Which graph best represents the function f(x) = (x - 1)(x + 3)(x-3)?

Answer:

The answer is 52.2

Step-by-step explanation:

Answer:

y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1

Step-by-step explanation:

y" + y' + y = 1

This is a second order nonhomogenous differential equation with constant coefficients.

First, find the roots of the complementary solution.

y" + y' + y = 0

r² + r + 1 = 0

r = [ -1 ± √(1² − 4(1)(1)) ] / 2(1)

r = [ -1 ± √(1 − 4) ] / 2

r = -1/2 ± i√3/2

These roots are complex, so the complementary solution is:

y = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t)

Next, assume the particular solution has the form of the right hand side of the differential equation.  In this case, a constant.

y = c

Plug this into the differential equation and use undetermined coefficients to solve:

y" + y' + y = 1

0 + 0 + c = 1

c = 1

So the total solution is:

y(t) = c₁ e^(-1/2 t) cos(√3/2 t) + c₂ e^(-1/2 t) sin(√3/2 t) + 1

To solve for c₁ and c₂, you need to be given initial conditions.

Answer:

[tex]\large\boxed{k=\dfrac{2m+3}{7-r}\ \text{for}\ r\neq7}[/tex]

Step-by-step explanation:

[tex]7k+2m=kr+4m+3\qquad\text{subtract}\ 2m\ \text{from both sides}\\\\7k+2m-2m=kr+4m-2m+3\\\\7k=kr+2m+3\qquad\text{subtract}\ kr\ \text{from both sides}\\\\7k-kr=kr-kr+2m+3\\\\7k-kr=2m+3\qquad\text{distribute}\\\\k(7-r)=2m+3\qquad\text{divide both sides by}\ (7-r)\neq0\\\\k=\dfrac{2m+3}{7-r}[/tex]

The scale is likely to show the mass is either 270.9g or 245.1g

Step-by-step explanation:

Actual mass = 258g

Percent error = 5% = ±0.05

Mass shown by scale = Actual mass*percent error

[tex]Mass\ shown\ by\ scale=258*(\±0.05)\\Mass\ shown\ by\ scale=\±12.9g[/tex]

Therefore,

Mass shown by scale = 258+12.9 , Mass shown by scale = 258-12.9

Mass shown by scale = 270.9g , Mass shown by scale = 245.1g

The scale is likely to show the mass is either 270.9g or 245.1g

Keywords: error, percentage

Learn more about percentages at:

#LearnwithBrainly

Answer:

A scale has a percent error of 5%. The actual mass of a rock is 258 g.

Select from the drop-down menus to correctly complete the statement.

The scale is likely to show the mass is either

245.1

g or

270.9

g.

Step-by-step explanation:

I copied an pasted from k-12

Answer:

C)  8, 15, 16 is NOT Pythagorean TRIPLET.

Step-by-step explanation:

There numbers  a, b and c are said to be a PYTHAGORAS TRIPLET if

[tex](a) ^2 + (b)^2 = (c) ^2[/tex]

Now, here in the given options:

A)5, 12, 13

[tex](5)^2 +   (12)^2 = 25 +  144 = 169 = (13)^2\\\implies (5) ^2 + (12)^2 = (13) ^2[/tex]

Hence, 5, 12, 13 is a Pythagorean TRIPLET.

B)7, 24, 25

[tex](7)^2 +   (24)^2 = 49 +  576=  625 = (25)^2\\\implies (7) ^2 + (24)^2 = (25) ^2[/tex]

Hence, 7, 24, 25 is a Pythagorean TRIPLET.

C)8, 15, 16

[tex](8)^2 +   (15)^2 = 64 +  225=  289 \neq (16)^2 = 256\\\implies (8) ^2 + (15)^2 \neq (16) ^2[/tex]

Hence, 8, 15, 16 is NOT Pythagorean TRIPLET.

D)11, 60, 61

[tex](11)^2 +   (60)^2 = 121 +  3600 =  3721 =  (61)^2\\\implies (11) ^2 + (60)^2 = (61) ^2[/tex]

Hence, 11, 60, 61 is a Pythagorean TRIPLET.

E)12, 35, 37

[tex](12)^2 +   (35)^2 = 144 +  1225 =  3721 =  (37)^2\\\implies (12) ^2 + (35)^2 = (37) ^2[/tex]

Hence, 12,35 , 37 is a Pythagorean TRIPLET.

Answer:It cost 2100 dollars

Step-by-step explanation:I did the math on calculator very very simple buddy

Answer:

We can conclude that Δ GHI ≅ Δ JKL by SAS postulate.

Step-by-step explanation:

Δ GHI and Δ JKL are congruents because:

1. Their sides GH and JK are equal (9 units = 9 units)

2. Their included angles ∠G and ∠J are equal (62° = 62°)

3. Their sides GI and JL are equal (17 units = 17 units)

Now, we can conclude that Δ GHI ≅ Δ JKL by SAS postulate.

Answer:

60 calories per day

Step-by-step explanation:

example: 60 calories per serving so obviously the non example is the opposite

Answer:

(A) 40.67

(B) 57.98

Step-by-step explanation:

I did it in my head

Multiply the weight by 5%, then subtract that from the weight for the lower value and add it for the higher value:

258 x 0.05 = 12.9g

Lower value: 258 - 12.9 = 245.1g

Higher value: 258 + 12.9 = 270.9g

Answer:

2

Step-by-step explanation:

but I would personally say FISH

Answer: Like I really told you what I just had said, "The answer to this basic math question with the given basic math expression is [tex]1+1=2.[/tex]"

Step-by-step explanation: Seriously, like I really told you what I just had said, "This seems extremely too simple and easy for me and the users of The Brainly in order to answer to this basic math question with your own given the basic math expression, there is just only 1 of the basic step-by-step explanation for the basic math question with the given basic math expression for me and the users of The Brainly in order to solve it that looks in the equation form like this: [tex]1+1=2.[/tex]"

So, anyway, I hoped that my own given quoted with my own given quoted basic answer and my own given quoted basic step-by-step explanation is being very helpful to your own basic math question with the given basic math expression what I've been just said and have a great rest of the weekend! :D

Sincerely,

Jason Ta,

The Ambitious of Brainly And The Role of The TDSB And WHCI Student of The High School.

Answer:

$9 to each person

Step-by-step explanation:

63/7=9

Answer: 9

Step-by-step explanation:

$63 divided by 7 people = $9 debt per person

Answer:

B.76

Step-by-step explanation:

4 quarts = 1 gallon

so 4 * 19=76

Step-by-step explanation:

= (11+13+14+15+18+20+23+26)/8

= 140/8

= 17.5

Answer:

16.5

Step-by-step explanation:

The inequality for the given condition is x ≥ 42 inches

Solution:

Given that, the condition is you must be at least 42 inches tall to ride the bumper cars at an amusement park.  

We have to write an inequality that represents this situation.

Equations and inequalities are both mathematical sentences formed by relating two expressions to each other. In an equation, the two expressions are deemed equal which is shown by the symbol =

Where as in an inequality, the two expressions are not necessarily equal which is indicated by the symbols: >, <, ≤ or ≥

Let "x" represent the heights of people who are allowed to ride the bumper cars

Height of people who are allowed to ride the bumper cars should be at least 42 inches

Height of people ≥ 42 inches [ since at least condition holds even at 42 value also ]

x ≥ 42 inches

Hence, the inequality for the given condition is x ≥ 42 inches

Answer:

C.)

Step-by-step explanation:

Denominator is the bottom part of a fraction

We can use the points (12, 5) and (9, 8) to solve.

Slope formula: y2-y1/x2-x1

= 8-5/9-12

= 3/-3

= -1

______

Best Regards,

Wolfyy :)

Answer:

  --g(x) = g(x) = x - 6

Step-by-step explanation:

The opposite of the opposite is the original.

the answer is 0

Step-by-step explanation:

on edge

Answer:

[tex]\large \boxed{24; 12; 8}[/tex]

Step-by-step explanation:

1. Calculate the number of milkshakes

[tex]\text{Number of milkshakes}= \dfrac{\text{Total volume}}{\text{Volume of each milkshake}} = 3 \div \dfrac{1}{8}[/tex]

Invert the denominator and change division to multiplication

[tex]3\div\frac{1}{8} = 3\times \dfrac{8}{1}  = \mathbf{24}\\\\\text{LiAnn can make $\large \boxed{\mathbf{24}}$ milkshakes}[/tex]

2. Calculate the number of double milkshakes

[tex]\text{Number of double milkshakes}= \dfrac{\text{Total volume}}{\text{Volume of each double milkshake}} = 3 \div \dfrac{1}{4}[/tex]

Invert the denominator and change division to multiplication

[tex]3\div\dfrac{1}{4} = 3\times \dfrac{4}{1}  = \mathbf{12}\\\\\text{LiAnn can make $\large \boxed{\mathbf{12}}$ milkshakes}[/tex]

3. Calculate the number of triple milkshakes

[tex]\text{Number of triple milkshakes}= \dfrac{\text{Total volume}}{\text{Volume of each triple milkshake}} = 3 \div \dfrac{3}{8}[/tex]

Invert the denominator and change division to multiplication

[tex]3\div\dfrac{3}{8} = 3\times \dfrac{8}{3}[/tex]  

Cancel the 3s

[tex]3\times \dfrac{8}{3} = \mathbf{8}\\\\\text{LiAnn can make $\boxed{\mathbf{8}}$ triple milkshakes}[/tex]

John is 34, Grandmother is 86.

2014 - 1980 = 34.

2014 - 1928 = 86.

:)

Answer:

Two such numbers are  10  , 2 .

Step-by-step explanation:

Here, the question is INCOMPLETE.

Here is the Complete question:

One number is 1/5 of another number. The sum of the two numbers is 12. Find the two numbers. Use a comma to separate your answers.

We can solve the given problem as follows:

Here, : One number is   1/5  of another number.

Let one such number = m

⇒ The other number = 1/5 (m)

Sum of both the given number = 12

[tex]\implies  m + \frac{1}{5}  m = 12\\\implies \frac{5m + m}{5}  = 12\\\implies \frac{6m}{5}  = 12[/tex]

or, 6  m = 12 x (5) = 60

or, m = 60 / 6  =  10

or, m = 1 0

Hence, the first number = m = 10

Second number is [tex]\frac{1}{5} m =  \frac{1}{5} \times 10 = 2[/tex]

Hence, two such numbers are 10  , 2 .

Answer:

To calculate the slope of a line you need only two points from that line, (x1, y1) and (x2, y2). There are three steps in calculating the slope of a straight line when you are not given its equation.

Step-by-step explanation:

Step One: Identify two points on the line. Step Two: Select one to be (x1, y1) and the other to be (x2, y2).

Answer:

39.3

Step-by-step explanation:

100 / 6 is about 16, 16.66667 to be exact:

2.36 * 16.66667 =  approx. 39.3

Final answer:

To determine 6% of what number is 2.36, divide 2.36 by 0.06, resulting in an answer of approximately 39.33.

Explanation:

To find 6% of what number equals 2.36, we set up an equation where 6% (or 0.06) multiplied by a number 'x' equals 2.36. The equation looks like this: 0.06x = 2.36. To solve for 'x', you divide both sides of the equation by 0.06, which yields x = 2.36 ÷ 0.06. After calculating, you get that x equals 39.33. Therefore, 6% of 39.33 is 2.36.

Answer:

y = 4x² + 36x + 80

Step-by-step explanation:

Since the roots are x = - 5 and x = - 4 then the factors are

(x + 5) and (x + 4)

The equation is the product of the factors

y = (x + 5)(x + 4) and with leading coefficient of 4 is

y = 4(x + 5)(x + 4) ← expand factors

  = 4(x² + 9x + 20)

  = 4x² + 36x + 80

Answer:

30 oversized rackets and 50 standard rackets

Step-by-step explanation:

To maximize profit, it is very essential she strikes a balance between the two type of rackets. It is important to note that the profit on oversized racket is twice that of standard racket. Hence, she must make as many oversized rackets as possible.

The highest number of oversized racket she can make is 30. Subtracting 30 from the total number of rackets give 50 standard racket

To maximize profit, represent the constraints as a system of inequalities, graph these to find a feasible region, and evaluate the profit function at each vertex of this region.

To determine how many of each type of tennis racket a manufacturer should produce daily to maximize profit, we can set up a system of inequalities based on the given constraints and then use linear programming. The constraints are that the daily production of standard rackets (S) should be between 30 and 80, and production of oversized rackets (O) should be between 10 and 30. Additionally, the total number of rackets produced (S + O) should not exceed 80 per day.

The profit function to be maximized is P = 15O + 8S. The optimization process involves graphing the inequalities to form a feasible region, then evaluating the profit function at each vertex of this region to find the maximum profit point.

The constraints can be written as:

We look for the corner points of the feasible region that satisfies all the constraints and calculate the profit at each of these points. The highest profit among these calculated values will give us the optimal number of each type of racket to produce.

By systematically evaluating the profit P at the corner points of the feasible region, the manufacturer can identify the production levels of standard and oversized rackets that will maximize profit within the given constraints.

This approach ensures that the manufacturer can meet dealer demand, maintain high quality through production limits, and optimize profit based on the profit margins of each racket type.

Answer:

Step-by-step explanation:

2 green of every 5:

[tex]\dfrac{2}{5}[/tex]

Convert to the percent:

[tex]\dfrac{2}{5}\cdot100\%=\dfrac{200}{5}\%=40\%[/tex]

Answer:

The simplified form would be [tex]6x^5[/tex]

Step-by-step explanation:

Given:

[tex]\frac{(3x^4)(12x^2)}{6x}[/tex]

Now multiplying the numbers and variable we get,

[tex]\frac{(3x^4)(12x^2)}{6x}\\\\\frac{(36x^{2+4})}{6x}\\\\\frac{36x^6}{6x}[/tex]

Now Dividing 36 by 6 we get,

[tex]\frac{6x^6}{x}=6x^6\times x^{-1} = 6x^{6-1}= 6x^5[/tex]

Hence the simplified form would be [tex]6x^5[/tex]