Answer:
7.07 units
Step-by-step explanation:
Given
[tex]A = (-3,6)[/tex]
[tex]B = (2,1)[/tex]
[tex]C = (9,5)[/tex]
See comment for complete question
Required
Side length AB
To do this, we make use of the following distance formula;
[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]
So, we have:
[tex]d = \sqrt{(-3 - 2)^2 + (6 - 1)^2}[/tex]
[tex]d = \sqrt{(-5)^2 + 5^2}[/tex]
[tex]d = \sqrt{25 + 25}[/tex]
[tex]d = \sqrt{50}[/tex]
[tex]d = 7.07[/tex]
RESOLVER LOS SIGUIENTES SISTEMAS DE ECUACIONES APLICANDO EL METODO DE SUSTITUCION
2x +3y = 2
-6x + 12y = 1
Answer:
x = 1/2; y = 1/3
Step-by-step explanation:
2x + 3y = 2 Eq. 1
-6x + 12y = 1 Eq. 2
Eq. 1
2x + 3y = 2
2x = -3y + 2
x = -3/2 y + 1
Eq. 2
-6x + 12y = 1
De Eq. 1 sabemos que x = -3/2 y + 1
-6x + 12y = 1
-6(-3/2 y + 1) + 12y = 1
9y - 6 + 12y = 1
21y - 6 = 1
21y = 7
y = 7/21
y = 1/3
Eq. 1
2x + 3y = 2
2x + 3(1/3) = 2
2x + 1 = 2
2x = 1
x = 1/2
Respuesta: x = 1/2; y = 1/3
You are making a committee from the class and need to have 6 students on it. There are 32 students in the class.
answer in permutations
Answer:
32P6
Step-by-step explanation:
nPr
n=32
r=6
. A real estate company charges a base amount of $ 400 plus 3 % of the selling price to sell a house. If a house sells for $ 250, 000. How much will the agent charge? *
Answer:
400 + .03(250,000) = $7900
Step-by-step explanation:
NO LINKS AND NO ANSWERING WHAT YOU DON'T KNOW!!! THIS IS NOT A TEST OR ASSESSMENT!!!
Please help and SHOW WORK on these parts.
Unit 1 Assignment- Who's Right?
Answer:
Part 1)
1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.
2) Dylan is perfectly correct.
3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.
Part 2)
Only Skyler's approach was incorrect. When Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.
Step-by-step explanation:
Part 1)
We want to simplify the expression:
[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7}[/tex]
We can divide. Recall that xᵃ / xᵇ = xᵃ ⁻ ᵇ. Hence:
[tex]\displaystyle =0.88\times 10^{-11-7}=0.88\times 10^{-18}[/tex]
In scientific notation, the coefficient is always between 1 or 10.
So, we can multiply 0.88 by 10. To keep the equality, we need to divide 10⁻¹⁸ by 10. Hence:
[tex]\displaystyle =0.88(10)\times \frac{10^{-18}}{10}[/tex]
(You can see that the 10s can cancel out, giving us our original expression.)
Simplify. Thus:
[tex]\displaystyle \frac{3.61\times 10^{-11}}{4.1\times 10^7} = 8.8\times 10^{-19}[/tex]
Therefore, as we can see:
1) Sylvia' process was incorrect. In her last step, when she multiplied 0.88 by 10, she also need to divide exponent by 10.
2) Dylan is perfectly correct.
3) Ethan's process was also incorrect. Instead of subtracting the exponents, he added them.
Part 2)
Reviewing their work, we can see that only Skyler's approach was incorrect.
729 is indeed 3⁶. However, when Skyler acquired (3⁶)ˣ = 9, he made the error of setting the exponent on the left to the value on the right.
Both Robert and Kevin are correct, having set each exponent equal to each other after their bases are equivalent and solving for x.
Joe bikes at the speed of 30 km/h from his home toward his work. If Joe's wife leaves home 5 mins later by car, how fast should she drive in order to overtake him in 10 minutes.
Answer:
Joe's wife must drive at a rate of 45km/hour.
Step-by-step explanation:
We are given that Joe leaves home and bikes at a speed of 30km/hour. Joe's wife leaves home five minutes later by car, and we want to determine her speed in order for her to catch up to Joe in 10 minutes.
Since Joe bikes at a speed of 30km/hour, he bikes at the equivalent rate of 0.5km/min.
Then after five minutes, when his wife leaves, Joe is 5(0.5) or 2.5 km from the house. He will still be traveling at a rate of 0.5km/min, so his distance from the house can be given by:
[tex]2.5+0.5t[/tex]
Where t represents the time in minutes after his wife left the house.
And since we want to catch up in 10 minutes, Joe's distance from the house 10 minutes after his wife left will be:
[tex]2.5+0.5(10)=7.5\text{ km}[/tex]
Let s represent the wife's speed in km/min. So, her speed times 10 minutes must total 7.5 km:
[tex]10s=7.5[/tex]
Solve for s:
[tex]\displaystye s=0.75\text{ km/min}[/tex]
Thus, Joe's wife must drive at a rate of 0.75km/min, or 45km/hour.
TIME REMAINING
49:02
What is the value of h?
The graph shows that f(x) = 3* is translated horizontally
and vertically to create the function g(x) = 3*- h + k.
81%
O-2
O-1
O 1
O 2
f(x)
001)
What is the answer to this photo
Answer:
h=2
Step-by-step explanation:
f is translated right 2 units (so h=2) and up 2 units (so k=2)
The value of h is 2.
What is Translation of Functions?Translation of functions is defined as the when each point in the original graph is moved by a fixed units in the same direction.
There are horizontal translation and vertical translation of functions.
A function f(x) when translated horizontally leads to the function g(x) which is equal to g(x) = f(x ± k) where k is the units to which the function is translated.
And the vertical translation leads to the function g(x) = f(x) ± k, where k is the units to which the function is translated.
Here the original function is, f(x) = 3ˣ.
The point corresponding to x = 0 in f(x) is x = 2 in g(x).
That is (0, 1) is translated to (2, 3).
f(x) is horizontally translated to the right.
3ˣ translates to 3ˣ⁻².
Hence the value of h is 2.
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g(x)=(cosθsinθ)^4 what's the differential
Answer:
sin²2θ. (cos θ sin θ). cos 2θ
Step-by-step explanation:
finding g'(x)
g'(x)
(x^n)' = nx^(n -1)= 4 (cosθsinθ)³ . { cosθ. (sinθ)' + sinθ. (cosθ)' }
(cosθ)' = - sinθ (sinθ)' = cosθ= 4 (cosθsinθ)³ { cosθ. cos θ + sinθ.(-sin θ)}
= 4 (cosθsinθ)³{ cos²θ - sin²θ}
cos²θ - sin²θ = cos 2θ2sinθ cosθ = sin 2θ= (4 cosθ sinθ)². (cosθ sinθ). { cos²θ - sin²θ}
= sin²2θ. (cos θ sin θ). cos 2θ
Monique made several batches of soup.
Each batch required 3/4 of a pound of potatoes. She used a total of 6 1/2 pounds. How many batches did she make?
Answer:
8 batches
in workings show whats left over but not counted.
As a batch its a whole number as the multiplier will usually be the fraction
and fraction / fraction should always show fraction but the whole number given with a remainder can be shown if not a whole number.
Step-by-step explanation:
6 1/2 = 6.5
and ;
3/4 of a pound = 0.75 of 1 pound
6.5 / 0.75 = 8.7 or in full workings write = 8.6666.....7
8.7/ 1 = 8 batches with 0.7 or 0.66667 left over
Answer In fraction for exam question given in fraction 8.7 = 8 batches
with 7/10 left over.
If a student walked 2 feet straight to the chalk board in 2 seconds and
then walked 2 feet back to his or her original position at his or her desk at
the same speed, what was the student's displacement at 2 seconds
compared to 0 seconds?
O 6 feet
O O feet
O2 feet
O 4 feet
Answer:
2 feet
Step-by-step explanation:
Displacement at 0 seconds is 0 feet.
Displacement at 2 seconds is 2 feet because it took them 2 seconds to walk 2 feet.
The Blacktop Speedway is a supplier of automotive parts. Included in stock are 7 speedometers that are correctly calibrated and two that are not. Three speedometers are randomly selected without replacement. Let the random variable z represent the number that are not correctly calibrated.
Complete the probability distribution table. (Report probabilities accurate to 4 decimal places.)
x P(x)
0
1
2
3
Answer:
x P(x)
0 0.4167
1 0.5
2 0.0833
3 0
Step-by-step explanation:
The speedometers are chosen without replacement, which means that the hypergeometric distribution is used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
In this question:
7 + 2 = 9 speedometers, which means that [tex]N = 9[/tex]
2 are not correctly calibrated, which means that [tex]k = 2[/tex]
3 are chosen, which means that [tex]n = 3[/tex]
Complete the probability distribution table.
Probability of each outcome.
So
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
[tex]P(X = 0) = h(0,9,3,2) = \frac{C_{2,0}*C_{7,3}}{C_{9,3}} = 0.4167[/tex]
[tex]P(X = 1) = h(1,9,3,2) = \frac{C_{2,1}*C_{7,2}}{C_{9,3}} = 0.5[/tex]
[tex]P(X = 2) = h(2,9,3,2) = \frac{C_{2,2}*C_{7,1}}{C_{9,3}} = 0.0833[/tex]
Only 2 defective, so [tex]P(X = 3) = 0[/tex]
Probability distribution table:
x P(x)
0 0.4167
1 0.5
2 0.0833
3 0
Identify the transformation that occurs to create the graph of k(x).
k(x)=9f(x)
Answer:
To create the graph of k(x) , the graph of f(x) undergoes a vertical stretching by a factor of 9.
Step-by-step explanation:
We are given that
[tex]k(x)=9f(x)[/tex]
We have to Identify the transformation that occurs to create the graph of k(x).
To create the graph of k(x) we will multiply the function f(x) value by 9.
Let f(x) be any function
[tex]g(x)=a f(x)[/tex]
Where a>1
It means to obtain the graph of g(x) the graph f(x) has undergone a vertical stretching by a factor of a.
We have k=9>1
Therefore, to create the graph of k(x) , the graph of f(x) undergoes a vertical stretching by a factor of 9.
Which System of inequalities has this graph as its solution?
A. y<2x-3
y<1/3x+4
B. y>2x-3
y>1/3x+4
C. y>2x-3
y<1/3x+4
D. y<2x-3
y>1/3x+4
Answer: B
Step-by-step explanation:
The line [tex]y=2x+3[/tex] is dotted and shaded above.
Eliminate A and D.Similarly, the line [tex]y=\frac{1}{3}x+4[/tex] is also shaded above.
Eliminate C.This leaves B as the correct answer.
convert 1.5% to decimal and a fraction. Show and explain your method
Answer:
0.015 and 3/200.
Step-by-step explanation:
1.5% is equal to 0.015. Percents are always equal to their decimal counterparts; basically, the number over 100. Dividing 1.5 by 100 will yield us 0.015.
0.015 is going to be equal to 15/1000, or 3/200. Since we did 1.5/100, we need to multiply both sides of the fraction by 10 so there are no decimal points. Therefore, this is 15/1000. If we divide both sides of this fraction by 5, then we get 3/200, which is the most simplified form.
A farmer sells four of his farm products Maize, Potatoes, carrots and tomatoes in each of 2 towns into classes of 3 customers. Consumers, Retailers, and wholesellers .
Town1 Maize, Potatoes Carrots tomatoes
consum. 4. 6. 7. 4.
Retailer. 3. 2. 1. 6.
wholesa. 4. 3. 5. 3.
Town2. Maize. Potatoes.Carrots.tomatoes
consum. 4. 5. 3. 6.
Retailer. 7. 8. 4. 4.
wholesa. 2. 4. 6. 1.
In order to sell his produce in these towns , the farmer pays commission to salesman, town managers and division managers as shown.
salesman.townmanagers.divisionmanage
6%. 5%. 2%
4%. 3%. 3%
Selling price per bag is:
Maize Sh 200
Potatoes sh 1000
Carrots sh 700
Find total sales in units by potatoes.
Answer:
Step-by-step explanation:
Suppose 243 subjects are treated with a drug that is used to treat pain and 52 of them developed nausea. Use a 0.01 significance level to test the claim that more than 20% of users develop nausea.
Part A- correct answer is C.
Part B- The test statistic for this hypothesis test is ___? (Round to two decimal places as needed)
Answer:
20%?
Step-by-step explanation:
An item is regularly priced at $84. Ashley bought it on sale for 70% off the regular price.
Use the ALEKS calculator to find how much Ashley paid
Answer:
58.80
Step-by-step explanation:
84 x .7(70%) =58.80
How do you complete the other two?
I know how to complete the first one but 3D Pythag confuses me so much
For now, I'll focus on the figure in the bottom left.
Mark the point E at the base of the dashed line. So point E is on segment AB.
If you apply the pythagorean theorem for triangle ABC, you'll find that the hypotenuse is
a^2+b^2 = c^2
c = sqrt(a^2+b^2)
c = sqrt((8.4)^2+(8.4)^2)
c = 11.879393923934
which is approximate. Squaring both sides gets us to
c^2 = 141.12
So we know that AB = 11.879393923934 approximately which leads to (AB)^2 = 141.12
------------------------------------
Now focus on triangle CEB. This is a right triangle with legs CE and EB, and hypotenuse CB.
EB is half that of AB, so EB is roughly AB/2 = (11.879393923934)/2 = 5.939696961967 units long. This squares to 35.28
In short, (EB)^2 = 35.28 exactly. Also, (CB)^2 = (8.4)^2 = 70.56
Applying another round of pythagorean theorem gets us
a^2+b^2 = c^2
b = sqrt(c^2 - a^2)
CE = sqrt( (CB)^2 - (EB)^2 )
CE = sqrt( 70.56 - 35.28 )
CE = 5.939696961967
It turns out that CE and EB are the same length, ie triangle CEB is isosceles. This is because triangle ABC isosceles as well.
Notice how CB = CE*sqrt(2) and how CB = EB*sqrt(2)
------------------------------------
Now let's focus on triangle CED
We just found that CE = 5.939696961967 is one of the legs. We know that CD = 8.4 based on what the diagram says.
We'll use the pythagorean theorem once more
c = sqrt(a^2 + b^2)
ED = sqrt( (CE)^2 + (CD)^2 )
ED = sqrt( 35.28 + 70.56 )
ED = 10.2878569196893
This rounds to 10.3 when rounding to one decimal place (aka nearest tenth).
Answer: 10.3==============================================================
Now I'm moving onto the figure in the bottom right corner.
Draw a segment connecting B to D. Focus on triangle BCD.
We have the two legs BC = 3.7 and CD = 3.7, and we need to find the length of the hypotenuse BD.
Like before, we'll turn to the pythagorean theorem.
a^2 + b^2 = c^2
c = sqrt( a^2 + b^2 )
BD = sqrt( (BC)^2 + (CD)^2 )
BD = sqrt( (3.7)^2 + (3.7)^2 )
BD = 5.23259018078046
Which is approximate. If we squared both sides, then we would get (BD)^2 = 27.38 which will be useful in the next round of pythagorean theorem as discussed below. This time however, we'll focus on triangle BDE
a^2 + b^2 = c^2
b = sqrt( c^2 - a^2 )
ED = sqrt( (EB)^2 - (BD)^2 )
x = sqrt( (5.9)^2 - (5.23259018078046)^2 )
x = sqrt( 34.81 - 27.38 )
x = sqrt( 7.43 )
x = 2.7258026340878
x = 2.7
--------------------------
As an alternative, we could use the 3D version of the pythagorean theorem (similar to what you did in the first problem in the upper left corner)
The 3D version of the pythagorean theorem is
a^2 + b^2 + c^2 = d^2
where a,b,c are the sides of the 3D block and d is the length of the diagonal. In this case, a = 3.7, b = 3.7, c = x, d = 5.9
So we get the following
a^2 + b^2 + c^2 = d^2
c = sqrt( d^2 - a^2 - b^2 )
x = sqrt( (5.9)^2 - (3.7)^2 - (3.7)^2 )
x = 2.7258026340878
x = 2.7
Either way, we get the same result as before. While this method is shorter, I think it's not as convincing to see why it works compared to breaking it down as done in the previous section.
Answer: 2.7Answer:
Qu 2 = 10.3 cm
Qu 3. = 2.7cm
Step-by-step explanation:
Qu 2. Shape corner of a cube
We naturally look at sides for slant, but with corner f cubes we also need the base of x and same answer is found as it is the same multiple of 8.4^2+8/4^2 for hypotenuse.
8.4 ^2 + 8.4^2 = sq rt 141.42 = 11.8920141 = 11.9cm
BD = AB = 11.9 cm Base of cube.
To find height x we split into right angles
formula slant (base/2 )^2 x slope^2 = 11.8920141^2 - 5.94600705^2 = sq rt 106.065
= 10.2987863
height therefore is x = 10.3 cm
EB = 5.9cm
BC = 3.7cm
CE^2 = 5.9^2 - 3.7^2 = sqrt 21.12 = 4.59565012 = 4.6cm
2nd triangle ED = EC- CD
= 4.59565012^2- 3.7^2 = sq rt 7.43000003 =2.72580264
ED = 2.7cm
x = 2.7cm
A driveway is in the shape of a rectangle 30 feet wide by 35 feet long. Find the perimeter in feet. & Find the area in square feet.
the shorter side of a rectangle is 60% of the longer side and the perimeter of the rectangle is 96 inches. find the side lengths
Answer:length 30, width 18
Step-by-step explanation:
60% +100%=160%
160% × 2 = 320 %
96/320 = 0.3 ×100 =30 ( length)
30 × 0.6 =18 (width)
Check: (18 + 30) 2 = 96
How do I solve this?
The answer for the first line segment : (-3,-7) (-4,0)
The answer for 2nd line segment is :(-3,8) (-9,-5)
Step-by-step explanation:
Let do line segment QR and ST. first.
Step 1: Find a line that contains a points that is perpendicular to the line of reflection
"A reflection of a pre image and new image is perpendicular to the line of reflection.
This means for points Q,S,T and R, there is a line that. contains one point that is perpendicular to the line of reflection.
A line that is perpendicular to the line of reflection is the negative reciprocal of the slope so this means all 4 lines must be on a different slopes but the slopes must be 1/2.
To simplify, things, here are the lines that will all 4 points be on
Point R will be on line y=1/2x-11/2Point Q will be on line y=1/2x+2Point S will be on line y=1/2x+19/2Point T will be on line y=1/2x-1/2Step 2: Find a point where both the line and line of reflection intersect at.
Now we need to find a line where both the line of reflections and the 4 lines will intersect at separately.
The line with Point R will intersect with the line of reflection at point (1,-5)The line with Point Q will intersect with line of reflection at Point (-2,1)The line with Point S will intersect at point (-5,7)The line worth Point T will intersect at Point(-1,-1).Step 3: Find the endpoints given the midpoint and the originally endpoint.
A reflection per and new image is equidistant from the point of reflection. So we. an say that the point where the line intersect is the midpoint of the pre and new image.
Using this info,
The endpoint for R prime is (-3, -7).The endpoint for Q prime is (-4,0). The endpoint of S prime is (-3,8).The endpoint of T prime is (-9,-5).Connect R prime and Q prime. And that the new line segments
Connects S prime and T prime and that the new line segments.
(10 points!) The function below has an input, x, and produces a specific output, c. (Pictured below.)
Answer:
x =[tex]x =(\frac{c}{4} )^{1/3} \\[/tex]
input 2 output 32
output 256 input 4
Step-by-step explanation:
express ratio as a fraction in it's lowest terms.48s to 5minutes
Answer:
4/25.
Step-by-step explanation:
We need to have the 2 values in the same unit so:
converting minutes to seconds:
5 mins = 5*60 = 300 seconds.
The require fraction =
48/300
The GCF of 48 and 300 is 12 so we have:
48/12 / 300/12
= 4/25
The required fraction of 48 seconds to 5 minutes is 4 / 5 minutes.
Given that,
To express the ratio as a fraction in its lowest terms.48s to 5 minutes.
In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
Here,
60 second = 1 minute
1 second = 1 / 60 minute
multiply both sides by 48
48 second = 48 / 60 minute
48 second = 4 / 5 minute
Thus, the required fraction of 48 seconds to 5 minutes is 4 / 5 minutes.
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In a box of chocolates, 12 of the chocolates are wrapped in red foil. That is 30% of the chocolates in the box. How many chocolates are there?
Answer:
The answer is 40 chocolates in the box in total
Skylar's grades on four math tests are 85, 78, 77, and 69. What does Skylar need to score on the next test in order to have a mean score of 80?
Answer:
91Step-by-step explanation:
The mean the the average of 5 numbers. If the next score is x, then the mean is:
(85 + 78 + 77 + 69 + x)/5 = 80Solve it for x:
309 + x = 80*5x = 400 - 309x = 91It is given that,
The mean is the average of 5 numbers.
Then if the,
Next score is x the mean will be.
We can solve now,
→ (85 +78 +77 + 69 + x)/5 = 80
→ (309 + x)/5 = 80
→ 309 + x = 80 × 5
→ 309 + x = 400
→ x = 400 - 309
→ x = 91
Hence, the next score is 91.
In studying the sampling distribution of the mean, you were asked to list all the different possible samples from a small population and then find the mean
of each of them. Consider the following:
Personal phone calls received in the last three days by a new employee were 2. 4, and 7. Assume that samples of size 2 are randomly selected with replacement from
this population of three values
What different samples could be chosen? What would be their sample means?
O A. Possible samples 2-4, 2-74-2: 4-7, 7-2,7-4
Sample means: 3,45,55
O B. Possible samples: 2-2.2-4,2-74-2, 4-4 4-7,7-2,7-4.7-7
Sample means: 2, 3, 4, 4.5,55,7
OC. Possible samples: 2-4 2-7, 4-7
Sample means: 3.4,45
a
Q
rd
5a2 + b(a2 + 5) + b2
[tex]\rightarrow\sf {5a}^{2} + {b(a}^{2} + 5) + {b}^{2} [/tex]
Solution:[tex]\rightarrow\sf {5a}^{2} + {b(a }^{2} + 5) + {b}^{2} \\ = \sf {5a}^{2} + {ba}^{2} + b \times 5 + {b}^{2} \\ = \large\boxed{\sf{\red{ {5a}^{2} + {ba}^{2} + 5b + {b}^{2} }}}[/tex]
Answer:[tex]\rightarrow\large\boxed{\sf{\red{ {5a}^{2} + {ba}^{2} + 5b + {b}^{2} }}}[/tex]
[tex]\color{red}{==========================}[/tex]
✍︎ꕥᴍᴀᴛʜᴅᴇᴍᴏɴǫᴜᴇᴇɴꕥ
✍︎ꕥᴄᴀʀʀʏᴏɴʟᴇᴀʀɴɪɴɢꕥ
There are 16 tablespoons in one cup. Which table correctly relates the number of cups to the number of tablespoons?
Answer:
The first table.
Step-by-step explanation:
1 cup = 1 * 16 = 16 tablespoons
2 = 2 * 16 = 32
3 = 3*16 = 48
4 = 4*16 = 64 and so on....
Graph the linear equation find three points that solve the equation then plot on the graph. x-y=0
Answer:
Step-by-step explanation:
> the equation given is x-y =0
> three points that will solve the equation could be
if x= -2 , y = -2 then x-y = 0 is -2 -(-2) =0 so it works point (-2,-2)
if x=1, y = 1 then x-y = 0 is 1-1 =0 is true so we have point (1, 1)
if x=2 ,y= 2 then x-y = 0 is 2-2 =0 is true so we have point (2, 2)
if cosA=3√2/5,then show that cos2A=11/25
Answer:
Step-by-step explanation:
Cos 2A = 2Cos² A - 1
[tex]= 2*(\frac{3\sqrt{2}}{5})^{2}-1\\\\=2*(\frac{3^{2}*(\sqrt{2})^{2}}{5^{2}})-1\\\\=2*\frac{9*2}{25} - 1\\\\=\frac{36}{25}-1\\\\=\frac{36}{25}-\frac{25}{25}\\\\=\frac{11}{25}[/tex]
Write the quadratic form in the form specified then give the vertex of its graph.
Answer:
Equation: f(x) = 2(x + 5)^2 + 2
Vertex: (-5, 2)
Step-by-step explanation:
The form the question wants us to write the quadratic function in is called "vertex form":
f(x) = a (x - h)^2 + k
a = the a in a standard quadratic equation (y = ax^2 + bx + c) or the coefficient of the x^2
h = x coordinate of the vertex
k = y coordinate of the vertex
To find the vertex, we are going to use the quadratic equation given:
2x^2 + 20x + 52
Comparing it to the standard quadratic equation (y = ax^2 + bx + c),
a = 2
b = 20
c = 52
Now we can start finding our vertex.
To find h, we are going to use this formula:
-b / 2a
We already know b = 20 & a = 2, so we can just substitute that into our formula:
- (20) / 2*2
Which equals:
-20/4 = -5
So h (or the x coordinate of the vertex) is equal to -5
Next we will find k, or the y coordinate of the vertex.
To do that, we are going to plug in -5 into 2x^2 + 20x + 52:
2(-5)^2 + 20(-5) + 52
2(25) -100 + 52
50 - 100 + 52
-50 + 52
2
k (or the y coordinate of the vertex) is equal to 2
The vertex is (-5, 2)
However, we still need to find our equation in vertex form.
We know a = 2, h = -5, & k = 2. Now we substitute these into our vertex form equation:
a(x - h)^2 + k
(2)(x - (-5))^2 + (2)
2(x + 5)^2 + 2
(Remember that the -5 cancels with the - in front of it, making it a positive 5)
The equation is f(x) = 2(x + 5)^2 + 2
Hope it helps (●'◡'●)
