please help me with steps​

Please Help Me With Steps

Answers

Answer 1

Answer:

x = (3 − √5) / 2, (3 + √5) / 2, and 1

Step-by-step explanation:

Using rational root theorem, ±1 are possible roots.  By trial and error, we find that +1 is a root.  Therefore, x − 1 is a factor.  Knowing this, we can use grouping or long division.  Using grouping:

x⁴ − 5x³ + 8x² − 5x + 1 = 0

x⁴ − 5x³ + 4x² + 4x² − 5x + 1 = 0

x² (x² − 5x + 4) + 4x² − 5x + 1 = 0

x² (x − 4) (x − 1) + (4x − 1) (x − 1) = 0

(x² (x − 4) + 4x − 1) (x − 1) = 0

(x³ − 4x² + 4x − 1) (x − 1) = 0

Repeating the process, possible rational roots of x³ − 4x² + 4x − 1 are ±1.  We already know -1 isn't a root.  By trial and error, we find that +1 is again a root.  Using grouping to factor:

(x³ − 4x² + 3x + x − 1) (x − 1) = 0

(x (x² − 4x + 3) + x − 1) (x − 1) = 0

(x (x − 3) (x − 1) + x − 1) (x − 1) = 0

(x (x − 3) + 1) (x − 1) (x − 1) = 0

(x² − 3x + 1) (x − 1)² = 0

To find the roots of x² − 3x + 1, we use the quadratic formula.

x = [ -(-3) ± √((-3)² − 4(1)(1)) ] / 2(1)

x = [ 3 ± √(9 − 4) ] / 2

x = (3 ± √5) / 2

So the roots are x = (3 − √5) / 2, (3 + √5) / 2, and 1.


Related Questions

. After reading to a kindergarten class at the library, Tobey gives out stickers. He has 9
zoo animal stickers and 16 scratch-n-sniff stickers. If Tobey gives the stickers out at
random, what is the probability that the first child gets a scratch-n-sniff sticker and
the second child gets a zoo animal sticker?

Answers

Answer:

If Tobey gives the stickers out at random, what is the probability that the first child gets a scratch-n-sniff sticker and the second child gets a zoo animal sticker?

P(zoo 2nd | scratch 1st) = (9/25)(16/24) = (9/25)(2/3) = 6/25

Justin used 42 centimeters of tape to wrap 14 presents. How many presents did Justin wrap if
he used 45 centimeters of tape? Solve using unit rates.

__ presents

Answers

Answer:

15 presents

Step-by-step explanation:

42 cm / 14 presents = 3 cm / 1

3cm / 1 presents = 45 / 15

Answer:

15 presents

Step-by-step explanation:

Since we are using unit rate, we have to find out how many centimeters he uses for 1 present. Therefore 42÷14=3 So he uses 3 centimeters of paper for 1 present. Since he used 45 centimeters of paper we divide that by 3 to see how many presents is in 45 centimeters. When dividing the answer is 15. Therefore he wraps 15 presents

PLEASE HELP
Find the diameter of the object.

Answers

Answer:

d the diameter is 4 inches.

Step-by-step explanation:

d=2r=2×2=4

the diameter of the object is 4

Kayla has a red number cube and a blue number cube. Each number cube has faces labeled 1 through 6.
What is the probability Kayla rolls an even number on the red cube and a multiple of 3 on the blue cube?
ΟΑ.
16%
B. 25%
O c 33%
D. 50%
E. 83%

Answers

The probability Kalya rolls an even number on the red cube and a multiple of [tex]3[/tex] on the blue cube is [tex]16%[/tex] percent, when both the cubes have faces labeled [tex]1[/tex] through [tex]6[/tex].

Probability

The ratio of the favourable number of outcomes to the total number of outcomes is known as Probablity.

How to find the probability?

First, find the possible outcomes.

Kalya has a red number cube and a blue number cube. Each number cube has faces labeled [tex]1[/tex] through [tex]6[/tex].

So, possible outcomes [tex]=(6[/tex]×[tex]6)=36[/tex]

Let, [tex]S[/tex] be the sample space.

Then, [tex]n(S)=36[/tex]

Let, [tex]E=[/tex]the event of getting an even number on the red cube and a multiple of [tex]3[/tex] on the blue cube.

[tex]E=(2,3),(2,6),(4,3),(4,6),(6,3),(6,6)[/tex]

Then, [tex]n(E)=6[/tex]

Let, [tex]P[/tex] is the probability of the event [tex]E[/tex].

So, [tex]P(E)=\frac{n(E)}{n(S)}=\frac{6}{36}=\frac{1}{6}[/tex]≈[tex]16[/tex] percent

Thus, the probability Kalya rolls an even number on the red cube and a multiple of [tex]3[/tex] on the blue cube is [tex]16[/tex] percent.

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Answer:

Α. 16%

Step-by-step explanation:

Two friends share 1/6 of a large peach pie. What fraction of the whole pie does each friend get? Let n represent the fraction of the whole pie each friend gets.

Enter an equation as a multiplication equation.

The equation is n=?

Each friend gets ? of a whole pie.

Answers

Answer:

n= 1/12

Step-by-step explanation:

1/6 ÷ 2

1/6×1/2=1/12

Two friends are sharing 1/6 of a pie. That's why it is 1/6 divided by 2. In fractions when you switch from division to multiplication, you switch the denominator and numerator, so 2/1 becomes 1/2. Then, you multiply 1/6 and 1/2. You end up with 1/12, so n= 1/12.

Each friend gets 1/12 of the pie.

Hey guys I really need help with this one exercise soo maybe can someone plzz help for 20 points? Write also the whole detail of your answer plz!

Math Problem: A photograph is reduced to 75% of its original size. The photo was originally 12 inches by 16 inches. What are the new dimensions after it has been reduced 75%?

Answers

Answer:

3 by 4

Step-by-step explanation:

12 reduced by 75% is 3

16 reduced by 75% is 4

Answer:

100%-75% is equal to 25%

So 12 times 25% is 3

And 16*25% is 4

The new dimensions are 3 by 4

Step-by-step explanation:

What is the answer to this?

Answers

Answer:

I think it's 945 but i'm not sure. actually i'm probably wrong, sorry

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

960/15=64

Square root of 64 is 8

What is the equation of a line that passes through points (0, 4) and (-4, -8)? y = 2x + 4 y = 2x - 4 y = 3x + 4 y = 3x - 4

Answers

Answer:

y= 3x +4

Step-by-step explanation:

The equation of a line is usually written in the form of y=mx +c, where m is the gradient and c is the y-intercept.

To find the value of m, use the gradient formula below:

[tex]gradient = \frac{y1 - y2}{x1 - x2} [/tex]

Gradient

[tex] = \frac{4 - ( - 8)}{0 - ( - 4)} \\ = \frac{4 + 8}{0 + 4} \\ = \frac{12}{4} \\ = 3[/tex]

Subst. m=3 into the equation.

y= 3x +c

To find the value of c, substitute a coordinate.

When x=0, y=4,

4= 3(0) +c

c=4

Thus, the equation of the line is y= 3x +4.

BRAINLIEST!!!
2. Use the unit circle to find the value of cot (–90°).

Answers

Answer:

cot(- 90)° = 0

Step-by-step explanation:

Using the identity

cot x = [tex]\frac{cosx}{sinx}[/tex] , then

cot(- 90)° = [tex]\frac{cos(-90)}{sin(-90)}[/tex] = [tex]\frac{0}{-1}[/tex] = 0

Please answer CORRECTLY !!!! Will mark brainliest !!!!!!!!

Answers

Answer:

Step-by-step explanation:

4u + 8v = -3u + 2v

7u + 8v = 2v

7u = -6v

h(u) = -6v/7

Find the value of x?


23.5°


43°


47°


86°

Answers

Answer:

x = 23.5°

Step-by-step explanation:

The 4 angles 90, 43, x , x lie on a straight angle, thus

90 + 43 + x + x = 180, that is

133 + 2x = 180 ( subtract 133 from both sides )

2x = 47 ( divide both sides by 2 )

x = 23.5°

Solve each equation in the interval from 0 to 2pi. Round your answer to the nearest hundredth.
a. 3cos 4theta= -2
b. cos(pi theta)= -0.6

Answers

I think the answer is b. cos(pi theta)= -0.6

The requried solution of the equations in the interval form are a. (-0.575, 0.575) and b. (0.71, 3.43).

What are trigonometric equations?

These are the equation that contains trigonometric operators such as sin, cos.. etc.. In algebraic operations.


a.

We can solve for theta by dividing both sides by 3, then taking the inverse cosine of both sides. Remember that there will be two solutions in the given interval because cosine has a period of 2π.

3cos(4Ф) = -2

cos(4Ф) = -2/3

4Ф = ±cos⁻¹(-2/3)

cos⁻¹(-2/3) ≈ 2.300

4Ф = ±2.300

Ф = ±0.575

Similarly,

b.

For cos(πФ)= -0.6
Ф=  0.71, 3.43

Thus, the requried solution of the equations in the interval form are a. (-0.575, 0.575) and b. (0.71, 3.43).

Learn more about trigonometry equations here:

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Find an ordered pair (x, y) that is a solution to the equat
4x - y = 7

Answers

Answer:

(0,-7),(1,-3),(2,1)

Step-by-step explanation:

Some answers could be .......
(5,13)

(3,5)

(2,1)

(4,9)

What is the surface area of the pyramid?
24 Square feet
37 square feet
39 square feet
69 square feet

Answers

Answer:

39

Step-by-step explanation:

square= lw

triangle= 1/2lw

s=9

triangle=15 divided by 2 times 4=30

you add 30 + 9 which will give you 39

39 square feet that is the answer

1. Triangle ABC is dilated by a scale factor of 1.5 to create triangle A'B'C'. Which of
the following it not a true statement?

Answers

Answer:

d

Step-by-step explanation:

because it gets bigger so they are not going to have the same measures or lenghts.

The statement that is not true about the dilation is (c) the segment AB is congruent to the segment A'B

How to determine the false statement?

When a shape is dilated, the orientation of the shapes is preserved but the side lengths of the shapes are not congruent

This means that the side lengths of triangle A'B'C are not congruent to triangle A'B'C

Hence, the statement that is not true about the dilation is (c) the segment AB is congruent to the segment A'B

Read more about dilation at:

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The ratio of the number of students at the zoo in the morning to the number of students at the zoo in the afternoon was 5:3. There were 145 students at the zoo in the morning. What was the number of students at the zoo in the afternoon?

Answers

Answer:

87 in the afternoon

Step-by-step explanation:

morning: afternoon

5                   3

There were 145 in the morning

145/5 =29

Multiply each side by 29

morning: afternoon

5*29                 3*29

145                  87

There are 87 in the afternoon

john wants to build a slide for his daughter's tree house. the slide is made from aluminum material that is cut from a roll. The aluminum materials is sold by the foot. The tree house is 6 feet off the ground and he wants the slide to be built at a 60 angle . triangle PQR is a right triangle.
Will reward brainliest please show all work

Answers

Answer:7 ft

Step-by-step explanation:

Given

Height of tree house is [tex]6\ ft[/tex]

inclination of slide [tex]\theta =60^{\circ}[/tex]

In [tex]\triangle PQR[/tex] we can write

[tex]\sin \theta =\frac{PQ}{PR}[/tex]

[tex]\sin 60=\frac{6}{PR}[/tex]

[tex]PR=\frac{6}{\sin 60^{\circ}}[/tex]

[tex]PR=\frac{6\times 2}{\sqrt{3}}[/tex]

[tex]PR=6.928\approx 7\ ft[/tex]

So, [tex]7 \ft[/tex] of aluminium is required for slide

What is the range of f(x) = 4^x?

A. All positive real numbers

B. All real numbers greater than 4

c. All real numbers

D. All real numbers greater than or equal to 4

Answers

Answer: A because it goes from (0,infinity) so all positive real numbers

Solve the following problem 2x + 4 + 5x = 8x -6
Please help

Answers

x=10

2X +4+ 5X = 8X -6
combine like terms on both sides
7X +4=8X -6
subtract the four on both sides
7X +4 = 8X -6
-4. -4
7X = 8x-10
subtract 8x from both sides
7X = 8X -10
-8x. -8x
-x = -10
Divide negative one from both sides to get the X by itself
-x/-1. -10/-1
x = 10

Plz help. I am very stuck. Its due today and I have none to ask help to.

Answers

Answer:

Hi there!

The correct answers for the question are:

For 45 mph, the trip time is: 9.78

For 55 mph, the trip time is: 8.36

For 65 mph, the trip time is: 7.38

Step-by-step explanation:

The values given to you represent the variable "S" so therefore you just plug in the values into the equation and you get "t"

Answer:

For 45 mph the trip time is 9.78 For 55 mph the trip time is 8.36 For 65 mph the trip time is 7.38

Step-by-step explanation:

Make Me brainliest

Find the constant of proportionality k. Then write an equation for the

relationship between x and y.

X | 2 | 4 | 6 | 8 |

_______________

Y | 10 | 20 | 30 | 40 | I tried to make the table

Answer: k = _, y =

Answers

Answer:

see explanation

Step-by-step explanation:

Given x and y are in proportion then the equation relating them is

y = kx ← k is the constant of proportion

To find k use an ordered pair from the table

Using (2, 10 ), then

10 = 2k ( divide both sides by 2 )

5 = k , thus

y = 5x ← relationship between x and y

Find each product

(6v^2+2v+7)(2v^2-2v+6)​

Answers

12v^4-8v^3+46v^2-2v+46

remove parentheses and collect like terms

write (x^2)^4 without exponents

Answers

Answer: x8 i really don't know if it is correct tell me plz

Step-by-step explanation:

The expression (x²)⁴ without exponents can be written as x × x × x × x × x × x × x × x.

The given expression is (x²)⁴.

It is known that the power rule of exponents states that:

(xᵃ)ᵇ = xᵃᵇ

Here, a = 2 and b = 4.

So using the power rule,

(x²)⁴ = x²⁽⁴⁾

       = x⁸

Now, it is known that exponents are actually the multiplication of the number with the same number again and again.

Here x is multiplied by itself 8 times.

So the expression can be written as:

x × x × x × x × x × x × x × x.

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f(x) = x^2. What is g(x)?

Answers

Answer:

g(x)=x²/4

Step-by-step explanation:

g(x)=ax²+bx+c

g(0)=0  => c=0

g(-2)=1 => 4a-2b=1;

g(2)=1  => 4a+2b=1   (+)

                8a=2   => a=1/4

4*1/4+2b=1=> b=0

=> g(x)=x²/4

GIVING BRAINLIEST BRAINLIEST!!!! Easy mathhh

Answers

Answer:

is D i had this on my math test

Step-by-step explanation:

Answer:

the area is 20 units

Step-by-step explanation:

if you plot the points then draw the rectangle then you count the amount on each side and multiply 4 times 5

Find the value of the power.
(3/4) to the power of 4​

Answers

Answer:

81/256

Step-by-step explanation:

3^4 = 81

4^4 = 256

put them as a fraction and u get 81/256

Answer:

25

Step-by-step explanation:

9 students can make a poster in 10 hours. How many students should join them so that they altogether can make this poster in 6 hours?

Answers

Answer:

  6

Step-by-step explanation:

The work involved in making the poster is the product of students and hours:

  work = students × hours = (9 students)(10 hours) = 90 student·hours

__

needed

If hours are reduced to 6, the necessary number of students is ...

  90 student·hours = (6 hours)(students)

  (90 student·hours)/(6 hours) = 15 students . . . . . . divide by 6 hours

additional

If 15 are needed, then the number that must be added is ...

  15 -9 = 6 . . . . students need to be added

How can we classify the triangles based on the length of the sides?

Answers

Answer:

They are the same so it'd be isosceles

Step-by-step explanation:

Hope this helps!!!

Answer:

There are Equilateral, Isosceles and Scalene triangles

Step-by-step explanation:

When all three sides of a triangle are all the same length, it is a equilateral triangle. When only 2 of the sided are the same length, it is a isosceles triangle. When none of the sides are the same, it is scalene.

Two lines meet at a point that is also the endpoint of a ray. Set up and solve an equation to find the value of w.

Answers

Answer:

w=35

Step-by-step explanation:

See the angle to the right of 125? Put those angles together, and you get 180 degrees. For starters, we want to find the measure of the angle to the right of 125.

180-125=55

We can basically do this all over again to find w. The angle 55 + w + the square angle is 180 degrees. You can tell by the flat line. So we will find w like this:

180-90-55=w

Thus, w equals 35

6(3p – 1) = 84 can you help me with this question please? i am struggling to explain this to my son. thanks in advance.

Answers

On photos i showed 2 ways of possible solutions

Answer: p=5

Step-by-step explanation:

6(3p-1)=84

You can now do it two ways. This is the first way:

Divide by 6 so the equation now writes:

3p-1= 14

Then add the one onto the other side.

3p=15

Then divide 15 by 3

P=5

The other way is to expand the brackets first.

18p-6=84

Then add the 6 onto the other side.

18p=90

Then divide 90 by 18.

P=5

This is a bit more complex so I recommend the first way. Hope you can now explain to your son. Have an amazing day!

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