Let a and b be the zeroes of x² + kx + 12 such that |a - b| = 1.
By the factor theorem, we can write the quadratic in terms of its zeroes as
x² + kx + 12 = (x - a) (x - b)
Expand the right side and equate the coefficients:
x² + kx + 12 = x² - (a + b) x + ab
Then
a + b = -k
ab = 12
The condition that |a - b| = 1 has two cases, so without loss of generality assume a > b, so that |a - b| = a - b.
Then if a - b = 1, we get b = a - 1. Substitute this into the equations above and solve for k :
a + (a - 1) = -k → 2a = 1 - k → a = (1 - k)/2
a (a - 1) = 12 → (1 - k)/2 • ((1 - k)/2 - 1) = 12
→ (1 - k)²/4 - (1 - k)/2 = 12
→ (1 - k)² - 2 (1 - k) = 48
→ (1 - 2k + k²) - 2 (1 - k) = 48
→ k² - 1 = 48
→ k² = 49
→ k = ± √(49) = ±7
A train is traveling at 60 km down the tracks, it continues traveling for 6
hours, how far did the train travel? *
A. 10 km
B. 120 km
C. 360 km
D. 12 km
please help with this!!
Answer:
the answer is a
Step-by-step explanation:
because 60/6= 10
can somebody help me with this problem ???
Answer:
r7
Step-by-step explanation:
Solve by taking square roots (r+8)(4r-1)=0
Answer:
The answer is r={-8,1/4}
Find the slope of a line that passes through the
following ordered pairs. Reduce to lowest
terms.
(-6, 9) & (2,9).
Given that,
Point 1 = (-6,9)
Point 2 = (2,9)
To find,
The slope of a line that passes through the given pair.
Solution,
We have,
x₁ = -6, x₂ = 2, y₁ = 9, y₂ = 9.
The formula for the slope of a line is given by :
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}\\\\=\dfrac{9-9}{2-(-6)}\\\\=0[/tex]
Hence, the slope of the line that passes through the given pair is 0.
2(x -1) + 1/2 (4x + 6)=5
X: -4. Y: -3
Step-by-step explanation:
fgh is a right triangle
Answer: FALSE
Step-by-step explanation:
A P E X
Answer:
true
Step-by-step explanation:
10. A hobby pack of baseball cards contain 9 cards and a jumbo pack
contains 35 cards. Ethan bought 7 packs for a total of 141 cards. How
many packs of hobby and jumbo did Ethan buy?
Answer:
He bought 3 jumbo packs and 4 hobby packs.
Step-by-step explanation:
Ethan bought 4 number of hobby packs and 3 number of jumbo packs.
What are Linear Equations?Linear equations are equation involving one or more expressions including variables and constants and the variables are having no exponents or the exponent of the variable is 1.
Linear equations may include one or more variables.
Let x be the number of hobby pack that Ethan buy and y be the number of jumbo packs that Ethan buy.
Ethan bought 7 packs for a total of 141 cards.
We got two linear equations here :
x + y = 7
9x + 35y = 141
Multiplying the first equation throughout by 9,
9x + 9y = 63
Subtracting the resulting equation we get from the second equation,
(9x + 35y) - (9x + 9y) = 141 - 63
35y - 9y = 78
26y = 78
y = 3
x = 7 - y = 4
Hence Ethan bought 4 hobby packs and 3 jumbo packs.
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choose the best answer
Answer:
the best answer
Step-by-step explanation:
20% of all the children in a class are left handed. 4 children are left handed. How many children are there in the class all together?
statistical models predict that the price (in dollars) of a 500 gb hard drive will change according to the function p(t)
The required expression that gives the number of months t in terms of the price p is, t(p) =√1/2 (600-p).
The given function is p(t) = 600 − 2t².
We need to find the expression that gives the number of months t (passed since January 1) in terms of the price p.
What is the function?Functions are the fundamental part of calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x. Mapping or transformation is used to denote a function in math. These functions are usually denoted by letters such as f, g, and h.
Here, the expression that gives p in terms of t is, p(t) = 600 − 2t²----(1)
Where p represents the price and t represents the number of months t (passed since January 1).
From equation (1),
p= 600 − 2t²
⇒2t²=600-p
⇒t²=1/2 (600-p)
⇒t=±√1/2 (600-p)
But, the number of months can not be negative, t=√1/2 (600-p).
Since in this expression t is in the term of p.
Hence, the required expression that gives the number of months t in terms of the price p is, t(p) =√1/2 (600-p).
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Your question is incomplete, probably the complete question/missing part is:
Statistical models predict that the price (in dollars) of a 500 GB hard drive will change according to the function p(t) = 600 − 2t², where t is the month. Which expression gives the number of months t (passed since January 1) in terms of the price p?
Help please stuck on this !!!!!
Answer:
rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
Step-by-step explanation:
rrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrr
-8(4+7)=-88 PLEASE HELP
Answer:
Step-by-step explanation:
-8 (4+7)
Add the numbers: = -8. 11
Multiply the numbers
= -88
.6203 rounded to the nearest tenths
Answer:
.6200
Step-by-step explanation:
3 rounds down to 0.
Answer: 0.62
Step-by-step explanation: 0.62
Whats The Answer Marking Brainliest, Please explain your answer:D...
what is a equation with variables on both side the equals 18
The equation contains variables on both sides equals 18 can be written as (2x - 18) = x.
What is defined as the linear equation in one variable?A linear equation would be a type of equation with each variable's degree is completely identical to one.
Linear equations in one variable include those in which only one variable is present and there is only one solution to the equation. When drawn on the a graph, it appears to be either a horizontal or vertical straight line.Unknown quantities can be represented by any variable or symbol, but in most cases, a variable 'x' is used to symbolize the unknown quantity in a linear equation with one variable.Now, for the given question, the equation which could be represented in the form of variable on both side and has the solution equals to zero is;
(2x - 18) = x
The solution can be obtained as;
2x - 18 = x
Bring variable part on one side and constant on other.
2x - x = 18
x = 18.
Therefore, the equation with variables on both side the equals 18 is obtained as (2x - 18) = x.
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what is the equation of the line that passes through the point 4,8 and has a slope of 3/2
Answer:
[tex]y = \frac{3}{2} x + 2[/tex]
Step-by-step explanation:
It gives us the slope in the question (3/2), so we can write an equation that looks like this:
[tex]y = \frac{3}{2} x + b[/tex]
To find the y-intercept we can plug the point (4,8) in the equation. Remember that 4 is x and 8 is y.
[tex]8 = \frac{3}{2} (4)+ b[/tex]
Now solve for b
[tex]8 = \frac{12}{2} + b\\8 = 6 + b\\2 = b[/tex]
Next, write the full equation using the slope and y-intercept:
[tex]y = \frac{3}{2} x + 2[/tex]
I hope this helps!!
- Kay :)
Answer:
[tex]y=\frac{3}{2}x+2[/tex]
Step-by-step explanation:
The image below shows proof that the equation [tex]y=\frac{3}{2}x+2[/tex] is the line that passes through point (4, 8) and has a slope of [tex]\frac{3}{2}[/tex].
Hope this helps! :)
Given f(x) = 6(1-x) , what is the value of f(-8) ?
Answer:
The value of f(-8) is 54
Step-by-step explanation:
Plug -8 in for x, a negative, and a subtraction sign is an addition.
Hope this helps!
Which statistic (mean, median, or mode) is most appropriate in each of the following situations?
Tables in the dining hall are numbered 1 through 12 for students who eat there. The principal calls
out a number for the table that will go through the buffet line first. The other tables followin
order of the table numbers. One student is sure the principal calls certain tables more often. She
keeps track of which numbers are called over a 21-day period.
• Mean
• Median
• Mode
The statistic which is most appropriate in the given situation is Mode.
Mode is defined as the statistical method which gives the value of an entity that occurs the greatest number of times in a set of values of data. For example, if the marks of 5 students scored in a test are given as 35, 45, 35, 35, 50 then the mode of the given set of data is 35 as it occurs the maximum number of times. Here, the student is sure that the principal will call out the name of a certain number of tables very often. She keeps track of the tables over 21 days and as the table number was called out for the maximum number of times within 21 days the value of the table number will be given by the Mode of the data.
Thus, the most suitable method is Mode.
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Put the following equation of a line into slope-intercept form, simplifying all
fractions.
3x+ 3y= 24
HELP ME
Answer:
[tex]y=-x+8[/tex]
Step-by-step explanation:
[tex]3x+3y=24\\\\3x-3x+3y=24-3x\\\\3y=24-3x\\\\\frac{3y=24-3x}{3}\\\\y=8-x\\\\\boxed{y=-x+8}[/tex]
Hope this helps.
Okay so I'm working on this assignment and I see this question and I'm very confused, aren't the first 2 answers the same and the next 2 are? I am very confused...
Answer:
actually no.
Step-by-step explanation:
I assume you know the 4 inequalites:
The 4 Inequalities
Symbol Words Example
> greater than x+3 > 2
< less than 7x < 28
≥ greater than or equal to 5 ≥ x−1
≤ less than or equal to 2y+1 ≤ 7
The "open circle" represents less than or greater than, and the "closed circle" represents greater than or equal to or less than or equal to.
Hope it helps! Have a great day! :) let me know if it helped
Answer:
No
Step-by-step explanation:
The first and 2nd answer are different because in the first one the circle is open and in the 2nd one the circle is closed. When the circle is open it means that the number that the circle is on is not a part of the asnwer. This is represented by < or > signs. When the circle is closed it means the number is included in the answer. This is represented by the [tex]\leq or \geq[/tex] symbol.
Select the correct answer from each drop-down menu.
♡︎♥︎
1. 1 or 2
2. 1 or 2
What is
-10x -1 > 39
Answer:
Step-by-step explanation:
x<−4
hope this helps
I need help right away
Graph the following piecewise function. x^2+2 if -5
Answer:
4
Step-by-step explanation:
Hope this helps
Which expression is equivalent to −2(5x + 3y)?
3y(5x − 2)
5x(−2 + 3y)
−10x − 6y
−10x + 3y
Answer:
−10x − 6y
Step-by-step explanation:
−2(5x+3y)
=(−2)(5x+3y)
=(−2)(5x)+(−2)(3y)
=−10x−6y
Determine the solution for the system of equations: y = -2x + 1 3x - 2y = 5 A. (1, -1) B. (-1, 1) C. (-1, 0) D. No Solution
Answer:
Step-by-step explanation: d
Madison bought a dress priced at $98.25. The dress was 20% off. If she purchases the dress, what would the discounted price be?
A. $15.89
B. $78.25
C. $19.65
D. $78.60
Answer:
C. $19.65
Step-by-step explanation:
You have to find 20% of $98.25
This is equal to,
20% * $98.25 Because of usually means multiplication
= .20 * 98.25 Because .20 = 20%
= 19.65!
K(x) = 2x^2 + 7
What is k(4)
Answer:maybe this helps
Step-by-step explanation: k*(x)-(2*x^2+7)=0
STEP
1
:
Equation at the end of step 1
kx - (2x2 + 7) = 0
STEP
2
:
Trying to factor a multi variable polynomial
2.1 Factoring kx - 2x2 - 7
Try to factor this multi-variable trinomial using trial and error
Factorization fails
Equation at the end of step
2
:
kx - 2x2 - 7 = 0
STEP
3
:
Solving a Single Variable Equation:
3.1 Solve kx-2x2-7 = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.
We shall not handle this type of equations at this time.
PLEASE HELP!! BRAINILIESTTTT
Answer:
The element is Boron(B)
Step-by-step explanation:
This is because on the periodic table, it shows that Boron has 5 protons and 5 electrons
Tabby read 254 pages in 8 days. What is her unit rate in pages per day?
Answer:
31.75 round it off to 32 pages per day
Step-by-step explanation:
254/8=31.75 but you cant but a decimal so its 32
Which graph represents the solution set of the inequality x + 2 greater-than-or-equal-to 6
A number line goes from negative 9 to positive 9. A solid circle appears on positive 3. The number line is shaded from positive 3 through negative 9.
A number line goes from negative 9 to positive 9. An open circle appears at positive 3. The number line is shaded from positive 3 through positive 9.
A number line goes from negative 9 to positive 9. A closed circle appears at positive 4. The number line is shaded from positive 4 through positive 9.
A number line goes from negative 9 to positive 9. An open circle appears at positive 4. The number line is shaded from positive 4 through negative 9.
please help for me in studying maths tomorrow my exam
Answer: x ≥ 4; solid circle at 4 and shaded to the right
Step-by-step explanation:
Given:
x +2 ≥ 6
Subtract 2
x +2 -2 ≥ 6 -2
x ≥ 4