Surface area = area of base + 4 * area of triangular side.

= 8^2 + 4 * 1/2 * 8 * 6

= 64 + 96

= 160 cm^2.

Answer:

179.38cm²

Step-by-step explanation:

By using the formula, it is 179.38cm.

Answer: x + 4

Step-by-step explanation:

    If it is asking us for (f - g)x, then we will subtract the function g from function f. Why? The x distributes creating f(x) - g(x), so we use this to solve.

   Given:

g(x) = 2x - 2

f(x) = 3x + 2

   Set up:

f(x) - g(x)

(3x + 2) - (2x - 2)

   Distribute the negatie:

3x + 2 - 2x + 2

   Reorder to combine like terms:

3x - 2x + 2 + 2

   Combine like terms:

x + 4

    (f - g)(x) = x + 4

The algebra tile configuration that represents the factors of 2x² + 5x + 3 must have a product of (2x + 3) and (x + 1)

The expression is given as:

2x² + 5x + 3

Expand the expression

2x² + 5x + 3 = 2x² + 2x + 3x + 3

Factorize the expression

2x² + 5x + 3 = 2x(x + 1) + 3(x + 1)

Factor out x + 1

2x² + 5x + 3 = (2x + 3)(x + 1)

The above means that the algebra tile configuration that represents the factors of 2x² + 5x + 3 must have a product of (2x + 3) and (x + 1)

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Answer:

(A)    (2x+3)(x+1)

Step-by-step explanation:

got it right on edge 2022

Answer:

Everyone got 3 pens, 21 remained

Step-by-step explanation:

111:30=3 21/30

The mean , median and mode of the data are 35.875, 44 and 48

The mean, median and mode can be found as follows:

mean = sum of terms / number of terms

mean = 48 + 12 + 11 + 45 + 48 + 48 + 43 + 32 / 8

mean = 287 / 8 = 35.875

11, 12, 32, 43, 45, 48, 48, 48

The median is the centre number.

Hence,

median = 43 + 45 / 2 = 88 / 2 = 44

The mode is the number that appears most which is 48.

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The Mean, Median and Mode of the given set of data ( 11, 12, 32, 43, 45, 48, 48, 48 ) are 35.875, 44 and 48 respectively.

Arithmetic mean is simply the average of a given set numbers. It is determined by dividing the sum of a given set number by their number of appearance.

Mean = Sum total of the number ÷ n

Where n is number of numbers

Given the sets;

First, we arrange in ascending order.

11, 12, 32, 43, 45, 48, 48, 48

Mode

Mode is the number with the highest appearance

Number with highest appearance  or frequency is 48 ( 3 appearance )

Mode = 48

Median

Middle numbers fall between 43 and 45

Median = ( 43 + 48 ) / 2

Median = 88 / 2

Median = 44

Mean

We add the numbers

11 + 12 + 32 + 43 + 45 + 48 + 48 + 48 = 287

Mean = Sum total of the number ÷ n

Mean = 287 /  8

Mean = 35.875

Therefore, the Mean, Median and Mode of the given set of data ( 11, 12, 32, 43, 45, 48, 48, 48 ) are 35.875, 44 and 48 respectively.

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Answer:

See below

Step-by-step explanation:

Expansion

[tex]f(x)=3(x+6)^2-75\\\\f(x)=3(x+6)(x+6)-75\\\\f(x)=3(x^2+12x+36)-75\\\\f(x)=3x^2+36x+108-75\\\\f(x)=3x^2+36x+33[/tex] <-- Stop here if this is what you need

Factorization

[tex]f(x)=3(x^2+12x+11)\\\\f(x)=3(x+1)(x+11)[/tex]

We know from vertex form that the vertex of the parabola is [tex](-6,-75)[/tex] and when factored, the zeroes are [tex]x=-1[/tex] and [tex]x=-11[/tex].

Check the picture below.

well, on the child's 26th birthday that'll be 26 years later, so

[tex]~~~~~~ \textit{Continuously Compounding Interest Earned Amount} \\\\ A=Pe^{rt}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill & \$25000\\ r=rate\to 3\%\to \frac{3}{100}\dotfill &0.03\\ t=years\dotfill &26 \end{cases} \\\\\\ A=25000e^{0.03\cdot 26}\implies A=25000e^{0.78}\implies A\approx 54536.81[/tex]

By the angle sum property of a triangle, the value of x would be equal to 9.

The angle sum property of a triangle states that the sum of the interior angles of a triangle is 180 degrees.

The sum of the triangle of angles is 180.

6x + 56 + 38 + t = 180

t = 180 - 94 - 6x

t = 86 - 6x

By linear pair

10x + 58 + t = 180

10x + 58 +  86 - 6x = 180

4x + 144 = 180

4x = 180 - 144

4x = 36

x = 9

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Answer:

There are a total of 8 different schedules.

Step-by-step explanation:

In situations like these, it's best to write down all possible combinations on a tree diagram. However, I use a different way to solve problems like these. For the equation multiply the choices of the first period with the choices of the second period. 2×4=8

You can do this other problems that can include 3 choices, 4 choices, and so on.

Answer:

area=volume/height

area=1200cm cubed/12cm

area=100cm squared

Answer:

49 + 32 = 81       81 divided by 9 is 9 in

Step-by-step explanation:

The discriminant of the function is 120, and the function has 2 different x-intercepts

The function is given as:

f(x) = -7x^2 + 8x + 2

The discriminant (d) is calculated using:

D =b^2 - 4ac

So, we have:

D = 8^2 - 4 * (-7) * 2

Evaluate

D = 120

Because the value of D is greater than 0, then the function has 2 different x-intercepts

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Answer:
-7x + 5

Step-by-step explanation:

2(4x + 1) - 3(5x - 1)

8x + 2 - 3(5x-1)
8x + 2 - 15x + 3
8x + 5 - 15x
-7x + 5

Hope it helped !
Adriel

Melody need 155 bags of 140 cu. inches to fill the vegetable garden.

The volume of the cuboid is the measure of the space occupied within a cuboid. The cuboid is a three-dimensional shape that has length, breadth, and height.

Here, Length of vegetable garden = 48 inch

          breadth of garden = 30 inches

          height of garden = 15 inches

Volume of garden = Length X width X height

                              = 48 X 30 X 15

                              =  21600 cu. inches

Volume of each bag = 140 cu. inches

Number of Bags required = Volume of garden/Volume of each bag

                                            = 21600 / 140

                                            ≈ 155

Thus, Melody need 155 bags of 140 cu. inches to fill the vegetable garden.

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The independent events are illustrations of probability, and the value of P(B) is 0.40

The given parameters are:

P(A) = 0.50

P(A and B) = 0.20

Two events A and B are independent, if

P(A and B) = P(A) * P(B)

So, we have:

0.50 * P(B) = 0.20

Divide both sides by 0.50

P(B) = 0.40

Hence, the value of P(B) is 0.40

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Answer:

7x8

Step-by-step explanation:

none of those seem right

Answer: 44/9 ----> 22/9

I hope this helps you

Answer:

To make such a frequency distribution table, first, write the class intervals in one column. Next, tally the numbers in each category based on the number of times it appears. Finally, write the frequency in the final column. A frequency distribution table drawn above is called a grouped frequency distribution table.

Answer:

Part A: Rate of change of a bushel of corn is 7

Part B: 2 dollars more is the price of a bushel of corn in the current year than the price of a bushel of corn in the previous year

Step-by-step explanation:

Let me know if you have any questions !

B

because it starts at the rarefraction.

The value of the tangent of  C in fraction form will be 2 / 7.

The branch of mathematics sets up a relationship between the sides and the angles of the right-angle triangle are termed trigonometry.

Given that:-

The value of Tanc will be calculated as:-

tanC = P  /  B

tanC = 6 / 21

tanC = 2 / 7

Therefore the value of the tangent of  C in fraction form will be 2 / 7.

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Answer:

See below ~

Step-by-step explanation:

Change in KE if mass is doubled

Change in KE if speed is doubled

Answer:

  4: 264°; 5: 120°; 6: 54°; 7: 45°; 8: 87°; 9: 27°

  9: x=200, y=100; 10: x=68; y=99

Step-by-step explanation:

The relations between angles and arcs in this problem set are ...

__

no identifier is given

Arc DBC is the difference between a full circle (360°) and short arc DC. The measure of short arc DC is marked as 96°, so ...

  arc DBC = 360° -96° = 264°

Αrc BC is twice the measure of the inscribed angle BDC it subtends.

  arc BC = 2×60° = 120°

Arc AB is the difference between 360° and the sum of arcs AD, DC, and CB.

  arc AB = 360° -(90° +96° +120°) = 54°

Angle ACD is half the measure of arc AD.

  Angle ACD = 90°/2 = 45°

Angle ADC is half the measure of arc AC, which is the sum of arcs AB and BC

  angle ADC = (54° +120°)/2 = 87°

Angle ACB is half the measure of arc AB

  angle ACB = 54°/2 = 27°

__

x° is the arc whose central angle is 200°

  x° = 200°

y° is half the measure of x°

  y° = 200°/2 = 100°

The relations between arcs and inscribed angles mean that opposite angles in an inscribed quadrilateral are supplementary.

 x° = 180° -112° = 68°

  y° = 180° -81° = 99°

Answer:

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Step-by-step explanation:

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