solve using the quadratic formula:
3x=2x^2-2
Answer:
[tex]x=2\\x=-\frac{1}{2}[/tex]
Step-by-step explanation:
1) Move terms to the left side.
[tex]3x=2x^{2} -2\\3x-(2x^{2}-2)=0[/tex]
2) Distribute.
[tex]3x-(2x^{2} -2)=0\\3x-2x^{2} +2=0[/tex]
3) Rearrange terms.
[tex]3x-2x^{2} +2=0\\-2x^{2} +3x+2=0[/tex]
4) Common factor.
[tex]-2x^{2} +3x+2=0\\-(2x^{2} -3x-2)=0[/tex]
5) Divide both sides of the equation by the same term.
[tex]-(2x^{2} -3x-2)=0\\2x^{2} -3x-2=0[/tex]
6) Use the quadratic formula.
[tex]x=\frac{-b+\sqrt{b^{2}-4ac } }{2a}[/tex]
Once in standard form, identify a, b, and c from the original equation and plug them into the quadratic formula.
[tex]2x^{2} -3x-2=0\\a=2\\b=-3\\c=-2[/tex]
[tex]x=\frac{-(-3)+\sqrt{(-3)^{2} -4*2(-2)} }{2*2}[/tex]
7) Simplify.
Evaluate the exponent
[tex]x=\frac{3+\sqrt{(-3)^{2}-4*2(-2) } }{2*2}[/tex]
[tex]x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}[/tex]
Multiply the numbers
[tex]x=\frac{3+\sqrt{9-4*2(-2)} }{2*2}[/tex]
[tex]x=\frac{3+\sqrt{9+16} }{2*2}[/tex]
Add the numbers
[tex]x=\frac{3+\sqrt{9+16} }{2*2}[/tex]
[tex]x=\frac{3+\sqrt{25} }{2*2}[/tex]
Evaluate the square root
[tex]x=\frac{3+\sqrt{25} }{2*2} \\x=\frac{3+5}{2*2}[/tex]
Multiply the numbers
[tex]x=\frac{3+5}{2*2}[/tex]
[tex]x=\frac{3+5}{4}[/tex]
8) Seperate the equations.
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
[tex]x=\frac{3+5}{4}[/tex]
[tex]x=\frac{3-5}{4}[/tex]
9) Solve.
Rearrange and isolate the variable to find each solution.
[tex]x=2\\x=-\frac{1}{2}[/tex]
Two negative integers have a sum of -18 and a
product of 80. What are the integers?
Separate the answers with a coma.
Answer:
-10, -8
Step-by-step explanation:
a + b = -18
a * b = 80
Solve:
from the first eq.
a = 18 - b
replacing this value in the secon eq.
(18-b)*b = 80
18*b + b*-b = 80
-b² + 18b = 80
-b² + 18b - 80 = 0
b = {-18±√((18)² - (4*-1*-80))] /(2*-1)
b = {-18±√(324.320)} / -2
b = {-18±√4} / -2
b = {-18±2} / -2
b₁ = {-18-2} / -2 = -20/-2 = 10
b₂ = {-18+2} / -2 = -16/-2 = 8
The two number must be negatives, so the numbers are:
-10 and -8
Check:
-10 + (-8) = -10 - 8 = -18
-10*-8 = 80
Find the slope of the following graph and write ur results in the empty box.
On Sunday, Sheldon bought 4 1/2 kg of plant food. He used 1 2/3 kg on his strawberry plants and used 1/4 kg for his tomato plants. How many kilograms of plant food did Sheldon have left? Write one or more equations to show how you reached your answer.
Answer:
Step-by-step explanation:
What
Which of the following numbers are whole numbers
A-0.6122
B-2469
C- 759084.2
D-435.752
E-6564.27
F-183
Answer:
B - 2469 and F - 183
Step-by-step explanation:
B and F are whole numbers because they don't have any decimal places.
Answer:
b
Step-by-step explanation:
because it's a b so you would automatically wanna put down B because It's a B
25*10to the power of 6 in standard form
Answer:
2.5 x 10^7
Step-by-step explanation:
PLEASE HELP ME I WILL GIVE A BRAINLIST
First, we can get rid of d(x) simply by looking at it because we can tell it's linear (it's a straight line). If we look at the table, we can see a(x) is also linear because it has a steady rate of growth. b(x) and c(x) both represent exponential growth. The curved shape of b(x) shows us this is exponential growth, and the exponent in c(x) tells us it's also exponential.
Hope this helps!
Answer: b(x) and c(x)
Step-by-step explanation:
Choose the inequality that correctly represents the following sentence:
6 less than a number is at most 9.
Answer:
x - 6 ≤ 9
Step-by-step explanation:
using the keywords 'less than', 'a number', and 'atmost' we can identify the problem.
Now simplify the expression.
(2x − 3)(5x + 6)
Answer:
10x+18
Step-by-step explanation:
2x*5x=10x
-3*6=18
10x+18=
x=1.8
Mr. Smith collected 200 eggs from his chickens on Saturday. When he sorted the eggs by their sizes, he found out tha 60% of the eggs are extra-large. How many extra-large eggs did Mr. Smith collect from his chickens? need help ASAP pls
Answer: 120
Step-by-step explanation:
I do not understand, like why did it give me a problem with one number and is not a exponent?
what is 13 divied it by 2
Answer:
6.5
Step-by-step explanation:
6.5 is 13 divided by 2. You can check your work by adding 6.5 to 6.5 or multiplying 6.5 by 2
Select the correct answer.
A pound is approximately 0.45 kilogram. A person weighs 87 kilograms. What is the person's weight, in pounds, when rounded to the nearest
whole number?
ОА
52 lb
B.
180 lb
OC. 39 lb
OD. 193 lb
Answer:
193
Step-by-step explanation:
87 divided by .45
193.333333333
Rachel baked a pie with an area of 94.985 square inches. She gave away a slice of pie with an area of 13.56 square inches. Find the central angle measure of the slice. Numerical answer round to the nearest degree.
It is 103.68 degrees :)
help me please help me help
Answer:
18
Step-by-step explanation:
The question is pretty much asking to find the LCM of the denominators, which is the LCD, Least Common Denominator
First list out the two numbers, then list its multiples,
6: 6, 12, 18, 24
9: 9, 18, 27
since both of them have 18, and its the least, that is the LCD/LCM
Sarah is 2 inches taller than the quotient of billy’s height and 5. Let b represent Billy’s height. write an expression that represents Sarah’s height
Answer:
1
Step-by-step explanation:
5(x+1) = 12
5(x+1) = 5x + 12
5(x+1) = 5x + 5
5(x=1) = 0
what one is an infinite solution
Answer:
[tex]2 + \frac{b}{5} [/tex]
Hope you could get an idea from here.
Doubt clarification - use comment section.
hello guys .. can y’all help me with this question and explain it to me ? please and thank you:) 25 POINTS !
Answer:
B, 5.4
Step-by-step explanation:
BC = 36
FE = 7.2
AB = 27
x = Unknown value
They are proportional so...
[tex]\frac{36}{27} =\frac{7.2}{x}[/tex]
x = 5.4
The figure shows triangle DEF and line segment BC, which is parallel to EF:
Triangle DEF has a point B on side DE and point C on side DF. The line BC is parallel to the line EF.
Part A: Is triangle DEF similar to triangle DBC? Explain using what you know about triangle similarity. (5 points)
Part B: Which line segment on triangle DBC corresponds to line segment EF? Explain your answer. (3 points)
Part C: Which angle on triangle DBC corresponds to angle F? Explain your answer. (2 point
Part A: Yes, Triangle DEF and DBC are the same triangle, but DBC is smaller than DEF because it is just a cut off of DEF.
Part B: I am pretty sure it is angle C.
Part C: I am pretty sure it is angle D.
Answer:
Step-by-step explanation:
Part A.
m < B = m < E (corresponding angles, (BC parallel to EF))
m < C = m < F ( as above)
So triangles DBC and DEF are similar ( by 2 equal angles).
Part B.
Line segment BC ( as they are both opposite < D)
Part C.
< C as its in same relative position to < F.
Math problem (easy)
………………………………………
Answer:
7/24
Step-by-step explanation:
Hope this helps
Answer:
1/6
Step-by-step explanation:
Decimal Form 0.16
PLEASE HELP! IT'S A GRAPH-TYPE QUESTION!
Answer:
Step-by-step explanation:
[tex]\sf -8(6x+3)[/tex]
Answer:
[tex] - 8(6x + 3) = - 8 \times 6x + - 8 \times 3 \\ = - 48x - 24[/tex]
A plane travelled at an average speed of 528.6 km/h on a flight. How far did the plane travel in 4.75 hours? Round off your answer to the nearest whole number.
Answer: 2,511 km
Step-by-step explanation:
5828.6*4.75 = 2,510.85 rounded to 2,511
The ratio of three numbers is 4 : 1 : 7. The sum of the numbers is 24. What are the three numbers?
Answer:
8, 2, 14
Step-by-step explanation:
sum the parts of the ratio, 4 + 1 + 7 = 12 parts , then
24 ÷ 12 = 2 ← value of 1 part of the ratio, then
4 parts = 4 × 2 = 8
7 parts = 7 × 2 = 14
The 3 numbers are 8, 2, 14
Solve for a.
a+(−1.2)=−5.5
Enter your answer in the box.
a =
Answer:
-4.3
Step-by-step explanation:
a+(-1.2)= -5.5
a-1.2=-5.5
add 1.2 to both sides
a-1.2+1.2= - 5.5+1.2
simplify
a= - 4.3
Answer:
a=-4.3
Why?:
You would have to keep the answer negative, this is because if it were to be positive it would make the negative decrease.
You could easily get a line paper and line up-
-4.3
+ -1.2
_______
-5.5
-5.5-(-1.2) would make the equation end up like -5.5+1.2, and -5.5+1.2=-4.3
Therefore,
a=-4.3
more fr33 points for u amazing people, stream scientist by twice while ur at it!!!! :))
Answer:
ye
Step-by-step explanation:
AMMA
Richard owned n cows
Ellis had exactly 4 times as many cows as Richard,
Richard buys 13 extra cows.
Ellis sells 9 of his cows
Ellis still has more cows than Richard
Form an inequality, in terms of n
Solve the inequality to find the least value of n
You must show all your working
Answer:
n ≥ 8
Step-by-step explanation:
Let R and E stand for the number of cows owned by Richard and Ellis, respectively.
We are told that:
R = n
E = 4n
Then:
R = n+13 [Bought 13 cows]
and
E = 4n-9 [Sold 9 cows]
Still:
E > R [Ellis still has more cows]
Therefore:
4n-9 > n+13
3n > 22
n > 7 1/3
Since no rancher wants 1/3 of a cow, we need to round either up or down to a whole number. The least value of n is therefore 8 cows or higher. Since 8 is a valid number, change the > inequality to ≥.
n ≥ 8
Danny buys,
1 loaf of bread for £1.20
1 bottle of milk for 70p
2 packets of cheese for £2.30 each packet
Danny pays with a £10 note.
He says,
“I should get £3.30 change.”
Is Danny correct?
You must show how you get your answer.
Answer:
Danny is incorrect.
Step-by-step explanation:
1 loaf of bread = 1.2
1 bottle of mil = 0.7
2 packets of cheese = 4.6
1.2+0.7+4.6 = 6.5
10-6.5 = 3.5
Danny is incorrect as he should be given £3.50 change instead of £3.30 change.
pleaseeee asapppppp asapppppp
Answer:
7.07
Step-by-step explanation:
Angle M is 63 degrees because all 3 angles must add to 180.
Now use the law of sines:
sin(90)/x = sin(63)/6.3
Cross multiply: 6.3 sin (90) = x sin (63)
Divide by sides by sin (63): (6.3 sin (90))/sin (63) = x
Use a calculator: 7.07
Can I get a simple answer
Answer:
The y-intercept of Function A is greater the Function B's.
Step-by-step explanation:
Function B's y-intercept is -5.
Function A's y-intercept is 5.
1 point
#8. What is the slope of a graph that passes through (5,5) and (5, -7)? *
0
-12
- 12/0
Undefined
12
Answer:
The answer is undefined
Because it passes through x