f(x)=x^2. what is g(x)? NEED ASAP WILL MARK BRAINLIEST

Step-by-step explanation:

By the fundamental theorem of algebra, the degree of the polynomial equals the number of roots (including complex and multiplicities, i.e. multiple roots).

Since n=4, we expect to find 4 roots, although we are only given three, namely -1,3,2+4i.

Fortunately, if the polynomial has real coefficients (which we will ASSUME), for any complex root to exist, its conjugate is also a root to the equation.

Since the conjugate of 2+4i is 2-4i, we now have all four roots, -1, 3, 2+4i, 2-4i.

An n-degree polynomial may be construct by the product of (x-ri) where ri are the roots.  This means

P(x) = (x-(-1))(x-3)(x-2-4i)(x-2+4i), which is

P(x) = (x+1)(x-3)(x-2-4i)(x-2+4i)

When expanded, P(x) = x^4-6x^3+25x^2-28x-60

Check:

sum of roots = (-1+3+2+4i+2-4i) = 6  (same as negative of coefficient of term x^3)  ok

product of roots = (-1)(3)(2+4i)(2-4i)=-3*20 = -60  = constant term,  ok.

Note: kP(x) is also a polynomial with the same four roots, where k=any real number.  P(x) is a particular case where k=1.

The 4th degree polynomial with given zeros -1, 3, and 2+4i, can be derived from these roots and is of the form f(x) = a(x+1)(x-3)(x-2-4i)(x-2+4i). Complex roots always appear in conjugate pairs if the coefficients of the polynomial are real numbers.

The subject of the question is related to the Mathematics of polynomials. Specifically, the question requests the equation of an nth degree polynomial function with n=4 where the zeros include -1, 3, and 2+4i. Given that we have a 4th degree polynomial and we already have 3 roots, we are missing one more. In mathematics, complex roots always come in pairs, so if 2+4i is one of the roots, then its conjugate 2-4i must also be a root.

So, the four roots are: -1, 3, and 2±4i. The polynomial can then be constructed by setting these roots as factors of the polynomial which would then be of the form:

f(x) = a(x+1)(x-3)(x-2-4i)(x-2+4i)

Where 'a' is a constant that will be 1 if the leading coefficient is not specified in the problem.

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Answer:

The correct option is 2.

Step-by-step explanation:

The given inequalities are

[tex]50<2x+10[/tex]             .... (1)

[tex]2x+10<110[/tex]            .... (2)

Solve each inequality.

Subtract 10 from each side of inequality (1).

[tex]50-10<2x+10-10[/tex]

[tex]40<2x[/tex]

Divide both the sides by 2.

[tex]20<x[/tex]

The value of x is more than 20.

Subtract 10 from each side of inequality (2).

[tex]2x+10-10<110-10[/tex]

[tex]2x<100[/tex]

Divide both the sides by 2.

[tex]x<50[/tex]

The value of x is less than 50.

Since x > 20 and x < 50, therefore Malcolm needs to consume more than 20 grams of carbohydrates, but less than 50 grams of carbohydrates.

Hence the correct option is 2.

Answer:

its number 2

Step-by-step explanation:

Possible number of permutaions that the sum is 4 on two fair dice:

1 & 3

2 & 2

3 & 1

There are only 3 ways to make a sum of 4. Each cube has 6 digits. So, 6 x 6 is 36.

Answer: 3/36 or 1/12

Answer:

300 people were satisfied

Step-by-step explanation:

If 85% were unsatisfied, we assume the remaining 15% were satisfied. That percentage of 2000 is ...

0.15×2000 = 300

Answer:

300

Step-by-step explanation:

PLATO

Answer:

for every 1000 there is 1  kilogram so therefore there are 5 kilograms to equal 5000 grams

Step-by-step explanation:

Answer:

5

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

  72 turkeys were bought at $5.11 each for a total cost of $367.92.

Step-by-step explanation:

Trial and error isn't so difficult for this problem. The final price will be an even number of cents. Without those pennies added, the price per turkey must be below an integer number of cents, but within 1/8 cent of that integer number.

For higher first digits of the total cost, the per-turkey cost is more than 3 digits.

For our "good candidate", the per-turkey cost will be $5.11, so the total bill will be $5.11×72 = $367.92  . . . .  matches the required digits.

Answer:

Bob, Jill, Betty, Herb, James

Final answer:

A valid seating arrangement for the five friends is either Bob, Betty, Herb, James, Jill, or Jill, James, Herb, Betty, Bob. Each arrangement adheres to all given conditions: Bob is on an aisle, Betty and Herb are seated together, and James is not sitting next to Jill.

Explanation:

To solve the seating problem for the five friends going to the theater, we must adhere to the conditions: Bob must sit on an aisle, James cannot sit next to Jill, and Betty and Herb want to sit next to each other. Bearing in mind that there's an aisle on either side of the row of five seats, we can begin by placing Bob on an aisle seat since he must sit on one. This can either be the first seat on the left or the right. Since James doesn't want to sit next to Jill, we can't place Jill next to Bob if we sit James on the other end to maximize distance between them. Betty and Herb must sit together, which can only happen in the three seats left in the middle.

Here is a seating arrangement that satisfies all conditions: Bob, Betty, Herb, James, Jill. In this arrangement, Bob is on an aisle, Betty and Herb are seated together, and James is not sitting next to Jill.

Alternatively, if we place Bob on the other aisle, we get: Jill, James, Herb, Betty, Bob. Again, all conditions are met. Bob is on an aisle, Betty and Herb are sitting together, and James is not sitting next to Jill.

Answer:

C

Step-by-step explanation:

Step 1: find BC

Given Triangles ABC and ADE are similar,

[tex]\frac{AB}{AD}[/tex] = [tex]\frac{BC}{DE}[/tex]

BC = [tex]\frac{AB}{AD}[/tex] x DE

= [tex]\frac{8}{8 + 4}[/tex] x 9

= 6 cm

Step 2: use Pythagorean theorem to find AC and / or AE

Consider triangle ABC,

by Pythagorean theorem,

AB² + BC² = AC²

AC² = 6² + 8² = 100

AC = √100 = 10 (answer... we can see that C is the only one with AC=10.

Step 3: Verify.. even though we know that it is C because AC  = 10,  you can verify that the ansewer is correct by finding CE and confirming that CE=5

By using similar triangles ABC and ADE,

AC/AE = AB / AD

AE = AD/AB x AC = 12/8 x 10 = 15

CE = AE - AC = 15 - 10 = 5 (answer confirmed)

Answer:

  {12, 13}

Step-by-step explanation:

Whole numbers that round to 50 will be in the range 45 to 54. Multiples of 4 in that range are 48 and 52.

  48 = 4·12

  52 = 4·13

Dev's number could be either 12 or 13.

Step-by-step explanation:

-4(27)+100

-108+100

=-8

To find the 27th term in the sequence defined by the formula an = -4n + 100, you substitute 27 for 'n' in the equation. The yielded result is -8, which is the 27th term in the sequence.

In Mathematics, a sequence can be defined by an equation, where each term an is defined in terms of its place in the sequence ('n'). In the given equation, an = -4n + 100,  the nth term is determined by multiplying 'n' by -4 and then adding 100. If we want to find the 27th term of the sequence, we substitute n with 27 in the equation.

So, a27 = -4(27) + 100 = -108 + 100 = -8.

Therefore, the 27th term of the sequence is -8.

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Answer:

131

Step-by-step explanation:

We need to find the area of the top of the pie that is leftover. To do this, we use the formula for the area of a circle and multiply by 0.65 since that is how much of the pie is left.

A = 0.65π[tex]r^{2}[/tex] = 0.65π[tex]8^{2}[/tex] = 130.69025 [tex]in^{2}[/tex]

If each strip of dough is 1 square inch, the total strips of dough needed is 131.

The total strips of dough needed is 131 if Sherrie is baking a pie for her family. she leaves the room and comes back to 35% of the pie.

It is described as a set of points, where each point is at the same distance from a fixed point (called the center of a circle)

We have:

Sherrie is baking a pie for her family. she leaves the room and comes back to 35% of the pie having been eaten before she can put the topping on.

Area of circle:

A = 0.65πr² = 0.65π(8)²

A =  130.69025 square inches ≈ 131 square inches

If each strip of dough is 1 square inch

The total strips of dough needed = 131/1 = 131

Thus, the total strips of dough needed is 131 if Sherrie is baking a pie for her family. she leaves the room and comes back to 35% of the pie.

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Answer:

C) -9.6

Step-by-step explanation:

1) The answer will be negative because a negative divided my a positive will always be negative and visa-versa.

2) 5 goes into 48 9 times; 5(9) = 45

3) 5 cannot go into 3 so add a 0 to make 30 and place a decimal after -9

4) 5 can go into 30 6 times; 5(6) = 30

5) The remainder is 0 and your answer is C. -9.6

Answer:

Option B

Step-by-step explanation:

Plot points A, B, C and line y=x on the coordinate plane (see attached diagram, blue points)

1. The reflection across the line y=x has the rule

(x,y)→(y,x)

So,

Points A', B', C' are marked in red on the diagram

2. The rotation by 90° clockwise about the origin has the rule

(x,y)→(-y,x)

So,

Answer:

A (−7, −13) → A ′(−13, −7) → A ″(7, −13);

B (12, −8) → B ′(−8, 12) → B ″(−12, −8);

C (−17, 19) → C ′(19, −17) → C ″(17, 19)

Step-by-step explanation

The coordinates of the vertices of the preimage are given.

To find the image as it reflected from the preimage across the y=x line, use the transformation rule: (x,y)→(y,x).

Apply the transformation rule to vertices A(−7,−13), B(12,−8), and C(−17,19).

A(−7,−13)→A'(−13,−7).

B(12,−8)→B'(−8,12).

C(−17,19)→C'(19,−17).

To determine the vertices of the image after the rotation of 90∘ about the origin, use the rule: (x,y)→(−y,x).

Apply the rotation rule to the vertices of △A'B'C'.

A'(−13,−7)→A''(7,−13).

B'(−8,12)→B''(−12,−8).

C'(19,−17)→C''(17,19).

Therefore,

A(−7,−13)→A'(−13,−7)→A''(7,−13)

B(12,−8)→B'(−8,12)→B''(−12,−8)

C(−17,19)→C'(19,−17)→C''(17,19)

represents the reflection of △ABC across the line y=x and its rotation of 90∘ about the origin.

Answer:

14.18 units  &  4.88 units

Step-by-step explanation:

The right triangle in this problem is shown in the attached image.

Using trigonometry, the adjacent leg would be 15 Cos 19°

and the opposite leg would be 15 Sin 19°

Thus,

one leg is 15 Cos 19 = 14.18 units, and

another leg is 15 Sin 19 = 4.88 units

Answer:

For plato users the correct option is D.

Step-by-step explanation:

D. 4.9 units, 14.2 units

Answer:

d 38 months

Step-by-step explanation:

Answer:

The correct answer is D. 38 months

Step-by-step explanation:

Abby took out a car loan with monthly payments over 5 years. Each year has 12 months. So the total number of payments will be 5 (years) multiplied by 12 (months).

x=5*12=60 months

The first 22 months are without interest, so the months that have interest are the rest of then.

x'= 60-22= 38 months

OK, f is the graph and g is the table.

f(-2) > g(-2)

f(-2) means the y coordinate of the graph when x=-2.  That's y=2, so f(-2)=2

g(-2) we look up in the table, g(-2)=1

So it's true that f(-2) > g(-2)

Answer: f(-2) > g(-2)   TRUE

-----

The characteristic of an absolute value function, possibly shifted and scaled, is the distinct V shape.   Clearly f is an absolute value function; the slopes are -1 and 1 and the vertex is at (-3,1) so f(x) = |x+3|+1

g kinda also has the characteristic V shape, but it has a slope of -3  in one place and -1 in the other, so it isn't a straight line.

Answer: f(x) and g(x) are absolute value functions.   FALSE

-----

For all x, f(x) > g(x)

Presumably this means for all x in g's domain, which is only five points.  We already checked x=-2; let's do the rest.

f(-5) = 3, g(-5) = 4

So at x=-5 it's not true

For all x, f(x) > g(x)   FALSE

-----

f(x) and g(x) intersect at exactly two points.

We already know they don't at x=-5 and x=-2.  Let's check the other three.

f(-5) = 3, g(-5) = 4

f(-4) = 2,  g(-4)=1

f(-3) = 1, g(-3) = 0

f(-2) = 2, g(-2) = 1

f(-1) = 3, g(-1) = 4

This one's tricky.   All we really know about g is the points listed.   g may be a parabola where the function is continuous between the table points.   If that's true the functions intersect at exactly two points.  We don't really know that for sure so I'll go with:

Answer: f(x) and g(x) intersect at exactly two points.  FALSE

I may be marked wrong on this last one but I'm sticking with my answer.

Answer:

A and D are both true.

Step-by-step explanation:

f(x) is a quadratic. It is the graph in red. Its equation is y = (x + 3)^2

g(x) is an absolute value formula. It is the graph in blue. Its equation is y=abs(x + 3) + 1

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

The last statement is correct. The two figures cross at (-1.382,2.618) and (-4.618, 2.618) so D is true. But don't stop reading. You'll learn much from this question.

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

From the right intersect point to the left intersect point, the blue graph is greater than the red one. C is false. Remember the red graph is f(x)

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

B is false. g(x) is a quadratic

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

Unfortunately I'm getting that A is true

f(-2) = 2 and

g(-2) = 1

Answer:551.25

Step-by-step explanation:

500 x .05 =25+500= 525 which is the second concert. Multiply that by .05 which is 26.25, add that to 525 to get 551.25 which is not 650.

Answer:

1/6

Step-by-step explanation:

landing on heads is a 1/2% and landing on a 3 or 4 is a 1/3 then multiply together

Answer:

Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30

When x disappears from the equation and the two sides of the equation not equal each other , then the equation has no solution

When x disappears from the equation and the two sides of the equation equal each other , then the equation has infinite solutions

Step-by-step explanation:

* Lets read the problem and solve it

- There are three sisters ⇒ Maggie , Karen , Jasmine

- Each sister bought a gift for their mom

- Maggie spent 3 times as much as Karen

- Karen spent half as much as Jasmine

- Altogether, they spent $60

- Let Jasmine spent x

∵ Karen spent half as much as Jasmine

∴ Karen spent 1/2 x

∵ Maggie spent 3 times as much as Karen

∴ Maggie spent 3 × 1/2 x = 3/2 x

∵ Altogether, they spent $60

∴ x + 1/2 x + 3/2 x = 60

∴ 3x = 60 ⇒ divide both sides by 3

∴ x = 20

* Lets find the share of each one

∵ Jasmine spent x

∴ Jasmine spent $20

∵ Karen spent 1/2 x

∴ Karen spent 1/2 × 20 = $10

∵ Maggie spent 3/2 x

∴ Maggie spent 3/2 x 20 = $30

* Karen spent $ 10 , Jasmine spent $20 , Maggie spent $30

* Lets describe what happens when an equation has no solution

- "No solution" means that there are no values of x satisfy the equation

- When x disappears from the equation and the two sides of the

 equation not equal each other , then the equation has no solution

- Ex: solve the equation 2 + 2x – 8 = 7x + 5 – 5x

∵ 12 + 2x – 8 = 7x + 5 – 5x ⇒ add the like terms

∴ 4 + 2x = 2x + 5 ⇒ subtract 2x from both sides

∴ 4 = 5 ⇒ the two sides not equal

∴ There is no value of x satisfy this equation

∴ There is no solution

* Lets describe what happens when an equation has infinite solutions

- "Infinite solutions" means all numbers are solutions.

- When x disappears from the equation and the two sides of the

 equation equal each other , then the equation has infinite solutions

- Ex: solve the equation 2x + 3 = x + x + 3

∵ 2x + 3 = x + x + 3 ⇒ add the like terms

∴ 2x + 3 = 2x + 3 ⇒ subtract 2x from both sides

∴ 3 = 3 ⇒ the two sides are equal

∴ All values of x satisfy the equation

∴ There are infinite solutions

Answer:

88

Step-by-step explanation:

Nine innings have a mean of 58 runs, and the tenth inning will have x runs.  So the overall mean is:

μ = (9×58 + x) / 10

We want the mean to be 61, so:

61 = (9×58 + x) / 10

610 = 522 + x

x = 88

The cricketer must score 88 runs to raise the mean to 61.

Answer:

An estimate of a population parameter that provides an interval of values

believed to contain the value of the parameter is known as the inveral estimate.

Step-by-step explanation:

Therefore, the correct answer C.

* Hopefully this helps:)) Mark me the brainliest :))

Answer:

11,394  years old

Step-by-step explanation:

The equation looks like this:

[tex]N=N_{0}e^{kt}[/tex]

The only thing left up to us is to decide what value should go in for N.  Since we are told that 32% of the original amount is what the hiker finds, we are operating in percentages.  Before any decomposition took place, the amount of skull was 100%.  Filling in now we have:

[tex]100=32e^{.0001t}[/tex]

Divide both sides by 32 to get

[tex]3.125=e^{.0001t}[/tex]

In order to get that t out of the exponential position that it is currently in, we will take the natural log of both sides, since a natural log "undoes" an e (that is because the base of a natural log is e).  Taking the ln of both sides and utilizing that rule for natural logs and e's gives us:

ln(3.125) = .0001t

Divide both sides by .0001 to get that

t = 11,394 years

Answer:

Q'(0.4,-1.7),R'(2.4,9.3), S'(-10.6,7.3)

Step-by-step explanation:

we know that

The rule of the translation is equal to

(x,y) -----> (x-7.6,y+4.3)

That means---> the translation is 7.6 units left and 4.3 units up

Find the coordinates of the vertices of the image

Q(8,-6) -----> Q'(8-7.6,-6+4.3)

Q(8,-6) -----> Q'(0.4,-1.7)

R(10,5) -----> R'(10-7.6,5+4.3)

R(10,5) -----> R'(2.4,9.3)

S(-3,3) -----> S'(-3-7.6,3+4.3)

S(-3,3) -----> S'(-10.6,7.3)

The coordinates of the vertices Q, R, and S of the image of the triangle after a translation are (0.4, -1.7), (2.4, 9.3), and (-10.6, 7.3)

Translation is a way of changing the location of an object on the xy plane.

Given the vertices of the triangle QRS as

Q(8, –6)

R(10, 5)

S(–3, 3)

If the coordinate of the vertices is translated under the rule (x–7.6, y+4.3)

For Q'

Q' = (8-7.6, -6+4.3)

Q' = (0.4, -1.7)

For R':

Q' = (10-7.6, 5+4.3)

Q' = (2.4, 9.3)

For the coordinate S'

S' = (-3-7.6, 3+4.3)

S' = (-10.6, 7.3)

Hence the coordinates of the vertices Q, R, and S of the image of the triangle after a translation are (0.4, -1.7), (2.4, 9.3), and (-10.6, 7.3)

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The translation could result in:

Translation--

It is  a transformation which changes the location of the figure but the shape and size of the figures remains the same i.e. the shape and size of the figure is retained after the transformation.

It either moves the figure up or down by some units.

i.e. f(x) → f(x)+k

then the graph of the function f(x) is shifted k units up is k>0

and k units down if k<0

Similarly it may shift the figure k units to the left or to the right.

i.e. if f(x) → f(x+k)

if k<0 then the function f(x) is shifted k units to the right.

and if k>0 then the function is shifted k units to the left.

Options B, D, and E are correct. A translation could result in a figure moving up, down, and left or right.

Translation in geometry refers to moving a figure from one location to another without changing its shape, size, or orientation. It involves sliding the figure over a plane.

Let's analyze each option:

A. "A figure getting smaller" suggests a transformation involving a reduction in size or being scaled down.

B. "A figure moving up" implies a vertical translation, where the figure is shifting in the upward direction.

C. "A figure flipping upside down" suggests a reflection transformation rather than a translation. It involves a change in orientation rather than a shift in position.

D. "A figure moving left" indicates a horizontal translation, where the figure is shifting to the left.

E. "A figure moving down" signifies a vertical translation, where the figure is shifting in the downward direction.

Based on the given options, a translation can result in:

B. a figure moving up

D. a figure moving left

E. a figure moving down

Translations do not result in a figure getting smaller (Option A) or flipping upside down (Option C).

Complete question:

Which could a translation result in? Select all that apply.

A. a figure getting smaller

B. a figure moving up

C. a figure flipping upside down

D. a figure moving left

E. a figure moving down

Answer:

x^(7/5)

Step-by-step explanation:

Root goes on bottom of fraction

Power goes on top

x^(7/5)

Answer:

[tex]x^{\frac{7}{5}}[/tex]

Step-by-step explanation:

Rewrite the radical expression as an expression with rational exponents.

fifth root of x to the power of 7

[tex]\sqrt[5]{x^7}[/tex]

To write the given expression with radical exponent we use the rule

[tex]\sqrt[n]{a^m}=a^{\frac{m}{n}}[/tex]

Move the index n to the denominator of exponent

[tex]\sqrt[5]{x^7}=x^{\frac{7}{5}}[/tex]

Expression with rational exponent is [tex]x^{\frac{7}{5}}[/tex]

Let x = legs of right triangle.

The set up would be:

x^2 + x^2 = (hypotenuse)^2

Understand?

To find the legs of a right triangle with only the hypotenuse known, the Pythagorean theorem is used. Without extra information like an angle or one leg length, it's impossible to find the specific leg lengths due to the infinite possibilities of right triangle configurations with the same hypotenuse length.

The question involves finding the lengths of the legs of a right triangle when only the length of the hypotenuse is known. Utilizing the Pythagorean theorem, which states that in a right triangle the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b), expressed as a² + b² = c². To find the lengths of the legs (a and b) given the hypotenuse (c), one needs additional information such as the angle of the triangle or the length of one of the legs.

Without such information, it is not possible to determine the specific lengths of the legs because there are infinitely many right triangles with different sets of leg lengths that could have the same hypotenuse length. Therefore, to address this problem, one might use trigonometry if any angle is known, or apply other relevant context or given data.

Answer:

1/8

Step-by-step explanation:

There's two ways you can solve this.

Method 1: Let's say you grab the socks one at a time.  The first sock you grab has a 6/16 probability of being red.  If the sock is red, then the second sock you grab has a 5/15 probability of being red, because there's one less red sock and one less sock total.  So the overall probability is:

P = 6/16 × 5/15 = 1/8

Method 2: There are ₆C₂ ways to choose 2 red socks from 6 red socks.  There are ₁₆C₂ ways to choose any 2 socks from all 16 socks.  So the probability that both socks you choose are red is:

P = ₆C₂ / ₁₆C₂ = 15 / 120 = 1/8

The probability that both socks are red is 1/8 if the drawer contains 6 red socks and 10 blue socks

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We have:

Total number of socks= 6+10 = 16

Total ways of selecting = C(16, 2) = 120

Ways of selecting 2 red socks from 6 = C(6, 2) = 15

The probability = 15/120 = 1/8

Thus, the probability that both socks are red is 1/8 if the drawer contains 6 red socks and 10 blue socks

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Answer:

55 small boxes, 65 large boxes.

Step-by-step explanation:

First, we let x = the amount of big boxes and let y = the amount small boxes. Then, we know that any combination of such will equal 120 so we say

x + y = 120

We also know that we have to fill 4900 pounds, so we can say

50x + 30y = 4900

Then, we can use either substitution or elimination. I'll do substitution. we make the first equation

x = 120 - y

And now we can plug this into our second equation

50(120 - y) + 30y = 4900

Then we distrubute

6000 - 50y + 30y = 4900

Then simplify

6000 - 20y = 4900

Subtract 6000 from both sides

-20y = -1100

then divide both sides by -20

y = 55

so there are 55 small boxes, which means we can subtract 55 from 120 to get 65 large boxes.

The truck is carrying 65 large boxes and 55 small boxes,

x + y = 120 (total number of boxes)

50x + 30y = 4900 (total weight of the boxes in pounds)

First, we can solve one of the equations for one variable and then substitute that into the other equation. Starting with the first equation:

x = 120 - y

Now substitute x in the second equation:

50(120 - y) + 30y = 4900

6000 - 50y + 30y = 4900

-20y = -1100

y = 55

Now we know there are 55 small boxes, we can go back to the first equation to find x:

x + 55 = 120

x = 120 - 55

x = 65

Therefore, the truck is carrying 65 large boxes and 55 small boxes.

Answer:

8

Step-by-step explanation:

Because if you do 15•8•8 then it equals 960 and the formula for volume is l•w•h