Simplify this expression
Distribute first in the box below
2 (3x − 6) (2x + 1)

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,∞)

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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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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Tom’ mot recent book earned 10*4 time a much money a hi firt book. then The amount that Tom’s most recent book earn is 10^7.

How to illustrate the exponent?

The exponent is the number of times that a number is multiplied by itself. It should be noted that the power is an expression which shows the multiplication for the same number. For example, in 6⁴ , 4 is the exponent and 6⁴ is called 6 raise to the power of 4.

Since Tom’s most recent book earned 10*4 times as much money as his first book which was 10³.

The total amount of the recent book will be:

= 10⁴ × 10³

= 10^(4 + 3)

= 10^7

The amount is 10^7.

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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 details of the angles in the diagram used to prove the congruency of the triangles ΔABC ≅ ΔCDA  indicates;

Statements                                               [tex]{}[/tex]   Reasons

1.  ∠D ≅ ∠B                                             [tex]{}[/tex]  1. Given

∠ACB ≅ ∠CAD

2. Therefore; ∠ACD ≅ ∠CAB               [tex]{}[/tex]  2. Angle sum property of a triangle

3.  [tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]                             [tex]{}[/tex]               3. Reflexive property

4. ΔABC ≅ ΔCDA   [tex]{}[/tex]                                4. ASA congruency rule

Therefore, the completed flowchart is presented as follows;

∠D ≅ ∠B                   [tex]{}[/tex]              ∠ACB ≅ ∠CAB                [tex]{}[/tex][tex]\overline{AC}[/tex] ≅ [tex]\overline{AC}[/tex]

∠ACB ≅ ∠CAB                       Angle sum property        Reflexive prop

Reason; Given

            [tex]{}[/tex]                             ΔABC ≅ ΔCDA

                                        [tex]{}[/tex]

What are congruent triangles?

Triangles are congruent if the three sides on both triangles are congruent or if two angles and a non included side in one triangle are congruent to two angles and a non included side of the other triangle

The details of the reasons used to prove the ΔABC ≅ ΔCDA are as follows;

Angle sum property of a triangle

The angle sum property of a triangle indicates that the sum of the three interior angles of a triangle is 180°

Reflexive property

Reflexive property of congruency states that a geometric figure is congruent to itself.

ASA congruency rule

The Angle-Side-Angle, ASA, congruency rule states that the if two angles and a non included side of one triangle are congruent to two angles and a non included side of the other triangle, then both triangles are congruent

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0.688 will be the probability of getting a nickel from the jar.

Given,

Probability;-

Simply put, probability is the likelihood that something will occur. When we don't know how an event will turn out, we can discuss the likelihood or likelihood of several outcomes. Statistics is the study of events that follow a probability distribution.

Here,

The number of fortunate situations divided by the total number of coins would be the product between the probability of each occurrence and the likelihood of each event.

Therefore,

P(nickel) = 19/69

P(penny) = 17/68

That is,

P = 19/69 × 17/68

P = 323/4692

P = 0.0688

That is,

The probability of getting nickel from the jar is 0.06888

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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:

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

Parallel lines have equal slopes.

Given line has a slope of m = 1/5.

Use point-slope form and the coordinates of the point (5, - 4) find the parallel line:

Correct choice is D.

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: 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]

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

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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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: 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: Yes.

Step-by-step explanation:

1.7 divided by 1.700 is 1

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:

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:

lol

Step-by-step explanation:

hahahaha

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: 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:

No

Step-by-step explanation:

The cost of running six seminars is [tex]10000+1500+6(400+250)=\$15400[/tex].

The revenue earned is about [tex]1500(6)=\$9000[/tex].

Since the revenue is significantly less than the cost, there will not be a profit.

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

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

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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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:

The definite integral of the function f shown in the graph below, over the limits from 0 to 3.

In the given question, we have to find the definite integral of the function f shown in the graph below, over the limits from 0 to 3.

On the interval [a, b], the definite integral of a real-valued function f(x) with respect to a real variable x is written as

[tex]\int^{b}_{a}f(x)dx = f(b) - f(a)[/tex]

Any function's definite integral can be written as the upper limit of a sum or, if an anti-derivative F exists for the interval [a, b], as the difference between the values at the points a and b.

[tex]\int^{3}_{0}f(x)dx[/tex] = Area under the curve from 0 to 3

[tex]\int^{3}_{0}f(x)dx[/tex] = 1/2 ×3×12

[tex]\int^{3}_{0}f(x)dx[/tex] = 18

Hence, the definite integral of the function f shown in the graph below, over the limits from 0 to 3 is 18.

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Answer:

4

Step-by-step explanation:

.....