Given:
The function is:
[tex]f(x)=-2x^2+7x+4[/tex]
To find:
Express the quadratic equation in the form of [tex]f(x)=a(x-h)^2+k[/tex], then state the minimum or maximum value,axis of symmetry and minimum or maximum point.
Solution:
The vertex form of a quadratic function is:
[tex]f(x)=a(x-h)^2+k[/tex] ...(i)
Where, a is a constant, (h,k) is the vertex and x=h is the axis of symmetry.
We have,
[tex]f(x)=-2x^2+7x+4[/tex]
It can be written as:
[tex]f(x)=-2\left(x^2-3.5x\right)+4[/tex]
Adding and subtracting square of half of coefficient of x inside the parenthesis, we get
[tex]f(x)=-2\left(x^2-3.5x+(\dfrac{3.5}{2})^2-(\dfrac{3.5}{2})^2\right)+4[/tex]
[tex]f(x)=-2\left(x^2-3.5x+(1.75)^2\right)-2\left(-(1.75)^2\right)+4[/tex]
[tex]f(x)=-2\left(x-1.75\right)^2+2(3.0625)+4[/tex]
[tex]f(x)=-2\left(x-1.75\right)^2+6.125+4[/tex]
[tex]f(x)=-2\left(x-1.75\right)^2+10.125[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=-2,h=1.75,k=10.125[/tex]
Here, a is negative, the given function represents a downward parabola and its vertex is the point of maxima.
Maximum value = 10.125
Axis of symmetry : [tex]x=1.75[/tex]
Maximum point = (1.75,10.125)
Therefore, the vertex form of the given function is [tex]f(x)=-2\left(x-1.75\right)^2+10.125[/tex], the maximum value is 10.125, the axis of symmetry is [tex]x=1.75[/tex] and the maximum point is (1.75,10.125).
A study was conducted by a team of college students for the college research center. From the study, it was reported that most shoppers have a specific spending limit in place while shopping online. The reports indicate that men spend an average of $230 online before they decide to visit a store. If the spending limit is normally distributed and the standard deviation is $19.
(a) Find the probability that a male spent at least $210 online before deciding to visit a store. Ans: ____________
(b) Find the probability that a male spent between $240 and $300 online before deciding to visit a store. Ans: ____________
(c) Find the probability that a male spent exactly $250 online before deciding to visit a store. Ans: (d) Ninety-one percent of the amounts spent online by a male before deciding to visit a store are less than what value? Ans: ____________
Answer:
0.8536
0.29933
Step-by-step explanation:
Given :
Mean amount spent, μ = $230
Standard deviation, σ = $19
1.)
Probability of spending atleast $210
P(x ≥ 210)
The Zscore = (x - μ) / σ = (210 - 230) / 19 = - 1.052
P(Z ≥ -1.052) = 1 - P(Z ≤ - 1.052) = 1 - 0.1464 = 0.8536
2.)
Probability that between $240 and $300 is spent:
P(x < $240) = Zscore = (240 - 230) / 19 = 0.526
P(Z < 0.526) = 0.70056
P(x < 300) = Zscore = (300 - 230) / 19 = 3.684
P(Z < 3.684) = 0.99989
P(Z < 3.684) - P(Z < 0.526)
0.99989-0.70056 = 0.29933
Persons taking a 30-hour review course to prepare for a standardized exam average a score of 620 on that exam. Persons taking a 70-hour review course average a score of 749. Find a linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course. Round your answer to the tenths place.
Given:
30-hour review course average a score of 620 on that exam.
70-hour review course average a score of 749.
To find:
The linear equation which fits this data, and use this equation to predict an average score for persons taking a 57-hour review course.
Solution:
Let x be the number of hours of review course and y be the average score on that exam.
30-hour review course average a score of 620 on that exam. So, the linear function passes through the point (30,620).
70-hour review course average a score of 749. So, the linear function passes through the point (70,749).
The linear function passes through the points (30,620) and (70,749). So, the linear equation is:
[tex]y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
[tex]y-620=\dfrac{749-620}{70-30}(x-30)[/tex]
[tex]y-620=\dfrac{129}{40}(x-30)[/tex]
[tex]y-620=\dfrac{129}{40}(x)-\dfrac{129}{40}(30)[/tex]
[tex]y-620=\dfrac{129}{40}(x)-\dfrac{387}{4}[/tex]
Adding 620 on both sides, we get
[tex]y=\dfrac{129}{40}x-\dfrac{387}{4}+620[/tex]
[tex]y=\dfrac{129}{40}x+\dfrac{2480-387}{4}[/tex]
[tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex]
We need to find the y-value for [tex]x=57[/tex].
[tex]y=\dfrac{129}{40}(57)+\dfrac{2093}{4}[/tex]
[tex]y=183.825+523.25[/tex]
[tex]y=707.075[/tex]
[tex]y\approx 707.1[/tex]
Therefore, the required linear equation for the given situation is [tex]y=\dfrac{129}{40}x+\dfrac{2093}{4}[/tex] and the average score for persons taking a 57-hour review course is 707.1.
what is the length of KM ? NO LINKS .
Answer:
80 units
Step-by-step explanation:
KN = MN
9x - 5 = 7x + 7
2x = 12
x = 6
KM = 2KL
KM = 2(6x + 4)
KM = 12x + 8
KM = 12(6) + 8
KM = 80
Answer:
80
Step-by-step explanation:
a train leaves Westchester at 6:30. What time should it arrive at Middlewich
Answer:
a). 6:51
b). 6:30 am
c). 34 minutes
Step-by-step explanation:
a). Train leaves Westchester at 6:30.
From the arrival - departure table in column (2),
Arrival time of the train at middlewich = 6:51
b). Kate has to reach Southam before 9:00 am
Therefore, time of the latest train that she can catch to get to work on time is 6:30 am
By this train she can reach at 07:19 at Southam.
c). Duration of journey from Westchester to Eastwick = 06:34 - 06:00
= 00:34
≈ 34 minutes
In the coordinate plane, two vertices of square ABCD are A (0, 0) and B (0, m). What are the coordinates of points C and D? Do not introduce any new variables.
Answer:
The coordinate of point C is (m,m) and the coordinate of point D is (m,0).
Step-by-step explanation:
Square:
In a square, all sides have the same length.
A (0, 0) and B (0, m).
This means that the length of the sides is m.
So:
From A, adding m vertically, we get point (0,m), which is B.
From A, adding m horizontally, we get point (m,0), which I will call D.
From B, adding m horizontally, we get point (m,m), which I will call C.
The coordinate of point C is (m,m) and the coordinate of point D is (m,0).
In ∆ABC ,D and E are points on the sides AB and AC respectively such that DE is parallel to BC , 1) If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC. 2) If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm , find x 3) I f AD =2cm ,BD = 4cm , show that BC = 3 DE
Answer:
1). AC=8.25cm
2). DB=7cm & EC=14cm
3). See Explanation
Step-by-step explanation:
According To the Question,
Given That, In ∆ABC, D and E are points on the sides AB and AC respectively such that DE is parallel to BC.
1). If AD= 2.5 cm ,BD = 3cm ,AE = 3.75 cm find length of AC.
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD / BD = AE / EC
⇒ 2.5 / 3 = 3.75 / EC
On Solving we get,
⇒ EC * 2.5 = 3.75 * 3
⇒ EC * 2.5 = 11.25
⇒ EC = 11.25 / 2.5
⇒ EC = 4.5 cm
Thus,
AC = AE + EC
⇒ AC = 3.75 + 4.50
⇒ AC = 8.25 cm
Hence the measure of AC is 8.5 cm.
2). If AD = 4 cm , AE =8cm ,DB =x – 4 cm ,EC =3x -19 cm
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD / BD = AE / EC
⇒ 4 / (x-4) = 8 / (3x-19)
on solving we get,
⇒ 3x-19 = 2(x-4)
⇒ 3x-19 = 2x-8
⇒x=11
Thus, DB =x–4 ⇒ 11-4 ⇒ DB=7cm
And, EC =3x-19 ⇒ 3×11-19 ⇒ EC=14cm
3). If AD=2cm , BD= 4cm , show that BC = 3 DE
Thus, AB = AD + DB = 2+4 = 6cm
Well we can apply Basic proportionality Theorem.
Since DE ║ BC ⇒ Sides are proportional and the angles are equal.
⇒ AD/AB = DE / BC
⇒ 2 / 6 = DE / BC
on solving we get
⇒ BC = 3 DE Hence, Proved
fy
This graph shows a portion of an even function,
Use the graph to complete the table of values.
6
X
f(x)
-1
4
-3
-5
-6
2
DONE
2
Answer:
From top to bottom;
1,1,3,3
Step-by-step explanation:
mathematically, for an even function;
f(x) = f(-x)
what this mean is that;
f(-1) = f(1)
f(-3) = f(3)
f(-5) = f(5)
f(-6) = f(6)
so we have it that;
f(-1) = 1
f(-3) = 1
f(-5) = 3
f(-7) = 3
What is the answer??
Answer:
80°
Step-by-step explanation:
Triangle ABC and CYZ are similar so the angles would also be same
Can someone help me with this
Answer:
use system of equations
Step-by-step explanation:
Set one up for the Smith family and one for the Jones family
Find the area
Please help me
Answer: 24 square cm.
8*6=48
48/2=24
Answer:
24 cm^2
Step-by-step explanation:
(w*h)/2
Type the correct answer in each box.
Bridget went fishing with her dad. Bridget caught the first fish of the day, and it weighed f ounces. That day, she caught four more fish. One was
2
times the weight of the first fish, another was
2
more than
3
times the weight of the first fish, the next was
1
2
the weight of the first fish, and the last was
3
5
the weight of the first fish.
Bridget’s dad caught four fish. The first fish he caught weighed
2
more than
3
times the weight of the first fish caught that day.
One fish weighed
4
5
the weight of the first fish caught that day, one weighed
4
more than
2
times the weight of the first fish caught that day, and the last weighed
1
2
the weight of the first fish caught that day.
Answer:
PLZZ MARK ME BRAINLIEST..!
Step-by-step explanation:
Bridgets fish: f , 2f, 3f+2 , 1/2f, 3/5f
Add for total weight: 7 1/10 f +2
Dads fish: 3f+2, 4/5f, 2f+4, 1/2f
Add for total weight: 6 3/10f +6
set the 2 total weights equal:
6 3/10f +6 = 7 1/10f +2
Subtract 6 3/10f from each side:
6 = 8/10f + 2
Subtract 2 from each side:
4 = 8/10f
Divide both sides by 8/10:
f = 5
Bridget's first fish weighed 5 ounces.
Dads first fish weighed: 2 more than 3 times :3(5) + 2 = 15 +2 = 17 ounces.
Use the graph to estimate the solutions to 4 log2 (2x) = x + 4. Select all that apply.
Given:
The equation is:
[tex]4\log_2(2x)=x+4[/tex]
The graph of the [tex]4\log_2(2x)[/tex] and [tex]x+4[/tex] are given on a coordinate plane.
To find:
The solution of the given equation from the given graph.
Solution:
From the given graph it is clear that the graphs of [tex]4\log_2(2x)[/tex] and [tex]x+4[/tex] intersect each other at points (1.24,5.24) and (16,20).
It means the values of both functions [tex]4\log_2(2x)[/tex] and [tex]x+4[/tex] are equal at [tex]x=1.24[/tex] and [tex]x=16[/tex].
So, the solutions of given equation are [tex]x=1.24[/tex] and [tex]x=16[/tex].
Therefore, the correct option is only F.
PLS HELP FAST! I NEED THIS FAST :((
Answer:
In order:
Distributive Property
Subtraction Property of Equality
Division Property of Equality or Reciprocal Property
Step-by-step explanation:
Graph the solution set to this inequality. -4(x+ 3) ≤-2x
Answer:
hey hope the given pic are helpful(sorry for my bad writing)
6. Find the value of x to the nearest tenth.
Answer:
Step-by-step explanation:
[tex]Cos \ 39 = \frac{adjacent \ side}{hypotenuse}\\\\0.7771 = \frac{7}{x}[/tex]
x * 0.7771 = 7
[tex]x =\frac{7}{0.7771}=9.007[/tex]
x = 9
Brainly to whomever somehow solves for g & k. I WILL REPORT SCAMS AND UNHELPFUL/ UNRELATED ANSWERS.
Answer:
g = 48
k = 18
Step-by-step explanation:
h / 10 = 60 / 12
h / 10 = 5
h = 5 x 10
h = 50
40 / h = g / 60
40 / 50 = g / 60
4 / 5 = g / 60
g = ( 60 x 4 ) / 5
= 12 x 4
g = 48
90 / k = 60 / 12
90 / k = 5
k = 90 / 5
k = 18
the question is in the picture below
Answer:
$843.67
Step-by-step explanation:
We can use a proportion to solve this problem:
12 : 100 = x : 896
x =(896 * 12)/100 = $107,52
896 - 107.52 = $788,48 (price of the computer after the discount)
7 : 100 = x : 788,48
x = (788,48 * 7)/100 = $55,1936
788.48 + 55,1936 = 843,6736 = $843.67 (final price)
It take 4 people 40 minutes to clean a garden. How long will it take 6 people to clean the same garden
Answer:
4/9 of an hour (26.666 minutes)
Step-by-step explanation:
4 * x * 40/60 = 1
x * 160/60 = 1
x=60/160 = 6/16 = 3/8 (this is the rate for one worker)
~~~~~~~~~~~~~~~~
6 * (3/8) * x = 1
x = 4/9
Peter owned a juice shop. He sold a cup of lemon juice for $1.25 and a cup of apple juice for $2.50. If Peter sold a total of 155 cups of juice and collected a total of $256 approximately, how many cups of each type did he sell?
The number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.
What is a system of equation?A system of equations is a set or collection of equations that you deal with all together at once. For a system to have a unique solution, the number of equations must equal the number of unknowns.
For the given situation,
Peter sold a cup of lemon juice = $1.25
Peter sold a cup of apple juice = $2.50
Total number of cups sold = 155 cups
Total amount = $256
Let number of cup of lemon juice be x and
let number of cup of apple juice be y
The equations for the above statements are
[tex]x + y = 155 ------- (1)\\1.25x +2.50y = 256 ------- (2)[/tex]
From equation 1,
⇒ [tex]x=155-y[/tex]
Now substitute x in equation 2,
⇒ [tex]1.25(155-y)+2.50y=256[/tex]
⇒ [tex]193.75-1.25y+2.50y=256[/tex]
⇒ [tex]1.25y=256-193.75[/tex]
⇒ [tex]1.25y=62.25\\[/tex]
⇒ [tex]y=\frac{62.25}{1.25}[/tex]
⇒ [tex]y=49.8[/tex] ≈ [tex]50[/tex]
Now substitute y in equation 1,
⇒ [tex]x=155-50[/tex]
⇒ [tex]x=105[/tex]
Hence we can conclude that the number of cup of lemon juice is 105 cups and number of cup of apple juice is 50 cups.
Learn more about the system of equation here
https://brainly.com/question/12760602
#SPJ3
if a third plane could be drawn which contains both lines a and b .
Answer:
must be parallel
Step-by-step explanation:
They must be parallel.
does anyone know the domain and range of this?
Answer:
domain=1
range= -2
hope it helps
stay safe healthy and happy.If / is a midsegment of /, find x.
A.
2
B.
3
C.
6
D.
9
Please select the best answer from the choices provided
A
B
C
D
Answer:
It is d
Step-by-step explanation:
a bag contains three red marbles five blue marbles and seven green marbles.what is the ratio of blue marbles to the total number of marbles
Answer:
5:15 simplified as 1:3
Step-by-step explanation:
Length of a rope is 5 metre. What does it mean?
Step-by-step explanation:
Length of a rope is 5 meter. it means the rope is 5 meter long..
hope it helps.stay safe healthy and happy...Please help me out here
Answer:
vbw-kafw-hxy p.l.e.a.s.e join
Answer:
146 cm²
Step-by-step explanation:
The net is composed of 3 sets of congruent rectangles
top/ bottom + front/ back + sides
SA = 2(9 × 5) + 2(9 × 2) + 2(5 × 2)
= 2(45) + 2(18) + 2(10)
= 90 + 36 + 20
= 146 cm²
find the area of the rectangle whose dimensions are 9cm and 8cm.
Answer:
72 cm²
Step-by-step explanation:
Area = 9(8) = 72
..............
Which of the following statements is true?
A) All squares are rectangles.
B) All parallelograms are rectangles.
C) All rhombuses are squares.
D) All rectangles are squares. (D is Not the answer)
Which expression is equivalent to 8-(6r+2) HELP SMB PLEASE!
Answer:
A.
Step-by-step explanation:
A.-6r+6
the question is on the image.
Hi there!
[tex]\huge\boxed{\text{22 cm}}[/tex]
We know that:
Area of a rectangle = l × w
The areas are the same, so:
3x · 4 = 6(3x - 2.5)
Simplify:
12x = 18x - 15
Solve for x:
15 = 6x
x = 2.5
Plug in this value of x to find the perimeter of rectangle B:
P = 2l + 2w
l = 6
w = 3(2.5) - 2.5 = 5
P = 2(6) + 2(5) = 22 cm
Question
Example
Step by Step
A
You can represent the measures of an angle and its complement as xºand (90-x)º.
Similarly, you can represent the measures of an angle and its supplement as x and
(180 - x )°. Use these expressions to find the measures of the angles described.
The measure of an angle increased by 68° is equal to the measure of its complement.
The measure of the angle is
and the measure of its complement is
Answer:
The measure of the angle is 11 and its complement is 79 degrees
Step-by-step explanation:
Mathematically, when two angles are complementary, the sum of the angles equal 90 degrees
so now, if the first angle is x , the second angle which is increased by 68 degrees will be x + 68
So now if we add these two, the value we will get is 90 degrees
Mathematically, we have this as;
x + x + 68 = 90
2x + 68 = 90
2x = 90-68
2x = 22
x = 22/2
x = 11
the measure of the angle is 11 and its complement will be 11 + 68 = 79
