18. If the graph of y = ax² + 5x + c has x- intercepts at 1 and 3, what is the value of a + c? ​

Answer:

mean is the average of all the values:

( 15.07 + 15.47 + 15.93 + 15.86 + 15.07 ) / 5 = 15.48g

median is the middle value AFTER it has been arranged in increasing order:

the increasing order is: 15.07, 15.07, 15.47, 15.86, 15.93

the middle value is 15.47g making it the median.

the mode is the most repeated value: 15.07g

Answer:

4

Step-by-step explanation:

.....

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.

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

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 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:

75287520

Step-by-step explanation:

Combination formula: [tex]\frac{n!}{r!(n-r)!}[/tex]

n = the amount of members of the US senate (100)

r = number of members chosen to be committee (5)

= [tex]\frac{100!}{5!(100-5)!}[/tex]

= [tex]\frac{100!}{5! * 95!}[/tex]

=   75287520

Answer:the answer is 17  

Step-by-step explanation:

The required simplified solution of the given expression is 17.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given expression,
= 4×5 -10 -2 (1 - 2) + 5
Following the PEMDAS rule,
= 20 - 10 - 2(-1) + 5
= 20 - 10 + 2 + 5
= 20 + 2 + 5 - 10
= 27 - 10
= 17

Thus, the required simplified solution of the given expression is 17.

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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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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: 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.

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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The value of x that will make the equation of the model true is: x = 5.8.

Create an equation using the model given, then isolate the variable in order to determine its value, which will make the equation true.

Given the model above, the following equation would be created below:

x + x + 9.4 = 21

Combine like terms

2x + 9.4 = 21

Subtract 9.4 from both sides

2x + 94 - 9.4 = 21 - 9.4 [subtraction property of equality]

2x = 11.6

Divide both sides by 2:

2x/2 = 11.6/2 [division property of equality]

x = 5.8

The value of x is: 5.8.

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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:

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

The system of inequalities that is represented by the graph is given as follows:

The system of linear inequalities is defined with linear functions, which have the slope-intercept format given as follows:

y = mx + b.

In which the parameters are given as follows:

For the upper bound of the inequality, we have that the linear function:

Then the upper bound of the inequality has the definition given by:

y ≤ -x + 1.

For the lower bound of the inequality, we have that the linear function:

Hence the lower bound of the inequality has the definition given by:

y ≥ -0.75x + 0.5.

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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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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:

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

Two angles are called complementary when their measures add up to 90 degrees. Two angles are called supplementary when their measures add up to 180 degrees.

Complementary angles add up to 90°- example: 15° & 75° are complimentary

For example:

Suppose if one angle is x then the other angle will be 90° – x.

Now, to find the complement of 2x + 52°, subtract the given angle from 90 degrees.

90o –  (2x + 52o) =  90o – 2x – 52o  = -2x + 38o

The complement of 2x + 52o is 38o – 2x.

Supplementary angles add up to 180°- example: 50° & 130° are supplementary

if the two angles form a linear angle, such that, if one angle is x, then the other angle is 180° – x

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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:

To avoid consecutive b's, the string of b's must be divided into one or more groups of 1, 2, or 3 b's. There are a total of 5 + 1 = 6 possible places to insert the dividers to create these groups. For example, suppose we have a string of 7 b's and we insert dividers between the 3rd and 4th b's, and between the 5th and 6th b's. This would create the following groups of b's: bb|bb|b. In general, the number of possible ways to divide the string of b's into groups of 1, 2, or 3 b's is equal to the number of ways to insert 6 dividers into a string of 7 b's. This is equal to the number of ways to choose 6 of the 8 possible places to insert the dividers, which is equal to $\binom{8}{6} = 28$.

Since the 5 a's and the 1 c must be arranged in a specific order, there is only 1 way to arrange these letters. Therefore, the total number of words consisting of 5 letter a's, 7 letter b's, and 1 letter c is equal to $1 \times 28 = 28$.

Answer:

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

According to the question there are 7 'b' s  and we can't have them together. We assume more than two consecutive 'b' s contain two consecutive 'b' s and hence not considering any option of having 3, 4, 6 or 7 'b' s.

There is only one way to place 'b' s apart which leaves us with 6 gaps.

There are 5 + 1 = 6 other letters which is just the number to fill in the gaps between 7 'b' s.

We have only an option for 'c' to have any of the 6 gaps, it gives us 6 options and no other options for 'a' s.

Therefore in total we have 6 possible ways.

Displacement from the origin will be 16.76 block

Pythagoras Theorem:

                                   Pythagoras theorem can be used to find the unknown side of a right-angled triangle.Theorem stats that,

                c² = a² + b²

                         where 'c' is the hypotenuse and 'a' and 'b' are the two legs.

In figure,

              O is origin,

             First travel 21 block north that means OA = 21 block.

             then,

                         travel 16 block East that means AB = 16 block.

             again finally,

                        travel 26 block South that means BC = 26 block.

Join OC,

            OC = 16 block

            CD = 5 block

we have to find the value of OD

Apply Pythagoras theorem,

                                                OD² = OC² + CD²

                                                OD = √(OC² + CD²)

                                                OD =√(16² + 5²)

                                                OD =√(256 + 25)

                                                 OD = √(256 + 25)

                                                 OD = √281 block

                                                 OD = 16.76 block

Thus,

              Displacement from the origin will be 16.76 block

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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.

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:

There are 14 members in the club, and there are 4 leadership positions. Each position can be filled by any of the 14 members, so there are 14 ways to fill the first position, 14 ways to fill the second position, and so on. However, we have overcounted because we have not taken into account that a member cannot serve in two positions simultaneously. To correct for this overcounting, we divide by the number of ways that a member can serve in two positions simultaneously, which is 1. Therefore, the total number of ways that the club leadership can be organized is:

14 * 14 * 14 * 14 / 1 = 14^4 = 20736 ways.

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

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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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 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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