Find the vertex of a quadratic function written in standard form.
f(x) = 3x2 + 18x + 32
PLS HELP!!
Answer:
our vertex for f(x) = 3x² + 18x + 32 = (-3, 5 )
Step-by-step explanation:
let me write the standard form of a quadratic equation
[tex]a {x}^{2} + bx + c[/tex]
Now let me rewrite the original equation
[tex]3 {x}^{2} + 18x + 32[/tex]
Now we use this simple formula to find the vertex (h, k)
[tex]x = h = - \frac{b}{2a} \\ = - \frac{18}{2(3)} = - \frac{18}{6} = - 3 \\ h = - 3[/tex]
substitute -3 for x back into our original equation to solve for y our k value of our vertex
[tex]y = 3 ({ - 3})^{2} + 18( - 3) + 32 \\ = 3(9) - 54 + 32 \\ = 27 + 32 - 54 \\ = 59 - 54 \\ k = 5[/tex]
our vertex for f(x) = 3x² + 18x + 32 = (-3, 5 )
Scores on the ACT exam have a N(μ = 18,σ = 6) distribution, while scores on the SAT
exam have a N(μ = 500,σ = 100) distribution. Suppose Xiaoyu got a 27 on the ACT
exam, while Emily got a 720 on the SAT exam. Who has the higher relative score? Why?
Answer:
Emily has a higher relative score since her z-score is higher. This would mean she scored further above the mean than Xiaoyu.
Step-by-step explanation:
Find the z-scores by subtracting the score they got by the mean and then dividing by the standard deivation of their respective exams.
Xiaoyu:
z = [tex]\frac{27 - 18}{6}[/tex] = 1.5
Emily:
z = [tex]\frac{720 - 500}{100}[/tex] = 2.2
______
Emily has a higher relative score since her z-score is higher. This would mean she scored further above the mean than Xiaoyu.
(4) The volume of a cuboid shaped tank is 3600 cm?. Its height, breadth and length are three consecutive perfect squares. Find its length, breadth and height. (Write 3600 as a product of prime factors).
Answer:
15×15×16=3600
15×15=225
225×16=3600
ASAP NEED HELP PLEASE 70 points ?!!!!
Answer:
f(1) = 5Step-by-step explanation:
Use the given formula and substitute the value of x:
f(x) = 4 + xf(1) = 4 + 1 = 5f(1)
4+15Done
The domine of definition of the function
[tex]f(x) = \frac{1}{ \sqrt{ |\cos(x)| + \cos(x) }} \: is \\ [/tex]
[tex]\large\underline{\sf{Solution-}}[/tex]
Given function is
[tex]\rm \longmapsto\:f(x) = \dfrac{1}{ \sqrt{ |cosx| + cosx} } [/tex]
Now,
[tex]\rm \longmapsto\:f(x) \: is \: defined \: if \: |cosx| + cosx > 0[/tex]
We know,
[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |x| = \begin{cases} &\sf{ - x \: \: when \: x < 0} \\ \\ &\sf{ \: \: x \: \: when \: x \geqslant 0} \end{cases}\end{gathered}\end{gathered}[/tex]
So,
[tex]\begin{gathered}\begin{gathered}\bf\: \rm \longmapsto\: |cosx| + cosx = \begin{cases} &\sf{ \: \: 0 \: \: when \: cosx \leqslant 0} \\ \\ &\sf{ \: \: 2 \: cosx \: \: when \: cosx > 0} \end{cases}\end{gathered}\end{gathered}[/tex]
So,
[tex]\rm\implies \:f(x) \: is \: defined \: when \: cosx > 0[/tex]
So, from graph we concluded that cosx > 0 in the following intervals.
[tex]\begin{gathered}\boxed{\begin{array}{c|c} \bf cosx & \bf \: x \: \in \: \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf + ve & \sf \bigg( - \dfrac{\pi}{2} ,\dfrac{\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{3\pi}{2} ,\dfrac{5\pi}{2} \bigg) \\ \\ \sf + ve & \sf \bigg(\dfrac{7\pi}{2} ,\dfrac{9\pi}{2} \bigg) \end{array}} \\ \end{gathered}[/tex]
So, if we generalized this we get
[tex]\rm\implies \:cosx > 0 \: when \: x \: \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z[/tex]
Hence,
Domain of the function is
[tex]\red{\rm\implies \boxed{\tt{ \: x \in \: \bigg(\dfrac{(4n - 1)\pi}{2} ,\dfrac{(4n + 1)\pi}{2} \bigg) \: \forall \: n \in \: Z}}}[/tex]
[tex]\textsf{More to know :-} \\[/tex]
[tex]\begin{gathered}\begin{gathered}\boxed{\begin{array}{c|c} \bf T-eq & \bf Solution \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf sinx = 0 & \sf x = n\pi \: \forall \: n \in \: Z\\ \\ \sf cosx = 0 & \sf x = (2n + 1)\dfrac{\pi}{2}\: \forall \: n \in \: Z\\ \\ \sf tanx = 0 & \sf x = n\pi\: \forall \: n \in \: Z\\ \\ \sf sinx = siny & \sf x = n\pi + {( - 1)}^{n}y \: \forall \: n \in \: Z\\ \\ \sf cosx = cosy & \sf x = 2n\pi \pm \: y\: \forall \: n \in \: Z\\ \\ \sf tanx = tany & \sf x = n\pi + y \: \forall \: n \in \: Z\end{array}} \\ \end{gathered}\end{gathered}[/tex]
ANSWER THIS ASAP PLEASE !
Simple the answer is: n=14
I need an answer for this please.
Answer:
N0O0O0O0O0O0O0O0O0O0O
Step-by-step explanation:
PLEASE HELP WILL MARK BRAINLIEST NO RANDOM ANSWERS
Answer:
2 is the correct answer
Round off to the nearest hundredth: 3.6789
if f(x)=3x-5 and g(x)=x², find (f o g)(3)
Answer:
(f ∘ g) (3) = 22
Step-by-step explanation:
f( x + 3x - 5; g (x) = x² ∴ g ( 3 ) = 3² = 9
( f ∘ g ) ( 3 ) = f(g(3)) = f ( 9 ) = 3 · 9 - 5 = 27 - 5 = 22 [Ans]
0.810x0.00084/0.000400x0.0270leave the answer in a standard form
Answer:
4.5927 x 10^-2 ?
Step-by-step explanation:
Need a bit of help here
Answer:
Answer 1 is 4:2 or also write as 2:1.
You have 112 feet of fencing to enclose a rectangular region. What is the maximum area?
what part of 63 is 18
Answer:
If you mean percent, its 350%
Answer:
1134
Step-by-step explanation:
1134/63=18
what number is represented by each point on the number line
Answer:
Every point of a number line is assumed to correspond to a real number, and every real number to a point. The integers are often shown as specially-marked points evenly spaced on the line.
Which angle is not necessarily congruent to 1?
Answer:
12
Step-by-step explanation:
the answer is just 12.
Ms. Nguyen needs to separate $385 into three parts to pay some debts. The second part must be five times as large as the first part. The third part must be $35 more than the first part. How much money must be in each part?
Answer:
1st: $50 2nd: $250 3rd: $85
Can someone help me.
Answer:
see explanation
Step-by-step explanation:
substitute the values of x in the table into g(x)
Using the rule of exponents
[tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex]
g(- 2) = [tex]4^{-2}[/tex] = [tex]\frac{1}{4^{2} }[/tex] = [tex]\frac{1}{16}[/tex]
g(- 1) = [tex]4^{-1}[/tex] = [tex]\frac{1}{4}[/tex]
g(0) = [tex]4^{0}[/tex] = 1
g(1) = [tex]4^{1}[/tex] = 4
g(2) = 4² = 16
can someone help me please ?
Answer:
Any number in the form of p/q where p and q are integers and q is not equal to 0 is a rational number.
So, 323.2685109 is IRRATIONAL number.
Please help i reward brainliest
plz no silly answers
Answer:
64, -64, -64
-27, 27, 27
Step-by-step explanation:
If x = 4,
x³ = 4³ = 64
-x³ = -4³ = -64
(-x)³ = (-4)³ = -64
If x = -3,
x³ = -3³ = -27
-x³ = -(-3)³ = 27
(-x)³ = (-(-3))³ = 27
Please help me, write the step by step explanation plz?
Answer:
i think the answer is 171,500 i don't know i am trying.
Step-by-step explanation:
first you multiply 35 times 3 you will get 85,750 then you multiply 10 times 2 you will 20 and multiply both of them and you will get 171,500.
Solve for x
A 130
B 120
C 23
D 70
Answer:
B)120º
Step-by-step explanation:
70+50=x
120=x
Sum of two interior angles=exterior angle
[tex]\\ \sf\longmapsto 50+70=x[/tex]
[tex]\\ \sf\longmapsto x=120[/tex]
Option B
On average, Carson spends about 26% of his allowance each month on candy and soft drinks. When creating a circle graph of what Carson does with his money, which of the following fractions would be the best to represent how much he spends on food?
Estimate the circumference of a circle that has a diameter of 6 ft.
Answer: 1/4
Given : On average, Carson spends about 26% of his allowance each month on candy and soft drinks.
To Find : When creating a circle graph of what Carson does with his money, which of the following fractions would be the best to represent how much he spends on food?
If these are your Choices:
A) 1/4
B) 1/3
C) 3/4
D) 1/2
Solution:
To Convert fraction into % multiply by 100
(1/4) * 100 = 25 %
(1/3) * 100 = 33.33 %
(3/4) * 100 = 75 %
(1/2) * 100 = 50 %
Therefore 1/4 fraction best represent how much he spends on food
A dance studio has a raffle and sells 125 tickets. Kenton bought 33 of the tickets. What percent of the tickets
does Kenton have?
What’s the slope of (-7,2) and (1,4)
Answer:
1/4
Step-by-step explanation:
Slope = (change in the y-values)/(change in the x-values)
Slope = (4 - 2)/(1 - (-7) )
Slope = (4 - 2)/(1 + 7)
Slope = 2/8
Slope = 1/4
Plzzzzzzzz help with your own handwritten picture
120−96×[5 ÷ {23 − 3 × (12 − 22 − 16)}]
Find the area of the credit card. 2 1/4 in and 3 1/3 in
Answer:
Step-by-step explanation:
A= W*L
A= 31/3*21/4
A=10.3*5.25
A=54.075cm^2
Answer:
7 1/2in^2
Step-by-step explanation:
LxW=A
2 1/4 x 3 1/3 = A
A = 7 1/2
On a blueprint, the scale says that 2 cm represents 3 m. What is the actual length of a wall if it's measurement on the blueprint is 7 cm?
Answer:
7!!
Step-by-step explanation:
Kelly runs a distance of 100 metres in a time of 10.52 seconds.
The distance of 100 metres was measured to the nearest metre.
The time of 10.52 seconds was measured to the nearest hundredth of a second.
(a) Write down the upper bound for the distance of 100 metres.
The upper bound means the highest number that you can round up to the nearest unit, in this case meters. So the upper bound for the distance of 100 meters is 100.4 meters.
Answer:
bye
Step-by-step explanation:
Mya says the value of 6 in 0.006 is 1-10 of the value of 6 in 0.6. Is the correct?
Answer:
no, it is incorrect it is 1-100 the value
Step-by-step explanation:
0.006×10= 0.06
0.006×100=0.6