write the equation of a porabola whose vertex is (2,5) and passes through the point (1, 1)
Answer:
y=5-4(x-2)^2
Step-by-step explanation:
Using the quadratic formula to solve 5x = 6x^2 – 3, what are the values of x?
Answer:
Correct Choice: Second Option
[tex]\displaystyle x=\frac{5\pm \sqrt{97}}{12}[/tex]
Step-by-step explanation:
Standard Form of Quadratic Function
The standard representation of a quadratic function is:
[tex]f(x)=ax^2+bx+c[/tex]
where a,b, and c are constants.
Solving with the quadratic formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
We have the following equation to solve:
[tex]5x = 6x^2 -3[/tex]
Rearranging all the terms to the left side:
[tex]6x^2 -5x- 3=0[/tex]
Comparing with the general form of the quadratic equation: a=6, b=-5, c=-3. Apply the formula:
[tex]\displaystyle x=\frac{-(-5)\pm \sqrt{(-5)^2-4(6)(-3)}}{2(6)}[/tex]
[tex]\displaystyle x=\frac{5\pm \sqrt{25+72}}{12}[/tex]
[tex]\boxed{\displaystyle x=\frac{5\pm \sqrt{97}}{12}}[/tex]
Correct Choice: Second Option
The opening of a tunnel that travels through a mountainside can be modeled by [tex]y = - \frac {2}{15} (x - 15)(x + 15)[/tex], where x and y are measured in feet. The x-axis represents the ground.
a. Find the width of the tunnel at ground level.
b. How tall is the tunnel?
Answer:
(a) 30 feet
(b) 30 feet.
Step-by-step explanation:
Given that the opening of a tunnel that travels through a mountainside can be modeled by
[tex]y=\frac{-2}{15} (x-15)(x+15)[/tex], where x and y are measured in feet.
[tex]\Rightarrow y=\frac{-2}{15}(x^2-15^2}[/tex]
[tex]\Rightarrow y=\frac{-2}{15}{x^2-225}\cdots(i)[/tex]
(a) At the ground level, [tex]y=0[/tex]
So, the width of the tunnel at ground level is distance between the extreme point of the tunnel on the grount.
For, [tex]y=0[/tex], the extreme points of the tunnel.
[tex]0=\frac{-2}{15} (x-15)(x+15)[/tex]
[tex]\Rightarrow (x-15)(x+15) =0[/tex]
[tex]\Rightarrow x= 15, -15[/tex]
So, the extreme points of the tunnel are, [tex]x_1=15[/tex] and [tex]x_2=-15[/tex].
Hence, the width of the tunnel at the ground level
[tex]= | x_1 - x_2 |[/tex]
[tex]=|15-(-15)|[/tex]
[tex]=30[/tex] feet.
(b) The maximum height of the tunnel can be determiment by determining the maxima of the given function.
First determining the value of x for which the slope of the graph is zero.
[tex]\frac{dy}{dx}=0[/tex]
From equation (i),
-2x=0
[tex]\Rightarrow x=0[/tex]
And [tex]\frac{d^2y}{dx^2}= -2[/tex]
which is always negative, so at x=0 the value of y is maximum.
Again, put x=0 in equation (i), we have
[tex]y=\frac{-2}{15}{0^2-225}[/tex]
[tex]\Rightarrow y=30[/tex] feet.
Hence, the tunnel is 30 feet tall.
Jill spends $525 for monthly bills. Of this amount she spends 110 on her cell phone bill and 25% on her car payment. The remainder pays her utilities. How much money does she spend on utilities?
Answer:
283.75
Step-by-step explanation:
525/4=131.25
131.25+110=241.25
525-241.25=283.75
$3.75 for 5 apples: division pls
Answer: 0.75
Step-by-step explanation:
It is easier to divide if you get rid of the decimal, divide 375/5, and then add the decimal back.
[tex] \frac{100}{1} = {10}^{x} [/tex]
Triangle ABC is transformed to create triangle MNO and triangle PQR as described below
Answer:
The correct answer is the second option
Multiply. Write your answer as a fraction in simplest form.
5/6⋅(−4 1/2)⋅(−2 1/5)=
Answer:
7425
Step-by-step explanation:
First let's make the last two fractions improper.
-4 1/2 = -9/2 -2 1/5 = -11/5
Now we have to find the least common denominator.
[tex]\frac{5}{6} *\frac{-9}{2}*\frac{-11}{5}[/tex]
The least common denominator is 30 because all the denominators can be multiplied by something to get 30.
[tex](\frac{5}{5})*\frac{5}{6}* (\frac{15}{15})*\frac{-9}{2}* (\frac{6}{6})*\frac{-11}{5}[/tex] Simplify
[tex]\frac{25}{30}*\frac{-135}{30}*\frac{-66}{30}[/tex] simply
[tex]\frac{-3375}{30}*\frac{-66}{30}[/tex]
[tex]\frac{222750}{30}[/tex] simply
7425
I need some help with geometry.
Answer:
x = 17, angle 1 and 2 = 45
Step-by-step explanation:
Find the slope of the line that passes through the following pair of coordinates: (15,18) (0,6)
Answer: y= (4/5)x+6
Step-by-step explanation:
(0,6) is the y intercept/b . Use y2-y1 for the slope/m. Y= Mx+b now is y=(4/5)x+6.
Mandi has $40 to spend at the fair. The admission to get into the fair is $5 and each ride is $1.75
Write an inequality to represent the situation using r for the number of rides
If you were to roll the
dice two times what is the
probability it will land on a
3 both times?
Answer:
1/36
Step-by-step explanation:
A dice have 6 faces, each face have 1/6 chance to land on, so the chance of landing on 3 two times in a row is 1/6 x 1/6 = 1/36
If you can walk 3 miles in an hour, how many miles can you walk in 30 minutes, given the
3
same pace?
A. 1 1/6 miles
B. 1 2/3miles
C. 6 2/3miles
D. 1 1/3 miles
PLS ANSWER QUICKLY!
A line passes through the point (-2,3) and has a slope of 1/5.
show work to write the equation of the line in point-slope form.
Y-3=1/5(x+2) is the answer.
Mrs. Flossi is hosting a trivia contest for 40 students and 24 staff members. To be fair,
Mrs. Flossi wants there to be the same number of students and the same number of
staff members on each team.
What is the greatest number of teams Mrs. Flossi can make?
1. 3 teams
2. 4 teams
3. 5 teams
4.8 teams
(I WILL GIVE BRAINLIEST)
Answer:
8 teams is answer
Step-by-step explanation:
The sum of three numbers is 79. The sum of five times the first number and two times the
second number increased by the third number is 859. Two time the first number, increased by
three times the second number plus nine times the third number is 498. Write a system.
Answer:
(x+y+z)=79
5x+2y+z=859
2x+3y+9z=498
Step-by-step explanation:
Its writing 3 different equations that have the same value for the same variable.
What value of x makes this equation true? 0.6x − 5 = 0.1x + 7
Answer:
Step-by-step explanation:
0.6x − 5 = 0.1x + 7
.6x-.1x=.5x
.5x -5 = 7
7 + 5 = 12
.5x = 12
12/.5 = 24
x = 24
Hi, i would really appreciate if someone helped me out!
A corner store sells two kinds of baked goods: cakes and pies. A cake costs $11 and a pie costs $10. In one day, the store sold 11 baked goods for a total of $117. How many cakes did they sell?
Answer:
7cakes and 4 pies
Step-by-step explanation:
need help, plz answer
Answer:
55 r5
Step-by-step explanation:
Answer:
390/7=55 with a remainder of 5.
Step-by-step explanation:
we can get this answer by subtracting fifty-five sevens from three-hundred ninty.
390-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7-7=5
Help me...PLEASE... :(
Answer:THE ANSWER IS BLOCKED AND DELETED FROM THE ACCOUNT OR THE INTERNET ACCESS IS LOW OR YOUR BATTERY IS NOT WORKING PROPERLY TRY AGAIN LATER
Which of the following best describes the English expression fourteen less
than the quantity of a number plus one?
A. (1 - x) +14
O B. 4 - 1
O C. (x + 1) - 14
D. (x - 1) +14
Answer:
c
Step-by-step explanation:
What is the slope of the line that passes through the points (8,7) and (4, 5)? Write
your answer in simplest form.
Answer: 1/2
Step-by-step explanation: got it right
The slope of the line that passes through the points (8,7) and (4, 5) is 1/2.
What is slope of a line?The slope of the line is the ratio of the rise to the run, or rise divided by the run. It describes the steepness of line in the coordinate plane.
The formula to find the slope of a line is slope = (y₂-y₁)/(x₂-x₁).
The given coordinate points are (8, 7) and (4, 5).
Substitute (x₁, y₁)= (8, 7) and (x₂, y₂)= (4, 5) in slope formula, we get
Slope = (5-7)/(4-8
= -2/(-4)
= 1/2
Therefore, the slope of the line that passes through the points (8,7) and (4, 5) is 1/2.
To learn more about the slope of a line visit:
https://brainly.com/question/14511992.
#SPJ6
Aaron is considering getting his car a new paint job. Doing so will have a total cost of $264.83. Can Aaron afford this? Explain a. Yes, he can make the purchase and still have money left over. b. Yes, but doing so will clear out his account. c. No, purchasing that would overdraw his account. d. No, he is overdrawn already.
Answer:
Yes, but doing so will clear out his account.
Step-by-step explanation:
CHECK THE COMPLETE QUESTION BELOW
Aaron's bank account has a balance of $1213.69 before he starts spending money. He makes the following transactions:
Transaction
Cost ($)
Car payment
260.16
Groceries
97.98
Parking ticket
75.00
DVD box set
115.35
Antique lamp
68.53
Suit
331.84
Aaron is considering getting his car a new paint job. Doing so will have a total cost of $264.83. Can Aaron afford this? Explain a. Yes, he can make the purchase and still have money left over. b. Yes, but doing so will clear out his account. c. No, purchasing that would overdraw his account. d. No, he is overdrawn already
Aaron's bank account balance=$1213.69
He made all this transactions below;
Car payment
260.16
Groceries
97.98
Parking ticket
75.00
DVD box set
115.35
Antique lamp
68.53
Suit
331.84
The summation of all his transactions is;260.16+97.98+75.00+115.35+68.53+
331.84= $948.86
Which means after performing those transactions above, he was left with $948.86.
We were informed that Aaron is considering getting his car a new paint job. Doing so will have a total cost of $264.83.
For him to paint his car now he will spend $264.83, if we add with the previous transactions it sum up to $1213.69 which was actual amount he has at hand. I.e ($264.83+$948.86)=
$1213.69
Therefore, the answer is Yes, but doing so will clear out his account.
The answers are on the pic
please answer fast!!
Answer:
27
Step-by-step explanation:
A television and DVD player cost $1053 the cost of the television is two times the cost of the DVD player
Answer:
2106
Step-by-step explanation:
what are the last ones
0.75 cups and 144 teaspoons
Step-by-step explanation:
I'm 99.99% sure I got it right
The price of stock market in at 9 AM was 13.17 then the price has been increasing at a rate of 0.11 each hour at noon the price of stuff he was 13.67 it begins to decrease at the rate of 0.12 each hour if the two rates continue and how many hours were the prices of the two stocks with the same
Answer:
2.26 hours
Step-by-step explanation:
Given that:
Stock 1:
Initial price = 13.17
Rate of increase = $0.11 per hour
13.17 + 0.11h - - - (1)
Stock 2 :
Initial price = 13.69
Rate of decrease = 0.12 per hour
13.69 - 0.12h - - (2)
13.17 + 0.11h = 13.69 - 0.12h
0.11h + 0.12h = 13.69 - 13.17
0.23h = 0.52
h = 0.52 / 0.13
h = 2.26 hours
What is the definition of rate of change?
Answer:
Value over a defined period of time, and it represents the momentum of a variable. ✨
Step-by-step explanation:
Write the following equation in slope intercept form.
7x-4y=22
y= x+
Answer:
y= -7x+22/-4
Step-by-step explanation:
Answer:
y=7/4x-11/2
Step-by-step explanation:
Move the Y and x values to separate sides
-4y=-7x+22
divide whatever it takes to make y alone (dived by -4)
y=7/4x-11/2
A quadratic function has a line of symmetry at x = –3.5 and a zero at –9. What is the distance from the given zero to the line of symmetry? What is the other zero of the quadratic function?
Given:
A quadratic function has a line of symmetry at x = –3.5 and a zero at –9.
To find:
The other zero.
Solution:
We know that, the line of symmetry divides the graph of quadratic function in two congruent parts. So, both zeroes are equidistant from the line of symmetry.
It means, line of symmetry passes through the mid point of both zeroes.
Let the other zero be x.
[tex]-3.5=\dfrac{(-9)+x}{2}[/tex]
Multiply both sides by 2.
[tex]-7=-9+x[/tex]
Add 9 on both sides.
[tex]-7+9=-9+x+9[/tex]
[tex]2=x[/tex]
Therefore, the other zero of the quadratic function is 2.
Answer: A=0, B=6, C=4.
The axis of symmetry is x = ½
The smaller zero is -2
The larger zero is 3
Step-by-step explanation: Correct in edge 2020, the format makes it hard to find answers online but I just did the assignment