PLEASE ASAP!! ALSO PLEASE INCLUDE AN EXPLANATION OF HOW YOU GOT THE ANSWER!!! THANK YOU! BTW THERE ARE TWO PICTURES! :)

Answer:

  f(x) = x³ -4x² +9x +164

Step-by-step explanation:

When a function has a zero at x=p, it has a factor (x-p). When a polynomial function with real coefficients has a complex zero, its conjugate is also a zero.

Given the two zeros and the one we can infer, we can factor our 3rd-degree polynomial function as ...

  f(x) = a(x -(-4))·(x -(4+5i))·(x -(4-5i))

Using the factoring of the difference of squares, we can combine the complex factors to make a real factor.

  f(x) = a(x +4)((x -4)² -(5i)²) = a(x +4)(x² -8x +16 +25)

The value of this at x=1 is ...

  f(1) = a(1 +4)(1 -8 +41) = 170a

We want f(1) = 170, so ...

  170 = 170a   ⇒   a=1

The factored polynomial function is ...

  f(x) = (x +4)(x² -8x +41)

Expanding this expression, we have ...

  f(x) = x(x² -8x +41) +4(x² -8x +41) = x³ -8x² +41x +4x² -32x +164

  f(x) = x³ -4x² +9x +164

The attached graph verifies the real zero (x=-4) and the value at x=1. It also shows that the factor with complex roots has vertex form (x -4)² +25, exactly as it should be.

Answer:

[tex]f(x) = (x+4)(x^2-8x+41)[/tex]

Step-by-step explanation:

Ok, so there are a couple of things to note here. The first thing is that there is a complex solution

Complex Conjugate Root Theorem:

    if [tex]a-bi[/tex] is a solution then [tex]a+bi[/tex] is a solution and vice versa

Fundamental Theorem Of Algebra:

   Any polynomial with a degree "n", will have "n" solutions. Those solutions can be real and imaginary numbers

So since we're given the root: [tex]4+5i[/tex], we can use the Complex Conjugate Root Theorem to assert that: [tex]4-5i[/tex] is also a solution.

So now we know 3 solutions/zeroes, and since n=3 (the degree), we can know for a fact that we have all the solutions due to the Fundamental Theorem of Algebra.

So using these roots, we can express the polynomial as it's factors. When you express a polynomial as factors it'll look something like so: [tex]f(x) = a(x-b)(x-c)(x-d)...[/tex] where a, b, and d are zeroes of the polynomial. Also notice the "a" value? This will affect the stretch/compression of the polynomial.

So let's express the polynomial in factored form:

[tex]f(x) = a(x-(-4))(x-(4+5i))(x-(4-5i))[/tex]

Simplify the x-(-4)

[tex]f(x) = a(x+4)(x-(4+5i))(x-(4-5i))[/tex]

Now let's distribute the negative sign to the complex roots

[tex]f(x) = a(x+4)(x-4-5i)(x-4+5i))[/tex]

Now let's rewrite the two factors (x-4-5i) and (x-4+5i) so the (x-4) is grouped together

[tex]f(x) = a(x+4)((x-4)-5i)((x-4)+5i))[/tex]

If you look at the two complex factors, this looks very similar to the difference of squares: [tex](a-b)(a+b) = a^2-b^2[/tex]

In this case a=(x-4) and b=5i. So let's use this identity to rewrite the two factors

[tex]f(x) = a(x+4)((x-4)^2-(5i)^2)[/tex]

Let's expand out the (x-4)^2

[tex]f(x) = a(x+4)(x^2+2(-4)(x)+(-4)^2-(5i)^2)[/tex]

Simplify

[tex]f(x) = a(x+4)(x^2-8x+16-(5i)^2)[/tex]

Now simplify the (5i)^2 = 5^2 * i^2

[tex]f(x) = a(x+4)(x^2-8x+16-(-25))[/tex]

Simplify the subtraction (cancels out to addition)

[tex]f(x) = a(x+4)(x^2-8x+41)[/tex]

So just to check for the value of "a", we can substitute 1 as x, and set the equation equal to 170

[tex]170 = a(1+4)(1^2-8(1)+41)\\170 = a(5)(1-8+41)\\170 = a(5)(34)\\170 = 170a\\a=1[/tex]

In this case it's just 1, so the polynomial can just be expressed as:
[tex]f(x) = (x+4)(x^2-8x+41)[/tex]

[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]

[tex]\textsf{ \underline{\underline{Steps to solve the problem} }:}[/tex]

Take HJ = x, GH = y and GJ = z

put the value of x from equation 1 in equation 2

[tex]{ \qquad❖ \: \sf \:z = (y + 2) + y - 17} [/tex]

[tex]{ \qquad❖ \: \sf \:z = 2y - 15} [/tex]

now, put the value of x and z in equation 3

[tex]{ \qquad❖ \: \sf \:y + 2 + y + 2y - 15 = 73} [/tex]

[tex]{ \qquad❖ \: \sf \:4y - 13 = 73} [/tex]

[tex]{ \qquad❖ \: \sf \:4y = 86} [/tex]

[tex]{ \qquad❖ \: \sf \:y = 21.5 \: \: in} [/tex]

Now, we need to find HJ (x)

[tex]{ \qquad❖ \: \sf \:x = y + 2} [/tex]

[tex]{ \qquad❖ \: \sf \:x = 21.5 + 2} [/tex]

[tex]{ \qquad❖ \: \sf \:x = 23.5 \: \: in} [/tex]

[tex]{ \qquad \large \sf {Conclusion} :} [/tex]

Answer:

No solution

Step-by-step explanation:

[tex]\sqrt{6x-3}=2\sqrt{x} \\ \\ 6x-3=4x \\ \\ -3=2x \\ \\ x=-\frac{3}{2} [/tex]

However, this would make the right hand side of the equation undefined over the reals, so there is no solution.

Answer:

3%, 32%

Step-by-step explanation:

winning 1 game only: two possibilities

a. winning balltoss, losing dart, which is 20%*85% = 17%

b. winning dart, losing ball toss, which is 15%*80% = 12%

so winning 1 game only: 29%

winning both games:

20% * 15% = 3%

winning either one: winning both games+winning 1 game only

29% + 3% = 32%

Answer: [tex]\pm1,\pm3,\pm5, \pm15[/tex]

Step-by-step explanation:

We can list the possible rational roots of this polynomial using the Rational Root Theorem. This theorem states that all the possible rational roots of an equation follow the structure [tex]\frac{p}{q}[/tex], where p is any of the factors of the constant term and q is any of the factors of the leading coefficient.

In this example, -15 is the constant term and 1 is the leading coefficient ([tex]x^4[/tex] has a coefficient of 1).

The factors of -15 are [tex]\pm1,\pm3,\pm5, \pm15[/tex], while the factors of 1 are [tex]\pm1[/tex]. p is can be any one of the factors of -15, while q can be any of the factors of 1.

[tex]\frac{\pm1,\pm3,\pm5, \pm15}{\pm1}[/tex]

The possible roots can be any of the numbers on the top divided by any of the numbers on the bottom. Since dividing by 1 or -1 won't change any of the numbers on the top, the rational roots of this function are [tex]\pm1,\pm3,\pm5, \pm15[/tex].

The exponential model for the data is: [tex]y = 693(1.5)^x[/tex]

When the cost is of $6000, the weight is of approximately 5.3 carats.

An exponential function is modeled by:

[tex]y = ab^x[/tex]

In which:

From the table, the rate of change is given by:

b = 4980/3210 = 3210/2140 = 2140/1430 = 1.5.

When x = 1, y = 1040, hence the initial value is found as follows:

1.5a = 1040.

a = 1040/1.5

a = 693.

So the model is:

[tex]y = 693(1.5)^x[/tex]

When the cost is of $6000, the weight is found as follows:

[tex]693(1.5)^x = 6000[/tex]

[tex](1.5)^x = \frac{6000}{693}[/tex]

[tex]1.5^x = 8.658[/tex]

[tex]\log{1.5^x} = \log{8.658}[/tex]

x log(1.5) = log(8.658)

x = log(8.658)/log(1.5)

x = 5.3

When the cost is of $6000, the weight is of approximately 5.3 carats.

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The number of tickets sold are:

From the question, we have the following parameters:

Number of tickets = 63

Total amount = 444 Birr

Adult ticket = 8 Birr per adult

Children ticket = 6 Birr per adult

Represent the children tickets with x and adults ticket with y.

So, we have the following system of equations

x + y = 63

6x + 8y = 444

Express the equations as a matrix

x      y

1       1       63

6      8       444

Apply the following transformation

R2 = R2 - 6R1

This gives

x      y

1       1       63

0      2       66

Apply the following transformation

R2 = 1/2R2

x      y

1       1       63

0      1       33

From the above matrix, we have the following system of equations

x + y = 63

y = 33

Substitute y = 33 in x + y = 63

x + 33 = 63

Subtract 33 from both sides of the above equation

x = 30

Hence, 30 children tickets were sold and 33 adult tickets were sold

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The answer is 4) 140.

If we closely examine the pattern of the series, we see that after a number is subtracted by a value, it is multiplied by the same value, and then it moves on to the next natural number.

The next step, according to the pattern, would be to multiply 4.

Answer:

400$

Step-by-step explanation:

Let C.P. of the watch = Rs. 100

When profit =5%; S.P. = Rs. (100+5)

= Rs. 105

and when profit = 11%;

S.P. = Rs. (100+11)

=Rs.111

Difference of two selling prices

= Rs. 111-Rs.105 = Rs.6

When watch sold for Rs. 6 more; then C.P. of the watch = Rs.

100

6

When watch sold for Rs. 24 more; then C.P. of the watch = Rs.

100

6

×

24

= Rs.

100

×

24

6

=400

Answer:

t2=8/5

Step-by-step explanation:

using this formula

t1/s1 =t2/s2

4/5=t2/2

cross multiply

5t2=8

t2=8/5

The correct answer for the value of t₂ is [tex]1.6[/tex].

Given:

Time t₁ = 4,

Distance s₂ =2

Distance s₁ = 5.

To find value of t₂ , use the concept of proportion:

[tex]\dfrac{t_1}{s_1} = \dfrac{t_2}{s_2}[/tex]

Put value of [tex]t_1 ,s_1 ,s_2[/tex]:

[tex]\dfrac{t_2}{2} =\dfrac{4}{5}\\\\t_2 =\dfrac{8}{5}\\\\ t_2 = 1.6[/tex]

The correct value of [tex]t_2[/tex] is [tex]1.6[/tex].

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[tex]X[/tex] and [tex]Y[/tex] are independent and identically distributed with PMF

[tex]\mathrm{Pr}(X = x) = \begin{cases}1/6 & \text{if } x \in\{1,2,3,4,5,6\} \\ 0 & \text{otherwise}\end{cases}[/tex]

If [tex]Z=X-Y[/tex], then [tex]Z[/tex] has range/support

{-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}

where we can get

and so on, so that the PMF of [tex]Z[/tex] is

[tex]\mathrm{Pr}(Z=z) = \begin{cases}1/36 & \text{if } z\in\{-5,5\} \\ 2/36 & \text{if } z\in\{-4,4\} \\ 3/36 & \text{if }z\in\{-3,3\} \\ 4/36 & \text{if } z\in\{-2,2\} \\ 5/36 & \text{if } z\in\{-1,1\} \\ 6/36 & \text{if } z =0 \\ 0 & \text{otherwise}\end{cases}[/tex]

Using Euler's Formula, the number of faces is given by: 8.

It states that the number of vertices, edges and faces is related by the following equation:

V - E + F = 2.

In this problem, the parameters are given as follows:

E = 15, V = 9.

Hence the number of faces is given by:

V - E + F = 2.

9 - 15 + F = 2

F - 6 = 2

F = 8.

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Answer:

a

Step-by-step explanation:

[tex]\sqrt{9^2 + 12^2 + 5^2}=\sqrt{250}=5\sqrt{10}[/tex]

Step-by-step explanation:

Monday has 6 different letters.

and we have therefore 6 positions to put letters.

so, for the first position we have 6 choices.

for the second position the 5 choices, and so on.

that makes all together

6! = 6×5×4×3×2×1 = 720

ways to arrange the letters.

if the arrangements must not begin with M, we are taking one choice away for the 1st position.

we can express that as all the ways with only 5 choices for the first position, or as the total number of possibilities minus the ones that start with M.

1.

5×5×4×3×2×1 = 600

2.

6! - 1×5! = 720 - 120 = 600

now, for the possibilities that start with M but do not end with Y.

that is the same as demanding that the second position does not have a Y.

so, the first position has only one choice, and the second position has one choice less :

1×4×4×3×2×1 = 96

The only ordered pair that is a solution to the given system of equations is (-2, -6)

From the question, we are to determine if each ordered pair is a solution to the given system of equations

The given system of equations is

-9x + 2y = 6

5x - 3y = 8

That is,

x = 7, y = 9

Putting the values into the first equation

Is -9(7) + 2(9) = 6

-63 + 18 = 6

-45 ≠ 6

Thus, (7,9) is not a solution

That is,

x = 0, y = 3

Putting the values into the first equation

Is -9(0) + 2(3) = 6

0 + 6 = 6

6 = 6

The ordered pair satisfies the first equation

Testing for the second equation

Is 5(0) - 3(3) = 8

0 - 9 = 8

-9 ≠ 8

Thus, (0, 3) is not a solution

That is,

x = 5, y = -4

Putting the values into the first equation

Is -9(5) + 2(-4) = 6

-45 - 8 = 6

-53 ≠ 6

Thus, (-5,4) is not a solution

That is,

x = -2, y = -6

Putting the values into the first equation

Is -9(-2) + 2(-6) = 6

18 - 12 = 6

6 = 6

The ordered pair satisfies the first equation

Testing for the second equation

Is 5(-2) -3(-6) = 8

-10 + 18 = 8

8 = 8

The ordered pair satisfies the second equation

∴ The ordered pair that is a solution to the system of equations is (-2, -6)

Hence, the only ordered pair that is a solution to the given system of equations is (-2, -6)

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The number of ways the program can be arranged for this segment is 8, 648, 640 ways

It is important to note that the formula for finding the permutation or arrangement of a set of dats is given as;

Permutation = [tex]\frac{n!}{(n-r)!}[/tex]

where

Let's substitute the values into the formula for permutation, we have

Permutation = [tex]\frac{13!}{13 - 7!}[/tex]

Find the difference of the denominator

Permutation = [tex]\frac{13!}{6!}[/tex]

Find the factorial of the values

Permutation = [tex]\frac{6,227,020,800}{720}[/tex]

Divide the numerator by the denominator

Permutation = 8, 648, 640 ways

Thus, the number of ways the program can be arranged for this segment is 8, 648, 640 ways

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Answer: 2.25 meters

Step-by-step explanation: 1 in = 2 meters. 0.75 is 75 percent of 1 so the length of the window is 75 percent of 2 which is 1.5. 1.5 squared is 2.25 so the length of the window is 2.25 meters

Answer:

Two Equal Angles = 45°

Third Angle = 90°

Step-by-step explanation:

Given information

Two equal angles of an isosceles triangle are half the third angle

Set variables

Let x be the angle of the equal angles of the isosceles triangle

Let 2x be the angle of the third angle

Set equations

x + x + 2x = 180 (Triangle angle sum theorem)

Combine like terms

2x + 2x = 180

4x = 180

Divide 4 on both sides

4x / 4 = 180 / 4

[tex]\Large\boxed{x=45^\circ}[/tex]

Substitute the x value into the expression to find the third angle

Third angle = 2x

                   = 2 (45)

                   = [tex]\Large\boxed{90^\circ}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

The insinuation of calling the volume of a solid 3-dimentional shape 10in³ is that the product of all of its dimensions as measured in units is; 10 in.³.

It follows from the task content that the shape in discuss is a solid shape and consequently, one of it's measures is its volume which describes the space it occupies.

On this note, the meaning of a solid having a volume of 10in³ as indicated is that it's volume is; 10 times as large as the volume occupied by an object with unit dimensions 1“ x 1“ x 1“ in which case, the volume is; 1 in³.

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The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

According to the statement

We have given that one evaluating expression which is √6 +√6+√27-√12

And we have to simplify this expression by evaluating it.

So, Given expression is:

√6 +√6+√27-√12

√6 +√6+√(9*3)-√(4*3)

√6 +√6+3√(3)-2√(3)

√6 +√6+√3( 3-2)

After evaluating the expression it become

√6 +√6+√3(1)

√(3*2) +√(3*2) +(1)√3

Take common from above expression then

√3(√2 +√2 ) +√3

√3(2√2) +√3

√3(2√2+ 1)

Now the expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

So, The Evaluating expression √6 +√6+√27-√12 become √3(2√2+ 1) after simplification.

Disclaimer: This question was incomplete. Please find the full content below.

Question:

Which choice is equivalent to the expression below?

√6 +√6+√27-√12

A. √3(2√2+ 1)

B. 2√3-√21

C. 3√3+√6

D. 5√3

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Answer:

16

Step-by-step explanation:

when we multiply we have 16n so thats is d coefficient

Answer:

[tex]\boxed {AB = 52 m}[/tex]

Step-by-step explanation:

This forms a right triangle.

Therefore, by using the Pythagorean Theorem, we can find AB.

AB = √AC² + BC²

I hope it helped you solve the problem.

Good luck on your studies!

Answer: Distance AB = 52 m

Step-by-step explanation:

Given information

Point A = 20 m north of point C

Point B = 48 m east of point C

Please refer to the attachment below for a graphical understanding

Concept

According to the graph drawn, Point A, Point B, and Point C form a right angle, and the distance between Point A and B would form a right triangle.

Therefore, we can use the Pythagorean theorem to find the distance between points A and B.

Given formula

a² + b² = c²

Substitute values into the formula

a² + b² = c²

(20)² + (48)² = c²

Simplify exponents

400 + 2304 = c²

Simplify by addition

2704 = c²

c = √2704

c = 52  or  c = -52 (reject, since no distance can be negative)

Therefore, the distance AB is [tex]\Large\boxed{52~m}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

100 miles and 5.5 inches

Answer:

8

Step-by-step explanation:

-32/-4 the minus takes out the second minus then we are left with 32/4which makes the answer a positive 8

Answer:

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

Find the cost, x:

Find the price to get 12% profit:

Answer:

Step-by-step explanation:

Draw UT                         Construction

UT = UT                         Reflexive Property

BT = EU                           Given

BU = ET                           Given

ΔUBT = ΔEUT                SSS = SSS

<B = <E                             CPCTC

The bolded parts are the blanks you need to fill in.

Answer:

Draw UT                         construction

UT = UT                         reflexive property

BT = EU                           given

BU = ET                           given

ΔUBT = ΔEUT                SSS = SSS

<B = <E                             CPCTC

hope this helps!

Answer: [tex]4(x+2\sqrt{2})(x-2\sqrt{2})[/tex]

Step-by-step explanation:

We can first take out the common factor of 4, as both 4x² and -32 are divisible by 4.

[tex]4(x^2-8)[/tex]

From here, we can assume that x²-8 is a difference of two squares even though 8 is not a perfect square.

For review, a difference of two squares [tex]a^2-b^2[/tex] can be factored into [tex](a+b)(a-b)[/tex].

[tex]4(x^2-8)\\4(x+\sqrt{8})(x-\sqrt{8})\\4(x+2\sqrt{2})(x-2\sqrt{2})[/tex]

The probability that the instructor asks one of Sam and John whose probabilities of being asked are as indicated in the task content is; 0.12.

It follows from the task content that the probability that Sam is being asked is; 0.05 while that for John being asked is; 0.07.

Consequently, we may conclude that the probability of either of the two classmates being asked the question in discuss is; the sum of the probabilities and hence, we have;

P(Sam or John) = 0.05 + 0.07

= 0.12.

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1. According to the affordability formulas given, Joe-Bob cannot afford to take out another loan.

2. Joe-Bob should follow the affordability formulas if he wants to live without financial stress caused by debts.

3. Joe-Bob may decide not to follow the affordability formula, if he can reduce his fixed monthly payments or increase his income.

4. Taking out the car loan will force Joe-Bob to increase his DTI and reduce his savings, investments, and discretionary spending.

Affordability refers to a person's financial ability to afford some fixed expenses without impacting negatively the variable expenses.

Affordability can be measured as a Debt To Income (DTI) ratio.

Current monthly income = $3,500

Monthly mortgage payment = $900

Monthly student loan payment = $350

Total monthly debt payment = $1,250

Debt To Income (DTI) = 35.7% ($1,250/$3,500 x 100)

Thus, with a DTI of 36%, Job Bob should not take out an additional car loan.

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