3. What are the roots of the polynomial y = x³ - 8?

Answer:

Option 2 and 5 are correct. Look down for my explanation↓:

Step-by-step explanation:

So We need to tell which one of them is quadratic function.

Option 1 is exponential decay so, it is not quadratic.

Option 2 is quadratic because the diver will take the parabolic shape when jumps.

Option 3 is not quadratic. Option 4 is not quadratic it is linear.

Option 4 is again exponential not quadratic.

Option 5 is quadratic because it takes the parabolic shape again.

The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2

An equation is an expression that shows the relationship between two or more numbers and variables.

Given the equation:

f(x) = x(x + 5)(x - 2)

x(x + 5)(x - 2) = 0

x = 0, x + 5 = 0, x - 2 = 0

x = 0, -5 and 2

The graph of the function f(x) = x(x + 5)(x - 2) have x intercepts at x = 0, -5 and 2

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Answer:

The answer is either 30 degrees or 36 degrees.
You need a protractor to measure it.
Most probably, the answer is 30 degrees.
BUT PLEASE MEASURE THE ANGLE WITH A PROTRACTOR!

Answer:

d. 60°

Step-by-step explanation:

Since the clock is a full circle, it has a degree span of 360°.

∴ every 5-min interval on the clock

= 360° ÷ 12 five min intervals

= 30°

∴ acute angle formed by clock in figure

= two 5-min intervals

= 60°

The changes in account balances for Elder Company for 2021 are net income will be $160000

We have given debt common stock = $680000

Credit liabilities = 350000

Credit paid in capital = 190000

And an excess of par 30,000 credit Assuming the only changes in retained earnings

So 680000 = 350000+190000+30000+ retained earning

Net income is an entity's income minus the cost of goods sold, expenses, depreciation and amortization, interest, and taxes for an accounting period.

So retained earning = $110000

Dividend paid = $50000

So Net income = dividend paid + retained earning

Net income = $110000+$50000

Net income = $160000

So option (c) will be the correct answer.

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[tex]{\large{\textsf{\textbf{\underline{\underline{Given :}}}}}}[/tex]

★ Curved surface area of right circular cylinder is 4.4 m².

★ Radius of base of the cylinder is 0.7 m.

★ [tex]\tt \pi = \dfrac{22}{7}[/tex]

[tex]{\large{\textsf{\textbf{\underline{\underline{To \: Find :}}}}}}[/tex]

★ The height of cylinder.

[tex] {\large{\textsf{\textbf{\underline{\underline{Using \: Formula :}}}}}}[/tex]

[tex] \star \: \tt C.S.A \: of \: cylinder = \boxed{ \tt \pink{{ 2πrh}}}[/tex]

[tex] {\large{\textsf{\textbf{\underline{\underline{Solution :}}}}}}[/tex]

Let,

❍ The height of circular cylinder be [tex]h[/tex]

❍ Radius [r] of base of cylinder be 0.7 m

We know,

[tex] \star \: \tt C.S.A \: of \: cylinder = 2πrh[/tex]

Putting,

☆ [tex]\tt \pi = \dfrac{22}{7}[/tex]

☆ r as 0.7

[tex] \longrightarrow \tt 4.4 {m}^{2} = 2πrh[/tex]

[tex] \longrightarrow \tt 4.4 {m}^{2} = \bigg( 2 \times \dfrac{22}{7} \times 0.07 \times h \bigg)m[/tex]

[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( {2 }\times \dfrac{22}{ \cancel{7}} \times \dfrac{ \cancel{7}}{10} \times h \bigg)m[/tex]

[tex] \longrightarrow \tt \dfrac{44}{10} {m}^{2} = \bigg( 44 \times \dfrac{ {1}}{10} \times h \bigg)m[/tex]

[tex] \longrightarrow \tt \dfrac{44}{ \cancel{10}} \times \cancel{10} \: m = \bigg( 44 \times 1 \times h \bigg)[/tex]

[tex] \longrightarrow \tt 44 m = 44h[/tex]

[tex]\longrightarrow \tt \dfrac{44}{44} m = h[/tex]

[tex]\longrightarrow \tt \red{ 1 m } = h[/tex]

Therefore, the height of cylinder = 1 m.

[tex]\begin{gathered} {\underline{\rule{290pt}{2pt}}} \end{gathered}[/tex]

The values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1

The function is given as:

[tex]g(x) = \left[\begin{array}{cc}-2&-2.5 < x \le -1.5\\-1&-1.5 < x \le -0.5\\0&-0.5 < x < 0.5&1&0.5 \le x < 1.5\end{array}\right[/tex]

To calculate g(-0.5), we make use of the domain -1.5 < x ≤ -0.5

At this domain;

g(x) = -1

So, the value of g(-0.5) is

g(-0.5) = -1

To calculate g(0.3), we make use of the domain -0.5 < x  0.5

At this domain;

g(x) = 0

So, the value of g(0.3) is

g(0.3) = 0

To calculate g(0.5), we make use of the domain 0.5 ≤ x  1.5

At this domain;

g(x) = 1

So, the value of g(0.5) is

g(0.5) = 1

Hence, the values of the functions are g(-0.5) = -1, g(0.3) = 0 and g(0.5) = 1

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I assume you meant [tex]f(x)=0.5(4)^{x}[/tex]. The graph is shown below.

Answer:

12

Step-by-step explanation:

2k+4= 2*4 +4=8+4=12

hope it will help

Answer:

12

Step-by-step explanation:

Given:

[tex]\displaystyle \sum^n_{k=1}2k+4[/tex]

The 4th term in the sequence is when k = 4.  

Therefore, substitute  k = 4  into  2k + 4:

⇒ 2k+ 4 = 2(4) + 4

              = 8 + 4

              = 12

Therefore, the 4th term in the sequence is 12

Answer:

$11.72

Step-by-step explanation:

Add: $42.29 + $87.99 = $130.28

Subtract: $142 - $130.28 = $11.72

Answer:

he would have spent 131.08 dollars meaning he has 11.72 dollars left.

Step-by-step explanation:

Assuming average cost of $55.5, the cost of goods sold by Olympic Enterprises for the June 14 sale is equal to $444.

In Financial accounting, the cost of goods sold for a business firm can be calculated by multiplying the total quantity of goods by an average cost. Mathematically, this is given by:

Cost of goods = quantity × average cost

Note: We would assume an average cost of $55.5.

Substituting the parameters into the formula, we have:

Cost of goods sold = 8 × 55.5

Cost of goods sold  = $444.

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Answer:

x=−2 and y=−1

Step-by-step explanation:

Problem:

Solve y=x2;y=−x−3

Steps:

I will solve your system by substitution.

y=1/2x;y=−x−3

Step: Solve y= 1/2x for y:

Step: Substitute 1/2 x for y in y=−x−3:

y=−x−3

1/2x= =−x−3

1/2x+x=−x−3+x(Add x to both sides)

3/2x = -3

3/2x/3/2 = -3/3/2 (Divide both sides by 3/2)

x=−2

Step: Substitute −2 for x in y=1/2x:

y=1/2x

y=1/2(-2)

y=−1(Simplify both sides of the equation)

Answer:

x=−2 and y=−1

Answer:

[tex]\displaystyle - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}[/tex]

Step-by-step explanation:

Fundamental Theorem of Calculus

[tex]\displaystyle \int \text{f}(x)\:\text{d}x=\text{F}(x)+\text{C} \iff \text{f}(x)=\dfrac{\text{d}}{\text{d}x}(\text{F}(x))[/tex]

If differentiating takes you from one function to another, then integrating the second function will take you back to the first with a constant of integration.

Given integral:

[tex]\displaystyle -\int \dfrac{\sin(2x)}{e^{2x}}\:\text{d}x[/tex]

[tex]\textsf{Rewrite }\dfrac{1}{e^{2x}} \textsf{ as }e^{-2x} \textsf{ and bring the negative inside the integral}:[/tex]

[tex]\implies \displaystyle \int -e^{-2x}\sin(2x)\:\text{d}x[/tex]

Use integration by parts.

[tex]\boxed{\begin{minipage}{5 cm}\underline{Integration by parts} \\\\$\displaystyle \int u \dfrac{\text{d}v}{\text{d}x}\:\text{d}x=uv-\int v\: \dfrac{\text{d}u}{\text{d}x}\:\text{d}x$ \\ \end{minipage}}[/tex]

[tex]\textsf{Let }\:u=\sin (2x) \implies \dfrac{\text{d}u}{\text{d}x}=2 \cos (2x)[/tex]

[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]

Substituting the defined parts into the formula:

[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\sin (2x)- \int \dfrac{1}{2}e^{-2x} \cdot 2 \cos (2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\sin (2x)- \int e^{-2x} \cos (2x)\:\text{d}x\end{aligned}[/tex]

[tex]\displaystyle \textsf{For }\:-\int e^{-2x} \cos (2x)\:\text{d}x \quad \textsf{integrate by parts}:[/tex]

[tex]\textsf{Let }\:u=\cos(2x) \implies \dfrac{\text{d}u}{\text{d}x}=-2 \sin(2x)[/tex]

[tex]\textsf{Let }\:\dfrac{\text{d}v}{\text{d}x}=-e^{-2x} \implies v=\dfrac{1}{2}e^{-2x}[/tex]

[tex]\begin{aligned}\implies \displaystyle -\int e^{-2x}\cos(2x)\:\text{d}x & =\dfrac{1}{2}e^{-2x}\cos(2x)- \int \dfrac{1}{2}e^{-2x} \cdot -2 \sin(2x)\:\text{d}x\\\\& =\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x\end{aligned}[/tex]

Therefore:

[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+ \int e^{-2x} \sin(2x)\:\text{d}x[/tex]

[tex]\textsf{Subtract }\: \displaystyle \int e^{-2x}\sin(2x)\:\text{d}x \quad \textsf{from both sides and add the constant C}:[/tex]

[tex]\implies \displaystyle -2\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{2}e^{-2x}\sin (2x) +\dfrac{1}{2}e^{-2x}\cos(2x)+\text{C}[/tex]

Divide both sides by 2:

[tex]\implies \displaystyle -\int e^{-2x}\sin(2x)\:\text{d}x =\dfrac{1}{4}e^{-2x}\sin (2x) +\dfrac{1}{4}e^{-2x}\cos(2x)+\text{C}[/tex]

Rewrite in the same format as the given integral:

[tex]\displaystyle \implies - \int \dfrac{\sin(2x)}{e^{2x}}\: \text{d}x=\dfrac{\sin(2x)}{4e^{2x}}+\dfrac{\cos(2x)}{4e^{2x}}+\text{C}[/tex]

Differentiation Rules used:

[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\sin(k)$}\\\\If $y=\sin(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=k\cos(kx)$\\\end{minipage}}[/tex]

[tex]\boxed{\begin{minipage}{5.7 cm}\underline{Differentiating $\cos(k)$}\\\\If $y=\cos(kx)$, then $\dfrac{\text{d}y}{\text{d}x}=-k\sin(kx)$\\\end{minipage}}[/tex]

Integration Rules used:

[tex]\boxed{\begin{minipage}{4 cm}\underline{Integrating $e^{kx}$}\\\\$\displaystyle \int e^{kx}\:\text{d}x=\dfrac{1}{k}e^{kx}+\text{C}$\end{minipage}}[/tex]

Answer:

7/6=2/7/6

7/6=2

7/6=27/6

7/6=2

7/6

The domain of the function is whole numbers from 0 to 10.

Given the graph of function represents the tickets sold vs cost. A movie theater sells up to 10 tickets at a time online. we have to find the domain of the graph.

As shown in the graph the number of tickets sold is 0 to 10 and also the number of tickets are always positive and a whole number. It can never be negative or in fraction form.

Hence, the value of x is a positive whole number. The domain of the function is the complete set of possible values of x. The domain of the function is whole numbers from 0 to 10.

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Answer:

Step-by-step explanation:

Answer:

Answer:

A,B,D

Step-by-step explanation:

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients. The correct option is B.

Polynomials are mathematical expressions involving variables raised with non-negative integers and coefficients(constants who are in multiplication with those variables) and constants with only operations of addition, subtraction, multiplication, and non-negative exponentiation of variables involved.

Example:

 x² + 3x + 5

In order to find the values at which the given polynomial will have zeros of the function, we need to find the values at which f(x) changes from positive to negative or vice versa. Since this is the range at which the function must have crossed the x-axis on the graph.

As per the given table, the value of f(x) is changing from negative to positive and positive to negative are between 2.5 and 3.0 and between 4.0 and 4.5.

Hence, the correct option is B.

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The solution set for the given inequality is 3<x<5.

The given inequality is 6<x+3<8.

In mathematics, a solution set is the set of values that satisfy a given set of equations or inequalities.

Now, solve the given inequality:

6<x+3<8⇒6<x+3 and x+3<8

6-3<x ⇒3<x

x+3<8⇒x<5

Thus, 3<x<5.

Therefore, the solution set is 3<x<5.

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Inequality and graph the solution set and a number line, express the Solution set in interval notation is 3 < x < 5

6<x+3<8

[tex]6 < x+3\quad \mathrm{and}\quad \:x+3 < 8[/tex]

[tex]\mathrm{If}\:a < u < b\:\mathrm{then}\:a < u\quad \mathrm{and}\quad \:u < b[/tex]

[tex]\mathrm{Combine\:the\:intervals}[/tex]

[tex]x > 3\quad \mathrm{and}\quad \:x < 5[/tex]

[tex]3 < x < 5[/tex]

Therefore the Inequality and graph of the solution set and a number line, express the Solution set in interval notation as 3 < x < 5.

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We can subtract the function that represents the cost in 2000 from the function that represents the cost in 1990.

Doing this gives us [tex](-20t^{2}+1000)-(-10t^{2}+1500)=\boxed{-10t^{2}-500}[/tex]

Answer:

angle 2 = 7x + 1 ( vertically opposite angles)

7x + 1 + 18x + 4 = 180° ( forming linear pair).

7x + 18x + 4 +1 = 180°

25x + 5 = 180°

25x = 180 - 5

25x = 175

x = 7°

angle 2 = 7(7)+ 1

= 50°

The measure of angle ∠2 of the parallel lines is ∠2 = 50°

Angles in parallel lines are angles that are created when two parallel lines are intersected by another line. The intersecting line is known as transversal line.

We can conclude three factors determining parallel lines ,

Alternate angles are equal

Corresponding angles are equal

Co-interior angles add up to 180°

Given data ,

Let the parallel lines be b and c

Now , the measure of ∠1 + ∠2 = 180° ( angles on the same line )

And , the measure of ∠2 = ( 7x + 1 )° ( alternate angles are equal )

So , ( 7x + 1 ) + ( 18x + 4 ) = 180° ( angles on the same line )

On simplifying , we get

25x + 5 = 180

25x = 175

x = 7

So , the measure of angle ∠2 = ( 7 ( 7 ) + 1 )

The measure of angle ∠2 = 50°

Hence , the angle is ∠2 = 50°

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Answer:

1282kg

Step-by-step explanation:

1.0*1.12*1.1=1.232 tonnes

50kg + 1232kg = 1282kg

Hope this helps :)

The probability that all three components fail is 1.756 × 10⁻⁷. The probability of at least one of the components does not​ fail 0.9999998244.

Probability is the likelihood for an event to occur. In a given statistical distribution, the probability explains the range of values and probabilities that a randomized variable could have.

From the given information;

Assuming each​ component's failure/success is independent of the​ others: the probability that all three components fail is:

P(three components fail) = (0.0056)^3

P(three components fail) = 1.756 × 10⁻⁷

The probability that at least one does not fail is:

P(at least one does not fail) = 1 - P(all three components fail)

P(at least one does not fail) = 1 - 1.756 × 10⁻⁷

P(at least one does not fail) = 0.9999998244

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In the expressions that we are given, we can note that there is a negative in all of them. This means that we can factor out the negative.

With the negative factored out, it will look like this: [tex]-(\frac{8}{11} + \frac{3}{4} + \frac{1}{4} )[/tex]
The reasoning for this is because you distribute the negative to each term. For example 8/11 is a term, and so is 3/4, and 1/4. So our first answer is D.

Another way we can do this is by combining like terms. We see that in the denominator for -3/4 and -1/4 they both share 4. We can combine it so it becomes -4/4 or -1. It would be E.

The third way we can do this is by rewriting it. Answer A rewrites it so that it is + -, effectively just -. This allows us to treat the equation as if it were the original one.

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The  property that justifies the statement is the commutative law of addition

This law occurs if the same number or constant is added to both sides of an equation.

Given the equation

AB - BC = 12

Add BC to both sides

AB - BC + BC = 12 + Bc

AB = 12 + BC

Hence the  property that justifies the statement is the commutative law of addition

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The function  (f-g) (x) is represented as 5^2x - 3 - x .

The function is a type of relation, or rule, that maps one input to specific single output.

Given;

f(x)=5^2x-2

g(x)=x+1

Then, the function

(f-g) (x) = 5^2x-2  - (x+1)

Distribute the negative;

(f-g) (x) = 5^2x-2  - x - 1

(f-g) (x) = 5^2x - 3  - x

Hence, the function  (f-g) (x) is represented as 5^2x - 3 - x .

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