Mrs. magil asks her students to draw a right triangle with one angle measuring 63 degrees. Which equation can be used to determine a, the measure of the third angle in their triangle?

The polynomial is of degree 4, and the leading coefficient is -6.

A polynomial of degree N with a leading coefficient A and the zeros {x₁, x₂, x₃, ..., xₙ} (notice that we have as many zeros as the degree of the polynomial) is written as:

p(x) = A*(x - x₁)*...*(x - xₙ)

Here we have the polynomial:

g(x) -2*(3x + 4)*(x - 1)*(x - 3)²

We can expand this as:

g(x) = -2*(3x + 4)*(x - 1)*(x - 3)*(x - 3)

Think that as we have "two zeros" at x = 3.

So we have 4 factors, then the degree of the polynomial is 4.

To find the leading coefficient we just need to look at the term that comes by multiplying all the terms with "x", we will get:

-2*(3x)*x*x*X

-6*x⁴

The leading coefficient is negative.

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Answer:

[tex]\huge\boxed{\sf HF=71.4}[/tex]

Step-by-step explanation:

If ΔCDE is similar to ΔFGH, their sides are proportional.

So,

[tex]\displaystyle \frac{23}{HF} =\frac{19}{59} \\\\Cross \ Multiply\\\\23 \times 59 = 19 \times HF\\\\1357 = 29HF\\\\Divide \ 19 \ to \ both \ sides\\\\1357/19 = HF\\\\71.4 = HF\\\\HF=71.4\\\\\rule[225]{225}{2}[/tex]

Answer: 7

Step-by-step explanation: 7+2

Answer:

n=37

Step-by-step explanation:

The first thing to do would be to eliminate the 40 from the left side of the equation, leaving n by itself. Then, you subtract the 40 from the 55, then add the result to 22.

hope this helps!!! :3

The required simplification of given function is [tex]\frac{(x-1)^{2}}{x-2}[/tex] and restriction on domain are x  ≠ 1, 2.

The domain of a function is the set of all possible inputs for the function. For example, the domain of f(x)=x² is all real numbers, and the domain of g(x)=1/x is all real numbers except for x=0. We can also define special functions whose domains are more limited.

We have,

[tex]\frac{(x+3)(x-1)}{x-2}[/tex] ÷ [tex]\frac{x+3}{x-1}[/tex]

[tex]\frac{(x+3)(x-1)}{x-2}[/tex] × [tex]\frac{x-1}{x+3}[/tex]

[tex]\frac{(x-1)^{2}}{x-2}[/tex]

For domain, Function should have solution should not be not defined.

For this, denominator must not equal to zero

Then, x -2 ≠ 0, x - 1  ≠ 0

x  ≠ 2, x  ≠ 1

Thus, option(3) [tex]\frac{(x-1)^{2}}{x-2}[/tex] x  ≠ 1,2 is correct.

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Answer:

  (b)  (x -1)²/(x -2), x ≠ -3, 1, 2

Step-by-step explanation:

You want to know the domain restrictions and the simplified form of ...

  [tex]\dfrac{(x+3)(x-1)}{(x-2)}\div\dfrac{x+3}{x-1}[/tex]

We can "invert and multiply", then cancel the common factor from numerator and denominator.

  [tex]\dfrac{(x+3)(x-1)}{x-2}\div\dfrac{x+3}{x-1}=\dfrac{(x+3)(x-1)}{x-2}\times\dfrac{x-1}{x+3}=\dfrac{(x+3)(x-1)^2}{(x+3)(x-2)}\\\\=\dfrac{(x-1)^2}{x-2}\qquad x\ne -3[/tex]

The values of x that must be excluded from the domain are those values for which any part of this expression is undefined. The expression is undefined when any denominator is zero: at x = 2 (left "factor"), at x = 1 (right "factor"), and at x = -3.

The factor (x +3) doesn't show up in the simplified form, but it is a "hole" in the graph of the original expression—a value of x where the function is not defined.

Here is a summary of what you get at the restricted values:

The simplified form with restrictions is ...

  [tex]\boxed{\dfrac{(x-1)^2}{x-2},\ x \ne -3,1,2}[/tex]

Answer:

haha

Step-by-step explanation:

The value of w for the expression of angle 6w + 13 will be 13. The correct option is A.

The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

Given that a quadrilateral has 4 sides. One angle of regular quadrilateral measures (6w+13).

The value of 'w' will be calculated as,

6w + 13 = 90

6w = 90 - 13

6w = 77

w = 12.83 or 13

Therefore, the value of w for the expression of angle 6w + 13 will be 13. The correct option is A.

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The three quadratic equation with different maximum and/or minimum values are y = (x-4)² – 1, y = -(x-4)² + 1, and y = -3(x-4)² + 3.

Quadratic equation:

In math, quadratic equation is the algebraic equation of the second degree in x.

The general form of quadratic equation is

ax² + bx + c = 0,

where a and b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x² is a non-zero term(a ≠ 0).

Given,

Here we need to find the three equations for quadratics in vertex form that have roots at 3 and 5 but have different maximum and/or minimum values.

As per the definition of quadratic equation, here we have to write the quadratic equation, that have the roots of 3 and 5,

Here the problem was going to call for two equations but then we have realized that it could be as simply as multiplying the a and c values by -1. Therefore, the equation are,

=> y = (x-4)² – 1,

=> y = -(x-4)² + 1,

=> y = -3(x-4)² + 3.

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The null hypothesis is it takes a customer less than or equal to 25 minutes to eat lunch.

The alternate hypothesis is it takes a customer more than 25 minutes to eat lunch.

What is null and alternate hypothesis?

The null hypothesis in inferential statistics is that two possibilities are equal. The underlying assumption is that the observed difference is just the result of chance. The alternative hypothesis is one of the suggested hypotheses in statistical hypothesis testing.

We are given a statement,

The manager of a restaurant believes that it takes a customer less than or equal to 25 minutes to eat lunch.

According to null hypothesis, There is no difference or change

Hence the null hypothesis is, it takes a customer less than or equal to 25 minutes to eat lunch.

Where as in alternate hypothesis, There should be a difference of change

Hence the alternate hypothesis is it takes a customer more than 25 minutes to eat lunch.

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By using the concept of circle, it can be concluded that-

Center = (1, 0) lies on x axis

The radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

What is a circle?

Circle is a two dimensional round figure in which every point on the circle maintains a fixed distance from a point known as the center of the circle and the fixed distance is called radius of the circle

The equation of circle is

[tex]x^2 + y^2 - 2x - 8 = 0.[/tex]

[tex]x^2 - 2x + 1 - 1-8+y^2 =0\\(x -1)^2 + y^2 = 9\\(x - 1)^2 + y^2 = 3^2[/tex]

Center = (1, 0) lies on x axis

Radius of the given circle is 3 units

Radius of x² + y² = 9 is 3

So, the radius of this circle is the same as the radius of the circle whose equation is x² + y² = 9.

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Answer: About 25

Step-by-step explanation: So, to find how many helium balloons, we need to subtract 35 from 125, then divide it by 3.50. So, 125-35 = 90. So, 90 / 3.50 = 25.714285714285715. So, we are around 25.7 up to 26. But, we can't do this. This is because they can't spend over $91 on balloons. So, we have to round down. If it was 26, they would spend $91, 1 dollar over their budget. So, it would be about 25, which would be 87.50. So, they would have $3.50 left over.

2 parts to 5 parts  does not belong to the given options and  2 for every 5 does not matches.

A division is a process of splitting a specific amount into equal parts.

Given,

2 parts to 5 parts

2 for each 5

2 out of every 5

2 for every 5

Division has two parts the numerator and denominator.

The numerator represents the part and denominator represents the whole.

2 parts to 5 parts  does not belong to the given options and  2 for every 5 does not matches.

Hence, 2 parts to 5 parts  does not belong to the given options and  2 for every 5 does not matches.

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The measure of PQ in the triangle is 28 units.

The line segment connecting the midpoints of  two sides of a triangle is parallel to the third side and is congruent to one half of the third side.

Therefore, using the mid point theorem, Let find the measure of PQ.

ST = -22 + 9x

PQ = 9x - 8

The measure of PQ can be found as follows:

ST = 1 / 2 (PQ)

-22 + 9x = 1 / 2 × (9x - 8)

-22 + 9x = 9x - 8 / 2

cross multiply

2(-22 + 9x) = 9x - 8

-44 + 18x = 9x - 8

-44 + 8 = 9x - 18x

- 36 = - 9x

x = - 36 / - 9

x = 4

Therefore,

PQ = 9(4) - 8 = 36 - 8 = 28 units

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Answer:[tex]522\pi[/tex] [tex]sq. inches[/tex]

Step-by-step explanation:

        [tex]2\pi (9)^{2} +2\pi (9)(20)\\162\pi +360\pi \\=522\pi sq. inches[/tex]

Answer: 6 miles exactly

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

A=πr^2

113.04=3.14×r^2

113.04/3.14=r^2

36=r^2

√36=r

r=6

Answer:

$40.63

Step-by-step explanation:

If the phone company charges $17.75 already, and each minute costs $0.13, then we can do an equation that looks something like this:

17.75 + (0.13 × 176) = total price

We need to figure out how much 0.13 multiplied by 176 is.

0.13 × 176 = 22.88

Now that we figured out that 0.13 multiplied by 176 is equal to 22.88, we need to add the monthly access fee.

22.88 + 17.75 = 40.63

The monthly cost will be $40.63.

The lowest cost per ounce is  12 ounces of soda which cost $0.72.

An 8-ounce of soda can costs $0.96, a 12-ounce soda can costs $0.72 and 32 ounces of a cup of soda costs $2.24.

The lowest cost per ounce can be calculated as follows:

For  8 ounces of soda can costs $0.96.

cost per ounces = 0.96 / 8

cost per ounce = 0.12 dollars per ounce

For  12 ounces soda can costs $0.72.

cost per ounces = 0.72 / 12

cost per ounce = 0.06 dollars per ounce

For  32 ounces soda can cost $2.24.

cost per ounces = 2.24 / 32

cost per ounce = 0.07 dollars per ounce

Therefore, the lowest is 12 ounces of a soda can.

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It will take 54 days for Teri's account to earn an amount of $5000.

Compound interest, also known as interest on principal and interest, is the practice of adding interest to the principal amount of a loan or deposit.

It occurs when interest is reinvested, or added to the loaned capital rather than paid out, or when the borrower is required to pay it, so that interest is generated the next period on the principal amount plus any accumulated interest. In finance and economics, compound interest is common.

It is given by formula

A = [tex]p*e^{r*t}[/tex]

where:

A is final amount

p is principal amount

r is rate of interest and

t, is time period

Given: A= $5000, p=$1500, r=2.25% = 0.0225

To find: time period to get compounded amount

5000=1500×[tex]e^{0.0225*t}[/tex]

[tex]e^{0.0225t}[/tex] = [tex]\frac{10}{3}[/tex]

0.0225t = ㏑ ([tex]\frac{10}{3}[/tex])

t = 53.5099 ≈ 54 days  

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These pairs of sets of numbers: (a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} b) {{1}},{1,{1}} ) ∅,{∅}  are  equal, not equal and not equal respectively

The given pairs of sets of numbers are

a) (1, 3, 3, 3, 5, 5, 5, 5, 5}, {5, 3, 1} b) {{1}}, {1, {1}} c) Ø, {0}​

To determine the reasons for the answers we have

(a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1}

All the number are distinct elements without any repetition is the same in both sets.

This implies that the sets are equal

b) {{1}},{1,{1}}

From the second set of numbers, the number of elements is not the same in both sets. The number of elements in the two sets are 1 and 2.

This therefore means that the pair of numbers are not equal

c) ∅,{∅}

In the third set of numbers, the number of elements is not the same in both sets.

The number of elements in the pairs are 0 and 1 in each of the sets . This implies that the pair of sets of numbers are not equal

In conclusion these pairs of sets of numbers: (a) {1, 3, 3, 3, 5, 5, 5, 5, 5},{5, 3, 1} b) {{1}},{1,{1}} ) ∅,{∅}  are  equal, not equal and not equal respectively

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The pressure of 28 inches of mercury occurs about 6 miles from the eye of hurricane.

In essence, atmospheric pressure is the force that the weight of the air above a particular point on the Earth's surface exerts at that location.

In other words, the weight of the air molecules as a whole determines the atmospheric pressure, which is produced by the air that surrounds the Earth.

Lower pressure is felt by air molecules at higher altitudes because there are fewer molecules pressing down on them from above, while higher pressure is felt by air molecules at lower altitudes because they are closer together and are under more pressure from molecules piled on top of them.

F(x) is the pressure in inches of mercury

It is given pressure 28 inches of mercury

Put F(x) equal to 28

F(x) = 0.48㏑(x+2) +27

28 = 0.48㏑(x+2) + 27

28-27= 0.48㏑(x+2)

1= 0.48㏑(x+2)

1/0.48= ㏑(x+2)

25/12= ㏑(x+2)

x+2= [tex]e^{\frac{25}{12} }[/tex]

x+2=8.03119

x=8.03119-2

x= 6.03119

x = 6(round off)

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The interest rate required for Ariana to end up with $233,000 is approximately 6.6%.

The compound interest formula can be expressed as;

A = P(1 + r/n)^(n*t)

Where A is accrued amount, P is principal, r is interest rate, t is time elapsed.

Given the data in the question;

Using the formula A = P(1 + r/n)^(n*t).

Solve for r when interest is compounded continuously.

r = In( A / p ) / t

Plug the given values into the above equation.

r = In( $233,000 / $62,000 ) / 20

r = In( $233,000 / $62,000 ) / 20

r = 0.0661952

Now, convert r to R as a percentage

R = r × 100%

R = 0.0661952 × 100%

R = 6.6%

Therefore interest rate needed by Ariana to the nearest tenth of a percent is 6.6%.

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line AB is original figure, line A'B' is transformed figure. the length A'B' is given by √[(2.5x₂-2.5x₁)²+(2.5y₂-2.5y₁)²]

What is dilation?

A process of transformation in which an image or figure changes from the original shape.

What is dilating point?

The point which is acted as the center for all contraction and expansion is termed as dilation point.

let, point A is (x₁,y₂) and point B is (x₂,y₂). By using scale factor 2.5, both A and B transformed to the position A' and B'.

hence, A' = (2.5x₁, 2.5y₁) and B'=(2.5x₂,2.5y₂)

now length of A'B' =√[(2.5x₂-2,5x₁)²+(2.5y₂-2.5y₁)²]

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The amount the she had in her savings before the trip was $825.

Calculating amount

From the question, we are to calculate how much Janessa has in her savings before the trip

Let the amount she has in her savings before the trip be x

From the given information,

Janessa spent a third of her savings on airfare for a vacation"

That is,

She spent (1/3)x

The amount remaining after this time will be x - (1/3)x = (2/3)x

"She then spent another $300 on hotels"

The amount remaining after this time will be (2/3)x - $300

"If she has $250 left for meals and souvenirs"

That is,

(2/3)x - $300 = $250

Now, solve for x

(2/3)x - $300 = $250

(2/3)x = $250 + $300

(2/3)x = $550

x = $550 × 3/2

x = $825

Hence, the amount the she had in her savings before the trip was $825

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If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.

If two objects are having the same shape then they will be termed as similar. So in mathematics, if two figures have the same shapes, lines or angles then they are called similar.

If two figures have three sides similar then they will be similar by side-by-side property which is written as SSS.

Now in the given figure, the side YD is similar and equal to the side OD so option C will be the correct answer.

Hence the information do you need to prove the triangles are congruent by SSS Will be YD ≅ OD.

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The probability of getting a Hybrid car = 3/14

The probability formula states that the ratio of favorable outcomes to all outcomes determines the likelihood that an event will occur.

The formula for the probability of an event is given by

P(E) = No of favorable outcomes/ total number of outcomes  

Here we have

The ratio of hybrid cars to gasoline-powered cars is 3:11

Let 3x and 11x be the number of hybrid cars and gasoline-powered cars
[ Since they are in 3: 11 ratio]  

Then total number of cars = 3x + 11x = 14x

From the given data,

Total number of cars = 280

=> 14x = 280

=>  x = 20

Number of Hybrid cars, 3x = 3(20) = 60

Here we select a car from a random experiment

Number of outcome = 280

Number of outcomes that we get Hybrid car = 60  

Thus the probability of getting a Hybrid car = [tex]\frac{60}{280}[/tex]

= [tex]\frac{6}{28}[/tex] =  [tex]\frac{3}{14}[/tex]  

Therefore,

The probability of getting a Hybrid car = 3/14

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Complete question:

The ratio of hybrid cars to gasoline-powered cars in the parking lot of a local office building is 3:11. if there are 280 cars in the lot and one is to be selected at random to get the reserved parking space nearest the building, find the probability the car selected is a hybrid. express your answer as a fraction.

The required integer to represent the loss on each play is -5m-5.

Any positive or negative number without fractions or decimal places is known as an integer, often known as a "round number" or "whole number."

Given:

During a football game, a team lost 10 yards on its first play and 20 yards on its third play.

To write an integer to represent the loss on each play:

Use -10 to represent losing 10 yards.

Use -20 to represent losing 20 yards.

Add both of the expression,

(-10) + (-20)

= -10 -20.

Whenever we add two negative values, the sum is negative.

(-10) + (-20) = -10 -20 = - 30

Let m be the required integer.

So, -5m-5  is the loss on each play.

Where m is the number of play.

Therefore, the required integer is -5m-5.

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The polynomial functions of the given zeroes are:

5) f=x³+x²-10x+8

6) f=x³+4x²-15x-18

7) f=x²-x(1-i-7)+7i+7

8) f=x²-x(1-i)+2i+2

A function is said to as polynomial when a variable in an equation, such as a quadratic equation or cubic equation, etc., has only positive integer exponents or non-negative integer powers. One polynomial with an exponent of 1 is 2x+5, for instance. One that has more than two algebraic terms is referred to as a polynomial expression. Polynomial is a monomial or binomial that is repeatedly added, as the name suggests.

A mathematical expression containing one or more algebraic terms, where each algebraic term is made up of a constant multiplied by one or more variables raised to a nonnegative integral power.

5) The given zeroes are -4, 1, 2

(x+4)(x-1)(x-2)=0

x³+x²-10x+8=0

6) (x+6)(x+1)(x-3)=0

x³+4x²-15x-18=0

7) (x-7)(x-(1+i))=0

x²-x(1-i-7)+7i+7=0

8) (x-2i)(x-(1-i))=0

(x-2i)(x-1+i)=0

x²-x(1-i)+2i+2=0

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Answer: (x,y) = (-3,3)

Step-by-step explanation:

1. Solve the equation for y

y=9+2x

2. Substitute the given value of y into the equation 5x+y= -12

5x+9+2x= -12

3. Solve x variable

x= -3

4. Substitute the given value of x into the equation y=9+2x

y=9+2x(-3)

5. Solve the equation for y

y=3

Final answer:

x=-3

y=3

Answer:

490 miles

Step-by-step explanation:

Since Ahmad is driving 350 miles in 5 hours, he's averaging 70 miles per hour.

350/5 = 70 mph

Driving 7 miles at 70 mph:

7 x 70 = 490 miles

Answer: 490 miles!

Step-by-step explanation:

350 x 7hrs divided by 5hrs would be = 490miles

How did I get 490? or why didn't you do 350 x 5?

Well because the question asks how many miles would he drive in 7 hours? you will need to multiple the droven miles which is 350miles because that is part of the getting answer, and the question of having to know how many miles would he drive in 7 hours, you wouldn't do 350 x 5 because its not asking " Ahmad drove 350 miles in 5 hours, how many miles would he drive in 5 hours? and which would equal 250 which not correct because it doesn't make sense if he's drove 350 miles in 5 hours and then drove 250miles in 7 hours, back to the explanation, after multiplying 350 into 7 you will end up at 2450, no this isn't the answer you need to divide because it would take more than 7 hours to drive 2450 miles, next you divide by the hours driven in 350 miles which in this in this case would be 5 because your diving  2450 by 5 because sense u cannot get the answer by multiplying 350x5 so this is time where your gonna use the 5 because 350 x 7= 2450 is too large in miles for 7 hours your gonna divide the 2450 to lower it down to 490 miles, doesn't that sound more accurate? the miles increase by  1.4 ( 140 miles ) so another way u could have gotten the answer was by doing 350 + 140 = 490 but however you would need to know how much the miles have increase which u can do by 490 - 350 which equals to 140 miles.