find the polynomial f(x) of degree 5 that has the following zeros -3(mulitiplicity 2),5,8,-7

Answer:

See explanation below

Step-by-step explanation:

Let's use Q10 as an example and you will work on Q11-12 as they are the same.

I believe the middle column (5x-4) wants you to substitute the given x, so:

Q10.1: 5(-2)-4

Q10.2: 5(4)-4

Q10.3: 5(0)-4

Q10.4: 5(1)-4

The right most column (f(x)) should be asking you the answers from your middle column, so:

Q10.1: -14

Q10.2: 16

Q10.3: -4

Q10.4: 1

As for the domain and range, let's define these two names in case you haven't learnt them:

Domain: What reasonable x values can be inputted into the function.

Range: What reasonable results will be shown after calculating.

In these case, you can input any real numbers into x as you like into the function, the results will always be other real numbers.

Hence, for Q10-12, D and R should be "All real numbers"

Just some extra info, Let the function f(x) be [tex]\frac{1}{x+1}[/tex]. Since the denominator cannot be 0 in a fraction, we say that the domain of x is "All real numbers except -1" as [tex]-1+1 = 0[/tex] and [tex]\frac{1}{0}[/tex] is undefined.

Answer:

A

5(b+2)

Step-by-step explanation:

Solution:

Note that:

Let's reread the sentence carefully.

Five times the sum of b and two.

       ↥                            ↥          ↥

       5                           (b   +    2)

Putting them together gives us 5(b + 2).

Answer:

y = 6x - 1

Step-by-step explanation:

Hope it helps.

Answer:

college

Step-by-step explanation:

Answer:

Given Integral is:

[tex] \\ { \displaystyle{ \int{ \large{ \rm{ \frac{1}{x( {x}^{3} + 1) }dx }}}}} \\ [/tex]

Can be written as:

[tex] \\ { \large{ \longrightarrow{ \displaystyle{ \int { \rm{\frac{3 {x}^{2} }{3 {x}^{2} \times x( {x}^{3} + 1) } dx}}}}}}[/tex]

[tex] \\ { \large{ \longrightarrow \frac{1}{3} \: { \displaystyle{ \int{ \rm { \frac{ {3x}^{2} }{ {x}^{3} ( {x}^{3} + 1)} dx}}}}}}[/tex]

Now to evaluate this integral , we use the method of Substitution.

So, Substitute:

[tex] \: \: \: \: \: \: \: \: \: \: \: \: { \rightarrow \: {\large{\rm{ {x}^{3} = y}}}}[/tex]

[tex] \: \: \: \: \: \: \: \: \: \: \: \: \rightarrow \: { \large{ \rm{3 {x}^{2} dx = dy}}}[/tex]

So, on Substituting the values in above integral, we get:

[tex] \\ { \large{ \longrightarrow{ \frac{1}{3} \: \displaystyle{ \int{\rm{ \frac{1}{y(y + 1)} }}}}}}[/tex]

[tex] \\ { \large{ \longrightarrow{ \frac{1}{3} \: { \displaystyle{ \int{ \rm{ \frac{1 + y - y}{y(y + 1)}dy }}}}}}}[/tex]

[tex] \\ { \large{ \longrightarrow{ \frac{1}{3} \: { \displaystyle{ \int{ {\rm{ \frac{y + 1 - y}{y(y + 1)}dy }}}}}}}}[/tex]

[tex] \\ { \large{ \longrightarrow{ \frac{1}{3} \: { \displaystyle{ \int{ \rm{ \left[ \frac{1}{y} - \frac{1}{y + 1} \right ] }dy}}}}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{ \frac{1}{3} \left( log |y| - log |y + 1| \right) + c}}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{ \frac{1}{3} log | \frac{y}{y + 1} | + c }}}}[/tex]

[tex]{ \large{ \longrightarrow{ \rm{ \frac{1}{3} log | \frac{ {x}^{3} }{ {x}^{3} + 1 } | + c }}}}[/tex]

Hence,

[tex] \\{ \boxed{ \pink { \large{ \displaystyle{ \int{ \rm{ \frac{dx}{x ({x}^{3 } + 1 )} = \frac{1}{3 } log{ \huge{ |}} \frac{ {x}^{3} }{ {x}^{3} + 1} { \huge{ | }} + c}}}}}}}[/tex]

After applying algebraic substitution, partial fraction decomposition and integration rules the integral of the non-trascendental expression [tex]\frac{1}{x\cdot (x^{3}+1)}[/tex] is equal to the trascendental expression [tex]I = \frac{1}{3}\cdot \ln \left|\frac{x^{3}}{x^{3}+1} \right| + C[/tex].

According to the statement we have an integrable rational expression formed by non-trascendental expressions, that is, expressions whose behavior is described solely by algebraic components. This expression can be solved by algebraic substitution after making the following modifications:

[tex]\int {\frac{dx}{x\cdot (x^{3}+1)} } = \int {\frac{3\cdot x^{2}}{3\cdot x^{3}\cdot (x^{3}+1)} } \, dx = \frac{1}{3}\int {\frac{3\cdot x^{2}}{x^{3}\cdot (x^{3}+1)} } \, dx[/tex]

And the following substitutions are used: u = x³, du = 3 · x² dx

[tex]\frac{1}{3} \int {\frac{du}{u \cdot (u+1)} }[/tex]

This is expression is equivalent to the following by partial fraction decomposition:

[tex]-\frac{1}{3}\int {\frac{du}{u+1} } \, du +\frac{1}{3}\int {\frac{du}{u} }[/tex]

And the integral is now solved:

[tex]I = -\frac{1}{3}\cdot \ln |u+1| + \frac{1}{3}\cdot \ln |u| + C[/tex]

[tex]I = \frac{1}{3}\cdot \ln \left|\frac{u}{u+1} \right| + C[/tex]

[tex]I = \frac{1}{3}\cdot \ln \left|\frac{x^{3}}{x^{3}+1} \right| + C[/tex]

Where C is the integration constant.

After applying algebraic substitution, partial fraction decomposition and integration rules the integral of the non-trascendental expression [tex]\frac{1}{x\cdot (x^{3}+1)}[/tex] is equal to the trascendental expression [tex]I = \frac{1}{3}\cdot \ln \left|\frac{x^{3}}{x^{3}+1} \right| + C[/tex].

To learn more on integrals, we kindly invite to check this: https://brainly.com/question/22008756 #SPJ5

Answer:

equation= y-y¹=m(x-x¹)

where m= slope = y²-y¹

x²-x¹

= 10-4

6-0

= 6

6

= 1

= y-10=1(x-4)

y-10=1x-4

y=1x-4+10

y=1x+6

hope this helps

Answer:

33.3333333%

Step-by-step explanation:

Let's set up the equation:

x             27

---     =    ---

100          81

100 x 27 = 2700

2700 ÷ 81 = 33.3333333

So x equals 33.3333333 of a hundred, or in other words, 33.3333333%

Therefore 27 is 33.3333333% of 81.

-kiniwih426

Answer:

21 is the correct answer kids.so do it ok bye

Answer:

Step-by-step explanation:

1960 = 88,000,000

2010 = 242,000,000

formula: (new-old)/old* 100

(242,000,000 - 88,000,000)/88,000,000 * 100

154,000,000/88,000,000*100

1.75*100

=1.75%

I'M SORRY NOT SURE OF THE SECOND PART

Answer:

D) -4

Step-by-step explanation:

Step 1: Divide 24 by 6.

Step 2: Put in the negative sign.

Thus, the answer is D) -4.

Answer:

1st option

Step-by-step explanation:

Complementary angles sum to 90°

∠ BFC and ∠ AFB form a right angle and sum to 90°

These angles are therefore complementary

Answer:
Multiplication -> Division
Squaring -> Square rooting

Cubing -> Taking the cube root

Addition -> Subtraction

Alternative:

* -> /

^2 -> √

+ -> -

^3 -> 3√

Basically, an inverse is a mathematical manipulation where one operation undoes the action of the other.

Answer:

(1, -3)

Step-by-step explanation:

To find the solution of the system of linear equations, first you need to set them equal to each other and solve.

y = x-4

y = -2x-1

x-4 = -2x-1

x + 2x = -1 + 4

3x = 3

x = 1

To find the corresponding y-value, plug the calculated x into one of the equations (it doesn't matter which one you choose because they will give the same result).

y = x-4

y = 1 - 4

y = -3

If the graph hadn't been provided, you could check this problem by plotting both equations and determining their intersection. Since the graph was provided you can just compare your results to the shown intersection.

Answer: (1,-3)

Step-by-step explanation: The solution of a system of linear equation is where the two lines intersect, in this case, (1,-3). (that's why the dot is there)

Answer:

The correct answer is C, x = 1; x = -8

Step-by-step explanation:

[tex]x^2+7x=8[/tex]

[tex]x^2+7x-8=0[/tex] <== a = 1, b = 7, c = -8

[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a} \\\\x=\frac{-7\±\sqrt{7^2-4*1*-8}}{2*1} \\\\x=\frac{-7\±\sqrt{7^2-4*-8}}{2} \\\\x=\frac{-7\±\sqrt{49+32}}{2} \\\\x=\frac{-7\±\sqrt{81}}{2} \\\\x=\frac{-7\±9}{2} \\\\x=\frac{-7+9}{2}\ \ and\ \ x=\frac{-7-9}{2} \\\\x=\frac{2}{2}\ \ and\ \ x=\frac{-16}{2} \\\\x=1\ \ and\ \ x-8\\\\x=1,\ x-8[/tex]

Hope this helps!

Answer:

[tex]\log_{10}2=0.3010[/tex]

Step-by-step explanation:

[tex]a^c=b \implies \log_ab=c[/tex]

Given:  [tex]2=10^{0.3010}[/tex]

Therefore,

[tex]10^{0.3010}=2 \implies \log_{10}2=0.3010[/tex]

Answer:

there is no graph and y=y makes no sense

Step-by-step explanation:

Answer:

One thousand three hundred forty eight

Step-by-step explanation:

Answer:

10³

Step-by-step explanation:

10 x 100 = 10¹ x 10² = 10³

Answer: 10³

Step-by-step explanation: 10³

Answer:

here’s what I got

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

9.1

Step-by-step explanation:

(13*70)/100

Answer:

Explanation:

13/100 with 70 = (13÷100)*70= (13*70)÷100=9.1

hope this helps.

An equation can be used to define any non-vertical line in the Cartesian Coordinate system. The correct option is C.

A nonvertical line is a line that has a slope and is defined by its steepness.

It can be represented by a straight line equation y = mx+c, here m is the slope and c is the y-intercept.

The slope can be determined by using two points on the line (x₁,y₁) and (x₂,y₂)

m = (y₂-y₁)/(x₂-x₁)

From the options given, An equation can be used to define any non-vertical line in the Cartesian Coordinate system.

The correct option is C.

The complete question is attached with the answer.

To know more about Nonvertical Line

https://brainly.com/question/14517469

#SPJ2

Answer:

  56 cm²

Step-by-step explanation:

The area of the composite shape is the sum of the areas of the parts. In this case, that is the sum of the areas of the central rectangle and four (4) congruent triangles.

The rectangle has dimensions 11 cm × 4 cm, so its area is ...

  A = LW = (11 cm)(4 cm) = 44 cm²

Each triangle has a base of 2 cm, and a height of 2+1 = 3 cm. The area of each triangle is ...

  A = 1/2bh = 1/2(2 cm)(3 cm) = 3 cm³

The total area of the rectangle and 4 triangles is ...

  area of the figure = (44 cm²) +4(3 cm²) = 56 cm²

Answer:

False

Step-by-step explanation:

10x3=30

30-20=10

10=20

These equations dont match.

Hence, the equation is false

Answer: This equation is FALSE. The left side 10 does not equal to the right side which is 20.

Step-by-step explanation:

Answer:

Angle 2 = angle 6 = 180 - angle 5 = 180 - 75 = 105

Angle 8 - 180 - angle 6 = 180 - 105 = 75

Angle 7 = 180 - angle 8 = 180 - 75 = 105

Answer:

y - 2= -8(x - 1)

(I believe so)

Step-by-step explanation:

Since the formula of a point-slope form is y-y1=m(x-x1), you should just substitue the values into the formula.

(If needed simplified version : y-2=-8x+8)

Answer:

B. The United States Constitution