List the important features for the graph of a quadratic function.
Answers
Answer:
VertexMinimum PointMaximum PointRootsAxis of SymmetryStep-by-step explanation:
The bottom (or top) of the U is called the vertex, or the turning point. The vertex of a parabola opening upward is also called the minimum point. The vertex of a parabola opening downward is also called the maximum point.
The x-intercepts are called the roots, or the zeros. To find the x-intercepts, set ax^2 + bx + c = 0.
The parabola is symmetric (a mirror image) about a vertical line drawn through its vertex (turning point). This line is called the axis of symmetry.
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The quadratic function can be expressed in the form of vertex form and the parabola is symmetric about the line which is passing through focus.
What is a quadratic equation?The quadratic equation is given as ax² + bx + c = 0. Then the degree of the equation will be 2.
The important features for the graph of a quadratic function will be
The parabola is symmetric about the line which is passing through focus.
The quadratic function can be expressed in the form of vertex form.
Let the point (h, k) be the vertex of the parabola and a be the leading coefficient.
Then the equation of the parabola will be given as,
y = a(x - h)² + k
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Related Questions
Share 32 beads between Joshua and kitty in the ratio 6:10 How much does Joshua gets ? Beads and kitty gets ?
Answers
Answer:one would get 12 one would get 20
Step-by-step explanation:just plug it in to the equation
Someone would get 12 and the other would get 20 beads
Let f(x) = -2x + 7 and g(x) = -6x + 3. Find fg and state its domain.
Answers
Answer:
f(g(x))=12x+1
Step-by-step explanation:
f(g(x)) = -2(-6x+3)+7
f(g(x))= 12x-6+7
f(g(x))=12x+1
Domain: All real numbers
Freddie put an empty bucket underneath a leaking pipe. After 34 hours, Freddie collected 12 cups of water. What is the rate, in cups per hour, at which the water is leaking from the pipe?
Answers
Answer:
0.35 cups/hour
Step-by-step explanation:
To be able to determine the rate at which the water is leaking from the pipe with the information given, you have to divide the number of cups by the number of hours in which they were collected:
12 cups/34 hours= 0.35 cups/hour
According to this, the answer is that the rate at which the water is leaking from the pipe is 0.35 cups/hour.
please help me on this work please !
Answers
Donte simplified the expression below. 4(1+3i) - (8-5i)
4 + 3i - 8 + 5i
-4 + 8i
What mistake did donte make?
Answers
Answer:
Donde didn't multiply 4(1+3i)
Answer: it’s A he did not apply distributive property yo
Step-by-step explanation:
If theta=3pi/4
Sin theta=?
Cos theta=?
Answers
Answer:
For ease of writing, θ [tex]=x[/tex]
[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]
[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]
Step-by-step explanation:
Our angle is [tex]x=\frac{3\pi }{4}[/tex]
To find our answers for [tex]sin(\frac{3\pi}{4} )[/tex] and [tex]cos(\frac{3\pi}{4} )[/tex], we will need to use a unit circle. (I have attached the image of one).
Recall that the [tex]sin[/tex] of an angle is equal to the y-value of the corresponding ordered pair.
And the [tex]cos[/tex] of an angle is equal to the x-value of the corresponding ordered pair.
For the angle [tex]x=\frac{3\pi }{4}[/tex], the ordered pair is [tex](-\frac{1}{\sqrt{2}} }, \frac{1}{\sqrt{2} } )[/tex]
This means that
[tex]sin(x)=\frac{1}{\sqrt{2} }[/tex]
[tex]cos(x)=-\frac{1}{\sqrt{2} }[/tex]
The radius r of a sphere is increasing at a rate of 3 inches per minute. (a) Find the rate of change of the volume when r = 9 inches. in.3/min (b) Find the rate of change of the volume when r = 37 inches. in.3/min
Answers
Answer:
[tex]\frac{dV}{dt}[/tex] = 1017.87 in³/min
[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min
Step-by-step explanation:
given data
radius r of a sphere is increasing at a rate = 3 inches per minute
[tex]\frac{dr}{dt}[/tex] = 3
solution
we know volume of sphere is V = [tex]\frac{4}{3} \pi r^3[/tex]
so [tex]\frac{dV}{dt} = \frac{4}{3} \pi r^2 \frac{dr}{dt}[/tex]
and when r = 9
so rate of change of the volume will be
rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (9)^2 (3)[/tex]
[tex]\frac{dV}{dt}[/tex] = 1017.87 in³/min
and
when r = 37 inches
so rate of change of the volume will be
rate of change of the volume [tex]\frac{dV}{dt} = \frac{4}{3} \pi (37)^2 (3)[/tex]
[tex]\frac{dV}{dt}[/tex] = 17203.35 in³/min
Giving a test to a group of students, the grades and gender are summarized below
A B C Total
Male 7 20 14 41
Female 3 4 19 26
Total 10 24 33 67
If one student is chosen at random,
Find the probability that the student was male OR got an "A".
Answers
Answer:
46/ 67
Step-by-step explanation:
The numbers of students irrespective of grades is;
The sum of the last roll of numbers:
10+24+ 33+ 67 = 134
The number of males irrespective of grades is the sum of the numbers in the male row ;
7 +20+ 14 +41= 82
The numbers of students with grade A is the first column at the last row and is 10;
Hence;
the probability that the student was male OR got an 'A' is
the probability that the student was male plus the probability that he/she got an 'A'.
The probability that it's a male is ;
Number of males/ total number of students
=82/134
The probability that he got an A is;
The number of students that got A/ the total number of students;
10/134
Hence
the probability that the student was male OR got an 'A' is;
82/ 134 + 10/134 = 92/134 = 46/ 67
This table gives a few (x,y) pairs of a line in the coordinate plane. What is the y-intercept of the line?
Answers
Answer:
(0,34)
Step-by-step explanation:
I graphed the coordinates of the table on the graph below to find the y-intercept.
On his way out to meet a friend for lunch, David realized that his financial record was not up to date. He notices that he forgot to record three transactions. The first transaction was on August 2nd in the amount of $12.32, another transaction on that same day in the amount or $52.34, and finally a transaction on August 8th in the amount of $85.35. Determine David's balance carried forward for the 8th of August using the table below and the information provided. A check register. The Balance on August fifth is 1,049 dollars and 16 cents. a. $975.32 b. $899.15 c. $1,049.16 d. $848.84
Answers
Answer:
b
Step-by-step explanation:
add the three numbers together then minus from the main total
Answer:
B. $899.15
Step-by-step explanation:
Twice the difference of a number and 4 is equal to three times the sum of the number and 6. Find the number.
The number is
Answers
Answer:
-26
Step-by-step explanation:
2(x-4)=3(x+6)
2x-8=3x+18
2x-2x -8 = 3x-2x +18
-8 =X+18
-8-18=x+18-18
-26 = x
The value of the unknown number is -26.
Given that, twice the difference of a number and 4 is equal to three times the sum of the number and 6.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Let the unknown number x.
Twice the difference of a number and 4 = 2(x-4)
Three times the sum of the number and 6 = 3(x+6)
So, equation is 2(x-4)=3(x+6)
⇒ 2x-8=3x+18
⇒ 3x-2x=-8-18
⇒ x=-26
Therefore, the value of the unknown number is -26.
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Evie has two sets of blocks of identical size and shape with the colors given. Evie will randomly select on block from each set. What is the probability she will select an orange block and a red block?
set A has 4 orange blocks and 3 yellow blocks.
set B has 5 blue blocks and 2 red blocks.
3/7
2/7
8/49
6/49
Answers
Answer:
[tex]\frac{8}{49}[/tex]
Step-by-step explanation:
Orange: [tex]\frac{4}{7}[/tex]
Red: [tex]\frac{2}{7}[/tex]
[tex]\frac{4}{7} *\frac{2}{7} =\frac{8}{49}[/tex]
Abena travelled 40% of the distance of her trip alone, went another 35 miles with Saralyn,
and then finished the last half of the journey alone. How many miles long was the journey?
Answers
Answer:
350 miles long.
Step-by-step explanation:
First, we analyze the breakdown of the journey
Abena travelled 40% of the distance of her trip alone.She went 35 miles with Saralyn.She finished the last half (50%) of the journey alone.Let the total distance of the journey =x
Therefore:
10% of the total distance of the journey =35 miles
10% of x=35
0.1x=35
Divide both sides by 0.1
x-350 miles
Therefore, the journey was 350 miles long.
Answer:
The journey was 350 miles long
Step-by-step explanation:
The parameters given are;
Distance traveled by Abena alone = 40% and the last half
∴ Distance traveled by Abena alone = 40% + 50% = 90%
Distance Abena traveled with Saralyn = 35 miles = 100% - 90% = 10%
Hence 10% of Abena's journey = 35 miles
The total distance of Abena's journey therefore, is given as follows
10% = 35 miles
Total distance of Abena's journey = 100% of Abena's journey = 10 × 10%
10 × 10% = 10 × 35 miles = 350 miles
The total distance of Abena's journey = 350 miles.
What’s the correct answer for this question?
Answers
Answer:
A.
Step-by-step explanation:
Density = Mass / Volume
D = 3/0.2
D = 15 kg/m³
Answer:
density=mass/volume
d=3kg/0.2m3
=15kgm-3
A box lunch costs b. A bag of chips is $2 extra. Choose the expression to show the cost of 12 lunches with chips and 10 lunches without?
Answers
Answer:
22b+24
Step-by-step explanation:
If a box lunch costs b and a bag of chips is $2 extra then we would have:
box lunch = b dollars
box lunch with bag of chips = b + 2 dollars
Now, we need to find the expression for the cost of 12 lunches with chips and 10 lunches without chips, this would be:
12 lunches with chips = 12 (b + 2)
10 lunches without chips = 10b
Let's sum up and simplify these two expressions:
[tex]12(b+2)+10b\\12b+24+10b\\22b+24[/tex]
Thus, the cost of 12 lunches with chips and 10 lunches without chips is 22b+24
ASAP! GIVING BRAINLIEST! Please read the question THEN answer CORRECTLY! NO guessing. I say no guessing because people usually guess on my questions.
Answers
Answer:
B. 4x² - 20x + 26
Step-by-step explanation:
→Set it up, like so:
(2x - 5)² + 1
4x² - 20x + 25 + 1
→Add like terms (25 and 1):
4x² - 20x + 26
In a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined, and the vehicle speed at impact was recorded for each one. For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph. A histogram revealed that the vehicle speed at impact distribution was approximately normal.
a. Roughly what proportion of vehicle speeds were between 27 and 57 mph?
b. Roughly what proportion of vehicle speeds exceeded 57 mph?
Answers
Answer:
(a) Roughly 68% of vehicle speeds were between 27 and 57 mph.
(b) Roughly 16% of vehicle speeds exceeded 57 mph.
Step-by-step explanation:
We are given that in a study investigating the effect of car speed on accident severity, 5000 reports of fatal automobile accidents were examined.
For these 5000 accidents, the average speed was 42 mph and the standard deviation was 15 mph.
Let X = vehicle speed at impact
SO, X ~ Normal([tex](\mu=42,\sigma^{2} = 15^{2}[/tex])
Here, [tex]\mu[/tex] = population average speed = 42 mph
[tex]\sigma[/tex] = standard deviation = 15 mph
Since, the distribution is approximately normal; so the 68-95-99.7 empirical rule states that;
68% of the data values lies within one standard deviation points.95% of the data values lies within two standard deviation points.99.7% of the data values lies within three standard deviation points.(a) Since, it is stated above that 68% of the data values lies within one standard deviation points, that means;
68% data values will lie between [ [tex]\mu-\sigma , \mu+\sigma[/tex] ] , i.e;
[ [tex]\mu-\sigma , \mu+\sigma[/tex] ] = [42 + 15 , 42 - 15]
= [57 , 27]
So, it means that roughly 68% of vehicle speeds were between 27 and 57 mph.
(b) We have observed above that roughly 68% of vehicle speeds were between 27 and 57 mph which leads us to the conclusion that (100% - 68% = 32%) of the data values will be outside this range.
It is stated that of this 32%, half of the data values will be less than 27 mph and half of the data values will be more than 57 mph.
This means that roughly 16% of vehicle speeds exceeded 57 mph.
What is 9/8 squaredto the power of 2 ?
Answers
1.265
Or
81/64
Answer:
81/64
Step-by-step explanation:
(9/8)²=9²/8²=81/64
Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than negative 1.15−1.15 and draw a sketch of the region.
Answers
Answer:
Step-by-step explanation:
Let x be the random variable representing the test scores from the bone density test. Since it is normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 0
σ = 1
the probability that a given score is less than negative 1.15 is expressed as
P(x < - 1.15)
z = (- 1.15 - 0)/1 = - 1.15
Looking at the normal distribution table, the probability corresponding to the z score is 0.13
P(x < - 1.15) = 0.13
The sketch of the region is shown in the attached photo
Fiad the sample variance and standard deviation.
21, 10, 3, 7, 11
Answers
Answer:
SD = 5.987, Var(X) = 35.85
Step-by-step explanation:
Apply the standard deviation formula, remembering that n represents the sample size. Then, just take the square of the standard deviation to obtain the variance.
Hope this helps!
Please answer this correctly
Answers
Answer:
4 pizza recipes
Step-by-step explanation:
It shows 4 Xs after the [tex]\frac{3}{4}[/tex] mark. So there are 4 recipes that use MORE than [tex]\frac{3}{4}[/tex] cups of cheese.
Answer:
4 cups of cheese
Step-by-step explanation:
More than 3/4 are (3+1) = 4 cups of cheese
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solve 5(x+4)<75 sdsdsd
Answers
Answer:
x < 11
Step-by-step explanation:
[tex]5(x+4)<75 \\ open \: the \: bracket \: using \: 5 \\ 5x + 20 < 75 \\ subtract \: - 20 \: from \: both \: sides \: [/tex]
[tex]5x + 20 - 20 < 75 - 20 \\ 5x < 55 \\ divide \: both \: sides \: of \: the \: equation \: \\ by \: 5[/tex]
[tex] \frac{5x}{5} < \frac{55}{5} \\ x < 11[/tex]
The required solution of inequality is,
⇒ x < 11
We have to simplify the expression,
⇒ 5 (x + 4) < 75
We can simplify it by definition of inequality as,
⇒ 5 (x + 4) < 75
⇒ 5x + 20 < 75
Subtract 20 both side,
⇒ 5x + 20 - 20 < 75 - 20
⇒ 5x < 55
⇒ 5x - 55 < 0
⇒ 5 (x - 11) < 0
⇒ x - 11 < 0
⇒ x < 11
Therefore, The required solution of inequality is,
⇒ x < 11
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what equation results from completing the square and then factoring? x^2+24x=33
a.) (x+24)^2=57
b.) (x+12)^2=57
c.) (x+12)^2=177
d.) (x+24)^=177
Answers
The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.
The given equation is x²+24x=33.
We need to factorise the equation using completing the square method.
What is completing the square method?Completing the square means writing a quadratic in the form of a squared bracket and adding a constant if necessary.
Now, x²+24x-33=0
Add and subtract (b/2)²=144 to the equation.
x²+24x-33+144-144=0
⇒x²+24x+144-33-144=0
⇒(x+12)²-177=0
⇒(x+12)²=177
The factorisation of the given equation using completing square method is (x+12)²=177. Therefore, option D is correct.
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An extremely simple (and surely unreliable) weather prediction model would be one where days are of two types: sunny or rainy. A sunny day is 90% likely to be followed by another sunny day, and a rainy day is 50% likely to be followed by another rainy day. Model this as a Markov chain. If Sunday is sunny, what is the probability that Tuesday (two days later) is also sunny
Answers
Answer:
The probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.
Step-by-step explanation:
Let us denote the events as follows:
Event 1: a sunny day
Event 2: a rainy day
From the provided data we know that the transition probability matrix is:
[tex]\left\begin{array}{ccc}1&\ \ \ \ 2\end{array}\right[/tex]
[tex]\text{P}=\left\begin{array}{c}1&2\end{array}\right[/tex] [tex]\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right][/tex]
In this case we need to compute that if Sunday is sunny, what is the probability that Tuesday is also sunny.
This implies that we need to compute the value of P₁₁².
Compute the value of P² as follows:
[tex]P^{2}=P\cdot P[/tex]
[tex]=\left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\cdot \left[\begin{array}{cc}0.90&0.10\\0.50&0.50\end{array}\right]\\\\=\left[\begin{array}{cc}0.86&0.14\\0.70&0.30\end{array}\right][/tex]
The value of P₁₁² is 0.86.
Thus, the probability that if Sunday is sunny, then Tuesday is also sunny is 0.86.
Please help me with this question, I need it to pass the class!!
Answers
Answer:
cos(20°)
Step-by-step explanation:
The "cofunction" is the function having the same value for the complement of the angle that this function has for the angle.
The cofunction of sine is cosine. The complement of 70° is 90° -70° = 20°.
sin(70°) = cos(20°)
Solve Ixl >-9
No solution
All reals
(X|X<-9 or X>9)
Answers
Answer:
all reals
Step-by-step explanation:
all reals as |x| >= 0 for every x real
so |x| > -9 is always true
What’s the correct answer for this?
Answers
Answer:
D.
Step-by-step explanation:
Since opposite angles of a quadrilateral inscribes in a circle add up to 180°
So,
<P + <N = 180°
2x+2x-12 = 180°
4x = 180+12
4x = 192
Dividing both sides by 4
x = 48
Now
<P = 2(48)
<P = 96
Now
<N = 2(48)-12
<N = 96-12
<N = 84
A hotel rents 220 rooms at a rate of $ 40 per day. For each $ 1 increase in the rate, two fewer rooms are rented. Find the room rate that maximizes daily revenue. The rate that maximizes revenue is $ .
Answers
Answer:
The rooms should be rented at $75 per day for a maximum income of $11250 per day.
Step-by-step explanation:
If the daily rental is increased by $ x
then
Rental: R (x )=( 40 + x ) dollars per room-day
Number of rooms rented: N ( x ) = ( 220 − 2 x ) and
Income: I ( x ) = ( 40 + x ) ( 220 − 2 x ) =8800+140x-2x² dollars/day
The maximum will be achieved when the derivative of I ( x ) is zero.
[tex]\frac{dI(x)}{dx} =140-4x=0[/tex]
x=35
so, ($40+$35)=75$per day
I ( x35) =8800+140(35)-2(35)²= 11250
Which transformations could be performed to show that
AABC is similar to AA"B"C"?
10
8
B
4
VX
2
A
-10 -3 -6 -4 -21 14
B"
4
8 10
X
O a reflection over the x-axis, then a dilation by a scale
factor of 3
O a reflection over the x-axis, then a dilation by a scale
factor of
O a 180° rotation about the origin, then a dilation by a
scale factor of 3
O a 180° rotation about the origin, then a dilation by a
scale factor of
6
8
-10
Save and Exit
Next
Submit
Mark this and return
Answers
Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
What is mean by Transformation?Transformation is the movement of a point from its initial location to a new location. Types of transformation are rotation, translation, reflection and dilation.
Given that;
Triangle ABC is similar to A"B"C".
Now, If a point A(x, y) is rotated clockwise by 180 degrees, the new point is at A'(y, -x)
Hence, Triangle ABC was rotated 180° about the origin, then a by a scale factor of 1/3 was done to form triangle A'B'C'.
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Suppose that a company's sales were $1,000,000 6 years ago and are $9,000,000 at the end of the 6 years. Find the geometric mean growth rate of sales. (Round your answer to 4 decimal places.)
Answers
Answer:
The geometric mean growth rate of sales is 1.4422.
Step-by-step explanation:
We have two sales values, one from 6 years ago and the other from now.
We have to calculate the geometric growth rate of sales.
We have:
[tex]y(-6)=1,000,000\\\\y(0)=9,000,000[/tex]
We can write the relation between these two values as:
[tex]y(0)=y(-6)k^{0-(-6)}\\\\9,000,000=1,000,000k^6\\\\k^6=9\\\\k=9^{1/6}= 1.4422[/tex]
The geometric mean growth rate of sales is 1.4422.