Describe the transformation

Parent function: f(x) = x^4
Transformed function: g(x) = 5 - x^4

patterns a and d have a constant difference, pattern c has a constant difference, and patterns b, e, and f do not have a constant difference or a constant ratio.

a. The pattern has a constant difference. The first term is 1, the second term is 4, which is 3 more than 1, the third term is 10, which is 6 more than 4, and the fourth term is 19, which is 9 more than 10.

b. The pattern does not have a constant difference or a constant ratio. The differences between consecutive terms are 3, 2, and 4, respectively, which are not constant. The ratios between consecutive terms are 2.5/2, 1.4/2.5, and 11/1.4, respectively, which are also not constant.

c. The pattern has a constant difference. The first term is 3, the second term is 7, which is 4 more than 3, the third term is 13, which is 6 more than 7, and the fourth term is 21, which is 8 more than 13.

d. The pattern has a constant difference. The first term is 12, the second term is 10, which is 2 less than 12, the third term is 6, which is 4 less than 10, and the fourth term is 0, which is 6 less than 6.

e. The pattern does not have a constant difference or a constant ratio. The differences between consecutive terms are 4, 7, and 10, respectively, which are not constant. The ratios between consecutive terms are 2.5/2, 13/2.5, and 23/13, respectively, which are also not constant.

f. The pattern does not have a constant difference or a constant ratio. The differences between consecutive terms are 6, 12, and 18, respectively, which are not constant.

The ratios between consecutive terms are 13/7, 25/13, and 43/25, respectively, which are also not constant.

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The inverse of f(x) is f⁻¹(x) = (x - 3)/3.

To find the inverse of the function f(x), we need to switch the roles of x and y and solve for y.

Given:

f(x) = 3x + 3

Step 1: Replace f(x) with y:

y = 3x + 3

Step 2: Swap x and y:

x = 3y + 3

Step 3: Solve for y:

x - 3 = 3y

3y = x - 3

y = (x - 3)/3

Therefore, the inverse of f(x) is f⁻¹(x) = (x - 3)/3.

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Using a pattern we can find the missing values in the table, these are:

When you look at the table, you can see that for each increase of 1 unit in the value of x, we have an increase of 14 units in the value of y. So we have a really simple pattern:

f(x) = f(x - 1) + 14

Then to get the next values in the table, just add 14 to the previous ones.

A = 42 + 14 = 56

B = 56 + 14 = 70

C = 70 + 14 = 84

Thes are the 3 missing values in the table.

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I recommend use of simple random sampling to determine the three possible toppings to be used for the vegetarian pizza.

It is a sampling technique in which each member of the population has an equal chance of being selected for the sample. Here, the population would be students who regularly eat at the school cafeteria.

By using the sampling, we make sure that each student has an equal chance of being selected to taste test the different pizza toppings. This will help to eliminate bias and provide a representative sample of the population's preferences. They will provide feedback which will be used to determine which topping should be used for the vegetarian pizza.

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if its constant rate or unit rate its just multiple 6 until u get 30

The coefficients and degree of each term are:

Second term:

degree = 4, coefficient = -8

Third term:

degree = 3, coefficient = 6

Fourth term:

degree = 0, coefficient = -1 (constant term)

Fifth term:

degree = 1, coefficient = -1

To find the leading coefficient, degree of the leading term, and degree of the polynomial, we need to identify the term with the highest degree:

The leading term has the highest degree: -8x^4

Leading coefficient = -8

Degree of the leading term = 4

Degree of the polynomial = 4

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The median number of pages of the 9 books that Mary read during the summer reading program is  195 pages .

To find the median number of pages of the 9 books that Mary read during the summer reading program, we first need to arrange the pages in ascending order:

112 pages, 138 pages, 138 pages, 159 pages, 195 pages, 210 pages, 217 pages, 270 pages, 356 pages

The median is the middle value in this ordered list. Since there are an odd number of values, the middle value is the fifth one, which is 195 pages.

The median is a measure of central tendency that divides a dataset into two equal halves. In this case, it represents the number of pages that is halfway between the smallest and largest values. It is a useful measure because it is less affected by outliers or extreme values than the mean.

In Mary's case, the median number of pages of the 9 books she read during the summer reading program is 195 pages. This means that half of the books she read had fewer than 195 pages and half had more than 195 pages. It gives us a good idea of what to expect in terms of the length of the books she read.

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Answer:

-0.91 = strong, as it is close to -1 and if it's close to -1 that means it is linear.

0.82 = strong. Again, it's approaching 1 and is, therefore, approaching linearity.

-0.49 = moderate

0.26= weak

0.54 = moderate

-0.18 = weak

Step-by-step explanation:

Answer:

This quadratic function has no roots.

There are no roots of the quadratic function shown in the graph

We we consider the quadratic equation given be of the form ax^2 + bx + c = 0, then

The quantity b^2 - 4ac is known its discriminant.

The solution contains the term [tex]\sqrt{b^2 - 4ac}[/tex] which will be:

Real and distinct if the discriminant is positive

Real and equal if the discriminant is 0

Non-real and distinct roots if the discriminant is negative

Therefore, it has to be two roots of a quadratic equation always(assuming existence of complex numbers). We say that the considered quadratic equation has 2 solutions if roots are distinct, and have 1 solution when both roots are the same.

Hence, we can conclude that there are no roots. so option D is correct.

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The value of missing side length is, 51.11

We have to given that;

A triangle is shown.

And, To find the missing side of triangle.

Since, An angle is a combination of two rays (half-lines) with a common endpoint. The latter is known as the vertex of the angle and the rays as the sides, sometimes as the legs and sometimes the arms of the angle.

And, A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.

Now, By using trigonometry formula, we get;

⇒ cos 63° = Hypotenuse / Base

⇒ cos 63° = 23 / x

⇒ 0.45 = 23 / x

⇒ x = 23 / 0.45

⇒ x = 51.11

Therefore, The value of missing side in the triangle is,

⇒ x = 51.11

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The solution to the system of equations, using the Gauss-Jordan method, is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&14.28\\0&1&0&-21.4\\0&0&1&1.2\end{array}\right][/tex]

The matrix representing the system of equations is given as follows:

[tex]\left[\begin{array}{cccc}-5&-3&-4&-12\\0&-2&-7&38\\0&1&4&-22\end{array}\right][/tex]

First we want a value of 1 at line 1, column 1, hence we multiply the first line by -1/5, that is:

R1 -> -1/5R1

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&-2&-7&38\\0&1&4&-22\end{array}\right][/tex]

First we want a value of 1 at line 2, column 2, hence we multiply the second line by -1/2, that is:

R2 -> -1/2R2

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&1&4&-22\end{array}\right][/tex]

We want an element of zero at line 3, column 2, hence:

R3 -> R3 - R2

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&0&2.5&-3\end{array}\right][/tex]

First we want a value of 1 at line 3, column 3, hence we multiply the third line by 2.5, that is:

R3 -> 1/2.5R3

Hence:

[tex]\left[\begin{array}{cccc}1&0.6&0.8&2.4\\0&1&1.5&-19\\0&0&1&1.2\end{array}\right][/tex]

Then the solution to the system of equations is given as follows:

Hence the row-echelon form is given as follows:

[tex]\left[\begin{array}{cccc}1&0&0&14.28\\0&1&0&-21.4\\0&0&1&1.2\end{array}\right][/tex]

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Answer:

Step-by-step explanation:

Use Pythagorean Theorem to find the missing hypotenuse x:

The matching choice is C.

Answer:

Initial amount: 934 g

After 80 years: 147 g

Step-by-step explanation:

[tex] A(t) = 934 (\dfrac{1}{2})^\frac{t}{30} [/tex]

The initial amount occurs at t = 0.

[tex] A(0) = 934 (\dfrac{1}{2})^\frac{0}{30} [/tex]

[tex] A(0) = 934 (\dfrac{1}{2})^0 [/tex]

[tex] A(0) = 934 \times 1 [/tex]

[tex] A(0) = 934 [/tex]

After 80 years, t = 80.

[tex] A(80) = 934 (\dfrac{1}{2})^\frac{80}{30} [/tex]

[tex] A(80) = 934 (\dfrac{1}{2})^\frac{8}{3} [/tex]

[tex] A(80) = 934 (0.15749) [/tex]

[tex] A(80) = 147 [/tex]

Since 6 is less than 84, the statement is correct. The roof with dimensions 12 meters by 7 meters is sufficient to accommodate 6 solar panels, each with a width of 1 meter.

To verify Sam's statement, we can calculate whether a roof that is 12 meters long and 7 meters wide can accommodate 6 solar panels, with each panel having a width of 1 meter.

The total area required to install 6 solar panels with a width of 1 meter each is:

6 panels * 1 meter = 6 square meters

Now, let's calculate the area of the roof:

Area of the roof = length * width = 12 meters * 7 meters = 84 square meters

Since the area required for the solar panels is 6 square meters and the area of the roof is 84 square meters, we can determine if the statement is correct.

If 6 square meters is less than or equal to 84 square meters, then the roof is indeed enough to install the 6 solar panels.

6 square meters ≤ 84 square meters.

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Answer:

midsegment = 20

Step-by-step explanation:

the midsegment is half the sum of the bases, that is

midsegment = [tex]\frac{12+28}{2}[/tex] = [tex]\frac{40}{2}[/tex] = 20

3. To find the number of ways to choose the winners, you use combinations.

n = 100 (total number of people)

k = 10 (number of winners to be chosen)

The formula for combinations is:

C(n,k) = n! / (k! * (n-k)!)

Substituting n and k into the formula, we get:

C(100,10) = 100! / (10! * (100-10)!)

We do not need to simplify this expression.

For the club with 30 students, the number of ways to choose the officers is given by permutations because the order in which the officers are chosen matters.

n = 30 (total number of students)

k = 3 (number of officers to be chosen)

The formula for permutations is:

P(n,k) = n! / (n-k)!

Substituting n and k into the formula, we get:

P(30,3) = 30! / (30-3)!

We do not need to simplify this expression.

In the given diagram, the area of the shape is 2π units²

From the question, we are to calculate the area of the given shape.

In the given diagram, the shape is a quadrant.

The area of a quadrant is given by the formula

Area = 1/4 πr²

Where r is the radius

From the given information,

Radius = 8

Thus,

Area of the quadrant = 1/4 × π × 8

Area of the quadrant = 2π units²

OR

Area of the quadrant = 2 × 3.14 units²

Area of the quadrant = 6.28 units²

Hence,

The area of the shape is 2π units² OR 6.28 units².

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If Angle 2 Is-congruent-to Angle 6, then the statement which must be true about Angle 2 is that Angle 2 is supplementary to Angle 8.

We, have,

This refers to the type of angle where two different angles are said to have equal measure on their corresponding sides.

With this in mind, we can see that based on the two horizontal parallel lines are intersected by a third line, there is a third line that intersects the top line and forms four angles.

Hence, if If Angle 2 Is-congruent-to Angle 6, then the statement which must be true about Angle 2 is that Angle 2 is supplementary to Angle 8 because the sum of either angles is 180 degrees.

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complete queston:

Two lines are intersected by a third line.

Two horizontal parallel lines are intersected by a third line. The third line intersects the top line and forms 4 angles. Labeled clockwise, from uppercase left, the angles are 1, 2, 4, 3. The third line intersects the bottom line and forms 4 angles. Labeled clockwise, from uppercase left, the angles are 5, 6, 8, 7.

If Angle2 Is-congruent-to Angle6, which must be true about Angle2?

Angle2 Is-congruent-to Angle5

Angle2 is complementary to Angle5.

mAngle2 = mAngle8

Angle2 is supplementary to Angle8.

[tex] \qquad\longrightarrow \sf f(x) = sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\[/tex]

The Derivative of f(x) with respect to x-

[tex] \qquad\longrightarrow \sf \dfrac{d}{dx} \:sin^{-1} \bigg(\dfrac{x}{2}\bigg)\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x}{2}\bigg)^2}}\;\times \dfrac{d}{dx}\:\dfrac{x}{2}\\[/tex]

[tex]\qquad\sf\because\boxed{\sf{ \: \dfrac{d}{dx} sin^{-1}x = \dfrac{1}{\sqrt{1-x^2}}}}\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \:x^{1-1}\\[/tex]

[tex]\qquad \sf\because\boxed{\sf{ \dfrac{d}{dx }x^n = nx^{n-1}}}\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \times 1\\[/tex]

[tex] \qquad\longrightarrow \sf \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\;\times\dfrac{1}{2} \\[/tex]

[tex] \qquad\longrightarrow \sf\dfrac{1}{2}\: \dfrac{1}{\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}\\[/tex]

[tex] \qquad\longrightarrow \underline{\sf\: \dfrac{1}{2\:\sqrt{1-\bigg(\dfrac{x^2}{4}\bigg)}}}\\[/tex]

Henceforth, Option C) is the correct answer.

Answer:

Not rational

Step-by-step explanation:

A rational number is any integer, fraction, terminating decimal, or repeating decimal.

Anything with a square root is automatically not a rational number.

have a great day and thx for your inquiry :)

The Earth's human population, approximately 7,900,000,000 people, can be expressed using scientific notation as 7.9 x 10^9.

Scientific notation is used to express extremely large numbers using a number between 1 and 10.

In this case, that number is 7.9

We need to move that decimal spot 9 places to the right to get 7,900,000,000. Therfore, to state that number in scientific notation, we would write it as:

7.9 * 10^9

~~~Harsha~~~

Hello !

Answer:

198 apples

Step-by-step explanation:

12 apples <=> 7 pounds of dough

x apples <=> 115 pounds of dough

Let's use a cross product :

[tex]x = \frac{12 \times 115}{7} \approx197.14 [/tex]

198 apples are needed.

Have a nice day

The measure of arc MN is 144 degrees

measure of POQ is 322 degrees

The measure of arc PQ  is 132 degrees

The measure of arc MN is 72×2 = 144 degrees

The measure of arc NQR is 180 degrees

We have to find measure of NQ

First we have to measure of POQ

92+22+POQ=180

POQ=180-114

POQ=66 degrees

Now measure of arc POQ is (95+66)×2 which is 322 degrees

Measure of arc QR is 72×2 = 114 degrees

The measure of MOR is 108×2 =216 degrees

The measure of PQ is 66×2 which is 132 degrees

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Hello !

total = $375,42 + $24,95 = $400,37

in cash = $45

the remaining amount = $400,37 - $45 = $355,37

The equivalent statement using parenthesis using the de Morgan laws would be (not q) or (not p).

De Morgan's Laws. To write an equivalent statement using parentheses for P and not Q (P ∧ ¬Q), we'll apply De Morgan's Law:
De Morgan's Law states that:
1. ¬(P ∧ Q) ≡ ¬P ∨ ¬Q
2. ¬(P ∨ Q) ≡ ¬P ∧ ¬Q
In your case, you have P ∧ ¬Q, which doesn't directly match either of these forms. However, we can manipulate it to apply De Morgan's Law by taking the negation of both sides and then applying De Morgan's Law:
Original statement: P ∧ ¬Q
Negate both sides: ¬(P ∧ ¬Q)
Now, we can apply De Morgan's Law to the negated statement:
¬(P ∧ ¬Q) ≡ ¬P ∨ ¬¬Q
Since ¬¬Q is equivalent to Q, we have:
¬(P ∧ ¬Q) ≡ ¬P ∨ Q
Now we have an equivalent statement with parentheses:
Your answer: ¬(P ∧ ¬Q) ≡ ¬P ∨ Q

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The outcomes in set A U B are 1, 3, 5, 6, 7, 8, 9, 10, 11, 12 (the odd sums) 4, 8, 12 (the sums divisible by 4)

The sum of the number cubes is odd if one die shows an even number and the other shows an odd number, or vice versa.

There are 3 even numbers and 3 odd numbers on a number cube, so there are 3 x 3 = 9 ways to get an odd sum.

The sum of the number cubes is divisible by 4 if both dice show either 2 or 4.

There are 2 ways to get a 2 on a number cube and 2 ways to get a 4, so there are 2 x 2 = 4 ways to get a sum of 4.

Therefore, the outcomes in A U B are 1, 3, 5, 6, 7, 8, 9, 10, 11, 12 (the odd sums) 4, 8, 12 (the sums divisible by 4)

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To have an infinite number of solutions the value of a would be

D. 20

Information given in the problem includes

5(x - 3) + a = 5(x + 1)

To have an infinite number of solutions we can simplify as follows

5(x - 3) + a = 5(x + 1)

opening the parenthesis

5x - 15 + a = 5x + 5

collecting like terms

-15 + a = 5

Adding 15 to both sides, we get:

a = 20

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Answer:8

Step-by-step explanation:

The determinant of the given matrix is -43.

We are given that;

The matrix= 3 2 -2

1 2 4

-1 3 2

Now,

To evaluate the determinant of the matrix

[3  2 -2]

[1  2  4]

[-1 3  2]

you can use the rule of Sarrus. First, you need to copy the first two columns of the matrix and place them next to the third column:

[3  2 -2 | 3  2]

[1  2  4 | 1  2]

[-1 3  2 | -1 3]

Then, you can calculate the sum of the products of the three diagonals going from left to right:

(3 * 2 * 2) + (2 * 4 * -1) + (-2 * 1 * 3) = 12 -8 -6 = -2

and subtract from it the sum of the products of the three diagonals going from right to left:

(-1 * 2 * -1) + (3 * 4 * 3) + (2 * 1 * 2) = 1 +36 +4 =41

-2 -41 = -43.

Therefore, by the matrices the answer will be -43.

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