Answer:
Basic parabola: y = ax2 + bx + c
We have 3 points we can plug in for (x, y) to create 3 simultaneous equations
(-2, 24): 24 = 4a - 2b + c {equation 1}
(3, -1): -1 = 9a + 3b + c {equation 2}
(-1, 15): 15 = a - b + c {equation 3}
Solve this system to find the values of a, b, c
Let's first eliminate variable c:
4a - 2b + c = 24 {equation 1}
a - b + c = 15 {equation 3}
--------------------- subtract
3a - b = 9
9a + 3b + c = -1 {equation 2}
a - b + c = 15 {equation 3}
-------------------- subtract
8a + 4b = -16
We now have two equations with 2 unknowns we can use to find a, b
3a - b = 9 {equation 4}
8a + 4b = -16 {equation 5}
Multiply equation 4 through by 4 and add equations
12a - 4b = 36
8a + 4b = -6
----------------- add
20a = 30
a = 30/20
a = 3/2
8a + 4b = -6
8(3/2) + 4b = -6
12 + 4b = -6
4b = -6- 12
4b = -18
b = -18/4
b = -9/2
Plug these 2 values into one of the original equations and solve for c
15 = a - b + c {equation 3}
15 = 3/2 + 9/2 + c
15 = 12/2 + c
15 = 6 + c
c = 15-6
c = 9
y = (3/2)x2 - (9/2)x+ 9
Upvote
•
0
Downvote
Add comment
Still looking for help?
Step-by-step explanation:
ANSWER ASAP PLS
convert 70m/s to km/hr
1000=1km
Answer:
70 m/s = 252 km/hr
1 m/s = 3.6 km/hr
Jayden's car gets 23 miles to a gallon of gasoline. He filled up his car's gas tank with g gallons. Write an expression that shows how far Kurt can drive on a tank of gasoline.
Answer:
D= distance covered by amount (g) gallons
D=23g
Step-by-step explanation:
What is the perimeter of figure 12? (Show your work).
Round or fraction form round all the WAY!
Answer:
The answer to the question provided is
[tex] - \frac{3}{2} [/tex]
Solve the equation.
x2 + 13x + 30 = 0
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
O A. The solution(s) is/are x =
(Type an integer or a simplified fraction. Use a comma to separate answers as needed.)
O B. There is no solution.
Given that,
An equation : [tex]x^2 + 13x + 30 = 0[/tex]
To find,
The value of x.
Solution,
We have, [tex]x^2 + 13x + 30 = 0[/tex]
We can solve it as follows :
[tex]x^2 + 10x +3x+ 30 = 0\\\\x(x+10)+3(x+10)=0\\\\(x+3)(x+10)=0\\\\(x+3)=0\ \text{and}\ (x+10)=0\\\\x=-3\ \text{and}\ x=-10[/tex]
So, the solution of the given equations are -3 and -10.
250% of a number is the same as increasing the number by what percent?
Answer:
Since I am not given an increase number i will solve for numbers 1-5
1 - 25000%
2 - 12500%
3 - 8333.333333333332% (I recommend you don't use this one)
4 - 6250%
5 - 5000 %
Each number, it will increase by 250% no matter what
Its the same as increasing by 250%
Hope this helps <3
I NEED HELP PLZ I WILL GIVE THANKS AND BRAINLIST
Answer: Yes, it is in the blue shaded area
Step-by-step explanation:
15 = 5/ 3(x + 12) solve for x in simplest form
Answer:
x= -10 1/5 or -10.2
Step-by-step explanation:
Round the number 2.72603 to 2 decimal places.
Answer:
2.73
Step-by-step explanation:
You round 6 up to get 2.73
Please give brainliest and thank me if it helped
Which is the constant of proportionality for the relationship shown in the graph?
Answer:
COP: 2X
Step-by-step explanation:
K= Y/X
K= 4/2
K= 8/4
K= 12/6
K=16/8
A computer’s random number generator produces random integers from 1 to 50. What is the probability that the first 3 integers generated are single-digit numbers?
Answer:
A. 0.0058
Step-by-step explanation:
John jogged 4.5 miles on Thursday, 7 2/5 miles on Friday, and 10.4 miles on Saturday. How many miles does John have to run in order to run 25 miles for the week
im giving 20 points
Answer:
2.7 miles
Step-by-step explanation:
25 - 10.4 - 4.5 - 7 2/5 will give you 2.7
Answer:
8 miles
Step-by-step explanation:
If we divide 70 by 50, we get the unit rate for the ratio 70 minutes for every 50 miles.
70÷50=1.4
So the runner is running 1.4 minutes per mile. We can multiply this unit rate by the number of miles:
1.4 minutes mile × 5 miles = 7 minutes
Thus it will take her 7 minutes to run 5 miles at this pace.
If it takes her 7 minutes to run 5 miles, it will take her 7÷5 = 1.4 minutes to run 6÷3=2 miles at the same pace.
If it takes her 1.4 minutes to run 5 miles, it will take her 1.4×5=7 minutes to run 4×2=8 miles at the same pace. Since 60 minutes is 1 hour, she is running at a speed of 8 miles per hour.
We found her pace in minutes per miles in part (a).
Please help!!:
What is the length of DE in the image provided? (Please explain so I can understand in the future)
A. DE=4
B. DE=5
C. DE=6
D. DE=7
==========================================================
Explanation:
We have these three facts:
The arc markings on angles C and D indicate those angles are congruent. We can say that angle ACB = angle EDB.Another pair of congruent angles are angle ABC and angle EBD. These are vertical angles. Lastly, we have a pair of congruent sides AB and BE because of the tickmarks.Those three facts allow us to use the AAS (angle angle side) congruence theorem to prove that triangle ABC is congruent to triangle EBD.
Then by CPCTC (corresponding parts of congruent triangles are congruent), we know that AC = DE. Note how 'A' and 'C' are the first and last letters of ABC; similarly, 'E' and 'D' are the first and last letters of EBD. Segment ED is the same as segment DE.
So to find the length of DE, we need to find the length of AC. To do that, we need the value of x.
----------------
Recall earlier that AB = BE. Use this to find x
AB = BE
1.5x = 3x-6
1.5x-3x = -6
-1.5x = -6
x = -6/(-1.5)
x = 4
Now we can find the length of AC
AC = x+3
AC = 4+3
AC = 7
This must mean DE = 7 as well.
Answer:
DE=7
Step-by-step explanation:
I just took test
Also please make me Brainliest
Solve for p. p/8 + 12 = 36
9514 1404 393
Answer:
p = 192
Step-by-step explanation:
p/8 +12 = 36 . . . . . given
p/8 = 24 . . . . . . . . .subtract 12
p = 8·24 . . . . . . . . .multiply by 8
p = 192
the two angles measuring (30 + 2 a)degree and (125 -a) degree supplementary to each other, then find the value of a.
Answer:
The value of a is 25
Step-by-step explanation:
When two angles are supplementary, they add up to 180 degrees
Mathematically,
(30 + 2a) + (125-a) = 180
30 + 2a + 125 - a = 180
a + 155 = 180
a = 180-155
a = 25 degrees
(9x + 5) - (4x + 3)
Please show work
Answer:
Step-by-step explanation:
Simplifying
(9x + 5) + -1(4x + 3) = 0
Reorder the terms:
(5 + 9x) + -1(4x + 3) = 0
Remove parenthesis around (5 + 9x)
5 + 9x + -1(4x + 3) = 0
Reorder the terms:
5 + 9x + -1(3 + 4x) = 0
5 + 9x + (3 * -1 + 4x * -1) = 0
5 + 9x + (-3 + -4x) = 0
Reorder the terms:
5 + -3 + 9x + -4x = 0
Combine like terms: 5 + -3 = 2
2 + 9x + -4x = 0
Combine like terms: 9x + -4x = 5x
2 + 5x = 0
Solving
2 + 5x = 0
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-2' to each side of the equation.
2 + -2 + 5x = 0 + -2
Combine like terms: 2 + -2 = 0
0 + 5x = 0 + -2
5x = 0 + -2
Combine like terms: 0 + -2 = -2
5x = -2
Divide each side by '5'.
x = -0.4
Simplifying
x = -0.4
easy boy
sorry but i have another question :| tysm all yall for helping meee ^w^
9514 1404 393
Answer:
4: {8, 12, 16, 24}7: {7, 42, 49}neither: {6, 11, 17}Step-by-step explanation:
Looking at the numbers individually, we have ...
16 = 4×4
42 = 2×3×7
6 = 2×3
17 = 1×17 (prime)
12 = 3×4
49 = 7×7
24 = 2×3×4
7 = 1×7 (prime, a multiple of 7)
11 = 1×11 (prime)
8 = 2×4
__
Multiples of 4:
16, 12, 24, 8
Multiples of 7:
42, 49, 7
Multiples of neither:
6, 17, 11
90 coins
Use the original price and the markup to find the retail price.
Original price: $50; Markup: 15%
The retail price is $ ?
Answer:
50 + 50(.15)
50(1+ .15)
50(1.15)
RP= $57.5
Step-by-step explanation:
[tex]f(x)= \frac{X^2-x-12} {5x^2+4x}[/tex]
Find all x-intercepts of the following function. Write your answer or answers as coordinate points. Be sure to select the appropriate number of x-intercepts.
Answer:
(- 3, 0 ), (4, 0 )
Step-by-step explanation:
To find the x- intercepts let f(x) = 0
[tex]\frac{x^2-x-12}{5x^2+ 4x}[/tex] = 0
The denominator cannot equal zero as this would make f(x) undefined.
Equate the numerator to zero and solve for x
x² - x - 12 = 0 ← in standard form
(x - 4)(x + 3) = 0 ← in factored form
Equate each factor to zero and solve for x
x - 4 = 0 ⇒ x = 4
x + 3 = 0 ⇒ x = - 3
x- intercepts are (- 3, 0 ) and (4, 0 )
7th grade math help me please :)
Answer:
8x+10y cannot be simlified because they do not have a common variable
so until you find the value for x and y u cannot simplify
Answer:8 x+ 10 y can not be simplified .
Step-by-step explanation:
Explanation:This is because the term are not the same.8x has the term x while 10 y has the term y.
If there are 5 soccer players, 10 baseball players, and 15 basketball players, what is the ratio of baseball players to soccer players?
Answer:
2 to 1
Step-by-step explanation:
baseball=10
soccer =5
10:5 = 2:1(lowest term)
There are 24 carnations in each bunch and 12 roses in each bunch. Use your expression from question 1 or question 2 to determine the total number of carnations and the total number of roses Alison will distribute to each flower shop this week.
Answer: r/c
Step-by-step explanation:
96/48
or
24/12
need help on this asap pleaase
Maria and laurie are making orange juice.Maria use 2 cups of concentrate and 5 cups of water. Laurie uses 3 cups of concentrate and 7 cups of water . Whose mix would be the strongest? Why?
Answer:
Step-by-step explanation:
To obtain the strongest mix :
Maria:
2 cups of concentrate ; 5 cups of water
Ratio = 2/5 = 0.4 concentrate per 1 cup of water
Laurie:
3 cups of concentrate ; 7 cups of water
Ratio = 3/7 = 0.4285714 concentrate per 1 cup of water
0.4285714 > 0.4
Hence, Laurie's mix is the strongest as it has higher concentrate per cup of water.
In March, you have $220 in your savings account. By the end of April, your savings have increased by 30%. How much money do you have in your savings account at the end of April?
Answer:
286
Step-by-step explanation:
I dit 220+30%=286
Answer:
$286
Step-by-step explanation:
220 • 0.3 = 66
220 + 66 = 286
7th grade help me please:)
Answer:
4^9
262144
Step-by-step explanation:
What is the exact value of tan(67.5°) ?
Answer:
[tex]\sqrt\frac{2+\sqrt{2}}{2-\sqrt{2}}[/tex]
Step-by-step explanation:
correct on edge2020
The required exact value of tan(67.5°) is -2 + √(2).
What are trig ratios?If you know the lengths of two sides of a right triangle, you can use trigonometric ratios to calculate the measures of one (or both) of the acute angles.
Here,
The exact value of tan(67.5°) can be found using the half-angle identity for the tangent, which states that:
tan(x/2) = (1 - cos(x)) / sin(x)
We can use this identity with x = 135 degrees since 67.5 degrees is half of 135 degrees. So:
tan(67.5°) = tan(135°/2) = (1 - cos(135°)) / sin(135°)
We can then use the following exact values:
cos(135°) = -√(2)/2
sin(135°) = -√(2)/2
Substituting these values, we get:
tan(67.5°) = (1 + √(2)/2) / (-√(2)/2)
Rationalizing the denominator, we get:
tan(67.5°) = -2 + √(2)
Therefore, the exact value of tan(67.5°) is -2 + √(2).
Learn more about trig ratios here:
https://brainly.com/question/14977354
#SPJ6
Arlene has raised $56 for her class field trip. This is $14
more than three times the amount Adam has raised.
Which equation could you use to find how much money
Adam has raised?
Assuming Adams amount is x, three times his amount will be 3x. $14 more than the times Adam's amount will be 14 +3x.
Therefore if Arlene's money is $56 which is $14 more than three times Adam's amount, then the equation will be ;
14+3x=56
2.(03.07)
Solve 2x^2 - 8x = -7. (2 points)
Answer:
Step-by-step explanation:
Make a quadratic:
2[tex]x^{2}[/tex]-8x+7=0
Then use quadratic formula to solve.
It would be x= 2 ± [tex]\frac{2}{\sqrt{2} }[/tex]
Divide 2x^4+3x^3-5x+6 by x^2+3x-2 .
2x^4 + 3x^3 - 5x + 6 ÷ x^2 + 3x - 2
= 2x^6 + 3x^5 − 2x^3 − 2x^2 + 6/ x^2