#9Change from standard form to vertex formy= -x²+4x-1
Answers
So the vector form of the equation is: y = -1(x - 2)² + 3.
To convert from standard form to vertex form, we complete the square by following these steps:
Factor out the coefficient of the x-squared term:
y = -x² + 4x - 1
= -1(x² - 4x) - 1
To complete the square inside the parentheses, add and subtract the square of half of the coefficient of the x-term (-4/2)^2 = 4:
y = -1(x² - 4x + 4 - 4) - 1
Simplify the expression inside the parentheses by factoring a perfect square:
y = -1((x - 2)² - 4) - 1
Distribute the -1 and simplify:
y = -1(x - 2)² + 3
Therefore, the vertex of the parabola is at (2, 3), and the negative coefficient of the x-squared term means that the parabola opens downwards.
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Related Questions
I don’t understand it I tried it
Answers
Answer: Slope = -3/2
Step-by-step explanation:
slope = rise / run or
change in y / change in x
y2 - y1 / x2 - x1
we can look at the points (0,-4) <-1's and (4,-10) <-2's
rise is -6 as -10- -4 = -6
run is 4 as 4-0 = 4
-6 / 4 simplify
-3/2
find the height of the tree to the nearest foot.
Answers
Answer:
height = 50 ft (nearest foot)
Step-by-step explanation:
This creates a right triangle, where:
horizontal leg = 72 ftvertical leg = height of treeangle of elevation (between horizontal leg and hypotenuse) = 34.6°Use the tan trig ratio to find the height.
\(\mathsf{\tan\theta=\dfrac{opposite \ side}{adjacent\ side}}\)
\(\implies \mathsf{\tan(34.6)=\dfrac{height}{72}}\)
\(\implies \mathsf{height=72\tan(34.6)}\)
\(\implies \mathsf{height=50 \ ft \ (nearest\ foot)}\)
\(\\ \rm\Rrightarrow tan\theta=\dfrac{Perpendicular}{Base}\)
\(\\ \rm\Rrightarrow tan34.6=\dfrac{x}{72}\)
\(\\ \rm\Rrightarrow x=72tan34.6\)
\(\\ \rm\Rrightarrow x=72(0.689)\)
\(\\ \rm\Rrightarrow x=49.61ft\)
height approximately 50ft
4dy + 12 = 7dy, solve for y. Show how you solved it
Answers
Answer:
y = -12/(4d - 7d)
Step-by-step explanation:
Step 1: Write equation
4dy + 12 = 7dy
Step 2: Solve for y
Subtract 7dy on both sides: 4dy + 12 - 7dy = 0
Subtract 12 on both sides: 4dy - 7dy = -12
Factor out y: y(4d - 7d) = -12
Divide both sides by 4d - 7d: y = -12/(4d - 7d)
Hello! :)
First thing you do is add -7dy to both sides
4dy + 12 + -7dy = 7dy + -7dy
-3dy + 12 = 0
Next you will have to add -12 to both sides
-3dy + 12 + -12 = 0 + -12
-3dy = -12
Last thing you have to do is divide both sides by -3d
-3dy/-3d = -12/-3d
y = 4/d (ANSWER)
Verify the following Hoare triples:
3.1 {x = y} if (x = 0) then x := y + 1 else z := y + 1 {(x = y + 1) ⋁ (z = x + 1)}
3.2 {{y > 4} if (z > 1) then y:= y + z else y:= y − 1 endif {y > 3}ang
3.3 {3 ≤ |x| ≤ 4} if x < 0 then y := -x else y := x endif {2 ≤ y ≤ 4}
Hint: First rewrite each if-then-else statement as its guarded-command equivalent before calculating a new precondition
Answers
Hoare triples can be defined as a way of proving the correctness of programs through a method that uses assertions. Here, the following Hoare triples are verified.
3.1 {x = y} if (x
= 0) then x :
= y + 1 else z :
= y + 1 {(x
= y + 1) ⋁ (z
= x + 1)}Hoare triple can be written as follows: Precondition {x = y} is given where x and y are variables.If statement is used with the condition x
=0. Therefore, the following Hoare triple is obtained:{x
=y and x
=0}->{x
=y+1}.The first condition x
=y is maintained if the if-statement is false. The second condition x
=y+1 will hold if the if-statement is true. The or operator represents this with (x
=y+1)⋁(z
=x+1). 3.2 {{y > 4} if (z > 1) then y:
= y + z else y:
= y − 1 endif {y > 3}} Hoare triple can be written as follows: Precondition {y>4} is given where y is a variable.If statement is used with the condition z>1. Therefore, the following Hoare triple is obtained:{y>4 and z>1}->{y>3}.The first condition y>4 is maintained if the if-statement is false.
The second condition y>3 will hold if the if-statement is true. 3.3 {3 ≤ |x| ≤ 4} if x < 0 then y := -x else y := x endif {2 ≤ y ≤ 4}Hoare triple can be written as follows: Precondition {3≤|x|≤4} is given where x and y are variables. If statement is used with the condition x<0. Therefore, the following Hoare triple is obtained:{3≤|x|≤4 and x<0}->{2≤y≤4}.If the condition is false, y=x and the precondition is satisfied because |x| is either 3 or 4. If the condition is true, y=-x and the precondition is still satisfied. The resulting range of y is [2, 4] because the absolute value of x is between 3 and 4.
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how many arrangements of 4 letters from the word combine
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Suppose that the number of bacteria in a certain population increases according to a continuous exponential growth model. The sample of 2100 bacteria selected from this population reach the size of 2249 bacteria in two and a half hours. Find the hourly growth rate parameter.This is a continuous exponential growth model.Write your answer as a percentage. Do not round any intermediate computations, and round your percentage to the nearest hundredth.
Answers
In this problem, we have a continuous exponential growth model
so
the equation is of the form
\(y=a(e)^{kt}\)where
a is the initial value ------> a=2,100
y is the number of bacteria
x ----> number of hours
so
\(y=2,100(e)^{kt}\)For x=2.5 hours, y=2,249 bacteria
substitute
\(2,249=2,100(e)^{(2.5k)}\)solve for k
apply ln both sides
\(\ln (\frac{2,249}{2,100})=2.5k\cdot\ln (e)\)k=0.0274
convert to percentage
k=2.74%Can somebody plz help answer these questions (only if u know them)
Thanks so much!! :D
WILL MARK BRAINLIEST WHOEVER ANSWERS FIRST:DD
Answers
Answer:
22=90 23=15 24=60 25=0.75 26=70 37=$0.58
Step-by-step explanation:
22. So, we can divide 360 kmh by 4 hours
so 360/4 =90
So 90 kmh in 1 hr
23
So, we can divide 3 packages by $15
so 15÷3 = $5
So $5 per package
24 So, we can divide 720 m by 12s
So, 720/12= 60
60 m in 1 s
25
So, we can divide $4.50 by 6
So, we get $0.75
26
So, we can divide 210 words by 3 min
So, 210÷3=70
70 words per minute
27
So, we can divide 23.20 by 40l
So, 23.20÷40 = 0.58
$0.58
PLS HELP ME
XXXXXXXXX
Answers
Answer:
1
Step-by-step explanation:
To find the median number of musical instruments played, we first need to arrange the data in ascending order:
0, 0, 0, 0, 1, 1, 2, 2, 3, 3, 3
Next, we count the total number of responses, which is 15. Since 15 is an odd number, the median will be the average of the middle value.
The middle value is 1
Hence, the median number of musical instruments played is 1.
Select ALL polynomials that are in standard form. Please help
Answers
Answer:
i attached my answer. hope it's helpful
Rewrite the expression using positive exponents
1. 1/9x^-2y^-1
2. a^-5*a^-8
Answers
Answer:
Property : a^-b = 1/a^b
Using this property, we can rewrite the expression using positive exponents :
\(1. \frac{1}{9}*x^{-2} *y^{-1} =\frac{1}{9}\frac{1}{x^{2} } \frac{1}{y} =\frac{1}{9x^{2} y} \\2. a^{-5} a^{-8} =\frac{1}{a^{5}a^{8} } =\frac{1}{a^{13} }\)
HELP ME PLEASE I NEED THE ANSWERS ASAP. geometry
Answers
Answer:
\(6\pi\), 6pi
Step-by-step explanation:
The area of the full circle would be \(\pi *4^{2}\), which is \(16\pi\)
A full circle is 360 degrees. Since we are only taking a part of that, 135, we would put it in a fraction. \(\frac{135}{360}\)
Last, multiply 16pi and 135/360 since we are taking a part of 16pi.
\(16\pi *\frac{135}{360}\)
\(\frac{2160\pi}{360}\)
\(6\pi\)
Find the mean of thefollowing probability distribution. x 0 1 2 3 4 P(x) 0.19 0.37 0.16 0.26 0.02
Answers
The mean of this probability distribution is 1.55.
To find the mean of a probability distribution, we need to multiply each possible value by its corresponding probability, and then add up these products. So, the mean is:
mean = (0)(0.19) + (1)(0.37) + (2)(0.16) + (3)(0.26) + (4)(0.02)
= 0 + 0.37 + 0.32 + 0.78 + 0.08
= 1.55
Therefore, the mean of this probability distribution is 1.55.
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A bottle of iron supplement has 45g of iron in 330ml of solution. How many grams of iron are in
100ml of solution?
Answers
Answer:
45 * 100 / 330 = amount in 100 ml of solution
13.6363636364 grams
Step-by-step explanation:
An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succe
and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment.
Compute the probability of each of the following events.
Event A: The sum is greater than 6.
Event B: The sum is divisible by 2 or 6 (or both).
Write your answers as fractions.
(a) P (A) =
(b) P (B) =
Answers
Answer:
P(A) = 21/36 = 7/12
P(B) = 21/36 = 7/12
Step-by-step explanation:
(a) To find the probability of Event A (the sum is greater than 6), we can list all the possible outcomes of rolling two dice and adding their face values together. There are 36 possible outcomes, as each of the six sides on the first die can be combined with each of the six sides on the second die. We can then count the number of outcomes that have a sum greater than 6:
2: impossible, as the minimum sum is 1+1=2
3: 2 outcomes (1+2, 2+1)
4: 3 outcomes (1+3, 2+2, 3+1)
5: 4 outcomes (1+4, 2+3, 3+2, 4+1)
6: 5 outcomes (1+5, 2+4, 3+3, 4+2, 5+1)
7: 6 outcomes (1+6, 2+5, 3+4, 4+3, 5+2, 6+1)
8: 5 outcomes (2+6, 3+5, 4+4, 5+3, 6+2)
9: 4 outcomes (3+6, 4+5, 5+4, 6+3)
10: 3 outcomes (4+6, 5+5, 6+4)
11: 2 outcomes (5+6, 6+5)
12: 1 outcome (6+6)
Thus, there are 6+5+4+3+2+1 = 21 outcomes with a sum greater than 6. Therefore, the probability of Event A is:
P(A) = 21/36 = 7/12
(b) To find the probability of Event B (the sum is divisible by 2 or 6), we can again list all the possible outcomes and count the number of outcomes that meet the criteria:
Divisible by 2: 18 outcomes (1+1, 1+3, 1+5, 2+2, 2+4, 2+6, 3+1, 3+3, 3+5, 4+2, 4+4, 4+6, 5+1, 5+3, 5+5, 6+2, 6+4, 6+6)
Divisible by 6: 4 outcomes (1+5, 2+4, 4+2, 5+1)
Note that the outcomes that are divisible by 6 are also divisible by 2, so we need to count them only once. Thus, there are 18+4-1=21 outcomes that are divisible by 2 or 6. Therefore, the probability of Event B is:
P(B) = 21/36 = 7/12
1. Assume you are on an island inhabited only by knights and knaves, where knights always tell the truth and knaves always lie. You encounter two people, A and B. Determine, if possible, what A and B are if they address you in the ways described. a. A says "The two of us are both knights" and B says "A is a knave." b. A says "At least one of us is a knave" and B says nothing.
Answers
a. If A says "The two of us are both knights" and B says "A is a knave," then we know that one of them must be lying, and thus that one of them is a knave. However, we cannot determine from this information alone which of them is the knave and which is the knight.
b. If A says "At least one of us is a knave" and B says nothing, then we know that one of them is a knave, but we cannot determine from this information alone which of them is the knave and which is the knight.
POSSIBILITY SCENARIOIn the first scenario, person A claims that both he and person B are knights, which is a true statement if A is a knight. However, person B says that A is a knave, which means that A is a liar. These statements contradict each other, so we know that one of them is not telling the truth and is therefore a knave. But we cannot determine which one of them is the knave, because we don't have enough information.
In the second scenario, person A says that at least one of them is a knave, and person B remains silent. This means that A could be telling the truth, or could be lying. If A is a knight, then he is telling the truth and at least one of them, B, is a knave. But if A is a knave, then he could be lying and both of them could be knights. So we don't have enough information to know who is a knave and who is a knight.
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solve
please help me.
Answers
Answer:
x ≥ 3
Step-by-step explanation:
Jim went to the playground. He played on the swings for 45 minutes and went on the slide for 55 minutes. It was 4:35 P.M. when Jim left the playground. What time was it when Jim arrived at the playground?
Answers
Answer:
2:55 P.M.
Step-by-step explanation:
First, add the amount of time Jim played outside; 45+55=100
100 minutes is equal to 1 hour 40 minutes.
If he left the playground at 4:35 P.M., then you have to subtract in order to find out when he arrived there.
Subtract 1 hour 40 minutes from 4:35 P.M. to then get 2:55 P.M.
To confirm your answer, you can add back the 1 hour and 40 minutes to 2:55 P.M. and you'll get 4:35 P.M.; back with what you started with.
Hope this helped !!!
Which of the following statements are true?(Choose all correct answers)Methods cannot be written with parameters.Parameter values can never be used within the method code block.Methods can be written with any number of parameters.Methods can never be written with more than four parameters.Parameter values can be used within the method code block
Answers
The true statement is, Parameter values can be used within the method code block. (option e).
In computer programming, methods are used to group a set of instructions together that can be executed repeatedly. Parameters are used to pass values to a method so that the method can perform specific actions based on the values passed. Let's discuss the given statements one by one to determine which ones are true.
Parameter values can be used within the method code block.
This statement is true. Parameter values can be used within the method code block to perform specific actions. The parameter values can be manipulated or combined with other values to produce the desired result.
In summary, methods can be written with any number of parameters, and parameter values can be used within the method code block to perform specific actions. The number of parameters needed will depend on the specific task the method is designed to perform.
Hence the option (e) is correct.
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let us suppose that sixteen adult polar bears are weighed in an attempt to estimate the average weight of all adult polar bears. the standard deviation of the population of weights is not known, so a t-interval will be reported. what will be the degrees of freedom for the t-procedure?
Answers
Answer:
your mom + your mom = big mama there you go your welcome
Step-by-step explanation:
your mom + your mom = big mama there you go your welcome
The table shows the time it took a group of students to complete a puzzle.
Time (t) in minutes
Frequency
5
2
10
9
15
20
WOO
25
a) Work out an estimate for the mean time it took the students.
Round your answer to 2 significant figures.
b) What fraction of the students finished in less than 20 minutes?
Answers
Answer:
a) The mean time it took the students, t ≈ 17.08 minutes
b) The fraction of the students that finished under 20 minutes is 2/3 of the students
Step-by-step explanation:
a) The mean of the frequency of grouped data is given as follows;
The given data arranged in tabular form is presented as follows;
\(\begin{array}{cccc}Time \, (t) \, in \, minutes & Midpoint, m & Frequency, f & Product \ m \cdot f \\5\leq t < 10 & 7.5 & 2 & 15 \\10\leq t < 15 & 12.5 & 9 & 112.5\\15\leq t < 20 & 17.5 & 5 & 87.5 \\20\leq t < 25 & 22.5 & 5 & 112.5 \\25 \leq t < 30 & 27.5 & 3 & 82.5 \\Sum & 87.5 & N = 24 & \Sigma (m\cdot f) = 410 \end{array}\)
Therefore, the mean time it took the students = ∑(f·m)/N = 410/24 = \(17\frac{1}{12}\)
The mean time it took the students, t ≈ 17.08 minutes
b) The number of the students that finished under 20 minutes = 2 + 9 + 5 = 16 students
The fraction of the students that finished under 20 minutes = 16/24 of the = 2/3 of the students.
A rectangle rug has an area of 500 square inches. The width of the rug is 20 inches. How many inches long is the rug?
Answers
Answer:
Step-by-step explanation:
Answer: 25 inches
Step-by-step explanation:
The equation for area of a rectangle is Length x Width, since we have the width which is 20 in., we can multiply it by a variable and set it equal to 500.
20(b)=500
divide both sides by 20
b=25
Multiply: (4x^2+4x+1)by(2x^2+x-2)
no spam step by step explanation
Answers
Answer:
the answer is 34
Step-by-step explanation:
first we put the equation together (4x^2+4x+1)by(2x^2+x-2)
so we multiply the formula together so we (4x^2+4x+1) (2x^2+-2) and that's how you get 34
Help me with this pleaseeee
Answers
Answer:
-5/9
Step-by-step explanation:
-11/72 + (-5/8) + 2/9
find the lcm of 72, 8 and 9, which is: 72
-11/72 + (-45/72) + 16/72 = -5/9
1. Find the magnitude and phase of the following complex numbers -2 +3i (a) 5+81 (b)-5-81 4+2i 2. A system with the transfer function is subject to a sinusoidal input U(s) 7s9 u(t) 10sin(1.5t). Find the response y() at steady state. x) 25 F(s) s100 3. A system with transfer function is subject to a sinusoidal input with amplitude of one, that is, f)-1sin W. Find the amplitude of the response x (a) the input frequency is very (b) the input frequency is very large at steady state when 10 4. A system with transfer function Fs) 40s +14s +I is subject to a sinusoidal input f)-10sin(0.2). Find the response x) at steady state 5. A certain system has a frequency response function 400-+io Plot (a) the magnitude M of this function versus frequency W, on linear axes (b) the magnitude M versus frequency, with both Mand W on logarithmic axes. (c) the log-magnitude m(in decibels) versus frequency, with W on a log axis. (d) the phase versus frequency, on linear axes. (e) the phase versus frequency, with W on a log axis. For each plot, choose the limits of the axes so that the part of the curve near W ; 20 rad/sec is clearly visible
Answers
For -2+3i, the magnitude is √13 and the phase is -56.31°. For 5+81i, the magnitude is 81.54 and the phase is 86.41°. For -5-81+4i, the magnitude is 81.97 and the phase is -83.26°. The response y(t) at steady state will be, y(t) = 2.92cos(1.5t) - 0.35sin(1.5t).
For -2+3i, the magnitude is √( (-2)^2 + (3)^2 ) = √13 and the phase is arctan(3/-2) = -56.31° (or 303.69°).
For 5+81i, the magnitude is √( 5^2 + 81^2 ) = 81.54 and the phase is arctan(81/5) = 86.41°.
For -5-81+4i, the magnitude is √( (-5)^2 + (-81)^2 + 4^2 ) = 81.97 and the phase is arctan((-81)/(-5)) = -83.26° (or 276.74°)
To find the response y(t) at steady state, we need to evaluate the transfer function F(jω) at the frequency of the input signal, which is ω = 1.5. Thus, we have,
F(j1.5) = (7(j1.5)^9) / ((j1.5)^2 + 100) = -2.92 + 0.35j
The steady-state response will be a sinusoidal signal at the same frequency as the input, with amplitude equal to the magnitude of the transfer function evaluated at that frequency, and with a phase shift equal to the phase of the transfer function evaluated at that frequency. Therefore, the response y(t) at steady state will be:
y(t) = 2.92cos(1.5t) - 0.35sin(1.5t)
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--The complete question is, For the complex numbers -2 +3i, 5+81i, and -5-81+4i, find their magnitude and phase.
A system with the transfer function F(s) = 7s^9/(s^2+100) is subject to a sinusoidal input U(s) = 10/(s^2+2.25). Find the response y(t) at steady state.--
What is the answer pls help
Answers
Answer:
The answer B
Step-by-step explanation:
I took the test
Answer:
The correct answer is 210 degrees.
Step-by-step explanation:
It's obviously obtuse so we can rule out 60 degrees. 105 degrees is closer to 90 degrees so we can rule that out. If it was 150 degrees, the angle would not look upside down. So, we can conclude that the measure of the angle would be 210 degrees.
The equation of circle D is (x + 2)2 + y² = 32.
Select all the points that lie on circle D.
□ (-6,-4)
□ (-2,16)
□ (-4,6)
□ (0,14)
□ (2,4)
Answers
The equation of circle D is (x + 2)2 + y² = 32 then the points (-6,-4) and (-4,6) lie on circle D
The equation of a circle with center (h,k) and radius r is (x - h)² + (y - k)² = r².
This is called the standard form of the equation of a circle.
In the given equation, (x + 2)² + y² = 32, we can see that the center of the circle is (-2, 0) and the radius is √32 = 4√2.
To determine which points lie on the circle, we substitute the x and y coordinates of each point into the equation and check if the equation is true.
If it is true, then the point lies on the circle.
Let us check if (-6, -4) lies on the circle, we substitute x = -6 and y = -4 into the equation:
(-6 + 2)² + (-4)² = 32
(-4)² + (-4)² = 32
16 + 16 = 32
32 = 32
Since the equation is true, (-6, -4) lies on the circle.
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the diameter of circle Q is 14 cm. Find the arc length of PR.
Answers
Answer:
4.15, or 1.32pi
Step-by-step explanation:
arclength is circumference(34/360)
so pi x d (34/360)
3.14 x 14 x (34/360) = 4.15, or 1.32pi
The arc length PR is 4.151 cm.
What is a circle?A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Moreover, every angle has rotational symmetry around the centre.A section of a line that runs from a circle's centre to any point on the circle itself. "R" or "r" stand for the circle's radius.
As per the given data:
The diameter of circle Q = 14 cm
From the given diagram:
∠PQR = 34°
For finding out the arc length PR:
arc length = angle in radian × radius
radius = diameter / 2 = 14 / 2 = 7 cm
angle in radian = 34° × (π / 180°) = 0.593 radians
arc length PR = 0.593 × 7 = 4.151 cm
Hence, the arc length PR is 4.151 cm.
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A box contains 23 yellow, 33 green and 37 red jelly beans. if 9 jelly beans are selected at random, what is the probability that:_________
Answers
The probability that exactly 10 are yellow out of 9 random selections is 0.
ProbabilityTo calculate the probability of exactly 10 jelly beans being yellow out of 9 selected at random, we need to consider the total number of favorable outcomes (selecting exactly 10 yellow jelly beans) divided by the total number of possible outcomes (selecting any 9 jelly beans).
The total number of jelly beans in the box is 23 (yellow) + 33 (green) + 37 (red) = 93.
The number of ways to select exactly 10 yellow jelly beans out of 9 is 0, as we have fewer yellow jelly beans than the required number.
Therefore, the probability of exactly 10 yellow jelly beans is 0.
In this case, it is not possible to have exactly 10 yellow jelly beans out of the 9 selected because there are not enough yellow jelly beans available in the box.
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A box contains 23 yellow, 33 green and 37 red jelly beans. if 9 jelly beans are selected at random, what is the probability that: exactly 10 are yellow?
What do you call the formula y =Mx+b
Answers
Answer:The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis
Step-by-step explanation:
Write the system first as a vector equation and then as a matrix equation. 5x1 + x2 - 3x3 = 8 2x2 + 4x3 = 0
Answers
The system can be written as a vector equation as [5, 1, -3] [x1, x2, x3]^T = [8, 0]^T and as a matrix equation as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].
To write the given system as a vector equation, we group the variables and the constants into vectors and write the equations in a matrix form. Thus, the system can be written as [5x1 + x2 - 3x3; 2x2 + 4x3] = [8; 0], which is a vector equation.
To write the system as a matrix equation, we can write the coefficients of the variables in a matrix A, the variables in a vector X, and the constants in a vector B. Thus, the system can be written as AX = B, where A = [5 1 -3; 0 2 4], X = [x1; x2; x3], and B = [8; 0].
We can then solve for X by finding the inverse of A and multiplying both sides of the equation by it.
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