Is my answer correct?

Answer:

Step-by-step explanation:

[tex]i=\sqrt{-1} \ \ \ \ \ \ \ \ i^2=(\sqrt{-1})^2=-1[/tex]

a) ±2, 3

[tex](x-2)(x-(-2))(x-3)=\\\\(x-2)(x+2)(x-3)=\\\\(x^2-4)(x-3)=\\\\x^3-4x-3x^2+12=\\\\x^3-3x^2-4x+12[/tex]

b) -2, ±i

[tex](x-(-2))(x-i)(x-(-i))=\\\\(x+2)(x-i)(x+i)=\\\\(x+2)(x^2-i^2)=\\\\(x+2)(x^2-(-1))=\\\\(x+2)(x^2+1)=\\\\[/tex]

[tex]x^3+x+2x^2+2=\\\\x^3+2x^2+x+2[/tex]

c) 3, -1 ±i

[tex](x-3)(x-(-1-i))(x-(-1+i)=\\\\(x-3)(x+1+i)(x+1-i)=\\\\(x-3)((x+1)+i)((x+1)-i)=\\\\(x-3)((x+1)^2-i^2)=\\\\(x-3)((x+1)^2-(-1))=\\\\(x-3)((x+1)^2+1)=\\\\(x-3)(x+1)^2+(x-3)(1)=\\\\(x-3)(x^2+2x+1)+(x-3)=\\\\x^3+2x^2+x-3x^2-6x-3+x-3=\\\\x^3-x^2-4x-6[/tex]

d) -1, -2±√2

[tex](x-(-1))(x-(-2-\sqrt{2}))(x-(-2+\sqrt{2}))=\\\\ (x+1)(x+2+\sqrt{2})(x+2-\sqrt{2})=\\\\(x+1)((x+2)+\sqrt{2})((x+2)-\sqrt{2})=\\\\ (x+1)((x+2)^2-(\sqrt{2})^2)=\\\\(x+1)((x+2)^2-2)=\\\\(x+1)(x+2)^2-2(x+1)=\\\\(x+1)(x^2+4x+4)-2x-2=\\\\x^3+4x^2+4x+x^2+4x+4-2x-2=\\\\x^3+5x^2+6x+2[/tex]

Answer: Yes, they can.

Step-by-step explanation: Since quarters weigh 0.2 oz. 1 dollar weighs 0.8 oz. 0.8x150=120oz. 120ozs is about 7.5 pounds, so yes.

Answer:

Perimeter = 2(Length + Width)

308m = 2(96m + x)

308m = 192m + 2x

308m - 192m = 2x + 192m - 192m

116m = 2x

x = 58m

therefore, the width is 58m

Step-by-step explanation:

Answer: Yes.

Step-by-step explanation:

1.7 divided by 1.700 is 1

The differences f(x) = (x-2)(x+3)(x-7) and g(x)=(x-2)(x+3)(x-7) is 0.

What is the polynomial equation?

A polynomial is a function in which the least power of the unknown is 2.

The root of a polynomial is the value of the unknown which makes the polynomial equal to zero.

We  have,

f(x) = (x-2)(x+3)(x-7)

g(x) = (x-2)(x+3)(x-7).

( f – g ) ( x ) = ?

( f – g ) ( x ) = f ( x ) – g ( x )

= (x - 2) (x + 3) (x - 7)  – (x - 2) (x + 3) (x - 7)

= 0

Hence, the differences f(x) = (x-2)(x+3)(x-7) and g(x)=(x-2)(x+3)(x-7) is 0.

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Answer:

Step-by-step explanation:

You want the equations of the graphed parallel lines with y-intercepts of 2 and -1, and a rise/run of 3/1.

The slope-intercept form equation with slope m and y-intercept b is ...

  y = mx +b

Each of these lines rises 3 units for each 1 unit to the right, so has a slope of ...

  m = rise/run = 3/1 = 3

The red line crosses the y-axis at y=2, so its equation is ...

  y = 3x +2

The blue line crosses the y-axis at y=-1, so its equation is ...

  y = 3x -1

The sales tax percentage of cookie jar is 1.6% .

           (sales tax / total cost of the item) x 100 = sales tax rate

To find the sales tax percentage:

Here given,

Total cost = $1.62

Gross price = $1.60

Tax amount = $1.62 - $1.60

                    = $0.02

By substracting the tax amount from total cost,

$1.62 - $0.02

= $1.6

The sales tax percentage = 1.6%.

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Answer:

1/2

Step-by-step explanation:

When you roll a 6-sided die, there are 6 possible outcomes:

1, 2, 3, 4, 5, 6

3 of the outcomes are even, and 3 of the outcomes are odd.

p(A) = p(even) = 3/6 = 1/2

p(Ac) = 1 - p(A) = 1 - 1/2 = 1/2

For the equation -3x - 20 to have an infinite solution, it should be equal to -3x + 20 = -3x + 20, so the blank will be + 20

Given the data in the question,

Let the equation be - 3x + 20 = - 3x blank

These situations could be turned into producing an infinite number of solutions only if the lines are coincident and have the same y-intercept.

The quantities being coincident demonstrates the equality of the expressions printed on the left and right sides.

The lines with the same slopes are equal lines.

If the lines are making equal patterns, they will be giving infinite answers as output. As we can see in the result the equations are containing infinite solutions.

So, the missing blank will be = +20 to make the equation have infinite solutions.

Therefore, the value of the blank will be +20 and the equation will be =

- 3x + 20 = - 3x + 20

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Answer:

l = S / (2*pi*r)

[tex]l = \frac{S}{2\pi r}[/tex]

Step-by-step explanation:

S = 2 pi * r * l

Then:

l = S / (2*pi*r)

l = length

pi = 3.1416

r = radius

S = surface

y = 7 x is the situation's linear equation in two variables and 7 is Slope of line.

To determine a line's inclination or steepness, use the slope formula. By calculating the ratio of the change in the y-axis to the change in the x-axis, it may be used to calculate the slope of any line. A line's slope is determined by how its "y" coordinate changes in relation to how its "x" coordinate changes.

The faucet leakage rate is shown here to be 7 gallons per hour.

Since y gallons could leak in x hours , we have

Leakage rate is expressed as gallons per hour divided by the number of hours.

Given that our leakage was y gallons, and

The duration of the leaking is x hours, as well.

7 gallons per hour is the leakage rate, so we have;

Amount of gallons leaked = Gallons leaking per hour × Number of hours

The situation is represented by the linear equation =

y = 7 × x.

By comparing this with y=mx+c, Slope of line is 7

y = 7 x is the situation's linear equation in two variables and 7 is Slope of line.

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Answer: see below

Step-by-step explanation:

The denominator of the equations cannot equal zero.

a. [tex]9+y^{2}[/tex] [tex]= 0[/tex]

[tex]y^{2} = -9[/tex]

[tex]\sqrt{y^{2} } = \sqrt{-9}[/tex]

[tex]y=-3i,3i[/tex]

The domain is all real numbers.

D:xE(−∞,∞)

b.3x(x+12)=0

3x=0, x+12=0

x=0,x=-12

D:xE(−∞.-12) U (-12,0) U (0,∞)

c.(a+1)(a-4)=0

a+1=0, a-4=0

a=1, a=4

D:xE(−∞.1) U (1,4) U (4,∞)

Answer: y=-(1/4)x+5

Step-by-step explanation:

(-4,6)   (4,4)

                    [tex]\boxed {\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} }[/tex]

x₁=-4    x₂=4    y₁=6    y₂=4

Hence,

[tex]\displaystyle\\\frac{x-(-4)}{4-(-4)}=\frac{y-6}{4-6} \\\\\frac{x+4}{4+4}=\frac{y-6}{-2} \\\\\frac{x+4}{8} =\frac{y-6}{-2} \\[/tex]

Multiply both parts of the equation by -2:

[tex]\displaystyle\\-\frac{x+4}{4} =y-6\\\\-\frac{1}{4}x -1=y-6\\\\-\frac{1}{4} x-1+6=y-6+6\\\\-\frac{1}{4} x+5=y\\\\Thus,\ y=-\frac{1}{4} x+5[/tex]

Answer: B

Step-by-step explanation:

Let's pick 2 points ( 0,80) ( 5, 70)

The rate of change or slope is rise/run

We see that the y decrease by 10 and x increases by 5, so the slope is

-10/5 = -2 ft/s

So the aswer is B

Answer:

x ≤ 25/7

Step-by-step explanation:

3.5x + 5.5 ≤ 18

3.5x ≤ 18 - 5.5

3.5x ≤ 12.5

x ≤ 12.5/3.5

x ≤ 25/7

Answer:

4

Step-by-step explanation:

.....

The 2 linear equation which passes through point (-5,3) are:

so option A and B is correct

in order to check the answer we will check for all options which satisfies the the given point (-5,3)

putting the values in equation 1

 3 = 5*-2+13 so 3 =3 and the given points satisfies the above equation.

 putting the vlaues in equation 2

 LHS = y= 3

 RHS = -(-5) -2 =5-2 = 3

 so LHS = RHS  this equation also satisfies

putting the vlaues in equation 3

 LHS = y= 3

 RHS = 3*-5 -5 = -20

 so LHS ≠ RHS  so, this equation not satisfies

 putting the vlaues in equation 4

 LHS = y= 3

 RHS = -0.5 *5 + 6 = 3.5

 so LHS ≠ RHS  so, this equation not satisfies

 putting the vlaues in equation 5

 LHS = y= 3

 RHS = -2*-5- 2=8

 so LHS ≠ RHS  so, this equation not satisfies

 so only equation i and ii is true for the given point

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Complete question :

On a coordinate plane, a point is at (negative 5, 3). to which linear equations is the coordinate a solution? select two options.

A. y = 2x + 13

B. y = –x – 2

C. y = 3x – 5

D. y = negative one-half * 6

E . y = –2x – 2

Answer: There are a total of 6 * 6 = 36 outcomes when two dice are thrown.

The outcomes that result in a product at most 6 are (1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (3, 1), (3, 2), (3, 3), (4, 1), and (5, 1).

There are a total of 15 outcomes that result in a product at most 6.

Therefore, the probability of getting a product at most 6 in a single throw of 2 dice is 15/36, which is approximately 0.417.

Step-by-step explanation:

Answer:

p(product of at most 6) = 13/36

Step-by-step explanation:

When throwing 2 dice, there are 36 possible outcomes.

Here are the 36 possible outcomes and their products.

1, 1: 1    <---- at most 6

1, 2: 2    <---- at most 6

1, 3: 3    <---- at most 6

1, 4: 4    <---- at most 6

1, 5: 5    <---- at most 6

1, 6: 6    <---- at most 6

2, 1: 2    <---- at most 6

2, 2: 4    <---- at most 6

2, 3: 6    <---- at most 6

2, 4: 8

2, 5: 10

2, 6: 12

3, 1: 3    <---- at most 6

3, 2: 6    <---- at most 6

3, 3: 9

3, 4: 12

3, 5: 15

3, 6: 18

4, 1: 4    <---- at most 6

4, 2: 8

4, 3: 12

4, 4: 16

4, 5: 20

4, 6: 24

5, 1: 5    <---- at most 6

5, 2: 10

5, 3: 15

5, 4: 20

5, 5: 25

5, 6: 30

6, 1: 6    <---- at most 6

6, 2: 12

6, 3: 18

6, 4: 24

6, 5: 30

6, 6: 36

There are 36 possible outcomes.

There are 13 outcomes of at most 6.

p(product of at most 6) = 13/36

The Power series representation of f(x) = [tex]x^8tan^-^1x^3[/tex] is [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]

The Maclaurin series expansion method can be used to get the power series of such functions if the function has a composite part, such as the multiplication or quotient form.

An infinite series in mathematics known as a "power series" can be compared to a polynomial with an infinite number of terms.

The Maclaurin series will be used in this instance to expand the function:

[tex]tan^-^1x[/tex] = [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^2^n^+^1}{2n+1}[/tex]

and for    [tex]tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{(x^3)^2^n^+^1}{2n+1}[/tex]

=>  [tex]tan^-^1x^3 = $$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}[/tex]  -------(i)

and f(x) = [tex]x^8tan^-^1x^3[/tex]

now we need to multiply [tex]x^8[/tex] in the above equation to get the power series expansion of f(x)

[tex]x^8tan^-^1x^3[/tex] = [tex]x^8[/tex] [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3}{2n+1}[/tex]

=> [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^3^+^8}{2n+1}[/tex]

=>  [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]

so the expansion of f(x) = [tex]x^8tan^-^1x^3[/tex] is [tex]$$ \Sigma_{n=0}^\infty $$ (-1)^n\frac{x^6^n^+^1^1}{2n+1}[/tex]

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Answer:

x=12

Step-by-step explanation:

5x-4 is vertically opposite and 124 + 5x-4 should add up to 180 because they are cointerior anglesthen you look for the value of x by 124+5x-4=180

124-4+5x-4=180

x=12

Answer:

The vertex form equation of a parabola is y = a(x - h)^2 + k, where (h, k) is the vertex and a is a constant that determines the shape of the parabola.

To write the vertex form equation of each parabola, we need to find the values of a, h, and k for each equation.

A. y = x^2 + 4 To find a, we can compare the coefficients of x^2 in the given equation and the vertex form equation. We see that a = 1 in this case.

To find h and k, we can complete the square for the x-term in the given equation. We add and subtract (b/2a)^2, where b is the coefficient of x and a is the coefficient of x^2.

y = x^2 + 4 y = x^2 + 4 + (0/2)^2 - (0/2)^2 y = x^2 + 4 + 0 - 0 y = (x + 0)^2 + 4 - 0 y = (x + 0)^2 + 4

We see that h = -0 and k = 4 in this case. The vertex form equation is y = (x + 0)^2 + 4, or y = x^2 + 4.

B. y = (x - 2)^2 + 4 This equation is already in vertex form, so we can directly read the values of a, h, and k. We see that a = 1, h = 2, and k = 4 in this case. The vertex form equation is y = (x - 2)^2 + 4.

C. y = (x + 4)^2 - 1 This equation is also already in vertex form, so we can directly read the values of a, h, and k. We see that a = 1, h = -4, and k = -1 in this case. The vertex form equation is y = (x + 4)^2 - 1.

D. y = (x + 4)^2 - 2 This equation is also already in vertex form, so we can directly read the values of a, h, and k. We see that a = 1, h = -4, and k = -2 in this case. The vertex form equation is y = (x + 4)^2 - 2.

The scaled versions of the given rectangle are A rectangle with a height of 18.75 units and a width of 12 units, A rectangle with a height of 50 units and a width of 32 units and A rectangle with a height of 1.25 units and a width of 0.8 unit

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Given that, A rectangle has a height-to-width ratio of 6.25:4.

4/6.25 = 0.64

The ratio of width to height should be 0.64 for the scaled versions of this rectangle.

A) A rectangle with a height of 18.75 units and a width of 12 units = 12/18.75 = 0.64

B) A rectangle with a height of 50 units and a width of 32 units = 32/50 = 0.64

C) A rectangle with a height of 1.25 units and a width of 0.8 unit = 0.8/1.25 = 0.64

Hence, The scaled versions of the given rectangle are A rectangle with a height of 18.75 units and a width of 12 units, A rectangle with a height of 50 units and a width of 32 units and A rectangle with a height of 1.25 units and a width of 0.8 unit

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Mariol pays $12 for a pound of cheese and a pound of sausage, and $42 for 4 pounds of cheese and 1 pound of sausage.

To solve this problem, we can apply simple algebra. Let's use the letter for the initial, C for a pound of cheese, and S for a pound of sausage.

3 C + 3 S = $36

If the sausage cost $2.00 per pound, so

3 C + 3 ($2) = $36

3 C + $6 = $36

To know the price for a pound of cheese, do as follow

3 C = $36 - $6

3 C = $30

1 C = $30 : 3 = $10

Thus, 1 pound of cheese and 1 pound of sausage would be $2 + $10 = $12

Moreover, if 4C + 1S = 4($10) + 1($2) = $40 + $2= $42

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Answer:

lol

Step-by-step explanation:

hahahaha

assume that the true mean is 25,000 . store this value in sample hits.No, this value does not match the theoretical value.

This code is calculating the number of "hits" in a list of "CIS" that match the specified true mean of 25,000. The loop iterates through each item in the list and if the value matches the true mean, the sample_hits counter is incremented by one. After the loop has finished iterating through the list, the sample_hits value should represent the number of times the true mean was found in the list. The result does not necessarily match the theoretical value because it is dependent on the contents of the list and whether or not the true mean is actually present.

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there are 15 different ways to form a committee of 6 people from the department if the number of men in the committee is less than the number of females in the committee by combination.

There are 15 different ways to form a committee of 6 people from the department if the number of men in the committee is less than the number of females in the committee. This is because the number of possible combinations of 6 people with varying numbers of men and women is equal to the number of combinations of 6 people with 1 more female than male, plus the number of combinations of 6 people with 1 more male than female (which is equal to the number of combinations of 6 people with 1 more female than male).

Mathematically, this can be expressed as:

Number of combinations = (number of 6-person combinations with 1 more female than male) + (number of 6-person combinations with 1 more male than female)

Number of combinations = (6C4 x 5C2) + (6C5 x 5C1)

Number of combinations = 15

Therefore, there are 15 different ways to form a committee of 6 people from the department if the number of men in the committee is less than the number of females in the committee.

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Answer:

Step-by-step explanation:

2x - 3(6x - 3) = 25

2x - 18x + 9 = 25

-16x + 9 = 25

-16x = 16

x = -1

y = 6(-1) - 3 = -6 - 3 = -9

(-1, -9)

Expenses are $12.50 less than the budget of 100$ given to Jackie Pope.

Tabulate the expenses of all the things. Calculate the sum of all expenses to get Expenses.

Now for the given question:

Given:

Expenses of travelling of Jackie pope are

It costed $30.00 for Gas/Oil for car;

It costed $5.00 for Parking of car.

It costed $7.00 for Tolls on road.

It costed $45.50 for commuting.

Now total expenses is sum of all the above four expenses:

Expenses=30+5+7+45.5=$87.50.

Now budget=$100.

So, Remaining amount= Budget-Expenses;

Remaining amount= 100-87.5=$12.50;

Remaining amount from the budget is $12.50

Expenses are $12.50 less than the budget of 100$ given to Jackie Pope.

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Answer:

8 students

Step-by-step explanation:

Let's say there are x students in the theater club. We can set up the following equations to represent the information given in the problem:

We are told that there are 70 students in the theater club, so we can substitute 70 for x in the equations above to find the number of students in each show:

Therefore, there will be 8 students in the first show.

When it comes to researching bats in captivity, we expect the sample size to be small for a few reasons.

Firstly, there may be a limited amount of time that bat keepers are able to devote to this activity due to other obligations. Secondly, we would not want to unnecessarily stress the animals by collecting too many samples. Lastly, there is a limited number of bats in captivity, so the sample size will be small.

On the other hand, there are many bats in the wild, which means that the sample size does not have to be small. Researchers can take advantage of this by collecting data from a larger sample size. However, researchers must be mindful of the impact that their research may have on the environment, and the stress that it may cause the animals.

In conclusion, the sample size for studying bats in captivity is likely to be small due to the limited amount of time that bat keepers can devote to this activity, the need to avoid unnecessarily stressing the animals, and the limited number of bats in captivity. On the other hand, a larger sample size is possible when studying bats in the wild, but researchers must be mindful of the impact of their research on the environment and the animals.

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