Answers
Answer:
[tex]x=\pm1 \:\textsf{or}\:x=\pm3[/tex]
Step-by-step explanation:
[tex]x^4-10x^2+9=0[/tex]
[tex]\textsf{let}\:x^2=y[/tex]
[tex]\implies y^2-10y+9=0[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex], find 2 two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex].
⇒ two numbers that multiply to 9 and sum to -10: -9 and -1
Rewrite [tex]b[/tex] as the sum of these 2 numbers:
[tex]\implies y^2-y-9y+9=0[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies y(y-1)-9(y-1)=0[/tex]
Factor out the common term [tex](y-1)[/tex]:
[tex]\implies (y-9)(y-1)=0[/tex]
[tex]\implies (y-9)=0 \implies y=9[/tex]
[tex]\implies (y-1)=0 \implies y=1[/tex]
Change [tex]y[/tex] back to [tex]x^2[/tex]:
[tex]\implies x^2=9\implies x=\pm3[/tex]
[tex]\implies x^2=1\implies x=\pm 1[/tex]
[tex]\textsf{So}\: x=\pm1 \:\textsf{or}\:x=\pm3[/tex]
Answer:
[tex]$x=\pm1\;\textrm{or}\;x=\pm3$[/tex]
Step-by-step explanation:
Substitute [tex]u = x^2[/tex] into the equation. This will make the quadratic formula easy to use.
[tex]\implies u^2 - 10u + 9 = 0[/tex]
Consider the form [tex]x^2 + bx + c = 0[/tex]. Find a pair of integers whose product is [tex]c[/tex] and whose sum is [tex]c[/tex]. In this case, whose product is [tex]9[/tex]and whose sum is [tex]10[/tex]. And write the factored form using the integers.
[tex]\implies (u - 9)(u - 1) = 0[/tex]
If any individual factor on the left side of the equation is equal to [tex]0[/tex], the entire expression will be equal to [tex]0[/tex].
[tex]\implies \begin{cases}u - 9 = 0 \\ \\ u - 1 = 0\end{cases}[/tex]
Set [tex]u - 9[/tex] equal to [tex]0[/tex] and solve for [tex]u[/tex]. Similarly, Set [tex]u - 1[/tex] equal to [tex]0[/tex] and solve for [tex]u[/tex].
[tex]\implies \begin{cases}u = 9 \\ \\ u = 1\end{cases}[/tex]
Substitute the real value of [tex]u = x^2[/tex] back into the solved equation.
[tex]\implies \begin{cases}x^2 = 9 \\ \\ x^2 = 1\end{cases}[/tex]
Take the square root of both sides of the equations to eliminate the exponent on the left side.
[tex]\implies \begin{cases}x = \sqrt{9} \\ \\ x = \sqrt{1}\end{cases}[/tex]
Solve both the equations for the value of [tex]x[/tex].
[tex]\implies \begin{cases}x = \pm3 \\ \\ x = \pm1\end{cases}[/tex]
Hence, this is our required solution for this question.
[tex]\rule{300}{1}[/tex]
Additional information:
There are three ways to solve a quadratic equation:
FactoringComplete the SquareQuadratic FormulaFactoring uses the logic that the product of any number and zero is zero. Complete the square method uses square root, and the quadratic formula is the simpler method of it.
Quadratic Formula [tex]x=\dfrac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
Related Questions
PLS HELP ME
••Pls show your work pls and thank you••
Answers
Question 6 of 10
15
10
Which function is graphed?
5
-8 6 4 2 0 2
6
8
-5
O A. y.
{x+6,> 3
{-x+6, x83
B. y - {x? +6,x< 3
1-x+6,23
O C. Y-
{x? +6.53
1-x+6, x>3
Tx2 +6.x23
O D. y =
{-x+6, x<3
Answers
Answer:
b
Step-by-step explanation:
The function represented by the graph is
y = { x² + 6 , x < 3
-x + 6 , x ≥ 3}
What is a function ?In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable. In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences.
According to the graph
When x < 3 then y = + 6
and, at x = 3 we get an open interval.
So, y = x² + 6 is valid for x < 3 not at x =3.
Also , y = -x + 6 is valid for x ≥ 3 and we get a close interval.
Thus, the function represented by the graph is
y = { x² + 6 , x < 3
-x + 6 , x ≥ 3}
learn more about functions here:
brainly.com/question/23104523
#SPJ7
Mark's age 15 years ago can be expressed as:
Answers
A bracelet costs $15. A matching necklace costs 3 times as much as the bracelet.
fcis the cost of the necklace, which equation models the cost of the
necklace and
shows the solution?
$15 = 3= CC= $5
А
B
$15 X 3 = cc = $45
С
$15 + 3 = cc = $18
3 x $15 + $15 = cc = $60
D
Answers
Answer:
B
$15 X 3 = cc = $45
Step-by-step explanation I asked my teacher and it was right
PLS HELP ME
••Pls show your work pls and thank you••
Answers
$36 every 4 hours is $9 an hour
(36 divided by 4)
A.
$144 divided by $9 is 16
So A. is 16
B.
$222 divided by $9 is 24.6 rounded to 25
C.
$9•40=$360 (40hour work week)
$9•7=$63 (7 hour day)
Apologies for the messy writing
Dr. Orchid has 9 paintings she wants to hang side by side on her wall.
(A) in how many ways can she arrange all 9 paintings? Show your work.
(B) if she only wants to display 4 of the paintings, in how many ways can she choose the paintings she wishes to display? Show your work.
Answers
The number of ways Dr. Orchid can arrange all 9 paintings and 4 paintings is, 362880 and 126 respectively.
What is arrangement?Arrangement of the things or object is mean to make the group of them in a systematic order, in all the possible ways.
The number of possible ways to arrange is n!. Here, n is the number of objects.
Dr. Orchid has 9 paintings she wants to hang side by side on her wall.
(A) Number of ways, she arranges all 9 paintings.There are total 9 paintings. So the number of arrangement of these painting is,
[tex]9!=9\times8\times7\times6\times5\times4\times3\times2\times1\\9!=362880[/tex]
(B) Number of ways can she choose the paintings she wishes to display-There are total 9 paintings, in which Dr. Orchid wants to display 4 of the paintings. Thus, the number of ways can she choose the paintings she wishes to display is,
[tex]^9C_4=\dfrac{9!}{4!(9-4)!}\\^9C_4=\dfrac{9\times8\times7\times6\times5!}{4!5!}\\^9C_4=126[/tex]
Hence, number of ways Dr. Orchid can arrange all 9 paintings and 4 paintings is, 362880 and 126 respectively.
Learn more about the arrangement here;
https://brainly.com/question/6032811
#SPJ1
Ms. Johnson's sixth grade class handed out surveys,
one to each student, about hair color and later posted the results:
75% of students had brown hair
20% of students had red hair
10% of students had blonde hair
What is the error in this sampling?
OA. Not that many students had brown hair.
O B. No one kept track of the number of surveys that went out.
O C.
The results add up to more than 100%
O D. Only two students were involved in tabulating the results.
Answers
Answer:
b
Step-by-step explanation:
Answer:
C.
Step-by-step explanation:
this should be obvious as 75 + 30 = 105
If you sell 175 shares of Michaels Flowers at $7.28 per share and 445 shares of Nanotech One at $10.80 per share, how much money will you receive, to the nearest dollar?
Answers
Answer:6080$
Step-by-step explanation:I did the same question on my test
The car you are taking is reliable and in good condition. The insurance is paid, the maintenance is up to date, and it gets about 27 miles to the gallon. The gas tank holds 18.5 gallons, and the low gas light will turn on when there are 2.5 gallons left in the tank. You have saved up $1,264
to spend on these trips. You must get gas if your low gas light turns on. The average gas price in
Oregon right now is $3.20 a gallon.
a. How much does it cost to fill up your gas tank?
b. How far can you travel on a tank of gas?
c. Write that as an equation.
Answers
Answer:
a=$59.20b=432 milesC
27g=x miles on a full tank of gas
27(16)=x
x=432 miles
Step-by-step explanation:
$3.20x18.5=$59.2018.5-2.5=16 gallons16 gallons x 27 miles= 432 miles27g=x miles on a full tank of gas27(16)=xx=432 milesEXPLAIN WHAT YOU PISCOVERED ABOUT THE NATURAL BASE E
Answers
Answer:
It's called the Natural Logarithm because so many processes in nature can be described mathematically using it.
For example:
1) The population of a colony of rabbits that reproduce at a constant rate
2) The decay rate of a charged capacitor
3) The decay rate of a radioactive isotope
4) The rate at which your money will grow if you apply an interest rate continuously over a period of time.
5) The population of seeds in a sun flower
6) etc.
Julia's car used 1/100 of a gallon to travel 0.25 miles. How many miles can the car go on one gallon of gas? On the double number line below, fill in the given values, then use multiplication to find the missing value. Enter your answers as fractions, whole numbers, or decimals. miles 0 gallons Enter your final answer as a whole number or decimal.
Answers
Answer:
25 miles
Step-by-step explanation:
well
1/100 = 0.25
10/100 = 2.5 (Because 0.25 x 10)
100/100 = 25 (Because 0.25x100)
John, Musa and Mable shared 180,000 in the ratio of 2:3:4 respectively How much money did each get?
Answers
Answer:
2:3:4=40,000:60,000:80,000
Step-by-step explanation:
plus 2+3+4
thats 9
divide 9 by total amount which is what ratio 1 got =20,000
so now you multiple each ratio with 20,000 to get the ratio.
Find the area and the circumference of a circle with radius 6 cm.
Write your answers in terms of it, and be sure to include the correct units in your answers.
Answers
Step-by-step explanation:
radius=6cm.
π=22 over 7
circumference=2πr
circumference=2×22 over7×6
circumference=51.04cm
find three consecutive positive integers such that the product of the first and the third integer os 29 more than the second
Answers
Answer:
5, 6, 7
Step-by-step explanation:
let the 3 consecutive integers be n , n + 1 , n + 2 , then
n(n + 2) = n+ 1 + 29
n² + 2n = n + 30 ( subtract n + 30 from both sides )
n² + n - 30 = 0 ← in standard form
(n + 6)(n - 5) = 0 ← in factored form
equate each factor to zero and solve for n
n + 6 = 0 ⇒ n = - 6
n - 5 = 0 ⇒ n = 5
n > 0 , then n = 5
the 3 integers are 5, 5 + 1, 5 + 2 , that is
5, 6, 7
-
A rectangle has dimensions 2x – 12 by 3x + 9 and area 60 cm². What are the actual
dimensions of the rectangle?
Answers
Answer:
2 x 30 cm
Step-by-step explanation:
L x W = 60
(2x-12)(3x+9) = 60
6x^2 -18x-168=0
use quadratic fromula to find x = 7 or -4 (throw out)
the sides then become ( using 7)
2 and 30 cm
Schools
Name
7th Grade Math EOY, L104 (Statistics and Probability)
Non-Uniform Probability Models
Homework
1. A box contains marbles of the following colors:
Blue
14
Green
10
Yellow
S
Red
68
(a) Create a probability model showing the theoretical probabilities of picking a marble
from the box
2. Tanya has 3 red hats and 2 blue hats. If she picks one hat at random 100 times, how
Date
Team
Answers
Answer:
this is too much, and I forgot how to do this
Find the mean 3,4,4,2,5,7,2
Answers
Answer:
pls refer to pic
well I am from India whats the time there now
jane has twice as many books as Kate. if jane gives 14 books to Kate , they will have the same number of books. how many books do they have altogether?
need help plss
Answers
Answer:
I believe the answer is 42 books.
Step-by-step explanation:
What is the surface area of the prism in the picture?
Answers
390 m^2
[tex]\bold{EXPLANATIONS:}[/tex]
Answer:
girl that is so easy, just look it up
Which algebraic expression is equivalent to the expression below?
(16x - 2) + (10 - 8x)
OA. 8x + 12
OB. 26x - 10
OC. 24x + 12
OD. 8x + 8
Answers
Answer:
D. 8x + 8
Step-by-step explanation:
16x - 8x - 2 + 10 = 8x + 8
Hope this helps
Answer:
D. 8x + 8
Step-by-step explanation:
Simplify the expression:
16x - 2 + 10 - 8x
Combine like terms:
16x + 8 - 8x
8x + 8
hope this helps!
what is 108 x 0.37 in money
Answers
saved: 12:19 PM
Week 1
Week 2
Week 3
Total
Lettuce
$5.48
?
$3.55
$12.00
Apples
$3.57
$ 2.12
$4.44
?
Chicken
$8.12
$10.13
?
$20.45
Enter his total cost for lettuce, apples, and chicken during Week 2.
$
Answers
135
Step-by-step explanation:
salamat po dana po makatulong
Can you please solve
Answers
7.25% of 38,000
10% = 3,800
5% = 1,900
1% = 380
0.50% = 190
0.25% = 95
1,900+380+380+95 = 2,755
38,000+2,755 = 40,755
Aman bootowed Rs 500 for 3 years at the oate for 5% Find his interest and amount
Answers
Answer:
Interest=75
Amount=575
Step-by-step explanation:
Interest= Principal×rate×time÷100
500×5×3÷100=75
Amount=Principal+Interest
Amount=575
I hope you find this helpful
Answer:
Amount =principa+simple interest.
=575
Step-by-step explanation:
Simple =(P*R*T) /100.
=(500*5*3)/100.
=75.
.....
500+75=575
what is the answer for 10^30 kg
Answers
Answer:
1000000000000000000000000000000 kg / 1E + 30 kg
Step-by-step explanation:
10³⁰ kg
Calculate 10 thirty times,
= (10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10 × 10) kg
=1000000000000000000000000000000 kg
= 1E + 30 kg
_____________
Hope it helps ⚜
[tex] {10}^{30} [/tex]
solution:[tex] {10}^{30} [/tex]
[tex] = 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10 \times 10[/tex]
[tex] = 100000000000000000000000000000[/tex]
[tex] = 1.0e30 \: kg[/tex]
help? I can’t figure out this problem
Answers
Answer:
B
Step-by-step explanation:
Euler's formula tells you that ...
cos(θ) +sin(θ)·i ≡ e^(i·θ)
__
So, for θ = 90° (= π/2 radians), this is ...
cos(π/2) +sin(π/2)·i = 0 +i = i = e^(i·π/2) . . . . . matches choice B
76/81*80/76 how to solve mentally
Answers
Answer:
[tex]\frac{80}{81}[/tex]
Step-by-step explanation:
The cross numerator and denominator of 76 can be crossed out leaving out simply.
[tex]\frac{76}{81} *\frac{80}{76}\\\frac{1}{81} *\frac{80}{1}=\frac{80}{81}[/tex]
please i really need help right now 25 points
Answers
Step-by-step explanation:
choice 2 ..............
A gardener uses 20 gallons of water each week on his 8-foot by 10-foot vegetable garden. He plans to enlarge his
garden to 24 feet by 30 feet.
How much water would he expect to use on his new garden? Show all of your work and provide a brief explanation with your answer.
Answers
Answer:
60 gallons
Step-by-step explanation:
so he enlarged it by three so it would be 24by30
because of that, you have to multiply 20g by 3 also
that gives you 60 gallons
Based on the family the graph below belongs to, which equation could represent the graph ?
Answers
Firstly this looks like translated log function graph
y=logxlog1=0
As per graph the graph is pulled some inwards y axis but little bit
y=log2xUsually log x leaves y axis at -1 but here it leaves at +2
So
y axis is moved upwards (+3)
Last function
y=log(2x)+3