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Given the expression: 5x^10 − 80x^2

Part A: Rewrite the expression by factoring out the greatest common factor. (4 points)

Part B:Factor the entire expression completely. Show the steps of your work. (6 points)

Answer:

The value of x = 3 or -1/2

Step-by-step explanation:

2x²-5x-3=0

=> 2x² - 6x + x - 3 =0

=> 2x ( x - 3) + 1 ( x -3) =0

=> (2x+1) ( x-3) =0

x = 3 or x = -1/2

Step-by-step explanation:

3.

the left cup is the summary of 2 cylinders.

the right cup is just a cone.

the volume of a cone is

pi×r²×h/3 = pi×3.5²×6/3 = pi×12.25×2 = pi×24.5 =

= 76.93 in³

the volume of a cylinder is

pi×r²×h

the first cylinder is

pi×3²×1.5 = pi×9×1.5 = pi×13.5 = 3.14×13.5 = 42.39 in³

the second cylinder is

pi×2²×2.25 = pi×4×2.25 = pi×9 = 28.26 in³

in total the cup has

42.39 + 28.26 = 70.65 in³

so, the cone has the larger volume by 6.28 in³ ≈ 6 in³.

that would be 3.479827 fl.oz. ≈ 3 fl.oz. of water.

I have no idea on what scale you need to quantify the amount of water. I just guessed.

2.

here we need the surface area.

the object consists of a large prism (or block) and a cylinder.

we don't need the bottom area for neither, as the cylinder is simply on top of the prism, and its bottom is not going to be painted either.

we need 5 sides of the prism :

front and back

left and right

top (and we need the full top, because the area the cylinder is covering up is the same area for the top of the cylinder).

and the we need to add only the side wall of the cylinder the "mantle".

so,

front and back rectangles are 10×3 × 2 = 60 in²

left and right rectangles are 10×3 × 2 = 60 in²

the top rectangle (square) is 10×10 = 100 in²

the cylinder mantle is

circumference of the circle × height

2×pi×r×h = 2×pi×4×6 = 3.14×48 = 150.72 in²

so, in total we have

60 + 60 + 100 + 150.72 = 370.72 in² ≈ 371 in²

Answer:

Question 2: 320.48 in^2

Question 3: 6.28 in^3

Step-by-step explanation:

Question 2)

The question tells us that the shape will be covered in paint. This means that we need to find the surface area instead of volume. In the question, I’ll find the surface area of the two individual shapes (The cylinder and the rectangular prism) and take away parts that will not be covered in paint.

Rectangular Prism

1. ((10x10)+(10x3)+(10x3))x2 — All rectangular prisms have 2 sides with the same area. Since there are 6 sides total, all we need to do is find 3 sides of different sizes and multiply them by 2. The number we get is 320 in^2.

2. We will not be painting the bottom, so we can take the area of the bottom away. The area of the bottom is 10x10, which is 100. 320 - 100 is 220 in^2.

3. We are also not painting the area where the cylinder is touching the top (The circle-shaped area). The formula of finding the area of a circle is radius x radius x pi. Since the radius is 4 and pi can be rounded to 3.14, the area of the circle will be 4x4x3.14, which is 50.24 in^2. We can take that away from 220, so 220 - 20.24 is 169.76 in^2.

Cylinder

1. 4x4x3.14 — We know that one side of the cylinder (The base) will not be painted, so all we need to do is find the area of one of the bases. Radius x Radius x pi, in this case, is 50.24 in^2.

2. (((4+4)x3.14)x6) — Now we need to find the area of the side of the cylinder. The area of the side is base x height. The base length is the perimeter of the circle. The equation of the circle perimeter is (radius + radius) x pi. In numbers, it will be 8x3.14 which is 25.12. The height of the side is 6, so the equation will be 25.12 x 6, which is 150.72.

3. The surface area of the cylinder (excluding the base at the bottom) is 150.72 in^2.

Since the rectangular prism and the cylinder is stuck together and is considered as a whole, we add the two numbers together. 169.76 + 150.72 = 320.48 in^2!

Question 3)

The amount of water the cups can hold is the same size as the volume of individual cups. In order to find out the amount of water each cup can hold, we need to find the volume first.

Cup #1

1. (2x2x3.14)(2.25) — This is the base times the height of the bottom cylinder. The formula to find a circle is radius x radius x pi, and the height was 2.25. The volume of this shape will be 28.26 in^3.

2. (3x3x3.14)(1.5) — The area of the bottom is radius x radius x pi, and the height was 1.5 If we multiply all of these numbers together, we get 42.39 in^3.

3. Now that we found the two cylinders of the first cup, we can add them together. 28.26 + 42.39 = 70.65.

4. The area of cup #1 is 70.65 in^3.

Cup #2

1. (3.5 x 3.5 x 3.14)(6)(1/3) — The formula for finding the area of a cone is base x height x 1/3. The area of the base is radius x radius x pi, and the height is 6. Then we multiply by 1/3 (or divide by 3). Then, we get 76.93 in^3.

2. The volume of cup #2 is 76.93 in^3.

The question asks: How much more water will the larger cup hold?

Comparing 70.65 in^3 (First cup) and 76.93 in^3 (Second cup), we know that the second cup is bigger. To find the difference in the amount of water it can hold, we can subtract 70.65 from 76.93. This equals 6.28 in^3.

The final answer for Question 3 will be 6.28 in^3!

The approximate probability that the 5 bushels will have a mean weight of more than 90 pounds is 0.41

The given parameters are:

Mean, μ = 89.46

Standard deviation, σ = 2.31

The z-score at x = 90 is calculated using

[tex]z = \frac{x - \mu}{\sigma}[/tex]

This gives

[tex]z = \frac{90 - 89.46}{2.31}\\[/tex]

Evaluate

z = 0.234

The probability is then calculated as:

P(x >90) = P(z > 0.234)

From z table of probabilities, we have:

P(x >90) = 0.41

Hence, the approximate probability that the 5 bushels will have a mean weight of more than 90 pounds is 0.41

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             [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Question:-}}}\rule{50}{1}[/tex]

          Write the equation of a line perpendicular to y=-12x+2 going

           through (0, -1)

     [tex]\rule{50}{1}\large\blue\textsf{\textbf{\underline{Answer and how to solve:-}}}\rule{50}{1}[/tex]

        First, let's take a look at our provided information:-

     If two lines are perpendicular to each other, their slopes are opposite reciprocals of each other.

   So we take the slope of the given line, which is -12, change its sign from minus to plus:-

[tex]\Large\textit{12}[/tex]

And now, We flip the number over:-

[tex]\Large\text{$\displaystyle\frac{1}{12}$}[/tex]

Now that we've found the slope of the line, let's find its equation.

     The first step is to write it in point-slope form as follows:-

[tex]\longmapsto\sf{y-y_1=m(x-x_1)}[/tex]

Replace letters with numbers,

[tex]\longmapsto\sf{y-(-1)=\displaystyle\frac{1}{12}(x-0)}[/tex]

On simplification,

[tex]\longmapsto\sf{y+1=\displaystyle\frac{1}{12} (x-0)}[/tex]

On further simplification,

[tex]\longmapsto\sf{y+1=\displaystyle\frac{1}{12} x}[/tex]

Subtracting 1 on both sides,

[tex]\longmapsto\sf{y=\displaystyle\frac{1}{12} x-1}[/tex]

[tex]\Uparrow\texttt{Our equation in slope-intercept form}[/tex]

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[tex]\rule{300}{1}[/tex]

Answer:

charlie brown chicken sandwich

Step-by-step explanation:

Answer:

volume = 216cm

Step-by-step explanation:

V = (1/2) × b × h × l

V = 1/2 × 6 × 8 × 9

v=216

Answer:

216 cubic centimeters

Step-by-step explanation:

To calculate the volume of a triangular prism, we can use the formula:

V = (length x width x height) / 2

To solve this problem, in particular, all we have to do is substitute the values:

V = (8 x 6 x 9) / 2

V = 216 cubic centimeters

Hope this helps!!

Answer:

c) 480

Step-by-step explanation:

Any percentage can be converted to a number ratio by dividing by 100%.

E.g. 100%/100% = 1

Following this concept, we can find the equivalent of 110% :

110%/100% = 1.1

Since 528 is 1.1 times the number we are looking for, we just need to divide 528 by 1.1 to find our number. This is because 1.1/1.1 = 1

528/1.1 = 480

Hope this helped!

Answer:

12 teaspoons

Step-by-step explanation:

Answer:

7/10

Step-by-step explanation:

There are 20 students in the class.

The scores are :

100, 95, 88, 62, 74, 90, 100, 58, 72, 60, 85, 90, 70, 72, 54, 100, 60, 80, 75, 51

* scores ≥ 70 have been highlighted in bold

Out the 20, 14 students have passed.

Hence, the fraction of students passed :

Step-by-step explanation:

Proof: equidistance means at an equal distance from two points

so: Take the distance formula and then plug the values in and compare.

Answer:

8.80 if it's the 40°/.

2.20 if it's the 10°/. processing fee

13.20 for how much he paid

The total cost of the piece of land for which James, John and Jane decided to buy a piece of land is 1,200,000.

Total cost or the final cost is the summation of all the cost spend while buying any good or taking any service.

James, John and Jane decided to buy a piece of land. James paid 3/5 of the total cost while John paid 3/8 of the reminder.  Thus, the fraction of amount paid by Jane is,

[tex]x=1-\dfrac{3}{5}-\dfrac{3}{8}\\x=\dfrac{40-24-15}{40}\\x=\dfrac{1}{40}[/tex]

The Jane paid, 30000 of total cost which is 1/40 part of it. Thus, the total cost of the piece of land is,

[tex]\dfrac{1}{40}x=30000\\x=30000\times40\\x=1200000[/tex]

Thus, the total cost of the piece of land for which James, John and Jane decided to buy a piece of land is 1,200,000.

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Answer:

The answer is D I hope this helps

The required domain for the function given on the graph represents the exponential function is x ≥ 1. Option C is correct.

Given that,
A graph of a function is shown that has 3 distinct functions for its domain, we have to determine which of these 3 functions shows an exponential function.

The function which is in format f(x) =   where, a is constant and x is variable,  the domain of this exponential function lies   (-∞, ∞).  

Since, as we can see throughout the graph the graph constantly decreases to -4 and then shows a parabolic function from -4 to 0.9 afterward it starts increasing exponentially.

Thus, the required domain for the function given on the graph represents the exponential function is x ≥ 1. Option C is correct.

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Answer:

[tex]\log_{9}4\approx 0.631[/tex]

Step-by-step explanation:

The change of base formula we can use is

[tex]\log_{b}a=\frac{\log{a}}{\log{b}}[/tex]

Not all calculators will allow the user to directly enter the logarithms with a given base, so the change of base can be used for all calculators, which use the common log.

Common logs have a base of 10.

Let's convert your expression:

[tex]\log_{9}4=\frac{\log4}{\log9}[/tex]

Using our calculator, we will compute log 4 divided by log 9:

[tex]\frac{\log4}{\log9}\approx0.631[/tex].

Step-by-step explanation:

the square root of x squared is x.

this means the( cube root of x ) to the power of 6 is what we need

Answer:

200

Step-by-step explanation:

(6 × 10^5) / (3 × 10^3) = 6/6 × 10^5/10^3 = 2 × 10^2 = 200

Answer:

200

Step-by-step explanation:

(6 × 10^5) / (3 × 10^3) = 6/6 × 10^5/10^3 = 2 × 10^2 = 200

Check the picture below.

the area of the triangle whose base is AC and height is BD, is the same area of the triangle whose base is AB and altitude is BC, namely

[tex]A=\cfrac{1}{2}(\stackrel{b}{6})(\stackrel{h}{6})\implies 18[/tex]

This line is fairly close to the majority of the points shown. Unfortunately there's an outlier left out, but it isn't too far from the main cluster. The further the outlier is, the more pull it will drag the line away from the main cluster.

Line Q

Q is correct

Answer:

No

Step-by-step explanation:

Identify the equation for the circle

[tex](x-h)^2+(y-k)^2=r^2\\(x-2)^2+(y-13)^2=5^2\\(x-2)^2+(y-13)^2=25[/tex]

Check if (2,-11) is a point on the circle

[tex](x-2)^2+(y-13)^2=25\\(2-2)^2+(-11-13)^2=25\\0^2+(-24)^2=25\\576\neq25[/tex]

Since both sides of the equation are not equal to each other, then (2,-11) is not a point on the circle.

To solve this problem, we just have to use trigonometric ratios and apply which of the ratios is needed here and proceed to solve. The value of side AC is 2.85 units

In the given diagram, we have the value of angle and hypothenuse and we are required to find the adjacent side of the triangle.

Data;

Let's use cosine rule for this.

[tex]cos\theta = \frac{adjacent}{hypothenuse}[/tex]

Proceed to substitute the values into the equation and solve.

[tex]cos 32.9 = \frac{AC}{3.4} \\AC=3.4cos32.9\\AC = 2.85[/tex]

From the calculations above, the value of side AC is 2.85 units

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Answer:

540

Step-by-step explanation:

If you divide 540 by 100 (100%) you get 5.4 then multiply it by 10 (10%) to get 54 again. THIS WAS TO CHECK TO GET: 10% or 100% is 10 so multiply 54•10=540

Hope this helps! ;-)

Using a proportional relationship, it is found that when x = -7, the value of y will be of y = 6.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

When y varies inversely with x, the rule is given by:

[tex]y = \frac{k}{x}[/tex]

y = −3 when x = 14, hence we use this to find k.

[tex]-3 = \frac{k}{14} \rightarrow k = -42[/tex]

Then:

[tex]y = -\frac{42}{x}[/tex]

Then when x = -7, y = -42/-7 = 6.

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if this helped you say meow

i may be wrong but i think you should divide 2.4% by the 15000 wicth  is

0.00000016 or just 0.16 or maybe  muptication 2.4% x15000 whicth is 360 hope this helps :D

Answer:

[tex]\displaystyle x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex]

Step-by-step explanation:

[tex]\displaystyle 5\cos x-\sqrt{3}=3\cos x;\:0\leq x < 2\pi\\\\5-\frac{\sqrt{3}}{\cos x}=3\\ \\-\sqrt{3}\sec x=-2\\\\\sec x=\frac{2}{\sqrt{3}}\\\\\sec x=\frac{2\sqrt{3}}{3}\\ \\\cos x=\frac{3}{2\sqrt{3}}\\ \\\cos x=\frac{3\sqrt{3}}{6}\\ \\\cos x=\frac{\sqrt{3}}{2}\\\\x=\biggr\{\frac{\pi}{6},\frac{11\pi}{6}\biggr\}[/tex]

Answer:

Based on hint and given formula, we can complete the problem. The question asks for square feet of grass so we know that we are solving for the area, A. It also tells us the height (looking downward) of the field is 75 ft,h, while the two bases are 125 ft and 81 ft (b1 and b2). So we can solve the equation. A = 75((125+81)/2) A = 75(206/2) A = 75(103) A = 7725 The area of the field is 7725 square feet.

Step-by-step explanation:

The equivalent equations of the trapezoid are:

h = 2A / (b₁ + b₂)

b₁ = 2A / h - b₂

b₂ = 2A / h - b₁

A = (b₁ + b₂) x h / 2

It is a quadrilateral that has one pair of parallel sides and a height.

The area is calculated as 1/2 x the sum of the parallel sides x height.

Examples:

Area of a trapezium that has the parallel sides as 3 cm and 4 cm and a heght o 5 cm.

Area = 1/2 x (3 + 4) x 5

Area = 1/2 x 7 x 5

Area = 35/2 = 17.5 cm^2

We have,

The formula for the area of a trapezoid can be rearranged in different ways to express the same relationship between the height, the bases, and the area.

Here are a few equivalent equations:

h = 2A / (b₁ + b₂) (solve for h)

b₁ = 2A / h - b₂ (solve for b₁)

b₂ = 2A / h - b₁ (solve for b₂)

A = (b₁ + b₂) x h / 2 (multiply both sides by 2 and divide by h)

These equations can be used interchangeably to calculate the area, height, or base of a trapezoid, depending on which variables are known or given.

Thus,

The equivalent equations are:

h = 2A / (b₁ + b₂)

b₁ = 2A / h - b₂

b₂ = 2A / h - b₁

A = (b₁ + b₂) x h / 2

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Answer:

1/1000, 0.001

1/1000

Convert the negative exponent of base 10 into decimal: move to the left thrice

=0.001

Answer:

x = 10

Step-by-step explanation:

The sum of the angles of a triangle is 180 degrees

6x-6 + 7x+1 +55 = 180

Combine like terms

13x+50=180

Subtract 50 from each side

13x+50-50=180-50

13x = 130

Divide by 13

13x/13 =130/13

x = 10

The answer is A!

From this, we will get the equation

(13x -5) + 55 = 180

+ 5 on both sides

13x + 55 = 185

-55 on both sides

13x = 130

Divide by 13 on both sides

x = 10

Answer:

80

Step-by-step explanation: