Answer:
[tex]\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}[/tex]
Or, by approximating:
[tex]x\approx-0.1835\text{ or } x\approx -1.8165[/tex]
Step-by-step explanation:
Let’s convert this to standard form. We have:
[tex]-6x-1+5x^2=8x^2[/tex]
Subtract 5x² from both sides:
[tex]-6x-1=3x^2[/tex]
And add 6x and 1 to both sides:
[tex]0=3x^2+6x+1[/tex]
This is not factorable. So, we will need to use the quadratic formula.
The quadratic formula for a quadratic in standard form is given by:
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}}[/tex]
In this case, a=3; b=6, and c=1.
Substitute appropriately:
[tex]\displaystyle x=\frac{-6\pm\sqrt{6^2-4(3)(1)}}{2(3)}[/tex]
Simplify:
[tex]\displaystyle x=\frac{-6\pm\sqrt{24}}{6}[/tex]
We can simplify the square root:
[tex]\sqrt{24}=\sqrt{4}\cdot\sqrt{6}=2\sqrt{6}[/tex]
Hence:
[tex]\displaystyle x=\frac{-6\pm2\sqrt{4}}{6}[/tex]
Simplify:
[tex]\displaystyle x=\frac{-3\pm\sqrt{6}}{3}[/tex]
Hence, we will have two solutions:
[tex]\displaystyle x=\frac{-3+\sqrt{6}}{3}\text{ and } x=\frac{-3-\sqrt{6}}{3}[/tex]
Approximating them, we can see that our solutions are approximately:
[tex]x\approx-0.1835\text{ or } x\approx -1.8165[/tex]
The 24 girls in 20 boys to school gym clothes have to be split into groups for a team building activity. If each group must be identical, what is the maximum number of groups that can be made?
Answer: 4
Step-by-step explanation:
Given: Total girls = 24
Total boys = 20
If each group must be identical, then the maximum number of groups that can be made = GCD(24,20) [GCD= Greatest common divisor]
Since 24 = 2 x 2 x 2 x 3
20 = 2 x 2 x 5
GCD(24,20)= 2 x 2 = 4
Hence, the maximum number of groups that can be made = 4
if i get off my online classes at 11:11 and get back on at 12:26 how much free time do i have?
Answer:
1 hr and 45 mins
Step-by-step explanation:
12:26-11:11 or 115, so an hour and 45 mins.
Hope this helps :D
Answer:
75 min
Step-by-step explanation:
I did 49+26 because from 11:11 to 12 theres 49 min and from 12 to 12:26 theres 26 min
sole w - 12 = -3 using mental math
Answer:
-15
Step-by-step explanation:
Answer:
w=9
Step-by-step explanation:
w - 12 = -3
w-12+12=-3+12
w=9
Help ASAP!!!! Please will mark brainiest
Answer:
is the first one
Step-by-step explanation:
Aidan had 13 tropical fish and gave 8 of them to his brother then Aidan bought 6 more from the pet store each fish cost $9.45 how many fish does Aidan have now
Answer:
11 fishes
Step-by-step explanation:
Answer:27
Step-by-step explanation: add all the answers
I NEED HELP!! WITH NUMBER 4 BOTH ANSWERS
Answer:
The first one is 12
The second one is -12
Just multiply, and remember the negative signs.
Answer:
1st Question- Positive Twelve
Second Question- Negative Twelve
Step-by-step explanation:
Please Help
Please let me know how to do it, I don't only want the answer. Thank you!
(4y+3)-(y-2)
(There is no equal sign in the math problem)
Christa is saving for a new tablet. It costs $70.45, including tax. She has already saved $35. How much more does she need to save?
Answer: Christa would need to save $35.45.
Step-by-step explanation:
70.45 - 35 = The amount Christa needs to save
70.45 - 35 = 35.45
what is the constant of proportionality for the table below?
Answer:
.75 or 3/4
Step-by-step explanation:
If you earn $134 in 8 hours, how much do you earn per hour?
Answer:$16.75
Step-by-step explanation:
Explain how to change a negative exponent to a positive one
Answer:
Flip the fraction that you are applying the exponent to, if it's a whole number, just imagine it's over one and flip it that way.
Explanation:
If you have 3/5 ^-3
You would flip the fraction to 5/3, then the exponent turns to positive 3
So 5/3 ^3
For a whole number, for example, 6, ^-2
In other words, it's 6/1 ^2, so you would make it 1/6, then the exponent turns positive.
So 1/6 ^2
Hope this helped :)
To change a negative exponent to a positive one, a flip it into a reciprocal.
Here,
We have to explain, change a negative exponent to a positive one.
What is Reciprocal?
The inverse of a number is called Reciprocal.
Now,
Let a number is, [tex]5^{-2}[/tex]
Then change it into positive exponent as;
Take reciprocal of [tex]5^{-2}[/tex], we get;
⇒ [tex](\frac{1}{5} )^2[/tex]
Hence, reciprocal of [tex]5^{-2}[/tex] = [tex](\frac{1}{5} )^2[/tex]
So, To change a negative exponent to a positive one, a flip it into a reciprocal.
Learn more about the reciprocal visit:
https://brainly.com/question/1955429
#SPJ2
The diagram (picture) shows the speed-time graph of a body moving in a straight line.
(a) Calculate he acceleration of the body during the first 15 seconds.
(b) Calculate the distance moves by the body in the first 40 seconds of its motion.
(c) Given that the body decelerate at 1.25 m/s[tex]^{2}[/tex]
Answer:
Below.
Step-by-step explanation:
(a)
The acceleration = the slope of the graph (change of velocity / time)
= 25/15
= 1.67 m/s/s.
(b)
The distance moved = the area under the graph for the first 0 seconds,
= area of the first triangle + area of the rectangle with height 25 and length (40 - 15)
= 1/2 * 15 * 25 + (40-15) * 25
= 187.5 + 625
= 812.5 m.
(c). ? what is the question?
Star bought a new pair of Ray Ban sunglasses, originally priced at $109.99, on sale for 25% with a 5% tax. How much does Star pay for the sunglasses?
Answer:
$22
Step-by-step explanation:
2/9x4/2=what. solve the equation
Answer:
0.44
Step-by-step explanation:
2/9 = 0.22
4/2 = 2
answer = 0.22 x 2
answer = 0.44
Answer:
4/9
Step-by-step explanation:
2/9 × 4/2
⇒ 2×4/9×2
⇒ 8/18
⇒ 4/9
hope this helps you!
What is the distance between the points (-9,-2) and (-1,4)
Answer:
The answer is: (98-3)
Answer:
8,2
Step-by-step explanation:
becuase it is 8 points away from the origanal but also 2 points away
−3−(−5)
PLease Help me
Answer:
2
Step-by-step explanation:
Simplify the expression.
Answer:
2
Step-by-step explanation:
Two subtraction/negative signs make a positive so it's pretty much -3 + 5
So if you take 3 away from 5 you are left with 2
what is the slope of (-4,7) and (6,2)
Answer:
use the slope formula to find the slope m
m = - 1/2
Write an equation in slope-intercept form of the line that passes through the points.
Answer:
y=-2x
Step-by-step explanation:
slope is -2 and the y intercept is 0 so if you plug these answers into slope intercept form (y=mx+b) then it comes to y=-2x
Need help pls im poor
Answer:
The mom is 30 times older than the son and the son is 30 years younger
Step-by-step explanation:
it says so
????? help out ( not good with math )
Answer:
The answer is x = 3
Step-by-step explanation:
5x + 9 = 24
5x +9 -9 = 24 - 9
5x = 15
x = 15/5 = 3
Therefore, x = 3
Kelly multiplied 5 to each side when she solved for x, which is incorrect.
Answer:
Kelly had incorrectly solved for [tex]x[/tex] where she had multiplied by [tex]5[/tex] instead of dividing by [tex]5[/tex] to find for [tex]x[/tex].
Step-by-step explanation:
How Kelly should have solved it:
[tex]5x+9 = 24[/tex]
[tex]5x + 9-9= 24-9[/tex]
[tex]5x=15[/tex]
[tex]5x\div 5=15\div 5[/tex] (mistake occurred during this step in Kelly's work where she had multiplied by [tex]5[/tex])
[tex]x=3[/tex]
Checking:
To check if [tex]x=3[/tex], we can use substitution:
[tex]5x+9 = 5(3)+9[/tex]
[tex]=15+9[/tex]
[tex]=24[/tex]
∴ The solution for [tex]x[/tex] is correct.
Hope this helps :)
A painter is going to paint the rooms of a building. The painter has used 80 gallons of paint and has painted 32% of the rooms. How many more gallons of paint does the painter need to finish painting all of the rooms in the building?
The painter needs ______ gallons of paint to finish painting all of the rooms.
Answer:
30 gallons
Step-by-step explanation:
? apartments in 3 floors = 5 apartments per floor
-Ꮾb > 42 or Ꮞb + Ꮾ > 2
Answer:
b<-7 or b>-1
Step-by-step explanation:
explanation: -6b>42 turns into -42>6b then divide by 6 on both sides and you get -7>b
for the other inequality, you take 4b+6>2 and then subtract6 from both sides, from there you will get 4b>-4 and that will be b>-1
Write an equation of a line parrallel to y=-3x+5 that has a y-intercept of 8.
Answer:
y=-3x+8
Step-by-step explanation:
if u want them to be parallel make the slope the same
(in this case, -3x)
and the y-int at the end is +8
Write the equation in vertex form given the vertex (4, 7) and passing through the point (0, 10).
Answer:
f(x) = ³/₁₆ (x - 4)² + 7Step-by-step explanation:
The vertex form of the equation of the parabola with vertex (h, k) is:
f(x) = a(x - h)² + k
so the equation of parabola with the vertex (4, 7) is
f(x) = a(x - 4)² + 7
passes through the point (0, 10) means if x=0 then f(x)=10
10 = a(0 - 4)² + 7
10 -7 = a(-4)² + 7 -7
3 = 16a
a = ³/₁₆
Therefore the equation of parabla is:
f(x) = ³/₁₆ (x - 4)² + 7
$60 is the original price and the sale price is $45 what is the percent discount
Answer:
your discount would be 25
Step-by-step explanation:
start, first subtract 45 from 60 to find the amount of money taken off from the discount:
60-45
=15
Because 15 dollars have been taken off the original price, you can find the percent of discount by setting up this proportion where x represents the percent of discount:
15/60=x/100
Now, cross multiply and solve for x:
1500=60x
x=25
Therefore, your discount would be 25%.
Answer:
25% !
Step-by-step explanation:
I looked it up and it makes sense!
When x = 2,what is the value of y for the equation – 3x + 2y = 10?
Answer:
y=x+5
Step-by-step explanation:
Answer:
[tex] \huge{ \boxed{ \bold{ \tt{y = 8}}}}[/tex]
☪ What is the value of y for the equation given below when x = 2 ?
-3x + 2y = 10☪ Step - by - step explanation :
[tex] \sf{ - 3x + 2y = 10}[/tex]plug the value of x ( i.e 2 )
➳ [tex] \sf{ - 3 \times 2 + 2y = 10}[/tex]
Remember : Multiplying or dividing a negative integer by a positive integer gives a negative integer.
➳ [tex] \sf{ - 6 + 2y = 10}[/tex]
Move 6 to right hand side and change it's sign
➳ [tex] \sf{2y = 10 + 6}[/tex]
Add the numbers : 10 and 6
➳ [tex] \sf{2y = 16}[/tex]
Divide both sides by 2
➳ [tex] \sf{ \frac{2y}{2} = \frac{16}{2}} [/tex]
➳ [tex] \boxed{ \sf{y = 8}}[/tex]
——————————————————
✏ Now, let's check whether the value of y is 8 or not !
✑ Verification :
[tex] \sf{ - 3x + 2y = 10}[/tex]
→ [tex] \sf{ - 3 \times 2 + 2 \times 8 = 10}[/tex]
→ [tex] \sf{ - 6 + 16 = 10}[/tex]
→ [tex] \sf{10 = 10}[/tex]
L.H.S = R.H.S ( Hence , the value of y is 8 . )
——————————————————
☞ Additional Info :
✒ Sign rules of addition and subtraction of integers:
The positive integers are always added and posses the positive ( + ) sign.The negative integers are always added but posses the negative ( - ) sign.The negative and positive integers are always subtracted but posses the sign of the bigger integer.✒ Sign rules of multiplication and division of integers :
Multiplying or dividing positive integers gives a positive integer.Multiplying or dividing positive integer by any negative integer gives a negative integer.Multiplying or dividing a negative integer by a positive integer gives a negative integer.Multiplying or dividing a negative integer by a negative integer gives a positive integer.✒ Rules for solving an equation :
If any equation contains fractions , multiply each term by the LCM of denominators.Remove the brackets , if any.Collect the term with the variable to the left hand side and constant terms to the right side by changing their signs ' + ' into ' - ' and ' - ' into ' + '.Simplify and get the single term on each side.Divide each side by the coefficient of variable and then get the value of variable.Hope I helped!
Have a wonderful time ツ
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What is 5 + 5???????????????????????
Answer:
10 is the correct answer
Step-by-step explanation:
5+5=10
Pls HELP FAST
At Fridays game sold 1,294 tickets and made $8,816 if each student ticket cost $5 and adult ticket cost $8 how many student tickets were bought?
Answer
512 student tickets were purchased.
Step-by-step explanation:
Mary rolls a fair dice and flips a fair coin.
What is the probability of obtaining an even number and a tail?
Answer:
1/4
Step-by-step explanation:
even number is 3/6 = 1/2
and the coin is 1/2
so 1/2 x 1/2 = 1/4
Answer:
1/4
Step-by-step explanation: