Expand the following quadratic to standard form.
y=(x-2)^2+6

Answer: b. 1923

Step-by-step explanation:

Answer:

(2,1) , (-4,-17)

x  = 2  ,  y =  1

x =  − 4  ,  y =  −  17

Answer:

input = 6 leads to output = 15

input = 9 leads to output = 21

==================================================

Explanation:

If the input is x = 6, then,

y = 2x+3

y = 2(6)+3

y = 12+3

y = 15 is the output

Repeat those steps for x = 9

y = 2x+3

y = 2(9)+3

y = 18+3

y = 21 is the output

Answer:

She needed 3,000

Step-by-step explanation:

65% of the total amount= 1950

0.65x = 1950

x=3,000

Hope it helps :)

Answer:

The equation of the line with a slope of 3 that passes through (-4,-7) is;

Explanation:

We want find the equation of the line with;

Using the point slope form of linear equation;

substituting the given values into the equation above we have;

Above is a point slope form of the equation.

solving further we have;

The equation of the line with a slope of 3 that passes through (-4,-7) is;

Answer:

x = 3

Step-by-step explanation:

10 + 2(7 - 9x) = 5(2x - 12)

10 + 14 - 18x = 10x - 60

24 - 18x = 10x - 60

+60                 +60

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

84 - 18x = 10x

     +18x    +18x

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

84 = 28x

/28    /28

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

3 = x

Answer:

x = 3

Step-by-step explanation:

Do multiplication for the parenthesis terms, then add and subtract accordingly.

Answer:

a) Non car si le fils a 10 ans la mère a 30 ans et le père 33 or 10+30+33=73

b) Oui car si le fils a 12 ans la mère a 36 ans et le père 39 et 12+36+39=87

Step-by-step explanation:

The value of the function g o f (x) will be;

⇒  (2x + 3) / 4

What is Function?

A relation between a set of inputs having one output each is called a function.

Given that;

The value of the function are;

f (x) = 2x + 3

And, g (x) = x / 4

Now,

The value of composite function is,

g o f (x) = g ( f(x) )

           = g (2x + 3)

           = (2x + 3) / 4

So, g o f (x) = (2x + 3) / 4

Thus, The value of the function g o f (x) will be;

⇒  (2x + 3) / 4

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Answer:

town b

Step-by-step explanation:

-3.33 degrees is smaller than 2/5 of 1.00 because 2/5 is 0.4 so -3.4 degrees is colder than -3.33.

Answer:

m  =  12

Step-by-step explanation:

2m − 44 = 76 − 8m

Move all terms containing m to the left side of the equation

10m − 44 = 76

Add 44 to both sides of the equation

10m = 120

Divide each term by 10 and simplify.

10m/10  = 120/10

m  =  12

Answer:

\(\boxed{m = 12}\)

Step-by-step explanation:

\(2m-44=76-8m\)

Simplify both sides of the equation.

\(2m + -44 = 76 + -8m\)

\(2m - 44 = -8m + 76\)

Add 8m to both sides.

\(2m - 44 + 8m = -8m + 76 + 8m\)

\(10m - 44 = 76\)

Add 44 to both sides.

\(10m - 44 + 44 = 76 + 44\)

\(10m = 120\)

Divide both sides by 10.

\(\frac{10m}{10} = \frac{120}{10}\)

\(m= 12\)

Hope this helped you!

Triangle N P O is shown. Line O N extends through point M to form exterior angle P N M. The statement that is true is x > 38.

Since the sum of the measures of the lines of angles in a triangle is 180 degrees, we have:

angle NPO + angle PON + angle ONP = 180

Substituting the given values, we get:

38 + 39 + angle PNM = 180

Simplifying, we have:

angle PNM = 103

Therefore, the statement that is true about the value of x is as per the given triangle: x > 38.

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The set of all 2×3 matrices with entries from ℝ, where each row of entries sums to zero, is indeed a vector space.

To determine if the set of 2×3 matrices with entries from ℝ, where each row sums to zero, forms a vector space, we need to verify if it satisfies the necessary properties of a vector space. These properties include closure under addition and scalar multiplication, associativity, commutativity, existence of a zero vector, existence of additive inverses, and distributive properties.

To check closure under addition, we need to ensure that the sum of any two matrices from the given set is also a matrix in the set. Let's take two arbitrary matrices A and B from the set. Each row of A and B sums to zero. Now, when we add corresponding entries of A and B, the resulting matrix C will also have rows that sum to zero. Thus, the set is closed under addition.

For closure under scalar multiplication, we need to verify that multiplying any matrix from the set by a scalar also produces a matrix within the set. Let's consider an arbitrary matrix A from the set and a scalar c from ℝ. When we multiply each entry of A by c, the resulting matrix cA will also have rows that sum to zero. Therefore, the set is closed under scalar multiplication.

Matrix addition is associative, meaning that for any matrices A, B, and C in the set, (A + B) + C = A + (B + C). This property holds true for matrices in this set since addition of matrices follows the same rules regardless of their row sums.

Matrix addition is commutative, meaning that for any matrices A and B in the set, A + B = B + A. This property also holds true for matrices in this set because the order of addition does not affect the row sums of the resulting matrix.

A zero vector is an element of the set that when added to any other matrix in the set, leaves the other matrix unchanged. In this case, the zero vector is a 2×3 matrix with all entries equal to zero. When we add this zero matrix to any other matrix in the set, the resulting matrix still has rows that sum to zero. Hence, the set contains a zero vector.

For every matrix A in the set, there must exist an additive inverse -A in the set such that A + (-A) = 0. Since each row of A sums to zero, the additive inverse -A will also have rows that sum to zero. Therefore, the set contains additive inverses.

The set needs to satisfy the distributive properties of scalar multiplication over addition and scalar multiplication over scalar addition. These properties hold true for matrices in this set, as the row sums are preserved when performing these operations.

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The answer is that the director can fill the positions in 5040 ways.

A personnel director for a corporation has hired 10 new engineers. If four distinctly different positions are open at a particular plant, in how many ways can the director fill the positions?

The answer is that the director can fill the positions in 5040 ways.

First, let's find out how many ways there are to choose four distinct positions out of the ten engineers. This is a combination problem, so we can use the formula nCr (n choose r), where n is the total number of items and r is the number of items being chosen:

nCr = n! / r!(n-r)!

In this case, n = 10 and r = 4, so:

nCr = 10! / 4!(10-4)! = 10! / 4!6! = (10 x 9 x 8 x 7) / (4 x 3 x 2 x 1) = 210

Now, for each of these combinations of positions, there are 10 x 9 x 8 x 7 ways to choose one engineer for each of the four positions.

This is a permutation problem, so we can use the formula nPr (n permute r), where n is the total number of items and r is the number of items being chosen:

nPr = n! / (n-r)!

In this case, n = 10 and r = 4, so:

nPr = 10! / 6! = 10 x 9 x 8 x 7 = 5040

Therefore, the director can fill the positions in 5040 ways.

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The z test statistic needed for this hypothesis test is 0.75 .

Z test is a statistical test that is conducted on data that approximately follows a normal distribution. The z test can be performed on one sample, two samples, or on proportions for hypothesis testing. It checks if the means of two large samples are different or not when the population variance is known.

NOW,

sample proportion =  p = x / n = 0.23

Test statistics

z = ( p - p0 ) / \(\sqrt{ p0*(1-p0)}\) / n

= ( 0.23 - 0.20) /  \(\sqrt{ (0.20*0.80) / 100}\)

= 0.75

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A check or quadrangle is defined by the intersection of pairs of diagonals of a parallelogram.

A parallelogram is a quadrilateral with two pairs of parallel sides. In a parallelogram, the opposite sides are parallel and have the same length. The opposite angles of a parallelogram are equal. A parallelogram is a unique type of quadrilateral with specific characteristics.

A quadrangle or check is defined as the intersection of pairs of diagonals of a parallelogram. In other words, it is the area inside the parallelogram that is divided into four triangles, each of which shares a common vertex in the center of the parallelogram.

The diagonals of a parallelogram are the line segments that connect the opposite vertices of a parallelogram. When these diagonals intersect, they form four triangles, which are also known as the parallelogram's "sub-triangles." The point where the diagonals intersect is called the center of the parallelogram, and it divides each diagonal into two equal parts.

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A/an database schema diagram can be used to show how the tables in a database are defined and related.

This type of diagram provides a visual representation of the structure and organization of the database. It illustrates the tables ,and  their attributes, and the relationships between them.

The database schema diagram helps in the  understanding the logical design of the database, including primary keys, for  foreign keys, and the connections between different tables. It allows developers, database administrators, and stakeholders to visualize the database structure and serves it as a reference for in  designing, modifying, and querying the database effectively.

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Answer:

Convert to decimals:

1.5 and 0.75

Then, set up a proportion

1.5/0.75=x/1

proportion x/y=x/y

since the 3/4 and 1 are the same topic ( the room) we put them together.

Solve: 1.5/0.75=x

x=2

So 2 gallons

Hope this helps plz hit the crown :D

Let's say that the cost of each postcard is "p".

We can write the equation as follows:

7p + 15.89 = 19.32

If we solve for "p", we get:

7p = 19.32 - 15.89

p = 3.43 / 7

p = $<<3.43/7=0.49>>0.49

Therefore, each postcard costs $0.49.

Answer

The answer is B

Answer:

Ok

Step-by-step explanation:

Answer:

A. -259

B. inverse function is 1/2 √(-x-3)

Step-by-step explanation:

Here, we want to find f(8)

Simply substitute x = 8 in the equation.

The equation is

f(x) = -4x^2 -3

So f(8) = -4(8)^2-3

f(8) = -256-3

f(8) = -259

Inverse of f(x) = -4x^2 -3

Simply equate this to m

m = -4x^2-3

-4x^2 = m + 3

x^2 = (m + 3)/-4

x^2 = -m/4 -3/4

x = √(-m-3)/4

x = 1/2√(-m-3)

Put back the value of x for m

x = 1/2 √(-x-3)

a. All real zeros of the polynomial function is t = 0, ±\(\sqrt{7}\)

b. Smallest t value is -\(\sqrt{7}\), t is 0 and Largest t value is \(\sqrt{7}\).

c. The maximum possible number of tuning points of the graph of the function is 4.

Given that,

The function is g(t) = t⁵ − 14t³ + 49t

a. We have to find all real zeros of the polynomial function.

t(t⁴ - 14t² + 49) = 0

t(t⁴ - 2×7×t² + 7²) = 0

t(t² - 7)² = 0

t = 0, and

t² - 7 = 0

t = ±\(\sqrt{7}\)

Therefore, All real zeros of the polynomial function is t = 0, ±\(\sqrt{7}\)

b. We have to determine whether the multiplicity of each zero is even or odd.

Smallest t value : -\(\sqrt{7}\)(multiplicity = 2)

                       t  : 0 (multiplicity = 1)

Largest t value : \(\sqrt{7}\)(multiplicity = 2)

Therefore, Smallest t value is -\(\sqrt{7}\), t is 0 and Largest t value is \(\sqrt{7}\).

c. We have to determine the maximum possible number of tuning points of the graph of the function.

Number of turning points = degree of polynomial - 1

= 5 - 1

= 4

Therefore, The maximum possible number of tuning points of the graph of the function is 4.

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Answer:

D

Step-by-step explanation:

We want to prove that ΔMNP is similar to ΔRSP using Angle-Angle Similarly.

First, we already have one congruent angle, ∠P.. So, we will need to acquire another angle. We can see that we either need to know one of two things: 1) ∠NMP and ∠SRP are congruent or 2), ∠MNP or ∠RSP are congruent.

So, we can eliminate choices A, B, and C. Knowing any one of the specific angles won't give us the value of the other, corresponding angle.

Therefore, the correct answer is D. If MN is parallel to SR, then we will have two parallel cut be a traversal NP or MP.

Then by the corresponding angles theorem, ∠NMP and ∠SRP are congruent and/or ∠MNP or ∠RSP are congruent.

The forecast for May using a five-month moving average is 39 (Option E).

Moving average is used for smoothing out time series data to find any trends or cycles within the data. A five-month moving average is the average of the past five months. To calculate the moving average, add up the sales for the previous five months and divide it by five.

According to the question, the sales for the previous five months are: Nov. 39 Dec. 27 Jan. 40 Feb. 42 Mar. 41 April 47

We have to add the sales of these five months, which gives:

27 + 40 + 42 + 41 + 47 = 197

To find the moving average for May, we divide this sum by 5:

197 / 5 = 39.4

Since we have to round the answer to the nearest whole number, we round 39.4 to 39, which is option E.

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In Animal Farm, Boxer, many piglets, hens, and a lot of other nameless creatures all perish under Napoleon's tyranny.

The framework, the structure, within which a story is produced, is known as the plot of a story. It almost acts as the blueprint for how all the many parts of a literary work fit together to form a finished product. The five elements that make up a story's plot are as follows: the introduction, also known as exposition, in which the reader is given background information on the narrative's characters and setting as well as other essential details.

The three main parts of a story are the rising action, the climax, and the falling action. The rising action is when the writer builds up the information and develops the story to lead the reader to the story's crucial point. The climax is essentially the heart of the story and the point at which the action reaches its highest pitch. To prepare for the story's conclusion, the loose ends also start to be tied off. The conclusion of the story, or resolution, comes last.

Boxer is now known as the most pitiful of Orwell's characters because of his death in this chapter. Napoleon has completely brainwashed him; as a result, he lives (and dies) for the benefit of the farm, whose boss sells him to a knacker as soon as he becomes unfit for labor.

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Answer: I think the answer is 84

Step-by-step explanation: I just did 3×28

Emily can't get an A in the class, even if she gets an A on the last exam. This expectancy theory might explain.

Expectancy theory suggests that indivisuals are motivated to perform if they know that their extra performance is recognized and rewarded. Consequently companies using performance-based pay can expect improvements.

Expectancy theory explains the process of why someone chooses one behavior over another. In making this conclusion choice, there are three elements considered: expectancy, instrumentality and valence.

Expectancy is the belief that your effort will lead to better performance.

Instrumentality is the trust that if you perform well you will achieve the outcome you expect.

Valence is the how important you feel the outcome, and any related reward is to you personally.

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\({ \qquad\qquad\huge\underline{{\sf Answer}}} \)

In the first sequence,

let's take ratio of the next term with its preceding term, so we will get the common ratio ~

\(\qquad \sf  \dashrightarrow \: \cfrac{4}{16} = \dfrac{1}{4} \)

So, we can imply that The next term of the sequence is 1/4 times the previous term.

hence, the unknown term will be 1/4 times of previous term.

Therefore, the next term here is 1

In the second sequence,

Do the same procedure as above, we will get common ratio as :

\(\qquad \sf  \dashrightarrow \: \cfrac{18}{6} = 3\)

So, the next term is 3 times the preceding term, that is :

Therefore, the next term is 162