Write 3 quadratic equations that are NOT
equivalent, each forming a graph with vertex (-2, 3)
Answers
Answer:
the vertex of a quadratic equation:
a*x^2 + b*x + c = y
Is located at:
x = -b/2a.
In this case, x = -2
Then:
-b/2a = -2.
And we also have that:
a*(-2)^2 + b*-2 + c = 3
Then we have two equations:
-b/2a = -2
a*(-2)^2 + b*-2 + c = 3
We have only 2 equations and 3 variables, so we can just give the variable c different values and we will find different quadratic equations that are not equivalent.
Let's begin with c = 0, our equations are:
-b/2a = -2
a*(-2)^2 + b*-2 + 0 = 3
In the first equation we can isolate b and get:
b = 4*a
Now we can replace this in the other equation and solve this for a.
a*4 + 4*a*-2 = 3
-4*a = 3
a = -3/4
then:
b = 4*a = 4*-3/4 = -3
The first quadratic equation is:
(-3/4)*x^2 - 3*x = y.
Now, to find the second let's use a different value of c.
c = 1
b = 4*a
a*(-2)^2 + b*-2 + 1 = 3
Let's solve in the same way as before:
a*4 + (4*a)*-2 + 1 = 3
-4*a = 2
a = 2/-4 = -1/2
b = 4*-1/2 = -2.
Then our equation is:
(-1/2)*x^2 - 2*x + 1 = y
For the last equation, let's use c = 2.
then our equations are:
b = 4*a
a*(-2)^2 + b*-2 + 2 = 3
Same as before, replace the first equation in the second.
a*4 + (4*a)*-2 + 2 = 3
-4*a + 2 = 3
-4*a = 1
a = -1/4
Then:
b = 4*(-1/4) = -1
Our third equation is:
(-1/4)*x^2 - 1*x + 2 = y
Now, below you can see all of them graphed.
Where red is the first one, blue the second and green the third one. (and as you can see, all of them share the vertex (-2,3) )
Related Questions
There are 1 × 1014 good bacteria in the human body. There are 2.6 × 1018 good bacteria among the spectators in a soccer stadium. About how many spectators are in the stadium? Express your answer in scientific notation.
Answers
Answer:
There are [tex]2.6\times 10^{4}[/tex] spectators in the soccer stadium.
Step-by-step explanation:
From this statement, we can calculate the number of spectators in a soccer stadium by dividing the amount of bacteria among the spectators in a soccer stadium by the amount of bacteria in the human body. That is:
[tex]x = \frac{2.6\times 10^{18}\,bacteria}{1\times 10^{14}\,bacteria}[/tex]
[tex]x = \frac{2.6}{1}\times \frac{10^{18}}{10^{14}}[/tex]
[tex]x = 2.6\times 10^{18-14}[/tex]
[tex]x = 2.6\times 10^{4}[/tex]
There are [tex]2.6\times 10^{4}[/tex] spectators in the soccer stadium.
HELP PLEASE SHOW YOUR WORK TO!!!!!!!
Answers
Answer:
V/3k = t
Step-by-step explanation:
Isolate the variable (t)
V = 3k/t
We have to get rid of 3 and k to isolate t
Since 3 and k are part of a fraction we can multiply it by their reciprocal
V = 3k/t × 1/3k
What we do to one side, we must do to the other
V × 1/3k = 3k/t × 1/3k
The reciprocals equals 1
V × 1/3k = t × 1
Any number or variable multiplied by 1 equals itself (applies to both sides of the equation)
V/3k = t
11. In AWTY, if mZW is five less than twice mZY and mZX is 21 more than m_Y find the measure
of each angle.
Answers
9514 1404 393
Answer:
angles (W, X, Y) = (77°, 62°, 41°)
Step-by-step explanation:
Given:
ΔWZY
∠W = 2(∠Y) -5°
∠X = ∠Y +21°
Find:
∠X, ∠Y, ∠W
Solution:
Using angle measures in degrees, we have ...
∠X + ∠Y + ∠Z = 180
(∠Y +21) +∠Y + (2(∠Y) -5) = 180
4(∠Y) +16 = 180 . . . . . simplify
∠Y +4 = 45 . . . . . . . . . divide by 4
∠Y = 41 . . . . . . . . . . . . subtract 4
∠W = 2(41) -5 = 77
∠X = 41 +21 = 62
The angle measures of angles (W, X, Y) are (77°, 62°, 41°), respectively.
What is the best estimate of the measure of the angle shown?
Answers
*answer was incorrect please see below*
as the angle is obviously larger than 90°, but not large enough to be 171° as if it were so it would be closer to a straight line (since 171° is closer to 180°) hence, the answer is 141° as it is the only option in between.
Average movie prices in the United States are, in general, lower than in other countries. It would cost $79.98 to buy three tickets in Japan plus two tickets in Switzerland. Three tickets in Switzerland plus two tickets in Japan would cost $75.02. How much does an average movie ticket cost in each of these countries?
Answers
Answer:
$79.98-$75.02=$04.96
Answer:
$04.96 is right answer am I right or wrong hope I am right
A 1-litermbottle of orange juice used to cost $2.85 at a food market. its price has increased; the new price is 110 percent of the original price. What is the new price? Round your answer to the nearest cent
Answers
Help out hereeeeeeeeeeee
Answers
Answer:
C.
Step-by-step explanation:
Solve for g in the proportion
g 15
4 6
Answers
Answer:
g times 15 if it's a algebraic question
g=6
Refer to the explanation for the process.
Explanation:
Solve:
9 g=15 10
Cross multiply each denominator by the opposite numerator.
9×10=15×g
Simplify.
90=15g
Divide both sides by 15
90 15=g
Simplify.
6=g
Switch sides.
g=6
Hope this helps!
HELPPPPPPPPP ASAPPPPPPPP PLSSSS
Answers
-1/3(px-2) = 9
ok! so first we want to isolate x.
multiply both sides by -3/1 (this is the reciprocal of -1/3)
(px-2) = -27
px = -27 + 2
px = -25
x = -25/p
hope this helped!
Simplify (6g4h5)2
What is the answer
Answers
Answer:
12g8h10
Multiply each variable quantity by 2 and combine.
Nick and his family traveled by train to New York City. The clocks show when the train left the station and when it arrived in New York City. How long was the train ride?
Answers
Answer:
Answer: 4 hr 15 min is the right answer
7. Elijah's puppy weighs 35 ounces. If he weighed 19 ounces at the last visit
to the veterinarian's office, what is the percent increase in the puppy's
weight rounded to the nearest whole number?
Answers
Answer:
40 make me brainliest whbsbsvssvvsgwvwv
Answer:
52%
Step-by-step explanation:
so 35 is a hundred and the divide by 2 which is 17.5 and round the colosestwhich is 52
The number of tons of wheat the government can afford to buy if it spends total of $100 million, wheat costs $300 per ton, and it must buy 5 fighter planes at $15 million each.
Answers
Total amount, T = $100 million.
Cost of wheat per ton, C = $300 .
Price per fighter plane, c = $15 million.
Now,
Price of 5 fighter planes, P = $( 15 × 5 ) = $75 million.
Amount left = $( 100 - 75 ) = $25 million.
So,
Number of tons of wheat government can buy is :
[tex]n=\dfrac{25\times 1000000}{300}\\\\n = 83333.33\ tons[/tex]
Therefore, number of tons of wheat the government can afford is 83333.33 tons.
Hence, this is the required solution.
What makes math word problems challenging for you? If word problems are not hard for you, explain what you do to solve them.
Answers
Well.
Step-by-step explanation:
For me, typically I dont read the question properly and do the math wrong. Other moments I cant even figure out what exactly the question is even asking.
Step-by-step explanation:
You can try to read the word problem once first (no need to be really through just need to get an idea of what's really happening), and then read again, now a little more through, where you need to understand what the question wants of you. Once you understood the question, relate it to the topic you have learnt and see if there's any formula in this topic that you have been taught. If there is, keep all of these formulas in mind. If there isn't then it's good just search for all the numbers given in the question and form and equation in it or just solve. If there may be formulas involved, try relate the question/info given to the formulas you have in your head and yeah
pls help I will give you brainliest just help please
Answers
Answer:
The answer is A & D.
Step-by-step explanation:
Hope this helps
Given: -2(5x-3/4)=-10x+3/2
-2(5x)+(-2)(-3/4)
=-10x+3/2
bye cus im so bad at math smh.
on top it says:
“The graph shows the amount two cleaning companies are charged based on the number of hours it takes them to clean.”
SOMEONE HELP PLS
Answers
The answer is the third one. Trust me. I don't feel like explaining.
Step-by-step explanation:
8. A yard is closest in distance to a
a. kilometer.
b. centimeter.
C. meter.
d. millimeter.
Answers
Answer:
meter
Step-by-step explanation:
Answer:
Meter
Step-by-step explanation:
Kilometer is too long
Centimeter is too shot
Millimeter is way too short
Meter is the closest to yard
1 meter equals 1.09361 yards
The radius of a circle is 16.7 in. Find the circumference to the nearest tenth.
Answers
16.7 inches times 3.14 in or pie, equals 52.4 inches, and because you were given the radius and not the diameter, you multiply 52.4 inches by 2 to get 104.9 or 105 inches.
The circumference of the circle is 105 in to the nearest tenth.
What is the circumference of the circle?The circumference of the circle that has a radius of r is defined as the product of diameter to the pie value.
The circumference of the circle = 2πr
We are given that the radius of a circle is 16.7 in.
We need to determine the circumference to the nearest tenth.
Radius r = 16.7
Then circumference of the circle = 2πr
= 2 x 3.14 x 16.7
= 104.87
Therefore, the circumference of the circle is 105.
Learn more about circumference here;
brainly.com/question/12512221
#SPJ2
what is the answer?
Answers
Answer:
(2/5, 26/5)
Step-by-step explanation:
Factorise 3x^2 +37x+70
Answers
Answer:
If it needs to be factored by grouping the answer would be (3x+7) and (x+10).
Step-by-step explanation: I don't know how to explain but I hope this helped.
Put these in order starting from the smallest
5^2 2^4 3^3 1^8
Answers
Answer:
1^8, 2^4, 5^2, 3^3 is the answer.
The numbers ordered from the smallest to the largest is [tex]1^{8} , 2^{4} , 5^{2} , 3^{3}[/tex].
What is the order of the numbers?In order to determine the order of the numbers, we have to solve for the numbers. The power of a number can be solved by multiplying a number by its number of power.
[tex]5^{2}[/tex] = 5 x 5 = 25
[tex]1^{8}[/tex] = 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 = 1
3³ = 3 x 3 x 3 = 27
[tex]2^{4}[/tex] = 2 x 2 x 2 x 2 = 16
To learn more about perfect squares, please check: https://brainly.com/question/22947195
Richard spent $30 at a store. He spent $14 on a book and bought some CD's at $4 each. How
many CD's did Richard buy at the store? Write an equation to represent the problem, then
solve.
Answers
Answer:
4
Step-by-step explanation:
30 minus 14 = 16 and 16 divided by 4 is 4. so the answer is 4
Today, everything at a store is on sale. The store offers a 20% discount.
a. The regular price of a T-shirt is $18. What is the discount price?
Type the answer in the box below.
$
b. If the regular price of an item is x dollars, what is the discount price in dollars?
Type the correct expression in the box below.
$$
c. The discount price of a hat is $18. What is the regular price?
Type the answer in the box below.
$
Answers
Answer:
A. $14.40
B. ?
C. $21.60
Step-by-step explanation:
I just know it’s right lol
I need help with this
Answers
Answer:
-6
Step-by-step explanation:
greater than -8
absolute value is even
absolute value is between 5 & 11
An object was dropped off the top of a building. The function
f
(
x
)
=
−
16
x
2
+
256
f(x)=−16x
2
+256 represents the height of the object above the ground, in feet,
x
x seconds after being dropped. Find and interpret the given function values and determine an appropriate domain for the function.
f(−1)= , meaning that seconds after the object was dropped, the object was feet above the ground. This interpretation in the context of the problem.
f
(
1.5
)
=
f(1.5)= , meaning that seconds after the object was dropped, the object was feet above the ground. This interpretation in the context of the problem.
f
(
6
)
=
f(6)= , meaning that seconds after the object was dropped, the object was feet above the ground. This interpretation in the context of the problem.
Based on the observations above, it is clear that an appropriate domain for the function is .
Answers
Answer:
What is the equation, it’s hard to understand
Step-by-step explanation:
For the Noah and Andres question: To make orange fizz Noah mixes 4 scoops of powder with 6 cups of water. Andre mixes 5 scoops of powder with 8 cups of water what would that look like on a double number line? Sorry this is long
Answers
Answer:
On the number line:
a) 0.6666666667 scoops per powder
b) 0.625 scoops per powder
Step-by-step explanation:
For the Noah and Andres question:
To make orange fizz Noah mixes 4 scoops of powder with 6 cups of water.
Unit rate = scoops per cup
= 4 Scoops/6 cups
= 2/3 scoops per powder
= 0.6666666667 scoops per powder
Andre mixes 5 scoops of powder with 8 cups of water what would that look like on a double number line?
Unit rate = scoops per cup
= 5 Scoops/8 cups
= 0.625 scoops per powder
What is the given point on the line of this equation y +2 = (1 - 3)2
Answers
Answer:
4
Step-by-step explanation:
Move numbers to right hand side
write this equation in word form.
x3 + 1
Answers
Answer:
X cubed plus one
Step-by-step explanation:
What is the value of x
Answers
Answer:
x=39
Step-by-step explanation:
First I try to find the angle measurements for the rest of the angles inside the triangle. I saw that the 68 degrees and I notice that it was vertical angles, meaning that the inside is also 68. I then notice that the 107 and the other unknown angle besides x must be 180 when adding up, so I can do 180-107=73. Now I know that that angle is 73 degrees I can find x by solving this equation 180=73+68+x, which the answer comes out to be 39. so x=39.
Hope this helps you
Rewrite the product as a power: a^7 *y^7
Answers
Answer:
ay^7
Step-by-step explanation:
just give me the points.