[tex]h = - \frac{b}{2a} \\ k = \frac{4ac - {b}^{2} }{4a} [/tex]
Vertex Form[tex]y = a{(x - h)}^{2} + k [/tex]
Where the a-term determines how wide, narrow, upward or downward the graph is.
The h-term determines the horizontal shift of graph. (x-axis)
The k-term determines the vertical shift of graph. (y-axis)
The vertex of graph is at (h,k). We can find the vertex by using the given formulas.
Find the vertexFrom the equation, the coefficients are:
[tex] \begin{cases} a = - 1 \\ b = 12 \\ c = - 31 \end{cases}[/tex]
Substitute these values in the formulas.
Find the value of h
[tex]h = - \frac{12}{2( - 1)} \\ h = - \frac{12}{ - 2} \\ h = - \frac{ - 6}{1} \longrightarrow - ( - 6) = 6 \\ h = 6[/tex]
Hence, the value of h is 6.
Find the value of k
[tex]k = \frac{4( - 1)( - 31) - {(12)}^{2} }{4( - 1)} \\ k = \frac{124 - 144}{ - 4} \\ k = \frac{ - 20}{ - 4} \longrightarrow \frac{5}{1} = 5 \\ k = 5[/tex]
Hence, the value of k is 5. Then we substitute both value of h and k in the vertex form
Rewrite the equation of vertex form by substituting the value of h and k[tex]y = a {(x - h)}^{2} + k \\ y = - 1 {(x - 6)}^{2} + 5 \\ y = - {(x - 6)}^{2} + 5[/tex]
AnswerSince the vertex is at (h,k). Therefore the value of h is 6 and k is 5. Therefore:
[tex] \large{(h, k)=(6, 5)}[/tex]
(6,5) is the vertex.
On 9th May, 2009, there were 3440 people in the world with swine flu. Of these people, 1639 were in the USA. The 3440 people who had swine flu on 9th May was an increase of 37.6% on the number of people who had swine flu on 8th May. Calculate the number of people who had swine flu on 8th May.
Answer:
2500
Step-by-step explanation:
let a represent the number of people that had swine flu on the 8th of May
a increased by 37.6% on the 9th of May. The 37.6% increase is equal to 3440
the equation that can be used to represent this is:
a x 1.376 = 3440
to find a, divide both sides by 1.376
a = 2500
7
9
3
10
Simplify the answer if possible.)
i don't really get what the question is could you write it again?
Use the figure shown below to find the value of x
what i don't understand why you are not answer that question
The sum of two numbers is 18 and their difference is 4 what are the two numbers?
Answer:
7 and 11
Step-by-step explanation:
Let the two numbers be x and y
x+y = 18
x-y = 4
Add the two equations together to eliminate y
x+y = 18
x-y = 4
----------------
2x +0y = 22
Divide each side by 2
2x/2 = 22/2
x = 11
Solve for y
x+y = 18
11+y =18
Subtract 11 from each side
11+y-11 =18-11
y = 7
The two numbers are 7 and 11
Write the equation of an exponential function that satisfies these characteristics:
1. y intercept of (0,5)
2. range is all y values greater than 0
The value of the exponential equation is y = 5ˣ + 4
What are the laws of exponents?When you raise a quotient to a power you raise both the numerator and the denominator to the power. When you raise a number to a zero power you'll always get 1. Negative exponents are the reciprocals of the positive exponents.
The different Laws of exponents are:
mᵃ×mᵇ = mᵃ⁺ᵇ
mᵃ / mᵇ = mᵃ⁻ᵇ
( mᵃ )ᵇ = mᵃᵇ
mᵃ / nᵃ = ( m / n )ᵃ
m⁰ = 1
m⁻ᵃ = ( 1 / mᵃ )
Given data ,
Let the exponential equation be represented as A
Now , the value of A is
The y intercept is ( 0 , 5 )
So , when x = 0 , the value of y = 5
Substituting the values in the equation , we get
y = 5ˣ + 4 be equation (1)
when x = 0
y = 5⁰ + 4
y = 1 + 4
y = 5
when x = 2
y = 5² + 4
y = 25 + 4 = 29
Therefore , the range is all y values greater than 0
Hence , the equation is y = 5ˣ + 4
To learn more about exponents click :
https://brainly.com/question/28966438
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Pass a brotha some help :(
Answer and Step-by-step explanation:
Distribute the 1p to the y and -6 and distribute the 2 to the 3y and 6.
10y - 50 + 6y + 12
Now, combine like terms.
16y - 38
#teamtrees #PAW (Plant and Water)
Please help due tonight
Tom buys 3 burgers and 5 drinks for $34. Jane buys 2 burgers and 6 drinks for $36. How much is each burger and each drink?
While shopping at Best Buy, you find the brand new laptop you have been wanting. The laptop originally costs $189.99 but is marked for 25% off. Find the discount amount and the new purchase price of the laptop before taxes.
Answer:
$142.49
Step-by-step explanation:
1. 25% = 0.25
2. 189.99 × .25 = 47.4975
3. 189.99 - 47.4975 = 142.4925
4. $142.49
solve :
4² ( 4³ )
with work shown
Answer:
1024
Step-by-step explanation:
4²(4³)
4×4(4×4×4)
16(16×4)
16(64)
16×64
=1024
Plz hurry
What is the measure of each angle?
40 points!!!!
Answer:
you didnt add a picture so im taking the points <3
Step-by-step explanation:
I would help if you provided more information
What is the slope of y = -4?
Answer:
0
Step-by-step explanation:
The line is horizontal.
Explanation:
Think of y = -4 as y = 0x+(-4)
We see that the equation matches the form y = mx+b
m = 0 = slope
b = -4 = y intercept
Side note: this equation graphs out a horizontal line. All horizontal lines have a slope of 0.
In ΔSTU, s = 3.8 inches, t = 9.8 inches and u=9.6 inches. Find the measure of ∠U to the nearest 10th of a degree.
Answer:
m∠U = 75.7°
Step-by-step explanation:
use Law of Cosines:
9.6² = 3.8² + 9.8² - 2(3.8)(9.8)·cos U
92.16 = 14.44 + 96.04 - 74.48·cos U
92.16 = 110.48 - 74.48·cosU
-18.32 = -74.48·cosU
cos U = -18.32/-74.48
cos U = 0.24597
arccos U = 75.7
Answer:
m∠U = 75.7°
Step-by-step explanation:
its on delta and if you use a calculator then its m∠U = 75.7°
A container is in the shape of a cuboid the cuboid is 2/3 full of water a cup holds 275 ml of water what is the greatest number of cups
Answer:
12 cups
Step-by-step explanation:
The first step is to calculate the volume of the cubiod
= 36 × 6 × 23
= 4968
= 4968/3 ×2
= 1656×2
= 3312
Therefore the greatest number of cups can be calculated as follows
= 3312/275
= 12
Hence the greatest number of cups is 12 cups
need help pls!!!! Algebra
Answer:
11
Step-by-step explanation:
Y=? Need help ASAP very much appreciated
Answer:
8
Step-by-step explanation:
I'm guessing the answer is 8 because when y is -8, x is 4. So, my thought in mind is when x is negative, y is positive. It also says, "If the value of "y" varies directly with "x". So, this means the answer is 8. You're very much welcome! Also, I'm sorry if this is incorrect. I tried my best with this question but I'm pretty sure the answer is 8! Have a great day sunshine!! :)
Answer: y = 8
Step-by-step explanation:
Burger patties come packed 6 in a package, and burger buns come packed 8 in a package. We want to buy the least number of patties and buns possible, while still making sure that we have exactly one patty for each bun (no leftovers). How many packages of burger patties do we need to buy?
Answer:
6 packs of buns 8 packs of patties
Step-by-step explanation:
6 x 8 = 48
8 x 6 = 48
The ratio of dogs to people at the park is 3 to 4. There are 336 total
dogs and people at the park.
How many people are at the park?
Answer:
you got this u are really smart
Step-by-step explanation:
HELP LAST ONE :”)) PLZ HELP ME I WILL LITERALLY LOVE U
Answer:
y=-2x+6
Step-by-step explanation:
Did on Calculator.
Answer:
its really simple x is increasing by 1 and y is decresing by 2
Step-by-step explanation:
David is running a unique coffee shop. He
charges $25 per coffee. If a customer pays
$67 for 2 coffees, how much change should
be given back by David?
Find the absolute value:
5.34 -4 2/11 0
-6 3/5 -2.12 8.2
Answer:
Change the positive numbers to negative and change the negative numbers to positive.
Step-by-step explanation:
I hope this helps u! :D
Brian and Mark are fishing. They both catch a fish. Brian's fish weighs 17
pounds less than Mark's fish. Mark's fish weighs 22 pounds
PLEASE HURRY.
Answer: 5 pounds
Step-by-step explanation:
We need to find how much Brian's fish weighs. We know that Mark's fish weighs 22 pounds, and Brian's fish weighs 17 pounds less than Mark's fish. To find how much Brian's fish weighs, we can subtract 17 from 22.
22 - 17 = 5.
Therefore, Brian's fish weighs 5 pounds.
Hope this helps, and good luck :D
Answer:
5 pounds
Step-by-step explanation:
22-17 =5
si el dividendo es 800 el cociente es 160 y el residuo es 0 ¿cuál es el divisor?
ayudaaa
Answer:
Él dividendo seria 5
Step-by-step explanation:
Por que si dividimos 800 ÷ 5 = 160 y no nos quedan residuos
ESPERO Y TE AYUDE ;)
which expression is equivalent to z+(z+6)?
Answer:
2(z+3)
Step-by-step explanation:
This is a Doubt. Can someone tell me if it is right or wrong?
Answer:
It's correct
Step-by-step explanation:
;)
8 m (cubic meters) = dm3 (cubic decimeters)
Answer: 8000 dm³
Step-by-step explanation:
1 m³= 1000 dm³
----------------------------------------------------
Given
8 m³= dm³
Solve
8 m³ × 1000 dm³/m³=8000 dm³
Hope this helps!! :)
Please let me know if you have any questions
need help please will give brainliest
Answer:
y=1/5x+7
Step-by-step explanation:
factorise 3x^2+5x-12
Answer:
3x^2+9x-4x-12(3x^2+9x)-(4x+12)3x(x+3)-4(x+3)(x+3)(3x-4) please mark me brainlisthelp will MARK BRAINLIST
Answer:
-21
Step-by-step explanation:
put in -3 where x is
-3^2 9
-9-12 = -21
Answer:
-21
Step-by-step explanation:
We know that [tex]f(x)=-x^2-12[/tex] and we also know that [tex]f(x)=f(-3)[/tex]. Therefore, you will have to substitute x with -3.
Calculations:
[tex]f(x)=-x^2-12[/tex]
[tex]f(-3)=-(-3)^2-12[/tex]
[tex]-9-12=-21[/tex]
PLEASE HELP ASAP ILL GIVE U A LOT OF POINTS AND BRAINLIEST
Answer: a=1.5+1
Step-by-step explanation:
b jvgfcd vbkbhyg
Answer:
15x
Step-by-step explanation:
Which of the following equations have no solutions?
Choose all answers that apply:
A
152 - 45 = 750 + 75
B.
15% - 45 = 15x + 75
c
45x – 45 = -15% + 75
D
-450 – 45 = -75x + 75
Answer: B
Step-by-step explanation:
Equation A:
15x - 45 = 75x + 75
=> -120 = 60x
=> x = -2
Equation B:
15x - 45 = 15x + 75
=> 0 = 15
No Solutions
Equation C:
45x - 45 = -15x + 75
=> 60x = 120
=> x = 2
Equation D:
-45x - 45 = -75x + 75
=> 30x = 120
=> x = 4