Answers
ANSWER
[tex]y = 3 \pm \sqrt{21} [/tex]
EXPLANATION
The quadratic equation is:
[tex] {y}^{2} - 6y - 12 = 0[/tex]
Group variable terms:
[tex] {y}^{2} - 6y = 12[/tex]
Add the square of half, the coefficient of y to both sides.
[tex] {y}^{2} - 6y + ( - 3) ^{2} = 12 + ( - 3) ^{2} [/tex]
[tex] {y}^{2} - 6y + 9= 12 + 9[/tex]
The LHS us now a perfect square trinomial:
[tex]{(y - 3)}^{2}= 21[/tex]
Take square root:
[tex]y - 3 = \pm \sqrt{21} [/tex]
[tex]y = 3 \pm \sqrt{21} [/tex]
The first choice is correct.
3±√21. The equation [tex]y^{2}-6y-12=0[/tex] has two possible solutions 3+√21 y 3-√21.
If we have a general quadratic equation [tex]ay^{2} +by+c=0[/tex] we can solves the equation by completing the square. First, we divide the quadratic equation by a, we obtain [tex]y^{2} +\frac{b}{a} y+\frac{c}{a} =0[/tex].
For this problem, we have [tex]y^{2}-6y-12=0[/tex]
We can skipped division in this example since the coefficient of [tex]x^{2}[/tex] is 1.
Move the term c to the right side of the equation
[tex]y^{2}-6y=12[/tex]
Completing the square on the left side of the equation and balance this by adding the same number to the right side of the equation, with b = -6.
[tex](\frac{b}{2})^{2} =(\frac{-6}{2})^{2}=(-3)^{2} =9[/tex]
[tex]y^{2}-6y+9=12+9[/tex]
[tex](y-3)^{2}=21[/tex]
Take the square root on both sides of the equation:
y - 3 = ±√21
Add 3 from both sides:
y = 3 ± √21
Related Questions
The longest river in the UK is the river Severn which has a length of 24 cm on a map. If the map is drawn at a scale of 1:1,500,000, then how many kilometers is the river actually?
Answers
Answer:
360 km
Step-by-step explanation:
we know that
The scale of the map is
1:1,500,000
That means
1 cm on a map ------> represent 1.500.000 cm in the actual
or
1 cm on a map ------> represent 15,000 m in the actual
or
1 cm on a map ------> represent 15 km in the actual
therefore
In this problem
24 cm on a map-------> represent 24*15=360 km actually
The actual length of the river Severn is 360 kilometers.
To determine the actual length of the river Severn, we need to apply the map scale to the map length. The scale given is 1:1,500,000, which means that 1 unit of measurement on the map corresponds to 1,500,000 of the same units in reality.
The map length of the river Severn is given as 24 cm. To find the actual length, we multiply the map length by the scale factor:
[tex]\[ \text{Actual length} = \text{Map length} \times \text{Scale factor} \] \[ \text{Actual length} = 24 \, \text{cm} \times 1,500,000 \][/tex]
Since the scale is in centimeters to kilometers, we need to convert the map length from centimeters to kilometers before multiplying by the scale factor. There are 100,000 centimeters in a kilometer, so:
[tex]\[ 24 \, \text{cm} = \frac{24}{100,000} \, \text{km} \] \[ 24 \, \text{cm} = 0.00024 \, \text{km} \][/tex]
Now, we multiply this by the scale factor:
[tex]\[ \text{Actual length} = 0.00024 \, \text{km} \times 1,500,000 \] \[ \text{Actual length} = 360 \, \text{km} \][/tex]
Therefore, the actual length of the river Severn is 360 kilometers.
help needed asap on this
Answers
Answer:
option D is correct.
Step-by-step explanation:
The real number y=a is the root of the polynomial f(y) if and only if
f(a) =0
So, when we see a graph of the polynomial, the x-intercepts are the real roots of the graph f(y)
We can find x-intercept of graph, by looking at the graph and finding out points that touch the x-axis on the graph.
In the graph given the points -6 and 2 touch the x-axis of the graph, So these are the real roots of the graph.
So, option D is correct.
Which word describes an angle with a measure of 98"?
A) Obtuse
B) Right
C)Acute
D) Complementary
Answers
Answer:
A) Obtuse.
Step-by-step explanation:
Angles of value between 90 and 180 degrees are called obtuse.
Answer:
obtuse
Step-by-step explanation:
because an obtuse angle is any angle from 91°-180°
Please help me, I need to divide this problem (-2/7)(5/-8)
Answers
Answer:
5/28 (Decimal: 0.178571)
Step-by-step explanation:
(−2/7) (5/−8)
= −2/7 (5/−8)
=−2/7 (−5/8)= 5/28
The equation of a circle is given. What is the diameter of the circle? Round to the nearest tenth.
(x-2)2 + (y+3)2 = 52
Answers
Answer:
14.2 is the diameter.
Step-by-step explanation:
The radius squared = 52.
What you have given is the general equation of the circle with a center at (2,-3) and a radius of sqrt(52)
You can break the 52 down.
sqrt(52) = sqrt(4 * 13) = 2 sqrt(13). Notice that 4 is a perfect square.
d = 2*radius.
d = 2(2 sqrt(13) )
d = 4 sqrt(13)
That is the diameter. You want it to the nearest 1/10
d = 14.222 but it is to the nearest 1/10
d = 14.2
Archie used 1/3 of a jar of tomato sauce to 3/8 make of a pizza. How
many jars of tomato sauce will Archie need to make one whole pizza?
Answers
For this case we make a rule of three:
[tex]\frac {1} {3}[/tex] jar ---------------> [tex]\frac {3} {8}[/tex] pizza
x -----------------------------------------> 1 pizza
Where the variable "x" represents the amount of sauce jars to make a pizza.
[tex]x = \frac {1 * \frac {1} {3}} {\frac {3} {8}}\\x = \frac {8} {9}[/tex]
So, you need [tex]\frac {8} {9}[/tex] jars of sauce to make a pizza.
Answer:
[tex]\frac {8} {9}[/tex]
Answer:
Final answer is [tex]\frac{8}{9}[/tex] of a jar.
Step-by-step explanation:
Given that Archie used 1/3 of a jar of tomato sauce to make 3/8 of a pizza. Now we need to find about how many jars of tomato sauce will Archie need to make one whole pizza.
We can setup ratio of sauce and pizza to easily solve that problem.
Let amount of sauce needed to make 1 pizza = x
then ratio will be :
[tex]\frac{sauce}{pizza}=\frac{x}{1}=\frac{\frac{1}{3}}{\frac{3}{8}}[/tex]
[tex]\frac{x}{1}=\frac{\frac{1}{3}}{\frac{3}{8}}[/tex]
[tex]x=\frac{\frac{1}{3}}{\frac{3}{8}}[/tex]
[tex]x=\frac{1}{3}\cdot\frac{8}{3}[/tex]
[tex]x=\frac{8}{9}[/tex]
Hence final answer is [tex]\frac{8}{9}[/tex] of a jar.
Pocket contains 15 white eight pink three yellow and 10 blue golf balls. A ball is chosen at random, not replaced then another is chosen at random. What is the probability of blue, then pink
Answers
Answer:
4/63
Step-by-step explanation:
The probability of first choosing a blue golf ball and then a pink golf ball, without replacement, from the pocket is 4/63.
The question asks for the probability of selecting a blue golf ball and then a pink golf ball from a pocket that contains 15 white, 8 pink, 3 yellow, and 10 blue golf balls, without replacement. To solve this, we need to find the probabilities of each event happening sequentially and then multiply them.
Firstly, the probability of choosing a blue ball initially is 10 out of the total number of balls (15 white + 8 pink + 3 yellow + 10 blue), which gives us 36.
Therefore, the probability is 10/36 or 5/18. Once a blue ball has been chosen, it is not replaced, so the total count of balls is reduced by one, making it 35, and the count of blue balls is now 9.
Secondly, with the blue ball removed, we now calculate the probability of choosing a pink ball. There would still be 8 pink balls, so the probability of now choosing a pink ball is 8 out of the remaining 35 balls. This gives us the probability of 8/35.
To find the overall probability of both events happening in sequence (first a blue ball, then a pink ball), we multiply the individual probabilities: (5/18) × (8/35) = 40/630, which can be simplified to 4/63.
Zoo tickets for 5 people cost a total of $41. Write an equation that can be used to determine the cost, c in dollars of each ticket
Answers
Answer:
Step-by-step explanation:
5t=41
The equation to determine the cost, c, of each zoo ticket when five zoo tickets cost a total of $41 is 'c = $41 / 5'.
Explanation:To find the cost of each zoo ticket, we need to divide the total cost of all the tickets by the number of people. Given that 5 people's zoo tickets cost a total of $41, we can set up the equation for this situation like this:
c = $41 / 5
Here, 'c' represents the cost of each zoo ticket in dollars. The equation suggests that when you divide the total cost ($41) by the total number of tickets (5), you get the cost of each individual ticket (c).
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The general term of an arithmetic sequence is tn = 32 + 3n, where n ∈N and n ≥ 1. The sequence is A) 32, 35, 38, 41, 44, 47,... B) 32, 96, 288, 864, 2592, 7776,... C) 34, 39, 44, 49, 54, 59,... D) 35, 38, 41, 44, 47, 50,...
Answers
Answer:
35,38,41,44,47,50,....
Step-by-step explanation:
n ∈N means that n is an element of Natural numbers
Natural numbers are whole non-negative numbers
n ≥ 1, means that n = 1, 2, 3, 4, 5, 6,........
tn = 32 + 3n
the first term t1 = 32 + 3(1)
32 + 3 = 35
the second term t2 = 32 + 3(2)
32 + 6 = 38
the third term t3 = 32 + 3(3)
32 + 9 = 41
what changes in the parent graph y= |x| would you see if you graphed y= |x+3| ?
Answers
Answer:
The graph is shifted 3 units to the left
Step-by-step explanation:
Answer:
The parent graph will shift 3 units to the right.
Step-by-step explanation:
We are given that there is this parent graph with the equation [tex] y = | x | [/tex] and if we graph [tex] y = | x + 3 | [/tex], what are the changes that will be made to the parent graph to get this.
Since there is addition of 3 units in x, therefore the parent graph will shift 3 units to the right side.
The graph given above shows the following function
y= cos(x)
What is the amplitude of the function?
a. 2
b. pi
c. 2pi
d. 1
Answers
Answer:
D,1
Step-by-step explanation:
look at the wavelengths
Answer: For plato user the correct answer is C
Step-by-step explanation:
Just took the test and got it correct
The definition of an angle uses the undefined term_______.
line
plane
point
ray
Answers
Answer:
I believe the answer is C. Point
Step-by-step explanation:
Hope my answer has helped you!
Answer:
The correct answer is option C - point
Step-by-step explanation:
The definition of an angle uses the undefined term : POINT
An angle has two rays that share a common endpoint.
This common point is also referred to as the vertex.
Angles that meet at 90 degrees are called right angles.
Angles that are less than 90 degrees are called acute angles.
Angles that are exactly 180 degrees are called straight angles.
which number line shows the solution for
Answers
Answer:
It's the last choice.
Step-by-step explanation:
| n | ≤ 2 represents the distance between n and 0 that is less than or equal to 2. The dots on the 2 and -2 are black because the equal sign is part of the inequality.
Note the vertical lines about the n mean the absolute value of n - the positive distance between n and 0, which has a maximum of 2 either side of the 0.
The correct number line shows the solution for |n| ≤ 2 is shown in Option D.
What is mean by Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
We have to given that;
Inequality is,
⇒ | n | ≤ 2
Now, We can simplify as;
⇒ | n | ≤ 2
This gives,
⇒ n ≤ 2
⇒ - n ≤ 2
⇒ n ≥ - 2
Hence, The solution is belong in [- 2, 2].
Which shown in Option D.
So, The correct number line shows the solution for |n| ≤ 2 is shown in Option D.
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What is the reciprocal of (22z)/(11x)?
Answers
Hello!! The answer is 11x/22z
Your Welcome
11x/22z is the answer because the reciprocal just means you flip the fraction so the top is on on the bottom and vise versa
The phone company NextFell has a monthly cellular plan where a customer pays a flat monthly fee and then a certain amount of money per minute used on the phone. If a customer uses 210 minutes, the monthly cost will be $108.5. If the customer uses 620 minutes, the monthly cost will be $252.
A) Find an equation in the form
y
=
m
x
+
b
,
where
x
is the number of monthly minutes used and
y
is the total monthly of the NextFell plan.
Answer:
y
=
B) Use your equation to find the total monthly cost if 979 minutes are used.
Answer: If 979 minutes are used, the total cost will be
dollars.
Get help: Video
Answers
Answer:
1. y=0.35x+35
2. If 979 minutes are used, the total cost will be $377.65 dollars.
Step-by-step explanation:
1. Let $x be the flat monthly fee and $y be the amount of money paid per minute used on the phone.
If a customer uses 210 minutes, the monthly cost will be $108.5, thus
[tex]x+210y=108.5[/tex]
If the customer uses 620 minutes, the monthly cost will be $252, then
[tex]x+620y=252[/tex]
Subtract from the second equation the first one:
[tex]x+620y-(x+210y)=252-108.5\\ \\x+620y-x-210y=143.5\\ \\410y=143.5\\ \\y=0.35[/tex]
Substitute it into the first equation
[tex]x+210\cdot 0.35=108.5\\ \\x=108.5-73.5\\ \\x=35[/tex]
We get the flat fee is $35 and the amount of money per minure used is $0.35. So, the equation of the function is
[tex]y=35+0.35x,[/tex]
where x is the number of monthly minutes used and y is the total monthly of the NextFell plan.
2. When x=979, then
[tex]y=35+0.35\cdot 979=377.65[/tex]
solve the equation 2y²=13y
Answers
Step-by-step explanation:
2y² = 13y
2y² − 13y = 0
y (2y − 13) = 0
y = 0, y = 13/2
It can be tempting to divide by y at the beginning, but if you do, you lose one of the solutions. Instead, move everything to one side and factor.
The solutions to the equation 2y²=13y are y = 0 and y = 6.5. This is achieved by setting up the equation to zero, factoring it out and applying the zero product property.
Explanation:To solve the provided equation, 2y²=13y, you'll need to set the equation to zero by moving all the terms to one side: 2y² - 13y = 0. This becomes a quadratic equation in the form ax² + bx + c = 0.
Factor the equation by taking out a common factor of 'y', yielding y(2y - 13) = 0. According to the zero product property, if a product is zero then at least one of the factors must be zero. This means that y = 0 or 2y - 13 = 0. Solving the second equation gives y = 6.5.
So, the solutions of the equation are y = 0 and y = 6.5.
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Given the following triangle, if c = 25 and 2 A= 20°, find a.
Answers
Answer: A=2
Explanation:
1: c=25
2: 2a=20
3: 1 a=20
if i have a 0.75 ( F ) and i get an A x2 what will my grade be
Answers
Answer:
Maybe a C if the grade is summative
Step-by-step explanation:
F's are not hard to raise, you're gonna need more than 2 A's to get a "passing grade." Try extra credit!
A pyramid has a square base that is 9 inches on a side.If the height of the pyramid is 8 inches, then its volume is 24 cubic inches.
Answers
Answer:
The statement is false
The volume of the square pyramid is [tex]V=216\ in^{3}[/tex]
Step-by-step explanation:
we know that
The volume of the square pyramid is equal to
[tex]V=\frac{1}{3}b^{2}h[/tex]
we have
[tex]b=9\ in[/tex]
[tex]h=8\ in[/tex]
substitute
[tex]V=\frac{1}{3}(9)^{2}(8)[/tex]
[tex]V=216\ in^{3}[/tex]
ANSWER FOR BRAINLIEST AND 72 POINTS
If a normal distribution has a mean of 132 and a standard deviation of 20, what is the value that has a z-score of 2.4?
A. 168
B. 180
C. 144
D. 204
Answers
Answer:
-6.42
Step-by-step explanation:
looked it up swwaa
PLEASE HELP!!!
Driving across country, mike drove for 3 hours at a certain rate and for 4 hours at a rate 10 mph faster. If his total distance covered was 495 miles, then what was his slower rate?
Answers
Answer:
50 miles per hour
Step-by-step explanation:
Given: circle k(O), m LM = 164°, m WK = 68°, m∠MLK = 65° . Find: m∠LMW
Answers
Answer:
The measure of angle LMW is
[tex]m\angle LMW=67\°[/tex]
Step-by-step explanation:
see the attached figure to better understand the problem
step 1
Find the measure of arc MW
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m\angle MLK=\frac{1}{2}[arc\ MW+arc\ WK][/tex]
substitute the given values
[tex]65\°=\frac{1}{2}[arc\ MW+68\°]\\ 130\°=[arc\ MW+68\°]\\ arc\ MW=130\°-68\°=62\°[/tex]
step 2
Find the measure of arc LK
we know that
[tex]arc\ LM+arc\ MW+arc\ WK+arc\ LK=360\°[/tex] -----> by complete circle
substitute the given values
[tex]164\°+62\°+68\°+arc\ LK=360\°\\ 294\°+arc\ LK=360\°\\ arc\ LK=360\°-294\°=66\°[/tex]
step 3
Find the measure of angle LMW
we know that
The inscribed angle measures half that of the arc comprising
so
[tex]m\angle LMW=\frac{1}{2}[arc\ LK+arc\ WK][/tex]
substitute the given values
[tex]m\angle LMW=\frac{1}{2}[66\°+68\°]=67\°[/tex]
i dont know the answer. Can someone help me ?
Answers
Answer:
V = 18 pi unit ^3
Step-by-step explanation:
Volume of a cylinder is given by
V = pi r^2 h
where r is the radius and h is the height
V = pi * (3)^2 *2
V = pi *9(2)
V = 18 pi unit ^3
The volume of a cylinder is
(Pi) x (radius squared) x (height) .
Using this, you can FIND the volume of any cylinder, even when you don't know it. This one is 18 pi cubic units.
PLEASE HELP! the plot and table show the number of people, p, who have bought tickets to a concert ,t, minutes after they went on sale. complete the equation to show the relationship between p and t
Answers
The relationship is that (P) and (T) shows how many people come in that amount of time. Sorry I dont if that will work.
The relationship between the number of people (p) and time in hours (t) is represented by the linear equation p = 25t, where m = 25 is the slope, and b = 0 is the y-intercept.
To determine the relationship between the number of people (p) who bought tickets and the time in hours (t), we can use a linear equation of the form p = mt + b, where m is the slope and b is the y-intercept.
Looking at the table, we can observe that for every 1-hour increase in time, the number of people increases by 25. This indicates that the slope (m) is 25. To find the y-intercept (b), we can use the initial point (0, 0) from the table.
Substitute these values into the equation: 0 = m(0) + b.
Solving for b, we get b = 0.
Therefore, the equation describing the relationship is p = 25t, where p is the number of people and t is the time in hours.
Step-by-step solution:
1. Identify the slope (m): From the table, the number of people increases by 25 for each 1-hour increase in time, so m = 25.
2. Find the y-intercept (b): Use the initial point (0, 0) in the equation 0 = m(0) + b to find that b = 0.
3. Write the equation: The relationship is p = 25t, where p is the number of people and t is the time in hours.
What is 50 percent of 62?
Answers
Answer:
31
Step-by-step explanation:
An entire amount is 100% of the amount.
50% is half of 100%, so 50% means the same as half.
Half of 62 is the same as 62/2 = 31
Answer: 31
Generally you would need to do a [tex]\frac{part}{whole}[/tex] proportion but there is a shorter way to do just the specific question. If you would like to know how to do the proportion version let me know
Since it asks for 50% of 62 it means that it's looking for half of 62, so all you have to do is divide 62 by 2 which is...
62/2 = 31
31 is 50% of 62
Hope this helped!
Give the slope of y- 4 = 5(x - 2) and a point on the line.
A. The slope is 5 and (-2,-4) is on the line.
B. The slope is 5 and (2, 4) is on the line.
C. The slope is 4 and (2,5) is on the line.
D. The slope is 2 and (5, 4) is on the line.
Answers
Answer:
B. The slope is 5 and (2, 4) is on the line.Step-by-step explanation:
The point-slope form of an equation of a line:
[tex]y-y_1=m(x-x_1)[/tex]
m - slope
(x₁, y₁) - point
We have the equation:
[tex]y-4=5(x-2)[/tex]
Therefore
m = 5
(x₁, y₁) = (2, 4)
Answer:B The slope is 5 and (2,5) is on the line
Step-by-step explanation:
.
What is the solution to -41-2x + 61 = -24?
x = 0
x = 0 or x = -6
x = 0 or x = 6
no solution
Answers
Answer:
No solution
Step-by-step explanation:
Anyone of the values of x satisfies the equation. We can see it even calculating with basic math. If x is 0, then -41 -2(0) + 61 = -24
-41 +61 =-24
20 = -24 is incorrect
If x is -6, then -41 -2(-6) =-24
-41+12=-24
-29 = -24 incorrect.
If x is 6, then -41-2(6) + 61 = -24
-41-12+61 = -24
-53 + 61 = -24
8 = -24 is incorrect.
So it has no solution.
what point is a solution?
Answers
(3,2) is the solution
Answer:(3,2) is the solution.
Step-by-step explanation:
Which equation would best help solve the following problem?
Maria releases a javelin 1.5 m above the ground with a initial vertical velocity of 22 m/s. How long will it take the javelin to hit the ground?
(Possible answer in picture)
Answers
Answer:
- 4.9t + 22t= 1.5 is the answer
Use the table from a random survey about the preferred service for streaming movies. Out of 750 people, how many would you expect to prefer Company B?
Answers
Answer:
The correct answer option is 192.
Step-by-step explanation:
We are given the results of a random survey about the preferred service for streaming movies.
We are to find the number of people we would expect to prefer Company B.
Number of people using service B = 32
Total number of people = 125
Number of people expected to prefer Company B = [tex] \frac{32}{125} \times 7 5 0 [/tex] = 192
Answer: Option A
192 people[
Step-by-step explanation:
From the participation survey
[tex]n =75+32+18=125[/tex] people
Among these 125 people, only 32 preferred the company B
Now assuming that this sample is representative of the total population, then the probability that a randomly selected person prefers company B is:
[tex]P =\frac{X_B}{n}[/tex]
Where
[tex]X_B=32[/tex]
[tex]n=125[/tex]
[tex]P =\frac{32}{125}[/tex]
[tex]P =0.256[/tex]
Finally, the expected number of people who prefer company B is:
[tex]E = P * m[/tex]
Where m is the number of people in the total population. [tex]m = 750[/tex]
[tex]E=0.256*750[/tex]
[tex]E=192\ people[/tex]