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
I will mark you brainlist if you helppp me pls and thankyouuu
Answers
Answer:
1 option is correct nd your answer is also correct
I have a lot of algebra problems. Someone help me even with this one please!
Answers
Answer: Choice A
L = 65 - 15d; discrete
===============================================
Explanation:
He starts with 65 cm of bread. After the first day he has 65-15 = 50 cm left over. After the second day he has 65-15*2 = 35 cm left over, and so on.
In general, he has 65-15d centimeters left over after d number of days have elapsed. For example, if d = 3 days pass by, then he has 65-15d = 65-15*3 = 65-45 = 20 cm left over.
So that's why the equation we're after is L = 65-15d where d is the number of days, and L is the amount left over in cm.
The number of days is discrete because we're dealing with the set of nonnegative numbers {0,1,2,3,4,...}. We can't have d = 2.5 for instance.
Because the input variable d is discrete, this automatically means L is discrete as well. Consider a finite domain such as {0,1,2,3}. This finite domain would map to the finite range {65,50,35,20}. These two finite sets are sufficient to say we have a discrete function.
A discrete function leads to a discrete graph which is simply a set of points. You would not connect the dots to form a straight line (simply leave the points as separate islands).
find k so that x-1 is a factor of x^3 - 3x^2 + kx - 1
Answers
Answer:
[tex]{ \bf {factor : { \tt{x - 1}}}} \\ x - 1 = 0 \\ x = 1 \\ { \tt{f(x) = {x}^{3} - {3x}^{2} + kx - 1}} \\ { \tt{f(1) : {(1)}^{3} - 3 {(1)}^{2} + k(1) - 1 = 0}} \\ { \tt{k - 3 = 0}} \\ { \tt{k = 3}}[/tex]
Answer:
k = 3
Step-by-step explanation:
If x-1 is a factor of x³ - 3x² + kx - 1 then value of x is 1.
f (x ) = x³ - 3x² + Kx - 1 , then
plug 1 as x in the expression.
f ( 1) = ( 1)³ - 3 ( 1)² + k (1) - 1 = 0expand exponents
1 - 3 + k - 1 = 0combine like terms
-3 + k = 0Add 3 to both side
k = 3A photograph measures five inches wide and six inches long. The picture is enlarged to fit on a wall. If the new larger picture is 150 inches wide, how long is it?
a. 180 inches
b. 250 inches
c. 210 inches
d. 200 inches
Answers
Answer:
A. 180Step-by-step explanation:
5×6= 30
150+30
= 180
Answer:
a
Step-by-step explanation:
x/150=6/5
x=6/5×150=6×30=180 inches.
Question 4 of 10 What is the equation of the following line? Be sure to scroll down first to see all answer options. (6,2) O A y= 22 B. y=-3x O c. y=6x O D. y = 1 x O E y=3x O F. y = 1 x
Answers
By using a (the slope) equals delta y divided by delta x
The equation of the line will be y = 1/3x. The correct option is F.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
The slope of the line is calculated as,
[tex]m = \dfrac{y_2-y_1}{x_2-x_1}[/tex]
The two points are (6,2) and (0,0). Calculate the slope of the line,
[tex]m = \dfrac{0 - 2}{0-6}[/tex]
m = 1 / 3
The equation of the line can be written as,
y = mx +c
y = 1/3x + 0
y = 1/3x
To know more about an equation of the line follow
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Which is expression is equivalent to (x^-4y/x^-9y^5)^-2
Answers
Answer:
[tex]\frac{y^8}{x^{10}}[/tex]
Step-by-step explanation:
Given
[tex](\frac{x^{-4}y}{x^{-9}y^5})^{-2}[/tex]
Required
The equivalent
Apply law of indices to the inner bracket
[tex](x^{-4--9}y^{1 -5})^{-2}[/tex]
[tex](x^{5}y^{-4})^{-2}[/tex]
Rewrite as:
[tex]\frac{1}{(x^{5}y^{-4})^2}[/tex]
Expand
[tex]\frac{1}{(x^{5*2}y^{-4*2})}[/tex]
[tex]\frac{1}{(x^{10}y^{-8})}[/tex]
Apply law of indices
[tex]\frac{y^8}{x^{10}}[/tex]
Suppose Ax = b always has at least one solution no matter what b is. Why AT y = 0 has only the trivial solution y = 0?
Answers
Answer:
For the first equation we have:
A*x = b
solving for x, we get:
x = b/A
If it always has a solution, then we can not have A = 0, because that causes an undefined operation.
so for example, if we have A = 1 and b = 2
x = b/A = 2/1
For the other case,
A*y = 0
dividing both sides by A
y = 0/A = 0
y = 0
Here we have only one possible solution, the trivial one, y = 0.
And the dependence on A disappears (because the quotient between zero and a number different than zero is always zero)
On a piece of paper graph f(x) 2x(3)^x then determine which graph represents the function
Answers
Answer:
ok
What do you want me to answer ?
does the point (-4, 2) lie inside or outside or on the circle x^2 + y^2 = 25?
Answers
Given equation of the Circle is ,
[tex]\sf\implies x^2 + y^2 = 25 [/tex]
And we need to tell that whether the point (-4,2) lies inside or outside the circle. On converting the equation into Standard form and determinimg the centre of the circle as ,
[tex]\sf\implies (x-0)^2 +( y-0)^2 = 5 ^2[/tex]
Here we can say that ,
• Radius = 5 units
• Centre = (0,0)
Finding distance between the two points :-
[tex]\sf\implies Distance = \sqrt{ (0+4)^2+(2-0)^2} \\\\\sf\implies Distance = \sqrt{ 16 + 4 } \\\\\sf\implies Distance =\sqrt{20}\\\\\sf\implies\red{ Distance = 4.47 }[/tex]
Here we can see that the distance of point from centre is less than the radius.
Hence the point lies within the circle .
Express 85mm as a percentage of 1metre
Answers
Answer:
Step-by-step explanation:
85/1000 because we said that 1 meter = 1000 mililiters
Divide both sides by 5 and then you have 17/200
then divide both sides by 2 (to get it over 100) =
8.5/100
.085%
Hope that helps!!
You could also just do 85/1000 you would get the same answer!!
A school bought 26 computers for a new computer lab. If each computer costs $740, how much did the school spend?
Answers
Answer:
= 19, 240 $
Step-by-step explanation:
cost of 1 computer = $ 740
cost of 26 computers = 26 × 740
= 19, 240 $
so the school spent 19, 240 $
PLEASE HELP ASAP
In the diagram below, ΔABC ≅ ΔSTR. Complete the statement BC ≅
A. AC
B. TR
C. ST
D. SR
Answers
Answer:
a
Step-by-step explanation:
The complete statement is BC ≅ TR.
What is triangle theorem?In mathematics, the Pythagorean theorem, or Pythagoras' theorem, exists a fundamental relation in Euclidean geometry among the three sides of a right triangle. It expresses that the area of the square whose side exists the hypotenuse stands equivalent to the sum of the areas of the squares on the other two sides.
Using the similarity of triangle theorem BC ≅ TR
To learn more about triangle refer to:
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Hi need help with this so plz help
Answers
Answer:
t > 28
Step-by-step explanation:
(3/2)^(-2).......................................................................
Answers
Answer:
4/9
Step-by-step explanation:
First of all we need to get rid of the -2 exponent and make it positive in order to solve this equation.
Therefore to do this we just use the reciprocal of 3/2 which is 2/3
Now we have (2/3)^2
Since 2/3 is being squared we used the following equation below:
(2/3) * (2/3)
We multiply 2/3 by itself twice since 2 is the exponent.
Then we get:
2^2
-----
3^2
2 squared is 4 and 3 squared is 9.
Therefore the final answer is 4/9.
I hope this helps have a good rest of your day!
Answer:
4/9
Step-by-step explanation:
(3/2)^(-2)
(3/2)^2=(3/2)(3/2)=9/4
However, ^(-2) means 1/(9/4), which gives you 4/9.
will give brainliest, look at the picture. HURRY PLSS
Answers
Answer:
triangle s
that is my answer
What is the shape of this distribution? A. Unimodal skewed B. Uniform C. Bimodal symmetric D. Unimodal symmetric E. Bimodal skewed
Answers
Answer:
D
Step-by-step explanation:
It can't be C and B since it doesn't have two parts, and if it was uniform it would have another part attached to the bottom. Moreover, it can't be A since it isn't positively skewed or negatively skewed, so it must be D.
The shape of this distribution is Unimodal symmetric.
Option D is the correct answer.
What is a histogram?A histogram is a representation of the distribution of data with intervals.
We have,
In statistics, a distribution is considered unimodal symmetric if it has a single mode or peak and is symmetric around that mode.
This means that the data is evenly distributed on both sides of the mode and is equally likely to occur on either side.
A common example of a unimodal symmetric distribution is the normal distribution, also known as the Gaussian distribution or bell curve.
Thus, the shape of this distribution is Unimodal symmetric.
Learn more about histograms here:
brainly.com/question/16819077
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Express tan J as a fraction in simplest terms
Answers
Answer:
SOH-CAH-TOA
tan = opposite/adjacent
tan J = 15/20 = 3/4
Step-by-step explanation:
Integration. Please help ASAP
Answers
Answer:
I hope this helps
Step-by-step explanation:
A rectangular floor of area 360 m2 is going to be tiled. Each tile is rectangular, and has an area of 240 cm2. An exact number of tiles can be put into the space. How many tiles will be needed?
Answers
Answer:
1500
Step-by-step explanation:
The area of the regtangular floor is 360m². The floor is going to be retired with tiles having area of 240cm² . We need to find the number of times . Therefore ,
[tex]\implies 360m^2 = 360 \times 10^4 \ cm^2 [/tex]
And , the number of tiles required will be ,
[tex]\implies n =\dfrac{Area \ of \ floor}{Area \ of \ a \ tile }\\\\\implies n =\dfrac{ 360 \times 10^4 \ cm^2}{240 cm^2} \\\\\implies \underline{\underline{ n = 1,500 }}[/tex]
Hence the required answer is 1500 .
Simplify 5^3 x 5^4
5^12
5^7
25^12
25^7
Please help ASAP. Please. The answer is one of those above.
Answers
Answer:
5⁷
Step-by-step explanation:
5³×5⁴
when bases are same powers are added
so..
5(³+⁴)
5⁷
Answer:
5^7
Step-by-step explanation:
Think of it like x^3 * x^4. Since when two variables with exponents are multiplied, the exponents are added, you get x^7. (But just use 5 instead of x.)
You can also check by seeing the result of 5^3*5^4 is 78,125 and 5^7 is also 78,125. Hope that helps!
Classify the following triangle. Check all that apply.
113
Jason
A. Isosceles
B. Scalene
O C. Acute
D. Right
E. Equilateral
OF. Obtuse
Answers
Answer:
A
Step-by-step explanation:
Because 113 %45*45 that gives you isosceles
Answer:isosceles and right.
Step-by-step explanation:
help pls and explain!!!
If x^2 + kx + 6 = (x+n)(x + 3) for all values of x, where k and n are constants, what is the value of k?
A) 5
B) 3
C) 2
D) 1
Answers
Answer:
A) 5
Step-by-step explanation:
We are given that:
[tex]x^2+kx+6=(x+n)(x+3)[/tex]
Where k and n are constants.
And we want to find the value of k.
We can expand the right-hand side:
[tex]\displaystyle =x(x+n)+3(x+n)\\ \\ = x^2+nx+3x+3n \\ \\ = x^2 + (n+3)x+3n[/tex]
Hence:
[tex]x^2+kx+6=x^2+(n+3)x+3n[/tex]
The coefficients of each term must be equivalent. In other words:
[tex]k=n+3\text{ and } 6=3n[/tex]
Solve for n:
[tex]n=2[/tex]
Now, we can solve for k:
[tex]k=(2)+3=5[/tex]
Our answer is A.
Solve for h. Make sure to use scrap paper to show your work.
( 136 + 6 x 8 ) ÷ 2 = g
Answers
Answer:
92
Step-by-step explanation:
6 x 8 = 48
48 + 136 = 184
184 / 2 = 92
G=92
6•8=48
136+48=184
184/2=92
PLEASE HELP!!! Urgent. Will mark as brainliest
Answers
Answer:
Step-by-step explanation:
m∠2 = [tex]\frac{1}{2}[/tex](55+41)
m∠2 = [tex]\frac{1}{2}[/tex](96)
m∠2 =48°
m∠1 = 180-48 = 132°
write additive inverse of a) 21/18 b) -2/8
Answers
Answer:
a) [tex]-\frac{21}{18}[/tex], b) [tex]\frac{2}{8}[/tex].
Step-by-step explanation:
Let be [tex]u[/tex] a real number, its additive inverse is a real number [tex]v[/tex] so that:
[tex]u+v = 0[/tex]
That is,
[tex]v = - u[/tex] (1)
Then, the additive inverses of [tex]\frac{21}{18}[/tex] and [tex]-\frac{2}{8}[/tex] are, respectively:
a) [tex]-\frac{21}{18}[/tex], b) [tex]\frac{2}{8}[/tex].
Help me out plz bbbhbbhh
Answers
hopefully that’s the answer you needed
the solution is in the picture ☝️
ANSWER: 240 hours
this is for n.12
The sum of the measures of the interior angles of a polygon is 2880°. How many sides does the polygon have?
14
16
18
20
Answers
Answer:
18
Step-by-step explanation:
Let
S = sum of the measures of the interior angles of a polygon
n = number of sides of a polygon
The equation is
S = (n - 2) * 180°
Where,
S = 2,880°
S = (n - 2) * 180°
2,880° = (n - 2) * 180°
2,880° = 180°n - 360°
2,880° + 360° = 180°n
3,240° = 180°n
Divide both sides by 180°
n = 3,240° / 180°
n = 18
Good evening everyone, the correct answer is 18 sides.
A polygon with 18 sides' interior angles will add up to 2880 degrees.
Have a blessed night.
Solve for x. Thank you
Answers
Answer:
Step-by-step explanation:
B/c the bigger triangle is a copy of the smaller we can say
8[tex]\sqrt{3}[/tex] / 12 = x / 8[tex]\sqrt{3}[/tex]
then, solve for x
8[tex]\sqrt{3}[/tex](8[tex]\sqrt{3}[/tex]/12) = x
(64 *3) 12 = x
192 /12 = x
16 = x
nice, the first answer looks good , then :P
Answer:
16
Step-by-step explanation:
Express 200 g as a percentage of 4 kg
Answers
Answer:
5%
Step-by-step explanation:
Both should be in same measurement. so convert 4 kg to gram
1 Kg = 1000 g
4 kg = 4 * 1000 = 4000 g
[tex]\frac{200}{4000}*100=\frac{2}{40}*100\\\\=\frac{1}{20}*100 = 1 * 5\\[/tex]
= 5%
What is the scale factor from abc to def?
Answers
Answer:
the answer is 8 because DEF is 8 times larger than ABC.
Step-by-step explanation:
hope that helps>3
Answer:
3
Step-by-step explanation:
To find scale factor, you need to divide two of the given sides. Meaning you can do any corresponding sides. So, for now, I will do 12 from DEF and 4 from ABC.
12 ÷ 4 = 3
To check if it is accurately 3, you will do it again (optional). You can use 15 from DEF and 5 from ABC
15 ÷ 5 = 3
Since both are 3, that will be the scale factor.
The answer is 3.
