Sketch the graph of each of the following quadratic functions: (a) f(x) = -2x² + 7x + 4 for -1 ≤ x ≤ 5.
Help me with this ques pleasee,i'll mark u as the brainliest!!
Answers
Answer:
Please find attached the graph of the function created with MS Excel showing the relevant points required to draw an approximate graph of the function on a graph paper
Step-by-step explanation:
The given quadratic function is f(x) = -2·x² + 7·x + 4
The range of the input (x) values = -1 ≤ x ≤ 5
The coefficient of the quadratic is negative -2, the graph is n shape
The intercept form of the function is given as follows;
-2·x² + 7·x + 4 = -1 × (2·x² - 7·x - 4)
-1 × (2·x² - 7·x - 4) = -1 × (2·x² + x - 8·x - 4)
-1 × (2·x² + x - 8·x - 4) = -1 × (x · (2·x + 1) - 4·(2·x + 1))
∴ -1 × (x · (2·x + 1) - 4·(2·x + 1)) = -1 × (2·x + 1)·(x - 4)
∴ f(x) = -2·x² + 7·x + 4 = -1 × (2·x + 1)·(x - 4)
At the x-intercepts, (2·x + 1) = 0 or (x - 4) = 0, which gives;
x = -1/2 or x = 4
Therefore, the x-intercepts are (-1/2, 0), (4, 0)
The equation in vertex form is given as follows;
f(x) = -2·x² + 7·x + 4 = -2·(x² - 7·x/2 + 2)
By applying completing the squares method, to x² - 7·x/2 - 2, we get;
Where x² - 7·x/2 - 2
x² - 7·x/2 = 2
x² - 7·x/2 + (-7/4)² = 2 + (-7/4)² = 81/15
(x - 7/4)² = 81/16
∴ (x - 7/4)² - 81/16 = 0 = x² - 7·x/2 - 2
∴ x² - 7·x/2 - 2 = (x - 7/4)² - 81/16
-2·(x² - 7·x/2 + 2) = -2·((x - 7/4)² - 81/16) = -2·(x - 7/4)² + 81/8
The vertex = (7/4, 81/8)
When x = 0, we get;
f(0) = -2 × 0² + 7 × 0 + 4 = 4
The y-intercept = (0, 4)
The sketch of the function should pass through the x-intercepts (-1/2, 0), (4, 0), the y-intercept (0, 4), and the y-intercept (0, 4), and the vertex, (7/4, 81/8) on a graph sheet
Please find attached a drawing of the function of the function created with MS Excel
Related Questions
a drinks company use 76.8 kg of sugar in April .How much sugar the day use each day?
Answers
Answer:
2.56 kgs
Step-by-step explanation:
76.8kg ÷ 30 days = 2.56 kgs
Amount of sugar used - 76.8 kg
No. Of Days in Month of April - 30 days
∴ Sugar used each day is = 76.8 ÷ 30
[tex]76.8 \div 30 \\ \\ = \frac{76.8}{30} \\ \\ = \frac{768}{30 \times 10} \\ \\ = \frac{ \cancel{768}}{ \cancel{30} \times 10} \fbox{cancelling by 3} \\ \\ = \frac{256}{10 \times 10} \\ \\ = \frac{256}{100} \\ \\ = 2.56 \: kg[/tex]
So 2.56 kg is used everyday.Hope This Helps YouIf a apple cost d dollars, which of the following expressions gives the cost for 20 apples in dollars?
Answers
Answer:
$ 20d
Step-by-step explanation:
Since each Apple costs d dollars , therefore 20 will cost , $ 20d .
The correct expression that gives the cost of 20 apples, in dollars, is 20a/d. So, correct option is A.
To find the cost of 20 apples, we need to determine the expression that correctly calculates the cost based on the given variables.
Given that a represents the cost of one apple in dollars and d represents the number of dollars, we can identify the expression that calculates the cost of 20 apples.
Let's analyze each option:
A. 20a/d: This expression calculates the cost of 20 apples by multiplying the cost of one apple (a) by 20 and then dividing by d. Therefore, this expression correctly gives the cost of 20 apples in dollars.
B. 20d/a: This expression calculates the cost of 20 apples by multiplying the number of dollars (d) by 20 and then dividing by the cost of one apple (a). This does not give the correct cost of 20 apples.
C. a/20d: This expression calculates the cost of 20 apples by dividing the cost of one apple (a) by 20 and then dividing by d. This does not give the correct cost of 20 apples.
D. 20/ad: This expression calculates the cost of 20 apples by multiplying 20 by d and then dividing by the cost of one apple (a). This does not give the correct cost of 20 apples.
Therefore, the correct expression that gives the cost of 20 apples, in dollars, is A. 20a/d.
To learn more about equation/expression click on,
https://brainly.com/question/26372151
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Complete question is:
If a apples cost d dollars, which of the following expressions gives the cost of 20 apples, in dollars?
A. 20a/d
B. 20d/a
C. a/20d
D. 20/ad
What percentage of temperatures are below 55°? A. 50% B. 25% C. 75% D. 20%
Answers
Step-by-step explanation:
C
im not sure of my answer. hope to help
How do I find question number 43
Answers
Answer:
[tex]8)79 + .3y |1| 5131x - 2884 \frac{ {8 - { { - 44 - {516}^{ |?| } }^{?} }^{?} }^{2} }{?} 5 - {1 {y {1 {40091 - \times \frac{?}{?} }^{?} }^{2} }^{2} }^{2} 444 = .3 = 547 - 274[/tex]
Which one of these would be geometry or is it none of the above.
Answers
PLEASE HELP ASAP!!!!
Use the graph of ƒ to find x if ƒ(x) = 2.
x = –0.5
x = –8
(–∞, –0.5)
x = 0.5
Answers
Answer:
[tex]{ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}[/tex]
Help and explain pls and ty
Answers
[tex]\displaystyle\bf (3-5\sqrt{5} )-(5\sqrt{3} -3)=3+3-5\sqrt{5} -5\sqrt{3} =\boxed{6-5\sqrt{5} -5\sqrt{3} } \\\\\\\\\sqrt{5} (\sqrt{5} -2x)=\boxed{-2x\sqrt{5} +5}[/tex]
Pls answer this pls pls
Answers
1) 520
2)60
3)2600
4)3760
Answer:
1. 520
2. 60
3. 2600
4. 3760
Step-by-step explanation:
[tex]{hope it helps}}[/tex]
Thank you for the help!
Answers
Answer:
see explanation
Step-by-step explanation:
cosM = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{MN}{LM}[/tex] = [tex]\frac{8}{17}[/tex]
sinM = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{LN}{LM}[/tex] = [tex]\frac{15}{17}[/tex]
tanM = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{LN}{MN}[/tex] = [tex]\frac{15}{8}[/tex]
Sandra needs a new bicycle tire. Her tire has a circumference of about 113,04 inches. What is the radius of her tire?
Answers
Answer:
113,04 square root is 10.632027088 divided by Pi
3.38427933228
so the radius of her tire is 3.38
Hope This Helps!!!
Step 1: Write equation
To find the radius, we will go through the formula for the circumference. Let’s write the example equation now.
C= 2πr
Step 2: Substitute numbers
Now we can write the full equation, using the information from the question. The r will be the only number to stay the same, as we ar s working to find the radius. Let’s substitute the C in the equation for 113.04 as given in the equation.
C= 2πr
113.04= 2πr
Step 3: Solve
For step 3, we can solve the equation. Let’s start by rewriting the equation.
113.04= 2πr
Now let’s multiply what is available on the right side. This would be 2 and pi. For the sake of the equation, pi will be rounded to 3.14.
113.04= 2πr
113.04= 2•3.14•r
113.04= 6.28r
Now let’s work to get r alone on the right side. We can do so by dividing each term by 6.28, on both the left and right side.
113.04= 6.28r
113.04/6.28= 6.28r/6.28
18= r
This is your answer! To be sure, let’s check our answer in the final step.
Step 4: Check
To ensure that we got the right answer, let’s rewrite the original formula, and solve it to see if the answer is the same on the left and right side.
C= 2πr
113.04= 2•3.14•18
113.04= 6.28•18
113.04= 113.04
Our answer is correct. 18 inches is the length of the radius. Hope this helps! Comment below for more questions.
please help me! im having trouble
Answers
Answers:
3 chocolate cones
1 strawberry cones
===========================================================
Explanation:
Let's isolate the variable c in the first equation
c+s = 4
c = 4-s
we subtract s from both sides to get c all by itself. This will then be plugged into the second equation. I'm using the substitution property.
1.75c + 1.3s = 6.55
1.75(4-s) + 1.3s = 6.55 ..... replace c with 4-s
1.75*4 + 1.75*(-s) + 1.3s = 6.55
7 - 1.75s + 1.3s = 6.55
-0.45s + 7 = 6.55
-0.45s = 6.55 - 7
-0.45s = -0.45
s = -0.45/(-0.45)
s = 1
So he bought 1 strawberry cone. Use this value of s to find c
c = 4-s
c = 4-1
c = 3
This says he also bought 3 chocolate cones.
-------------------
As a check, we see that c+s = 3+1 = 4, showing that he bought 4 cones total.
Also,
1.75c + 1.3s = 1.75*3 + 1.3*1 = 6.55
indicating he spent $6.55 total for the four cones. This matches with what the instructions tell us, so the answer is confirmed.
Answer:
Step-by-step explanation:
[tex]\left \{ {{c+s=4} \atop {1.75c+1.3s=6.55}} \right.[/tex]
1.75c + 1.75s = 1.75 × 4 ........ (1)
1.75c + 1.3s = 6.55 ........ (2)
(1) - (2)
0.45s = 0.45 ⇒ s = 1
c + 1 = 4 ⇒ c = 3
[ 3 ] chocolate [ 1 ] strawberry
A rectangular prism has a height of 12 centimeters and a square base with sides measuring 5 centimeters. A pyramid with the same base and half the height of the prism is placed inside the prism, as shown in the figure.
The volume of the space outside the pyramid is _ cubic centimeters.
Answers
Answer:
the answer is 200cm^3
explication
Which is the equation of a line perpendicular to the line with the equation: y = −14x + 7
y = -4x - 7
y = 4x + 2
y = 14x − 12
y = −14x + 3
Answers
Which set of numbers includes only integers?
a.)Negative 5, negative 3 and one-fourth, 1, one-eighth
b.)Negative 3, negative 2, 2, 3
c.)Negative 6, negative 4, negative 2, negative one-half
d.)One-half, two-thirds, StartFraction 6 Over 7 EndFraction, 0
Answers
Answer:
a
Step-by-step explanation:
in integer there will negative ,positive or rational number
HELP SOMEONE PLSSSSS
Answers
4y=8x
Isolate y by dividing both sides by 4
Y=2x
Sub every y with 2x
Answer is A
solve for x -3x+2=-11 please
Answers
Answer:
6.5
Step-by-step explanation:
We need to solve out for x , the given Equation is ,
[tex]: \implies[/tex] x - 3x + 2 = -11
[tex]: \implies[/tex] -2x = -11 -2
[tex]: \implies[/tex] -2x = -13
[tex]: \implies[/tex] x = -13/-2
[tex]: \implies[/tex] x = 6.5
Answer:
x = 6.5
Step-by-step explanation:
[tex]x - 3x + 2 = - 11 \\ - 2x + 2 = - 11 \\ - 2x = - 11 - 2 \\ \frac{ - 2x}{ - 2} = \frac{ - 13}{ - 2} \\ x = + 6.5 [/tex]
Which expression is equivalent to c+c - 7c?
7с
1- 6c
-5c
c- 6
Answers
[tex]\huge\textsf{Hey there!}[/tex]
[tex]\large\textsf{Variables by itself with no number with it is understood as an invisible}\\\large\textsf{1}[/tex]
[tex]\huge\textsf{c + c - 7c}[/tex]
[tex]\huge\textsf{= 1c + 1c - 7c}[/tex]
[tex]\huge\text{COMBINE the LIKE TERMS}[/tex]
[tex]\large\textsf{= (1c + 1c - 7c)}[/tex]
[tex]\large\textsf{1c + 1c = \bf 2c}[/tex]
[tex]\large\textsf{= 2c - 7c}[/tex]
[tex]\large\textsf{= \bf -5c}[/tex]
[tex]\boxed{\boxed{\huge\textsf{Answer: \underline{Option C. \bf -5c}}}}\huge\checkmarl[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
[tex]\boxed{\large{\bold{\textbf{\textsf{{\color{blue}{Answer}}}}}}:)}[/tex]
C+c-7c2c-7c(2-7)C-5C Classwork Let's tick (V) the correct answer.
a) The terms of expression 5x2 – 3xy are (i) 5x² and 3xy (ii) x and xy (iii) 5x2 and - xy
Answers
Answer:
Option i
Step-by-step explanation:
The given expression is , 5x² - 3xy .
We can clearly see that there are two terms in the expression , 5x² and 3xy .
Therefore option (i) is correct .
Can someone help me please this is my last one
Answers
Answer:
Domain and range: [0, ∞)
Step-by-step explanation:
There is no limit to the number of concert tickets someone can buy, but there cannot be negative concert tickets. The domain, or what the input can be, is [0, ∞) as it can be greater than or equal to 0
The range is the total cost, or what the output can be. Since the total cost is the number of tickets multiplied by 55 (as it is $55 per ticket), this can be represented by 55 * number of tickets. The total cost cannot be negative, but it can be 0 if no one buys tickets. As there is no limit to the amount of tickets someone can buy, there is no limit to what the total cost could be, making the range [0, ∞)
Sabe-se que EF = xcm , GH = (x + 6) cm , RS = 16 cm e NP = 28 cm . Sabendo que EF ,GH , RS ,e NP São, nessa ordem, segmentos proporcionais, determine o valor de x .
Answers
Answer:
The value of x is 8 .
Step-by-step explanation:
It is known that EF = x cm , GH = (x + 6) cm , RS = 16 cm and NP = 28 cm . Knowing that EF ,GH , RS , and NP are, in that order, proportional segments, determine the value of x .
As EF, GH, RS and NP are in proportion
So,
EF : GH = RS : NP
[tex]\frac{x}{x+6}=\frac{16}{28}\\\\7 x = 4 (x + 6)\\\\7 x = 4 x + 24 \\\\3 x = 24 \\\\x = 8[/tex]
−3x−8y=−8 y=2−x Is (0,1)(0,1)left parenthesis, 0, comma, 1, right parenthesis a solution of the system?
Answers
Answer:
(0,1) is not the solution to the equation
Step-by-step explanation:
Given:
−3x − 8y = −8 (1)
y = 2 − x (2)
Substitute (2) into (1)
−3x − 8y = −8 (1)
- 3x - 8(2 - x) = -8
- 3x - 16 + 8x = -8
- 3x + 8x = -8 + 16
5x = 8
x = 8/5
Substitute x = 8/5 into (2)
y = 2 − x (2)
= 2 - 8/5
= (10-8) / 5
= 2/5
y = 2/5
Solution to the equation:
(x, y) = (8/5, 2/5)
Therefore,
(0,1) is not the solution to the equation
Help me out please, thank you
Answers
Answer:
The answer is D (-0.7)
Step-by-step explanation:
Using d formular,a is 1,b is -5,c is -4
Input ur values and u will get ur answer
Type the correct answer in the box. Solve the given equation by completing the square. x^2+ 8x = 38 Fill in the values of a, b, and c to complete the solutions
Answers
Answer:
A=2
B=8
C=-38
X=2.8/X=-6.8
Step-by-step explanation:
can someone please help me solve this? thank you!:)
Answers
First, we need to set up our two equations. For the picture of this scenario, there is one length (L) and two widths (W) because the beach removes one of the lengths. We will have a perimeter equation and an area equation.
P = L + 2W
A = L * W
Now that we have our equations, we need to plug in what we know, which is the 40m of rope.
40 = L + 2W
A = L * W
Then, we need to solve for one of the variables in the perimeter equation. I will solve for L.
L = 40 - 2W
Now, we can substitute the value for L into L in the area equation and get a quadratic equation.
A = W(40 - 2W)
A = -2W^2 - 40W
The maximum area will occur where the derivative equals 0, or at the absolute value of the x-value of the vertex of the parabola.
V = -b/2a
V = 40/2(2) = 40/4 = 10
Derivative:
-4w - 40 = 0
-4w = 40
w = |-10| = 10
To find the other dimension, use the perimeter equation.
40 = L + 2(10)
40 = L + 20
L = 20m
Therefore, the dimensions of the area are 10m by 20m.
Hope this helps!
Answer:
Width: 10 m
Length: 20 m
Step-by-step explanation:
Hi there!
Let w be equal to the width of the enclosure.
Let l be equal to the length of the enclosure.
1) Construct equations
[tex]A=lw[/tex] ⇒ A represents the area of the enclosure.
[tex]40=2w+l[/tex] ⇒ This represents the perimeter of the enclosure. Normally, P=2w+2l, but because one side isn't going to use any rope (sandy beach), we remove one side from this equation.
2) Isolate one of the variables in the second equation
[tex]40=2w+l[/tex]
Let's isolate l. Subtract 2w from both sides.
[tex]40-2w=2w+l-2w\\40-2w=l[/tex]
3) Plug the second equation into the first
[tex]A=lw\\A=(40-2w)w\\A=40w-2w^2\\A=-2w^2+40w[/tex]
Great! Now that we have a quadratic equation, we can do the following:
Solve for its zeros/w-intercepts.Take the average of the zeros to find the w-variable of the vertex. (The area (A) in relation to the width of the swimming area (w) is what we've established in this equation, and the area (A) is greatest at the vertex. Finding the value of w of the vertex will tell us what the width needs to be for the area to be at a maximum.)Plug this w value into one of the equations to solve for l4) Solve for w
[tex]A=-2w^2+40w[/tex]
Factor out -2w
[tex]A=-2w(w-20)[/tex]
For A to equal 0, w=0 or w=20.
The average of 0 and 20 is 10, so the width that will max the area is 10 m.
5) Solve for l
[tex]40=2w+l[/tex]
Plug in 10 as w
[tex]40=2(10)+l\\40=20+l\\l=20[/tex]
Therefore, the length of 20 m will max the area.
I hope this helps!
__1. What is the other term for Q3?
2. What measure of position is divided into four equal parts?
3. How many equal parts is the quartile divided into?
4. How many percentile is equivalent to Q1?
5. What is the other term for Median?
_6. What is the equivalence of D2 to Percentile?
7. What measure of position is divided into 10 equal parts?
_8. What measure of position is divided into 100 equal parts?
9. What is the decile equivalence of P80?
10. What quartile is equivalent to P75?
Answers
Answer:
1. The third quartile
2. The quartile
3. Four
4. 25
5. The second quartile, Q₂
6. 20th percentile
7. Decile
8. Percentile
9. D₈
10. The third quartile, Q₃
Step-by-step explanation:
1. The other term(s) for Q₃ is third quartile (or upper quartile). It is the mid point between the distribution's largest number and the median
2. The measure of position divided into four equal parts is the quartile
3. The quartile is the division of the data at three points (Q₁, Q₂, and Q₃) into four equal parts equal parts
4. Q₁, which is the first quartile is equivalent to the 25th percentile
5. The other term for the median is the second quartile, Q₂
6. D₂ which is the second decile (a decile divides the data into 10 equal parts) is equivalent to 20th percentile
7. The decile, D, divides a given data into 10 equal parts
8. The percentile divides a given data into 100 equal parts
9. The decile equivalent to P80, which is the 80th percentile, is D₈
10. The quartile equivalent to P75, which is the 75th percentile or the three quarter mark point of the data is equivalent to the the third quartile, Q₃
How many ways can you order a hamburger if you can order it with or without cheese, ketchup, mustard, bacon, mayo, or lettuce?
1. 66
2. 69
3. 64
4. 68
Answers
Answer:
64
Step-by-step explanation:
2x2x2x2x2x2 = 64
STREAM WALLS BY LOUIS TOMLINSON
Answers
Being a directioner love there songs XD *smiles*
Answer:
OMG I LOVE LOUIS SO MUCH HE IS SO PERFECT
Step-by-step explanation:
If a circle has a diameter of 16 feet, which expression gives its area in square
feet?
A. 8^2•r
B. 16^2 •r
C.8•r
D. 16•r
Answers
Answer:
Area of a circle is denoted by: πr^2 where r is the radius of the circle. = 16/2 = 8 feet.
Step-by-step explanation:
-4y=-20
Graph each line that represents each linear equation
Answers
Answer:
y = 5
Step-by-step explanation:
The given equation to us is
⇒ -4y = -20
⇒ y = -20/-4
⇒ y = 5
Therefore this line will pass 5 units away from y axis. For graph refer to the attachment .
More Information :-
The equation of x axis is y = 0 The equation of y axis is x = 0 .The transformation which will map triangle PQR onto P'Q'R is
Answers
Given:
The graph of triangle PQR and triangle P'Q'R'.
To find:
The transformation that will map the triangle PQR onto P'Q'R'.
Solution:
From the given graph it is clear that the triangle PQR is formed in II quadrant and its base lies on the negative direction of x-axis.
The triangle P'Q'R' is formed in IV quadrant and its base lies on the positive direction of x-axis.
This is possible it the figure is rotated 180 degrees about the origin.
Therefore, the correct option is A.