Answers
Given:
The equation of a function is
[tex]y=(x-4)^2+1[/tex]
To find:
The graph of the given function.
Solution:
The vertex form of a parabola is
[tex]y=(x-h)^2+k[/tex] ...(i)
Where, (h,k) is vertex of the parabola.
We have,
[tex]y=(x-4)^2+1[/tex] ...(ii)
From (i) and (ii), we get
[tex]h=4, k=1[/tex]
The vertex of the parabola is (4,1).
Now, the table of values is
x y
2 5
3 2
4 1
5 2
6 5
Plot these points on a coordinate plane and connect them by a free hand curve.
The graph of given function is shown below.
Related Questions
2. Using the ruler below, construct a triangle that has side lengths of 3 cm, 4 cm, and 5 cm.
triangle does this appear to be? Verify by using your protractor to measure angles.
What type of
Answers
Step-by-step explanation:
if to apply the Piphagorean theoreme, then one of the angles is 90° (opposite to the side with the length 5):
3²+4²=5²; ⇔ 9+16=25.
Max walks 10 meters in 4 seconds what is his walking rate in meters per second
Answers
Answer:
2.5 m/s
Step-by-step explanation:
10/4 gets the answer. it is just distance over time
Answer: 2.5 m/s
Step-by-step explanation:
Given that P=x+y. Find P when: x=−5 and y=−3
Answers
Answer:
P = - 8
Step-by-step explanation:
Given
P = x + y ← substitute x = - 5 and y = - 3
P = - 5 + (- 3) = - 5 - 3 = - 8
Someone help me on question 10 please!
Answers
Answer:
Step-by-step explanation:
500÷9=55.56miles/h (correct to 3 decimal places)
Simplify using Synthetic Division
Answers
Write down the first coefficient without changes:
−3223−10−3
−3
2
3 −10 −3
2
Step 2
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223(−3)⋅2=−63+(−6)=−3−10−3
−
3
2
3
−10 −3
(
−
3
)
⋅
2
=
−
6
2
3
+
(
−
6
)
=
−
3
Step 3
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223−6−3−10(−3)⋅(−3)=9(−10)+9=−1−3
−
3
2 3
−
10
−3 −6
(
−
3
)
⋅
(
−
3
)
=
9
2
−
3
(
−
10
)
+
9
=
−
1
Step 4
Multiply the entry in the left part of the table by the last entry in the result row (under the horizontal line).
Add the obtained result to the next coefficient of the dividend, and write down the sum.
−3223−6−3−109−1−3(−3)⋅(−1)=3(−3)+3=0
−
3
2 3 −10
−
3
−6 9
(
−
3
)
⋅
(
−
1
)
=
3
2 −3
−
1
(
−
3
)
+
3
=
0
We have completed the table and have obtained the following resulting coefficients: 2,−3,−1,0
2
,
−
3
,
−
1
,
0
.
All the coefficients except the last one are the coefficients of the quotient, the last coefficient is the remainder.
Thus, the quotient is 2x2−3x−1
2
x
2
−
3
x
−
1
, and the remainder is 0
0
.
Therefore, 2x3+3x2−10x−3x+3=2x2−3x−1+0x+3=2x2−3x−1
2
x
3
+
3
x
2
−
10
x
−
3
x
+
3
=
2
x
2
−
3
x
−
1
+
0
x
+
3
=
2
x
2
−
3
x
−
1
Answer: 2x3+3x2−10x−3x+3=2x2−3x−1+0x+3=2x2−3x−1
4.(06.02 MC)
The equation of line AB is y = 2x + 4. Write an equation of a line parallel to line AB In slope-Intercept form that contains point (3,-2). (4 points)
O y = 2x + 4
O y = 2x - 8
Answers
Answer:
The equation of a parallel line in the slope-Intercept form that contains the point (3,-2) is:
y = 2x- 8Step-by-step explanation:
The slope-intercept form of the line equation
y = mx+b
where
m is the slopeb is the y-interceptGiven the equation of a line
y = 2x + 4
comparing with the slope-intercept form of the line equation
The slope of the line AB is m = 2
We know that the parallel lines have the same slope.
Thus, the slope of the new line is also 2.
now we have,
The slope of new line m = 2The point = (3, -2)Using the point-slope form of the line equation
[tex]y-y_1=m\left(x-x_1\right)[/tex]
where m is the slope of the line and (x₁, y₁) is the point
substituting the values m = 2 and the point (x₁, y₁) = (3, -2)
[tex]y-y_1=m\left(x-x_1\right)[/tex]
y - (-2) = 2(x - 3)
y + 2 = 2x - 6
subtracting 2 from both sides
y + 2 - 2 = 2x - 6 - 2
y = 2x- 8
Therefore, the equation of a parallel line in the slope-Intercept form that contains the point (3,-2) is:
y = 2x- 8* Use order of operations to solve the following.
* Use order of operations to solve the following.
3 + 5 2 × 2 −7
Answers
Answer:
5
3+5 2×2 -7
8+4-7
12-7
5
^^^^
need help on these math questions. please and thank u
Answers
9514 1404 393
Answer:
a) x = -3
b) y = (28/27)x -27
Step-by-step explanation:
a) College street has a slope of 0, so is a horizontal line. 2nd Ave is perpendicular, so is a vertical line, described by an equation of the form ...
x = constant
For 2nd Ave to intersect the point (-3, 1), the constant must match that x-coordinate. The equation is ...
x = -3
__
b) Since Ace Rd is perpendicular to Davidson St, its slope will be the opposite reciprocal of the slope of Davidson St. The slope of Ace Rd is ...
m = -1/(-27/28) = 28/27
Using the point-slope equation for a line, we can model Ace Rd as ...
y -y1 = m(x -x1)
y -1 = (28/27)(x -27)
y = (28/27)x -27
Suppose that E and F are points on the number line.
If EF = 12 and E lies at -9, where could F be located?
Answers
Answer:
either at -21 or 3
Step-by-step explanation:
we know that the length is a total of 12 so it either goes 12 spaces to the left or to the right of -9
-9 - 12 is -21 and -9 + 12 is 3
help! algebra question
Answers
What value of x satisfies the conclusion of the mean value theorem for f(x) = ln(x3) over the interval [1, e2]?
Answers
Answer:
[tex]x \approx 3.195[/tex] satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = \ln x^{3}[/tex] over the interval [tex][1,e^{2}][/tex].
Step-by-step explanation:
According to the Mean Value Theorem, for all function that is differentiable over the interval [tex][a, b][/tex], there is at a value [tex]c[/tex] within the interval such that:
[tex]f'(c) = \frac{f(b)-f(a)}{b-a}[/tex] (1)
Where:
[tex]a[/tex], [tex]b[/tex] - Lower and upper bounds.
[tex]f(a)[/tex], [tex]f(b)[/tex] - Function evaluated at lower and upper bounds.
[tex]f'(c)[/tex] - First derivative of the function evaluated at [tex]c[/tex].
If we know that [tex]f(x) = \ln x^{3} = 3\cdot \ln x[/tex], [tex]f'(x) = \frac{3}{x}[/tex], [tex]a = 1[/tex] and [tex]b = e^{2}[/tex], then we find that:
[tex]\frac{3}{c} = \frac{3\cdot \ln e^{2}-3\cdot \ln 1}{e^{2}-1}[/tex]
[tex]\frac{3}{c} = \frac{6\cdot \ln e-3\cdot \ln 1 }{e^{2}-1 }[/tex]
[tex]\frac{3}{c} = \frac{6}{e^{2}-1}[/tex]
[tex]c = \frac{1}{2}\cdot (e^{2}-1)[/tex]
[tex]c \approx 3.195[/tex]
[tex]x \approx 3.195[/tex] satisfies the conclusion of the Mean Value Theorem for [tex]f(x) = \ln x^{3}[/tex] over the interval [tex][1,e^{2}][/tex].
Answer:
C. 1/2(e^2-1)
Step-by-step explanation:
Edge AP Cal 2022
please answer for help
Answers
Answer:
TS=22
Step-by-step explanation: Since we know the triangles are proportional, we need to set up an proportion to find TS. First, let find which sides are correspond with each, TS and MN does and US and NQ does. So we set up a proportion that includes.
TS/US=MN/NQ: Let plug in the numbers
3x+1/26=5x-2/39: Then cross multiply
39(3x+1)=26(5x-2): Then simplify
117x+39=130x-52: Subtract 117x from both sides
39=13x-52: Add 52 to both sides
91=13x: Divide 13 by both sides
7=x: Then plug it in to TS
3(7)+1=22
PLZ HELP VERY EASY BRAINLIEST
Identify a pair of mutually exclusive events and a pair of independent events.
Answers
PLS HELP ILL GIVE YOU BRAINLIEST
What is the area of the circle in terms of pi?
Answers
Answer:
C=9
Step-by-step explanation:
A = πr^2
A = π 9
9
Write an algebraic expression. The product of two numbers is 94, and one of the numbers is n. What is the other number?
Answers
Answer:
Let say the another number y
N×Y=94
Y=94/N
So the algebric expression is 94/N
There were 10 bunches of roses and tulips. Each bunch had 5 of the same flowers. There were 2 more bunches of tulips than roses. How many tulips were there?
Answers
Answer:
I think the answer is 12 (sorry if i misunderstood the question)
Step-by-step explanation:
Because if there are 10 things of roses and tulips and then 2 more tulips are added in the question in total thats 12.... 10+2=12
Recall the Spice Girls Emporium example. A list of useful information is given below. n = 36 The sample mean income is $41,100 The population standard deviation is estimated to be $4,500 What if we wanted to change our level of confidence to be 99%? What would our new margin of error be? Your answer should be given as an integer.
Answers
Answer: Margin of error = 1932
Step-by-step explanation: Margin of Error is the amount of variation a survey's results have. In other words, it is understood as the measure of variation one can see if the same survey was taken multiple times.
Margin of error is calculated as [tex]z\frac{\sigma}{\sqrt{n}}[/tex]
z is z-score related to the percentage of confidence, in this z = 2.576
σ is population standard deviation
n is how many individuals are there in the sample or population
With a new level of confidence of 99%:
ME = [tex]2.576.\frac{4500}{\sqrt{36}}[/tex]
ME = 2.576(750)
ME = 1932
The new margin of error would be 1932.
Make y the subject of the formula
Answers
Answer:
[tex] y = \frac{w - x^2}{-2z} [/tex]
Step-by-step explanation:
Given:
w = x² - 2yz
Required:
Solve for y
Solution:
[tex] w = x^2 - 2yz [/tex]
Subtract x^2 from not sides
[tex] w - x^2 = - 2yz [/tex]
Divide not sides by -2z
[tex] \frac{w - x^2}{-2z} = \frac{-2yz}{-2z} [/tex]
[tex] \frac{w - x^2}{-2z} = y [/tex]
[tex] y = \frac{w - x^2}{-2z} [/tex]
Craig has 5/8 of a bottle of glue but the recipe calls for three quarters a bottle. Does he have enough
Answers
Answer:
No, he doesn't have enough
Step-by-step explanation:
In eights, three quarters of a bottle is equal to 6/8.
Since 5/8 is smaller than 6/8, Craig won't have enough glue.
So, the answer is no.
Answer:
NO
Step-by-step explanation:
3/4 converted to eighths is 6/8. and 6/8 is greater than 5/8
The sum of two numbers is 240. If one number is twice the other number, find the two numbers.
Answers
Answer:
The sum of two numbers is 240. The larger number is 6 less than twice the smaller. Find the numbers.
----------
Let the smaller be "x" ; Larger is "2x-6"
EQUATION:
x + 2x-6 = 240
3x= 246
x = 82 (smaller)
2x-6 = 158 (larger)
Step-by-step explanation:
Answer:
160 and 80
Step-by-step explanation:
solve for x -2x + 2 = x -13
Answers
Answer:
x = 5
Step-by-step explanation:
Add 2x to both sides: 2 = 3x - 13
Add 13 to each side: 15 = 3x
Divide both sides by 3: 5 = x
Isolate with the variable by dividing each side by factors that don't contain the variable. So, x= 15
A superball rebounds half the height it drops. A student drops the superball from the top of a building, 176 feet above the ground. How far
above the ground is the ball when it has traveled a distance of 500 feet?
Answers
Answer:
62.48 ft.
Step-by-step explanation:
Initial height: 50 ft.
First rebound: 10 ft.
Second rebound: 2 ft.
Third rebound: 0.4 ft.
Fourth rebound: 0.08 ft.
If we approximate the fourth rebound to zero, we'll have:
50 + 10 + 2 + 0.4 + 0.08 = 62.48 ft.
The amount Cami raised during last year’s charity walk, $45.50, is StartFraction 7 over 10 EndFraction of the amount she raised this year. Which equation represents n, the number of dollars she raised this year
Answers
Answer:
The equation is given by:
[tex]n = \frac{7}{10} \times 45.50[/tex]
Step-by-step explanation:
During last years's charity walk, she raised $45.50.
During this years walk, she raised n, which is 7/10 of this amount. So, the equation is given by:
[tex]n = \frac{7}{10} \times 45.50[/tex]
Answer: 45.50=0.7n
Step-by-step explanation:
True or false, A triangle with side lengths of 9 cm, 19 cm, and 17 cm is a right triangle.
Answers
Answer:
False
Step-by-step explanation:
A right triangle has all side lengths the same
Answer: give me brainliest now
Step-by-step explanation:
A fitness machine weigh 16.8 kg. How many grams does the fitness machine weigh?
Answers
Answer:
16800
Step-by-step explanation:
since the equaltiuon is 16.8*1000
1 kg = 1000 grams.
16.8 kg x 1000 = 16,800 grams
(THIS IS 30 POINTS!!) In Ms. Hollbrook's class, 62% of the class enjoys watching anime. If there are 32 students in Ms. Hollbrooks class, about how many students enjoy watching anime?
A) 12 students
B) 14 students
C) 16 students
D) 20 students
Answers
Answer:
D)
Step-by-step explanation:
32*0.62=19.84≈20.
In all, there are 52 blocks in the groups below. Each
group is the same size.
Which number sentence shows how to find the number
of blocks in each group?
52x4
B
52-4=
52+4=
D
52 -4 =
Answers
Answer:
D you divide
Step-by-step explanation:
The number sentence that shows how to find the number of blocks in each group is 52 ÷ 4.
What is the unitary method?The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a technique by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.
We are given that there are 52 blocks in the groups below. Each group is the same size.
Therefore, to find the number of blocks in each group, we have to divide the number of blocks by group.
That is;
52 / 4 = 13
Learn more about the unitary method, please visit the link given below;
https://brainly.com/question/23423168
#SPJ2
A local arts council has 200 members. The council president wanted to estimate the percent of its members who have had experience in writing grants. The president randomly selected 30 members and surveyed the selected members on their grant-writing experience. Of the 30 selected members, 12 indicated that they did have the experience. Have the conditions for inference with a one-sample z -interval been met
Answers
Answer:
Yes the sample can be use to make inference
Step-by-step explanation:
The inference is possible if the conditions:
p*n > 10 and q*n > 10
where p and q are the proportion probability of success and q = 1 - p
n is sample size
Then p = 12 / 30 = 0,4 q = 1 - 0,4 q = 0,6
And p*n = 0,4 * 30 = 12 12 > 10
And q*n = 0,6 * 30 = 18 18 > 10
Therefore with that sample the conditions to approximate the binomial distribution to a Normal distribution are met
To check the condition for inference with a one sample z-interval, we have to divide randomly selected member by total number of arts council.
No, the sample size is not less than 10% of the population size,
Given:
The total number of council member are 200.
The randomly selected members are 30 .
Calculate the ratio of randomly selected members and total number of council member.
[tex]\dfrac{n}{N}=\dfrac{30}{200}\\\dfrac{n}{N}=0.15\\\dfrac{n}{N}=0.15>0.10[/tex]
Thus, No, the sample size is not less than 10% of the population size.
Learn more about z-interval here:
https://brainly.com/question/7204089
HELP PLZZZ EASY AREA MATH
Answers
Answer:
4,400
Step-by-step explanation:
PLEASE HELP WITH THESE QUESTIONS I HAVE 5 MINUTES LEFT
What is 4 superscript 5 written in expanded form?
O 4 + 4 + 4 + 4 + 4
O 4 times 4 times 4 times 4 times 4
O 5 + 5 + 5 + 5
O 5 times 5 times 5 times 5
Answers
Answer:
4+4+4+4+5
Step-by-step explanation:
is 5 times the number only expanded
Answer:
4+4+4+4+5
Step-by-step explanation:
