Expanding out the equation, we get
[tex]x^2 - ax - bx+ab+x^2 -bx-cx+bc+x^2 -ax-cx+ac=0 \\ \\ 3x^2 -x(2a+2b+2c)+(ab+bc+ac)=0[/tex]
Considering the discriminant,
[tex](2a+2b+2c)^2 - 4(3)(ab+bc+ac) \\ \\ =4a^2 + 4b^2 + 4c^2 + 8(ab+bc+ac)-12(ab+bc+ac) \\ \\ =4(a^2 + b^2 + c^2 - ab - bc - ac) \\ \\ =2((a-b)^2 + (b-c)^2 + (c-a)^2)[/tex]
This is always non-negative, meaning the roots are real.
The roots are equal if and only if the discriminant is 0, which is when a=b=c.
Mei paid $1.64 in sales tax on a purchase of $20.50. What is the sales tax rate?
Round to the nearest given place.
1.80949 thousandths
Answer:
1.80950 because 9 is a strong number and it will affect all of them
Listed below are the numbers of doctor's office visits made by 8 families during the past year.
14, 15, 2, 12, 6, 2, 4, 3
Send data to calculator
(a) What is the median of this data set? If your answer is not
an integer, round your answer to one decimal place.
(b) What is the mean of this data set? If your answer is not an
integer, round your answer to one decimal place.
(c) How many modes does the data set have, and what are
their values? Indicate the number of modes by clicking in the
appropriate circle, and then indicate the value(s) of the
mode(s), if applicable.
0
0
zero modes
O one mode:
O two modes: and
Putting the data in sequential order, we get:
2, 2, 3, 4, 6, 12, 14, 15(a) The median is (4+6)/2 = 5.
(b) The mean is (2+2+3+4+6+12+14+15)/8, or about 7.3.
(c) There is one value that occurs the most, so there is one mode, which is 2.
please help and show your work :(
Answer:
Answer is the picture attached
How to find the equation of the line through (1/2,6) and parallel to x=3
Answer:
y=6
Step-by-step explanation:
x=3 is parallel to the y axis so the perpendicular line will be parallel to the x axis and will equals y=6 so it will pass through the point which have a y coordinate of 6
complete the table of values
Answer:
-2 = 1
-1 = 3
0 = 5
1 = 7
2 = 9
Step-by-step explanation:
screenshot shows questions HELP PLEASE ITS DUE TODAY
The operations between the data-sets are given as follows:
8. B ∩ A = {2,3}.
9. A ∩ U = {2,3,5,6}.
10. n(B) = {1,5,6,7}.
11. B x C = {{2,5}, {2, 1}, {2, 3}, {3, 5}, {3,1}, {3,3}}.
What is the intersection operation between two data-sets?The intersection operation between two data-sets is the set that is composed by all the elements that belong to both data-sets. The intersection operation is represented by the symbol ∩.
From the data-sets in this problem, we have that:
B ∩ A = {2,3}, as elements 2 and 3 both belongs to sets A and B.A ∩ U = {2,3,5,6}, as elements 2, 3, 5 and 6 both belongs to sets A and U.What is the negation of a data-set?The negation of a data-set is the set that contains all elements belonging to the universe set U but not to the data-set.
Hence, from the data-sets in this problem, we have that:
n(B) = {1,5,6,7}.
In which n(B) is the negation of set B.
What is the multiplication between two data-sets?The multiplication between two data-sets is given by all ordered pairs formed from the two data-sets.
Hence the solution for item 11 is given as follows:
B x C = {{2,5}, {2, 1}, {2, 3}, {3, 5}, {3,1}, {3,3}}.
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if x=8 than what us the value of 11x-12x
Answer: -8
Step-by-step explanation:
Multiply the 8 by the 11 and -12
11(8) - 12(8)
88-96
8
write an equation in slope- intercept form for the line described.
perpendicular to y = 1/4x + 2 passes through (0,0)
Answer:
y=-4x+0
Step-by-step explanation:
Slope form is y=mx+b
m is the slope, and b is the y intercept. If the line must pass through (0,0) then the y intercept would be zero.
This give you y=mx+0
Now to find the slope you need a perpendicular line to the previous line. This would mean you have to swap 1/4 which is the previous lines slope.
1/4 is a positive so make it a negative, -1/4
Now flip -1/4 to make is -4/1 which also equals -4
Now with the slope -4 and y-intercept 0, you know you equation
y=-4x+0
The following is the slope of line representing annual sale y in term of time x in year.
The line has a slope of m= –20.
Interpret the slope in the context of the problem
Answer:
m= -40
Step-by-step explanation:
each of Mrs.Whites two children received $50 for their savings account. The original amounts in their savings accounts were $500 and $300, respectively. Without calculating, which savings account had a greater percent of increase
Answer: 69
Step-by-step explanation: Your mom
$ 500 because the amount of percentage increase faster.
What is percentage increase?
The amount that has increased from the initial number to the final number in terms of 100 parts of the original is essentially what the concept of percent increase refers to.
As per the question
Each of Mrs. white two children received $50 of their saving account
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty We can only predict only the chance of an event to occur it is how likely they are to happen, using it.
So the original found in their saving account
Let a=$500
b=$300
A has greater amount in compared to be so
$500 I'd a greater percentage of increasing amounts.
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What number has a GCF of 5 and a LCM of 210
Answer:35 &75
Step-by-step explanation:
HELP 50 POINTS (see image attached)
5
1
2
8
-2
The value of the function f(3) is 1
How to determine the value of f(3)?The graph represents the given parameter
The value of f(3) implies that we calculate the value of the function when x = 3
From the graph, we have
f(x) = 1, when x = 3
This means that
f(3) = 1
The above is calculated by substituting 3 for x in the equation f(x) = 1
Hence, the value of f(3) is 1
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Please help me and don’t copy off the internet
Answer:
1. (-1.5,0), -3/2, or -1(1/2)
2.(-16,0)
Step-by-step explanation:
1. explanation:
the 2 and the -5 are 8 spaces apart (-5,-4,-3,-2,-1,0,1,2). the exact halfway point of them is -1.5. the exact halfway point between 5 and -5 is 0. thus led me to (-1.5,0.) I then graphed it on desmos to see if it was halfway, which it is. (refer to the image)
2. explanation:
the distance between -6 and 4 is 10, so -16 would be the first half of the endpoint location. Then the distance between 4 and 8 is 4, so 4-4 is 0. the start point of 2 is (-16,0)
Solve for all possible values of x.
√60 8x = x - 9
The possible values of x are 3 and 7
Solving rational expressionsGiven the rational expression below;
√60-8x = x - 9
Square both sides to have:
(60-8x)² = (x-9)²
60-8x = x²-18x+81
Equate to zero to have;
x²-18x+81 - 60 + 8x = 0
x² - 10x + 21 = 0
x² -3x-7x +21 = 0
x(x-3)-7(x-3) = 0
x = 3 and 7
Hence the possible values of x are 3 and 7
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PLS HELP ME SOLVE THIS LIKE THE EQUATION ABOVE!!!
-7(-2x + 6)= -168
Answer:
x = -9
Step-by-step explanation:
-7(-2x+6) = -168
distributive property:
-7*-2x + (-7*6) = -168
14x+-42 = -168
14x = -126
x = -9
Write the three numbers before and after 1022 five all in base five. Just enter the number. Please do
not enter base five. so 1022 five just enter 1022.
1022 five
The three numbers before 1022₅ are 1014₅, 1020₅, 1021₅ while the three numbers after 1022₅ are 1023₅, 1024₅, 1030₅
How to write the three numbers before and after 1022₅ all in base five?The number is given as
1022₅
As a general rule in number base.
If the base of a number is n
The highest digit in any number in that base is n - 1
This means that the highest digit in base 5 is 4
Using the above as a guide, the three numbers before 1022₅ are 1014₅, 1020₅, 1021₅ while the three numbers after 1022₅ are 1023₅, 1024₅, 1030₅
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A bag contains 3 red
marbles, 5 blue marbles and 4 green marbles. If three marbles
are drawn out of the bag, what is the exact probability that all three marbles drawn
will be blue?
Can y’all help me please??
Answer:
[tex]\frac{5}{42}[/tex]
Step-by-step explanation:
It makes a difference if the marbles are place bag into the bag after selecting. Since this is not stated, I am assuming that once a marble is selected, it is not placed back in the bag.
[tex]\frac{5}{9}[/tex] x [tex]\frac{4}{8}[/tex] x [tex]\frac{3}{7}[/tex] = [tex]\frac{60}{504}[/tex] This simplified would be [tex]\frac{5}{42}[/tex] The 5 represent the number of blue marbles available our of 9 total marbles. Next, we only have 4 blue marbles available out of a total of now 8 marbles and lastly, for the third draw we only have 3 blue marbles available and only 7 total marbles are left.
If the marbles are replaces that changes the problem and the answer would be [tex]\frac{5}{9}[/tex] x [tex]\frac{5}{9}[/tex] x [tex]\frac{5}{9}[/tex] = [tex]\frac{121}{729}[/tex]
help please asap i need answer correct
Answer
12 bottles
Step-by-step explanation:
recad
Is 2x-y=6 a function of x?
Answer:
Explanation:
one way is to find the intercepts, that is where the graph
crosses the x and y axes
∙
let x = 0, in the equation for y-intercept
∙
let y = 0, in the equation for x-intercept
x
=
0
→
0
+
y
=
−
6
⇒
y
=
−
6
←
y-intercept
y
=
0
→
2
x
+
0
=
−
6
⇒
x
=
−
3
←
y-intercept
plot
(
0
.
−
6
)
,
(
−
3
,
0
)
and draw a straight line
through them
graph{-2x-6 [-14.24, 14.24, -7.12, 7.12]}
Factor x² + xy-2x-2y.
Answer: (x-2)(x+y)
Step-by-step explanation:
x² + xy-2x-2y=
x(x+y)-2x-2y=
x(x+y)-2(x+y)=(x-2)(x+y)
Answer:
[tex] \large \boxed{(x- 2)(x+y)}[/tex]
Step-by-step explanation:
[tex] {x}^{2} + xy - 2x - 2y[/tex]
We are given with 4 terms. so use grouping method for factoring. To factor the given expression we take out GCF
[tex]x^2- 2x +xy - 2y[/tex]
we group first two terms and last two terms
then take out GCF from each group
[tex]x(x-2) +y(x-2)[/tex]
Now take out common factor x-2
[tex](x- 2)(x+y)[/tex]
state whether each function is a linerar function, write yes or no. explain y = 3/4x
Marlene earned $178 at her summer job. She already had savings of $98.25. She buys a T-shirt for $19.50. How much money does she have left.
Answer:
256.75 or 257 rounded to the nearest 10th
Step-by-step explanation:
What is
Tan x% =4 over 9
The value of x in tan x = 4 over 9 is x = 23.9
How to determine the value of x?The trigonometric equation is given as
tan x = 4 over 9
Rewrite the above equation properly
So, we have
tan(x) = 4/9
Evaluate the quotient
So, we have
tan(x) = 0.4444
Take the arc tan of both sides
x = 23.9
Hence, the value of x in tan x = 4 over 9 is x = 23.9
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Find x and y and i just need the answer, no need to show work.
Answer:
x= 20
y = 60
Step-by-step explanation:
y = 3x
6(3x) = 360
3x = 360/6
3x = 60
x = 20
y = 3*20
y = 60
Describe the values of C for which C has no solutions.
Explain Your Reasoning
/X-7/= C
WILL GIVE BRAINLIEST
Answer:
Negative values of c.=====================
Given equation|x - 7| = cThe left side is an absolute value, which is never negative.
So if c < 0, then the equation has no solutions.
Translate to an algebraic expression and simplify: the product of 8 and -13
Answer:
(8)(-13); -104
Step-by-step explanation:
Product means to mutliply, so the expression is (8)(-13), which evaluates to -104.
Jaquan passed a checkpoint jogging at a constant speed of 9 km/h. Then, 2 minutes later Odalis passed the same checkpoint.
If Odalis runs at a constant speed of 12 km/h, then how far past the checkpoint will Odalis be when they catch up to Jaquan?
The distance from the check point when Odalis catch up Jaquan is 1.2 kilometers.
What is relative speed ?Relative speed is the net speed difference when objects move in the same direction and sum of individual speeds when objects move in opposite direction.
Given Jaquan speed is 9km/hr which is 0.15km/minute and Odalis has a speed of 12km/hr which is 0.2km/minute.
∴ The relative speed difference between Jaquan and Odalis is
= (0.2 - 0.15) km/hr.
= 0.05 km/hr.
Given Odalis reached the check post after 2 minutes in this time Jaquan have covered (2×0.15) kilometers.
= 0.30 kilometers.
Now to catch up Jaquan, Odalis will need (0.30/0.05) minutes which is
= 6 minutes.
∴ The distance from the check post Odalis travelled to catch up with Jaquan is (0.2×6) kilometers.
= 1.2 kilometers.
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Answer:
1.2 km
Step-by-step explanation:
thats the answer on khan
When a die is thrown, the total number of possible outcomes are …………………?
Answer:
when a die is thrown,the total number of possible outcomes are 1 because die has cubical shape so only one outcomes is possible.
Find a relationship between x and y so that (x, y) is equidistant from the two points (4, –1) and (6, 3).