How many solutions does this equation have x^4 - 6x^2 -7 = 0

Answers

Answer 1

Answer:

2 solutions

Step-by-step explanation:

x^4-6x^2-7=0

Replace x^2 by y

(x^2)^2-6x^2-7=0

y^2-6y-7=0

D=b^2-4ac= (-6)^2-4*1*(-7)= 36+28=64

sqrtD=8

y1=(-b-sqrtD)/2a=-2/2=-1

y2= (-b+sqrtD)/2a=14/2=7

x^2=-1(n0 roots)    x^2=7 x=sqrt7 or x=-sqrt7

2 roots


Related Questions

Which rule is a recursive rule for the sequence 1,-6,36, -216

Answers

Answer:

3rd option

Step-by-step explanation:

There is a common ratio between consecutive terms , that is

r = - 6 ÷ 1 = 36 ÷ - 6 = - 216 ÷ 36 = - 6

To obtain a term in the sequence multiply the previous term by - 6

Then the recursive rule is

[tex]a_{n}[/tex] = - 6 . [tex]a_{n-1}[/tex]

Answer: 1*6°=6

1*(-6)^1=-6

1*(-6)^2=36

1*(-6)^3=-216

Sage is 7 years older than Jonathan. If Jonathan is x years old, how old was Sage 10 years ago?

Answers

Answer:

(x-3) years

Step-by-step explanation:

We are given that

Age of Jonathan= x years

Sage is 7 years older than Jonathan

It means

Age of Sage=(x+7) years

We have to find the age of Sage 10 years ago.

10 Years ago,

Age of Jonathan=(x-10) years

Age of Sage=(x+7-10) years

Age of Sage=(x-3) years

Hence, 10 years ago, age of Sage =(x-3) years


The length and width of a rectangle are in a 3 : 5 ratio. The perimeter of the
rectangle is 64. What are the length and width of the rectangle?

Answers

Answer:

Step-by-step explanation:

Rectangle:

Length : Width = 3 : 5

Length = 3x

Width = 5x

Perimeter = 64

2*(length + width) = 64

2*(3x + 5x) = 64           {Add like terms}

2 * 8x = 64                                

  16x = 64        {Divide both sides by 16}

      x = 64/16

      x = 4

Length = 3*4 = 12 units

Width = 5*4 = 20 units

Answer:

Step-by-step explanation:

solution;

here

let us suppose the ratios of length and width of rectangle be 3x and 5x

if the perimeter of rectangle is 64

we know that,

perimeter of rectangle=2 (l + w)

or,    64=2(3x +5x)

or,     64=2(8x)

or,     64=16x

or,      x=4

therefore length=3x

                      3*4=12

                 width=5x

                     5*4=20

Afreen says, "I am thinking of 3 consecutive numbers. The first is a multiple of 4, the second is a multiple of 5 and the third is a multiple of 6." What could the numbers be? Can you find 3 possible sets of numbers?

Answers

Answer:

The 3 ses that we found are:

{4, 5, 6}

{64, 65, 66}

{124, 125, 126}

Step-by-step explanation:

3 consecutive numbers are written as:

n, (n + 1), (n + 2)

We know that the first one is a multiple of 4.

Then n is a multiple of 4:

n = k*4

where k is an integer.

The second one is a multiple of 5, then:

(n + 1) = j*5

where j is an integer.

The last one is a multiple of 6.

(n + 2) = p*6

where p is an integer.

We want to find 3 sets.

The first one is trivial:

n = 4

n + 1 = 5

n + 2 = 6

4 is a multiple of 4

5 is a multiple of 5

6 is a multiple of 6.

Now let's find a set that is not trivial.

First, remember that all the multiples of 5 end with a 0 or a 5,

Then we can look for a value n, that is multiple of 4, and that has a last units digit equal to 4 (then the next one will have a units digit and will be multiple of 5)

For example, 4*6 = 24

24 is a multiple of 4.

The next number is 24 + 1 = 25, which is multiple of 5.

The next number is 25 + 1 = 26, which is not multiple of 6.

So let's try again.

4*11 = 44, is a multiple of 4.

The next number is 44 + 1 = 45

45 is a multiple of 5.

The next number is 45 + 1 = 46, which is not multiple of 6

So we need to try with another set.

4*16 = 64, is a multiple of 4.

The next number is 64 + 1 = 65, which is multiple of 5.

The next number is 66, which is multiple of 6:

6*11 = 66

Then the set:

n = 64

n + 1 = 65

n + 2 = 66

Is a possible set.

Now we can keep trying this, we can see that the next set  has the numbers:

n = 4*31  = 124 is a multiple of 4.

The next number, is 124 + 1 = 125, which is a multiple of 5.

The next number is 125 + 1 = 126, which is multiple of 6

6*21 = 126

Then the set:

n = 124

n + 1 = 125

n + 2 = 126

Is another possible set.

The 3 ses that we found are:

{4, 5, 6}

{64, 65, 66}

{124, 125, 126}

Does anyone know the answer to this math question?

Answers

Answer:

sorry i don,t know but i am finding

if i get then i hep you

Step-by-step explanation:

thanks and have nice day

A standard deck of 52 cards has 13 ranks (Ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King) and 4 suits ($\spadesuit$, $\heartsuit$, $\diamondsuit$, and $\clubsuit$), such that there is exactly one card for any given rank and suit. Two of the suits ($\spadesuit$ and $\clubsuit$) are black and the other two suits ($\heartsuit$ and $\diamondsuit$) are red. The deck is randomly arranged. What is the probability that the top card is a 3 and the second card is an eight

Answers

Answer:

4 / 663

Step-by-step explanation:

Given that :

Number of cards in a standard deck = 52

Number of 3's in s standard deck = 4 (each suit has one card each)

Number of 8's in a standard deck = 4 (each suit has one card each)

Probability, P = required outcome / Total possible outcomes

Choosing without replacement :

P(top card is a 3) = 4 / 52

P(second draw is 8) = 4 / 51

P(top card is a 3 and second is 8) :.

4/52 * 4/51 = 16 / 2652 = 4 / 663

identify each of the following as rational or irrational.

Answers

Answer:

Step-by-step explanation:

A rational number can be written as a fraction of two integers.

√23 is irrational because we do not know what the square root of 23 is in terms of integers in a fraction.

104.42 is rational because it can be expressed as 10442/100 . We can express it as this because

104.42 * 1 = 104.42 * 100/100 = 10442/100, and multiplying something by 1 keeps it the same

√64 is rational because it is equal to 8, and 8/1 is equal to 8

49.396 with the 6 repeating is rational because we can express 49.39 as

49.39 * 1 = 49.39 * 100/100 = 4939/100, and we are then left with

49.396- 49.39 = 0.006 (with the 6 repeating). A repeating decimal can be expressed as x/9, with the x representing all values before the repetition begins multiplied by 10.

For example, 0.6 with the 6 repeating can be represented as 6/9. This is because 0.6 * 10 = 6, and we divide that by 9. Similarly, 0.006 with the 6 repeating can be represented by 0.06/9

We add the two fractions together to get

4939/100 + 0.06/9

multiply both fractions by the other's denominator to even them out and make the numerator of the second fraction an integer

(4939*9)/(100*9) + (0.06*100)/(9*100)

= 44451/900 + 6/900

= 44460/900

Assuming that the last number has only the digits given, that is rational because, similarly to 104.42, it can be multiplied by a power of 10 to result in (integer)/(integer), making it rational. If the dots represent infinite digits, then it is not rational because there are infinite digits that are not repeating, and there is no way to know the last digit, so it is impossible to write a fraction from it

Year 10 girls = 70, year 10 boys = 140, what fraction of year 10 are boys?

Answers

Answer:

2/3

Step-by-step explanation:

140/(140+70)

=140/210

simplified

=2/3

Answer: 2/4

You add 70 and 140 which equals 210. 210 divided by 14 is 15 and 140 divided 14 equals 10. So you have 10 over 15 so you divide both by 5 and you get 2/3

Question 2.
If 0 is an angle in the first quadrant, and cos(θ) = 0.669, determine the value of
cos(π - θ), cos(π + θ), and cos(4π - θ) using Symmetry.

Answers

Answer:

1) -0.669

2) -0.669

3) 0.669

Step-by-step explanation:

Since we are subtracting or adding multipled of pi, we will either obtain 0.669 or -0.669 as our answer for each of the three different questions.

Cosine is the x-coordinate in our orderes pairs. If our point ends up on the right side of the y-axis, the cosine will be positive. If our point ends up on left side, it will be negative.

Choose a thetha (I'm going to choose it in degrees) in the first quadrant to help with a visual.

If theta=70:

1) then 180-70=110 which is in second quadrant, so our cosines will be opposite in value.

2) then 180+70=250 which is in third quadrant, so our cosines will be opposite in value.

3) then 4×180-70=720-70=650 =1(360)+290 which ends up in the 4th quadrant which means the consines will have the same value.

The first side of a triangle measures 5 in. less than the second side, the third side is 3 in. more than the first side, and the perimeter is 17 in. Set up an equation that relates the sides of the triangles in terms of the perimeter of the triangle.

3s - 10 = 17
3s - 7 = 17
2s -7 = 17
2s - 5 = 17

Answers

Answer:

3s-10=17

s=9

3×9-10=17

27-10=17

calculate the surface area of a hockey puck with a height of 1 in. and a diameter of 3 in

Answers

Answer:

23.56

Step-by-step explanation:

2([tex]\pi r^{2}[/tex]) + 2[tex]\pi[/tex]rh

2([tex]\pi[/tex] [tex]1.5^{2}[/tex])+ 2[tex]\pi[/tex](1.5)(1)

23.56

23.56 in² is the surface area

What is surface area?

A solid object's surface area is a measurement of the overall space that the object's surface takes up.

Given

2(πr²) + 2πrh

2π( 1.5)²+ 2π(1.5)(1)

= 23.56 in²

To know more about surface area refer to:

https://brainly.com/question/16082274

#SPJ2

Giải hệ pt :{ 2x-3y=1
{x+2y=4

Answers

x+2y=4 ] × (-2) —> -2x-4y=-8

2x-3y=1

-2x-4y=-8

_________o_o___

–7y=–7 —> y =1

2x-3y=1 —> 2x -3(1)=1 —> 2x-3=1 —> 2x=1+3 —> 2x=4

x=4/2 —> x=2

(x,y) > ( 2,1)

I hope I helped you ^_^

need help, please need help

Answers

Answer:

Step-by-step explanation:

thats your problem learn how to pay attention lol

Graph: f(x) = 3/2 (2)x
Step 1: Calculate the initial value of the function.
f(0)=

Answers

Answer:

Step 1: 1.5

Step 2: Plot the points (0, 1.5)

Step 3: 3, then 0.75

Step 4: Plot the points (1, 3) and (-1, 0.75)

Step 5: y=0

Step-by-step explanation:

Ur welcome and have a nice day :>

The initial value of the function f(x) = 3/2 (2)^x is 3/2

How to calculate the initial value of the function?

The function expression is given s:

f(x) = 3/2 (2)^x

Substitute 0 for x

f(0) = 3/2 (2)^0

Evaluate the exponent

f(0) = 3/2 * 1

Evaluate the product

f(0) = 3/2

Hence, the initial value of the function is 3/2

Read more about exponential functions at:

https://brainly.com/question/11464095

how many halves are in 2 whole objects​

Answers

4 halves if u have one object and you cut it in half you will get two then you do the same to another object so you’ll get 4 :) sorry if I’m wrong

6. Show how to simplify the expression 8x + 3 + 4x - 2 without using algebra tiles. Describe each step of the process.​

Answers

Answer:

12x+1

Step-by-step explanation:

8x+3+4x-2

8x+4x+3-2

Arranging Like terms

12x+1

Adding Like terms (8x+4x) and Substracting numbers ! ++- = - So we substrate it and in addition we don't change symbols so 3 is greatest number so we write + there !

Amanda has six more than four times the number of crayons that Clyde has. (write the equation)​

Answers

Answer:

y = 4x + 6

Step-by-step explanation:

Clyde has x crayons.

Amanda has y crayons.

The equation:

y = 4x + 6

Calculate the maximum absolute uncertainty for R if:

R = 9A / B
A = 32 +/- 2 seconds
B = 11 +/- 3 seconds

1 second


0.33 seconds


9 seconds


2 seconds


6 seconds

Answers

Answer:

1.1 small inches of the day

Step-by-step explanation:

Can someone help me with this math homework please!

Answers

Answer:

1.33 & n - 6 = 0.75(t - 8)

Explanation:

Speed can be calculated as miles ÷ minutes

4 ÷ 3 = 1.33 and 8 ÷ 6 = 1.33 as well

Since we know the n and t, we can substitute one into the equation to find the other (substitute t = 8 into all four equations and see do we get n = 6)

You can do this with t = 4 and n = 3 as well

Answer:

you are a great woman removing the sum o saare and pa and pa to the lord and your life to you for drawing the sum o the streets

You are playing the Integer Game. The goal of the game is for the sum of the cards in your hand to be as close to zero as possible. Here are the cards in your hand,
4
-8
-3
2
What is the current value of your hand?

Answers

-5 because the negatives equal to -11 then the positives equal to 6 and -11+6 is -5.

Tiana uses the equation c = 21h to figure out the total amount, c, she should
charge a customer for babysitting for h hours.
a. What is the constant of proportionality? What does it mean?
b. Tiana charges $94.50 for a job. How long did she babysit for?
Show your work.

Answers

Answer:

a. The constant of proportionality is, 21

b. Tiana charges $94.50 for a job, so, c=94.50

from the given equation,

c = 21h

or, 94.50 = 21h

or, h = 94.50/21

or, h = 4.5

She babysit for 4.5 hours.

Answered by GAUTHMATH

The constant of proportionality is 21 and it means the constant value that connects two variables together. If Tiana charges $94.50 for a job, she spent 4.5hours babysitting.

The equation used by Tiana c = 21h to figure out the total amount (c) she should charge a customer for babysitting for h hours.

The constant of proportionality, denoted by K, in a linear relationship shows how two variables relate to one another. In this case, the total amount (c) is directly proportional to time (h).

The constant of proportionality, which is 21, connects the variables 'c' and 'h'.

If Tiana charges $94.50 for a job, we can calculate the time spent on doing the job by using:

c = 21h

94.50 = 21h

h = 94.50 ÷ 21

h = 4.5hours.

Therefore, Tiana spent 4½ hours babysitting.

Learn more: https://brainly.com/question/20986361?referrer=searchResults

Need help !!!What is the first step to solve the following system of equations using substitution?

Answers

Answer:

It is the second one: Solve the first equation for x.

Step-by-step explanation:

SOMEONE PLEASE HELP ME!

Answers

FH = HG =GF
—— —— ——
IK JK IJ

8 =HG =3.2
—. —— ——
32 JK IJ

or, 2 3.2
—— = ——
8 IJ

or,2IJ=3.2*8

or,IJ=25.6
———-
2
.•.IJ=12.8
Hope this might help you

If eleven plus two equal one what does nine plus five equal?

Answers

Answer:

huh???

Step-by-step explanation:

how does that make sence

Carlos compro cierta cantidad de panes puso 1/4 de esa cantidad sorbre su bandeja y dejo el resto de panes en la bolsa ¿Cuantos panes dejo Carlos en la bolsa?

Answers

Answer:

The quantity of loaves left in the bag is 3/4.

Step-by-step explanation:

Carlos bought a certain amount of loaves, put 1/4 of that amount on his tray and left the rest of the loaves in the bag. How many loaves did Carlos leave in the bag?

Quantity of loaves in tray is 1/4

So, the quantity of loaves in the bag is

[tex]1-\frac{1}{4}=\frac{3}{4}[/tex]


I know you have to use the half life formula but I don’t know how to use it could someone show how to find the solution step by step? Thank you

Answers

Answer:

[tex]A = Pe ^{-0.03108 * t}[/tex]

Step-by-step explanation:

Note: these are typically two part questions...

you have the model and have to FIRST find a constant value "k"

once you have the "k" value you plug that into the model to finish the problem

[tex]A = Pe ^{-kt}[/tex] is a typical version of the continuous decay...

e is "e 2.717" not a variable "e"

so... step 1.. fink k

you are told that the 1/2 life is 22.3 years...

so lets assume that we started with 2 units of lead, and waited for it to decrease to 1 (1 is 1/2 of 2)

you would have

1 = 2[tex]e^{k * 22.3}[/tex]

.5 = [tex]e^{k * 22.3}[/tex]

ln(.5) = 22.3k ln(e)

ln(e) = 1

ln(.5) = 22.3k

ln(.5) = 22.3k ln(e)

[tex]\frac{ln(.5) }{22.3} = k[/tex]

[tex]\frac{\ln \left(0.5\right)}{22.3}=-0.03108[/tex] = k

The equation of line a is y=-x+ 3. If line b runs perpendicular to line a and
passes through (2, 6), what would be the equation of line b?

Answers

Answer:

y = 4x -2

Step-by-step explanation:

y = 4x + b

6 = 4(2) + b

6 = 8 + b

-2 = b

write y=4x+3 in mapping notation

Answers

Answer:

y=7x

Step-by-step explanation:

because y= 4x+3=7x

what is the value of 5 in the number 68.513?​

Answers

Answer:

00000000.1

Step-by-step explanation:

1+1=2-1%000.1

Help,anyone can help me do quetion,I will mark brainlest.​

Answers

Answer:

Step-by-step explanation:

7)  4*5 - 2*3 = answer

20-6 = 14

8)  5*4 - 2*(2*2) = answer

20 -8 = 12

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