Answer Seven hundred and thirty thousand eight hundred twelve
(08.07 HC)
An expression is shown below:
f(x) = 2x² - x - 10
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the
coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers
obtained in Part A and Part B to draw the graph. (5 points)
(10 points)
Answer:
[tex]\textsf{A)} \quad x=-2, \:\:x=\dfrac{5}{2}[/tex]
[tex]\textsf{B)} \quad \left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)[/tex]
C) See attachment.
Step-by-step explanation:
Given function:
[tex]f(x)=2x^2-x-10[/tex]
Part ATo factor a quadratic in the form [tex]ax^2+bx+c[/tex] , find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex] :
[tex]\implies ac=2 \cdot -10=-20[/tex]
[tex]\implies b=-1[/tex]
Therefore, the two numbers are -5 and 4.
Rewrite [tex]b[/tex] as the sum of these two numbers:
[tex]\implies f(x)=2x^2-5x+4x-10[/tex]
Factor the first two terms and the last two terms separately:
[tex]\implies f(x)=x(2x-5)+2(2x-5)[/tex]
Factor out the common term (2x - 5):
[tex]\implies f(x)=(x+2)(2x-5)[/tex]
The x-intercepts are when the curve crosses the x-axis, so when y = 0:
[tex]\implies (x+2)(2x-5)=0[/tex]
Therefore:
[tex]\implies (x+2)=0 \implies x=-2[/tex]
[tex]\implies (2x-5)=0 \implies x=\dfrac{5}{2}[/tex]
So the x-intercepts are:
[tex]x=-2, \:\:x=\dfrac{5}{2}[/tex]
Part B
The x-value of the vertex is:
[tex]\implies x=\dfrac{-b}{2a}[/tex]
Therefore, the x-value of the vertex of the given function is:
[tex]\implies x=\dfrac{-(-1)}{2(2)}=\dfrac{1}{4}[/tex]
To find the y-value of the vertex, substitute the found value of x into the function:
[tex]\implies f\left(\dfrac{1}{4}\right)=2\left(\dfrac{1}{4}\right)^2-\left(\dfrac{1}{4}\right)-10=-\dfrac{81}{8}[/tex]
Therefore, the vertex of the function is:
[tex]\left(\dfrac{1}{4},-\dfrac{81}{8}\right)=(0.25,-10.125)[/tex]
Part CPlot the x-intercepts found in Part A.
Plot the vertex found in Part B.
As the leading coefficient of the function is positive, the parabola will open upwards. This is confirmed as the vertex is a minimum point.
The axis of symmetry is the x-value of the vertex. Draw a line at x = ¹/₄ and use this to ensure the drawing of the parabola is symmetrical.
Draw a upwards opening parabola that has a minimum point at the vertex and that passes through the x-intercepts (see attachment).
help please
15 points
need by the end of today
9. Enrique would earn $7. 50 per hour. Option B
10. The number of girls that were at the assembly is 1390 . Option J
11. 40% of 60 is 24 . Option C
12. The simple interest is $72. 00 . Option F
13. The factory produces 1080 shoes on Tuesday. Option D
How to determine the value9. From the information given, we have;
He earns $420He works a total of 56 hoursHe would earn;
= 420/ 56
= $7. 50 per hour
10. We have that;
There are 1200 boys at the assemblyRatio of boys to girls is 20: 23The number of girls at the assembly would be;
= 23/ 20 × 1200
= 1. 15 × 1200
= 1380
11. Let the number be x
40% of x = 24
40/ 100x = 24
0. 4 x = 24
Make 'x' the subject
x = 24/ 0. 4
x = 60
12. The formula for simple interest is expressed as;
Simple interest = PRT / 100
Simple interest = 300 × 4 × 6/ 100
Simple interest = 7200/ 100
Simple interest = $72. 00
13. We have that;
Monday's production = 900 shoes
Tuesday's production = 900 + 900 × 20% = 900 × 20/ 100 = 18000/ 100 = $900 + 180
= $1080
Thus, the total amount Enrique earns per hour is $7. 50 .Option B
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Which list shows the numbers in order from least to greatest?
A)−3π,−9.4,−283,−95−−√
B)−95−−√,−3π,−9.4,−283,
C)−95−−√,−283,−9.4,−3π
D)−283,−9.4,−3π,−95−−√
Answer:
judging from the list of numbers i would pick a
Suppose that dollars in principal is invested for years at the given interest rates with continuous compounding. determine the amount that the investment is worth at the end of the given time period. p=1$2000, t=10yr
Amount after 10 years at 3%, 4% and 5.5% interest with principal $20000 is $26878.32, $29604.88 & $34162.88 respectively.
Although a part of your question is missing, you might be referring to this full question: Suppose that P dollars in principal are invested for years at the given interest rates with continuous compounding. Determine the amount that the investment is worth at the end of the given time period. p=$20000, t=10yr
a. 3% interest
b. 4% interest
c. 5.5% interest
P = $2000
T = 10 years
Formula to be used:
A = P(1+r/100)^n
A = total amount after n years
P = principal amount invested
r = rate of interest
n = number of years the money is invested
Solving for part a:
A = 20000(1+3/100)^10
= 20000*1.34
A = 26878.32
Solving for part b:
A = 20000(1+4/100)^10
= 20000*1.48
A = 29604.88
Solving for part c:
A = 20000(1+5.5/100)^10
= 20000*1.70
A = 34162.88
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PLEASE HELP ASAP!!
The equation of the graph is (x-3)(x+1), the y-intercept of y=[tex]x^{2} -5x+4[/tex] is "4" and the factors of y=[tex]x^{2} -5x+4[/tex] are (x-4) ad (x-1)
Given that a graph touch x-axis at 2 points i.e. 2 roots are there for given graph.The graph touches the x-axis at (3,0) and (-1,0) it implies x=3 and x=-1 are the solutions the equation,(x-3) and (x+1) are factors of equation
Therefore,the equation of graph is (x-3)(x+1).
Given the equation y=[tex]x^{2} -5x+4[/tex]
The y-intercept is defined as the graph passing a fixed point at x=0 line
i.e.(0,c) pass through it . c is the y-intercept
c=0-0+4
c=4
Therefore,The y-intercept of the equation y=[tex]x^{2} -5x+4[/tex] is 4
Factorising y=[tex]x^{2} -5x+4[/tex]
⇒ y=[tex]x^{2} -5x+4[/tex]
⇒y=[tex]x^{2} -x-4x+4[/tex]
⇒y=x(x-1)-4(x-1)
⇒y=(x-4)(x-1)
Therefore, the factors of y=[tex]x^{2} -5x+4[/tex] are (x-4) and(x-1)
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show that 2 1/4 - 6/7 = 11/28
blehh
Hence the required expression is Proved.
Given the expression is 2 1/4 ₋ 6/7 = 39/28
Consider L.H.S 2 1/4 ₋ 6/7
Convert improper fraction to proper fraction.
2 1/4 = 9/4
take LCM of the denominators.
The LCM is 28.
9×7/28 ₋ 6×4/28
63/28 ₋ 24/28
Now subtract.
63 ₋ 24/28
39/28
Hence proved.
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Your question is incomplete. Please find the missing content here.
Show that 2 1/4 ₋ 6/7 = 39/28
Point B is on line segment AC. Given AB = 7 and BC = 11, determine the length
AC.
What does AC equal?
Answer:
AC = 18
Step-by-step explanation:
AC = AB + BC = 7 + 11 = 18
Please help me I will give 30 points and brainiest
What is the absolute value of 30?
Write the distributive property of multiplication over addition a a conditional statement
The distributive property of multiplication over addition is A (B + C) = AB + AC.
Properties of Numbers.
Numbers are have 5 main properties of operation which are:
Closure PropertyAssociative PropertyCommutative PropertyDistributive PropertyIdentity PropertyGiven,
Here we have to write the distributive property of multiplication over addition of a conditional statement.
Basically, the distributive property defines the distributing ability of operation over another mathematical operation within a bracket.
It can be either distributive property of multiplication over addition or distributive property of multiplication over subtraction.
Here we need to write the distributive property of multiplication over addition of a conditional statement.
So, The distributive property of multiplication over addition is expressed as
=> A × (B + C) = AB + AC.
Let us verify this property with the help of an example.
For example:
The expression 2(1 + 4) using the distributive law of multiplication over addition.
=> 2(1 + 4) = (2 × 1) + (2 × 4)
⇒ 2 + 8 = 10
Hence, the distributive property of multiplication over addition is stated.
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A statistical tool used to synthesize the results of previous, separate studies is called a(n)?
A statistical tool used to synthesize the results of previous, separate studies is called a(n):Odds-ratio.
We know that, the odds ratio is one that is often calculated with the use of the number of case-patients who were or were not exposed to a factor (e.g. as a particular cream) and the number of controls that did or did not have the exposure.
Odds ratio is nothing but is a measure of association between exposure and an outcome.
It calculates the relationship between a variables and the likelihood of an event occurring.
Note that there are different kinds of statistical tool that are used for research purpose.
Therefore, A statistical tool used to synthesize the results of previous, separate studies is called a(n):Odds-ratio.
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Any tips for doing complicated order of operation problems. Algebra 2
1
tion
What fraction represents the shaded part of the circle?
Select one:
O a. 12
O b. 5
4555/5
O d.
12
O c. 7
12
7
Answer:
c
Step-by-step explanation:
because 7 of the 12 sections are shaded in blue.
Help asap I need to get this done asap and I’m struggling with it and I’d appreciate help and I’ll give you brainliest
Answer:
x = 10
Step-by-step explanation:
the angle is equally bisected from the middle so
3x - 3 = 4x - 13
13 - 3 = 4x - 3x
x = 10
<FGH = 3(10) - 3 = 27
< HGI = 4(10) - 13 = 27
<FGI = <FGH + <HGI = 27 + 27 = 54
What are the coordinates of the point on the directed line segment from (-4, 1)(−4,1) to (1, 6)(1,6) that partitions the segment into a ratio of 4 to 1?
Express the mass of 49,000 molecules of oxygen in scientific notation.
grams
The scientific notation for the mass of 49,000 molecules of oxygen is 4.9 × 10⁴ grams.
How do you define the scientific notation?To transform numbers into scientific notation, use the following rule: In scientific notation, the exponent equals the number of times the decimal point must always be shifted to produce a number between 1 and 10.
The proper scientific notation format is an x 10∧b, where an is a number or decimal number with an absolute value greater or equal to one and less than ten, or 1 |a| 10.Scientific notation is a method of writing extremely large or extremely small numbers in a way that makes them easier to read as well as work with. A number formed by multiplying a number greater or equal to one but less than ten by an integral power of ten.For the given value;
= 49,000 grams
write the number such that only one digit is left to the left of decimal of the number and the remaining digits to the write are written to the power of 10
= 4.9000 × 10⁴
This could be written as;
= 4.9 × 10⁴.
Therefore, the value of the mass of 49,000 oxygen molecules in the form of scientific notation is 4.9 × 10⁴ grams.
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Diferencia entre álgebra y aritmética
To find a baseball pitcher's earned run average (era), you can use the formula ei = 9r, in which e represents era, i represents the number of innings pitched, and r represents the number of earned runs allowed. solve the equation for e. what is a pitcher's era if he allows 33 earned runs in 45 innings pitched? if necessary, round your answer to the nearest hundredth.
The value of e is 33/5 or 6.6 era.
It is given in the question that:-
e*i = 9r
Where,
e represents era
i represents the number of innings pitched, and
r represents the number of earned runs allowed
Also, we are given that:-
i = 45 innings, and
r = 33 earned runs allowed
We have to find the value of e for the given data.
Hence, applying the formula given in the question, we get
e*45 = 9*33
Now, as only one variable is left in the equation, it has become a linear equation in one variable.
Hence, solving the linear equation, we get
e = (9*33)/45
e = 33/5
e = 6.6 era
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an attorney charges a fixed fee for an initial meeting and an hourly fee for all hours worked after this meeting. the attorney charges $850 for an initial meeting and $250 per hour. which equation represents the relationship between h, the number of hours, and c, the total cost?
The equation which represents the relationship between 'h' the number of hours, and c, the total cost is y = 250x+850.
How to write equation of straight line?A straight line equation is a mathematical equation that describes the relationship between the coordinate points on that straight line. It can be written in several ways and indicates the slope, x-intercept, & y-intercept of a line.
A straight line's general equation is y = mx + c, in which m is the gradient and y = c is the value at which the line intersects the y-axis. The above number c is known as the y-axis intercept. A straight line with gradient m as well as intercept c on the y-axis has the equation y = mx + c.Now, as per the given question;
The attorney charges price for an initial meeting = $850.
And, the charges for each hour is = $250.
Thus, the equation which shows the given situation is-
y = 250x + 850.
In which, 250 is the value of the slope 'm'.
The y- intercept is shown by 850.
Thus, the total cost will be found out by equation y = 250x+850.
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Y/6 - 3 = -11
Show your work
[tex]\frac{Y}{6} - 3 = -11[/tex]
[tex]\frac{Y}{6} - \frac{18}{6} = -\frac{66}{6}[/tex]
[tex]Y - 18 = -66[/tex]
[tex]Y = -66 + 18 = -48[/tex]
What is the value of the "?" in the figure below
Answer:
I think it is none of the choices.
Step-by-step explanation:
1/2 x = 10 it is a either a one step or two step equation just please help solve it
Answer:
x = 20
Step-by-step explanation:
Hello!
Solve for x by isolating the variable.
Solve for x0.5x = 100.5x * 2 = 10 * 2x = 20The value of x is 20.
What are the roots of the equation? 3x^2=7x+2 3x 2 =7x+2
Quadratic equations are equations that has a leading degree of 2. The solution to the given quadratic equation are 1/3 and 2
Solving linear equationQuadratic equation are equation that has a leading degree of 2. Given the quadratic equation as shown:
3x^2=7x+2
Equate to zero to have:
3x² - 7x + 2 = 0
Factorize
3x² - 6x - x +2 = 0
3x(x-2) - 1(x- 2) = 0
Group
(3x-1)(x-2) = 0
3x - 1 = 0 and x - 2 = 0
Determine the values of x
3x = 1 and x = 2
x = 1/3 and 2
Hence the solution to the given quadratic equation are 1/3 and 2
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Use the figure for Items 2 and 3. Lines PS and TR intersect at point Q.
P
T
R
(2m + 4)º
S
(3m + 1)⁰
Applying the linear pair postulate, m<SQR = 74°.
What is the Linear pair Postulate?According to the linear pair postulate, the equation below is holds true:
m<TQS + m<SQR = 180.
m<TQS = (3m + 1)°
m<SQR = (2m + 4)°
Substitute the values
(3m + 1) + (2m + 4) = 180
Solve for m
3m + 1 + 2m + 4 = 180
Add like terms
3m + 2m + 1 + 4 = 180
5m + 5 = 180
Subtract 5 from both sides of the equation
5m + 5 - 5 = 180 - 5
5m = 175
m = 35
m<SQR = (2m + 4)° = 2(35) + 4 = 74°.
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What is the answer ?
Answer:
xy + z = 16
5(2) = 10 + 6 = 16
The endpoint of the line segment is (4,6) and (-6,2). Point G divides the segment into two equal parts?
What are the coordinates of point of G?
Answer:
G = (-1,4)
I drew it and work it out tho
Find the equation of this line.
y = [? ]x + [ ]
Simplify your answer and enter as an integer.
Answer:
y =x + 3
Step-by-step explanation:
i gotchu
ARITHMATIC SEQUENCE
Grade 11 - one question
Answer:
a₁ = - 11 and d = 3
Step-by-step explanation:
the sum to n terms of an arithmetic sequence is
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
given S₄₀ = 1900 , then
S₄₀ = [tex]\frac{40}{2}[/tex] [ 2a₁ + 39d ] = 1900 , that is
20(2a₁ + 39d) = 1900 ( divide both sides by 20 )
2a₁ + 39d = 95 → (1)
the nth term of an arithmetic sequence is
[tex]a_{n}[/tex] = a₁ + (n - 1)d
given a₄₀ = 106 , then
a₁ + 39d = 106 → (2)
subtract (2) from (1) term by term to eliminate d
a₁ + 0 = - 11 , so
a₁ = - 11
substitute a₁ = - 11 into (2) and solve for d
- 11 + 39d = 106 ( add 11 to both sides )
39d = 117 ( divide both sides by 39 )
d = 3
An object is moving at a speed of 63 centimeters every 2 days. Express this speed in meters per hour.Round your answer to the nearest hundredth.
This speed in meters per hour is 0.01 meter per hour
How to determine the speed?The given parameter is
Speed = 63 centimeters every 2 days
Divide 63 by 2
So, we have:
Speed = 31.5 centimeters every day
There are 24 hours in a day
So, we have
Speed = 31.5 centimeters every 24 hours
100 cm equals 1 m
So, we have:
Speed = 0.315 meters every 24 hours
Divide
Speed = 0.013125 meter per hour
Approximate
Speed = 0.01 meter per hour
Hence, this speed in meters per hour is 0.01 meter per hour
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luna wants to sell a Tshirt
In her shop making a profit of
25%
if the cost of the Tshirt
is 100$, in the same time
the customer will have a discut
of 30%, what shall she put
on a Sale Tag
Answer:
Price: $178.57
30% off: -$53.57
Sale Price: $125.00
Step-by-step explanation:
She buys each shirt for $100.
She wants to make a profit of 25%.
25% of $100 = 0.25 × $100 = $125
She must sell the shirt at $125.
She wants to mark the shirt at a higher price than $125, so that after the 30% discount, she will still sell it for $125.
Call the higher price x.
x - 30% of x = 125
x - 0.3x = 125
0.7x = 125
x = 125/0.7
x = 178.57
The sale tag can read:
Price: $178.57
30% off: -$53.57
Sale Price: $125.00
Need help badly, I also need to know how you got the answer.
Answer:
-1/5
y=-1/5 x-8
-1/5 is the slope
Step-by-step explanation:
-1/5
Formula- y=mx+b
The slope-intercept form is
y=mx+b, where m is the slope and b is the y-intercept.
y=mx+b
Rewrite in slope-intercept form.
Simplify the left side
Simplify each term.
Combine 1/8 and x.
x/9+5y/8=-5
Subtract x/8 from both sides of the equation.
5y/8=-5-x/8
Multiply both sides of the equation by8/5.
8/5.5y/8=8/5(-5-x/8)
Simplify both sides of the equation.
Simplify the left side.
Simplify 8/5.5y/8
y=-x/5-8
y=-1/5 x-8
Step-by-step explanation:
Given equation:
1/8x + 5/8y =-5
Now write it in standard form like ax+by+c=0
1/8x + 5/8y + 5= 0
Now,slope of line (m) = -a/b
here value of a is 1/8 and value of b is 5/8
now by formula..
-(1/8)÷(5/8) = m(slope)
-1/8 × 8/5 = m
-1/5 = m
here ia your answer