Please help me solve this

Answer:

  p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90

Step-by-step explanation:

Assuming the desired polynomial has real and rational coefficients, each of the complex and irrational roots has a corresponding conjugate. That is, the roots of p(x) must include ...

  {3, 2 -i, 2 +i, √3, -√3}

Each of these roots corresponds to a linear factor. Root p corresponds to factor (x -p), for example.

__

Then the factored p(x) will be ...

  p(x) = k(x -3)(x -(2 -i))(x -(2 +i))(x -√3)(x +√3) . . . . for some scale factor k

Simplifying a bit, we have ...

  p(x) = k(x -3)((x -2)² +1)(x² -3) = k(x -3)(x² -4x +5)(x² -3)

__

At x=0, this evaluates to ...

  p(0) = k(0 -3)(0² -4·0 +5)(0² -3) = 45k

We want p(0) = -90, so we require ...

  45k = -90

  k = -2

__

Then the function p(x) factored to integers is ...

  p(x) = -2(x -3)(x² -4x +5)(x² -3)

When we multiply this out, we find the standard form equation is ...

  p(x) = -2x⁵ +14x⁴ -28x³ -12x² +102x -90

Answer:

300km south

Step-by-step explanation:

Go up once from original position then down four times

The gecko is about 10⁵ times bigger than the mite in length.

An equation is an expression that shows the relationship between two or more numbers and variables.

1 cm = 10 ml

The dust mite measures 10⁻³ ml. The gecko measures 10 cm

Length of gecko = 10 cm = 10 cm * 10 ml per cm = 100 ml

Magnitude of gecko to mite = 100 ml / 10⁻³ ml = 10⁵

The gecko is about 10⁵ times bigger than the mite in length.

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Answer:

it is 5

Step-by-step explanation:

Answer:

$321.75

Step-by-step explanation:

k = y/x

514.80/18= 28.6  

28.6 * 11.25 =321.75

Thus, Ashley will earn 321.75 in 11.25 Hours

~Lenvy~

Answer:

$321.75

Step-by-step explanation:

Formula ⇒ k = y/x

Dollar = y

x = Hour

Hence,

514.80/18= 28.6  

28.6 × 11.25 =321.75

Therefore, Ashley will make $321.75 in 11.25 Hour

[RevyBreeze]

Answer:

26 cm^3

Step-by-step explanation:

189.8 gm / ( 7.3 gm / cm^3) = 26 cm^3

Answer:

C) 26cm

Step-by-step explanation:

hope it helps!

Answer:

A = $6,625.00

Step-by-step explanation:

A = P(1 + rt)

A = 5000(1 + (0.065 × 5)) = 6625

Answer:

[tex]5=5^{3x}[/tex]

Step-by-step explanation:

[tex]log_5(5)=3x\\\\5=5^{3x}[/tex]

Answer:

15 planes

Step-by-step explanation:

none disappear, just change shape/ability. its a riddle.

Answer:

15-2-1 = 15-3 = 12.

there are 12 planes left.

Step-by-step explanation:

hope this helped have a nice day

Answer:

x = 5

Step-by-step explanation:

3x+5=20

Subtract 5 from both sides.

3x=20−5

Subtract 5 from 20 to get 15.

3x=15

Divide both sides by 3.

x= 15/3

​Divide 15 by 3 to get 5.

x=5

Answer:

A dodecagon is a shape with 12 sides

Step-by-step explanation:

Decagon is 10 and do is 2 so 12

Answer:

#2 mean is 90.3846154 and range is 40

#3 mean 91.9230769 and range is 20

(you might have mixed the second and third graph up)

Step-by-step explanation:

Answer:

⠀

Step-by-step explanation:

The triangle having two sides equal along with one different side is called an isosceles triangle.

⠀

⠀

We know that,

⠀

So, According to the question :

⠀

[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + x + x = 180{}^{ \circ} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { { 38 \: }^{ \circ} + 2x = 180{}^{ \circ} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { 2x = 180{}^{ \circ} - { 38 \: }^{ \circ}}}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { 2x = 142{}^{ \circ} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \ { x = \dfrac{142{}^{ \circ}}{2} }}}[/tex]

⠀

[tex]{\longrightarrow \it\qquad { \pmb { x = 71^{ \circ} }}}[/tex]

⠀

Therefore,

Step-by-step explanation:

use the above process and answer is $3.60

Answer:

if point bearing of k-l is 084 degree so the bearing of point l-k is 84 degree

The bearing of a point L from a point K is 264 degrees.

What is Addition?

A process of combining two or more numbers is called addition.

Given that;

The bearing of a point K from a point L is 084 degrees.

Now,

Since, The bearing of a point K from a point L is 084 degrees.

Hence, The bearing of a point L from a point K = 180° + 84°

                                                                         = 264°

Thus, The bearing of a point L from a point K is 264 degrees.

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#SPJ2

The approximate volume of the cylinderical tube is 1005 cm³  round to the nearest whole cubic centimeter.

Volume of cylinder is the amount of quantity, which is obtained by the bylinder in the 3 dimensional space.

Volume of cylinder is the can be given as,

[tex]V=\pi r^2h[/tex]

Here, (r) is the radius of the base of the cylinder and (h) is the height of the cylinder.

A cylindrical cardboard tube with a diameter of 8 centimeters and a height of 20 centimeters is used to package a gift.

The diameter is 8 cm and the radius of a cylinder is half of its radius. Thus the radius of the cylinder is,

[tex]r=\dfrac{8}{2}\\r=4\rm\; cm[/tex]

Put the values in the above formula a,s

[tex]V=\pi (4)^2(20)\\V=320\pi\\V=1005.31\\V=\approx 1005\rm\;cm^3[/tex]

The approximate volume of the cylinderical tube is 1005 cm³  round to the nearest whole cubic centimeter.

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Answer:

3

Step-by-step explanation:

1/4 x12= 12/4

12/4=3

Answer:

B and D

Step-by-step explanation:

vertical angles are ones that are formed by intersecting lines, and they are also equal to each other and opposite of each other.

its not A because they are not equal to each other.

B is correct because they are formed by intersecting line and equal to each other

C is incorrect since theres some random line that doesnt completely pass through on either side

D is correct

Answer:

y= 2x-5

Step-by-step explanation:

The slope formula is m=(y2-y1)/(x2-x1)

-3-1 / 1-3 = -4/-2= 2=m

The Y interception- y=mx+b using coordinates (3,1)

1=2(3)+b

1=6+b (subtracting 6 on both sides to isolate b)

-5=b

plug it in

y=2x-5

The transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:

The transformation of a function may involve any change.

Usually, these can be shift horizontally (by transforming inputs) or vertically (by transforming output), stretching (multiplying outputs or inputs) etc.

If the original function is [tex]y = f(x)[/tex], assuming horizontal axis is input axis and vertical is for outputs, then:

For this case, we're specified that:

y = cos(x) (the parent cosine function) was transformed to [tex]y = 0.35\cos(8(x-\pi/4))[/tex]

We can see its vertical stretch by 0.35, right shift by [tex]\pi/4[/tex]horizontal stretch by 1/8

Period of cos(x) is of [tex]2\pi[/tex] length. But 1.8 stretching makes its period shrink to [tex]2\pi/8 = \pi/4[/tex]

Thus, the transformations that are needed to change the parent cosine function to y = 0.35×cos(8(x-π/4)) are:

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When we want to know if the diagonals or sides are congruent we would use the D. Slope.

It should be noted that congruent in geometry simply means when two objects have same shapes and size.

In this case, when we want to know if the diagonals or sides are congruent we would use the slope. This can show the equality in the shape.

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Answer:

32.3m

Step-by-step explanation:

Use equation A = Ao(0.5)^(t/t½)

Now input values: 40 = 980(0.5)^(t/7)

rearrange for t: t = [7ln(2/49)]/ / ln(0.5). Then from here, you can extract 32.3 as your answer

Answer:

t = 32.3 min

Step-by-step explanation:

This is an example of half-life exponential decay.

For situations like this we have a formula.

[tex]N = N_{0} * (\frac{1}{2})^n[/tex]

N represents the end amount of parent element, N (naught) represents the starting amount of the parent element, and n being the amount half-lifes that have occurred.

Now n, can be broken down further into t/p, which means the time elapsed (t) divided by time it takes for one decay period (p), which essentially gives you the amount of half-lifes that have occurred. So you can represent the formula as:

[tex]N = N_{0} * (\frac{1}{2})^{t/p}[/tex]

The question tells you you start off with 980 grams of Element x, so put that for N naught. [tex]N = 980g * (\frac{1}{2})^{t/p}[/tex]. Then it tells you half-life is 7 minutes, which means the period it takes for one half-life to occur is 7, which is p. [tex]N = 980g * (\frac{1}{2})^{t/7min}[/tex]. You are also told that you end up with 40 grams, so put that in for N. [tex]40g = 980g * (\frac{1}{2})^{t/7min}[/tex]. Now we solve for t, the time elapsed.

(This is the part where you use logs to solve, but if you are still rough on this, I'll walk you through it)

Start off by dividing on both sides.

[tex]\frac{40g}{980g} = (\frac{1}{2})^{t/7min} \\, \frac{2}{49} = (\frac{1}{2})^{t/7min}[/tex]

Take the log of both sides.

[tex]log(\frac{2}{49}) = log( (\frac{1}{2})^{t/7min})[/tex]

Now we gotta get t out of the exponent, we'll do this by using log laws. More specifically the exponent law for log laws which states. [tex]log(b^x) = x*log(b)[/tex]. If we apply that to our situation like so.. [tex]log((\frac{1}{2})^{t/7min}) = \frac{t}{7min} * log(\frac{1}{2})[/tex]

Now our whole equation now looks like this:

[tex]log(\frac{2}{49}) = \frac{t}{7min} * log( \frac{1}{2})[/tex]

keep simplifying,

[tex]\frac{log(\frac{2}{49}) }{log(\frac{1}{2}) } = \frac{t}{7min}[/tex]

[tex]7min *\frac{log(\frac{2}{49}) }{log(\frac{1}{2}) } = t\\\\t = 32.3min \\[/tex]

Now you have your answer!

Answer:

167

Step-by-step explanation:

Answer:

(3,5)

Step-by-step explanation:

We first need to substitute x for 3 in the equation :)

y = 2(3) - 1

y = 6 - 1

y = 5

The cordinate will be (3,5)

Have an amazing day!!

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Answer:

A rectangular prism would be best to model a suitcase

Step-by-step explanation:

Hope that helps!

Answer:

Rectangular Prism

Step-by-step explanation:

If you look at a suitcase, it resembles a rectangular prism quite well.

Answer:

8.0 * 10^4

Step-by-step explanation:

Move the decimal so there is one non-zero digit to the left of the decimal point. The number of decimal places you move will be the exponent on the 10. If the decimal is being moved to the right, the exponent will be negative. If the decimal is being moved to the left, the exponent will be positive.

Answer:

8.0 x 10 4

Step-by-step explanation:

This is right

Answer:

5/2

Step-by-step explanation:

to find the reciprocal you just flip the fraction.

Answer:

the answer is 5/2 because reciprocal means to flip the equation

Step-by-step explanation:

Answer:

a) 3/286

b) 7/286

Step-by-step explanation:

We start with 13 drinks. After the first person takes one drink, there are 12 drinks left, After the second person takes one drink, there are 11 drinks available for the third person.

a) From the 13 drinks, there are 3 colas, From the 12 remaining drinks, there are 3 ginger ales. From the 11 remaining drinks, there are 2 colas. We have:

[tex] \frac{3}{13} \times \frac{3}{12} \times \frac{2}{11} = \frac{3}{286} [/tex]

b) From the 13 drinks, there are 3 colas. From the 12 remaining drinks, there are 2 colas. From the 11 remaining drinks, there are 7 root beers. We have:

[tex] \frac{3}{13} \times \frac{2}{12} \times \frac{7}{11} = \frac{7}{286} [/tex]