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Answer:

A third-degree polynomial can be written as:

f(x) = a*x^3 + b*x^2 + c*x + d

Where the leading coefficient is a, and all the coefficients are real.

If we know that the leading coefficient is 1, then the equation becomes:

f(x) = x^3 + b*x^2 + c*x + d

Now, we also know that:

(6 + i) and 5 are zeros.

This means that:

(6 + i)^3 + b*(6 + i)^2 + c*(6 + i) + d = 0

remember that:

i^2 = - 1

This is equal to:

(6 + i)*(36 + 2*6*i  + i^2) + b*(36 + 2*6*i  + i^2) + c*(6 + i) + d = 0

(6 + i)*(35 + 12i) + b*(35 + 12i) + c*(6 + i) + d  =0

(210 + 35i + 72i - 12) +  b*(35 + 12i) + c*(6 + i) + d  = 0

198 + 107i +  b*(35 + 12i) + c*(6 + i) + d  = 0

sparating in real and imaginary part, we get:

(198 + b*35 + c*6 + d) + (107 + b*12 + c)*i = 0

Then each parentheses needs to be zero, this means that:

198 + b*35 + c*6 + d = 0

107 + b*12 + c =  0

Knowing that 5 is another zero, we have:

5^3 + b*5^2 + c*5 + d = 0

125 + b*25 + c*5 + d = 0

Then we have a system of 3 equations and 3 variables:

198 + b*35 + c*6 + d = 0

107 + b*12 + c =  0

125 + b*25 + c*5 + d = 0

To solve this, we first need to isolate one of the variables in one of the equations.

Let's isolate d in the last one, so we get:

d = -125 - b*25 - c*5

now we can replace this in the first equation to get:

198 + b*35 + c*6 + d = 0

198 + b*35 + c*6 + (  -125 - b*25 - c*5) = 0

70 + b*10 + c = 0

So now we have two equations:

70 + b*10 + c = 0

107 + b*12 + c =  0

Again, now we can isolate the one variable in one of the equations, this time let's isolate c in the first one.

c = -70 - b*10

now we can replace this in the other equation:

107 + b*12 + c = 0

107 + b*12 + (-70 - b*10) = 0

38 + b*2 = 0

now we can solve this for b

b*2 = -38

b = -38/2 = -19

Now, with the equation c = -70 - b*10 we can find the value of c.

c = -70 - b*10 = c = -70 - (-19)*10 = 120

And with the equation  d = -125 - b*25 - c*5

we can find the value of d:

d = -125  - b*25 - c*5 = -125 - (-19)*25 - (120)*5 = -250

Then we have:

a = 1

b = -19

c = 120

d = -250

The eqation is:

f(x) = 1*x^3 - 19*x^2 + 120*x - 250

Answer: [tex]x=1[/tex]

Step-by-step explanation:

[tex]2^x-4=4^x-6[/tex] is the equation that you've given us.

Now if we plot these two equations on the graph we notice there's an intersection at (1,-2). Therefore meaning that [tex]x=1[/tex].

We can prove that by doing the following calculations to prove that both sides are equal to each other.

The left side of the equal sign:

Step 1: Write the equation down:

[tex]2^x-4[/tex]

Step 2: Substitute x for the numerical value we found.

[tex]2^1-4[/tex]

Step 3: Find the square of [tex]2^1[/tex], which is itself, 2.

[tex]2-4[/tex]

Step 4: Subtract 2 from 4. Which is a negative number, thus being -2.

[tex]-2[/tex]

The right side of the equal sign:

Step 1: Write the equation down:

[tex]4^x-6[/tex]

Step 2: Substitute x for the numerical value we found.

[tex]4^1-6[/tex]

Step 3: Find the square of [tex]4^1[/tex], which is itself, 4.

[tex]4-6[/tex]

Step 4: Subtract 4 from 6. Which is a negative number, thus being -2.

[tex]-2[/tex]

We know that [tex]x=1[/tex] because when substituting x with 1, we get -2 on both sides. Therefore making this statement true and valid.

[tex]-2=-2[/tex]

Answer:

(-3)

Step-by-step explanation:

follow me if you want

Step-by-step explanation:

hơi khó hiểu thông cảm UwU

Answer:

with my own opinion the answer is b

9514 1404 393

Answer:

  (0, 8)

Step-by-step explanation:

The y-value of the y-intercept is the function value when x=0. That is the constant in the equation, since x=0 will make all of the x-terms be zero.

  y-intercept = 8

Answer:

1

Step-by-step explanation:

a*log(b) = log(b^a), so (1/2)*log(196)=log(14)

So 1+log(15)-log(14)=1

Answer: 28

Step-by-step explanation:

The pattern is multiply the right and bottom, add the left

For example, 9*8+7=79

So, 24*3+x=100

72+x=100

x=28

Step-by-step explanation:

if

c = 3 + 6 = 9

and

n = 4 + 5 = 9

then it could be true

Answer:

-2,-3

Step-by-step explanation:

Answer:

-2 -3

It worked for me on acellus

Step-by-step explanation:

Answer:

[tex]y= 3[/tex]

Step-by-step explanation:

Given

[tex]RT = 6[/tex]

[tex]k = 1.5[/tex] --- dilation ratio

See attachment

Required

Determine length, y

First, we calculate length R'T.

Since point T is the center of dilation, then:

[tex]R'T = k * RT[/tex]

Substitute known values

[tex]R'T = 1.5 * 6[/tex]

[tex]R'T = 9[/tex]

y is between R'T and RT;

So:

[tex]y = R'T - RT\\[/tex]

[tex]y = 9 -6[/tex]

[tex]y= 3[/tex]

Answer:

either 4 or 9

Step-by-step explanation:

Answer:

x = 136

Step-by-step explanation:

x and 44 are same- side interior angles and sum to 180° , that is

x + 44 = 180 ( subtract 44 from both sides )

x = 136

Answer:

⅗hrs

Step-by-step explanation:

1hr =60 min

? = 36 min

cross-multiply .........

36 min × 1hr/60 min= 36min/60min × 1hr

=36/60 × 1 hr

= ⅗hrs

Answer:

[tex] = { \tt{(0, \: 0)}}[/tex]

Step-by-step explanation:

Let:

[tex]{ \bf{ - x - 2y = 0 - - - (a)}} \\ { \bf{y = - 8x - - - (b)}}[/tex]

Substitute for y in equation (b) to equation (a):

[tex]{ \tt{ - x - 2( - 8x) = 0}} \\ { \tt{ - x + 16x = 0 }} \\ { \tt{x = 0}}[/tex]

Also, y = 0

Answer:

Step-by-step explanation:

∠OST = 90° as ST ⊥ OS (tangent is perpendicular to radius at same point)

m∠OSP = 1/2(180° - m∠SOP) = 90° - 96°/2 = 42° (sum of interior angles of the triangle SOP)

m∠PST = 90° - m∠OSP = 90° - 42° = 48° (angle addition postulate)

Correct choice is B

Answer:

Option B

Step-by-step explanation:

From the picture attached,

In ΔABC,

m∠B = m∠C = 75° [Isosceles triangles]

By applying triangle sum theorem,

m∠A + m∠B + mC = 180°

m∠A + 75° + 75° = 180°

m∠A = 180° - 150°

m∠A = 30°

In triangle PQR,

m∠P = m∠Q [Isosceles triangle]

By applying triangle sum theorem,

m∠P + m∠Q + m∠R = 180°

2(m∠P) + 30° = 180°

m∠P = 75°

m∠P = m∠Q = 75°

In ΔABC and ΔRPQ,

m∠B ≅ m∠Q [Given]

m∠C ≅ m∠R [Given]

Therefore, by AA property of similarity of two triangles, both the triangles will be similar.

ΔABC ~ ΔRPQ

Option B will be the answer.

Answer:

a, c, d,

Step-by-step explanation:

I'm not sure if this is right but i think.

First you cant have exponents in a linear equation, so its not e or f. Then i just graphed the rest.

Answer:

18

Girl  = g

Boy = b

1g 1b  1g 2b  1g 3b

2g 1b  2g 2b  2g 3b

3g 1b  3g 2b  3g 3b

4g 1b   4g 2b  4g 3b

5g 1b   5g 2b  5g 3b

6g 1b   6g 2b  6g 3b

---------------------------------------

Another way you can do this,

6 × 3 = 18

In the end there will be 18 selections.

Answer:

Step-by-step explanation:

Measure of an inscribed angle intercepted by an arc is half of the measure of the arc.

From the picture attached,

m(∠A) = [tex]\frac{1}{2}m(\text{arc BD})[/tex]

           = [tex]\frac{1}{2}[m(\text{BC})+m(\text{CD}][/tex]

           = [tex]\frac{1}{2}[55^{\circ}+145^{\circ}][/tex]

           = 100°

m(∠C) = [tex]\frac{1}{2}[(360^{\circ})-m(\text{arc BCD})][/tex]

           = [tex]\frac{1}{2}(360^{\circ}-200^{\circ})[/tex]

           = 80°

m(∠B) + m(∠D) = 180° [ABCD is cyclic quadrilateral]

115° + m(∠D) = 180°

m(∠D) = 65°

m(arc AC) = 2[m(∠D)]

m(arc AB) + m(arc BC) = 2(65°) [Since, m(arc AC) = m(arc AB) + m(arc BC)]

m(arc AB) + 55° = 130°

m(arc AB) = 75°

m(arc ADC) = 2(m∠B)

m(arc AD) + m(arc DC) = 2(115°)

m(arc AD) + 145° = 230°

m(arc AD) = 85°

Answer:

The GCF of the coefficients is correct.

The variable c is not common to all terms, so a power of c should not have been factored out.

In step 6, David applied the distributive property.

Step-by-step explanation:

Given the polynomial :

80b⁴ – 32b²c³ + 48b⁴c

The Greatest Common Factor (GCF) of the coefficients:

80, 32, 48

Factors of :

80 : 1, 2, 4, 5, 8, 10, 16, 20, 40, and 80

32 : 1, 2, 4, 8, 16, and 32

48 : 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

GCF = 16

b⁴, b², b⁴

b⁴ = b * b * b * b

b² = b * b

b⁴ = b * b * b * b

GCF = b*b = b²

GCF of c³ and c

c³ = c * c * c

c = c

GCF = c

We can see that David's GCF of the coefficients are all correct

From the polynomial ; 80b⁴ does not contain c ; so factoring out c is incorrect

In step 6 ; the distributive property was used to obtain ; 16b²c(5b² – 2c² + 3b²)

Answer:

x = -5

Step-by-step explanation:

A vertical line is a line that goes up and down.  It is of the form x = constant

To go through (-5,6) is has to have the value of the x coordinate

x = -5

Answer:

50%

Step-by-step explanation:

6 professors younger than 50 years = 6/12 = 50

Answer:

%50

Step-by-step explanation:

If you count the number of proffessors that are under 50, there are six. If there are 12 proffessors then it would be 1/2. One half in percentage is %50.

Pls give Brainliest!

Answer:

1 cm

Step-by-step explanation:

Since the perimeter is 4 cm and all the sides of the square have the same length, each side must be 1 cm long.

The area of that square is 1 cm x 1 cm, which is 1 cm2.

Step-by-step explanation:

since the all side is same,the side length is just 1 cm. And the area is just the side length square =1cmsquare× 1 cm

= ans is 1cm^2

Answer:

6

Step-by-step explanation:

Answer:

x = 1

General Formulas and Concepts:

Pre-Algebra

Distributive Property

Equality Properties

Algebra I

Step-by-step explanation:

Step 1: Define

Identify

1/2(8x - 4) = 2x

Step 2: Solve for x

Answer:

x = 2/3

Step-by-step explanation:

(8x − 4) = 2x

8x - 4 = 2x

6x = 4

x = 2/3