[tex]\large\underline{\sf{Solution-}}[/tex]
Given Polynomial:
[tex] \rm \longmapsto f(x) = {x}^{2} + px - q[/tex]
Let α and β be the zeros of f(x)
Then:
[tex] \rm \longmapsto \alpha + \beta = - p[/tex]
[tex] \rm \longmapsto \alpha \beta = - q[/tex]
Now, it's given that:
[tex] \rm \longmapsto k = \dfrac{ \alpha }{ \beta } [/tex]
Consider the expression given:
[tex] \rm = \dfrac{k}{1 + {k}^{2} } [/tex]
[tex] \rm = \dfrac{ \dfrac{ \alpha }{ \beta } }{1 + { \dfrac{ \alpha {}^{2} }{ \beta {}^{2} } }} [/tex]
[tex] \rm = \dfrac{ \dfrac{ \alpha }{ \beta } }{ { \dfrac{ \alpha {}^{2} + { \beta }^{2} }{ \beta {}^{2} } }} [/tex]
[tex] \rm = \dfrac{ \alpha }{ { \dfrac{ \alpha {}^{2} + { \beta }^{2} }{ \beta } }} [/tex]
[tex] \rm = \dfrac{ \alpha \beta }{\alpha {}^{2} + { \beta }^{2} } [/tex]
[tex] \rm = \dfrac{ \alpha \beta }{ {( \alpha + \beta )}^{2} - 2 \alpha \beta } [/tex]
[tex] \rm = \dfrac{ - q }{ {p}^{2} + 2q} [/tex]
75.25-11.92
what is the answer
Answer:
63.33
Pretty easy if you use a calculator
Graph y ≤ 1 - 3x.
(picture added)
(7,0). (3.6)
What is the slope?
Step-by-step explanation:
given,
points = (7,0) & (3,6)
we know,
slope = y_2 - y_1 / x_2 - x_1
now,
→ 6 - 0/3-7
→ 6/-4
→ -1.5 or 3/-2
therefore , slope of line is -1.5 OR In the form of fraction it is 3/-2.
hope this answer helps you dear...take care and may u have a great day ahead!
PLEASE HURRY Which of the following is NOT a solution in the solution region.
(-4, -1)
(-4, -1)
(0, -4)
(0, -4)
(5, 2)
(5, 2)
(2, -8)
Answer:
Need full problem.
Step-by-step explanation:
Need full problem.
Solve for X in a given interval. csc x= 2, for 0 < x < pi/2
Answer:
x = π/6
Step-by-step explanation:
csc x=2
-> 1/sinx = 2
-> sin x = 1/2
x = π/6 or x =2π/3
for 0 less than or equal to x less than or equal to pi/ 2
-> x = π/6
Step-by-step explanation:
stan eric nam
When x = 3, evaluate: 4x
When x = -2, evaluate: x2 =
3x + 5y = 5 7x + 5y = 25 what would be x and y for them
If Marisa’s hair grew 1 and 1/4 in. In 2 months, what was her hair growth in 1 month?
HOPE IT HELPS YOU
CAN YOU BRAINLEST ME
Answer:
Step-by-step explanation:
hair grew 3/4 in. in 1 1/2 months? How long did her hair grow in one month? 1. See answer. Add answer+5 pts. The answer is 1/2.
series representation of
[tex]e[/tex]
[tex] \huge \underline \mathtt \colorbox{cyan}{ATTACHMENTS}[/tex]
All 3 are possibleItem 4
Which point has coordinates (−2, 1.5) ?
A
B
C
I don't know.
A coordinate grid with the x and y axis from negative 3 to 3, with each line on the graph representing a step of 1 fourth. Point A is 8 steps to the right and 6 steps up. Point B is 8 steps to the left and 6 points up. Point C is 6 steps to the left and 1 step up.
Point B. is 8 steps to the left and 6 points up has coordinate points (-2,1.5).
What is a coordinate grid?A coordinate grid is a plane in which we can graph 2D figures.
If we assume that each square box n the x-y plane is of 1 sq unit then the length of the sides of each box is 1 unit.
Now we can observe that 4 such sides or boxes have a value of 1 unit so we can say that the plane has been shrunk by a factor of 1/4.
If we observe point B which is 8 steps to the left and 6 points up we can conclude B( -8,6) and has a scale factor of (1/4).
∴ B(-2,1.5).
learn more about coordinate points here :
https://brainly.com/question/21950350
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What is the correct answer to this geometry question?
HI + IJ = HJ
=> x + 12 + 16 + x = 20
<=> 2x + 28 = 20
<=> 2x = -8
<=> x = -4
with x = -4 => HI = - 4 + 12 = 8
Step-by-step explanation:
Answer:
Step-by-step explanation:
20 = 12 + 16 + 2x
20 - 12 - 16 = 2x
-8 = 2x
x = -4
--------------------------------
check
20 = 12 + 16 + 2*-4
20 = 20
the answer is good
Which defines the relationship between the number -9 and its additive inverse?
A. -9x1= -9
B-9 +0= -9
C. (-9) X0 = 0
D. (-9) +9 = 0
How do you find the zero of a function by graphing?
Answer:
Look where the function intersects the x axis. The x coordinate of those points are the zeroes of the function
Step-by-step explanation:
Lauren is a waitress at a restaurant. Each day she works, Lauren will make a guaranteed wage of $30, however the additional amount that Lauren earns from tips depends on the number of tables she waits on that day. From past experience, Lauren noticed that she will get about $6 in tips for each table she waits on. How much would Lauren expect to earn in a day on which she waits on 17 tables? How much would Lauren expect to make in a day when waiting on t tables?
Answer:
132
Step-by-step explanation:
$6 x 17= 102
102+$30= $132
The perimeter of a rectangle is 28cm it’s length is more than 10cm more than it’s widith which equation can be used to find the dimensions
P = 2((10 + x) + x)
The perimeter of a rectangle is the sum of the length and width multiplied by 2
P = 2(l + w)
[to simplify the expression]
P = 2 × (l + w)
[using x to represent the width]
w = x
l = x + 10
P = 2 × ((10 + x) + x)
P = 2((10 + x) + x)
Any experts, help please.
Item 1
Which symbol correctly compares these fractions?
−3/5□−2/3
>
<
=
Answer:
The answer is -3/5 > -2/3
Step-by-step explanation:
okay
Answer:
the answer is. ......
−3/5>2/3
(solve equation)
7b=84
Answer:
b = 12
Step-by-step explanation:
7b = 84
We can break down 7b as 7 x b
7 x b = 84
We divide both sides by 7:
7 x b ÷ 7 = 84 ÷ 7
b = 12
-Chetan K
Which equation reveals the minimum or the maximum value of f(x) without changing the form of the equation?
A f(x) = (x – 1)2 + 2
6 f(x) = x2 – 2 – x + 1
© f(x) = x2 – 2x + 1
D f(x)= (x - 1)(x - 1)
Answer:
A): f(x) = (x – 1)² + 2
Step-by-step explanation:
The quadratic function, f(x) = (x – 1)² + 2 is in vertex form: y = a(x - h)² + k, where:
The vertex of the graph is (h,k).The value of a determines whether the graph opens up or down. If a is positive, the graph opens up and the vertex is its minimum point. If a is negative, then the graph opens down, and the vertex is its maximum point. The value of h determines how far left or right the parent function is translated. The value of k determines how far up or down the parent function is translated.The function, f(x) = (x – 1)² + 2, provides the pertinent information that allows us to determine the parabola's minimum value, as the value of a is a positive, which implies that the parabola is upward facing, and the vertex, (1, 2) is the minimum point.
Please mark my answers as the Brainliest if you find this helpful :)
Solve for h in terms of g and u
4u²(2u²) /g = -2u²h -gh²/2 +h
9514 1404 393
Answer:
h = (1 -2u² ± √(1 -4u²-12u⁴))/g
Step-by-step explanation:
This is a quadratic in h, so there are two solutions.
Written in standard form, the given equation is ...
(-g/2)h² +(1-2u²)h -8u⁴/g = 0
The quadratic formula tells you the solution for h is ...
h = (-(1 -2u²) ±√((1 -2u²) -4(-g/2)(-8u⁴/g)))/(2(-g/2))
h = (2u² -1 ± √(4u⁴ -4u² +1 -16u⁴))/-g . . . . . simplify
h = (1 -2u² ± √(1 -4u²-12u⁴))/g . . . . . . . . collect terms
On his bookshelf, Adam has the difference between two-thirds of Brett's books and two-thirds of Charlie's books. If Brett has 84 books and Charlie has 27 books, how many books does Adam have?
Answer:
30 books
Step-by-step explanation:
Decrease £180 by 25%
Answer:
the answer is 135 pounds
Answer:
180 - 25% = 135
Hope this helps
Please help! I will mark brainliest!
Answer:
1. is 283.9953
Step-by-step explanation:
360 degrees - 76.0047 degrees is 283.9953
True or false??????????
Answer:
True
Step-by-step explanation:
Answer:
TRue
Step-by-step explanation:
Did that also
no spams
need a well explained ans
if u don't know stay out of the question
The three inside angles need to equal 170 when added together.
When two sides are the same which is shown by the little lines through the sides the two bottom angles are the same.
1. X = 170-80-80 = 20
2. X = 180-75-75 = 30
3. X = 180-70 = 110/2 = 55
Step-by-step explanation:
1) x+80°+80°=180°
x=180°-160°
x=20°.
2) as it is a isosceles triangle, y =75°.
x+75°+75°=180°
x=180°-150°
x=30°.
3) 2x+70°=180°
2x=110°
x=55°.
hope all these helps you.
I need help on Absolute Value Equations!
|6x−18|=−1
Answer:
there is no solution
Step-by-step explanation:
no absolute value can be negative
Answer:
no solutions
Step-by-step explanation:
1. There's no solution to this equation because absolute values cannot be less than 0.
solve the question in the picture
Answer:
the answer you need is in the pic above
What is an equation of the line that passes through the point (−1,−3) and is parallel to the line 6x-y=1?
Answer:
y = 6x + 3
Step-by-step explanation:
6x - y = 1
6x -1 = y
Slope = 6
Point (-1,-3)
y-intercept = -3 - (6)(-1)
= -3 + 6 = 3
y = 6x + 3
Please answer bOtH questions ❤ tysm
Pablo has ten dollars. He wants to buy 7 packs of gum. Rach pack of gum costs $1.50. Does he have enough? How do you know?
Answer:
no. it costs $10.5
Step-by-step explanation: first you multiply 1.5 ( how much it costs) by 7 ( how much hes gonna get) and that equals 10.5. as you can see, thats 5 cents more than 10 dollars
Answer:
No, he does not have enough. Here's why.
Step-by-step explanation:
Pablo has 10 dollars, and each pack of gum costs $1.50. He wants 7 packs, so we do $1.50 times 7(for 7 packs.)
$1.50 times 7 is $10.50, which leaves Pablo 50 cents short.
He does not have enough money.
I hope this helps you! Have a great day.
A student earned a grade of 80% on a math test that had 20 problems.How many problems on this test did the student answer correctly
Answer:
16 problems
Step-by-step explanation:
1. First, we must know that to find how many problems the student solved, we have to multiply the percentage he got by the total number of problems.
2. (Solving)
[tex]\frac{80}{100}*20[/tex] [tex]\frac{4}{5} *20[/tex] [tex]\frac{80}{5}[/tex] [tex]16[/tex]Therefore, the student answered 16 problems correctly.
Answer:
16
Step-by-step explanation: