C) 1) if Z1 and 22 are complementary angles, and mZ1 = 74°; find m22.

Given the polynomial:

Let's factor the polynomial.

To factor, let's use the AC method.

Find a pair of numbers whose product is -18 and whose sum is 7.

We have the pair:

9 and -2

We have the factors:

(w + 9)(w - 2)

Therefore, the factored form of the polynomial is:

ANSWER:

Firstly, let us define natural numbers.

Natural numbers are simply positive intergers, that is integers that are greater than zero e.g 1,2,3,4...

Secondly, when is a set said to be closed under a particular operation?

A set is said to be closed under an operation if and only if the operation on any two elements of the set produces another element of the same set. for example when you perform an operation (like addition) on a set of number (like natural numbers) it must give you a number from that same set.

E.g

let's check whether natural numbers are closed under the operation of adddition.

taking two numbers 3 and 5.

since the operation gives us 8, which is a natural number, it means natural numbers are closed under the operation of addition.

Back to the main question, which is to check whether natural numbers are closed under the operation of subtraction.

taking two cases.

case 1; taking numbers 3 and 5

case 2: taking numbers 7 and 2

From the two cases, case 2 gave us a natural number while case 1 does not give us a natural number.

This means that Natural numbers are not Closed under subtraction.

Because subtraction operation on natural numbers does not necessarily produce another natural number.

On a general note;

Natural numbers are closed under Addition and Multiplication operations

while They are not closed under subtraction and division operation

a. Median for name brands is greater than the median for store brands data values in the boxplots given.

b. Approximately 75% of the data values of name brands is greater than the median of the data values of store brands.

A boxplot displays the distribution of a data such that the median is represented by the vertical line that divides the rectangular box.

25% of a data distribution is represented by the beginning of the edge of the box, while 50% is represented by the median, and 75% is represented by the point at the end of the edge of the box in the boxplot.

Therefore:

a. The median of name brands peanut butter is approximately 82-83.

The median of store brands is approximately less than 80.

Thus, we can conclude that, the median for name brands is greater than the median for store brands.

b. The median for store brands is approximately below 25% of the data values for name brands. Therefore, we would conclude that, approximately 75% of name brands data value are greater, compared to the median of the store brands data value.

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Given:

The points are (-9,8) and (-4,-4).

Required:

We need to find the line equation in point-slope form.

Explanation:

Consider the slope equation.

Consider the point (-9,8).

Consider the point-slope form of the equation.

Final answer:

Given:

Required:

To complete the square that leads to the equivalent equation (x +__ )^2 = __.

Explanation:

Consider

Final Answer:

y² = -8(x - 4),  which is the required equation of the parabola.

All points in a plane that are equally spaced out from a given point and a given line make up a parabola.

The line is known as the directrix, and the point is known as the parabola's focus.

A parabola's axis of symmetry is perpendicular to the directrix, which does not touch the parabola.

The focus of the parabola is F(-6,0) and its directrix is the line x=−2 i.e., x+2=0

Let P(x,y) be any point in the plane of directrix and focus, and MP be the perpendicular distance from P to the directrix,then P lies on parabola if FP=MP

⇒(x+6)²+(y−0)² ​= ∣x+2∣​÷1

⇒x² + 12x+36+y² = x² +4x +4

⇒y² + 8x = -32

⇒y² = - 8x - 32

⇒y² =  -8(x - 4)

⇒ y² = -8(x - 4),  which is the required equation of the parabola.

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Answer:a

Step-by-step explanation:can i get brainiest

The graph is shown the following slope intercept formula y = 5/3x -4.

So, the slope-intercept formula: y = mx + b

Now, substitute the values in the formula and graph the slope-intercept on the graph as follows:

(Refer to the graph attached below )

Therefore, the graph is shown the following slope intercept formula y = 5/3x -4.

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The natural phenomena that follows an elliptical motion is:

D.

The motion of the planets around the sun

We have to round the number 36,236 to the nearest ten thousand (10,000).

Then, the number 36,236 is between 3 and 4 ten thousands. As 36,236 is over 35,000 we round it to 40,000.

Answer: 40,000

Answer:

The midpoint is (-1,1)

Equation: y = -x -2

Step-by-step explanation:

Midpoint:

([tex]\frac{-5+3}{2}[/tex], [tex]\frac{-5 + 3 }{2}[/tex])  You are taking the averages of the x values and the y values.

([tex]\frac{-2}{2}[/tex],[tex]\frac{-2}{2}[/tex])  

(-1,-1)

Equation:

The slope of the 2 points given is

[tex]\frac{3 - -5}{3- - 5}[/tex] = [tex]\frac{8}{8}[/tex] = 1  The slope is the change of y over the change in x.  Points are given in the form (x,y)  So, I subtracted the y values on top and the x values on  the bottom of the fraction.

The equation that is created is perpendicular to the original line, so it slope is the negative reciprocal.

1 as a fraction is [tex]\frac{1}{1}[/tex].  negative reciprocal means turn the fraction upside down and take the opposite  value.  If I flip [tex]\frac{1}{1}[/tex] upside down, I get the same fraction which is equal to 1.  Now I will take the opposite sign.  Since it is positive, the new slope will be negative

slope  -1

x = -1

y = -1  

I am using the point that will be on the new line. This is the midpoint that we just found (-1,-1)  I am going to plug in the number that I know and solve for b or the y=intercept.

y =  mx + b

- 1 = -1(-1) + b

-1 = 1 + b  Subtract 1 from both sides of the equation

-2 = b

y = mx + b

y = -1x -2

or

y = -x -2

19 ten pound tukeys

average of 2.9 hours

standar deviation 0.24

90% confidence

Interval with 90% confidence is 2.42961–3.37039

Part a)

Perimeter = 340 = 2•77 + Length doubled

then

Length x 2 = 340 - 154 = 186

Length= 186/2 = 93

ANSWER IS Length of parking lot is= 93 meters

Part b)

Area = 7410 = Width x Length

. 7410 = Width x 95

. 7410/95 = Width

THEN Width of the pool IS

78 square meters

In order to determine what is the correct statement, calculate the amount of money Elsie can spend per month, based on her earnings per year.

Divide 45,000 by 12:

45,000/12 = 3,750

You can notice that the amount of money Elsie can spend per month is lower than the total expenses shown in the table.

Hence, the correct statement is:

C. No, because she will only make $3750 per month before taxes are taken out.

The zero of x = 3 will be x - 3 = 0

The zero of x = 8 will be x - 8 = 0

Therefore, the quadratic equation will be

(x - 3) and (x - 8)

Multiplied by 15.5 to 3.75 is 58.125.

To solve the:

15.5 is multiplied by 3.75

Now,

15.5 × 3.75

=  58.125

What is the process of Multiplication ?

Multiplication is the process of calculating the total of one number multiplied by another. There will be simple tests in addition, subtraction, multiplication and division. 2. uncountable noun. The multiplication of things of a particular kind is the process or fact of them increasing in number or amount.

Hence, Multiplied by 15.5 to 3.75 is 58.125.

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$28 after 30% off

28 = regular price * (100 - 30)/100

28 = regular price * 70/100

28 = regular price *0.70

regular price = 28/0.70 = 40

Answer:

Regular price = $40

Select all the equations that share a solution with this system of equations. (Hint: try adding and subtracting the equations.)

5x + 4y = 24

2x – 7y = 26

____

a) 7x – 3y = 50

b) 7x + 3y = 50

c) 3x - 3y = -2

d) 3 x+ 11y = -2​

_____________________________

Try adding and subtracting the equations

5x + 4y = 24

+(2x – 7y = 26)

_______________

7x -3y= 50

5x + 4y = 24

-2x + 7y = -26

______________

3x + 11y = -2

Do you have any questions regarding the solution?

Rate of the current = 5 mph

The time taken to travel downstream from Greentown to Glenevon = 2/5 hours

The time taken to travel upstream from Glenevon to Columbia = 3/5 hours

Rate = Distance /time

Let the distance traveled = y miles

Rate of the downstream travel:

Rate = y ÷ 2/5

Rate = y x 5/2

Rate = 5y / 2

Rate of the upstream travel

Since the travel upstream from Glenevon to Columbia is 2 meters downstream:

Distance = y - 2

Rate = (y-2) ÷ 3/5

Rate = (y-2) x 5/3

Rate = 5(y-2)/3

Let the current rate be represented by k

The rate of the downstream travel will be:

15 + k = 5y/2...........(1)

The rate of the upstream movement will be:

15 - k = 5(y-2)/3............(2)

Add equations (1) and (2)

(15 + k) + (15 - k) = [5y/3] + [5(y-2)/3]

Substitute the value of y into equation (1)

The rate of the current = 5 mph

Answer:

W = A/L

Step-by-step explanation:

We are given the following formula:

A = LW

We want to solve for the width W. So

LW = A

L multiplies W, so it can go to the other side of the equality dividing. Then:

W = A/L

The composition of the function, (g o h)(0) = 0.

To find the composition of a function, first, find the value of the inner function by plugging in the given value of x. The output of the inner function would now be used as the input to evaluate the outer function.

We are given the following:

g(x) = 5x

h(x) = √x

To find the composition of the function, (g o h)(0), first, find h(0). To find h(0), substitute x = 0 into the inner function, h(x) = √x:

h(0) = √0

h(0) = 0

Find (g o h)(0) by substituting x = 0 into g(x) = 5x:

(g o h)(0) = 5(0)

(g o h)(0) = 0

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Problem N 25

we know that

C=132 in

Remember that

The formula to calculate the circumference is given by

using pi=3.14

C=132 in

substitute given values in the formula

The diameter D=42.04 in ( with pi=22/7 the diameter is 42 in exact)

Find out the radius r

r=D/2=42.04/2=21.02 in -----> the radius is half the diameter

Find out the area of the circle

The area is given by the formula

we have

r=21.02 in

pi=3.14

substitute

therefore

Answer

{(–3, 2), (–2, 3), (–1, 2), (0, 4), (1, 1)}

Step-by-step explanation

The options have the form:

In a function, every input can be related to only one output.

In the case of the first option, the input -1 is related to two outputs, 3 and 2, then it is not a function.

In the case of the second and third options, the input 0 is related to two outputs, 4 and 1, then they are not a function.

Given the points (5,-2) and (5,-3), we can find the slope of the line that passes through them with the following formula:

since we have that the slope is not defined, the line that passes through the points (5,-2) and (5,-3) is the vertical line x=5

price = $3.50

Sale tax = 6%

Multiply the price by the tax percentage in decimal for ( divided by 100)

3.50 x (6/100) = 3.50 x 0.06 = $0.21

Answer: Number of children = 112, number of adult = 140

Let the number of children = x

Let the number of adult =

According to the question, 252 people entered the park

Mathematically, the number of adult and children that entered the park sum up to 252

x + y = 252 ------- equation 1

$1.5 is charged for children for the admission fee into the park

$4 is charged for adult for the admission fee into the park

A totaled of $728 was realized from both children and adult that were admitted into the park

This implies that the total amount realized is equal to the number of children and adults inside the park per amount charged respectively

1.5* x + 4 * y = 728

1.5x + 4y = 728 -------- equation 2

Equation 1 and 2 can be solve simultaneously using substitution method

x + y = 252 ----- 1

1.5x + 4y = 728 ------ 2

Make x the subject of the formula in equation 1

x + y = 252

x = 252 - y ----- equation 3

Substitute equation 3 into equation 2

1.5(252 - y ) + 4y = 728

Open the parenthesis

1.5 x 252 - 1.5 x y + 4y = 728

378 - 1.5y + 4y = 728

Collect the like terms

-1.5y + 4y = 728 - 378

2.5y = 350

Divide both sides by 2.5

y = 350/2.5

y = 140

To find x, put the value of y into equation 1

x + y = 252

x = 252 - y

x = 252 - 140

x = 112

The number of children = 112

The number of adults = 140

For a transformation like the one shown in the graph, note that the points have switched as follows;

This is a 90 degree anticlockwise rotation about the origin.

That means point P would now be translated as follows;

After this rotation, the coordinates have now moved from their position one unit upwards. That now makes the final coordinates;

ANSWER

24

EXPLANATION

The median of a data set is the middle number of the set - when they are arranged from least to greatest. If the amount of numbers in the data set is even, the median is the average of the two middle numbers.

In this case, there are 7 charts. To find the middle number we have to arrage the set from least to greatest: 13, 17, 22, 24, 35, 38, 43

The middle number is 24. This is the median.

we will need to solve the first inequality,

5+x>=-3 , we will subtract -5 from both sides and the solution is

x>=-2

for the second inequality

6x+1<-29, we will subtract 1 from bothe sides and get

x<-5

is your choice B