Answers
Value of [tex]x[/tex]is [tex] - 12[/tex].
Final Answer is [tex]480[/tex]
Step-by-step explanation:
Assume that:
First number = x
Second number = 20 - x
Putting the given conditions,
[tex]2x^{2} + 3(20 - x)^{2} [/tex]
Putting the formula (a-b)²=(a²+2ab+b²) in (20-x)²,
[tex]2 {x}^{2} + 3(20^{2} - 2 \times 20 \times x + {x}^{2})[/tex]
[tex] = > 2 {x}^{2} + 3(400 - 40x + x^{2})[/tex]
Opening the brackets,
[tex]2 {x}^{2} + 3 \times 400 - 3 \times 40x + 3 \times {x}^{2} [/tex]
[tex] = > 2 {x}^{2} - 1200 - 120x + 3{x}^{2}[/tex]
[tex] = > (2x^{2} + 3 {x}^{2}) - 120x + 1200[/tex]
[tex] = > 5 {x}^{2} - 120x + 1200[/tex]
[tex]As \: x= - \frac{b}{2a}[/tex]
[tex] = > - \frac{120}{2 \times 5}[/tex]
[tex] = > - \frac{120}{10} [/tex]
[tex] = > - 12[/tex]
Now substituting the value of x in 5x²-120x+1200,
[tex] = > (5 \times {12}^{2} )-(120 \times 12)+1200[/tex]
[tex] = > (5 \times 144)-(1440)+1200[/tex]
[tex] = > 720 - 1440 + 1200[/tex]
[tex] = > 720 - (1440 - 1200)[/tex]
[tex] = > 720 - 240[/tex]
[tex] = > 480[/tex]
Related Questions
If line q bisects EG at point T, and if ET= 1/3 x and TG= x-2, then find EG
please help I have no idea how to do this its geometry problem for my math hw even my parents and siblings who are older than me don't know how to do this
Answers
Answer:
EG = 2 units
Step-by-step explanation:
Given that line q bisects EG at T , then
ET = TG ( substitute values )
[tex]\frac{1}{3}[/tex] x = x - 2 ( multiply through by 3 to clear the fraction )
x = 3x - 6 ( subtract x from both sides )
0 = 2x - 6 ( add 6 to both sides )
6 = 2x ( divide both sides by 2 )
3 = x
Then
ET = [tex]\frac{1}{3}[/tex] x = [tex]\frac{1}{3}[/tex] × 3 = 1
TG = x - 2 = 3 - 2 = 1
Thus
EG = ET + TG = 1 + 1 = 2 units
EG = [tex] \frac{4x}{3} - 2[/tex]
Step-by-step explanation:
( First check the attached image for diagram )
[tex]EG=ET+TG[/tex]
Substituting the given values,
[tex]EG = \frac{1}{3}x + (x - 2)[/tex]
Opening the brackets and multiplying,
[tex]EG = \frac{1 \times x}{3} + x - 2 [/tex]
[tex] = > EG = \frac{x}{3} + x - 2[/tex]
Finding LCM,
[tex] = > EG = ( \frac{x}{3} + \frac{x \times 3}{1 \times 3} ) - 2[/tex]
[tex] = > EG = ( \frac{x}{3} + \frac{3x}{3}) - 2[/tex]
Combining them,
[tex]EG =( \frac{x + 3x}{3}) - 2[/tex]
[tex]EG = \frac{4x}{3} - 2[/tex]
Note:- T is midpoint of EG
because ET = TG
Write a whole number that rounds 2000 if we round it to the nearest hundred
Answers
Answer:
1,995 would round to 2,000
Step-by-step explanation:
1,995 is 5 away from 2,000 so if you were rounding to the nearest hundred 2,000 would be it
NIE
VIEW
(Score for Question 3: of 5 points)
Admissions to a zoo cost $12 for adults and $8 for children. A group of 34 people attending the zoo paid a
total of $312 in admission fees
(a) Write and solve a system of equations that model the problem. Show all your work,
(b) How many adults went to the zoo?
(c) How many children went to the zoo?
Answer:
Answers
Hi!
Please see the attached image for your answer with explanation.
Have a great day!
Answer this correctly please
Thank you so much^^
Answers
Step-by-step explanation:
40% of 60= 24 boys80% of 35= 28 gamesIf a(x)=5x^2+7x+4 and b(x)=4x^2+3x+2
Then 4a(x) + 2b(x) =
Answers
Answer:
[tex]28x^2+34x+20[/tex]
Step-by-step explanation:
figure out 4a(x) and 2b(x) separately by distributing, and then add them together to get your answer.
hope this helps :)
Average house prices in Hobart are expected to grow by 8%
per year for the next 5 years. What is the expected average
value of a house in Hobart in 5 years time, to the nearest
dollar, if it is currently valued at $370000?
Answers
Answer:
518000 if it increases 8% per year
Step-by-step explanation:
8 times 5, because there are 5 years, is 40%
we take 40% out of 370000 and we get 148000 then we add 370000 and 148000 together and we get 518000
not sure if anyone can see this but can someone give me the answers i am super confussed and my teacher wont help me at all!
Answers
Okay so, to solve these problems what you're gonna want to do is substitute the given x and y values into the equation.
For example, number 7.
11(d-c) + 3(c+d), when c=6, d=9
if d=9, you will substitute the d in the problem to 9.
11(9-c) + 3(c+9)
if c=6 you will substitute c for 6.
11(9-6) + 3(6+9)
You can solve now that you have a simpler problem to work with.
11(9-6) + 3(6+9) first...
11(9-6) 11*9=99 11*-6=-66, so, 11(9-6)= 99-66= 33.
3(6+9) 3*6=18 3*9=27 18+27=45
33+45=78
Your answer for number 7 is 78.
Hope this helps, just do the same for the other problems like this one.
a = 12, b = 16, c = ?
b) a = 15, b = ?, c = 18
c) a = ?, b = 6, c = 15
d) a = 4.1, b = 3.3, c = ?
e) a = ?, b = 6.5, c = 12.2
Answers
a) c = 20
b) b = 16.5
c) a = -3
d) c = 2.5
e) a = 0.8
There are not enough information on these sequences, so I will just do them base on the difference of the numbers.
Pardis recently deposited $5,000 in a savings account that pays a return of 2 percent per year. Explain why her investment will grow over the years. What opposing force will impact the value of her investment?
Answers
Answer:
Her investment will grow over the years due to the 2 percent interest. Inflation will impact the value of her investment
For the given data. the simple interest will be $100.His investment will grow over the years. Because of the simple interest.
What is simple interest?It is defined as the interest based on the principal amount, it does not include the compounded amount. The interest calculates on the initial amount or borrowed amount.
It is given that, Pardis recently deposited $5,000 in a savings account that pays a return of 2 percent per year.
Principal = $5,000
Rate= 2%
Time= 1 year
SI = (P×R×T)/100
SI = (5000×2×1)/100
SI=100
Thus, for the given data. the simple interest will be $100.His investment will grow over the years. Because of the simple interest.
Learn more about the simple interest here:
brainly.com/question/22621039
#SPJ5
8 4/5 - 2/3 - ? = 3 1/10
Answers
Answer: 5 1/30
Step-by-step explanation:
8 + 4/5 - 2/3 - 3 - 1/10 = 5 + 1/30
Suppose you have 12 chips, each a different color. How many different stacks of 5 chips can you make
Answers
Answer:
2
Step-by-step explanation:
i am not sur but 12 5 = 2?
The table shows the results of a survey of 200 randomly selected people on whether they like watermelon, cantaloupe, or both. A 4-column table with 3 rows. The first column has no label with entries cantaloupe, not cantaloupe, total. The second column is labeled watermelon with entries 93, 66, 159. The third column is labeled not watermelon with entries 16, 25, 41. The fourth column is labeled total with entries 109, 91, 200. Which is the marginal relative frequency for the people who do not like cantaloupe? StartFraction 25 Over 91 EndFraction StartFraction 66 Over 200 EndFraction StartFraction 91 Over 200 EndFraction StartFraction 66 Over 91 EndFraction.
Answers
Answer: 91/200
Step-by-step explanation: i got it right on the quiz.
Answer:
C
Step-by-step explanation:
Colletta decides to do a savings plan where she doubles the amount of money each day. Starting on day 1 she saves $1, on day 2 she saves $2, on day 3 she saves $4, on day 4 she saves $8 and so on.
a. Is the money saved a function of the number of days? Explain your reasoning.
b. Is the relationship linear? Explain your reasoning.
100 POINTS TO ANYONE WHO CAN ANSWER IT CORRECT
Answers
Answer:
a. yes the money is a function the function is x = days
2^(x-1)
b. no its not it will go up by more and more every day a linear equation would mean it goes up by the same amount each day which it does not
Hope This Helps!!!
Mary sold 50 tickets for the school play Student tickets cost $2 and adult tickets cos $ 5. Mary's sales totaled $ 154.00. How many adult tickets and how many student tickets did Mary sell?
Answers
Answer:
the correct answer is that mary sold 18 adult tickets and 32 student tickets
if she sold 18 adult tickets it would be 90 dollars, and if she sold 32 student tickets she would get 64 from that, if we add the amount of people that bought tickets and how much she got it would work out
with 18 adults+32 students being exactly 50
and 90+64 being 154.
I tried different solutions, I did 18 adults and 32 Students, since there are 50 tickets sold, this is the correct answer since if we do this the amount she makes from the adults will be 90 and she will make 64 from the students this will add up to $154
64x-16 I need 3 equivalent expressions
Answers
Answer:
8 (8x - 2)
(64) x X - 16
4 (16 x- 4)
Step-by-step explanation:
-
Find the 7th term of the arithmetic sequence – 2x – 1, 4x – 5, 10x - 9, ...
Help
Answers
Explanation in image
can you please tell me how to do easy way can you please show me in numbers how to multiply
[tex] \frac{2 }{3} - \frac{1}{9} [/tex]
Answers
same as before, we look at the denominators, hmmm do a quick prime factoring.
3 = 3 * 1
9 = 3 * 3 * 1
since 9 already contains 3 and 1, we can us that
[tex]\cfrac{\underline{2}}{3}~~ - ~~\cfrac{1}{9}\implies \cfrac{(2)\underline{2}~~ - ~~(1)1}{\underset{\textit{using this LCD}}{9}}\implies \cfrac{4-1}{9}\implies \cfrac{\stackrel{1}{~~\begin{matrix} 3 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}{\underset{3}{~~\begin{matrix} 9 \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}}\implies \cfrac{1}{3}[/tex]
Can anybody help me with this
Answers
Answer:
c ≈ 9.1 m
Step-by-step explanation:
Using Pythagoras' identity in the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides , that is
c² = 4.1² + 8.1² = 16.81 + 65.61 = 82.42 ( take square root of both sides )
c = [tex]\sqrt{82.42 }[/tex] ≈ 9.1 m ( to the nearest tenth )
A student was asked to simplify the expression 2(x+3)+(4x−8)−7x .
Answers
Answer:
-x -2
Step-by-step explanation:
1- Apply the Distributive Property
2- Calculate the product or quotient
3- Determine the sign
4- Reorder and gather like terms
Collect coefficients of like terms
Calculate the sum or difference
1.5 divided by 12
i want an explanation cuz i don't know how to divide a small decimal with a larger number
Answers
Step-by-step explanation:
1.5 ÷ 12
1½÷12
³/²÷12
3/2 *1/12
3/24
1/8
__
12| 1.5 you bring the decimal up
. —
12| 1.>>5 = 15 :)
.1
12| 15
- 12
30
.12
12| 15 0 0|
|
|
- 12
30
- 24
60
.125
for each order, the website applies a 7. 7% sales tax to the price of the cards
Answers
Answer:
what's the full question...?
Step-by-step explanation:
The Amount of sales tax on a new car varies directly to the purchase price of the car. On a 25,000 car, sales tax is 1,750. What's the purchase price of a new car with 3,500 in sales tax?
Please show your work because I still don't understand it and don't know how to do it.
Answers
Answer:
50,000
Step-by-step explanation:
1st car had $1,750 tax
2nd car has $3,500 tax
1750(2) = 3500
so your tax doubled so the price must be doubled.
The car is $50,000
Algebraically using direct variation:
t = kp where t=tax, p = purchase price,
and k is constant of variation
1750 = 25000k
k = 1750/25000
k = 0.07
Your equation is: t = 0.07p
3500 = 0.07p
p = 3500/0.07
p = $50,000
6/9×1/2=
please simplify
please and thank you
Answers
Answer:
1/3
Step-by-step explanation:
[tex]\frac{6}{9}*\frac{1}{2}[/tex]
[tex]\frac{6*1}{9*2}[/tex]
[tex]=\frac{6}{18}[/tex]
Reduce by dividing both the numerator and denominator by the Greatest Common Factor GCF(6,18) = 6
[tex]\frac{6/6}{18/6}=\frac{1}{3}[/tex]
Therefore:
[tex]\frac{6}{9}*\frac{1}{2}=\frac{1}{3}[/tex]
[RevyBreeze]
4) Shown below is a series of steps to solve the equation 4x + 2(x - 4) = 28.
Given: 4x + 2(x - 4) - 28
Step 1 = 4x + 2x - 8 = 28
Step 2 => 6x - 8 = 28
Step 3 => 6x - 8 + 8 = 28 + 8
Step 4 = 6x = 36
6x36
Step 5
6 6
Step 6 => x = 6
Which THREE statements are correct?
A) Step 1 is justified by the distributive property.
B) Step 2 is justified by the subtraction property of equality
C) Step 3 is justified by the addition property of equality
D) Step 4 is justified by the additive Identity property.
E) Step 5 is justified by the division property of equality
Answers
HELP ME FAST I ONLY HAVE 5 MINS LEFT Wanda created the poster shown below:
A rectangle is shown. The length of the rectangle is labeled as length equal to 32 cm, and the width is labeled as width equal to 36 cm.
What would be the dimensions of the poster at fraction 1 over 4 times its current size? (5 points)
Length = 28 cm, width = 32 cm
Length = 128 cm, width = 144 cm
Length = 8 cm, width = 9 cm
Length = 36 cm, width = 40 cm
Answers
Length=8cm and width=9cm
Answer:
the correct answer is 8:9 or C.
Please help me asap!
Answers
Answer:
[tex]-3+2\sqrt{2}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{3} -\sqrt{6}}{\sqrt{3} +\sqrt{6}}[/tex]
[tex]=\frac{(\sqrt{3} -\sqrt{6})(\sqrt{3} -\sqrt{6})}{(\sqrt{3} +\sqrt{6})(\sqrt{3} -\sqrt{6})}[/tex]
[tex]=\frac{9-6\sqrt{2} }{-3}[/tex]
[tex]=\frac{3(3-2\sqrt{2} )}{-3}[/tex]
[tex]=-(3-2\sqrt{2})[/tex]
[tex]=-3+2\sqrt{2}[/tex]
Find the value please and ty
Answers
Answer:
-3
Step-by-step explanation:
The value of f(-3) can be found at looking at the x-value of -3, then drawing a vertical line. If you look at the point where the vertical line hits th graph, you get the point (-3,-3)
The y-value is what we are looking for, which is -3.
-Chetan K
Graph the solution to this inequality on the number line.
−12≥−4p
Answers
Answer:
A closed circle on 3 going right.
Step-by-step explanation:
-12 ≥ -4p
/-4 /-4
3 ≤ p which also mean p ≥ 3
This will be a closed circle on 3 going right.
Hope that helps!
HELP ME NOWWW PLS K12
Answers
Answer:
2 units
Step-by-step explanation:
How do I solve 6x-15+53=11x-12?
Answers
Add the numbers
6
−
1
5
+
5
3
=
1
1
−
1
2
6
x
−
15
+
53
=
11
x
−
12
6
+
3
8
=
1
1
−
1
2
6
x
+
38
=
11
x
−
12
2
Subtract
3
8
38
from both sides of the equation
3
Simplify
Solution
: x=10