Answer:
7
Step-by-step explanation:
1. Solve for x in [tex]x^2 = 3x - 1[/tex].
[tex]x=\frac{3+ \sqrt{5}}{2} ,\frac{3- \sqrt{5}}{2}[/tex]
2. Substitute [tex]x=\frac{3+ \sqrt{5}}{2} ,\frac{3- \sqrt{5}}{2}[/tex] into [tex]x^2 + \frac{1}{x^2} = y[/tex].
[tex]\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2} = y[/tex]
3. Solve for y in [tex]\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2} = y[/tex]
[tex]y=\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2}[/tex]
4. Therefore,
[tex]x=\frac{3 + \sqrt{5} }{2}, \frac{3-\sqrt{5}}{2}\\y=\frac{(3+\sqrt{5})^2}{(2,2(3-\sqrt{5}))^2} + \frac{(2,2(3-\sqrt{5}))^2}{(3 + \sqrt{5})^2}[/tex]
............
[tex]x= \frac{3-\sqrt{5}}{2}[/tex]≈[tex]0.381966011, y=7[/tex]
[tex]x= \frac{\sqrt{5}+3}{2}[/tex]≈[tex]2.618033989, y=7[/tex]
Hope this helps! Please let me know if you need more help, or if you think my answer is incorrect. Please rate and click the Thanks button if it helped you out. Brainliest would be MUCH appreciated. Have a great day!
Stay Brainy!
−Kallmekrish
The best way to predict the future is to create it.
- Abraham Lincoln, Past U.S. President
Answer:
7
Step-by-step explanation:
Given equation: [tex]x^2=3x-1[/tex]
Rearrange so that it is equal to zero:
[tex]\implies x^2-3x+1=0[/tex]
Quadratic formula
[tex]x=\dfrac{-b \pm \sqrt{b^2-4ac} }{2a}\quad\textsf{when}\:ax^2+bx+c=0[/tex]
Using the quadratic formula to solve the given equation:
[tex]\implies x=\dfrac{-(-3) \pm \sqrt{(-3)^2-4(1)(1)} }{2(1)}[/tex]
[tex]\implies x=\dfrac{3 \pm \sqrt{5}}{2}[/tex]
[tex]\implies x^2=\dfrac{7 \pm 3\sqrt{5}}{2}[/tex]
Substituting this into [tex]x^2+\dfrac{1}{x^2}[/tex]
[tex]\implies \dfrac{7\pm3\sqrt{5}}{2}+\dfrac{1}{\dfrac{7\pm3\sqrt{5}}{2}}[/tex]
[tex]\implies \dfrac{7\pm3\sqrt{5}}{2}+\dfrac{2}{7\pm3\sqrt{5}}[/tex]
[tex]\implies \dfrac{(7\pm3\sqrt{5})(7\pm3\sqrt{5})}{2(7\pm3\sqrt{5})}+\dfrac{4}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{(7\pm3\sqrt{5})(7\pm3\sqrt{5})+4}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{49\pm42\sqrt{5}+45+4}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{98\pm42\sqrt{5}}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{14(7\pm3\sqrt{5})}{2(7\pm3\sqrt{5})}[/tex]
[tex]\implies \dfrac{14}{2}[/tex]
[tex]\implies 7[/tex]
HELPP PLSS!!!!!!!
Find the volume of the following objects.
Answer:
First cone: 29.32
Steps:
1. 3.14(2^2)7/3
2. 3.14(4)7/3
3. 12.56(7/3)
4. 12.56(2.3
5. 29.32
Second cone: 1526.81
Divide 18 in half and so same steps as above to get the answer! :)
Have a great day!!
Please rate and mark brainliest!!
Answer:
Cone 1 = 29.32mi || Cone 2 = 1526.81
Step-by-step explanation:
Step 1) Apply formula (volume of cone)
V= 1/3 * π * r^2 * h [OR] V= π * r^2 * h/3
Step 2) Insert numbers. (cone 1)
V= π * 2^2 * 7/3
Step 3) Insert numbers. (cone 2)
V= π * 9^2 * 18/3 (r=9 because r=1/2 base diameter of circle, 18/2=9)
Step 4) Plug and solve.
Step 5) CHECK YOUR ANSWER BEFORE SUBMISSION. Do it a few times just to make sure it checks out, and then continue!
find the area of the trapezoid
Answer:
the answer is 8
Step-by-step explanation:
it is 8 because if you 2x2 = 4 then + 4 more equal 8. ( or just count the area )
I just need to fill the table out
Answer:
for cosine: 1, 0.97, 0.87, 0.71, 0.5, 0.26, 0..... for sine: 0, 0.26, 0.5, 0.71, 0.87, 0.97, 1.
Step-by-step explanation:
Calculator for Cos, reverse them for Sine.
Write the following as an inequality.
5 is greater than or equal to w, and -5 is less than or equal to w
use w only once in your inequality
Answer:
[tex]-5\leq w\leq 5[/tex]
[tex]\huge\underline\mathtt\red{Answer:}[/tex]
−5 ≤ w ≤ 5
A marketing company is designing a new package for a box of cereal. They have determined that the function C(x) = 4.5 x2 models the cost of a box with side lengths as shown (measured in inches).
Identify a reasonable domain and range for the function.
So the function is
[tex]\\ \rm\rightarrowtail y=4.5x^2[/tex]
As we know
x²≥0x≥0
hence domain is
[tex]\\ \rm\rightarrowtail D_f\in R[/tex]
Least value of function is at x²=0 i.e 0Hence range:-
[tex]\\ \rm\rightarrowtail R_f\in [0,\infty)[/tex]
Which is the better deal?
A) The 18 oz
B) The 12 oz
C) They are the same price per ounce
Answer:
a
Step-by-step explanation:
because you get more than you do in choice b
i
think of a number multiply it by seven then add 8 to it and the results is 29 find the number
Answer:
3
Step-by-step explanation:
29 - 8 = 21
21 / 7 = 3
Therefore, the answer is 3
Answer:
wouldnt it be 3? cause 3*7=21 then add 8 thats 29
Step-by-step explanation:
Evaluate the following, if a=7, b=3, c=2
what is a2 ( two is a exponet )-5bc-1
please hurry.
i'll give you 70 points!
Answer:
Step-by-step explanation:
a^2 - 5bc - 1
a = 7
b = 3
c = 2
7^2 - 5*3*2 - 1
49 - 30 - 1
18
To solve this equation for x, we must get x by itself. How would we do this?
X + 4 = 7
A. Add 4 to both sides.
B.Subtract 4 from both sides.
Answer:
B
Step-by-step explanation:
If you were to add 4 to both sides, you would have X + 8 = 11
But when you subract, you get X = 7-4, X = 3.
Ava buys 3.5 pounds of strawberries for $2.99 per pound. How much does she spend?
Answer:
10.50$
Step-by-step explanation:
3 dollars a pound
3x3=9
half a pound, half the price which is 1.50$
9+1.50= 10.50
Answer:
$10.465 ≈ $10.47
Step-by-step explanation:
3.5 lb of strawberries * $2.99/lb of strawberries = $10.465 ≈ $10.47
Please mark as brainliest.
write these polynomials in standard form
1). 5x^2- 15+7
2.) 4 + 8n- 3n^4＋ 10n2
Answer:
1. [tex]5x^{2} - 8[/tex]
2. [tex]NaN-16[/tex]
Step-by-step explanation:
Please Help I Don't Understand. Thank You.
Answer:
Step-by-step explanation:
Good evening! Can someone please answer this, ill give you brainliest and your earning 50 points. Would be very appreciated.
Answer:
on the 10th day from option A you would get $196.83. on the 10th day from option B you would get $1,000.
Step-by-step explanation:
Answer:
Option B.
Step-by-step explanation:
Given:
Option A: You Receive 1¢ on the first day, 3¢ on the second day, 9¢ on the third day, 27¢ on the fourth day,and so on, tripling each day.
Option B: You receive $100 each day(Day 1, you would receive $100, Day 2, you would receive $100..)
You will receive the month that is offered on day 10. Which option would you choose? Use the table and/ or graph to organize your thinking.
-------------------------------------------------------------------------------------------------------------
Option A Option B:
Tripling = times 3 Add $100
Table: Table:
[1] 1¢ [1] $100
[2] 3¢ [2] $200
[3] 9¢ [3] $300
[4] 27¢ [4] $400
[5] 81¢ [5] $500
[6]$2.43 [6] $600
[7] $7.29 [7] $700
[8] $21.87 [8] $800
[9] $65.61 [9] $900
[10] $196.83 [10] $1000
-------------------------------------------------------------------------------------------------------------
Thus, I will choose option B.
-------------------------------------------------------------------------------------------------------------
~lenvy~
Which of the following is an expression
A. 7x = 4
B. 7 = x = 4
C. 7 - x
D. 7n - 3 = 32
Answer:
D. 7n - 3 = 32 Because is contains the neccesary amount of variables needed to be considered as an expression.
Step-by-step explanation:
Hope this helps you! :D
6 workers can build a wall in 30 days. If after 6 days 3 more workers join, find the number of days to build the same wall?
The wall can be built in 22 days by 6 workers in first 6 days and 9 workers in the rest of time.
How to use inverse proportionality to determine building time of a wallIn this question we must use the definition of inverse proportionality, in which the number of workers ([tex]n[/tex]), no unit, is inversely proportional to the building time ([tex]t[/tex]), in days.
According to the statement, 6 workers spent 6 days building a wall and there are 24 days left for completion, but 3 more workers entered to reduce building time, which can be represented by the following expression:
[tex]x = 24\,days \times \frac{6}{9}[/tex]
[tex]x = 16\,days[/tex]
In this scenario, the wall can be built in 22 days. [tex]\blacksquare[/tex]
To learn more on inverse proportionality, we kindly invite to check this verified question: https://brainly.com/question/4838941
the education foundation hosted an anual fundrasing dinner. there were 192 tickets printed for the dinner and each dinner ticket cost $12.50. if 3/4 of the dinner tickets were sold, how much money was rasied frome the dinner ticket sales?
Answer:
Step-by-step explanation:
can someone help me with this question
Answer:
B
Step-by-step explanation:
Convert from mixed numbers to improper fractions:
[tex]\sf area=90 \frac{3}{10}=\dfrac{90 \cdot 10+3}{10}=\dfrac{903}{10}[/tex]
[tex]\sf length=10\frac12=\dfrac{10 \cdot 2+1}{2}=\dfrac{21}{2}[/tex]
Area of a rectangle = length x width
⇒ width = area ÷ length
[tex]\sf \implies width=\dfrac{903}{10} \div \dfrac{21}{2}[/tex]
[tex]\sf \implies width=\dfrac{903}{10} \times \dfrac{2}{21}[/tex]
[tex]\sf \implies width=\dfrac{1806}{210}[/tex]
[tex]\sf \implies width=\dfrac{1806 \div 42}{210 \div 42}[/tex]
[tex]\sf \implies width=\dfrac{43}{5}[/tex]
[tex]\sf \implies width=8\frac35[/tex]
[tex] \pink{ \text{Given:}}[/tex]
[tex] \\ [/tex]
[tex] \star \sf{}Area =90 \dfrac{3}{10} [/tex]
[tex] \\ [/tex]
[tex] \star \sf{}Length =10 \dfrac{1}{2} [/tex]
[tex] \\ \\ [/tex]
[tex] \purple{ \text{To~Find:}}[/tex]
[tex] \\ \\ [/tex]
[tex] \star \sf Width \: of \: rectangle[/tex]
[tex] \\ \\ [/tex]
[tex] \orange{ \text{Solution:}}[/tex]
[tex] \\ \\ [/tex]
So first convert length and area from fraction form to decible.
[tex] \leadsto\sf{}Area =90 \dfrac{3}{10} [/tex]
[tex] \\ [/tex]
[tex] \leadsto\sf{}Area = \dfrac{903}{10} [/tex]
[tex] \\ [/tex]
[tex] \leadsto\sf{}Area =90.3[/tex]
[tex] \\ [/tex]
Now convert value length into decibel .
[tex] \\ [/tex]
[tex] \leadsto\sf{}Length =10 \dfrac{1}{2} [/tex]
[tex] \\ [/tex]
[tex] \leadsto\sf{}Length = \dfrac{21}{2} [/tex]
[tex] \\ [/tex]
[tex] \leadsto\sf{}Length = 10.5[/tex]
[tex] \\ [/tex]
We know :-
[tex]\bigstar\boxed{\rm Area~of~rectangle= length \times width}[/tex]
[tex] \\ \\ [/tex]
So:-
[tex] \\ [/tex]
[tex]: \implies\sf Area~of~rectangle= length \times width \\ \\ \\ : \implies\sf 90.3= 10.5 \times width \\ \\ \\: \implies\sf 90.3 \div 10.5=width \\ \\ \\: \implies\sf \dfrac{ 90.3}{10.5}=width \\ \\ \\: \implies\sf \dfrac{ 90 \cancel.3}{10 \cancel.5}=width \\ \\ \\: \implies\sf \dfrac{ 903}{105}=width \\ \\ \\: \implies\sf width = \dfrac{ 903}{105} \\ \\ \\: \implies \underline{\boxed{\sf width = 8.6}} \pink\bigstar[/tex]
[tex]\\\\\\[/tex]
Know More:[tex]\begin{lgathered}\small\begin{gathered}\begin{gathered}\begin{gathered}\boxed{\begin {array}{cc}\\ \dag\quad \Large\underline{\bf \small{Formulas\:of\:Areas:-}}\\ \\ \star\sf Square=(side)^2\\ \\ \star\sf Rectangle=Length\times Breadth \\\\ \star\sf Triangle=\dfrac{1}{2}\times Base\times Height \\\\ \star \sf Scalene\triangle=\sqrt {s (s-a)(s-b)(s-c)}\\ \\ \star \sf Rhombus =\dfrac {1}{2}\times d_1\times d_2 \\\\ \star\sf Rhombus =\:\dfrac {1}{2}d\sqrt {4a^2-d^2}\\ \\ \star\sf Parallelogram =Base\times Height\\\\ \star\sf Trapezium =\dfrac {1}{2}(a+b)\times Height \\ \\ \star\sf Equilateral\:Triangle=\dfrac {\sqrt{3}}{4}(side)^2\end {array}}\end{gathered}\end{gathered}\end{gathered}\end{lgathered}[/tex]
can I get help with this please
Answer:
10d or less
Step-by-step explanation:
Joanne would want $50 left, and she has $250. 20 - 50 is 200. 20 goes into 100 5 times.
20 goes into 200 10 times. You just add five. (20, 40, 60, 80, 100)
If she wants at least $50 left, she would have to limit how many Dvd's she buys to 10 or less.
Because of the pitch of the attic's roof, a bookcase that is 5 feet high must be place
as shown. What is the measure of the angle formed by the roof and the floor of the attic
The measure of the angle formed by the roof and the floor of the attic is 22.62 degrees.
Right angle triangle
Right angle triangle are triangle that has one of its angles as 90 degrees. The angles formed can be found using trigonometric ratios.
Therefore,
tan x° = opposite / adjacent
tan x° = 5 / 12
tan x° = 0.41666666666
x = tan⁻¹ 0.41666666666
x = 22.6198649482
x = 22.62°
Therefore, the measure of the angle formed by the roof and the floor of the attic is 22.62 degrees.
learn more on right triangle here:https://brainly.com/question/10412877
Under his cell phone plan, Justin pays a flat cost of $56 per month and $5 per gigabyte. He wants to keep his bill under $65 per month. Write and solve an inequality which can be used to determine xx, the number of gigabytes Justin can use while staying within his budget
Answer:
56 + 5xx < 65
xx < 1.8
Step-by-step explanation:
56 + 5xx < 65
subtract 56 on both sides
56 + 5xx < 65
-56 -56
5xx < 9
divide by 5 on both sides
5xx/5 < 9/5
xx < 1.8 gigabytes
Help!! I'm stuck on these questions..
Answer:
65 degrees
Step-by-step explanation:
A property of a parallelogram is that opposite angles are congruent. opposite angle S is and angle that is 65 degrees, therefore angle S is 65 degrees
For each value of u, determine whether it is a solution to 6u-1< −19. u Is it a solution? Yes or No 5 −4 −3 8
Answer:
No it is not a solution to 6u-1<-19
2. Michelle invested $10,000 in an account that earns 8.5% interest that is compounded monthly. Write an exponential model for the balance of the account, then determine the amount of money in the account in 15 years.
[tex]~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{original amount deposited}\dotfill &\$10000\\ r=rate\to 8.5\%\to \frac{8.5}{100}\dotfill &0.085\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years\dotfill &15 \end{cases}[/tex]
[tex]A=10000\left(1+\frac{0.085}{12}\right)^{12\cdot 15}\implies A=10000\left( \frac{2417}{2400} \right)^{180}\implies A\approx 35626.53[/tex]
use the distributive property to write an equivalent expression to each of the following
(-4x +(2x)
Hey there!
(-4x + (2x)
= -4x + 2x
COMBINE the LIKE TERMS
= (-4x + 2x)
= -4x + 2x
= -2x
Therefore, your answer is: -2x
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
120 - 4.5x = 45 + 0.5x
Answer:
x = 15
Step-by-step explanation:
You're trying to solve for x by doing two-step equations.
120- 4.5x = 45 + 0.5x
Add 4.5x to both sides and subtract 45 to both sides.
**Note I did 2 things at once to make it easier to look at.
120-45 = 4.5x + 0.5x
75 = 5x
Now divide 75 by 5
x = 15
how many square yards of carpet should stella order if her bedroom measures nine by twelve feet
pls what is the awer
10/75=13.333333334 so around 66 people
you can also just divide 500 by 75 then take it times 10 :)
What classification is the following expression?
Answer:
Types of algebraic expressions may further be distinguished in the following five categories. They are: monomial, polynomial, binomial, trinomial, multinomial. 1. Monomial: An algebraic expression which consists of one non-zero term only is called a monomial.
Step-by-step explanation:
1+1=2
Can anyone help me with this question please ?
Answer: hard work
Step-by-step explanation: I dint know what your learning but it’s not easy
A square has a perimeter of 36 cm. What is the length of each side?
Answer:
a square has all its sides equal so you divide by 4
to get 9cm
hope it helps!Answer:
4cm
Step-by-step explanation:
4tmes side gives as perimeter
4side =36
x=4