This can be re-inserted into our vertex equation to obtain. y=2(x−2)2+3.
In "standard form," if your instructor desires it, we can expand the right side to get:
Write a quadratic function with a vertex of (2, "-3)" to show results
Find write a quadratic function with vertex of instead (2, -3)
Answer 1
A quadratic's common vertex form is. y=m(x−a)2+b.
In light of the vertex, this becomes (2,3).
So, we do. 11=m(4−2)2+3. f(x) = a(x - h)2 + k, where a, h, and k are constants, is the vertex form of a quadratic function (h, k). If the vertex form of the quadratic parent function f(x) = x2 is used, then y = a(x - h)2 + k, where a = 1, h = 0, and k = 0.
Putting it simply: 8=m(2)2. 8=4m. m=2.
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help pls and thanks
Answer:
43°
Step-by-step explanation:
Alternate interior angle are congruent.
56 out of 79 as a percentage
If AC is congruent to BD and EC is congruent to ED, prove that AE is congruent to BE
AE and BE are congruent lines or we can say lines with same length.
What are congruent lines?
Congruent line segments are geometrical figures in one dimension with identical dimensions. In terms of congruent lines, the word "congruent" refers to the equality of the two line segments. When two lines are the same length, they are said to be congruent.
As given in the question,
AC = BD, and
EC = ED
We can see in the figure that:
AC - EC = AE ___(1)
BD - ED = BE ___(2)
Substituting the value of AC and EC in equation (1):
AE = BD - ED ___(3)
From equations (2) and (3), we can conclude that,
AE = BC
Therefore, AE and BE are congruent lines.
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An angle measures 21.8° less than the measure of its complementary angle. What is the measure of each angle?
The measure of each angle is 34.1° and 55.9°
What are complementary angles?complementary angles are angles that gives 90° when added to together.
if the first angle is x and the other complementary angle is y,
then x+y=90
x= y-21.8
representing y-21.8 for x in equation x+y=90
y+ y-21.8= 90°
2y= 111.8
y= 55.9°
and x= 34.1°
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what is 0.294117647 equal to
The decimal is equal to (294117647)/(1000000000).
Will give branliest to the first person to answer. Pls answer ASAP. 40 points!! I'd appreciate your help so much!
Question: Which is the graph of the equation y - 1 = 2/3 (x - 3)?
Answer:
Option 2
Step-by-step explanation:
Using point-slope form, the line passes through (3, 1).
Option 2 is the only choice that satisfes this.
[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \: Graph \:\: 2[/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
The equation is given in its point slope form :
[tex]\qquad \tt \rightarrow \:y - 1 = \dfrac{2}{3} (x - 3)[/tex]
And the general equation in point slope form is :
[tex]\qquad \tt \rightarrow \:y - y_1 = m(x - x_1)[/tex]
by comparing these two, we can get
[tex]{ y_1 = 1 } [/tex][tex]{ x_1 = 3 } [/tex]And [tex]{ (x_1 , y_1) } [/tex] satisfies the equation, so the line (graph) of this equation should have point (3 , 1) lying on it.
And the only graph satisfying this condition is graph 2, therefore The graph 2 is the required graph.
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Define centroid. If (X₁,Y₁), (X2,Y2) and (x3.3) are the vertices of a triangle, find the co- ordinates of the centroid of that triangle. (Note: Show derivation)
The coordinates of a centroid of a triangle with vertices [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] are [tex](\frac{x_1+x_2+x_3}{3}, \frac{{y_1+y_2+y_3} }{3})[/tex].
Centroid of a triangle
For a triangle, the centroid is obtained by the intersection of its medians. The line segments of medians join vertex to the midpoint of the opposite side. All three medians meet at a single point (concurrent). The point of concurrency is known as the centroid of a triangle.
Let KLM be a triangle with the vertex coordinates [tex](x_1,y_1),(x_2,y_2),(x_3,y_3)[/tex] as K,L and M respectively.
Let the midpoints of the side LM, KL and KM are D, E, and F, respectively. The centroid of a triangle is represented as “G.”
As D is the midpoint of the side LM, we can write,
D = ((x2+x3)/2, (y2+y3)/2)
Now, we know that, G intersects AD in the ratio 2:1 , we get
Hence, using section formula we can write,
The x-coordinates of G will be:-
x = (2(x2+x3)/2 + 1.x1 )/ (2+1) = (x2+x3+x1)/3 = (x1+x2+x3)/3
The y-coordinates of G will be :-
y =(2(y2+y3)/2 + 1.y1 )/ (2+1) = (y2+y3+y1)/3 = (y1+y2+y3)/3
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HELP PLEASEEEEEEEE!!!!!!!!!
9. Option b. The two lines are perpendicular to each other
Given:
6x+10y = 20
5x- 3y = 21
Consider the first line,
10 y = -6x+ 20
y = -3/5 x + 2
This is of the form y = mx+ b
where, slope =m = - 3/5
Consider the second line,
5x- 3y = 21
3y = 5x- 21
y = 5/3 x - 21
This is of the form y = mx+ b
where, slope= m = 5/3
Since the slopes of the two lines are negative reciprocals ,they are perpendicular.
10. Option a. The equation of the line passing through (2, -9) with a slope -5 is y = - 5x + 1
Given:
slope = m= -5
point = (2,-9)
We know that ,the slope -intercept form is given by ,
y = mx+ b ---(1)
Substituting the given values in (1)
-9 = -5(2)+b
10- 9 = b
b = 1
Substituting m and b in (1)
y = -5x+1
Thus, the slope-intercept form equation of the line is y = -5x + 1
11. The equation of the line perpendicular to y= -2x+8 and passing through the point (4,-7) is y = 1/2x- 9
Given:
line = y = -2x+8
point = (x, y)= (4, -7)
The given equation is of the form,
y = mx+ b ---- (1)
m = -2
The line perpendicular to this line will have a negative reciprocal slope,
m = 1/2
The new line is of the form,
y = 1/2 x+ b ----(2)
Substituting the given point (4, -7) in (2)
- 7= 2 + b
b = - 9
Substituting b in (2)
y = 1/2x- 9 is the perpendicular line equation
12. The equation of the line parallel to 3x- 2y = 14 and passing through the point (-6,-11) is y = 3/2 x -2
Given:
line = 3x- 2y = 14
point = (x, y)= (-6,-11)
The slope - intercept form of the given line is ,
2y = 3x- 14
y = 3/2x - 7
slope = m = 3/2
The line parallel to this line will have the same slope,
m = 3/2
The new line is of the form,
y = 3/2 x+ b ----(1)
Substituting the given point (-6, -11) in (1)
- 11= -9 + b
b = - 2
Substituting b in (1)
y = 3/2 x -2 is the parallel line equation.
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Identify the vertex of the parabola.
(1, 0)
(−1, 0)
. (0, 1)
(0, −1)
It's (1, 0) - first option
Hope this helps!
PLS HELP WILL GIVE 100 POINTS AND BRAINLIEST.
Answers to your questions with explanations are below. You can ask a question, feel free. I wish you success!
Q2:This answer should be Vertical Angles.
Vertical angles are angles that are opposite of each other when two lines cross and equal each other. [tex](a^o=b^o)[/tex]
Q3:A pair of vertical angles is formed when two lines intersect each other at a single point. They are said to be linear if the angles are adjacent after the intersection of the two lines. The sum of the angles of a linear pair is always equal to [tex]180^o[/tex]. Such angles are also known as complementary or supplementary angles.
This way we eliminate the first option because they intersect at a point, but the sum of their angles is not equal to [tex]180[/tex] degrees.Second option is correct.Third option includes vertical angles. So that it is wrong.We see two angles intersecting at a single point and their sum is [tex]180[/tex] degrees. This option is the correct one.We see two right angles. This is also a correct option.The answer is [tex]2^{nd}+4^{th}+5^{th}[/tex]
Q4:The answer is the first option. Adjacent angles. The rule is simple. If [tex]a+b=90^o[/tex] if they're adjacate angles.
Q5:The answer is the third option. Supplementary angles. The rule is simple. If [tex]a+b=180^o[/tex] if they're supplementary angles.
the lifespans of lizards in a particular zoo are normally distributed. the average lizard lives 3.13.13, point, 1 years; the standard deviation is 0.60.60, point, 6 years. use the empirical rule (68-95-99.7\%)(68−95−99.7%)left parenthesis, 68, minus, 95, minus, 99, point, 7, percent, right parenthesis to estimate the probability of a lizard living between 2.52.52, point, 5 and 4.34.34, point, 3 years.
The probability of a lizard living for more than 2.5 years is 16%.
What is defined as the normally distributed?The proper term for just a probability bell curve is the normal distribution.The mean of a normal distribution is zero, and the standard deviation is one. It has a skew of 0 and a kurtosis of 3.Although all symmetrical distributions are normal, not all normal distributions are symmetrical.The average lifespan of a lizard is 3.1 years, with a standard deviation of 0.6 years.
Average lizard u = 3.1,
standard deviation σ = 0.6
To calculate the likelihood of a lizard living for more than 2.5 years;
p(X<2.5)
μ + aσ = 2.5
3.1 + a(0.6) = 2.5
a(0.6) = −0.6
a = −1
To calculate the probability, apply the empirical rule.
The total area = 100% (since total probability always is 1)
Area from μ to ∞ = p(X > μ) = 50%
Area between (μ−σ) and (μ+σ) = 68%
Area between (μ−σ) and μ is p((μ−σ) < X < μ) =34%
Thus,
p(X< (μ−σ)) = 1 − (p((μ−σ) < X < μ) + p(X > μ))
= 1 − (0.34 + 0.5)
p(X< (μ−σ)) = 0.16
Therefore, the probability that a lizard will live longer than 2.5 years 16%.
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i dont get this can anyone help me solve this problem
Answer:its D
Step-by-step explanation:
a women earns 16% more than her husband. Together they make 72,360 per year. what is the husbands annual salary
well, her husband makes "x" in salary, hmmm hers is 16% more than that, so
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{16\% of x}}{\left( \cfrac{16}{100} \right)x}\implies 0.16x[/tex]
so she really makes x + 0.16x = 1.16x, and we know their total is 72,360, so
[tex]\stackrel{husband}{x} + \stackrel{hers}{1.16x} = 72360\implies 2.16x=72360\implies x=\cfrac{72360}{2.16}\implies \boxed{x = 33500}[/tex]
What type of number is -1−1minus, 1? Choose all answers that apply: Choose all answers that apply: (Choice A) A Whole number (Choice B) B Integer (Choice C, Checked) C Rational (Choice D) D Irrational
Answer:
B and C
Step-by-step explanation:
I think that you mean -1 -1. That would equal -2
-2 is an integer and a rational number.
An integer are the whole numbers 0,1,2,3 and so on and their opposites, -1, -2, -3 ,-4 and so on
Rational number is when you can write a number as an integer over and integer. You can write -2 as -2/1
Answer: a,b,c
I did it in the test
Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 4 ≤x≤ 8.
Hence the average rate of change, in simplest form is -10 .
What is average rate of change?
The average rate at which one item is changing in relation to another is known as the average rate of change. A method that computes the amount of change in one item divided by the corresponding amount of change in another is known as an average rate of change function.Examples of average rates of change include: 80 km/h is the average speed of a bus. In a lake, fish population growth occurs at a pace of 100 per week.Using the coordinate points from the table ( 4,53) ( 8, 13 )
Substitute the coordinate into the expression
Average rate of change = y₂ - y₁/x₂ - x₁
= 13 - 53/8 - 4
= - 4 0/4 ⇒ -10
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Here is the set of numbers: 4, 5, 11, 12, 5, 38, 44
Based on your results of Mean and Median, is the Mean or Median larger in value?
Please answer with complete sentence(s), which explains why and how you made your choice.
Based on the results of Mean and Median, we can say that Mean is larger than median in value .
Mean of n observations can be calculated using the formula
Mean = (sum of all observations)/(number of observations) .
After arranging the data in ascending or descending order , the middle value can be called as Median .
In the question ,
the set of numbers is given as 4, 5, 11, 12, 5, 38, 44
rewriting them in ascending order ,we get 4, 5, 5, 11, 12 ,38 ,44 .
the sum of all the number = 4+5+5+11+12+38+44
= 119
number of observations = 7
hence the mean = 119/7 = 17
So, mean = 17
from the set of numbers 4, 5, 5, 11, 12 ,38 ,44 we can see that
the middle value of the set of numbers is 11 .
So , median = 11 .
On comparing the mean = 17 and the median = 11 ,
we can say that the mean is greater than median.
Therefore , based on the results of Mean and Median, we can say that
Mean is larger than median in value .
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Please Help
Deanna completed 60% of the levels in a recently released video game. If there are 75 levels in
the video game, how many levels did Deanna complete
Answer:
45 levels
Step-by-step explanation:
60% of 75 is 45 i think
Instructions: Interpret the function given in the context ofthe real-world situation described to answer the question.Nichole bought a new car. The depreciation equation isgiven by f(x) = 27,000(.86), where a representsthe number of years since the purchase of the car, andf(x) represents the value of the car. By what percentdoes Nichole's car depreciate each year?%
The depreciation equation is given by
[tex]f(x)=27000(0.86^x)[/tex]where x represents the number of years. Here, the initial value of the car corresponds to x=0, then we have
[tex]\text{ initial value = f\lparen0\rparen=27000}[/tex]After one year, the car value corresponds to x=1, that is,
[tex]\text{ after 1 year = f\lparen1\rparen=27000\lparen0.86}\rparen^1\text{=27000}\times0.86=\text{23220}[/tex]Now, let's find the depreciation percentage by means of a rule of three:
[tex]\begin{gathered} 2700\text{ ----- 100 \%} \\ 23220\text{ ------- x} \end{gathered}[/tex]so we have
[tex]x=\frac{23220\times100}{27000}=86\text{ \%}[/tex]So the difference between 100% and 86% is 14% This means Nichole's car depreciate 14% each year
geometry, is this answer correct?
Answer: yes, the value of x is 4 and angle HEB is 36 degrees
Step-by-step explanation:
1a. Find the value of angle CEB
Given that line segment AB and line segment EC are perpendicular you know they are right angles and therefore are equal to 90 degrees
2a.set up an equation
After noticing that angle CEB is 90 degrees you know that angle HEB+CEH=90 degrees: 13x+9x+2
3a. Solve the equation
13x+9x+2=90
22x+2=90 | combine like terms
22x=88 | subtract 2 from both sides
x=4 | divide by 22 on both sides
1b. Set up equation
Knowing x=4 and that angle HEB is 9x the equation is 9(4)
2b. Solve the equation
9(4)
36
= A metal pole is 500 cm long, correct to the nearest centimetre.
The pole is cut into rods each of length 5.8 cm, correct to the nearest millimetre.
Calculate the largest number of rods that the pole can be cut into.
The largest number of rods that the pole can be cut into is 86.
Given:
Length of Metal Pole = 500 cm
The pole is cut into rods.
Length of each rod = 5.8 cm
To determine the number of rods we can divide the total length of the pole by the length of each rod.
Number of rods that the pole can be cut into = (Length of Metal Pole) ÷ (Length of each rod )
⇒ Number of rods = 500 ÷ 5.8 = 86.2 ≈ 86
Therefore, the largest number of rods that the pole can be cut into is 86.
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C. For whole number n, n³ will be odd if n is odd and even if n is even.
Answer:
yes
Step-by-step explanation:
Which of the relations given by the following sets of ordered pairs is a function? (answer choices in picture)
Answer:
Option 4
Step-by-step explanation:
Each x-value corresponds to only one y-value
Please help me... 5 points
Answer:
Step-by-step explanation:
8(2+3)
( Please help + Will mark brainliest )
Answer the question in photo.
Answer: 5/3
Step-by-step explanation:
The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.
We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.
From Devon's total he decided to pay back his brother $17.50 and his best friend the $49 for
concert tickets. How much does Devon now have?
Answer:
Subtract 66.5 from Devon's total to find how much he has left
Prove the Lines are Parallel detailed two column proof for the following Given: 1 and 3 are supplementary Prove: a || b
The line a and b from the given line diagram is parallel since <2 and <3 are corresponding angles.
Column proof of angles
An angle is the point where two lines meet or intersect. From the given line diagram, we are told that <1 and <2 are supplementary.
Since the sum of supplementary angles is 180 degrees, hence;
<1 + <3 = 180 degrees
Also <1 + <2 = 180 degrees (sum of angles on a straight line)
<1 = 180 - <3
<1 = 180 - <2
Equate
180 - <3 = 180 - <2
-<3 = -<2
<2 = <3 (corresponding angle)
Since <2 is equivalent to <3, hence the line a is parallel to b
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Which is the surface area of the cube?
Answer:
54 cm
Step-by-step explanation:
A cube has six sides. The area of each face is found by squaring the length of a side. To get the total surface area of the cube, you'll multiply the area of one face by the number of faces.
a = edge
Area = 6a to the power of 2
Find the inverse Laplace of [tex]\displaystyle{L^{-1}\left \{ \dfrac{1}{s^3} + \dfrac{1}{s}\right \}}[/tex]
Compute the Laplace transform of [tex]f(t)=t^n[/tex], where [tex]n[/tex] is a non-negative integer.
[tex]\displaystyle L\left\{t^n\right\} = I_n = \int_0^\infty t^n e^{-st} \, dt[/tex]
Integrate by parts with
[tex]u=t^n \implies du = nt^{n-1} \, dt[/tex]
[tex]dv = e^{-st} \, dt \implies v = -\dfrac1s e^{-st}[/tex]
[tex]\displaystyle I_n = \frac ns \int_0^\infty t^{n-1} e^{-st} \, dt = \frac ns I_{n-1}[/tex]
By substitution,
[tex]\displaystyle I_n = \frac ns I_{n-1} = \frac{n(n-1)}{s^2} I_{n-2} = \cdots = \frac{n(n-1)\cdots(n-(k-1))}{s^k} I_{n-k}[/tex]
so that for [tex]k=n[/tex], we end up with
[tex]\displaystyle I_n = \frac{n(n-1)\cdots1}{s^n} I_0 = \frac{n!}{s^n} \int_0^\infty e^{-st} \, dt = \frac{n!}{s^{n+1}}[/tex]
We then have the inverse transform relation
[tex]\displaystyle L^{-1}\left\{ \frac1{s^n} \right\} = \frac{t^{n-1}}{(n-1)!}[/tex]
and so
[tex]L^{-1}\left\{ \dfrac1{s^3} + \dfrac1s \right\} = \dfrac{t^2}{2!} + \dfrac{0!}{t^0} = \boxed{\dfrac{t^2}2 + 1}[/tex]
Which of the following is a whole number?
-76
0
-34
11
-57
Answer:
11
Step-by-step explanation:
A whole number is an integer greater than 0.
-76 , -34 , -57 are all negative so they are not whole numbers.
0 is too small so it also is not a whole number.
By ruling out those numbers you are left with 11 which is positive and greater than 0. Therefore, the correct answer is 11.
Answer:
0 and 11
Step-by-step explanation:
Whole numbers are set yo to be real numbers that include zero and all positive numbers while it excludes fractions, negative integers and decimals.
Therefore, from our question, 0 and 11 are whole numbers while -76, -34 and -57 are excluded because they are negative integers.
find the constant of proportionality pls
Answer:
11, 110
Step-by-step explanation:
Constant of proportionality: Ratio of distance to time, which is 11.
Distance at 10s: Multiply time by the constant of proportionality, giving 110.