Based on the information given, the required equation of parabola will be y= -3x² - 14x + 12.
SolutionThe parabola passes through the points (-1, 23), (1, -5), (3, -57). Let the equation of the parabola be y = ax² + bx + c.
For point (-1, 23), this will be:
23 = a(-1)² + b(-1) + c
23 = a - b + c ..... equation i
For point (1, -5), this will be:
-5 = a(1)² + b(1) + c
-5 = a + b + c .... equation ii
For point (3, -57), this will be:
-57 = a(3)² + b(3) + c
-57 = 9a + 3b + c .... equation iii
From equation i, 23 = a - b + c
Therefore, c = 23 - a + b .... equation iv
Substitute c into equation ii
-5 = a + b + 23 - a + b
-5 = 2b + 23
2b = -23 - 5.
2b = -28
b = -28/2 = -14
Substitute c into equation iii
-57 = 9a + 3b + 23 - a + b
-80 = 8a + 4b.
-80 = 8a + 4(-14)
-80 = 8a - 56
8a = -80 + 56
8a = -24
a = -24/8 = -3
Therefore, the value of c will be:
c = 23 - a + b
c = 23 -(-3) + (-14)
c = 23 + 3 - 14
c = 12
In conclusion, the required equation of parabola will be y = -3x² - 14x + 12.
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Lourdes plans to jog at least 1.5 miles. Write and solve an inequality to find x, the number of hours that Lourdes will have to jog..
Answer:
An inequality compares two or more variables by using the <, >, ≤, or ≥ signs.
The number of hours Lourdes will have to jog is 0.4 hours
From the given parameters:
Lourdes plans to jog for at least a distance of 1.5 miles
If Lourdes can jog averagely at the speed of 3.75 mph
Then,
the inequality that can represent the information can be written as:
= 1.5 miles ≤ 3.75 (x) miles/hour
Solving the inequality;
= 1.5 ≤ 3.75 (x)
Making (x) the subject of the formula, we have:
x = 0.4 hours
Therefore, we can conclude that the number of hours lourdes will have to jog is 0.4 hours
Step-by-step explanation:
Look at the figures. How can you prove the triangles are congruent?
is it
A) ABC= DEF by the SAS postulate
B) It is not possible to determine if the triangles are congruent
C) ABC = DEF by the SSS postulate
Answer:
SAS
Step-by-step explanation:
AB ≅ DE Given
AC ≅ DE Given
∠ A and ∠B are right angles Given
∠A ≅ ∠B All right angles are ≅
PLEASE HELP QUICK :) multiple choice.
Which of the following functions has a factor of x + 9 ?
A: f (x) = x^3 - 8x^2 - 11x + 18
B: f (x) = x^3 + 10x^2 + 7x - 27
C: f (x) x^3 + 10x^2 + 7x - 18
D: f (x) = x^3 - 8x^2 - 11x + 27
Answer:
C. f(x) = x³ + 10x² + 7x - 18Step-by-step explanation:
If the function has a factor of x + 9, then the function will have a zero output at x = -9
Lets verify:
A. f(-9) = (-9)³ - 8*(-9)² - 11*(-9) + 18 = -1260, NoB. f(-9) = (-9)³ + 10*(-9)² + 7*(-9) - 27 = -9, NoC. f(-9) = (-9)³ + 10*(-9)² + 7*(-9) - 18 = 0, YesD. f(-9) = (-9)³ - 8*(-9)² + 11*(-9) + 27 = -1449, Nohelp please i need it with explanation
Answer:
10. x = -23
Step-by-step explanation:
-3.8x - 5.9x = 223.1
-9.7x = 223.1 (-3.8 minus 5.9)
x = -23 (223.1 divided by -9.7)
Answer:
12. x = 70
Step-by-step explanation:
(-3/5)x - (7/10)x + (1/2)x = -56
-(4/5)x = -56 ( -3/5 minus 7/10 plus 1/2)
x = 70 (-56 divided by -4/5)
–8(6+3)
-83
Please help me
Answer:
-155
Step-by-step explanation:
-8\cdot \:9-83
-72-83
=-155
Larry and Cathy study for a total of 24 hours each week. Larry studies 3 less than twice the hours than Cathy studies. How many hours does Cathy study per week?
ATQ
[tex]\\ \sf\longmapsto x+2x-3=24[/tex]
[tex]\\ \sf\longmapsto 3x-3=24[/tex]
[tex]\\ \sf\longmapsto 3x=24+3[/tex]
[tex]\\ \sf\longmapsto 3x=27[/tex]
[tex]\\ \sf\longmapsto x=9[/tex]
Answer:
ᎪꪀsωꫀᏒ9 hours Cathy study per week
Step-by-step explanation:
=> according to the question
➪ x+2x-3=23
➪ 3x-3=24
➪ 3x=24+3
➪ 3x=27
➪ x= 27/3
➪ x= 9
Find the slope of the line that passes through (20, -37) and (68, -56).
i believe it would be -19/48
match the inequality with its graph
10. Name the line three ways.
Two opposite angles of a parallelogram are always
Answer:
Two opposite angles of a parallelogram are always equal.
solve 10x-3(x-7)=x+39
Answer:
[tex]10x-3\left(x-7\right)=x+39[/tex]
[tex]-3\left(x-7\right)[/tex]
[tex]-3x+21[/tex]
[tex]10x-3x+21=x+39[/tex]
** Combine like terms ↓ **
[tex]10x-3x=7x[/tex]
** Subtract 21 from both sides ↓**
[tex]7x+21-21=x+39-21[/tex]
[tex]7x=x+18[/tex]
** Subtract x from both sides ↓ **
[tex]7x-x=x+18-x[/tex]
[tex]6x=18[/tex]
**Divide both sides by 6 ↓*
[tex]\cfrac{6x}{6}=\cfrac{18}{6}[/tex]
[tex]x=3[/tex]
Collin spent $34 on a new video game. How much money does he need to earn in order to have a net change of $0?
(1.5x10^-5)+(3.5x10^-2) what is this written in scientific notation??
Answer:
0.035015x
Step-by-step explanation:
tập nghiệm của phương trình 3tan+√3=0
Answer:
if 0° ≤ x ≤ 360°
x = 150° or x = 330° (5/6 π , 11/6 π)
if x can be beyond 2π (360°) , above or below
x = 5/6 π + 2nπ or x = 11/6 π + 2nπ
Step-by-step explanation:
3 tanx = -√3
tan x = - 1/√3
if 0° ≤ x ≤ 360°
x = 150° or x = 330° (5/6 π , 11/6 π)
if x can be beyond 2π (360°) , above or below
x = 5/6 π + 2nπ or x = 11/6 π + 2nπ
Help me :( please help me
Answer:
22.84, 5.83
Step-by-step explanation:
Pythagoras theorem states that: a^2+b^2=c^2
So, for red triangle, it will be: 9^2+21^2=b^2
81+441=b^2
522=b^2
square root of 522=b
22.84=b
For purple one,
3^2+5^2=a^2
9+25=a^2
34=a^2
square root of 34=a
5.83=a
find abc !!!!!!!! !!!!!
Answer:
58 degreess
3x+11=4x-5
-3x -3x
11=x-5
+5 +5
16=x
x=6
3(6)+11
18+11
29
29*2
58
Step-by-step explanation:
please help due today NO LINKS WILL REPORT
Answer:
Step-by-step explanation:
i think that the answer is a, because the def of natural numbers match's and there all integers.
A? B? C? or D? help meeeeee
Answer:
b) -5/9
Step-by-step explanation:
yeah-ya.... right?
what is the sum of the prime numbers of 420 do not repeat any prime factors A 15 B 16 C.17 D. 18 E. 19
Answer:
C)
Step-by-step explanation:
Prime factorization of 420 = 2 × 2 × 3 × 5 × 7 = 22 × 3 × 5 × 7.
If you take...
2 + 2 + 3 + 5 + 7...
You would get 17.
Hope this helps! :) Good Luck!
-kiniwih426
IT'S HOMEWORK WHOEVER GIVES ME A GOOD ANSWER I WILL MAKE BRAINLIST. For spirit week at the local high school, students were encouraged to wear their school colors of green and white. 1,200 students wore their school colors while 300 students did not wear their school colors. what is the ratio? write and solve a proportion with ration language.
Answer:
1200:300
4:1 is the final ratio
Write the value of
[tex]1 - 2 \cos {}^{2} c[/tex]
Step-by-step explanation:
1-2cos²c.
> (cos²c+sin²c)-2cos²c. (cos²c+sin²c=1)
> cos²c+sin²c-2cos²c
> sin²c-cos²c.
is your correct answer.
hope this helps you.
9 - 5n < -4n + 9 or 9n + 4 < 7n - 4
Write and solve an inequality that represents the values of x, in feet.
The perimeter is less than 16 feet.
Answer:
x < 16 ft
Step-by-step explanation:
Perimeter = x
If it is less than 16, the equation is:
x < 16
-Chetan K
In a particular part of the Volta lake, there is a population of 100000 tilapia. The number of tilapia is decreasing at a rate of 10% per year due to pollution from a human settlement on the shores of the Volta lake in this area.
2. Copy and complete the table below to show the number of tilapia P after 1, 2 and 3 years
Number of years (t) 0 1 2 3
Number of tilapia (N)
Criterion B 1-2
b) Write an exponential model for the number of tilapia N after t years
Criterion B 3-4
c) When the population of tilapia falls below 25000 it is at a ‘critical level’. Write an inequality and calculate how long it will take for this lake to be at a critical level.
Answer:
?????
Step-by-step explanation:
yolanda's yoga class charges a $20 membership fee and $20 per visit.
write an expression that represents the cost of "x" visits: C=_______
how many visits would it take for the two costs to be the same?
(use your expressions and make them equal to each other and solve)
The 2 expressions: 10x + 100 and 20x + 20
20x + 20:
20 dollars per visit (20x) ; 20 dollar fee (20)
10x + 100 = 20x + 20 Subtract 10x from both sides
100 = 10x + 20 Subtract 20 from each side
80 = 10x Divide by 10
x=8Let f(x)=8x−6. What is the value of f(12)?
Answer:
f(12) = 90
Step-by-step explanation:
This is more of a notation problem than anything else.
The x on the left means that the variable is x. That sounds weird I know, but it starts out this way.
f(variable) = 8*variable - 6
Where you see the word variable, you put the letter x and that gives you the question.
f(x) = 8*x - 6
That is math shorthand for whatever you see on the left, like an x or in this case 12, you put the value 12 in for x on the right. It will look like this.
f(12) = 8*12 - 6 Now it just becomes a calculator problem.
f(12) = 96 - 6
f(12) = 90
PLEASE HELP DUE TODAY NO LINKS WILL REPORT
Answer:
The first option
Step-by-step explanation:
Because you cannot have a negative squared root
Answer:
a.
Step-by-step explanation:
I had this question before lol.
Elaine old bicycle had tires with 12 inch diameter. Her new bicycle has tires with 16 inch diameter. What is the difference in the same conference of the tires
Answer:
12.56 inches
Step-by-step explanation:
Barry buys a new washing machine.
The value of the washing machine depreciates by 20% each year.
(a)
Barry says 'after 5 years the washing machine will have no value'.
Barry is wrong. Explain why.
Barry wants to work out the value of the machine after 2 years.
(b)
By what single decimal number should Barry multiply the value of the machine when new?
Answer:
The machine decreases in value by 20% each year.
After 1 year the machine is worth only .8 of its original value.
The machine will only decrease by .2 * (.8 A) in the second year not .2 * A where A is the original amount.
A1 = .8 A
A2 = .8 A1 = .64 A value of machine after 2 years
.8 is the value Barry needs when the machine is new
.8^n never goes to zero
After 10 years value = .8^10 A = .11 A of its original value
HELP THIS IS DUE SOON 30 POINTS
Answer:
x = 4
Step-by-step explanation:
f(x) = 4x-5
11 = 4x-5
4x-5 = 11
4x = 11+5
= 16
x = 16÷4
= 4