Find the domain of the function using interval notation.



f(x)=−2x(x−3)(x−6)

Oliver is left with $514.8

A percentage is a number or ratio expressed as a fraction of one hundred. If we need to calculate a percentage of a number, divide it by the whole and multiply by 100. As a result, the percentage represents one part in a hundred. The term % stands for one hundred percent.

His usual salary = $520 per week

This week he earned = Usual salary + 10% of usual salary

10% of usual salary =520 x (10/100)  

Thus, this week's earnings = $520 + $52 = $572

Amount spent = 10% of this week =572 x (10/100)    

= 57.2

Thus, the left amount is calculated by:

Left amount = this week's salary - the amount spent

Amount left  = $572 - $57.2 = $514.8

Thus, Oliver is left with $514.8

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The percent of families would be expected to have children who are all boys is 6.25%

The following can be illustrated:

all 4 boys BBBB 1 1/16

3 boys 1 girl BBBG,GBBB,BGBB,BBGB 4 4/16

2 boys 2 girl BBGG,BGBG,GBGB,BGGB,GBBG, GGBB 6 6/16

1 boy 3 grisl BGGG,GBGG,GGBG,GGGB 4 4/16

all 4 girls GGGG 1 1/16

Therefore, the percent of families would be expected to have children who are all boys will be:

= All boys × 100

= (1/16)*100

= 6.25%

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The height is 17.69 inches.

From the question, we have

Let height= h

width = h+4

diagonal = 28 inches

Using Pythagoras Theorem

28²  = h²  + (h+4)²

784 = h² +h² +16+8h

784  = 2h² +16+8h

2h²+8h-768 = 0

Solving this, we get

h=−2+2*√97

h=17.69 inches

Multiplication:

Finding the product of two or more numbers in mathematics is done by multiplying the numbers. It is one of the fundamental operations in mathematics that we perform on a daily basis. Multiplication tables are the main use that is obvious. In mathematics, the repeated addition of one number in relation to another is represented by the multiplication of two numbers. These figures can be fractions, integers, whole numbers, natural numbers, etc. When m is multiplied by n, either m is added to itself 'n' times or the other way around.

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Answer:

below

Step-by-step explanation:

12 hours is  .5 day   so a total of 3.5 days

2100 w-h / 3.5 d = 600 w-h per day

=========================================================

Explanation:

The three points are at these locations:

The notation "d(A,C)" means "the distance from A to C". It's equivalent to saying "the length of segment AC".

Then writing [tex]\left[d(A,C)]^2[/tex] means we'll square that distance.

Use the distance formula to get...

[tex]A = (x_1,y_1) = (10,6) \text{ and } C = (x_2, y_2) = (-5,3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-(-5))^2 + (6-3)^2}\\\\d = \sqrt{(10+5)^2 + (6-3)^2}\\\\d = \sqrt{(15)^2 + (3)^2}\\\\d = \sqrt{225 + 9}\\\\d = \sqrt{234}\\\\[/tex]

This is the exact length of segment AC. That value squares to 234.

[tex]d = \sqrt{234} \ \to \ d^2 = (\sqrt{234})^2 = 234\\\\[/tex]

The square root and squaring operation cancel each other out. Think of it like fire vs water.

So we really only care about what's under the square root; rather than the entire square root expression itself. Which is nice because we don't have to worry about pesky things like decimal values.

This is why 234 is typed into the first box.

---------------------

Next, use the distance formula to find how far it is from A to B. Square the result to get what you see below.

[tex]A = (x_1,y_1) = (10,6) \text{ and } B = (x_2, y_2) = (1,-3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(10-1)^2 + (6-(-3))^2}\\\\d = \sqrt{(10-1)^2 + (6+3)^2}\\\\d = \sqrt{(9)^2 + (9)^2}\\\\d = \sqrt{81 + 81}\\\\d = \sqrt{162}\\\\d^2 = (\sqrt{162})^2\\\\d^2 = 162\\\\[/tex]

This is the value of [tex]\left[d(A,B)\right]^2[/tex]

Now find the distance from B to C, and square the result.

[tex]B = (x_1,y_1) = (1,-3) \text{ and } C = (x_2, y_2) = (-5,3)\\\\d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}\\\\d = \sqrt{(1-(-5))^2 + (-3-3)^2}\\\\d = \sqrt{(1+5)^2 + (-3-3)^2}\\\\d = \sqrt{(6)^2 + (-6)^2}\\\\d = \sqrt{36 + 36}\\\\d = \sqrt{72}\\\\d^2 = \left(\sqrt{72}\right)^2\\\\d^2 = 72\\\\[/tex]

Add this to the previous squared value and we get 162+72 = 234, which matches exactly with the 234 found up toward the top.

We'll write 234 in the 2nd box as well.

This shows that [tex]\left[d(A,C)\right]^2 = \left[d(A,B)\right]^2+\left[d(B,C)\right]^2[/tex] is a true statement. By the converse of the Pythagorean theorem, we have confirmed this is a right triangle.

In other words, we've shown that [tex]a^2+b^2 = c^2[/tex] is a true statement (a,b,c are the sides of the right triangle such that c is the hypotenuse).

---------------------

Recall that we found these segment lengths:

[tex]AB = \sqrt{162} = \text{leg1}\\\\BC = \sqrt{72} = \text{leg2}\\\\AC = \sqrt{234} = \text{hypotenuse}\\\\[/tex]

The legs of a right triangle represent the base and height, in either order. This is because the legs are perpendicular to one another. They form a right (aka 90 degree) angle.

[tex]\text{area} = \frac{1}{2}*\text{base}*\text{height}\\\\\text{area} = \frac{1}{2}*\text{AB}*\text{BC}\\\\\text{area} = \frac{1}{2}*\sqrt{162}*\sqrt{72}\\\\\text{area} = \frac{1}{2}*\sqrt{162*72}\\\\\text{area} = \frac{1}{2}*\sqrt{11664}\\\\\text{area} = \frac{1}{2}*108\\\\\text{area} = 54\\\\[/tex]

Here are some alternative methods you can follow to find the area of this triangle.

As for verifying the answers, you can use a tool like GeoGebra.

Answer:

[tex][d(A,C)]^2=\boxed{234}[/tex]

[tex][d(A,B)]^2+[d(B,C)]^2=\boxed{234}[/tex]

[tex]\sf Area=\boxed{54}\; units^2[/tex]

Step-by-step explanation:

From inspection of the given diagram:

If ΔABC is a right triangle, the sum of the squares of the two shorter sides will equal the square of the longest side.  This is the definition of Pythagoras Theorem.

Use the distance formula to find the length of each side of the triangle.

[tex]\boxed{\begin{minipage}{7.4 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]

[tex]\begin{aligned}d[(A,C)]&=\sqrt{(x_C-x_A)^2+(y_C-y_A)^2}\\&=\sqrt{(-5-10)^2+(3-6)^2}\\&=\sqrt{(-15)^2+(-3)^2}\\&=\sqrt{225+9}\\&=\sqrt{234}\end{aligned}[/tex]

[tex]\begin{aligned}d[(A,B)]&=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\&=\sqrt{(1-10)^2+(-3-6)^2}\\&=\sqrt{(9)^2+(-9)^2}\\&=\sqrt{81+81}\\&=\sqrt{162}\end{aligned}[/tex]

[tex]\begin{aligned}d[(B,C)]&=\sqrt{(x_C-x_B)^2+(y_C-y_B)^2}\\&=\sqrt{(-5-1)^2+(3-(-3))^2}\\&=\sqrt{(-6)^2+(6)^2}\\&=\sqrt{36+36}\\&=\sqrt{72}\end{aligned}[/tex]

Therefore:

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

Therefore, the triangle is a right triangle if:

[tex][d(A,B)]^2+[d(B,C)]^2=[d(A,C)]^2[/tex]

Substitute the found side lengths into the formula:

[tex]\implies [\sqrt{162}]^2+[\sqrt{72}]^2=[\sqrt{234}]^2[/tex]

[tex]\implies162+72=234[/tex]

[tex]\implies 234=234[/tex]

Hence proving that ΔABC is a right triangle.

To find the area of a right triangle, half the product of the two shorter sides:

[tex]\begin{aligned}\implies \sf Area &= \dfrac{1}{2}bh\\&=\dfrac{1}{2} \cdot [d(A,B)] \cdot [d(B,C)]\\&=\dfrac{1}{2} \cdot \sqrt{162} \cdot \sqrt{72}\\&=\dfrac{1}{2} \cdot \sqrt{162 \cdot 72}\\&=\dfrac{1}{2} \cdot \sqrt{11664}\\&=\dfrac{1}{2} \cdot \sqrt{108^2}\\&=\dfrac{1}{2} \cdot 108\\&=54 \sf \; units^2\end{aligned}[/tex]

Answer:

x=3

Step-by-step explanation:

any horizontal line is equal to x

the y is equal to 0

a horizontal line is undefined

The question that can be represented by the equation ? × 1/8 = 3 is C. how many 1/8s are in 3?

An equation is the statement that illustrates that the variables given. In this case, two or more components are taken into consideration to describe the scenario.

In this case, the question is how many 1/8s are in 3. This will be:

= 3 ÷ 1/8

= 3 × 8

= 24

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Answer:

2400Watt Hours isn't it A Right Answer?

Answer:

x = 15

Step-by-step explanation:

Please refer photo

Answer:

She distributed incorrectly.

Step-by-step explanation:

In the first step, [tex]3(x-3)=3x-9[/tex], not [tex]3x-3[/tex].

Answer:

x=18-2/5y

y=-5/2x+45

Step-by-step explanation:

5x+2y=90

Nosotros queremos resolver para x o y

5x=90-2y

x=18-2/5y

o

2y=90-5x

y=-5/2x+45

Answer:

x=18-2y/5

Step-by-step explanation:

The equation of the line has a slope of 7 and passes through the point (-8,3) is y = 7x + 59.

A straight line on the coordinate plane is represented by a linear function.

A linear function always has the same and constant slope.

The formula for a linear function is f(x) = ax + b, where a and b are real values

The general form of a linear equation is the slope(m) and y-intercept (c) is given as

y = mx + c

Slope m =7

y = 7x + c

Substitute, (-8,3)

3 = 7(-8) + c

c = 59

Thus, y = 7x + 59 will be the equation.

Hence "The equation of the line has a slope of 7 and passes through the point (-8,3) is y = 7x + 59".

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The value of the coin after five years is 535 when the value increases with the function f(x) = 100(1.07)x

The value of a rare coin rises in accordance with the function f(x)

f(x) = 100(1.07)x

where x represents the number of years that the coin is owned and value is measured in US dollars

Now, Simplifying the given function, we have :

f(x) = 100(1.07)x

f(x) = 107x

Now, we need to find the value of the coin after five years, then

Putting x = 5 in the function,

f(x) = 107 * 5 = 535

Hence, the value of the coin after five years is 535 when the value increases with the function f(x) = 100(1.07)x

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The different ways that are there of selecting the trucks and the drivers to meet these requests is 240 ways.

Combinations are also referred to as selections. Combinations imply the selection of things from a given set of things. In this case, we intend to select the objects.

Combination formula

ⁿCr = n! / ((n – r)! r!)

n = the number of items.

r = how many items are taken at a time.

The number of ways to select 3 trucks will be:

= ⁵C₃ = 10

The number of ways to select 3 drivers will be:

= ⁴C₃ = 4

Number of ways to arrange them = 3! = 3 × 2 = 6

Therefore the total number of ways will be:

= 10 × 4 × 6

= 240 ways

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[tex]\qquad \textit{Amount for Exponential Growth} \\\\ A=P(1 + r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &810000\\ r=rate\to 11.3\%\to \frac{11.3}{100}\dotfill &0.113\\ t=\textit{years}\dotfill &5\\ \end{cases} \\\\\\ A=810000(1 + 0.113)^{5} \implies A=810000(1.113)^5\implies A \approx 1383441.63[/tex]

The set of side lengths that would not create a triangle is; 10, 20, 30.

It follows from the task content that the set of side lengths which will not create a triangle are to be determined from the given task content.

Since the triangle inequality theorem states that; the sum of two side lengths of a triangle is always greater than the third side length and also, the difference of two side lengths of a triangle is less than the third side length.

On this note, for a triangle with side-lengths a, b and c; the inequalities which hold are;

a + b > c and a - b < c.

Therefore, the set of side-lengths which will not create a triangle is; 10, 20, 30.

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The 0.566 meter, 0.87 meter, 10.7 rev/s and 7.7 rev/s radii and respective rotational speeds of young David's slings indicates.

a) The larger linear speed is 42.09 m/s

b) The centripetal acceleration of the sling at 7.7 rev/s is approximately 2,036.39 m/s²

A linear speed is a measure of the rate at which the distance traveled by an object in rotary motion changes with time.

When the length of the sling = 0.566 m, The rate of revolving of the sling = 10.7 rev/s

When the length of sling = 0.87 m, the rate of revolving the sling = 7.7 rev/s

Linear speed = Angular speed ×Radius length

The angular speed when the length of the is 0.566 m, ω₁, is found as follows;

One complete 360° rotation  = 2·π radians

ω₁ = 10.7 rev/s × 2·π ≈ 67.23 rad/s

The linear speed is; v₁ ≈ 67.23 rad/s × 0.566 m ≈ 38.05 m/s

The angular speed when the length is increased to 0.87 meters is therefore;

ω₂ = 7.7 rev/s × 2 × π ≈ 43.38 rad/sec

The larger of the two linear speed is approximately 42.09 m/s

Part 2: The centripetal acceleration, [tex]a_c[/tex], is found using the following formula;

[tex]a_c = \dfrac{v^2}{r}[/tex]

When the radius is r = 0.87 meters, the linear speed v₂ ≈ 42.09 m/s, which indicates;

[tex]a_c=\dfrac{42.09^2}{0.87} \approx 2,036.39[/tex]

The centripetal acceleration is approximately [tex]a_c[/tex] ≈ 2,036.39 m/s²

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Answer:

Step-by-step explanation:

2

Answer:

The leading coefficient is 2.

Step-by-step explanation:

Leading coefficients are the numbers with the highest degree or exponent.

Answer:

10 minutes.

Step-by-step explanation:

8 houses are done in 4 minutes

The ratio is 2:1

20 houses are done in 10 minutes
20:10 = 2:1

Answer:

It would take Angelo 10 minutes to construct 20 playing card houses.

first way to solve it (recommended):

Step one: See how much it takes to build one house

4 / 8 = 0.5

0.5 minutes to build one house

Step two: multiply by amount of houses (20)

0.5 x 20

Step three: get your answer!

It would take Angelo 10 minutes to make 20 houses.

second way to solve it (ratios):

Step one: see the ratio of minutes to houses

minutes : houses

          4 : 8

Step two: simplify the ratio

4 : 8

1 : 2 (divide both sides by four)

Step three: multiply

x minutes : 20 houses

1 minutes : 2 houses

multiply both sides by 10

10 minutes : 20 houses

Step four: get your answer!

It would take Angelo 10 minutes to make 20 houses.

I hope my answer helped you!

The information about the Falcon fly is represented below

Part A: 800 000 = 4r

part B: 200 000 meters per hour

Part C: 200 kilometer per hour

Part D: Kilometers makes more sense because it makes the number easier to write and remember

The rate as used refers to speed which is distance / time

using the representation 800 000 = 4r

rate, r = 800 000 / 4

r = 200 000 meters per hour

converting meter to kilometer is achieved by dividing by 1000

r = 200 000 meters per hour / 1000

r = 200 kilometers per hour

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Answer: 3/1

Step-by-step explanation:3   ÷  1   =1÷3 =3

5       5   = 5÷5=1

therefore, 3 by five divided by 1 by five is equal to 3 by 1 ,

If the given equation is y-25=-0.92(x-4). The equation in the slope-intercept form is y=-0.92x+28.68.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

The given equation is,y-25=-0.92(x-4)

The slope-intercept form of the equation is,

y=mx+c

m is the slope and c is the intercept.

Thus if the given equation is y-25=-0.92(x-4). The equation in the slope-intercept form is y=-0.92x+28.68.

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The linear equation shown in the graph is the one in the third option.

y + 2 = -3*(x - 1)

Here we have a graph, and there we can see a linear equation, on that graph, we can see that:

The y-intercept is y = 1.

For each horizontal unit, the line goes 3 units down, then the slope is -3.

Then the linear equation is:

y = -3*x + 1

If now we add 2 in both sides, we get:

y + 2 = -3x +1 + 2

y + 2 = -3x + 3

y + 2 = -3*(x - 1)

So the correct option is the third one.

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Answer: y=3x

Step-by-step explanation:

The equation can be found by finding the slope of the given line. Visually, this can be found by counting the distance between two points. From (1,3) and (2,6), the line "rises" 3 units and "runs" 1 unit to the right. Since slope is calculated as rise over run, this gives us 3/1, or just 3 for slope. In slope-intercept form, this becomes y=3x.

Just to note, we know it is not negative because of the direction of the slope. Visually, if the slope "moves" in the direction of upwards and to the left, it will be positive. This can be calculated more accurately using the slope formula (y2-y1/x2-x1)

Yes, it is possible for a number to be a product of 2, 5, and 10.

All multiples of 10 such as 10, 20, 30, 40, 50, 60, ,,,, are a product of 2, 5, and 10.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

A number that is a product of 2, 5, and 10.

Example:

10 = 2 x 5

10 = 5 x 2

10 = 10 x 1

20

20 = 2 x 10

20 = 5 x 4

20 = 10 x 2

100

100 = 2 x 50

100 = 5 x 20

100 = 10 x 10

We see that all multiples of 10 are a product of 2, 5, and 10.

Thus,

All multiples of 10 are a product of 2,5, and 10.

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Answer:

11

Step-by-step explanation:

11:1 = [tex]\frac{11}{1}[/tex] = 11

Answer: 11, 22:2, 33:3, etc.

Step-by-step explanation:

A ratio is dividing.

11/1 = 11.

This means that numerous ratios can be used, to the point where the answers are infinite.