1. To sketch the function f(x) = (2/3)x - 3, we first need to find two points that we can later join to sketch the line, for example the x- and y-intercepts.
a) The x-intercept occurs when f(x) = 0, so if f(x) = 0, then:
f(x) = (2/3)x - 3
0 = (2/3)x - 3
3 = (2/3)x (Add three to both sides)
3*(3/2) = x (Multiply both sides by 3/2)
9/2 = x
We have now found the x-intercept at (9/2, 0)
b) The y-intercept occurs when x = 0, so:
f(x) = (2/3)x - 3
f(0) = (2/3)*0 - 3
f(0) = -3
Now we know that the y-intercept is at (0, -3)
c) All that's left is to sketch the graph axes and label them, plot the two points, join them together using a ruler and label their coordinates.
2. The Domain is the range of x-values for which the function exists, and the Range is the range of y-values for which the function exists.
Since there haven't been any constraints specified, we can say that both the Domain and Range are (-∞, ∞), since the graph continues forever both along the x- and y-axis.
(Note that this isn't always the case and would change if, for example, the question stipulated that there was a domain of [0, 5] and you had to find the range. Then, you would calculate the value of y at each end of the domain (if x = 0, y = -3 and if x = 5, y = 1/3) - in my example, the range would thus be [-3, 1/3].)
Simplify square root of -36
a. 6i
b. -6i
c. 6
d. -6
Answer:
A. 6i
Step-by-step explanation:
Apply by the radicial rule.
[tex]\sqrt{-36}=\sqrt{-1}\sqrt{36}[/tex]
[tex]\sqrt{-1}\sqrt{36}[/tex]
Imaginary number.
[tex]\sqrt{36 i}[/tex]
Square root the numbers from left to right.
[tex]6^2=36[/tex]
[tex]\sqrt{6^2}=6[/tex]
6i is the correct answer.
I hope this helps you, and have a wonderful day.
Answer:
A
Step-by-step explanation:
Translate and solve. Write the solution in interval notation.
Nineteen less than p is no less than 47.
Answer:
[tex](p - 19) \geqslant 47[/tex]
[tex]p \geqslant 66[/tex]
Answer: The required interval notation of the solution is [66, ∞).
Step-by-step explanation: We are given to translate and solve the following inequality :
"Nineteen less than p is no less than 47".
Also, to write the solution in interval notation.
According to the given information, the inequality can be written as follows :
[tex]p-19\geq47.[/tex]
The solution of the above inequality is as follows :
[tex]p-19\geq47\\\\\Rightarrow p\geq47+19\\\\\Rightarrow p\geq 66.[/tex]
Thus, the required interval notation of the solution is [66, ∞).
Solve + (-4) = -2. 6 -18 18 -2
Answer:
Step-by-step explanation:
No solution
Answer:
First, before I answer, he or she forgot the n/3.
So the problem is n/3 + (-4) = 2
The answer is 6
Step-by-step explanation:
First, simply + -4 to -4, because different signs subtract
Second subtract -4 + 2 which equals 2
Now multiply 3 ( came from n/3) with 2
And its 6
I hope I helped you!!!
Which expressions are monomials? – 4 + 6 b + 2b + 2 (x – 2x)2 (rs)/(t) 36x2yz3 ax x(1)/(3)
Answer: A C and E
Step-by-step explanation:
-4+6 (x-2x)^2 36x^2yz-3
(A) (C) (E)
There's a screenshot of the answers below
Heather has 45.71 in her savings account.She brought six packs of markers to donate for school. Write an expression for how much money she has in her bank account after the donation
Answer:
45.71 - 6x
Step-by-step explanation:
If Heather bought markers to donate, the amount she donates is subtracted from her balance of 45.71. We know she bought 6 packs of markers, but we do not know how much each pack cost. We will make this our unknown "x". The expression for packs of markers costing "x" is 6x. Because she buys them from her account, which takes aways from her balance, the expression that represents this donation is:
45.71 - 6x
(Notice that the question asks for the EXPRESSION after she buys the markers, not the EQUATION. The difference between an expression and an equation is the lack of an equals sign in the expression.)
Answer:
M= 45.71 - 6x
Step-by-step explanation:
M represents money and x is how much each pack of markers cost. 45.71, which is the original amount, minus 6x will give the correct amount.
How would you plot the graph of x²-2x-4 ?
Please include an explanation. Thanks in advance :)
Step-by-step explanation:
This equation is written in standard form, y = ax² + bx + c.
a = 1 , b = -2 , c = -4
First, the x² tells you that this is going to be a parabola. Since the a is positive, the parabola will be facing up (with the ends pointing up).
Next, you find the axis of symmetry, or vertex, which is where the middle of the parabola is. The formula for this is [tex]\frac{-b}{2a}[/tex].
[tex]\frac{-(-2)}{2(1)}[/tex] Simplify
[tex]\frac{2}{2}[/tex] Simplify
1
So, the middle of your parabola will be at x = 1.
Now, find the x-intercept. Since the x-intercept of a graph is where y = 0, just plug 0 into the equation for y.
y = x² - 2x - 4 Plug in 0
0 = x² - 2x - 4 Factoring won't work, so use the Quadratic Formula.
[tex]$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$[/tex] Plug in[tex]$x=\frac{-(-2)\pm\sqrt{(-2)^2-4(1)(-4)}}{2(1)}$[/tex] Simplify
[tex]$x=\frac{2\pm\sqrt{4+16}}{2}$[/tex] Simplify
[tex]$x=\frac{2\pm\sqrt{20}}{2}$[/tex] The square root of 20 is about 4.47.
[tex]$x=\frac{2+4.47}{2}$[/tex] and [tex]$x=\frac{2-4.47}{2}$[/tex] Simplify
x = 3.235 and -1.235
These are your x-intercepts, where your parabola crosses the x-axis.
Now, just put all of this information together on a graph!
Find the exact value. sin135°
Hi!
To solve this, first let's decide what quadrant the 135 degrees lies in. Starting in quadrant one, it would end up landing in quadrant 2.
Coordinates:
(cos, sin)
In quadrant 2, the y value (sin) as a coordinate would be positive, therefore our final answer should be positive.
180 - 135 = 45
Therefore our reference angle will be sin45.
We should know that sin45 is equal to [tex]\cfrac{\sqrt{2} }{2}[/tex]
Now, remember that our final answer should be positive. We don't have to change this because it's already positive, so your final answer is:
[tex]\cfrac{\sqrt{2} }{2}[/tex]
The exact value of sin 135 degrees is - (√2)/2.
The unit circle and trigonometric identities can be used to calculate the sine of 135 degrees.
We can determine the location of the point on the unit circle that corresponds to an angle of 135 degrees by utilizing the unit circle. It is located in the third quadrant.
In the first and second quadrants, the sine function is positive; however, the third and fourth quadrants are where it is negative.
We can use the fact that the sine of an angle equals the y-coordinate of the point on the unit circle corresponding to that angle to determine the precise value.
The sine of 135 degrees is negative because the third quadrant's y-coordinate is negative.
We can determine the precise sine value of 135 degrees by using a reference angle.
In the third quadrant, the reference angle for 135 degrees is 45 degrees (180 degrees - 135 degrees).
The sine of a 45-degree angle is (2)/2 or 1/sqrt(2).
The sine of 135 degrees is a negative number because the reference angle is in the third quadrant.
Consequently, (2)/2 is the precise value of sin 135 degrees.
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let f(x) =4x and g(x) =3x-5. Find (g*f)(-4)
Answer: 272
Step-by-step explanation:
f(x) = 4x g(x) = 3x - 5
(g × f)(x) = (4x)(3x - 5)
= 12x² - 20x
(g × f)(-4) = 12(-4)² - 20(-4)
= 12(16) + 80
= 192 + 80
= 272
WILL GIVE BRAINLIEST
A pair of equations is shown below.
x + y = 2
y = one half x + 5
If the two equations are graphed, at what point do the lines representing the two equations intersect? (4 points)
(4, –2)
(–2, 4)
(2, 5)
(5, –2)
Answer:
(-2, 4)
Step-by-step explanation:
One of the equations is already solved for y, so let's solve the other one for y and by the transitive proprerty of equality, if y = y, then what those y's are equal to are equal to each other. Solving the first equation for y:
x + y = 2 so
y = -x + 2
Let's fill that in for y in the second equation. Where
[tex]y=\frac{1}{2}x+5[/tex], making the substitution,
[tex]-x+2=\frac{1}{2}x+5[/tex]
Combining like terms and getting the x on one side and the constant on the other side of the equals sign:
[tex]-\frac{3}{2}x=3[/tex]
The product of a fraction and its reciprocal is 1 so we will multiply both sides by
[tex]-\frac{2}{3}[/tex] to get:
[tex](-\frac{2}{3})(-\frac{3}{2})x=(3)(-\frac{2}{3})[/tex]
and we end up with x = -2.
Now that we know that, we can sub that in for x in either one of the original equations. I chose the first one:
If x + y = 2, then -2 + y = 2
and y = 4
Therefore, the solution set is (-2, 4)
Match each algebraic expression with the method to use for factoring.
Answer:
Prime: 3GCF: 1Factoring Trinomials: 4Difference of Squares: 2Perfect Square Trinomial (PST): 5Step-by-step explanation:
1. Each term has an even coefficient, so a factor of 2 can be removed:
2(3x^2 +7x -15)
The remaining quadratic factor is prime.
__
2. Each of these two terms is a square, so this is the difference of two squares.
__
3. This cubic has one irrational negative real root. It is prime.
__
4. This trinomial factors in the usual way: (x +15)(x -2). It is factored by "factoring trinomials."
__
5. The magnitude of the x-coefficient is double the square root of the (positive) constant, so this is a perfect square trinomial.
PLEASE HELP!! WILL MARK BRAINLY!!
For what values of the domain {-3, -1, 0, 2, 4} does f(x) = g(x)?
f(x) = 2x + 5
g(x) = x^2 - 3
Answer:
{4}
Step-by-step explanation:
It is helpful to let a calculator or spreadsheet perform the function evaluations for you. The two functions have the same value only for x=4 in the domain.
f(4) = 13 = g(4)
_____
The functions also have the same value for x=-2, but that is not in the domain given.
I need your help with these problems.
I'm only doing these because it's about a pet pig named Hammy.
5.
rate = distance / time
a.
rate: 36 inches per 3 seconds
b
unit rate: 12 inches per second
c
5 seconds × 12 inches per second = 60 inches
d
144 inches / 12 inches per second = 12 seconds
6.
a.
[tex] \frac 4 7 \div \frac 3 5 = \frac 4 7 \times \frac 5 3 = \dfrac{20}{21}[/tex]
b.
[tex]2 \frac 2 5 \div 1 \frac 7 9 = \frac{12}{5} \div \frac{16}{9} = \frac{12}{5} \times \frac{9}{16} = \dfrac{27}{20} [/tex]
c
[tex]3.24 \div 1.5 = 3.24 \div \frac 3 2 = 3.24 \times \frac 2 3 = 6.48/3 = 2.16[/tex]
d
[tex] \frac 8 9 \div 3\frac 1 3 = \frac 8 9 \times \frac{3}{10} = \dfrac{4}{15}[/tex]
Answer:
Step-by-step explanation:
(a) Hammy's rate is 36 inches in 3 sec.
(b) Hammy's unit rate is (36 inches) / (3 sec) = 12 in/sec
(c) In 5 sec Hammy can run (12 in/sec)(5 sec) = 60 in
(d) time = distance/rate, so here the time is (144 in) / (12 in/sec) = 12 sec
(6a) 4/7 divided by 3/5 is equivalent to 4/7 times 5/3, which comes out to 20/21.
(6b) Convert 2 2/5 to 12/5 and 1 7/9 to 16/9. Then invert the second improper fraction and multiply: 12/5 times 9/16 = 108/80, or 27/20.
(6c) 3.24 divided by 1.5 is equivalent to 3.24 times 2/3: 2.16, or 2 4/25
(6d) 8/9 divided by 3 1/3 is equivalent to 8/9 times 3/10, or 24/90, or 4/15.
what is the exact value of cos 45degrees as found on the unit circle
Answer:
sqrt of 2/2
Step-by-step explanation:
Answer:
The exact value of cos 45° is: [tex]\frac{\sqrt{2} }{2}[/tex].
Step-by-step explanation:
What is Steven’s slugging average if his stats are- Show steps. 25 singles 10 doubles 3 triples 10 homeruns 140 at-bats
a. 25 + 10 + 3 + 10 = 48/140 = .3428
b. 25(.1) + 10(.2) + 3(.3) + 10(.4) = 9.40/140 = .06714
c. 25(1) + 10(2) + 3(3) + 10(4) = 94/140 = .671
d. 25 + 10(2) + 3(3) + 10(3) = 84/140 = .600
The answer is:
The correct answer is c.
[tex]SluggingAverage=\frac{25(1)+10(2)+3(3)+10(40)}{140}=\frac{94bases}{140times}=0.671[/tex]
Why?To calculate the slugging average or slugging percentage, we need to divide the number of total bases by the total times at bat.
[tex]SluggingAverage=\frac{TotalBases}{TimesAtBat}[/tex]
We know that:
A single means 1 base.
A double means 2 bases.
A triple means 3 bases.
A homerun means 4 bases.
So, we know that:
[tex]Singles=25=25bases\\Doubles=2*10=20bases\\Triples=3*3=9bases\\Homeruns=10*40=40bases\\TimesAtBat=140[/tex]
Then, substituting and calculating we have:
[tex]SluggingAverage=\frac{25bases+20bases+9bases+40bases}{140}[/tex]
[tex]SluggingAverage=\frac{94bases}{140times}=0.671[/tex]
Hence, the correct answer is c.
[tex]SluggingAverage=\frac{25(1)+10(2)+3(3)+10(40)}{140}=\frac{94bases}{140times}=0.671[/tex]
Have a nice day!
Stuck on this question. May I please have some help?
Answer:
So a point is (-3,-5) and the vertex is (-4,-3)
Step-by-step explanation:
This is in vertex form. Vertex form is y=a(x-h)^2+k where (h,k) is the vertex.
The vertex here is (-4,-3)... now just use a value of x to plug in (any value besides -4)
I will choice -3. This gives -2(-3+4)^2-3
f(-3)=-2(1)^2-3
f(-3)=-2-3
f(-3)=-5
So a point is (-3,-5) and the vertex is (-4,-3)
Answer:(-4,-3)
Step-by-step explanation:
Bunny Hill Ski Resort charges $35 for ski rental and $10 an hour to ski. Black Diamond Ski Resort charges $40 for ski rental and $5 an hour to ski. Create an equation to determine at what point the cost of both ski slopes is the same
The equation of Bunny hill ski resort is z = 10x + 35 while z = 5x + 40 for the Black diamond ski resort at the point and at point (1,45) the cost of both will be the same.
How to form an equation?Determine the known quantities and designate the unknown quantity as a variable while trying to set up or construct a linear equation to fit a real-world application.
In other words, an equation is a set of variables that are constrained through a situation or case.
Let's say x number of hours a men sky
Then,
Bunny Hill Ski Resort charges $35 for ski rental and $10 an hour
So,
Total cost
z = 35 + 10x
Now,
Diamond Ski Resort charges $40 for ski rental and $5 an hour to ski
So,
Total cost
z = 40 + 5x
Now point where the cost of both resorts will same is
35 + 10x = 40 + 5x
x = 1
So,
z = 40 + 5(1) = 45
Hence, at point (1,45) the cost of both will be the same.
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Final answer:
To find when the costs are the same for both ski resorts, set up an equation based on their rates and solve for the number of hours, which in this case is 1 hour.
Explanation:
To determine at what point the cost of both Bunny Hill Ski Resort and Black Diamond Ski Resort is the same, we can set up an equation based on the given rates.
Let x be the number of hours spent skiing. Then the total cost at Bunny Hill Ski Resort is $35 (ski rental) plus $10 per hour (hourly rate), which is expressed as 35 + 10x.
Similarly, the cost at Black Diamond Ski Resort is $40 (ski rental) plus $5 per hour (hourly rate), or 40 + 5x. To find when the costs are equal, we set the two expressions equal to each other:
35 + 10x = 40 + 5x
Now we can solve for x:
35 + 10x = 40 + 5x
10x - 5x = 40 - 35
5x = 5
x = 1
Thus, after 1 hour of skiing, the cost of skiing at both resorts becomes the same.
BRAINLIEST write a verbal expression to represent the equation
m^3=52m^2
Step-by-step explanation:
A number cubed is equal to the product of 52 and the square of the number.
please help as soon as possible!!!!!!
Look at the parallelogram ABCD shown below:
The table below shows the steps to prove that if the quadrilateral ABCD is a parallelogram, then its opposite sides are congruent:
Which choice completes the missing information for reason 5 in the chart? (6 points)
congruent parallelograms
congruent triangles
similar angles
similar triangles
Answer:
congruent triangles
Step-by-step explanation:
The complete reason is, "corresponding parts of congruent triangles are congruent." This reason is sometimes abbreviated CPCTC.
It can be helpful to note that the previous step concluded that the relevant triangles are congruent.
Answer:
5. Congruent triangles
Step-by-step explanation:
Congruent Triangles : When two triangles are congruent, all its three sides are equal and have the same angles.
So in conguent traingles,
ΔADB ≅ BDC
Therefore, AB = DC and AD = BC
Thus this completes the missing information that proves that the quadrilateral ABCD ia a parallelogram, then its opposite sides are congruent.
Solve for the following system of equations. -7x+6y=9 -2x-5y=16 x=? y=?
Answer:
Step-by-step explanation: You are given the equation of -7x+6y=9 and -2x-5y=16 and you are asked to find what x=? and what y=?
First step is to write down the problem
-2x-5y=16
next add 5y over the equal sign.
-2x=5y+16
Next is too divide by -2
-2x/-2=5y+16/-2
after solving you get
x=-2.5y-8
now you substitute the equation into the other formula to get
-7(-2.5y-8)+6y=9
then solve by doing -7*-2.5y and -7*-8 to get 17.5y and 56 which will give you
17.5y+56+6y=9
Next you subtract 56 to the other side to get 9-56 or -47 now you have
17.5y+6y=-47
next is too add the 17.5y and 6y together to get 23.5y
23.5y=-47
next is too divide by 23.5
23.5y/23.5=-47/23.5
solve to get y=-2, now this is half you the problem
Step two is too substitute what y=-2 into the equation of x=-2.5y-8 to get
x=-2.5(-2)-8
Solve to get
x=5-8
Solve again to get
x=-3
Your answers are x=-3 and y=-2
Answer:
x = -3 and y = -2
Step-by-step explanation:
It is given that,
-7x + 6y = 9
----(1)
-2x - 5y = 16 -------(2)
To find the solution of given equations
eq(1) * 2 ⇒
-14x + 12y = 18 ------(3)
eq(2) * 7 ⇒
-14x - 35y = 112 ---(4)
eq (3) - eq(4) ⇒
-14x + 12y = 18 ------(3)
-14x - 35y = 112 ---(4)
0 4y = -94
y = 94/(-47) = -2
Substitute the value of y in eq (2)
-2x - 5y = 16 -------(2)
-2x - 5*-2 = 16
-2x +10 = 16
-2x = 6
x = 6/-2 = -3
Therefore x = -3 and y = -2
What is the y-coordinate of the solution to the system shown above?
Answer:
y = 3
Step-by-step explanation:
The solution is the point where the lines intersect, (x, y) = (6, 3). The y-coordinate of that point is 3.
Answer:
y = 3
Step-by-step explanation:
You must count the lines from the intersection to the Ox axis down.
NEED HELP WITH A MATH QUESTION
Answer:
Step-by-step explanation:
Add all the students: 4+6+2+2+3+4+6+3 = 30
Add all the male students = 14
divide : 14/30=0.466666
multiply by 100
0.466*100=4.66
round
Answer = 5
What is the nth term of the sequence below?
2, 6, 12, 20, . . .
3n
n^2 - 1
n^2 + 1
n (n+ 1)
Answer:
n(n+1)
Step-by-step explanation:
Only the last two formulas work for n=1; only the last formula works for n=2.
For n=1
3n = 3 ≠ 2
n² -1 = 0 ≠ 2
n² +1 = 2
n(n+1) = 2
For n=2
n²+1 = 5 ≠ 6
n(n+1) = 6 . . . . . this last formula works for the given sequence
Find the first four terms of the recursive sequence defined by the following formula:
an = an-14 where a4 = 2 14
, , , 2 14
Answer:
144, 36, 9, 2 [tex]\frac{1}{4}[/tex]
Step-by-step explanation:
The recursive formula allows us to find a term in a sequence from the previous term.
Given
[tex]a_{n}[/tex] = [tex]\frac{a_{n-1} }{4}[/tex]
Given the fourth term we require to work back to the third term , second and so on. Rearrange the formula to give
Multiply both sides by 4, then
[tex]a_{n-1}[/tex] = 4[tex]a_{n}[/tex]
Given a₄ = 2 [tex]\frac{1}{4}[/tex], then
a₃ = 4 × a₄ = 4 × 2[tex]\frac{1}{4}[/tex] = 9
a₂ = 4 × a₃ = 4 × 9 = 36
a₁ = 4 × a₂ = 4 × 36 = 144
The first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.
What is a geometric progression?When there is a constant between the two successive numbers in the series then it is called a geometric series. In other words, every next term is multiplied with that constant term to form a geometric progression.
The recursive formula allows us to find a term in a sequence from the previous term.
Given
[tex]a_n=\dfrac{a_n-1}{4}[/tex]
Given the fourth term, we require to work back to the third term, second, and so on. Rearrange the formula to give.
Multiply both sides by 4, then
a[tex]_{n-1}[/tex] = 4a[tex]._n[/tex]
Given a₄ = 2, then
The first four terms will be calculated as given below:-
a₃ = 4 × a₄ = 4 × 2 = 9
a₂ = 4 × a₃ = 4 × 9 = 36
a₁ = 4 × a₂ = 4 × 36 = 144
Therefore, the first four terms for the given series will be 144, 36, 9, and 2(1/4) respectively.
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Simplify the expression.
(4 - 1)[(1 + 6) + 2]
23
27
42
45
The function f(x) = ?(x + 5)(x + 1) is shown.What is the range of the function? all real numbers less than or equal to 4 all real numbers less than or equal to ?3 all real numbers greater than or equal to 4 all real numbers greater than or equal to ?3
It is best to graph the function when searching for the range.
For the function f(x) = (x + 5)(x + 1), the range is ALL REAL NUMBERS when y is greater than or equal to -4.
Get it?
Three different divers kept track of the number of treasure boxes they've found this year. Diver Dives Treasure boxes found Scuba Sam 11 33 Wet Suit Willy 18 81 Deep Diving Dan 26 104 Which diver found the most treasures per dive?
Answer:
Wet Suit Willy
Step-by-step explanation:
To find boxes per dive, divide boxes by dives:
Sam: 33/11 = 3 . . . boxes per dive
Willy: 81/18 = 4.5 . . . boxes per dive
Dan: 104/26 = 4 . . . boxes per dive
Wet Suit Willy found the most treasure boxes per dive: 4.5.
Solve the system of equations by finding the reduced row-echelon form of the augmented matrix for the system of equations. 2x+y+z=-3 3x-5y+3z=-4 5x-y+2z=-2
Answer:
(x, y, z) = (1, -1, -4)
Step-by-step explanation:
A suitable graphing or scientific calculator can find the reduced row-echelon form for you. There are on-line calculators that will do that, too.
_____
In general, if you want to do this by hand, you want to use row operations on the augmented matrix to make the diagonal elements 1 and the off-diagonal elements 0 as shown in the attached result.
If a[i,j] represents the element at row i, column j, you do that by dividing row i by a[i, i] (to make a[i, i] = 1), then subtracting the product of row i and a[k,i] from row k. (for all rows k ≠ i) For this 3-row matrix, repeat these steps for i = 1 to 3.
In the general case of an n by n+1 augmented matrix, you will be doing n^2 row operations, each one involving evaluation of n+1 expressions. The work rapidly grows with matrix size, so readily justifies use of a calculator.
As with many "elimination" problems, appropriate choice of sequence can reduce the work. The above algorithm always produces the reduced row-echelon form, but may result in messy arithmetic along the way.
Answer: A
Step-by-step explanation: edge 2021
Need help with this math question
ANSWER
[tex]x = 140 \degree[/tex]
EXPLANATION.
The two tangents each meet the radius at 90° each.
This implies that,
[tex]x + 40 + 90 + 90 = 360[/tex]
The sum of interior angles of a Quadrilateral is 360°
We simplify to get
[tex]x + 40 = 180[/tex]
[tex]x = 180 - 40[/tex]
[tex]x = 140 \degree[/tex]
Find the vertex of the parabola whose equation is y = x^2 - 4x + 6.
A. (-2, 18)
B. (2, 2)
C. (2, 6)
[tex]\bf \textit{vertex of a vertical parabola, using coefficients} \\\\ y=\stackrel{\stackrel{a}{\downarrow }}{1}x^2\stackrel{\stackrel{b}{\downarrow }}{-4}x\stackrel{\stackrel{c}{\downarrow }}{+6} \qquad \qquad \left(-\cfrac{ b}{2 a}~~~~ ,~~~~ c-\cfrac{ b^2}{4 a}\right) \\\\\\ \left(-\cfrac{-4}{2(1)}~~,~~6-\cfrac{(-4)^2}{4(1)} \right)\implies (2~~,~~6-4)\implies (2~,~2)[/tex]
Answer:
B. (2,2).
Step-by-step explanation:
Convert to vertex form y = a(x - b)^2 + c where (b, c) is the vertex.
y =x^2 - 4x + 6
y = (x - 2)^2 - 4 +6
y = (x - 2)^2 + 2.
Therefore the vertex is (2, 2).
Solve the system of equations Please help me! It would honestly mean so much to me! Thank you !
4x+2y=-2
8x+5y=1
Answer:
(x, y) = (-3, 5)
Step-by-step explanation:
There are many ways to solve a system of two equations with two unknowns. Almost all of them involve reducing the system to one equation in one unknown. (Graphical solution, as in the attachment, bypasses that algebraic manipulation.)
In general, the first step is to look at the equations to see if ...
one is of the form x = ( ) or y = ( )the coefficients of one of the variables are oppositesthe coefficients of one of the variables are related by a simple number.If the first condition is true, then the system may be easily solved by "substitution." The expression you have for one of the variables can be substituted for that variable in the other equation.
If the second condition is true, you can add the equations to eliminate the variable with opposite coefficients. (Opposites add to give zero.)
Here, the third condition holds: the coefficient of x in the first equation (4) is simply related to the coefficient of x in the second equation (8) by a factor of 2.
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So, we can eliminate the x-variable from the system of equations by multiplying the first equation by -2 and adding that result to the second equation:
-2(4x +2y) +(8x +5y) = -2(-2) +(1)
-8x -4y +8x +5y = 4 +1 . . . . eliminate parentheses
y = 5 . . . . . . . . . . . . . . . . . . . collect terms
Now, we can substitute this value into either equation to find the value of x. Using the first equation, we get ...
4x +2(5) = -2
4x = -12 . . . . . . . subtract 10
x = -3 . . . . . . . . . divide by 4
The solution to the system of equations is (x, y) = (-3, 5).