Can some please help me with this question? And can you show your work too? I will mark the best answer Brainliest
Answers
Answer:
Finding the vertex by completing the square
1) The vertex = (4/3, -4/3)
2) The vertex = (-1/2, 36)
3) The vertex = (2/3, 26/3)
Finding the value of x by completing the square
1) x = 1 or -4
2) x = 3/2 or -7/2
3) x = 1 or -3
Step-by-step explanation:
Finding the vertex by completing the square
The vertex form of the quadratic equation y = ax² + bx + c is written as follows;
y = a(x - h) + k
Therefore, we have;
Y = 3·x² + 4 - 8·x = a(x - h)² + k
Hence, a = 3
Which gives;
3×(x² - 2·x·h + h²) + k
Hence, we have 3×2×h = 8
h = 8/6 = 4/3
The constant term = k
We note that 3 × h² + k = 4
∴ k = 4 - 16/3 = -4/3
The vertex form is therefore;
Y = 3(x - 4/3)² - 4/3
The vertex = (4/3, -4/3)
2) Where Y = 4·x² + 4·x + 36
a = 4
4× -2·h = 4
∴ h = 4/(4 × (-2)) = 4/-8 = -1/2
Also, 4 × h² + k = 36
Which gives;
4 × (-1/2)² × k = 36
k = 36
The vertex form becomes
y = 4(x - (-1/2)) + 36
The vertex = (-1/2, 36)
3) Where Y = -3·x² + 4·x + 10, we have
a = -3
3×2×h = 4
∴ h = 4/(2×3) = 2/3
a×h² + c = k
-(3)×(2/3)² + 10 = 26/3
Which gives;
Y = -3(x - 2/3) + 26/3
The vertex = (2/3, 26/3)
To find the value of x by completing the square, we have;
1) 2·x² = -6·x + 8
2·x² + 6·x = 8
2·(x² + 3·x) = 8
x² + 3·x = 8/2 = 4
x² + 3·x + (3/2)² = 4 + (3/2)² = 25/4
(x + 3/2)² = 25/4
∴ x + 3/2 = ±5/2
x = 5/2 - 3/2 or -5/2 - 3/2
x = 1 or -4
2) 8·x² + 16·x = 42
8·(x² + 2·x) = 42
x² + 2·x = 42/8 = 21/4
x² + 2·x + 1 = 21/4 + 1 = 25/4
(x + 1)² = 25/4
x + 1 = √(25/4) = ± 5/2
x = 5/2 - 1 or -5/2 - 1
∴ x = 3/2 or -7/2
3) -x² + 2·x = -3
-x² + 2·x = -3
-1×(-x² + 2·x) = -1 ×-3 = 3
x² - 2·x = 3
x² - 2·x + 1 = 3 + 1 = 4
(x - 1)² = 4
x - 1 = √4 = ±2
∴ x = 2 - 1 or -2 - 1
x = 1 or -3
Related Questions
If g(x)=2x-1 and h(x)= swuare root x, find (g o h) (9)
Answers
Answer:
5
Step-by-step explanation:
To evaluate (g ￮ h)(9), evaluate h(9) , then use this value to evaluate g(x)
h(9) = [tex]\sqrt{9}[/tex] = 3, then
g(3) = 2(3) - 1 = 6 - 1 = 5
Ursula tosses two six-sided number cubes and ADDS the numbers rolled. Which of these is a list of the outcomes of the two row? A) 3, 4, 5, 6, 7, 8 B) 2,4,6,8, 10, 12 C) 5, 8, 11, 14, 17, 20 D) 0/25, 1/25, 3/25, 5/25, 6/25, 25/2
Answers
Answer:
A) 3, 4, 5, 6, 7, 8
Step-by-step explanation:
2+1, 2+2, 2+3, 2+4, 2+5, 2+6= 3, 4, 5, 6, 7, 8
For each hour he babysit,Anderson earns 1$ more than half of carey's hourly rate.Anderson earns 6$ per hour. wich equation can be used to solve for carey's hourly rate,c?
Answers
Answer:
The expression to find Carey's hourly rate is: [tex]c = 2*a - 2[/tex]. Carey's hourly rate is $10.
Step-by-step explanation:
Anderson receives 1 more than half of carey's hourly rate. If we call Anderson's rate by "a" and Carey's by "c", we can express this phrase in the following equation:
[tex]a = \frac{c}{2} + 1[/tex]
We want to find the Carey's rate, therefore we need to isolate the "c" variable.
[tex]\frac{c}{2} + 1 = a\\\frac{c}{2} = a - 1\\c = 2*a - 2[/tex]
Since Anderson earns $6, then we can find Carey's rate:
[tex]c = 2*6 - 2 = 12 - 2 = 10[/tex]
Answer:
A)
6 = c/2 + 1
Three tickets to attend an Off-Broadway show cost $81, 4 tickets cost $108, and 5 tickets cost $135. Show that the relationship between number and the cost is a proportional relationship by making a table of tickets for 1 to 5 tickets. Show your work. Number of Tickets 1 2 3 4 5 Total Cost ($) What is the constant of proportionality, k? Write and Equation for the relationship. (Remember to state what the variables represent)
Answers
Answer:
k=27y=27xStep-by-step explanation:
3 tickets to attend an Off-Broadway show cost $81,
4 tickets cost $108; and
5 tickets cost $135.
Let the price of a ticket=k
Therefore:
3k=814k=1085k=135Solving any of the equation above gives: x=27
We therefore have:
[tex]\left|\begin{array}{c|c|c|c|c|c}$Tickets&1&2&3&4&5\\$Total Cost(\$)&27&54&81&108&135\end{array}\right|[/tex]
Let y be the total cost of x tickets
From the above, the constant of proportionality, k=27An equation for the relationship is therefore:
y=27x (where x is the number of tickets and y is the total costs (in $)).
How many solutions exist for the given equation?
CO
3(x - 2) = 22-X
name
zero
one
two
infinitely many
can someone help me pls
Answers
Answer:
one
Step-by-step explanation:
3(x - 2) = 22 - x
3x - 6 = 22 - x
3x + x = 22 + 6
4x = 28
4x/4 = 28/4
x = 7
Use Cramers Rule to solve the system
-x-3y=-8
2x+4y=12
Answers
Answer:
x = 2 y = 2
Step-by-step explanation:
just do equation form
Answer:
[tex]x=2[/tex] and [tex]y=2[/tex]
Step-by-step explanation:
To use Cramer's Rule, we first need to turn this system of equations into a matrix
[tex]A=\left[\begin{array}{cc}-1&-3\\2&4\\\end{array}\right][/tex] , [tex]b=\left[\begin{array}{c}-8\\12\\\end{array}\right][/tex]
The first step to use Cramer's Rule is to find the determinant of the original matrix
[tex]detA=(4)(-1)-(2)(-3)\\\\detA=-4+6\\\\detA=2[/tex]
Next, we need to replace column 1 of matrix A with b and then find the determinant of that matrix
[tex]A_1=\left[\begin{array}{cc}-8&-3\\12&4\\\end{array}\right][/tex]
[tex]detA_1=(-8)(4)-(12)(-3)\\\\detA_1=-32-(-36)\\\\detA_1=4[/tex]
And now we need to replace column 2 of matrix A with b and then find the determinant of that matrix
[tex]A_2=\left[\begin{array}{cc}-1&-8\\2&12\\\end{array}\right][/tex]
[tex]detA_2=(-1)(12)-(2)(-8)\\\\detA_2=-12-(-16)\\\\detA_2=4[/tex]
Now that all of this is done, we can find the values for our x matrix.
Recall that Cramer's Rule states that
[tex]x=\left[\begin{array}{c}\frac{detA_1}{detA} \\\frac{detA_2}{detA} \\\end{array}\right][/tex]
Now that we know all of the required determinants, we can find x
[tex]x=\left[\begin{array}{c}\frac{4}{2} &\frac{4}{2} \end{array}\right] \\\\x=\left[\begin{array}{c}2\\2\\\end{array}\right][/tex]
This means that the solutions to this system are [tex]x=2[/tex] and [tex]y=2[/tex]
What is the answer to 2(5x+4)=8
Answers
Answer:
So first we have 10x = 0. We divide by 10 on both sides, so then we get x = 0. We still have 0 because 0/10 = 0.
So that means that the answer is
Write 10 in the first box 10 in the secondx=0Answer:
? = 10
Step-by-step explanation:
2(5x+4)=8 - DISTRIBUTE
= 10x + 8 = 8
10x + 8 = 8
- 8
10x = 0
10x/10 = 0/10
x = 0
Subtract the equations 5x+4y= 25 -(5x+2y=3)
Answers
Lou's Shoes is having its annual Flag Day Sale and is offering a 25% discount on all regularly priced shoes. Kayla spends $13.50 buying sandals and sneakers. Determine which equation represents how much Kayla will spend on sandals after the discount. $13.50 = 0.75(x + 10) $13.50 – 10 = 0.75x $13.50 + 10 = 0.75x $13.50 = 0.25(x + 10)
Answers
Answer:
13.50=0.75(x+10)
Step-by-step explanation:
From the options given, it seems the price of either of Sandals or sneakers is given as 10 and the other is x
If Price of Sandals or sneakers=x
And the price of the other one is 10
Total price=(x+10)
25% discount is given
So she will pay 75% of the total cost
75%=0.75
Total cost =$13.50
She would pay 75% of (x+10)
Which is
0.75(x+10)=13.50
13.50=0.75(x+10)
Answer:
The answer is $13.50 = 0.75(x + 10)
Step-by-step explanation:
I am doing the assignment right now
Your Welcome :)
Colin spends 1/3 of his wages on rent and 1/4 on food. If he makes £636 per week, how much money does he have left?
Answers
Answer:
£265
Step-by-step explanation:
Total fraction of money spent= [tex]\frac{1}{3} +\frac{1}{4}[/tex]
= [tex]\frac{7}{12}[/tex]
Actual money spent = [tex]\frac{7}{12}[/tex] * £636
= £371
Money he has left = £(636 - 371)
= £265
Answer:
$265
Step-by-step explanation:
Ken built a 20 foot square fence in his back yard and planted a tree every 5 feet along the fence. How many trees did Ken plant?
Answers
Answer: 41
Step-by-step explanation:
Answer:
c:16
Step-by-step explanation:
Which property allows you to write the expression
(3 + 7i) + (8 − 6i) as (8 − 6i) + (3 + 7i)?
Answers
Answer:
3+7i
Step-by-step explanation:
Answer:
Associative
Step-by-step explanation:
I got it on edge hope ur not as far behind as me boys
which expression is equivalent to: -9x^-1y^-9/-15x^5y^-3
Answers
Answer:
3 / 5x^6y^6
Step-by-step explanation:
= -9x^-1y^-9/-15x^5y^-3
= -9y-9 / -15x^6y^-3
= -9 / -15x^6y^6
= 3 / 5x^6y^6
Answer:
b on edge
Step-by-step explanation:
James has a bicycle. Each wheel has diameter 45cm. James cycles his bicycle in a straight line in the playground. The front wheel makes 15 complete revolutions. How far does the bicycle travel? Give your answer in metres.
Answers
Answer: 21.21 meters
Step-by-step explanation:
Hi, to answer this, first we have to calculate the circumference (C) of the wheel:
C = π x diameter
Replacing with the values given:
C = π x 45 = 141.37 cm
Then we multiply it by the number of revolutions:
141.37 x 15 = 2,120.6 cm
Since
1 cm = 0.01 m
2,120.6 x 0.01 = 21.21 meters
Feel free to ask for more if needed or if you did not understand something.
How many inches are in a square foot?
Answers
Answer:
144 inches.
Step-by-step explanation:
One foot = 12 inches
One square foot = 144 inches.
Answer:
144
Step-by-step explanation:
Foot=12 inch
Square foot= foot times foot
Square foot= 12 inch times 12 inch
Square foot= 144 square inch.
80 people were asked which was their favourite animal.
The pictogram shows the results.
The key is missing.
Cat
a)
Which animal was the least popular?
b)
How many people does
represent?
Dog
Giraffe DDI
Monkey D.
Dolphin
c)
How many more people preferred
giraffes than dogs?
Answers
Answer:
(a)Cat
(b)8 animals
(c)6 people
Step-by-step explanation:
From the attached diagram:
Let the [tex]\square[/tex] be x.
Half of [tex]\square[/tex] =x/2
From the pictogram, we then have:
[tex]Cat = x+\frac{x}{4} \\Dog=x+\frac{3x}{4}\\Giraffe=2x+\frac{x}{2}\\Monkey =x+\frac{x}{2}\\Dolphin=3x[/tex]
Therefore:
[tex]x+\frac{x}{4} +x+\frac{3x}{4}+2x+\frac{x}{2}+x+\frac{x}{2}+3x=80\\8x+\frac{x}{4}+\frac{3x}{4}+\frac{x}{2}+\frac{x}{2}=80\\10x=80\\x=8[/tex]
So we have the following numbers
[tex]Cat = x+\frac{x}{4} =8+\frac{8}{4}=10\\Dog=x+\frac{3x}{4}=8+\frac{3*8}{4}=14\\Giraffe=2x+\frac{x}{2}=2*8+\frac{8}{2}=20\\Monkey =x+\frac{x}{2}=8+\frac{8}{2}=12\\Dolphin=3x=3*8=24[/tex]
(a)Cat was the least popular
(b) [tex]\square[/tex] represents 8 animals
(c)
Number of People who preferred giraffe=20
Number of People who preferred dogs=14
Difference=20-14=6
Therefore, 6 more people preferred giraffes than dogs.
A pictogram is a simple drawing that represents something
(a). Cat is least popular animal
(b)Total 8 complete square in given pictogram represented 64 people.
(c) 6 more people preferred giraffes than dogs.
Let us consider that a large complete square represented by variable y .
Since, peoples whose favourite animal is cat is represented by a complete square and one fourth of square.
It means, Peoples who like cat = [tex]y+\frac{y}{4}[/tex]
Similarly,
People who like dog = [tex]y+\frac{3}{4}y[/tex]
Peoples who like Giraffe = [tex]2y+\frac{y}{2}[/tex]
Peoples who like monkey = [tex]y+\frac{y}{2}[/tex]
Peoples who like Dolphin = [tex]3y[/tex]
Since, total people = 80
Therefore,
[tex]y+\frac{y}{4}+y+\frac{3}{4}y+2y+\frac{y}{2}+y+\frac{y}{2} +3y=80\\\\10y=80\\\\y=\frac{80}{10}=8[/tex]
So, a complete large square is equivalent to 8 peoples.
Peoples who like giraffes = [tex]2y+\frac{y}{2}=2(8)+\frac{8}{2}=20[/tex]
Peoples who like dog = [tex]y+\frac{3}{4}y=8+(\frac{3}{4} ) 8=14[/tex]
So, 20 - 14 =6 more people preferred giraffes than dogs.
Thus,
(a) Cat is least popular animal
(b)Total 8 complete square in given pictogram represented 64 people.
(c) 6 more people preferred giraffes than dogs.
Learn more:
https://brainly.com/question/23021563
Divide 21a^3-14a by -7
Answers
Answer:
A
Step-by-step explanation:
[tex]\dfrac{21a^3-14a}{-7}= \\\\\\\dfrac{-7(-3a^3+2a)}{-7}= \\\\\\-3a^3+2a[/tex]
Hope this helps!
Please help ASAP! Correct answer only! I need to finish this assignment today.
There are 9 college students running for student government class president. The candidates include 5 biology majors.
If 5 of the candidates are randomly chosen to give the first 5 speeches, what is the probability that exactly 3 of the chosen candidates are biology majors?
Write your answer as a decimal rounded to four decimal places.
Answers
Answer:
0.4762
Step-by-step explanation:
There are 9C5 = 126 ways to choose 5 candidates to give speeches. There are (5C3)(4C2) = 60 ways that 3 of those candidates can be biology majors (and the other two can be non-biology majors). The probability of interest is ...
60/126 ≈ 0.4762
__
nCk = n!/(k!(n-k)!)
If f(x) = 3x2 + 1 and g(x) = 1 - x, what is the value of (f - g)(2)
Answers
Answer:
14
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= 3x² + 1 - (1 - x)
= 3x² + 1 - 1 + x
= 3x² + x , thus
(f - g)(2)
= 3(2)² + 2 = 3(4) + 2 = 12 + 2 = 14
Please answer the following:
Answers
CLASS 8 SPOT TEST
1. WHAT IS THE PROBABILITY THAT AN INTEGER CHOSEN AT RANDOM BETWEEN 1 TO 10 INCLUSIVE IS EVEN?
2. A BAG CONTAINS 5 WHITE, 4 BLACK AND 1 BLUE BALLS. ONE BALL IS CHOSEN AT RANDOM. WHAT IS THE PROBABILITY THAT IT IS BLACK?
3. FIND THE PROBABILITY OF GETTING AN ODD NUMBER IN A SINGLE TOSS OF A FAIR DIE?
4. A FAIR DIE IS THROWN 900 TIMES. FIND THE NUMBER OF TIMES YOU WOULD EXPECT TO GET A 6.
5. THE PROBABILITY THAT IT WILL BE CLOUDY TOMORROW IS 0.45. WHAT IS THE PROBABILITY THAT IT WILL NOT BE CLOUDY TOMORROW?
Step-by-step explanation:
1. Of the following 10 numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
Only these 5 are even: 2, 4, 6, 8, 10.
The probability on an even number is 5 / 10 = 0.5 = 50%
2. The total number of balls is 10.
5 WHITE, 4 BLACK AND 1 BLUE
The probability on a black ball is 4 / 10 = 0.4 = 40%
3. A fair die can show the following 6 numbers 1, 2, 3, 4, 5, 6.
Only these 3 are odd: 1, 3, 5.
The probability on an odd number is 3 / 6 = 0.5 = 50%
4. The probability of a six is 1 / 6. If the die is cast for 900 times you can expect it to be 900 * 1 / 6= 900/6 = 150. The number of times you would expect a 6 would be 150.
5. If the probability on a cloudy tomorrow is 0.45, then in mathematics, that defines the propability for an non cloudy tomorrow as 1 - 0.45 = 0.55, which is 55%.
(The total should always add up to 100%).
If h(x) = x – 7 and g(x) = x2, which expression is equivalent to (g circle h) (5)?
Answers
Answer:
4
Step-by-step explanation:
[tex]h(x)=x-7 \\\\g(x)=x^2 \\\\(g\circ h)(5)= (5-7)^2=(-2)^2=4[/tex]
Hope this helps!
Using composite functions, it is found that the equivalent expression at x = 5 is given by:
[tex](g \circ h)(5) = 4[/tex]
What is a composite function?A composite function is when a function is used as an input to another function, hence, that is:
[tex](g \circ h)(x) = g(h(x))[/tex].
In this problem, we have that the functions are given as follows:
h(x) = x - 7.g(x) = x².Then, the composite function is given by:
[tex](g \circ h)(x) = g(h(x)) = g(x - 7) = (x - 7)^2[/tex].
We want to find the value of the composite function at x = 5, hence we have that:
(5 - 7)² = 4.
More can be learned about composite functions at https://brainly.com/question/17684028
#SPJ2
pls help me I need to finish it!!
Answers
Answer:
2/7
Step-by-step explanation:
7/8 ÷ 3 1/16
Change to an improper fraction
3 /16 = (16*3+1)/ 16 =49/16
7/8 ÷49/16
Copy dot flip
7/8 * 16/49
Rewrite
7/49 * 16/8
Simplify
1/7 * 2/1
2/7
In RST, the measure of
Answers
Answer:
27.5 degrees
Step-by-step explanation:
First, choose which method would work in this problem, SOH, CAH, or TOA.
We have opposite, O and adjacent, A. So we have an O and an A.
Thus, we should use TOA.
Tangent x = 44/84
Tangent x= 0.52
x= Tangent^-1 (0.52)
x=27.5 degrees
Answer:27.6
Step-by-step explanation:
PLEASE HELP FOR A BRAINLIEST!!!! Create your own example and explain how to solve Quadratic Equation using Quadratic Formula. What part in the Quadratic Formula is the discriminant and how do you know the number of solutions based on the value of the discriminant?
Answers
Answer:I'm gonna be doing a quadratic equation explaining step by step and using the formula so the example i'm gonna be using for today is
3[tex]x^{2}[/tex] +5[tex]x^{}[/tex]=7 I'm gonna answer the question then explain how i got the answer the i will explain to you about the discriminant section
Step-by-step explanation:
So here is the explanation for the equation given above
One thing you need to know about quadratic equation is that there has to be a 0 on the other side of the equation given to you
3[tex]x^{2}[/tex]+5[tex]x^[/tex]-7=0
Therefore you have to group the numbers into a,b and c
a=3
b=5
c=7
Your'e gonna use a plus or minus sign like the one below
x=-(5)+[tex]\sqrt{}[/tex]5
sorry i cannot understand it very well i tried though
-
Please help me! Anyone know this answer :(
Answers
Answer:
A
Step-by-step explanation:
2x-3=5(x+6)
2x-3=5x+30
2x-33=5x
3x=-33
x=-11
Hope this helps!
Kate gets a paycheck twice a month. Every month, a total of $345.67 is deducted from her paychecks for taxes. If she has received 7 paychecks so far this year, which best represents the total effect the taxes have had on the amount she has earned??
Answers
Answer:
The correct answer is -$1,209.85-verified by Edg. Thank you.
Step-by-step explanation:
Answer:
B
Step-by-step explanation:
Help pls! I ended up getting the wrong answer, so an explanation would help! (:
Answers
Answer:
4p squared - 28pqStep-by-step explanation:
4p(p−7q)
=(4p)(p+−7q)
=(4p)(p)+(4p)(−7q)
=4p squared −28pq
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Help me please this is due today help me
Answers
Answer:
Below
Step-by-step explanation:
1. -4, -|2|, -1, |-3|, 4
2. -7.5, -7.2, 9.5, 10.5
3. 7
5. 13
6. -9
7. [tex]\frac{5}{12}[/tex]
8. -1.36
9. [tex]\frac{13}{5}*[/tex][tex]\frac{-4}{3}[/tex][tex]=\frac{-52}{15}[/tex]
10. -27.2
11. 22 * 2 + 7 * 0 - 5 * 1 = 39
How fast did the truck consume its fuel?
Pro
Choose 1 answer:
Tea
60 liters per kilometer
0.6 liters per kilometer
40 liters per kilometer
0.4 liters per kilometer
Answers
Answer: 0.6 liters per kilometer
Step-by-step explanation:
(A) 475L - 50km
(B) 375L - 200km
Subtract liters.
475-375=100L
Subtract km
200-50=150km
Divide liters per km
100/150=0.6L/km
What is the slope? 50 points + brainly
Simplify your answer and write it as a proper fraction, improper fraction, or integer.
Answers
Answer:
1/2
Step-by-step explanation:
Hi there, let me show you how to answer this question.
If you notice, the line goes over (-1,-10) and (1,-9). But overall, the rise/run is 1/2 as the rise is 1 and the run is 2.