Answers
Answer:
1 + i[tex]\sqrt{5}[/tex], 1 - i[tex]\sqrt{5}[/tex]
Step-by-step explanation:
A quadratic function is f(x) = a[tex]x^{2}[/tex] + bx + c
Your function with the given values is f(x) = 2[tex]x^{2}[/tex] - 4x + 12
To solve a quadratic function, you can use the quadratic formula
(-b +/- [tex]\sqrt{b^{2} - 4ac}[/tex]) / 2a
Fill in with your given values.
(4 +/- [tex]\sqrt{(-4^{2} - 4 (2) (12)}[/tex] ) / 2(2)
Simplify
(4 +/- [tex]\sqrt{16 - 96}[/tex]) / 4
(4 +/- [tex]\sqrt{-80}[/tex] ) / 4
Because there is a negative number under the square root making it an imaginary number put an i by it.
(4 +/- i[tex]\sqrt{80}[/tex]) / 4
80 is divisible by 16, a perfect square. 80 / 16 = 5
(4 +/- 4i[tex]\sqrt{5}[/tex]) / 4
Divide by 4
1 +/- i[tex]\sqrt{5}[/tex]
Your teacher may want you to list your radical without the i and just as [tex]\sqrt{-5}[/tex], so keep that in mind.
Don't forget to list it both as addition and subtraction.
Related Questions
The sum of four consecutive odd integers is three more than five times the least of the integers. Find the integers.
Answers
Answer:
9, 11, 13, 15Step-by-step explanation:
{k - some integer}
2k+1 - the first odd integer (the least)
5(2k+1) - five times the least
5(2k+1)+3 - three more than five times the least
2k+1+2 = 2k+3 - the odd integer consecutive to 2k+1
2k+3+2 = 2k+5 - the next odd consecutive integer (third)
2k+5+2 = 2k+7 - the last odd consecutive integer (fourth)
2k+1+2k+3+2k+5+2k+7 - the sum of four odd consecutive integers
2k+1 + 2k+3 + 2k+5 + 2k+7 = 5(2k+1) + 3
8k + 16 = 10k + 5 + 3
- 10k -10k
-2k + 16 = 8
-16 - 16
-2k = -8
÷(-2) ÷(-2)
k = 4
2k+1 = 2•4+1 = 9
2k+3 = 2•4+3 = 11
2k+5 = 2•4+5 = 13
2k+7 = 2•4+7 = 15
Check: 9+11+13+15 = 48; 48-3 = 45; 45:5 = 9 = 2k+1
A teacher earns $28,500 per year. If 18% of her income is withheld for taxes, how
much money is withheld for taxes? How much of her income is left after taxes?
Answers
Answer:
23,370
Step-by-step explanation:
Because 18% of 28,500 is 5130 and 28500-5130=23370
at the end of the pizza party 1/3 of the chesse pizza and 1/6 of the peperoni pizza were left. brad ate 1/2 of all the leftover pizza . what is the fractional part of a whole pizza did brad eat A.1/12 B.1/9 C.1/6 D.1/4
Answers
Answer:
It's 1/6
Step-by-step explanation:
Point P is located on the segment between point A(1, 4) and point D(7, 13). The
distance from A to P is twice the distance from P to D. What are the coordinates
of point P?
Answers
Answer:
(5, 10)
Step-by-step explanation:
If AP : PD = 2 : 1, then ...
P = (2D +1A)/(2+1)
P = (2(7, 13) +(1, 4))/3 = (14+1, 26+4)/3 = (5, 10)
The coordinates of point P are (5, 10).
5x + 25 = 100
what is X
Answers
Answer:
x= 15
Step-by-step explanation:
Step 1- Subtract 25 to both sides.
5x+25= 100
-25 -25
Step 2- Divide both sides by 5.
5x= 75
5 5
x= 15
The value of x for the equation 5x + 25 = 100 is 15.
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
5x + 25 = 4 is an equation
We have,
5x + 25 = 100
Subtract 25 on both sides.
5x = 100 - 25
5x = 75
Divide both sides by 5.
x = 15
Thus,
The value of x is 15.
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Which expression is equal to zero?
0 -27 = 3-9
O 9 + (-27) - -3
O 27+ 3 + 9
O-27 (-3) - 9
Answers
Answer:
D
Step-by-step explanation:
-27 (-3) - 9
Multiply the - 3 with the - 9
-27 +27
= 0
Answer:
Your last choice is the correct answer.
Step-by-step explanation:
1 do the division. -27/(-3)= 9
2 do the subtraction. 9-9=0
Therefore your answer is -27÷(-3)-9
HOPE THIS HELPS!
The diameter of a circular sign is 13.5 inches. Which of the following is a reasonable value for three diameters?
Answers
Answer:
[tex]3\ diameters = 40.5\ inches[/tex]
Step-by-step explanation:
The options are not given; but, the question is still solvable
Given
[tex]Diameter = 13.5\ inches[/tex]
Required
Determine the value of 3 diameters
This is calculated as follows:
[tex]3\ diameters = 3 * diameter[/tex]
[tex]3\ diameters = 3 * 13.5\ inches[/tex]
[tex]3\ diameters = 40.5\ inches[/tex]
Hence, 3 diameters is 40.5 inches
A recipe for 114 dozen cupcakes calls for 123 cups of flour, but Rashida has only 1 cup of flour. How many cupcakes can she make? Hint: Pay close attention to the units! Enter your answer as a mixed number. For example, if your answer is 4212, enter 42 1/2
Answers
Answer:
9 cups
Step-by-step explanation:
Given
[tex]1\frac{1}{4}\ dozen\ cupcakes = 1\frac{2}{3}\ cups[/tex]
Required
Determine the number of cupcakes for 1 flour
Represent this with x
[tex]x = 1\ cup[/tex]
[tex]1\frac{1}{4}\ dozen\ cupcakes = 1\frac{2}{3}\ cups[/tex]
Cross Multiply
[tex]x * 1\frac{2}{3}= 1\frac{1}{4}\ dozen * 1[/tex]
[tex]1\frac{2}{3}x = 1\frac{1}{4}\ dozen[/tex]
Convert fractions to improper fraction
[tex]\frac{5}{3}x = \frac{5}{4}\ dozen[/tex]
Solve for x
[tex]x = \frac{5}{4} * \frac{3}{5}\ dozen[/tex]
[tex]x = \frac{3}{4}\ dozen[/tex]
[tex]1\ dozen = 12[/tex]
So, we have:
[tex]x = \frac{3}{4} * 12[/tex]
[tex]x = 9\ cups[/tex]
Help me please
Jsjejjrhjdososjhsxbxhxjdhdsh
Answers
Answer:
It's 18.
Step-by-step explanation:
17 plus 18 plus 19 equals 54, and the middle number is 18.
4|3x+4|=4x+8 algerbra 2 questions
Answers
Answer:
x=-1 or x=-3/2
Step-by-step explanation:
There was a junior and senior division for the runners in the Friendly 5K Race. Two friends, Boomer and Paulina,
argued about who was faster, relative to their divisions. In the junior division, Boomer had a standardized score of z =-
0.23, while in the senior division, Paulina's standardized score was z = -0.28. Which of the following best describes the
conclusion between the two friends?
Because Boomer has a larger standardized score, he did better relative to his division than Paulina.
Because Boomer has a smaller standardized score, he did better relative to his division than Paulina.
Because Boomer has a larger standardized score, Paulina did better relative to her division than Boomer.
Because Boomer has a smaller standardized score, Paulina did better relative to her division than Boomer.
Because the standardized scores are essentially the same, Boomer and Paulina tied each other, relative to their
divisions.
Answers
Answer:
The correct option is;
Because Boomer has a larger standardized score, he did better relative to his division than Paulina
Step-by-step explanation:
The standard score of Boomer in the junior division = -0.23
The standard score of Paulina in the senior division = -0.28
We note that the standard score is the same as the z-score which is given as follows;
[tex]Z=\dfrac{x-\mu }{\sigma }[/tex]
Where;
μ = The mean or average score (average speed of the runners in a division)
x = The recorded score (the speed recorded by a given runner)
σ = The standard deviation of the data set (of the division)
Therefore, given that we have;
The standard score of Boomer in the junior division = -0.23
The standard score of Paulina in the senior division = -0.28
Therefore, since -0.23 > -0.28, we have;
The standard score of Boomer > The standard score of Paulina
Which gives;
Because Boomer has a larger standardized score, he did better relative to his division than Paulina
Answer:
Because Boomer has a larger standardized score, he did better relative to his division than Paulina.
Explanation:
On the z-table, Boomers score is 59.10% and Paulina’s score is 38.97%. Boomer’s score is larger.
Find the quotient of 1 1/5 and 3 4/5
Answers
Answer:
6\19
Step-by-step explanation:
I put in 4 14\25 like the other peson said to do it was WRONG the real answer is 6\19 Please put me as brainlies!!! Hope this helped! :)
PLZZ HELP ASAP !!!!!!!!
Answers
Answer:
Pretty sure it's negative 3, cause then X would become -3X. Then when you would add 3X to both sides, it would cancel out both of the -3X then you would be left with 5 = 7, which we all know is not right.
Please help me!!!!!!!
Answers
Answer:
Step-by-step explanation:
B or c for the first one
What can you use to show the similarities and differences between what two authors have written on the same topic?
(1 point)
a pie chart
a Venn diagram
a bar graph
a timeline
Answers
Answer:
Venn Diagram
Step-by-step explanation:
Compared similarities and differences
how does increasing the mass affect the gravity of the planet? How do you know?
I’m rlly struggling on this question so I’ll give brainliest to the best answer and 50 points<3
Answers
Answer:
there are two factors to the strength of the gravitational force, mass and distance. if the mass between 2 objects is increased the gravitational force between the 2 objects is also increased.
Since the mass of a body is directly proportional to the graviational force so by increasing the mass the gravitational force also increases.
What is gravitational force?The gravitational force is a force that attracts any two objects with mass. We call the gravitational force attractive because it always tries to pull masses together, it never pushes them apart. In fact, every object, including you, is pulling on every other object in the entire universe.This is called Newton's Universal Law of Gravitation.
The formulas for the universal gravitational force is given by
[tex]F=\dfrac{Gm_1m_2}{r^2}[/tex]
Here G is the universal gravitational constant m1 and m2 are the masses of the two planets. r is the distance between the two bodies.
So from the formula, it is clear that the gravitational force between the two bodies is directly proportional to the masses of the planets.
So when the mass of the planets is high then the gravitational force will also be higher.
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Help ASAP 10 points please
Answers
Answer:
-6 and -7
Step-by-step explanation:
sqrt of 49 is 7 and sqrt of 36 is 6 and 44 is between those two
You plan to buy
discount movie tickets for your
friends that costs $3.50 per ticket
and popcorn that costs $2.50.
Write and solve an inequality to
find out the most amount of
friends you can invite if your
allowance is $13.
Answers
Answer:
2 friends...............
1. & 2. In the diagram below, points A, B, and C are collinear. Answer each of the following questions. The figure shown below is not drawn to scale, meaning you cannot determine your answers by using your ruler.
Answers
Answer:
a) [tex]\overline{AB}[/tex] = 8 in
b) When the length of AC = [tex]6\frac{1}{2}[/tex] in. and BC = [tex]3\frac{1}{2}[/tex] in. [tex]\overline{AB}[/tex] = 10 in
c) When the length of AB = 10.2 in. and BC = 3.7 in. [tex]\overline {AC}[/tex] = 6.5 in
d) When the length of AB = [tex]4\frac{3}{4}[/tex] in. and BC = [tex]3\frac{1}{4}[/tex] in. in. [tex]\overline {BC}[/tex] = [tex]1\frac{1}{2}[/tex] in
Step-by-step explanation:
a) When the length of AC = 5 in. and CB = 3 in. we have;
The length of [tex]\overline {AB}[/tex] = AC + CB (segment addition postulate)
Therefore;
[tex]\overline{AB}[/tex] = 5 in. + 3 in. = 8 in.
b) When the length of AC = [tex]6\frac{1}{2}[/tex] in. and BC = [tex]3\frac{1}{2}[/tex] in. we have;
The length of [tex]\overline {AB}[/tex] = AC + CB (segment addition postulate)
Therefore;
[tex]\overline{AB}[/tex] = [tex]6\frac{1}{2}[/tex] in.+ [tex]3\frac{1}{2}[/tex] in. = 10 in.
c) When the length of AB = 10.2 in. and BC = 3.7 in. we have;
The length of [tex]\overline {AC}[/tex] = AB - BC (converse of the segment addition postulate)
Therefore;
[tex]\overline {AC}[/tex] = 10.2 in.+ 3.7 in. = 6.5 in.
d) When the length of AB = [tex]4\frac{3}{4}[/tex] in. and BC = [tex]3\frac{1}{4}[/tex] in. in. we have;
The length of [tex]\overline {BC}[/tex] = AB - AC (converse of the segment addition postulate)
Therefore;
[tex]\overline {BC}[/tex] = [tex]4\frac{3}{4}[/tex] in. - [tex]3\frac{1}{4}[/tex] in.= [tex]1\frac{1}{2}[/tex] in.
1/3 (6x +12) - 2(x-7)=19
Answers
Answer:
no solution
Step-by-step explanation:
Given
[tex]\frac{1}{3}[/tex](6x + 12) - 2(x - 7) = 19 ← distribute parenthesis on left side
2x + 4 - 2x + 14 = 19 , that is
18 = 19 ← not possible
This indicates the equation has no solution
Please oh please help me I don’t want too fail!
Answers
Answer:
D
Step-by-step explanation:
The best bet would be D because if its going counterclockwise 360 degrees then it would make a full rotation going back to the same position although I would work out the problem to the best of your ability just to make sure because I'm not entirely sure about my answer.
how would I figure out what the value of N is in the question n+3 divided by 8= -4
Answers
Answer:
4
Step-by-step explanation:
What is the solution of the equation: -3m - 21 =-6
answer choices
-45
-5
9
-81
Answers
Answer:
-5
Step-by-step explanation:
Add 21 to both sides:
-3m - 21 = -6
-3m = 15
Divide each side by -3
m = -5
Answer:
-5
Step-by-step explanation:
-3m-21=-6
switch sides to remove the negative sign
6-21=3m
-15=3m
-15/3=m
m=-5
[6(22+4)^2 - 2(19+3)^2]^0 what is the answer
Answers
Answer:
infinite solutions
Step-by-step explanation:
type sum random i will mark brainlist
Answers
Answer: Ummm Thanks :D
Step-by-step explanation:
Find R, if 5R²+ (22.255)² = (27.45)²
Answers
Answer:
R = 7.186340863
Step-by-step explanation:
5R^2 + 495.285025 = 753.5 5025
5R^2 = 258.217475
R^2 = 51.643495
R = 7.186340863
Are u Asian
PLEASE HELP I WILL MARK BRAINIST!!!!
An education budget went from $800,000 to $900,000. What is the approximate percent increase?
A.The approximate percent increase is 13%.
B.The approximate percent
increase is 89%.
C. The approximate percent increase is 98%.
D. The approximate percent increase is 113%.
Answers
Answer:
The answer is A
Step-by-step explanation:
I got it right on edge.
Answer:
The approximate percent increase is 13%.
Step-by-step explanation:
Those that finish the marathon will get a medal - if-then form
Answers
Answer:
if they finish the marathon then they will get a medal
Step-by-step explanation:
Hope this helps
When StartFraction 2 x squared Over y EndFraction = StartFraction w + 2 Over 4 EndFraction is solved for w, one equation is w = StartFraction 8 x squared Over y EndFraction minus 2 Which of the following is an equivalent equation to find w?
Answers
Answer:
a. w=8x^2+2y/y
Step-by-step explanation:
edge 2022
Answer:
a. w=8x^2+2y/y
Step-by-step explanation:
True or False: A method of creating a geometric figure that is mathematically precise by using a compass and
straightedge is called drawing or copying.
Answers
Answer:
true
Step-by-step explanation:
True, A method of creating a geometric figure that is mathematically precise by using a compass and straightedge is called drawing or copying.
Given that,
A statement is given we have to determine whether the statement is true or false.
In congruent geometry, the shapes that are so identical. can be superimposed to themselves.
Here,
The statement is given is, "A method of creating a geometric figure that is mathematically precise by using a compass and straightedge is called drawing or copying."
The given statement si true because the statement is the true definition of drawing or copying, drawing or copying are the methods of creating a figure or portrait of something in precise order.
Thus, the given statement is true.
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