(2/9) of students in a school are in the sixth grade.

How many sixth graders are there if the school has 90 students?

How many sixth graders are there if the school has 27 students?

How many students are in the school if 42 of them are sixth graders?

The option that describes the null and alternative hypothesis, test statistic and conclusion will be B. test statistic = -1.5625 and the conclusion is to reject the null hypothesis.

In statistical hypothesis testing, the null hypothesis (H0) is a statement that assumes no significant difference or relationship between two or more variables. It represents the default position that there is no effect or change, or that any observed effect is due to chance.

The alternative hypothesis (H1), on the other hand, represents the opposite of the null hypothesis. It states that there is a significant difference or relationship between the variables being tested. The alternative hypothesis is typically what the researcher is trying to prove or support with their study.

The test statistic will be:

= (116 - 121) / 16(✓1/50 + 1/50)

= -1.5625

Learn more about hypothesis on;

https://brainly.com/question/25263462

#SPJ1

As we are looking for the distance to the nearest whole number, we can round this answer to 517 feet. This means that when the plane has reached an altitude of 300 feet, it has flown a distance of 517 feet.

To find the distance that the plane has flown when it has reached an altitude of 300 feet, we can use the formula d = x * tan(a) where d is the distance, x is the altitude, and a is the angle. We are given the altitude of 300 feet and the angle of 15°. Plugging those values into the formula, we get d = 300 * tan(15°) = 517.4 feet. Rounding this to the nearest whole number, we get 517 feet.

To find the distance that the plane has flown when it has reached an altitude of 300 feet, we can use the formula d = x * tan(a). This equation is derived from the Pythagorean Theorem, where d is the distance, x is the altitude, and a is the angle. We are given the altitude of 300 feet and the angle of 15°, so we can plug these values into the equation. When we do this, we get d = 300 * tan(15°) = 517.4 feet. As we are looking for the distance to the nearest whole number, we can round this answer to 517 feet. This means that when the plane has reached an altitude of 300 feet, it has flown a distance of 517 feet.

Learn more about distance here

https://brainly.com/question/28956738

#SPJ1

Therefore, it will take approximately 13.47 years for $2000.00 to double at an annual rate of 5.25% compounded monthly.

Percent is a way of expressing a number as a fraction of 100. The symbol for percent is "%". Percentages are used in many different contexts, such as finance, economics, statistics, and everyday life. Percentages can also be used to express change or growth, such as an increase or decrease in the value of something over time.

Here,

The formula for the accumulated amount (A) when interest is compounded n times per year at an annual interest rate of r, for t years, is:

[tex]A = P(1 +\frac{r}{n})^{nt}[/tex]

where P is the principal amount (initial investment).

To find approximately how long it will take $2000.00 to double at an annual rate of 5.25% compounded monthly, we need to solve for t in the above formula.

Let P = $2000.00, r = 0.0525 (5.25% expressed as a decimal), and n = 12 (monthly compounding).

Then, we have:

[tex]2P = P(1 +\frac{r}{n})^{nt}[/tex]

Dividing both sides by P, we get:

[tex]2= (1 +\frac{r}{n})^{nt}[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(2) =ln(1 +\frac{r}{n})^{nt}[/tex]

Using the properties of logarithms, we can simplify this expression as:

[tex]ln(2) = n*t * ln(1 + r/n)[/tex]

Dividing both sides by n*ln(1 + r/n), we get:

[tex]t = ln(2) / (n * ln(1 + r/n))[/tex]

Plugging in the values for r and n, we get:

[tex]t = ln(2) / (12 * ln(1 + 0.0525/12))[/tex]

Solving this expression on a calculator, we get:

t ≈ 13.47 years

To know more about percent,

https://brainly.com/question/29172752

#SPJ1

The coordinates of B' after the sequence of transformations are given as follows:

B'(3,-4).

The coordinates of B are given as follows:

B(-3,1).

After a reflection over the y-axis, the x-coordinate of B is exchanged, hence:

B'(3, 1).

The rule for a 90º clockwise rotation is that (x,y) becomes (y,-x), hence the coordinates of B' after the 90º clockwise rotation are given as follows:

B'(1, -3).

The translation (x + 2, y - 1) means that 2 is added to the x-coordinate while 1 is subtracted from the y-coordinate, hence the final coordinates of B' are given as follows:

B'(3,-4).

More can be learned about transformations at https://brainly.com/question/29209050

#SPJ1

If triangle ABC has points A(2, -4), B(-3, 1), and C(-2, -6) and you perform the following transformations, B' would be at B' (3, -4).

In Geometry, the rotation of a point 90° about the center (origin) in a clockwise direction would produce a point that has these coordinates (y, -x).

By applying a reflection over the y-axis to the coordinate of the given point B (-3, 1), we have the following coordinates:

Coordinate B = (-3, 1)   →  Coordinate B' = (-(-3), 1) = (-3, 1).

Next, we would apply a rotation of 90° clockwise as follows;

(x, y)                               →            (y, -x)

Coordinate B' = (-3, 1) → Coordinate B' = (1, (-3)) = (1, 3)

Finally, we would apply a translation (x + 2, y - 1) as follows:

Coordinate B' = (1, 3) → (1 + 2, 3 - 1) = B' (3, 2).

Read more on reflection here: brainly.com/question/10260342

#SPJ1

Rolling a number higher than 3 has a 2/6 or 1/3 chance of happening. Another way to say this is to round a decimal to the closest millionth, which is  [tex]0.333333[/tex]  .

A standard die has 6 sides, labelled with the numbers 1 through 6. When the die is rolled, each side has an equal probability of landing face up.

Since we want to find the probability of rolling a number greater than 3, we need to determine the number of outcomes that satisfy this condition and divide it by the total number of possible outcomes.

When you roll a standard die, there are six equally likely outcomes: 1, 2, 3, 4, 5, and 6. Since we want to find the probability of rolling a number greater than 3, we need to count how many of these outcomes satisfy that condition.

Therefore, the probability of rolling a number greater than 3 is 2/6 or 1/3. Alternatively, we could express this as a decimal rounded to the nearest millionth, which would be  [tex]0.333333[/tex] .

Learn more about fraction here:

https://brainly.com/question/29156749

#SPJ1

Answer:

Step-by-step explanation:

To solve this problem, we need to calculate the present value of the cash flows in both cases - the case where the payments are made at the beginning of each year and the case where the payments are made at the end of each year - and compare the two values.

First, let's calculate the present value of the cash flows when payments are made at the end of each year. We can use the formula for the present value of an ordinary annuity:

PV = PMT x [(1 - (1 / (1 + r)n)) / r]

where PV is the present value, PMT is the payment amount, r is the discount rate, and n is the number of periods.

In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:

PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] = R141,798.06

Now let's calculate the present value of the cash flows when payments are made at the beginning of each year. To do this, we can use the formula for the present value of an annuity due:

PV = PMT x [(1 - (1 / (1 + r)n)) / r] x (1 + r)

where PV is the present value, PMT is the payment amount, r is the discount rate, n is the number of periods, and (1 + r) adjusts the formula for the fact that payments are being made at the beginning of each year.

In this case, PMT = R15 000, r = 9%, and n = 13. Plugging in these values, we get:

PV = R15 000 x [(1 - (1 / (1 + 0.09)^13)) / 0.09] x (1 + 0.09) = R153,094.97

So the present value of the cash flows when payments are made at the beginning of each year is R153,094.97, and the present value of the cash flows when payments are made at the end of each year is R141,798.06. Therefore, the difference in present value is:

R153,094.97 - R141,798.06 = R11,296.91

So, receiving the payments at the beginning rather than at the end of each year would result in a present value that is R11,296.91 higher.

Using trigonometric identities, we found that sec Φ = -7/(2√10), sin Φ = 3/7, tan β = √11/5, and sin β = √11/6 for the given values of csc Φ, cot Φ, and sec β.

1. We can start by using the Pythagorean identity to find the values of sin Φ:

[tex]sin^2[/tex] Φ + [tex]cos^2[/tex] Φ = 1

Since csc Φ = 1/sin Φ, we can substitute and solve for sin Φ:

1/(7/3) = sin Φ

sin Φ = 3/7

Next, we can use the fact that cot Φ = cos Φ/sin Φ:

cot Φ = cos Φ/(3/7) = - (2√10)/(3)

Simplifying this expression, we get:

cos Φ = - (2√10)/(3) * (3/7) = - 2√10/7

Finally, we can use the fact that sec Φ = 1/cos Φ:

sec Φ = 1/(- 2√10/7) = -7/(2√10)

2. We can use the fact that sec β = 1/cos β to find the value of cos β:

sec β = 6/5

cos β = 5/6

Next, we can use the Pythagorean identity to find the value of sin β:

[tex]sin^2[/tex] β + [tex]cos^2[/tex] β = 1

sin β = √(1 - [tex]cos^2[/tex] β) = √(1 - 25/36) = √(11/36) = √11/6

Finally, we can use the fact that tan β = sin β/cos β:

tan β = (√11/6)/(5/6) = √11/5

To learn more about Pythagorean please click on below link        

https://brainly.com/question/29069676

#SPJ1

Answer:

Step-by-step explanation:

Answer:

Assuming that the expression is asking for the tangent of 1 radian, we can use the tangent half-angle formula to find an exact value:

tan(1) = 2tan(1/2) / (1 - tan^2(1/2))

To find tan(1/2), we can use the half-angle formula for tangent:

tan(1/2) = sin(1) / (1 + cos(1))

We cannot simplify this expression any further without a calculator. Therefore, the exact value of tan(1) is:

tan(1) = 2sin(1) / (cos(1) - cos^2(1) + 1)

Again, we cannot simplify this expression any further without a calculator.

For the second expression, we are asked to find the value of:

tan(arctan(6/4))

By definition, tan(arctan(x)) = x for all x, so we have:

tan(arctan(6/4)) = 6/4 = 3/2

Therefore, the exact value of the expression tan(6/4) is 3/2.

Answer:

If 18% of victims of financial fraud know the perpetrator of the fraud personally, and a sample of 156 people were victims of fraud, we can find the mean number of those victims that know the perpetrator by multiplying the sample size by the percentage. Therefore, the mean number of victims that know the perpetrator is 156 x 0.18 = 28.08. However, since we cannot have a fraction of a person, we can round the answer to the nearest whole number. Therefore, the mean number of victims that know the perpetrator is 28.

The probability that Angela gets to go to the meeting is 2/5 or 0.4.

What is probability?

There are a total of 5 people in the club, and they need to pick 2 people to go to the meeting. The number of ways to pick 2 people out of 5 is given by the binomial coefficient:

C(5,2) = 5! / (2! (5-2)!) = 10

This means there are 10 equally likely outcomes, which can be represented by the following probability model:

Outcome            Angela goes to meeting?                 Probability

A,B                                    Yes                                              1/10

A,C                                    Yes                                              1/10

A,D                                    Yes                                              1/10

A,E                                     Yes                                              1/10

B,C                                      No                                              1/10

B,D                                      No                                              1/10

B,E                                       No                                              1/10

C,D                                      No                                               1/10

C,E                                       No                                               1/10

D,E                                       No                                               1/10

The probability that Angela gets to go to the meeting is the sum of the probabilities of the outcomes where Angela goes to the meeting:

P(Angela goes to meeting) = P(A,B) + P(A,C) + P(A,D) + P(A,E)

= 1/10 + 1/10 + 1/10 + 1/10

= 4/10

= 2/5

Therefore, the probability that Angela gets to go to the meeting is 2/5 or 0.4.

To know more about the probability, visit:

https://brainly.com/question/11234923

#SPJ1

The product is decreased by a factor of 16.

What is a factor?

In mathematics, a factor is a number or quantity that, when multiplied with another number or quantity, produces a given result. For example, in the expression 3 x 4 = 12, 3 and 4 are factors of 12. Factors can also refer to algebraic expressions, where they are the expressions that are multiplied together to obtain a larger expression.

Let's say we have two numbers, A and B, and we want to find the product of A and B.

The product of A and B is AB.

If we decrease A by a factor of 2, the new value of A becomes A/2. If we decrease B by a factor of 8, the new value of B becomes B/8.

So the new product of A/2 and B/8 is:

(A/2)(B/8) = AB/16

Therefore, the product is decreased by a factor of 16.

To learn more about factors, visit the link:

https://brainly.com/question/25829061

#SPJ1

The value of the limit of the expression Limit x tend to π 1-sinx/2(π-x) ² is infinity (∝)

Given that

Limit x tend to π 1-sinx/2(π-x) ²

To solve this expression, we make use of

If limit of x to a+ of f(x) = limit of x to a- = L, then limit of x to a+ of f(x) = L

The interpretation is that we solve the expression by direct substitution

So, we have

Limit = 1 - sin(π)/2(π - π) ²

Evaluate the difference

Limit = 1 - sin(π)/2(0)²

Evaluate the exponent and the bracket

Limit = 1 - sin(π)/0

Divide

Limit = ∝

Hence, the limit of the expression is ∝

Read more about derivatives at

https://brainly.com/question/5313449

#SPJ1

Hence the value of c = 4 in [3,5] for Rolles theorem.

Rolle's Principle

If a function f is defined in the closed interval [a, b] in a manner that meets the requirements listed below.

The interval [a, b] is closed and the function f is continuous.

ii) On the open interval, the function f can be differentiated (a, b)

iii) If f (a) = f (b), then at least one value of x exists; in this case, let's assume that this value is c, which is situated between a and b, i.e. (a c b), in such a way that f'(c) = 0.

There exists a point x = c in (a, b) such that f'(c) = 0 if a function is continuous on the closed interval [a, b] and differentiable on the open interval (a, b).

let f(x)=x²-8x+12 in [3,5]

i) f(x) is continuous in closed interval [3,5] because f(x) is algebraic function.

ii) f(x) is differentiable in the open interval (3,5) since the algebraic function is differentiable.

now f(3)=3²-8*3+12

f(3)= 9-24+12

f(3)= -3

f(5) = 25-40+12

f(5)= - 3

f(3) = f(5)

f'(x)= 2x-8

x=c ,c in [3,5]

f'(c)= 2c-8

2c-8=0

c=4

Hence the value of c = 4 in [3,5] for Rolles theorem.

learn more about Rolles theorem.

https://brainly.com/question/13972986

#SPJ1

Evaluating the linear equation in x = 19 we can see that the temperature was 5.76 degrees, so your answer is correct.

Here we have a linear equation that relates the wind temperature with the wind's velocity.

The linear equation is:

y = -0.36*x + 12.6

Where y is the temperature and x is the wind speed. We want to find the temperature when the speed is 19 miles per hour, to get it, just replace x by 19 in the linear equation above, then we will get:

y = -0.36*19 + 12.6

y = -6.84 + 12.6

y = 5.76

So your answer is correct.

Learn more about linear equations at:

https://brainly.com/question/1884491

#SPJ1

The distance the plane traveled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).

An angle is a geometric figure formed by two rays, called the sides of the angle, that share a common endpoint, called the vertex of the angle. Angles are typically measured in degrees or radians, and they are used to describe the amount of rotation or turning between two lines or planes. In a two-dimensional plane, angles are usually measured as the amount of rotation required to move one line or plane to coincide with the other line or plane.

Let's first draw a diagram to visualize the problem:

                    /  |

                  /     |

                 /       |P (plane)

                /        |

               /         |

              /          | h = 6900 ft

            /            

           / θ2.        |  

         /                |

       /                  |

   B ___/θ1__  _|___ A

           d

We need to find the distance the plane traveled from point A to point B, which we'll call d. We can use trigonometry to solve for d.

From point A, we have an angle of elevation of 16° to the plane. This means that the angle between the horizontal and the line from point A to the plane is 90° - 16° = 74°. Similarly, from point B, we have an angle of elevation of 27° to the plane, so the angle between the horizontal and the line from point B to the plane is 90° - 27° = 63°.

Let's use the tangent function to solve for d:

x = h / tan(74°) = 19906.5 ft

d - x = h / tan(63°) = 23205.2 ft

So,

d = x + h / tan(63°) ≈ 43111.7 ft ≈ 8.15 miles.

Therefore, the distance the plane travelled from point A to point B is approximately 8.15 miles or 43056 feet (rounded to the nearest tenth of a foot).

To know more about Angles visit:-

brainly.com/question/25770607

#SPJ1

By rewritting the exponential equation, we can see that the correct options are B and C.

We know that the balance is modeled by the exponential equation below:

[tex]A = 328.23\times e^{0.045*(t - 2)}[/tex]

Now we want to see which of the other equations are equivalent to this one, so we need to rewrite this equation, so let's do that.

First we can rewrite the second part to get:

[tex]A = 328.23\times e^{0.045\times(t - 2)}\\\\A = 328.23\times(e^{-2*0.045*}\times e^{0.045\times t})\\\\A = 300\times e^{0.045\times t}[/tex]

So that is an equivalent equation.

We also can keep rewritting this to get:

[tex]A = 300\times e^{0.045\times t}\\\\A = 300\times(e^{0.045})^t\\\\A = 300\times(1.046)^t[/tex]

The correct options are B and C.

Learn more about exponential equation at:

https://brainly.com/question/11832081

#SPJ1

Answer:

p= -3-1/2

p= -7/2

Step-by-step explanation:

(you transpose the fraction /take the liketerms)

( you transpose your fraction will change the sign and become negative then -3-0.5or -3-1/2=-7/2.)then you substitute to the original equation 1/2+p=-3 check your answer .

Therefore, the value of x is 9.

A triangle is a closed two-dimensional geometric shape that is formed by connecting three non-collinear points with three-line segments. The three line segments that connect the three points are called sides of the triangle, and the points themselves are called vertices. The angle formed between any two adjacent sides of a triangle is called an interior angle of the triangle. The sum of the interior angles of a triangle is always 180 degrees.

There are many different types of triangles, including equilateral triangles, isosceles triangles, scalene triangles, acute triangles, obtuse triangles, and right triangles. An equilateral triangle is a triangle in which all three sides are equal, an isosceles triangle is a triangle in which two of the sides are equal, and a scalene triangle is a triangle in which none of the sides are equal. An acute triangle is a triangle in which all three interior angles are less than 90 degrees, an obtuse triangle is a triangle in which one of the interior angles is greater than 90 degrees, and a right triangle is a triangle in which one of the interior angles is exactly 90 degrees.

Given by the question.

According to Thel's theorems

[tex]\frac{5}{3} =\frac{15}{x}[/tex]

5x=45

x=9

To learn more about acute:

https://brainly.com/question/1311149

#SPJ1

Therefore , the solution of the given problem of unitary method comes out to be rectangle's size is 7/12 square inches.

The objective can be accomplished by using what was variable previously clearly discovered, by utilizing this universal convenience, or by incorporating all essential components from previous flexible study that used a specific strategy. If the anticipated claim outcome actually occurs, it will be feasible to get in touch with the entity once more; if it isn't, both crucial systems will undoubtedly miss the statement.

Here,

=>  A = L x W,

where A is the area, L is the length, and W is the breadth, is the formula for calculating the area of a rectangle.

Inputting the numbers provided yields:

=>  A = (7/4) x (1/3)

These fractions can be made simpler by eliminating any shared variables in the numerator and denominator before being multiplied. Since 7 and 3 are both prime integers in this instance, there are no shared factors to cancel.

The new numerator and denominator can then be obtained by multiplying the numerators and denominators, respectively. Thus, we get:

=>  A = (7 x 1) / (4 x 3)

When we multiply the numerator by the remainder, we obtain:

=> A = 7/12

The rectangle's size is 7/12 square inches as a result.

To know more about unitary method  visit:

https://brainly.com/question/28276953

#SPJ1

There is a significant linear correlation (r=0.80) between the heights of winning candidates and runners-up in recent US presidential elections.

Using the data from the table, here are the steps to determine the correlation coefficient and test for a linear correlation:

Calculate the correlation coefficient (r) using the formula: r = (nΣXY - ΣXΣY) / sqrt[(nΣX² - (ΣX)²)(nΣY² - (ΣY)²)], where n is the sample size, X and Y are the two variables (heights of candidates who won and runners-up), Σ denotes the sum of the values, and sqrt is the square root function.

Using a spreadsheet, we get r = 0.80.

Using the formula: df = n - 2.

The sample size (n) is 10, so df = 10 - 2 = 8.

Find the critical values of r using a table or calculator based on the degrees of freedom and the desired level of significance (0.05).

For a two-tailed test with df = 8 and α = 0.05, the critical values are ±0.632.

Since |0.80| > 0.632, we can conclude that there is a significant linear correlation between the heights of winning candidates and runners-up.

Therefore, the correlation coefficient is 0.80, and the critical values are ±0.632. There is a significant linear correlation between the heights of winning candidates and runners-up in recent presidential elections.

To learn more about linear correlation please click on below link        

https://brainly.com/question/28935414

#SPJ1

The value of the expression 34 - 9 x 2 is 16.

The order of operations is a set of rules that dictate the order in which mathematical operations should be performed in an expression. These rules help to ensure that mathematical expressions are evaluated correctly and consistently. The order of operations is typically summarized by the acronym PEMDAS, which stands for:

Parentheses: Perform operations inside parentheses first.

Exponents: Evaluate exponents (powers and square roots, etc.) next.

Multiplication and Division: Perform multiplication and division, from left to right.

Addition and Subtraction: Perform addition and subtraction, from left to right.

In the given questions,

In this case, there are no parentheses or exponents, so we move on to multiplication before subtraction.

We perform the multiplication first, following the rule of performing multiplication before addition or subtraction.

9 x 2 = 18

Then, we subtract the result from 34:

34 - 18 = 16

Therefore, the value of the expression 34 - 9 x 2 is 16.

To know more about order of operations, visit:

https://brainly.com/question/13079176

#SPJ1

Answer: decrease in the GDP by 2.5%.

Step-by-step explanation:

The five in 35.76 is 100 times bigger than the five in 26.95.

Here we want to compare the values of the 5's in two different numbers, which are 35.76 and 26.95.

To compare them we need to compare the place value in which each five is.

To compare them, just write the numbers but replacing all the other values by zeros:

35.76 = 05.00 = 5

26.95 = 00.05 = 0.05

Now take the quotient of these two, we will get:

5/0.05 = 100

Thus, the 5 in 35.76 is 100 times bigger than the 5 in 26.95.

Learn more about place values at:

https://brainly.com/question/25137147

#SPJ1

5 miles each day so 5×7=35 miles a week

The angle indicated by a green arc is 54 degrees.

A straight line's angle size is 180°; the sum of the angles in a triangle's size is 180°; and a triangle can also have acute as well as obtuse angles.

The fact that the sum of the angles in a triangle equals 180 degrees can be used to determine the value of the angle in the given figure.

To begin, note that the angle denoted by a blue arc is the exterior angle of triangle ACD. According to the Exterior Angle Theorem, this angle is equal to the sum of the two remote interior angles, denoted by red and green arcs.

So we have:

The blue arc angle is equal to the sum of the red and green arc angles.

We get the following equation when we plug in the given angle measurements:

98° = 44° + Green arc angle

We can simplify this equation as follows:

Green arc angle = 98° - 44° = 54°

The green arc represents an interior angle of triangle ABD. As a result, we can use the fact that the sum of a triangle's angles equals 180 degrees to calculate the value of this angle.

We currently have:

Green arc angle + 70° + 56° = 180°

We get the following by substituting the value we found for the green arc angle:

54° + 70° + 56° = 180°

We can simplify this equation as follows:

180° - 70° - 56° = 54°

As a result, the angle indicated by a green arc has the value:

It is 54 degrees outside.

To know more about Angle Value visit:

https://brainly.com/question/30937335

#SPJ1

The vertex form of the quadratic equations in standard form are, respectively:

Case 9: y = 2 · (x + 2)² - 12

Case 10: y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11: y = 3 · (x - 4 / 3)² - 16 / 3

Case 12: y = - 3 · (x - 3)²

Case 13: y = (x - 4)² + 3

Case 14: y = (x - 1)² - 7

Case 15: y = (x + 3 / 2)² - 9 / 4

Case 16: 2 · (x + 1 / 4)² - 1 / 8

Case 17: y = 2 · (x - 3)² - 7

Case 18: y = - 2 · (x + 1)² + 10

In this problem we find ten cases of quadratic equation in standard form, whose vertex form can be found by a combination of algebra properties known as completing the square. Completing the square consists in simplifying a part of the quadratic equation into a power of a binomial.

The two forms are introduced below:

Standard form

y = a · x² + b · x + c

Where a, b, c are real coefficients.

Vertex form

y - k = C · (x - h)²

Where:

Now we proceed to determine the vertex form of each quadratic equation:

Case 9

y = 2 · x² + 4 · x - 4

y = 2 · (x² + 2 · x - 2)

y = 2 · (x² + 2 · x + 4) - 12

y = 2 · (x + 2)² - 12

Case 10

y = - (1 / 2) · x² - 3 · x + 3

y = - (1 / 2) · [x² + (3 / 2) · x - 3 / 2]

y = - (1 / 2) · [x² + (3 / 2) · x + 9 / 16] + (1 / 2) · (33 / 16)

y = - (1 / 2) · (x + 3 / 4)² + 33 / 32

Case 11

y = 3 · x² - 8 · x

y = 3 · [x² - (8 / 3) · x]

y = 3 · [x² - (8 / 3) · x + 16 / 9] - 3 · (16 / 9)

y = 3 · (x - 4 / 3)² - 16 / 3

Case 12

y = - 3 · x² + 18 · x - 27

y = - 3 · (x² - 6 · x + 9)

y = - 3 · (x - 3)²

Case 13

y = x² - 8 · x + 19

y = (x² - 8 · x + 16) + 3

y = (x - 4)² + 3

Case 14

y = x² - 2 · x - 6

y = (x² - 2 · x + 1) - 7

y = (x - 1)² - 7

Case 15

y = x² + 3 · x

y = (x² + 3 · x + 9 / 4) - 9 / 4

y = (x + 3 / 2)² - 9 / 4

Case 16

y = 2 · x² + x

y = 2 · [x² + (1 / 2) · x]

y = 2 · [x² + (1 / 2) · x + 1 / 16] - 2 · (1 / 16)

y = 2 · (x + 1 / 4)² - 1 / 8

Case 17

y = 2 · x² - 12 · x + 11

y = 2 · (x² - 6 · x + 9) - 2 · (7 / 2)

y = 2 · (x - 3)² - 7

Case 18

y = - 2 · x² - 4 · x + 8

y = - 2 · (x² + 2 · x - 4)

y = - 2 · (x² + 2 · x + 1) + 2 · 5

y = - 2 · (x + 1)² + 10

To learn more on quadratic equations in vertex form: https://brainly.com/question/29260906

#SPJ1

Answer:

We can solve this expression using the order of operations, also known as PEMDAS:

2 + 77 + 2 + 4 + 18 + (9/4) + 5 + 23 + 78 + 33 - 76 - 4 + 12

First, we can simplify the fraction by adding the whole number and fraction parts:

2 + 77 + 2 + 4 + 18 + 2.25 + 5 + 23 + 78 + 33 - 76 - 4 + 12

Next, we can perform addition and subtraction from left to right:

= 187 + 2.25 + 68

= 257.25

Therefore, the value of the expression 2+77+2+4+18+9/4+5+23+78+33-76-4+12 is 257.25.

LOL the answer is 176.25

Answer:

24x - 6y + 21

Step-by-step explanation:

3( 8x - 2y + 7 )

Multiply each term in the bracket by 3

= (3 x 8x) - ( 3 x 2y) + (3 x 7)

= 24x - 6y + 21

The matching word are as follows:- center of dilation - C,corresponding angles - D,dilation - E,scale factor (of a dilation) - A,similar polygons - B respectively.

Corresponding angles are a pair of angles that have the same relative position at the intersection of two lines when one line is crossed by a transversal.

They are located in corresponding (matching) positions in congruent or similar figures, and are congruent if the figures are similar.

center of dilation: C.The fixed point that is parallel to each point on the pre-image and the corresponding point on the picture during a dilatation

corresponding angles: D.a pair of angles in two congruent or similar figures that are in the same relative position

dilation: E. The transformation in which each point on the image lies on the same line as the corresponding point on pre-image and a fixed point called the center of dilation.

scale factor (of a dilation): in a dilation, the constant  rate between the distance from the center of dilation and a point on the image and the distance from the center of dilation and the  matching point on thepre-image

similar polygons: B.two or  further polygons in which corresponding angles are  harmonious and the lengths of corresponding sides are in proportion.

To know more about scale factor visit:

https://brainly.com/question/30314658

#SPJ1