Answer:
f(x) = - ⁴/₉(x - 3)² + 6Step-by-step explanation:
The vertex form of the equation of the parabola with vertex (h, k) is:
f(x) = a(x - h)² + k
So for vertex (3, 6) it will be:
f(x) = a(x - 3)² + 6
y intercept: 2 means f(0) = 2
f(0) = a(0 - 3)² + 6
2 = a(-3)² + 6
2 -6 = 9a + 6 -6
-4 = 9a
a = ⁻⁴/₉
Therefore:
The vertex form of quardatic function with vertex: (3,6) and y intercept: 2 is
f(x) = - ⁴/₉(x - 3)² + 6
The vertex form of the parabola equation is f(x) = -4/9(x - 3)² + 6 if the vertex: (3,6) and y intercept: 2
What is a parabola?It is defined as the graph of a quadratic function that has something bowl-shaped.
(x - h)² = 4a(y - k)
(h, k) is the vertex of the parabola:
a = √[(c-h)² + (d-k²]
(c, d) is the focus of the parabola:
It is given that:
The vertex: (3,6) and y-intercept: 2
As we know,
The parabola equation:
f(x) = a(x - h)² + k
Here (h, k) is the vertex of the parabola and a is the leading coefficient.
f(x) = a(x - 3)² + 6
f(x) = 2 at x = 0
2 = a(0 - 3)² + 6
a = -4/9
f(x) = -4/9(x - 3)² + 6
Thus, the vertex form of the parabola equation is f(x) = -4/9(x - 3)² + 6 if the vertex: (3,6) and y intercept: 2
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10. At a certain company, the average starting salary s for a new worker is $25,000. The actual
salary has an absolute deviation of at most $1800. Write and solve an inequality to find the
range of the starting salaries.
Copyright © Big Ideas Learning, LLC
Integrated Mathematics 1
57
Answer:
Step-by-step explanation:
Let 'x' represent the actual salary.
|x - 25,000| <= 1800
- 1,800 <= x - 25,000 <= 1,800
25,000 - 1,800 <= x <= 25,000 + 1,800
23,200 <= x <= 26,800
The range of the salary is the closed interval [23,200, 26,800].
A state university is interested in where its students come from. They survey 300 of its students to find out if they are in-state, out-of-state, or foreign students. Match the vocabulary word with its corresponding example.
All students at the university
The proportion of the 300 surveyed students who are in-state students
The list of the 300 answers to the survey question
The answer in-state out-of-state or foreign
The 300 students who were surveyed
The proportion of all students from this university who are in-state students
population
Statistic
Data
Variable
Sample
Parameter
Answer:
The correct matches are;
All students at the university → Population
The proportion of the 300 surveyed students who are in-state students → Statistic
The list of the 300 answers to the survey question → Data
The answer in-state out-of-state or foreign → Parameters
The 300 students who were surveyed → Sample
The proportion of all students from this university who are in-state → Variable
Step-by-step explanation:
1) The population is the set that contains total number of possible observation in the question, the population is all the students of the university
2) A statistic is a calculated quantity derived from a sample's data value that can be used in estimating a parameter of the population or outlining a sample characteristic
The proportion of the in-state student in the sample is found by taking the ratio of the number of in-state student in the sample to the total number of student in the sample
3) Data are collected information which may be qualitative or quantitative variables
The answers collected in the survey are the data of the 300 surveyed student
4) A parameter is the value that is used as the means of measuring or classifying an item or system
5) A sample is a part or portion of a population, that serves as representative of the population
6) A variable is a quantity that can vary or cannot be said to be constant.
The number proportion of all students from the university who are in-state students can change due to change in the proportion during graduation and admission.
The vocabulary word when correctly matched to the corresponding example would give:
All students at the universityPopulation
The proportion of the 300 surveyed students who are in-state studentsParameters
The list of the 300 answers to the survey questionData
The answer in-state out-of-state or foreignVariable
The 300 students who were surveyedSample
The proportion of all students from this university who are in-state students populationStatistic
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The mean age of five people in a room is 24. One of the people (age 40) leaves the
room. The mean age of the remaining four people is
Answer:
thxss for the points love
Step-by-step explanation:
kisses
Answer:
16
Step-by-step explanation:
(-4,1) and (-8,7)
write an equation in slope-intercept form
Answer:
y = -2x - 9
Step-by-step explanation:
so we have our two points, (-4,-1) and (-8,7) What we need to do to find our slope is y2 - y1 over x2 - x1. Once plugging in the numbers and subtracting it should give you 8/-4. 8 divided by -4 is -2. m = -2. Now to find our "b" we plug in our slope, and plug in one of the two points into the format of y = mx + b.
-1 = -2(-4) + b
multiply -2 and -4
-1 = 8 + b
we subtract 8 from itself and -1
-9 = b
Our equation is y = -2x - 9
Write 3 quadratic equations that are NOT
equivalent, each forming a graph with vertex (-2, 3)
Answer:
the vertex of a quadratic equation:
a*x^2 + b*x + c = y
Is located at:
x = -b/2a.
In this case, x = -2
Then:
-b/2a = -2.
And we also have that:
a*(-2)^2 + b*-2 + c = 3
Then we have two equations:
-b/2a = -2
a*(-2)^2 + b*-2 + c = 3
We have only 2 equations and 3 variables, so we can just give the variable c different values and we will find different quadratic equations that are not equivalent.
Let's begin with c = 0, our equations are:
-b/2a = -2
a*(-2)^2 + b*-2 + 0 = 3
In the first equation we can isolate b and get:
b = 4*a
Now we can replace this in the other equation and solve this for a.
a*4 + 4*a*-2 = 3
-4*a = 3
a = -3/4
then:
b = 4*a = 4*-3/4 = -3
The first quadratic equation is:
(-3/4)*x^2 - 3*x = y.
Now, to find the second let's use a different value of c.
c = 1
b = 4*a
a*(-2)^2 + b*-2 + 1 = 3
Let's solve in the same way as before:
a*4 + (4*a)*-2 + 1 = 3
-4*a = 2
a = 2/-4 = -1/2
b = 4*-1/2 = -2.
Then our equation is:
(-1/2)*x^2 - 2*x + 1 = y
For the last equation, let's use c = 2.
then our equations are:
b = 4*a
a*(-2)^2 + b*-2 + 2 = 3
Same as before, replace the first equation in the second.
a*4 + (4*a)*-2 + 2 = 3
-4*a + 2 = 3
-4*a = 1
a = -1/4
Then:
b = 4*(-1/4) = -1
Our third equation is:
(-1/4)*x^2 - 1*x + 2 = y
Now, below you can see all of them graphed.
Where red is the first one, blue the second and green the third one. (and as you can see, all of them share the vertex (-2,3) )
Evaluate each value expression for the given value of x: 22-x/5 , x=20
Answer:
18
Step-by-step explanation:
or
for taking sq root:
x=√10 or x=−√10
20 points and brainliest.
Answer:
c.
Step-by-step explanation:
f(x)=3x+5
y=3x+5
x=3y+5
x-5=3y
y=(x-5)/3
y=1/3x-5/3
write the equation of a line that has a slope of 3 and passes through the point (1,2) in slope intercept form
Answer:
The equation is y = 3x - 1
Step by Step Explanation:
Ok, so your first step in solving this would be substituting m in the equation with the slope, since m represents the slope. So then you would have y = 3x + b. Now, to find b, you would have to substitue the point (1,2) into the equation. You would replace 2 with y since that's the y coordinate, and 1 with x since that's the x coordinate. Then you have 2 = (3*1) + b. Now, you solve for this. You get 2 = 3 + b. Isolating the variable b, you have b = -1. So, the result is y = 3x - 1. That's your answer
Why does the sequence of translating and reflections matter?
Answer:
If two or more of the transformations have a vertical effect on the graph, the order of those transformations will most likely affect the graph. If two or more of the transformations have a horizontal effect on the graph, the order of those transformations will most likely affect the graph.
Step-by-step explanation:
Hope this helps you with your math
Line p passes through point (0, 8) and is perpendicular to the graph of y = 1/4 x + 2. Line q is parallel to line p and passes through point (-3, 6). Which is the equation of line q in slope-intercept form? A. y= 1/4x+6 B. y = -1/4 x + 8 C. y = 4x – 8 D. y=-4x - 6
Answer:
A
Step-by-step explanation:
Because when the line passes through (0,8) with perpendicular to the graph of y =1/4 x =2 it equals y+1/4x+6.
The equation of line q in slope-intercept form is y = -4x - 6 if the line p passes through the point (0, 8) and is perpendicular to the graph of y = 1/4 x + 2.
What is a straight line?A straight line is a combination of endless points joined on both sides of the point.
The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).
The slope 'm' of any straight line is given by:
[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}[/tex]
It is given that:
Line p passes through the point (0, 8) and is perpendicular to the graph of y = 1/4 x + 2.
The slope of the line p is:
m(p) = -4
The slope of the line q parallel to line p:
m(q) = -4
The equation of the line q:
y - 6 = -4[x + 3]
Line q passes through the point (-3, 6).
The equation of the line:
y = -4x - 12 + 6
y = -4x - 6
Thus, the equation of line q in slope-intercept form is y = -4x - 6 if the line p passes through the point (0, 8) and is perpendicular to the graph of y = 1/4 x + 2.
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Can u help my 9-12 real quick
Answer:
9. B
10. C
11. A (probably)
12. D
Answer:
9) a
10) c
11) a
12) d
( I don't know if 11 and 12 are correct)
What is the area of a circle with equation (x+2)2+(y-4)2=36?
Answer:
X+Y=20
Step-by-step explanation:
(x+2)2+(y-4)2=36
2x+4+2y-8=36
2x+2y=36+4
X+Y=20
Final answer
X+Y=20
Two classes are having pizza parties. Ms. Rodriguez’s class decides to order enough so that every 3 students will have 2 pizzas. Mr. Becker’s class decides to order enough so that every 5 students will have 3 pizzas. Complete the following statements. You can enter whole numbers, decimals rounded to the hundredths place, or simplified fractions.
Each student in Ms. Rodriquez’s class will get _____ of a whole pizza.
Each student in Mr. Becker’s class will get _____ of a whole pizza.
Answer:
2/3
3/5
Step-by-step explanation:
Shelly pays $22.75 for 3.5 yards of fabric. What is the price per yard of fabric?
Answer:
Price per yard is $6,5
Step-by-step explanation:
22.75/3.5 = 6,5
which is the line of best fit and why?
Responder:
Opción de respuesta c
Explicación paso a paso:
Es una pendiente positiva como los datos, también coincide con muchos de los puntos.
Espero que te aya ayudado
Answer:
Answer choice c
Step-by-step explanation:
It is a positive slope like the data, it also matches up with many of the points.
giving extra points pls help
Answer:
x = 8mi
Step-by-step explanation:
Use Pythagorean theorem! It states that you can find any side of the triangle using the equation + = . The sides a and b are the sides that are shortest, and c is the longest/slanted side (hypotenuse). So plug in what they give you to get + = ( a and b can be used for either number that is not the hypotenuse). A little bit of basic algebra will lead you to get x=8 mi.
If three coins are tossed, how many outcomes are favourable to getting 1 head a 2 tails. Present the answer as a fraction.
Answer:
There are 8 possible outcomes
h h h
t t t
h t h
t h h
h h t
h t t
t t h
t h t
One head and 2 tails occurs in the sixth, seventh and eighth rows.
So, the probability is 3 out of 8 or 3/8 or .375
Step-by-step explanation:
Find an integer $x$ such that $\frac{2}{3} < \frac{x}{5} < \frac{6}{7}$.
Answer:
5
Step-by-step explanation
Aops Question
[x] can be any number between -
3.33 < x < 4.29.
What is a expression? What is a mathematical equation? What is Equation modelling ?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.
Given is the following inequality -
[tex]$\frac{2}{3} < \frac{x}{5} < \frac{6}{7}[/tex]
We can write -
x/5 > 2/3
x > 10/3
x > 3.33
and
x/5 < 6/7
x < 30/7
x < 4.29
[x] can be any number between -
3.33 < x < 4.29
Therefore, [x] can be any number between -
3.33 < x < 4.29.
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Josh and Corey met up for lunch. When they were done, Josh traveled 8 blocks east and Corey traveled 4 blocks west. How many blocks away from Josh was Corey?
Answer:
12
Step-by-step explanation:
Since they traveled in opposite directions, we would add the 2 numbers!
8+4=12.
WILL MARK BRAINIEST IF RIGHT
(AMC8, 2008) In square ABCE, A F = 2FE and CD = 2DE. What is the ratio of the area △BDF to the area of square ABCE?
A. 1/6 B. 2/9 C. 5/18 D. 1/3 E. 7/20
Answer:
The answer is A
Answer:
C
Step-by-step explanation:
is 45.213623 rational or irrational
Answer:
Rational
Step-by-step explanation:
PLEASE HELP WITH THIS!
Answer:
42
Step-by-step explanation:
Answer:
The answer would be (A.)
Step-by-step explanation:
Can you answer my question that i just posted please and thank you :)
can someone help wit this asap i have 10 more mins
A is the correct answer
the graph below shows a proportional relationship between x and y. what is the constant of proportionaliy y/x
Answer:
it is 4 i just did it
Step-by-step explanation:
Answer:
Four
Step-by-step explanation:
4
Choose the point-slope form of the equation below that represents the line that
passes through the points (-6, 4) and (2, 0). (2 points)
1) y - 4 =-1/2 (x+6)
2) y - 4 = 2(x + 6)
3) y+6=-1/2(x - 4)
4) y + 6 = 2(x - 4)
[tex]\mathfrak{\huge{\pink{\underline{\underline{AnSwEr:-}}}}}[/tex]
Actually Welcome to the Concept of the Straight lines.
Since the slope of the line, m = -1/2
and we know that, line equation is, y=mx+c
so the answer is, option 1.)
1.) y-4 = -1/2 (x+6)
i need help asap......
1. If g(x)= 4(3)* then g(-2)= ?
Help please
Answer:
-8
Step-by-step explanation:
Assuming that the in parentheses is what we are supposed to change (3)..We would replace the three with the negative two this means that we will solve for four times -2 which equals -8.Hope this helps!
If one quart is the same amount as 2 pints, how many pints are in 8 quarts
Answer:
16 pints
Step-by-step explanation:
Answer:
Step-by-step explanation:
1:2
1 q to 2 p
8q to 16 p or 8:16
CORRECT ANSWER GETS BRAINLIEST !
Vana lives 6 miles from the library and 18 miles from the museum . To the nearest mile . What is the shortest distance from the museum to the library ?
A.16mi
B.17mi
C.19mi
D.20mi
Answer:
C
Step-by-step explanation:
I just took the quiz :D
May I have Brainiest???
Complete the equation of the line through (3,-1) and (4,7)
Answer:
y=8x-25
Step-by-step explanation:
I put my work in the picture I attached
Answer:
y=8x-25
Step-by-step explanation:
1) You find the slope by doing y2-y1/x2-x1 (so 7-(-1)/4-3) then you get the slope of 8
2) then you plug in some points using the slope (I'll use the point (3,-1)) : -1=8(3)+b
3) to find "b", you solve: -1=24+b --> b=-1-24 --> b=-25
4) then you put everything together and you get y=8x-25