in your own words describe a “difference of squares.”

The slope of the line passing through the points (-12, 0) and (-12, 9) is

The given points that the line passes through are (-12, 0) and (-12, 9).

Since the x coordinates are same, the line will be parallel to the Y axis.

That is the line will be perpendicular to the X axis and thus slope is not defined.

If a line passes through two points (x, y) and (x', y'), then the slope of the line can be calculated as,

Slope = (y' - y) / (x' - x)

Here the line passes through the points (-12, 0) and (-12, 9).

We have to find the slope of the line.

Slope = (9 - 0) / (-12 - -12) = 9/0 = Not defined

Hence the slope is not defined.

Learn more about Slope here :

https://brainly.com/question/3605446

#SPJ1

Answer:

d is at -π (just to the left of -3 since -π<-3), e is at -√8 (just to the right of -3 since -√8>-3), and f is at -3/2 = -1.5 (halfway between -2 and -1).

This system has a unique solution, which can be found using standard methods of linear algebra

The missing data is:

x = -2,895

y = 37,315

z = 76,210

w = 15,895

2w = 31,790

Substituting w into the second and third equations, we get:

x = -2,895

y = 37,315

Finally, we can use the fourth equation to solve for z:

z + 2(15,895) = 108,000

z = 76,210

Therefore, the missing data is:

x = -2,895

y = 37,315

z = 76,210

w = 15,895

Learn more about equations on

https://brainly.com/question/2972832

#SPJ1

Julia scored at least 20 points. Inequality for the situation is: x ≥ 20, where x represent score of Julia.

Let the score of Julia be  "x". The inequality for this given situation would be:

x ≥ 20

According to this inequality, Julia's score, denoted by the letter "x," is greater than or equal to 20. Greater than or equal to is indicated by the sign "≥". The minimum score Julia must achieve is shown by the number 20 on the right side of the inequality. The "≥" sign makes sure Julia's score can be 20 or any number higher than 20, but it can never be less than 20.

The fact that Julia received at least 20 points is therefore indicates by the inequality : x ≥ 20

Know more about inequality,

https://brainly.com/question/25275758

#SPJ1

Answer:

Area of a sector= θ/360×π×r×r

=76/360×22/7×4×4

(Do your division and multiplication)

=10.615 units

To nearest hundredth=10.620units

Hence ,the percentage of students that take exactly one course is 71.43% and the value of N(P ∩ M) and  N(P ∩ E) is 36 and 30 respectively.

Principle of Inclusion and Exclusion is an approach which derives the method of finding the number of elements in the union of two finite sets. This is used for solving combinations and probability problems when it is necessary to find a counting method, which makes sure that an object is not counted twice.

In mathematics, a percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, although the abbreviations pct., pct, and sometimes pc are also used. A percentage is a dimensionless number; it has no unit of measurement.

Let  P, M, and E be the  sets of students  taking  Physics,  Mathematics,  and  English,  respectively.  Then:

|P| = 90, |M| = 72, |E| = 162

Let  X  be  the  set of students  taking all three  courses, Y be  the set of students taking  exactly  two courses,  and Z  be  the  set of  students  taking exactly one  course. Then:

|X| = ?, |Y| = ?, |Z| = ?

We know that , the  Principle of Inclusion and Exclusion (PIE) to  determine  the values  of |X|, |Y|, and |Z|. that means,

|P ∪ M ∪ E| = |P| + |M| + |E| - |P ∩ M| - |P ∩ E| - |M ∩ E| + |P ∩ M ∩ E|

We know that |P ∪ M ∪ E| = 252, so we can substitute the values we have to get:

252 = 90 + 72 + 162 - |P ∩ M| - |P ∩ E| - |M ∩ E| + |X|

To compute |P ∩ E| and |M ∩ E|,  according to given problem,

[tex]\frac{1}{3}[/tex] of  those  that take  physics take English, so |P ∩ E| =[tex]\frac{1}{3}[/tex] * |P| = 30

[tex]\frac{1}{4}[/tex] of  those  that take mathematics take English, so |M ∩ E| =[tex]\frac{1}{4}[/tex]* |M| = 18

[tex]\frac{1}{2}[/tex] of  those that take mathematics  take physics, so |P ∩ M| = [tex]\frac{1}{2}[/tex] * |M| = 36

Substituting these values, we get:

252 = 90 + 72 + 162 - 36 - 30 - 18 + |X|

|X| = 252-324+84=-72+84=12

So, there are 12  students who take all three courses.

now, To find  |Y|,  by using this formula:

|Y| = |(P ∩ M) ∪ (P ∩ E) ∪ (M ∩ E)|

We  already  know  in question |P ∩ E|  and  |M ∩ E|,  so we just need to find |P ∩ M ∩ E|.   from given problem

we know that:

|P ∩ M ∩ E| =[tex]\frac {(P ∩ E)}{P}[/tex]* |M| = ([tex]\frac{30}{90}[/tex]) * 72 = 24

Substituting these values, we get:

|Y| = |(P ∩ M) ∪ (P ∩ E) ∪ (M ∩ E)| = |P ∩ M| + |P ∩ E| + |M ∩ E| - |P ∩ M ∩ E| = 36 + 30 + 18 - 24 = 60

So, there  are  60 students  who take exactly two courses.

now, To  find |Z|, by using this  formula:

|Z| = |P| + |M| + |E| - |X| - |Y|

Substituting  the  values we have found, we get:

|Z| = 90 + 72 + 162 - 12 - 60 = 252 - 72 = 180

So, there   are 180 students  who take exactly one course.

Now ,To find the percentage of  students that  take exactly  one course, we can determine,

[tex]\frac{|Z|}{252}* 100%\\ =\frac{180}{252} * 100%\\=0.7143*100%\\=71.43%[/tex]%

Learn more about probability here:

https://brainly.com/question/13604758

#SPJ1.

Correct question is:

The school of engineering of a polytechnic required all student to take physics, mathematics or English in a graduating class of 252 students.90 students take physics,72 students take mathematics and 162 take English. 1/3 of those that take physics take English, 1/4 of those that take mathematics take English and 1/2 of those that take mathematics take physics. How many students take all courses, how many student take two more courses,what is the percentage of students that take exactly one course,what is the the value of N(P ∩ M) and N(P ∩ E).

The area of the shape they create is approximately 247 square feet.

We have,

Let's assume that Manuel is at point M, Khady is at point K, and Zoe is at point Z.

We can connect these points to form a triangle:

        Z

       / \

      /   \

  20 /     \ 30

    /       \

   /         \

  M-----------K

       15

T

o find the area of the triangle MKZ, we can use Heron's formula:

s = (a + b + c) / 2,

where a, b, and c are the lengths of the sides of the triangle

A = √(s(s - a)(s - b)(s - c)),

where A is the area of the triangle

In our case,

The sides of the triangle are:

a = 15 (MK)

b = 20 (MZ)

c = 30 (KZ)

We can use these values to calculate the area of the triangle:

s = (a + b + c) / 2 = (15 + 20 + 30) / 2 = 32.5

A = √(s(s - a)(s - b)(s - c)) = √(32.5(32.5 - 15)(32.5 - 20)(32.5 - 30)) =  247.2

Therefore,

The area of the shape they create is approximately 247 square feet.

Learn more about triangles here:

https://brainly.com/question/25950519

#SPJ1

The intercepts of the rational function m(x)=4(x-5)(x+8)/(x^2-2x-15) are given as follows:

The rational function in the context of this problem is defined as follows:

m(x)=4(x-5)(x+8)/(x^2-2x-15)

The denominator can be simplified as follows:

x² - 2x - 15 = (x - 5)(x + 3).

Simplifying the x - 5 terms, the function can be written as follows:

m(x) = 4(x + 8)/(x + 3).

The x-intercept is the value of x when y = 0, hence:

x + 8 = 0

x = -8.

The y-intercept is the value of y when x = 0, hence:

m(0) = 4 x 8/3

m(0) = 32/3.

More can be learned about the intercepts of a function at https://brainly.com/question/3951754

#SPJ1

The outcomes that make the complement of rolling a two are given as follows:

Hence the probability of the complement is given as follows:

p = 5/6.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The complement of an event are all the events out of the total outcomes that are not the event.

Supposing a dice with six sides, the complement of rolling a two is all outcomes which are not two.

And hence the probability of the complement is given as follows:

p = 5/6. (rolling a two is the only non-desired outcome).

More can be learned about probability at https://brainly.com/question/24756209

#SPJ1

Answer:

Step-by-step explanation:

12

Answer:

Penelope

Step-by-step explanation:

I don't think there is enough information - To find if two triangles are similar, you need 2+ common angles or at least some correlation between the lengths of the sides (not an exact definition). These rules cannot be applied to the 2 triangles.

Answer:

-2

Step-by-step explanation:

Plug in the values of 'x' and 'y':

[tex]\frac{2+-4}{3-2} =\frac{2-4}{1} =\frac{-2}{1} =-2[/tex]

Answer: So, the value of the expression 2+x/3-y when x=-4 and y=2 is -4/3.

Step-by-step explanation: To evaluate the expression 2+x/3-y for x=-4 and y=2, we can substitute the values of x and y into the expression. This gives us:

2 + (-4)/3 - 2

Solving this expression following the order of operations, we first solve the division:

2 + (-4/3) - 2

Then we solve the addition and subtraction from left to right:

= 2 - 4/3 - 2

= (6/3) - (4/3) - (6/3)

= -4/3

So, the value of the expression 2+x/3-y when x=-4 and y=2 is -4/3.

-15.2

I use the ai and calculated the answer.

Answer:  10,450

Step-by-step explanation:

If 5% of the 11,000 people who entered a drawing won a prize, that means that 95% of the people did not win a prize.

To find out how many people did not win a prize, we can calculate 95% of the total number of people who entered the drawing:

95% of 11,000 = 0.95 x 11,000 = 10,450

Therefore, 10,450 people did not win a prize.

Answer:

57

Step-by-step explanation:

We know that parentheses come first in the order of operations. Therefore, we will first evaluate (3 × 5).

3 × 5 = 15

↓ substituting this value back in for the parentheses

[tex]12+[15+2(15)][/tex]

Next, we will deal within the brackets, which act like parentheses. Multiplication comes before addition, so we will execute 2(15) first.

2(15) = 2 × 15 = 30

↓ substituting this value back in

[tex]12+[15+30][/tex]

Now, executing the addition:

15 + 30 = 45

↓ substituting this value back in for the brackets

[tex]12 + 45[/tex]

Finally, all there is to do is execute the addition.

12 + 45 = 57

[tex]\boxed{57}[/tex]

Your after - tax return on the investment is 0.61 %.

To find after-tax return on investment, we have to know the tax rate.  Assume you have a 30 % tax rate.

Total income from the salary and interest from an investment account is:

29,000 + 125 = 29,125

Your tax liability on this income is:

29,125 × 30 % = 29,125 × 30 / 100

= 29,125 × 3 / 10

= 8,737.5

So, after - tax income is:

29,125 - 8,737.5 = 20,387.5

After-tax return on the investment is:

125 / 20,387.5 = 0.0061 or 0.61 %

Therefore, your after-tax return on the investment is 0.61 %.

Learn more about Tax here

https://brainly.com/question/16423331

#SPJ1

The radius of the cone is 8 unit

The volume of the cone is 401.92 cubic unit.

Volume is the shape occupied by a solid shape.

To calculate the volume of the cone, we need to first find the radius of the base of the cone

(a) Radius (r) = √(l²-h²)................. Equation 1

Where:

Substitute these values into equation 1

Finally, to calculate the volume of the cone, we use the formula below

Given:

Substitute these values into equation 2

Learn more about volume here: https://brainly.com/question/1972490

#SPJ1

The solutions to the questions are provided below

The intersection is the point where the lines of the graph intersect

The solution to the system of two linear equations x = 3; y = 9 means that the lines intersect at (3, 9)

No, you cannot have more than one solutions

No, you cannot have exactly two solutions

Yes, you can have no solutions

Read more about system of equations at

https://brainly.com/question/13729904

#SPJ1

Answer:

14.4

Step-by-step explanation:

1) 16^2-7^2=207

2) square root of 207 is 14.4 (to 1 decimal place).

The main answer to the question "How many pounds of laundry detergent does Andrew make?" is 4.125 pounds.

he total amount of borax used to make 3 batches is:

8 ounces/batch x 3 batches = 24 ounces

The total amount of washing soda used to make 3 batches is:

10 ounces/batch x 3 batches = 30 ounces

The total amount of soap used to make 3 batches is:

6 ounces/batch x 3 batches = 18 ounces

To find the total weight of the laundry detergent, we need to add up the weight of each ingredient. Since 1 pound is equal to 16 ounces, we can convert the total weight from ounces to pounds by dividing by 16.

Total weight of laundry detergent = (24 + 30 + 18) ounces / 16 = 4.125 pounds

Therefore, Andrew makes 4.125 pounds of laundry detergent.

The area of a segment of a circle is (12π-9√3) square inches.

We have to determine the area of a segment of a circle.

The formula for the area of the sector that:

Arc length = πr² (θ/360)

Where r = the radius of the circle,

θ = the angle (in degrees) subtended by an arc at the center of the circle.

As per the shown figure, it is given that:

Central angle θ = 120°

The radius of a circle r = 6 in.

The area of the sector A₁ = π(6)² (120/360)

The area of the sector A₁  = 12π in²

The area of the triangle within the sector:

A₂ = 1/2 × (6√3)(3) = 9√3 in²

Now, the area of the segment is:

A₁ - A₂ = (12π - 9√3) in²

Therefore, the area of a segment of a circle is (12π-9√3) square inches.

Learn more about the arc of the circle here:

brainly.com/question/1577784

#SPJ1

Answer:

Step-by-step explanation: its a negative nonlinear interger.

Robin's graph of the function g(x) = -x² = -f(x)  is the reflection of Giselle’s graph over the x-axis. Robin’s graph is a reflection of Giselle’s graph over the x-axis.

What is  linear equation?

An algebraic equation with simply a constant and a first- order( direct) element, similar as y = mx b, where m is the pitch and b is the y- intercept, is known as a linear equation.

                         The below is sometimes appertained to as a" direct equation of two variables," where y and x are the variables. Equations whose variables have a power of one are called direct equations. One illustration with only one variable is where layoff b = 0, where a and b are real values and x is the variable.

To reflect a function across the x-axis, replace y with -y.

To reflect a function across the y-axis, replace every x with -x.

To translate a function vertically, add or subtract a number to the end of the function.

To translate a function horizontally, add or subtract a number before any exponents are applied.

The difference between Robin's and Giselle's functions are the negative in front of x².  This is the same as making y negative; this is a reflection across the x-axis.

Learn more about Linear equation

brainly.com/question/11897796

#SPJ1

The solution to the equation 3x² + x - 12 = 1 is x = -1/4; and x = 4

An equation is an expression that shows the relationship between numbers and variables using mathematical operators.

The polynomial is classified based on degree as linear, quadratic, cubic and so on.

Given the equation:

3x² + x - 12 = 1

subtracting 1 from both sides:

3x² - 11x - 4 = 0

3x² - 12x + x - 4 = 0

3x(x - 4) + 1(x - 4) = 0

(3x + 1)(x - 4) = 0

3x + 1 = 0; and x - 4 = 0

x = -1/4; and x = 4

The solution to the equation is x = -1/4; and x = 4

Find out more on equation at: https://brainly.com/question/17145398

#SPJ1

Two half-lives would be necessary for a sample of parent isotopes to decay to the point that only one-fourth of the sample is composed of parent isotopes.

Each half-life reduces the amount of parent isotopes by half, so after one half-life, the sample would consist of one-half parent isotopes and one-half daughter isotopes.

After the second half-life, half of the remaining parent isotopes would decay, leaving only one-fourth of the original sample as parent isotopes.

Number of half-lives = log(base 2) (original amount/final amount)

For example, if the half-life of a radioactive isotope is 5 years and you start with 100 atoms of the isotope, after one half-life (5 years), you will have 50 atoms remaining.

Thus, to get to one-fourth of the original amount, you need to go one more half-life, for a total of four half-lives.

For more details regarding half life, visit:

https://brainly.com/question/31666695

#SPJ1

The graph of the inequality y ≥ x² is shown in the image attached below.

In order to to graph the solution to the given linear equation on a coordinate plane, we would use an online graphing calculator to plot the given quadratic function and then take note of the x-intercept, zeros, or roots.

In this scenario and exercise, we would use an online graphing calculator to plot the given quadratic function as shown in the graph attached below;

y ≥ x²

Based on the graph (see attachment), we can logically deduce that the possible solution to the given quadratic function is given by the ordered pair (0, 0).

Read more on solution and equation here: brainly.com/question/25858757

#SPJ1

The expression for the inequality equation is -2 ≤ x ≤ 2

Given data ,

Let the number line be represented as A

Now , the value of A is

The number -2 and 2 are marked as colored bubbles in the line

So , the inequality states that the marked bubbles is also the solution to the relation and these numbers will be included

And , the inequality relation is given by -2 ≤ x ≤ 2

Hence , the inequality is -2 ≤ x ≤ 2

To learn more about inequality equations click :

https://brainly.com/question/11897796

#SPJ1

Answer:

10

Step-by-step explanation:

the quotient is the result of division , that is

120 ÷ 60 = 2

72 ÷ 9 = 8

then sum of quotients = 2 + 8 = 10

The equations which are equivalent to Negative one-fourth (x) + three-fourths = 12 are:

Negative 1 (StartFraction x over 4 EndFraction) + three-fourths = 12

StartFraction negative x + 3 over 4 EndFraction = 12

(StartFraction negative x over 4 EndFraction + three-fourths = 12

Given equation is,

Negative one-fourth (x) + three-fourths = 12

This can be written numerically as,

-1/4 x + 3/4 = 12

-x/4 + 3/4 = 12, which is the last option.

This can be written as,

-1 (x/4) + 3/4 = 12, which is the second option.

Since the denominators are same in left hand side, adding the fractions, we get,

(-x + 3) / 4 = 12, which is the third option.

Hence the second, third and last options are equivalent equations.

Learn more about Equivalent Equations here :

https://brainly.com/question/29013156

#SPJ1

The probability that it will rain on at most two of the seven days they are there is 0.002.

This is a binomial probability problem with the following parameters:

n = 7, the number of trials (days)

p = 0.87, the probability of success (rain) on any given day

x = 0, 1, or 2, the number of days it will rain

The probability mass function of a binomial distribution is given by:

P(X = x) = [tex]P(X=x)=(^nC_x). p^x(1-p)^(^n^-^x^)[/tex]

P(X ≤ 2) = P(X=0) + P(X=1) + P(X=2)

[tex]= (^7C_0)(0.87^0)(0.13^7) + (^7C_1)(0.87^1)(0.13^6) + (^7C_2)(0.87^2)(0.13^5)[/tex]

= 0.000005 + 0.000143 + 0.002093

= 0.002241

Therefore, the probability that it will rain on at most two of the seven days they are there is  0.002.

To learn more on probability click:

https://brainly.com/question/11234923

#SPJ1

18 liters of 15% acid, 18 liters of 35% acid, and 36 liters of 65% acid should be used.

Let x is the volume of 15% acid, y is the volume of 35% acid, and z is the volume of 65% acid.

Given that, the total mixture is 72 liters,

Implies that,

x + y + z = 72

Also,65% solution is used two times as 35% solution is used.

z = 2y

The amounts of acid add up to the final amount.

0.15x + 0.35y + 0.65z = 0.45 (72)      

Substitute the value of z here,

0.15x + 0.35y + 0.65 (2y) = 0.45 (72)

Simplify

x + 3y = 72

0.15x + 1.65y = 32.4      

Solve for x in the first equation, then substitute into the second.

x = 72 − 3y

0.15 (72 − 3y) + 1.65y = 32.4

Solve for y.

10.8 − 0.45y + 1.65y = 32.4

1.2y = 21.6

y = 18

Now find x and z.

x = 72 − 3y = 18

z = 2y = 36

18 liters of 15% acid, 18 liters of 35% acid, and 36 liters of 65% acid should be used.

Read more about acid solution here:

https://brainly.com/question/24255408

#SPJ1