Algebra
Algebra is a branch of mathematics that uses not only numbers and signs, but also letters to solve operations.
Algebraic term
The algebraic term is a simple expression where letters and numbers are combined, and variables are not added or subtracted. For example:
[tex]-7x^4[/tex]In the previous algebraic term we can identify its parts:
Sign: It can be positive or negative, as in the example.
Coefficient: The number that accompanies the variable, which in this case would be 5.
Variable: It is the unknown represented by the letter x.
Exponent: The power to which the variable is raised, which in the example would be 3. If no exponent appears, it is understood that it is 1.
Algebraic expression
The algebraic expression is a set of variables and numbers that can be combined with different mathematical operations, including addition and subtraction, unlike algebraic terms. An example can be the following:
[tex]-5x^2+4y[/tex]Expressions can be expressed as a function of the number of terms that contain them as
Monomial: Has a term:
[tex]15z[/tex]Binomial: It has two terms:
[tex]2x^2-7y[/tex]Trinomial: It has three terms:
[tex]3x^2+8y+2z[/tex]Polynomial: It has more than three terms:
[tex]5x^3-3y+6z-9[/tex]Algebraic equations
An equation is the association between two algebraic expressions through the equal sign. They can be mainly of two types:
First degree equation: When the variable is raised to the maximum power 1. It is known as an equation.
5x + 5y = 9
Second degree equation: When the variable is raised to the maximum power 2. It is also called a quadratic equation.
5x2-3y + 6z-9 = 3x
At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh. Two hours later, the forecast for solar generation for 12 PM has changed from 4 GW to 4.5 GW. The market is currently bid at 95 pounds/MWh and offered at 105 pounds/MWh. What would you do, and why? Please answer logically, stating all assumptions. Note that no additional research is needed
Expert Answer
I will sell 1MW electricity contract for 12pm with a bid price of £95/MW. Lock in losses in the region of £5/MW.
At 6 AM today, you purchased 1 MW of electricity contract for 12 PM at a price of 100 pounds/MWh.
Solar power is more affordable, accessible, and prevalent in the United States than ever before.
From just 0.34 GW in 2008, U.S. solar power capacity has grown to an estimated 97.2 gigawatts (GW) today.
This is enough to power the equivalent of 18 million average American homes.
Today, over 3% of U.S. electricity comes from solar energy in the form of solar photovoltaics (PV) and concentrating solar-thermal power (CSP).
Solar generation implies an increase of 4 GW to 4.5 GW. Which will provide more power than expected during 12 p.m. This will likely lower the market value.
A bid-offer spread of 10 pounds/MWh is typically wide. This basically indicates that the market is liquid and volatile. The price of which might turn against me if I wait.
Some of my guesses are:
I am a risk-averse trader. Who does not want to take unnecessary
exposure to power market.
I do not have any positions or hedging strategies in the electricity
market that would influence my decisions.
I am not obliged to buy and sell electricity at 12 PM.
Market prices and forecasts are reliable, reflecting actual supply and demand conditions.
Hence the answer is I will sell 1MW electricity contract for 12pm with a bid price of £95/MW. Lock in losses in the region of £5/MW.
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Trigonometry I’m a little stuck in this problem and I want to know we’re If I messing up and need help to proceed!
Problem 2.
Using the unit circle as our guide,
Point A would be at 0 degrees
There are 12 points on the circle
Take 360 degrees and divide by 12
360/12 = 30
Each pie shaped wedge is 30 degrees
C is 2 pie pieces so it is 2*30 or 60 degrees from point A
H is 8 pie shapes wedges so it is 8*30 or 240 degrees from point A
Looking at the diagram we can see that A and G are the same distance from the ground
B and F are the same distance from the ground
C and E are the same distance from the ground
H and L are the same distance from the ground
I and K are the same distance from the ground
how do you solve -2×+5=9
a) Write the three equations using three ordered pairs.EQ1:EQ2:EQ3:B) Write the linear system:C) Solve the system using substitution and then elimination. Show all work andsteps:
A) To get the three equations, we will substitute each of the 3 points on the parabola into the quadratic formula
Quadratic function formula is given by:
[tex]y\text{ = }ax^2\text{ + bx + c }[/tex]using point (-1, 5) = (x, y)
[tex]\begin{gathered} 5=a(-1)^2\text{ + b(-1) + c} \\ 5\text{ = a(1) - b + c } \\ 5\text{ = a - b + c }\ldots.(1) \end{gathered}[/tex]using point (0, -4) = (x, y)
[tex]\begin{gathered} -4=a(0)^2\text{ + }b(0)\text{ + c} \\ -4\text{ = c } \end{gathered}[/tex]using point (4, 0)
[tex]\begin{gathered} 0=a(4)^2\text{ + b(4) + c} \\ 0\text{ = 16a + 4b + c} \\ \text{16a + 4b + c = 0 . . . (2)} \end{gathered}[/tex][tex]\begin{gathered} \text{The 3 equations using orderd pair:} \\ EQ1\colon\text{ }5=a(-1)^2\text{ + b(-1) + c} \\ EQ2\colon\text{ }-4=a(0)^2\text{ + b(0) + c} \\ EQ3\colon\text{ }0=a(4)^2\text{ + b(4) + c} \end{gathered}[/tex]B) The linear system:
[tex]\begin{gathered} 5\text{ = a - b + c . . . (1)} \\ -\text{4 = c . . . (2)} \\ \text{0 = 16a + 4b + c . . . (3)} \end{gathered}[/tex]C) substitute for c in equation 1 and 2:
[tex]\begin{gathered} 5\text{ = a - b + c }\ldots.(1) \\ 5\text{ = a - b -4} \\ 5\text{ + 4 = a - b } \\ 9\text{= a - b }\ldots(4) \\ \\ \text{0 = 16a + 4b + c . . . (3)} \\ \text{0 = 16a + 4b }-4 \\ 0+\text{4 = 16a + 4b } \\ 4\text{ = 16a + 4b . . . (5)} \end{gathered}[/tex]Using elimnation for equation (4) and (5):
To eliminate a variable, it must have the same coefficient in both equations.
Let's elimnate b. We will multiply equation (4) by 4 so the coefficient will be the same:
4(9) = 4(a) - b(4)
36 = 4a - 4b ...(4)
4 = 16a + 4b ...(5)
Add equation 4 and 5 together:
36 +4 = 4a + 16a - 4b + 4b
40 = 20a
divide both sides by 20:
40/20 = 20a/20
a = 2
substitute for a in equation 5:
4 = 16(2) + 4b
4 = 32 + 4b
4 - 32 = 4b
-28 = 4b
divide both sides by 4:
-28/4 = 4b/4
b = -7
a = 2, b = -7, c = -4
The equation of the parabola becomes:
[tex]y=2x^2\text{ - 7x - 4}[/tex]What are the solutions of 3x^2 - x + 4 = 0
ANSWER
[tex]x\text{ = 0.167 + }1.142i\text{ and x = 0.167 }-\text{ 1.142i}[/tex]EXPLANATION
We want to find the solutions of the equation.
The solutions of the equation are the values of x that make that equation equal to zero (0).
The equation given is:
[tex]3x^2\text{ - x + 4}[/tex]We need to use the quadratic formula.
For a quadratic equation:
[tex]ax^2\text{ + bx + c}[/tex]the quadratic formula is:
[tex]x\text{ = }\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a}[/tex]So, we have that:
a = 3, b = -1, c = 4
So::
[tex]\begin{gathered} x\text{ = }\frac{-(-1)\text{ }\pm\sqrt[]{(-1)^2_{}-\text{ 4(3)(4)}}}{2(3)}\text{ = }\frac{1\text{ }\pm\text{ }\sqrt[]{1\text{ - 48}}}{6} \\ x=\text{ }\frac{1\text{ }\pm\text{ }\sqrt[]{-47}}{6}\text{ = }\frac{1\text{ }\pm\text{ }\sqrt[]{47}\cdot\text{ }\sqrt[]{-1}}{6}\text{ = }\frac{1\text{ }\pm\text{ }\sqrt[]{47}\text{ i}}{6} \\ x\text{ = }\frac{1\text{ + 6.86i}}{6}\text{ and x = }\frac{1\text{ - 6.86i}}{6} \\ x\text{ = 0.167 + }1.142i\text{ and x = 0.167 }-\text{ 1.142i} \end{gathered}[/tex]The equation has complex solutions.
Which graph shows point pas (-5,6)and point q as (3,-4)?
Answer
Option A is correct.
From the explanation, we can easily see that the first graph shows point P as (-5, 6) and Point Q as (3, -4).
Explanation
The key to marking points on the graph is to know that the coordinates are named as (x, y)
And to mark a point (-5, 6), it means x = -5 and y = 6
So, we move 5 units to the left from the origin along the negative x-axis and 6 units upwards along the y-axis.
And for (3, -4), x = 3, y = -4
We move 3 units to the right from the origin along the positive x-axis and 4 units downwards along the y-axis.
Hope this Helps!!!
The top of a desk would be a representation ofO a pointO a planeO a lineO none of the above
Given
The top of a desk.
To find:
The top of a desk is a representation of _____.
Explanation:
It is given that,
The top of a desk.
That implies,
Since,
The plane is a flat surface that extends infinitely in all directions.
Then, the top of a desk represents a plane.
Answer:
B-Plane tep-by-step explanation:
1. Corinne has a cell phone plan that includes 200 minutes for phone calls and unlimited texting. An additional fee is charged for using more than 200 minutes for phone calls. The figure below is the graph of C = f(m), where C is the monthly cost after m minutes used. Part A What is the minimum monthly cost for Corinne's cell phone plan? Show or explain your work. Part B What is the value of f(150). Explain its meaning in terms of the cell phone plan. Part C For what mis f(m) = 55? Explain its meaning in terms of the cell phone plan. Part D What is the cost per minute after Corinne uses her monthly allowance of 200 minutes? Show or explain your work.
Part A) Minimum cost = $30
Part B) Value of f(150) = $30
Part C) m = 275 minutes
Part D) Cost per minute after 200 minutes = $0.2
Explanations:From the graph shown:
Monthly rate for 200 minutes for phone calls = $30
An additional fee is charged for more than 200 minutes for phone calls
Part A) The minimum monthly cost of Corinne's cell phone plan.
Note that the minimum monthly cost of Corinne's cell phone plan will be when he does not use more than 200 minutes for phone calls.
Therefore, the minimum monthly cost, C = f(200) = $30
Part B)
The value of f(150)
f(150) means the cost of Corinne's cell phone plan when 150 minutes is spent for phone calls, i.e. m = 150
Since there is a flat rate of $30 for 0 to 200 minutes, f(150) = $30
Part C)
For what m is f(m) = 55
This means that we should find the number of minutes spent when the cost of the plan is $55
From the graph, $55 is charged at 275 minutes
Therefore, when f(m) = 55, m = 275 minutes
Part D)
Cost per minutes after the monthly allowance of 200 minutes
After the monthly allowance of 200 minutes, we would notice that, for every 50 minutes, there is a $10 charge. That means that for every 1 minute, there will be a charge of 10/50 = $0.2
Cost per minute = $0.2
How many fourteenths are there in 5/7
Use the Distributive Property to find each missing factor.6 x 8 = ( 4 x ____) + ( 2 x 8 )10 x 3 = (___ x 3 ) + ( 2 x 3 )(___ X 7 ) = ( 3 x 7 ) + ( 2 x ___)( 8 X ___) = (___ x 8 ) + ( 4 X 8 )3rd grade subject Distributive property
The question is given below as
[tex]6\times8=(4\times\ldots)+(2\times8)[/tex]The distributive property of multiplication states that when a number is multiplied by the sum of two numbers, the first number can be distributed to both of those numbers and multiplied by each of them separately, then adding the two products together for the same result as multiplying the first number by the sum.
[tex]a(b+c)=a\times b+a\times c[/tex]Let the missing factor in the question be x
[tex]\begin{gathered} 6\times8=(4\times\ldots)+(2\times8) \\ 6\times8=(4\times x)+(2\times8) \end{gathered}[/tex]By multiplying,
We will have
[tex]\begin{gathered} 6\times8=(4\times x)+(2\times8) \\ 48=4x+16 \end{gathered}[/tex]Collect like terms,by subtracting 16 from both sides
[tex]\begin{gathered} 48=4x+16 \\ 48-16=4x+16-16 \\ 32=4x \end{gathered}[/tex]Divide both sides by 4
[tex]\begin{gathered} 4x=32 \\ \frac{4x}{4}=\frac{32}{4} \\ x=8 \end{gathered}[/tex]Hence,
[tex]\begin{gathered} 6\times8=(4\times8)+(2\times8) \\ 6\times8=8(4+2) \\ 6\times8=6\times8 \end{gathered}[/tex]Therefore,
The missing factor = 8
Select the correct answer.Consider a regular polygon that has 12 congruent sides. Which angle of rotation will carry it onto itself?
Answer:
30 degrees
Explanation:
A regular polygon is a polygon in which all the side lengths are equal.
All regular polygons have rotational symmetry, that means it can be rotated so that the pre-image and the image are the same.
The angle by which this rotational symmetry occurs is the exterior angle of the polygon.
Given a regular polygon with 12 sides, the exterior angle is:
[tex]\frac{360}{12}=30\degree[/tex]Therefore, the angle of rotation that will carry onto itself is 30 degrees.
Yogi's yoga studio charges members $79 for Enrollment and $45 per month Write an equation to represent the relationship between x, the number of months and y, the total cost of membership
Data:
Enrollment: $79
Charge per Month: $45/month
x: number of months
y: Total cost
You can follow the next general expression:
[tex]y=kx+b[/tex]Where k is the constant of change, in this case the charge per month, and b is the charge at time 0, in this case the charge per enrollment.
Then, You get the next expression that represents the relationship:[tex]y=45x+79[/tex]A and _B are supplementary angles. If m_A = (4x - 16) and m B = (8x + 4), then find the measure of ZA.
A=48
Explanation
Two Angles are Supplementary when they add up to 180 degrees
Step 1
if A and B are supplementary angles, then
[tex]A+B=180[/tex]Let
A=4x-16
B=8x+4
Step 2
replace,
[tex]\begin{gathered} A+B=180 \\ 4x-16+8x+4=180 \\ 12x-12=180 \end{gathered}[/tex]Step 3
solve for x
[tex]\begin{gathered} 12x-12=180 \\ 12x=180+12 \\ 12x=192 \\ x=\frac{192}{12} \\ x=16 \\ \end{gathered}[/tex]Step 4
finally, replace the value of x= 16 to find A
[tex]\begin{gathered} A=4x-16 \\ A=4(16)-16 \\ A=64-16 \\ A=48 \end{gathered}[/tex]Calculate the value of the expression:1+1x100+2
In order to calculate the value of this expression, first we need to calculate the multiplication between 1 and 100. Then, w
What is the solution to the linear system 4x + 2y = 8 and 2x + 2y = 2?
Answer:
• x=3
,• y=-2
Explanation:
Given the linear system of the equations:
[tex]\begin{gathered} 4x+2y=8\cdots\cdots\cdots(1) \\ 2x+2y=2\cdots\cdots\cdots(2) \end{gathered}[/tex]First, subtract equation(2) from equation(1).
[tex]\begin{gathered} (4x-2x)+(2y-2y)=8-2 \\ 2x=6 \\ \text{Divide both sides by 2} \\ \frac{2x}{2}=\frac{6}{2} \\ x=3 \end{gathered}[/tex]Next, substitute x=3 into equation (1) to solve for y.
[tex]\begin{gathered} 4x+2y=8\cdots\cdots\cdots(1) \\ 4(3)+2y=8 \\ 12+2y=8 \\ \text{Subtract 12 from both sides.} \\ 12-12+2y=8-12 \\ 2y=-4 \\ \text{Divide both sides by 2} \\ \frac{2y}{2}=\frac{-4}{2} \\ y=-2 \end{gathered}[/tex]The solution to the linear system is x=3 and y=-2.
AcellusConvert this decimal into its fractionalform, simplified completely.0.450
we have the following:
[tex]0.450=\frac{45}{100}=\frac{9}{20}[/tex]therefore, the answer is 9/20
Find the volume of a right circular cone that has a height of 19 e ft and a base with acircumference of 7.6 ft. Round your answer to the nearest tenth of a cubic foot
In order to solve this problem we will take in account the following picture and formula:
Where:
π ≅ 3.14159
h = height of the cone
r = radius of the base
V = volume
Now, our cone has the following dimensions:
h = 19 ft
c = circunference = 7.6 ft
We see that in order to obtain the volume we must replace the radius in the formula of the picture.
So we obtain first the radius r from the value of the circunference.
The circunference in terms of the radius is:
[tex]c=2\pi r[/tex]So the radius is:
[tex]r=\frac{c}{2\pi}[/tex]Now that we have the radius, we replace that in the formula for the volume:
[tex]V=\frac{1}{3}\cdot\pi\cdot h\cdot r^2=\frac{1}{3}\cdot\pi\cdot h\cdot(\frac{c}{2\pi})^2[/tex]Now we replace the data of our right circular cone:
[tex]\begin{gathered} V\cong\frac{1}{3}\cdot3.14159\cdot19ft\cdot(\frac{7.6ft}{2\cdot3.14159})^2 \\ \cong29.1105ft^3 \\ \cong29.1ft^3 \end{gathered}[/tex]So the volume of the right circular cone to the nearest tenth is: 29.1 ft³
The runaway success of the switch prompted the company to raise it's sales and earnings by forecast for the second time since November. It now expects a 24% jump in profit from what it projects just three months ago, with 560 billion yen (5.6 billion) estimated for the year ending in March. What is the total now?
If the new forecast is 24% more than the 5.6 billion estimated, we can calculate this as:
[tex]\begin{gathered} Y_{\text{new}}=Y_{\text{old}}+0.24\cdot Y_{\text{old}}=(1+0.24)Y_{\text{old}}=1.24\cdot Y_{\text{old}} \\ Y_{\text{new}}=1.24\cdot5.6=6.944\approx6.9 \end{gathered}[/tex]Answer: The total now is approximately 6.9 billion.
Write each expression without the absolute value symbol.(x+7)
We must write the following expression without the absolute value symbol:
[tex]|x+7\left|\right?.[/tex]We have two cases:
1) If (x + 7) ≥ 0 or x ≥ -7, the expression is (x + 7).
2) If (x + 7) < 0 or x < -7, the expression is -(x + 7).
Combining these results, we have:
[tex]|x+7\left|=\right?\begin{cases}x+7\text{ if }x\ge-7 \\ -x-7\text{ if }x<-7\end{cases}[/tex]AnswerThe equivalent expression to |x + 7| without an absolute value symbol is:
[tex]|x+7\left|=\right?\begin{cases}x+7\text{ if }x\ge-7 \\ -x-7\text{ if }x<-7\end{cases}[/tex]B. Make a line graph for given the data on the table below. No plagiarism
NOTE ; Kindly ensure the x-axis have equal width
Your brother and sister took turns driving on a 635 mile trip that took 11 hours to complete. your brother drove at a constant speed of 60 miles per hour and your sister drove at a constant speed of 55 miles per hour. let x be the number of miles your brother drove and y be the number of miles your sister drove. find the number of miles each of your siblings drove.
Your brother and sister took turns driving on a 635 mile trip
Total distance travel on trip = 635
Let x be the disatnce travel by your borther and y be the miles travel by the sister
SO, x + y = 635
It took 11 hours to complete the trip
Speed of brother = 60 miles per hour
Speed of sister = 55 miles per hour
The general expression for the speed is :
[tex]\begin{gathered} \text{ Sp}eed=\frac{Dis\tan ce}{Time} \\ \text{Then, }Time=\frac{Dis\tan ce}{Spped} \end{gathered}[/tex]Then using these expression
Time taken by the brother is :
[tex]\begin{gathered} \text{ Time taken by brother =}\frac{x}{60} \\ \text{Time taken by the sister=}\frac{y}{55} \end{gathered}[/tex]As total time is 11 hours so:
[tex]\frac{x}{60}+\frac{y}{55}=11[/tex]So we get the two set of equation :
[tex]\begin{gathered} \frac{x}{60}+\frac{y}{55}=11 \\ x+y=635 \end{gathered}[/tex]Simplify the set of equation :
Simplify the first equation for x and then put it into another :
[tex]\begin{gathered} \frac{x}{60}+\frac{y}{55}=11 \\ \frac{x}{60}=11-\frac{y}{55} \\ x=660-\frac{12y}{11} \\ \text{Susbtitute the value of x in the second equation:} \\ x+y=635 \\ 660-\frac{12}{11}y+y=635 \\ \frac{-12}{11}y+y=635-660 \\ \frac{-12y+11y}{11}=-25 \\ \frac{-1}{11}y=-25 \\ y=25\times11 \\ y=275 \end{gathered}[/tex]Substitute y = 275 in the first equation :
x + y = 635
x + 275 = 635
x = 360
As x represent the distance travel by the bother and the rest by sister
Distance travel by brother is 360 miles and the distance travel by the sister is 275 miles
Answer : x = 360 miles, y = 275 miles
8. Reece made a deposit into an account that earns 8% simple interest. After 8 years, Reece had earned $400. How much was Reece's initial deposit?
PLEASE HELP NOW!!!!!!!!!!!!!!!
The rate of change of water capacity of the reservoir per year is -1725 acre - feet per year .
In the question ,
a line graph is given which represents the relation between time(t) and the reservoir capacity in acre - feet .
the two points on the line graph means
in the year 1928 the reservoir capacity was 300000 acre - feet .
and in the year 1986 the reservoir capacity was 200000 acre - feet .
the rate of change of water capacity of the reservoir per year can be calculated using the formula ,
rate of change = ( change in water capacity) / ( change in time)
= ( 200000 - 300000)/(1986-1928)
= -100000/58
= -1724.13
≈ -1725
here negative sign means the capacity of the reservoir is decreasing per year .
Therefore , The rate of change of water capacity of the reservoir per year is -1725 acre - feet per year .
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What is the area of the trapezoid shown? Te figure is not drawn to scale.thank you ! :)
Given a trapezoid with different dimensions, we are asked to find the Area.
To solve this we will have to use the area of a trapezoid formula:
Area = 1/2 (a + b)h
Where:
a = 29.2 in
b = 19 in
h = 12.6 in
A = ?
Inputting into the formula:
Area = 1/2 (29.2 + 19) * 12.6
Area = 1/2 (48.2) * 12.6
Area = 1/2 (607.32)
Area = 303.66 in²
Therefore, the Area of the Trapezoid is 303.66 in²
Therefore, the correct option is third option which is 303.66 in².
simplify 2(w+3)-(w-1)
we have
2(w+3)-(w-1)
apply distributive property first term and remove the parenthesis
2w+6-w+1
combine like terms
w+7Find the new position of the given point (1,3) after a translation of 3 units down and 3 units to the left.
Answer:
(-2, 0)
Explanation:
Given the point: (1,3)
• To translate the point ,3 units down,, ,subtract 3 from the y-value,.
,• To translate the point ,3 units left,, ,subtract 3 from the x-value,.
Therefore, the new position of the point is:
[tex](1-3,3-3)=(-2,0)[/tex]The new position is (-2, 0).
The Harrisburg Recreation Center recently changed its hours to open 1 hour later and close 3 hours later than it had previously. Residents of Harrisburg age 16 or older were given a survey, and 560 residents replied. The survey asked each resident his or her student status (high school, college, or nonstudent) and what he or she thought about the change in hours (approve, disapprove, or no opinion). The results are summarized in the table below. Student status Approve Disapprove | No opinion 30 High school College Nonstudent 4 10 353 6 85 Total 129 367 38. What fraction of these nonstudent residents replied that they disapproved of the change in hours? F. } HAWI- G. J. 353 367 K. 353 485
Explanation
to get the fraction of Nonstudents that disaproved
[tex]\text{fraction}=\frac{total\text{ nonstudents that disaproved}}{\text{total nonstudents}}[/tex]then
let
total nonstudents that disaproved=353
total nostudents=85+353+47=485
now, replace
[tex]\text{fraction}=\frac{353}{485}\rightarrow k[/tex]so,the answer is k
A function with an input of 1 has an output of 3. Which of the following could not be the function equation?options:y = 3 xy = - x + 4y = x - 2y = 2 x + 1
Solution:
A function with an input of 1 has an output of 3.
This means that
[tex]when\text{ }x=1,y=3[/tex]Step 1:
We will try the first option
[tex]\begin{gathered} y=3x \\ y=3(1) \\ y=3 \\ (1,3) \end{gathered}[/tex]Step 2:
We will try the second option
[tex]\begin{gathered} y=-x+4 \\ y=-1+4 \\ y=3 \\ (1,3) \end{gathered}[/tex]Step 3:
We will try the third option
[tex]\begin{gathered} y=x-2 \\ y=1-2 \\ y=-1 \\ (1,-1) \end{gathered}[/tex]Step 4:
We will try the fourth option
[tex]\begin{gathered} y=2x+1 \\ y=2(1)+1 \\ y=2+1 \\ y=3 \\ (1,3) \end{gathered}[/tex]Hence,
The final answer is
[tex]\Rightarrow y=x-2[/tex]Which of the following gives the correct range for the graph?
A coordinate plane with a segment going from the point negative 4 comma negative 2 to 0 comma negative 1 and another segment going from the point 0 comma negative 1 to 3 comma 5.
−2 ≤ x ≤ 5
−2 ≤ y ≤ 5
−4 ≤ x ≤ 3
−4 ≤ y ≤ 3
Answer:
The correct range is -2 < y < 5.
Re-arrange this vertex equation y = 2 (x + 1)2 - 6 in standard form?
When we have a quadratic equation, we can have it in vertex and standard form.
The vertex form comes in the form:
[tex]y=a\mleft(x-h\mright)^2+k[/tex]The standard form comes in the form:
[tex]y=ax^2+bx+c[/tex]Converting to/from either simply requires some manipulations via expansion of the bracket as will be seen.
[tex]\begin{gathered} y=2(x+1)^2-6 \\ y=2(x^2+2x+1)-6 \\ y=2x^2+4x+2-6 \\ y=2x^2+4x-4 \end{gathered}[/tex]Hence, we have our standard form.