Answer:
k = 1¹/₃
Step-by-step explanation:
Comparing (k-1)x² + kx + 1 with ax + bx + c where α, β be the zeroes of the quadratic equation, then
α + β = -b/a = -k/(k - 1) and αβ = c/a = 1/(k - 1)
Since one of the zeros is -3, β = -3
So,
α + β = -k/(k - 1)
α + (-3) = -k/(k - 1)
α - 3 = -k/(k - 1) (1)
and
αβ = 1/(k - 1)
-3α = 1/(k - 1) (2)
From (1), α = 3 - k/(k - 1) (3)
Substituting equation (3) into (2), we have
-3α = 1/(k - 1)
-3[3 - k/(k - 1)] = 1/(k - 1)
-9 + 3k/(k - 1) = 1/(k - 1)
-9 = 1/(k - 1) - 3k/(k - 1)
-9 = (1 - 3k)/(k - 1)
cross-multiplying, we have
-9(k - 1) = 1 - 3k
expanding the brackets, we have
-9k + 9 = 1 - 3k
collecting like terms, we have
-9k + 3k = 1 - 9
-6k = -8
dividing through by -6, we have
k = -8/-6
k = 4/3
k = 1¹/₃
company paid $48 for 2 cases of printer paper. Each case contained 12 packages of paper. Next month the company’s office manager needs to order 180 packages of the same paper. If the price per package does not change, what would be the total c
Answer:
the answer would be 384 dollars
HELP PLEASE !!
The drama teacher wants to determine whether more students at the school would attend a comedy or a musical performance. Select all the following that would NOT help the drama teacher draw conclusions about which performance more students would attend.
A. Students who do not act.
B. Every 4th student selected from an alphabetical list of all students at the school.
C. Students who are in drama club.
D. Students who are in theater class.
E. The same number of students from each grade whose names are randomly selected from a hat.
Answer:
A, B, and D
Step-by-step explanation:
This is my last question and then I’m done
Answer:
C. y = -2/3 x + 4
Step-by-step explanation:
y = mx + b
From the graph we see that b = 4, and m = 2/3.
y = -2/3 x + 4
Ben is monitoring a colony of bacteria. Initially, the colony consists of 159 bacteria. The following function represents the number of bacteria in the colony after x hours.
Which expression approximately represents the number of hours, x, it takes for the number of bacteria in the colony to reach 168?
Answer:
No solution is possible from the information provided
Step-by-step explanation:
you didn't include the function.
Analyze the rational function: f(x) = (x^2 - 4)/(x^3 - 3x^2 - 10x)
Answer:
The function [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] has a zero: [tex]x = 2[/tex], and two poles: [tex]x = 0[/tex] and [tex]x = 5[/tex].
Step-by-step explanation:
Let be [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] a rational function armed with polynomial function. We proceed to factor the expression to the find the zeros and poles of the rational function:
1) [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] Given
2) [tex]f(x) = \frac{(x + 2)\cdot (x-2)}{x\cdot (x^{2}-3\cdot x -10)}[/tex] [tex]a^{2} - b^{2} = (a + b)\cdot (a - b)[/tex]/Associative, commutative and distributive properties.
3) [tex]f(x) = \frac{(x+2)\cdot (x-2)}{x\cdot (x-5)\cdot (x+2)}[/tex] [tex]x^{2} -(a+b)\cdot x + a\cdot b = (x-a)\cdot (x-b)[/tex]
4) [tex]f(x) = \frac{x-2}{x\cdot (x-5)}[/tex] Commutative property/Existence of multiplicative inverse/Modulative property/Result
The function [tex]f(x) = \frac{x^{2}-4}{x^{3}-3\cdot x^{2}-10\cdot x}[/tex] has a zero: [tex]x = 2[/tex], and two poles: [tex]x = 0[/tex] and [tex]x = 5[/tex].
Please help me with this one …..
Answer:
is the clean area the desired one (I assume, yes)?
then y <= 3x + 5
if the dotted area is the desired area, then
y >= 3x + 5
Step-by-step explanation:
the factor of x is the slope of the line expressed as y/x ratio.
clearly, the line shows that for x changing by 1 unit y changes by 3 units. so, the slope is 3/1.
that leaves us only with the 2 middle options.
for "y <=" the desired values of y for a given x must be on the line (equal) or below (smaller than the value of the line equation). that is true, if the desired area is the clear one (no dots).
so, "y >=" is true, if the dotted area is desired.
PLEASE HELP ANGLE OF A TRIANGLE
Answer:
59°
Step-by-step explanation:
The angles of a triangle equal 180°.
Also the angle of a straight line is 180°.
So you first find the missing bottom angle by taking 180-147 to equal 33.
Then you take 33+88+x=180
solve for x by subtracting 88 and 33 from 180 to equal 59.
Answer:
59°
Step-by-step explanation:
180 - 147 = 33
88 + 33 = 121
180 - 121 = 59
Please help !!!!!!!!
Answer:
C = (4,4)
It is (4,4) because it means that it is twice as large as the original coordinates.
Brainliest goes to whoever answers correctly I have other questions if you want more points
Answer:
a. $1.50 per pound of weight.
b. C
Step-by-step explanation:
a. explanation:
1. pounds is increasing by +4 and dollars are increasing by +6.00
2. as a fraction it is 6/4.
3. simplified is 1 1/2 or 1.50
b. explanation
1. we know that the slope (or rate of change) is $1.50 /per pound of weight.
2. 4 - 4 = 0; $11.00 - 6.00 = $5.00
3. 0, $5.00
4. The y-int. is $5.00
5. answer is C
REALLY IMPORTANT
•
no files or i’ll report your answer
Answer:
c
Step-by-step explanation:
This is a parabola, so it is a quadratic parent function.
please help! will rank brainliest
Answer:
98 degrees
Step-by-step explanation:
We know that H is the same as G because the sides are marked equal.
41 + 41 = 82
In a triangle the measure of degrees in total is 180.
180 - 82 = 98
Which expression is equivalent to the following fraction?
Given:
The fraction is:
[tex]\dfrac{\dfrac{-2}{x}+\dfrac{5}{y}}{\dfrac{3}{y}-\dfrac{2}{x}}[/tex]
To find:
The expression that is equivalent to the given fraction.
Solution:
We have,
[tex]\dfrac{\dfrac{-2}{x}+\dfrac{5}{y}}{\dfrac{3}{y}-\dfrac{2}{x}}[/tex]
After taking LCM, we get
[tex]\dfrac{\dfrac{-2y+5x}{xy}}{\dfrac{3x-2y}{xy}}[/tex]
[tex]\dfrac{-2y+5x}{3x-2y}[/tex]
Therefore, the correct option is A.
a container of water is filled to 1/3 of it. if we add 2.5 liters the container will be half full. find how much is the volume of the container. convert it to cm³
Answer:
In picture
Step-by-step explanation:
Brainliest please
please please help me!!
explaining your answer will get you brainliest.
A figure with an area of 84 square cm is dilated by a factor is 2. The area of the dilated figure is ___ square cm.
Answer:
336 cm²
Step-by-step explanation:
Given a dilatation by a factor of 2 then the area factor is 2² = 4
area of figure = 4 × 84 = 336 cm²
Jonah's favourite number is a positive integer. One day, he decided to write down all of the positive integers starting at 1 and ending with his favourite number. He noticed, in doing so, that he wrote the digit 7 exactly 30 times. What is Jonah's favourite number?
Answer:
um I think its 14
Step-by-step explanation:
1. Which events below are dependent?
A. rolling a 6 on a die three times in a row
B. tossing a coin twice and it lands heads once
C. winning two consecutive games of bingo
D. randomly choosing a class president and vice-president
Answer:B
Step-by-step explanation:
I’m confused, please help
Answer: (a)
Step-by-step explanation:
Given
[tex]g(x)=x^2[/tex]
Clearly, [tex]f(x)[/tex] is obtained by shifting [tex]g(x)[/tex] 3 units down and multiplying it by a certain factor to amplify it.
Checking the option which is 3 units below and multiplying by a factor
option (a) is meeting both the cirterias.
The table represents a linear function
What is the slope of the function?
х
0-6
-2
-1
0
1
2
y
8
2.
-4
10
16
&
6
The slope of the function showing by table is,
⇒ m = - 6
What is Equation of line?The equation of line in point-slope form passing through the points
(x₁ , y₁) and (x₂, y₂) with slope m is defined as;
⇒ y - y₁ = m (x - x₁)
Where, m = (y₂ - y₁) / (x₂ - x₁)
Given that;
The table represents a linear function.
Let Two points on the line are (- 2, 8) and (- 1, 2).
Hence, Slope of the line is,
m = (y₂ - y₁) / (x₂ - x₁)
m = (2 - 8) / (-1 - (-2))
m = - 6 / 1
m = - 6
Thus, The slope of the function showing by table is,
⇒ m = - 6
Learn more about the equation of line visit:
https://brainly.com/question/18831322
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Pls I need this I will give brainly if u help me
[tex]4( \frac{1}{5} x + 7) = 2x - 2[/tex]
[tex]x = 25[/tex]
NEED IT ASAP!!!!!
3 in.
Robert is computing the volume of this sphere:
Where did Robert make a mistake? Identify Robert's computational error.
3 in.
V= (3)3
= 36
~ 113.10 in.3
Answer:
l think he used three which is the diameter as the radius instead of dividing it by two................
Answer my this question too uregent
Answer:
The correct answer is D.
A, B, and C are incorrect. <3
Hope this helps!
- Madeline
Please help me ASAP!
Answer:
B: 153ft2
Step-by-step explanation:
What is the product?
Answer:
Step-by-step explanation:
You can do this in two steps.
4s * (5s^2 + 10s + 3) Remove the brackets
20s^3 + 40s^2 + 12 s
2(5s^2 + 10s + 3)
10s^2 + 20s + 6
Now add them
20s^3 + 40s^2 + 12s + 10s^2 + 20s + 6
Rearrange them so the like terms are together.
20s^3 + 40s^2 + 10s^2 +12s + 20s + 6
20s^3 + 50s^2 + 32s + 6
If f left parenthesis x right parenthesis equals x squared minus 3 x plus 5 , then f left parenthesis 4 right parenthesis equals
Answer:
f(4) = 9
Step-by-step explanation:
f left parenthesis x right parenthesis equals x squared minus 3 x plus 5
f(x) = x² - 3x + 5
f left parenthesis 4 right parenthesis equals
f(4) =
f(x) = x² - 3x + 5
When x = 4
f(4) = 4² - 3(4) + 5
= 16 - 12 + 5
= 9
f(4) = 9
Answer:
Pretty sure its A
Step-by-step explanation:
PLEASE HELP ME WITH THIS
A system of equations consisting of a circle and a line is graphed. Which statements about the number of possible solutions are correct? Check all that apply.
A circle and a line always intersect, so the system can have an infinite number of solutions.
A circle and a line can intersect at one point, so the system can have one solution.
A circle and a line can intersect at three points, so the system can have three solutions.
A circle and a line can intersect twice, so the system can have two solutions.
A circle and a line do not have to intersect, so the system can have no solution.
Answer:
the solution is where the two objects intersect ...
1) A line can completely miss the circle (no solutions is possible)
2) a line can "kiss" the circle at one point (one solution)
3) note that a line can not "bend"... it can touch one side of the circle pass
through the center and touch the circle in a second spot (going out) .. two solutions...
those are the three possibility that are in the question that was posted...
three check comments are true
Step-by-step explanation:
Simplify this question please im really confused
Answer:
option A
Step-by-step explanation:
[tex]\frac{x^a}{x^b} = x^{a-b}[/tex] , [tex]z^0 = 1[/tex]
So,
[tex]\frac{18x^5 y}{6xy^8z^0} = \frac{18}{6} \times x^{5 -1} \times y^{1-8} = 3 x^4 \times y^{-7} = \frac{3x^4}{y^7}[/tex]
If the measure of ABC is 68°, what is the measure of arc AB? (the blue line)
Which inverse of the difference of 1/3 - 1/4?
Answer:
0/1
Step-by-step explanation:
Complete the table for the given rule.
Rule:y= 4/1 x+1y
Answer: 2, 3, 4
Step-by-step explanation:
In the table graph provided, you will a column that has "x" as it's title. Under x, 4, 8, and 12 should listed. You figure out the answers for y by inputting the x value into the rule: y = 1/4x + 1.
For y = 1/4(4) + 1, you would multiply 1/4 by 4 and since the fours eliminate one another, you would get 1. Now, you would do 1 + 1, which equals 2. For y = 1/4(8) + 1, you would multiply 1/4 by 8 and since four and eight share the number four as their greatest common factor, four would be eliminated and eight would be reduced to 2. Now, you would do 2 + 1, which equals 3.For y = 1/4(12) + 1, you would multiply 1/4 by 12 and since four and twelve share the number four as their greatest common factor, four would be eliminated and twelve would be reduced to 3. Now, you would do 3 + 1, which equals 4.