Answer:
(a) The coordinates of the inflection point are (1; 8) and, being the value of a less than zero, then these coordinates indicate the maximum of the function.
(b) The y-intercept has a value of 6
(c) The coordinates of the x-intercepts have a value of x=3 and x=-1
Step-by-step explanation:
You know y= -2*(x-1)² + 8
(a) Every quadratic function can be expressed by the canonical form:
f(x)=y= a*( x- h)² + k
where a is the principal coefficient and the ordered pair (h; k) are the coordinates of the vertex of the parabola.
The quadratic function will have a maximum or minimum value at the vertex. If a> 0, the parabola is concave, that is, it will have its branches upwards, therefore the vertex will indicate the minimum of the function. But if a <0 the parabola is convex and the vertex will indicate the maximum of the function.
Comparing the given equation with the canonical form of a quadratic function you can see that:
a=-2h=1k=8Then, the coordinates of the inflection point are (1; 8) and, being the value of a less than zero, then these coordinates indicate the maximum of the function.
(b) The y-intercept arises from evaluating the function at x = 0. So, in this case:
y= -2*(0-1)² + 8
Solving:
y= -2*(-1)² + 8
y= -2*1 + 8
y= -2+8
y= 6
The y-intercept has a value of 6
(c) The roots or coordinates of the x-intercepts arise from evaluating the function at y = 0. So, in this case:
0= -2*(x-1)² + 8
Solving:
-8= -2*(x-1)²
[tex]\frac{-8}{-2} =(x-1)^{2}[/tex]
4= (x-1)²
√4= |x-1|
⇒ 2=x-1 → 2+1=x → 3=x
⇒ -2=x-1 → -2+1=x → -1=x
The coordinates of the x-intercepts have a value of x=3 and x=-1
PLEASEE HELP! ASAP!!
If a figure starts off in a Quadrant I and is reflected along the x-axis and then rotated 180 degrees about the origin, what quadrant will it land on?
Answer:
Quadrant 2
Step-by-step explanation:
First you reflect and it goes to Quadrant 4(Positive,Negative). When rotating 90 degrees you go to the next quadrant. In this case it is 180 degrees, so it ends up two quadrants away. The final location is quadrant 2
Solve and Graph the System of Linear Equations
1) 3 X + 2 Y = 4
X + 2 Y = -4
Answer:
y=-4
x=-12
Step-by-step explanation:
Set up the system
Then you have to cancel out a variable
Then you solve for the remaining variable
Then plug in to find other variable
I'm sorry if that's confusing:/
Which values represent solutions to the equation?
Tan(3Pi/4-2x)=-1, where x = [0,pi]
The value of the variable x will be {0, pi/2, pi}. Then the correct option is B.
What is trigonometry?The connection between the lengths and angles of a triangular shape is the subject of trigonometry.
The trigonometric equation is given below.
tan (3π/4 - 2x) = - 1
We know that the value of tan 3π / 3 is negative one. Then the equation will be
tan (3π/4 - 2x) = tan 3π/4
Apply inverse of tangent on both sides, then the equation will be
(3π/4 - 2x) = 3π/4, -π / 4
- 2x = 0, -π
2x = 0, π
x = 0, π/2
Then the value of the variable x will be {0, pi/2, pi}.
Then the correct option is B.
The question was incomplete, but the complete question is given below.
Which values represent solutions to the equation? tan(3pi/4 - 2x) = -1, where x ∈ [0,pi]
A) {0, pi}
B) {0, pi/2, pi}
C) {0, pi, 2pi}
D) {0, pi/2, pi ⋅ 3pi/2}
More about the trigonometry link is given below.
https://brainly.com/question/22698523
#SPJ2
Write the equation of the line that passes through the given points. (0,3) and (-17,1)
Whats the answer? Need help ASAP
Answer:
the equation: y=2/17x+3
the slope: 2/17
Step-by-step explanation:
x/9 - 1 = 2 solve for x
Answer: x=27
Step-by-step explanation:
Question 2 (1 point) Which ordered pair is a solution to the equation below? -4x + 2y = 16 O (-3, 2) O (4, -1) (2-3)
Answer:
A. (-3, 2)
Step-by-step explanation:
First step is to revert the equation into y = mx + b form.
-4x + 2y = 16 turns into y = 2x+8
Now just plug in the points given to see which one matches.
(-3,2) the x is -3 so if you plug that into the equation it should get you 2 which is the y.
2 = 2(-3) + 8
2 = 2
So we know that (-3, 2) is the solution.
If you plug in the other points they wont come out equal. For example, (4,-1)
-1 = 2(4) + 8
-1 = 16
So (4,-1) cant be a solution. The same thing applies for (2, -3).
Can someone help please?!
Answer:
A.) Y.
Step-by-step explanation:
I'm not sure how to explain.
Evaluate the expression when c= 3.
c²+6c-3
Answer:
21
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASStep-by-step explanation:
Step 1: Define
c² + 6c - 3
c = 3
Step 2: Evaluate
Substitute: 3² + 6(3) - 3Exponents: 9 + 6(3) - 3Multiply: 9 + 18 - 3Add: 24 - 3Subtract: 21In a survey of 2,000 people who owned a certain type of car, 900 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
Answer:
45%
Step-by-step explanation:
900/2,000 = 45
Which best represents 3=x/6 -2
Answer:
30
Step-by-step explanation:
Answer: x = 30
Step-by-step explanation: To solve for x, first you’ll have to make sure that your result will equal to 3. ( x/6 -2). Next, look for a numerator that can make a fraction that equals to 5. Then, you would have to multiply 6 x 5, which equals to 30, so 30 will be x. 3 = (30/6 - 2) 3 = 5-2.
De acuerdo con una encuesta se determino que en una region hay igual numero de personas lic en administracion comercio servicio de salud y servicio municipal ademas se encontro que 35% de los administrativos 25% de los comerciantes 20% de los servidores de salud y 15% de servicio municipal son mujeres cual es la probabilidad de que una mujer escogida al azar del grupo sea administradora
Answer:
La probabilidad de que una mujer sea administradora es de 0,35
Step-by-step explanation:
Sean A B, C y D los eventos de las mujeres administrativas, comerciantes, trabajadoras de salud y proveedoras de servicios municipales.
Sus probabilidades están dadas por
P (a) = 35% = 0,35
P (b) = 25% = 0,25
P (c) = 20% = 0,2
P (d) = 15% = 0,15
Como los eventos son independientes, la probabilidad conjunta sería
P (B∩C∩D) = P (D) * P (B) * P (C) = 0.25 * 0.2 * 0.15 = 0.0075
P (A / B∩C∩D) = P (A∩B∩C∩D) / P (B∩C∩D)
= 0,35 * 0,0075 / 0,0075 = 0,35
Por lo tanto, la probabilidad condicional de obtener la mujer administradora es la misma que la probabilidad individual de obtener la administradora, ya que los eventos son independientes.
La probabilidad de que una mujer sea administradora es de 0,35
English
Let A B, C and D be the events of the women administrative, merchants, health workers and municipal services providers.
Their probabilities are given by
P (a) = 35% = 0.35
P (b)= 25% = 0.25
P (c) =20% = 0.2
P (d) = 15 % = 0.15
As the events are independent then the joint probability would be
P (B∩C∩D)= P(D) * P(B)* P (C) = 0.25* 0.2*0.15= 0.0075
P(A/B∩C∩D) = P(A∩B∩C∩D)/P(B∩C∩D)
= 0.35*0.0075/ 0.0075= 0.35
Therefore the conditional probability of getting the administrator woman is the same as the individual probability of getting the woman administrator as the events are independent.
Probability of woman administrator is 0.35
A 68-year old retiree has a pension savings of $43,000, a 401k of $75,000, and an IRA account of $62,000. Before 2008, he had 2% more cash in the pension, 12% more in the IRA, and −1% in the 401k. He wants to take out 2% from each account before he turns 72, which will cost him a penalty of an extra 3% from the current total amount in his pension, 4% from the 401k, and 6% from the IRA. What is the highest amount that will be taken from a single account, including the penalty, if the retiree takes the money out now from each?
Answer:
The answer is the IRA
Step-by-step explanation:
If he takes out 2% from each account, the highest penalty will be for the IRA account which is, 6% of 62,000 is $3,720. He will also take 2% of that 62,000 which will be $1,240. The total will be $4,960.
For the 401k account the withdrawal is $1,500 and the penalty is $3,000. That is $460 less than the IRA account.
I hope this answer helps.
Answer:
54280
Step-by-step explanation:
2+6=8
.08 * 59000=4720
59000-4720=54280
please help quick :) (I'll give brainliest, whatever it's called.)
A relation contains the points (−2, 0), (−1, −1), (0, 2), (1, 0), and (1, −2). (show work if you can)
A. The relation does not represent y as a function of x, because each value of x is associated with a single value of y.
B. The relation represents y as a function of x, because one value of y is associated with two values of x.
C. The relation does not represent y as a function of x, because one value of x is associated with two values of y
D. The relation represents y as a function of x, because each value of x is associated with a single value of y.
Answer:
C. The relation does not represent y as a function of x, because one value of x is associated with two values of y
Step-by-step explanation:
I chose choice c because in the relation we can see that the x-value 1 repeated but their y-values are different, one has 0 as its y-value and one has -2 as its y-value. In a function, this can't happen so it's not a function.
Hope this helps you
please help! asap! thanks! xoxoxo
Answer:
B
Step-by-step explanation:
Don't know how to type those here so see attachment
Answer:
x = √29
Step-by-step explanation:
a^2 + b^2 = c^2
5^2 + 2^2 = c^2
25 + 4 = c^2
29 = c^2
√29 = √c^2
√29 = c
x = √29
La regla de Ruffini es un procedimiento que nos permite dividir fácilmente un polinomio cuando el divisor es un binomio de la forma (x ± a). *
Verdadero
Falso
Answer:
si como estas chico
Step-by-step explanation:
HELPPP :(
Max is mountain hiking at a constant rate.
This equation y = 10x + 30 can be used to represent this situation, where y is Max's elevation in meters and x is the number of hours Max has been hiking.
Which statement best describes Max's elevation, given this equation?
Max started at a height of 10 meters and is ascending at 30 meters per hour.
Max started at a height of 10 meters and is descending at 30 meters per hour.
Max started at a height of 30 meters and is ascending at 10 meters per hour.
Max started at a height of 30 meters and is descending at 10 meters per hour.
(If you don’t know the answer, please don’t spam :<)
Answer:
D.) Max started at a height of 30 meters and is ascending at 10 meters per hour.
The statement that best describes Max's elevation, given this equation is
D.) Max started at a height of 30 meters and is ascending at 10 meters per hour.
Given that,
This equation y = 10x + 30 can be used to represent this situation, where y is Max's elevation in meters and x is the number of hours Max has been hiking.Explanation regarding the statement:The max should begins at the height of 30 meters. And, the ascending at 10 meters per hour.Learn more about the height here: https://brainly.com/question/5281804
Jesse plays basketball for his high school team. In his last 12 twelve games he scored the following points: 18, 22, 19, 15, 24, 22, 18, 15, 10, 14, 18, 10. Barbara plays basketball for her high school team. In her last 10 games she scored the following points: 15, 12, 12, 16, 18, 22, 16, 20, 20, 14. Determine which player had the largest range of points scored? What is the difference is the range of points between the two players?
In the form of a paragraph, explain in complete sentences the steps necessary to compute the range of the points, which team player had the largest range of points and include the final answer in your explanation. Complete your work in the space provided.
Answer:
Jesse has the largest range between the two players. The difference between their ranges is 2.
Step-by-step explanation:
Jesse's range: 14
Barbara's range: 10
Range is determined by using the largest number and the smallest number in a set of integers and subtracting them. Jesse's highest number was 24, and his lowest would be 10. 24-10=14.
Barbara's highest score was 22, while her lowest was 12. 22-12=10.
subtracting Jesse's range from Barbara's range would equal 2.
(please don't cook me if this is incorrect but i'm 97% sure i'm right)
abcd is a trapezium, calculate the area of abcd
What is 95 feet in inches
Answer:
1140 in.
Step-by-step explanation:
Multiply the length value by 12, so 95*12=1140
Have a beautiful day! v(⌒o⌒)v♪
Help me pleade help me
A. Explain how you know that Triangle ABC is similar to Triangle A'B'C'. (use complete sentences and show all your work to get full credit)
B. If AC = 8, A'C' = 12, and AB = 20 what is the length of A'B'?
Answer:
A. Since the 3 angles in ∆ABC are congruent to the corresponding 3 angles in ∆A'B'C', therefore, ∆ABC is similar to ∆A'B'C'.
B. A'B' = 30
Step-by-step explanation:
A. Two triangles are said to be similar if their corresponding angles are congruent to each other.
To know whether ∆ABC and ∆A'B'C' are similar, let's find the measure of their angles each, and see if their corresponding angles are congruent to each other.
∆ABC:
m<A = 59°
m<B = 37°
m<C = 180 - (37 + 59) = 84°
∆A'B'C':
m<A' = 59°
m<B' = 180 - (59 + 84) = 37°
m<C' = 84°
As we can see,
Angle A is congruent to Angle A'
Angle B is congruent to Angle B'
Angle C is congruent to Angle C'
Therefore, since the 3 angles in ∆ABC are congruent to the corresponding 3 angles in ∆A'B'C', therefore, ∆ABC is similar to ∆A'B'C'.
B. AC = 8; A'C' = 12; AB = 20
Since ∆ABC is similar to ∆A'B'C', the ratio of their corresponding sides would be equal.
Therefore:
AC/A'C' = AB/A'B'
Plug in the values into the equation
8/12 = 20/A'B'
Cross multiply
A'B'*8 = 20*12
A'B'*8= 240
Divide both sides by 8
A'B' = 240/8
A'B' = 30
Given point (2,-5) and slope 1, fill in the blanks to put in point slope form. y-____=____(x-___) *
Answer:
y =
[tex] \frac{ - 5}{2} x[/tex]
Step-by-step explanation:
The slope is 1 so that makes it
1x
1x is just x
x
y/x is the slope
-5/2
there is no y-int so the equation is
y= (-5/2)x
What is the equation of the line that passes through the points (4, 5) and (7, 3)
Answer:
y = -2/3x + 23/3
Step-by-step explanation:
Let equation of the line be y = mx + c
m = (3-5)/(7-4) = -2/3 gradient/slope formula
sub (4, 5)
5 = -2/3 (4) + c
c = 23/3
therefore, equation of the line is y = -2/3x + 23/3
Hope it helps! :)
This is a topic called coordinate geometry. If you would like to find out more you can follow learntionary on instagram. I'll be posting some notes on coordinate geometry soon and I'll also post other useful math stuff as well :)
Terry has $5.79 to go shopping Which mixed number below is the fraction equivalent to $5.79? 500 a 5 79/100 b. 5 79/1000 57 9/100 d 57 9/10
Answer:
579/100 is the same if u turned it into a decimal it would be 5.79
Step-by-step explanation:
you would do 579 divided by 100 and that will give you 5.79
Answer:
the answer is 579/100
Step-by-step explanation:
The sum of four consecutive integers is -118. What is the largest of the integers?
Answer:
-28
Step-by-step explanation:
the four number are -28, -29, -30, and -31. they are all consecutive meaning all before or after the previous number. The sum is -118 making then all negative so when you add all the negative numbers you get and even bigger negative number. it is -28 because -28 is closest to 0.
Evaluate the function f(x) = 2x + 8 when x= 6 .
A 28
B 96
C None of the other answers are correct
D 16
E 20
Answer:
-1 or f = 1.333333333 + 0.3333333333x
is what i got its not an answer so im sorry
Step-by-step explanation:
Simplifying
f(6) = 2x + 8
Reorder the terms for easier multiplication:
6f = 2x + 8
Reorder the terms:
6f = 8 + 2x
Solving
6f = 8 + 2x
Solving for variable 'f'.
Move all terms containing f to the left, all other terms to the right.
Divide each side by '6'.
f = 1.333333333 + 0.3333333333x
Simplifying
f = 1.333333333 + 0.3333333333x
Answer:
Answer is 28
Step-by-step explanation:
Had the same question and answer was 28 you can thank me later :D
Please hwlp! Ava is driving her car. At the end of 2 hours she has driven 92 miles, and at the end of 5 hours she has driven 245 miles. What is her average rate of change?
_(blank)_ miles per hour
Park rangers at a game preserve in Africa observed a cheetah run 3
3
5
miles in
1
20
hour. What was the cheetah’s speed in miles per hour (mph)?
A.
9
50
mph
B. 5
5
9
mph
C. 72 mph
D. 92 mph
2
Among other ingredients, a recipe for paella calls for
3
4
pound of chorizo and
1
2
cups of rice. What is the unit rate of pounds of chorizo to cups of rice in the recipe?
A.
3
10
pound of chorizo per cup of rice
B.
8
15
pound of chorizo per cup of rice
C. 1
7
8
pound of chorizo per cup of rice
D. 3
1
3
pound of chorizo per cup of rice
3
Mary Ellen has a white oak tree in her backyard. She observed that the tree had grown
2
3
foot in
3
4
year. What is the tree’s growth rate in feet p
Answer:
Cheetah's speed = 2.79 miles per hour
Step-by-step explanation:
Speed = Distance / Time
Distance = 335 miles, Time = 120 hours
So, speed = 335 / 120
Speed = 2.79 mph
Determime if the following lines are paraleel, perpendicular or neither.
The equation for the line that has a slope of −38 and passes through (0, 10) is please help me with this problem.
Answer:
y = -38x + 10Step-by-step explanation:
Slope- intercept form:
y + mx = bGiven
m = -38 and point (0, 10)As per given point, y-intercept is b = 10
So the equation is:
y = -38x + 10