The nature of the roots for the equation ax² + bx + c is
α + β = -b/a and αβ = c/a
where α and β are the two roots of the equation.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
A quadratic equation ax² + bx + c.
Now,
There will be two roots of the equation α and β,
Now,
The nature of the roots are
α + β = -b/a
αβ = c/a
Thus,
The roots are α and β and α + β = -b/a and αβ = c/a.
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The nature of roots of quadratic depends on its discriminant, formula is D=√(b²-4ac).
What is root of quadratic equation?It is the value of the unknown variable for which the quadratic equation holds true. Its nature can be real, imaginary, rational, irrational, equal and unequal as well that depends on the value of the discriminant.
For equation ax²+ bx + c =0 , expression b²- 4ac is called discriminant and denoted by D.
Given equation is , ax²+ bx + c =0
then, according to quadratic formula for the roots of quadratic equation
x = {-b±√(b²-4ac)}/4ac
Let us take a real number
k > 0
√k can be defined and is a positive quantity but √-k can not be defined.
The quantity which is under square root in the expression for roots is
b²-4ac, which is called discriminant of the quadratic equation. It is represented by D.
If D>0 and is perfect square then the equation will have two real, rational and distinct roots.
If D>0 and is not a perfect square then the equation will have two real, irrational and distinct roots.
If D=0 the equation will have two real and equal roots.
If D<0, the equation will have no real roots.
Hence, nature of roots formula for quadratic equation depends on the value of √b²-4ac.
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i need help with this
Answer:
151
Step-by-step explanation:
Answer:
151
Step-by-step explanation:
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Answer:
Side length = 5.8 in
Perimeter = 29
Area = 58 in²
Step-by-step explanation:
✔️Find Side length using trigonometric ratio:
Angle at center of a pentagon is always 36° (we have measure of a full circle, 360, divided by 10 smaller triangles = 36°)
So:
Reference angle = 36°
Adjacent side = 4 in.
Opp = ½ of the side length of the polygon = x (let's represent this as x)
Thus, apply TOA:
Tan 36 = Opp/Adj
Tan 36 = x/4
4*Tan 36 = x
x ≈ 2.9 in (nearest tenth)
Side length = 2*x = 2*2.9 = 5.8 in
✔️Perimeter = 5*side length
Perimeter = 5*5.8 = 29 in
✔️Area = ½aP
Where,
a = 4 in
P = 29
Plug in the values
A = ½*4*29
A = 58 in²
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Answer:
Answer
Correct option is
D
all of the above
For any two rational numbers a and b,
(a+b),(a−b),(b−a) & (a×b) are all rational numbers.
Thus, rational numbers are closed under addition, subtraction and multiplication.(for the first one)
Answer:
The sum of x and y is a rational number
Step-by-step explanation:
X+Y or 5+7=12
A rational number is any number that can be divided without going on and on forever. ( for the 2nd one)
Caleb has at least $5. Which inequality is correct?
c < 5
or
c < 5
Answer:
It would be c is greater than or equal to five
Step-by-step explanation:
c≥5
5≤c
Is 80, 150, 170 a pythagorean triple?
Answer:
Yes
Step-by-step explanation:
80² + 150² = 170²
6400 + 22500 = 28900
28900 = 28900
What is 92 - (12 + 16) ÷ 4? I keep re-doing my math for it, but when I check it with a calculator I'm always wrong.
Answer:
85
Step-by-step explanation:
92 - (12 + 16) ÷ 4
PEMDAS states we do the equation in the paranthesis 1st
92 - (28) ÷ 4
PEMDAS states we do division next
92 - 7
85
Please help me with this it was due yesterday.
Answer:
domain= infinity on both sides. range= -3<y<infinity
Step-by-step explanation:
hope this helps
Have a nice day :)
geometry ^
please help me
Which is the most accurate way to estimate 26% of 91?
A: 3/4 x 92
B: 1/4 x 92
C: 1/3 x 90
D: 1/2 x 90
Answer:
B
Step-by-step explanation:
26% is close to 25%, which is equal to 1/4th.
You're adding to the number and removing from the percentage so it balances it out.
The estimation of 26% of 91 is 1/4 x 92.
The correct option is (B).
What is Percentage?To determine the quantity or percentage of something in terms of 100, use the percentage formula. Per cent simply means one in a hundred. Using the percentage formula, a number between 0 and 1 can be expressed. A number that is expressed as a fraction of 100 is what it is. It is mostly used to compare and determine ratios and is represented by the symbol %.
Given:
26% of 91
Now solving the above Quantity
= 26 /100 x 91
Now, We take 1 from 26 make it 25 and add that 1 to 91 make 92.
Then, 25 / 100 x 92
= 1/4 x 92
Hence, the estimation is 1/4 x 952.
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Answer:
8.64%
Step-by-step explanation:
Write it as a decimal
7/81 = 0.0864
0.0864 is the decimal representation for 7/81
For Percentage Conversion :
step 1 To represent 0.0864 in percentage, write 0.0864 as a fraction
Fraction = 0.0864/1
step 2 multiply 100 to both numerator & denominator
(0.0864 x 100)/(1 x 100) = 8.64/100
8.64% is the percentage representation for 7/81
Please help, solve for x
Answer:
x = 6
Step-by-step explanation:
10x = 5 x 12 = 60
x = 6
Help please, i give brainlist
prime factorization of 154
Answer:
The prime factors of 154 are 2, 7, 11.
Step-by-step explanation:
Answer:
See below
Step-by-step explanation:
[tex]154 = 2 \times 7 \times 11[/tex]
please help me answer this!
Answer:
right
Step-by-step explanation:
tell me if i was wrong
PLEASE PLEASE HELP!! I NEED THE ANSWERS ASAP
Answer:
Pictures below showing the answer :)
Step-by-step explanation:
PLEASE HELP!!!!! WORTH 40 POINTS
Answer:
B : 3/2
Step-by-step explanation:
Answer:
hi
Step-by-step explanation:
answer is B. i think so...
[tex] \frac{54}{36} = \frac{3}{2} [/tex]
have a nice day
For all values of x,
f(x) = 2x-3 and g(x) = x²+1
a) Find fg(x)
Simplify and give your answer in the form ax² + b
b) Find gf(x)
Simplify and give your answer in the form ax² + bx+c
Answer:
For f(x) = 2x + 3 and g(x) = -x 2 + 1, find the composite function defined by (f o g)(x)
(f o g)(x) = f(g(x))
= 2 (g(x)) + 3
= 2( -x 2 + 1 ) + 3
= - 2 x 2 + 5 Given f(2) = 3, g(3) = 2, f(3) = 4 and g(2) = 5, evaluate (f o g)(3)
Step-by-step explanation:
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Hello again, hehelol12.
PQ is equal to CB. So the length of PQ must be 9.
Angle PQR is equal to CBA. Therefore the measure of angle PQR is 46.
I hope this helps!
Step-by-step explanation:
since they are congruent triangles, all your have to done is the compare the longest side of the first triangle is equal to that of the other; the smallest side of the first triangle is equal to that of the second, and so for the corresponding angles
using the above method,
Answer:
a) from mere observation line PQ is the longest therefore it is equal to the length of the longest side of the other triangle. so line PQ = 9
b) again, ang PQ is the smallest, using the method, ang PQ = 46 degrees
but mind you, you could use a ruler to measure the length to find the longest more accurately.
5th grade math. correct answer will be marked brainliest
Answer:
70/9
Step-by-step explanation:
You can rewrite 8 pounds as 72/9.
Take away 2/9 and you are left with 70/9.
Answer:
[tex]\frac{2}{9} x \frac{8}{1} = \frac{16}{9} = 1 \frac{7}{9}[/tex]
Rewrite the function in standard form.
f(x) = 4(x - 2)^2+ 3
Answer:
f(x) = 4x^2 - 13
Step-by-step explanation:
f(x)=4(x-2)^2 + 3 parentaties first
f(x) = 4 (x^2 - 4)+ 3 multiply by what's infront parentaties
f(x) = 4x^2 - 16 + 3 combine light terms
f(x) = 4x^2 - 13 Answer
Hope I helped :)
At least pet snake is 42 inches long and Royals pet snake is 8 feet long.How many inches longer is Royals snake
Answer:
54 inches
Step-by-step explanation:
At least pet snake is 42 inches long and Royals pet snake is 8 feet long.How many inches longer is Royals snake
Step 1
We would be converting the length of the Royal's pet snake to inches
1 foot = 12 inches
8 feet = x
Cross Multiply
x = 8 × 12 inches
x = 96 inches
Step 2
How many inches longer is Royal's snake?
This is calculated by subtracting the length of the Royal's pet snake from the least length
= 96 inches - 42 inches
= 54 inches
Therefore, the Royal's snake is 54 inches longer
Use this picture to name one pair of VERTICAL angles
Answer:
YOU LAIR HOW COULD YOU
Step-by-step explanation:
Answer:
1 and 6
Step-by-step explanation:
HURRYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYYY
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Four expressions are shown:
6(5x + 3)
6(6x + 2)
36x + 12
30x + 18
Which two expressions are equivalent to 6(5x + 2 + x)?
Answer:
B 6(6x + 2)
C 36x + 12
Step-by-step explanation:
I just did this question myself and I got it correct.
What is the value of x in 7x-18
Answer:
x = 21
Step-by-step explanation:
Although the picture is a bit blurry towards the bottom, I believe the opposite exterior angle is 129°
Opposite exterior angles are equivalent by the opposite exterior angles postulate. Of course, this only applies if the transversed lines are parallel, which they are in this case, because of the small orange arrows.
Anyhow, the equation should be set up as follows:
[tex]129 = 7x-18\\129 + 18 = 7x - 18 +18\\147 = 7x\\21=x[/tex]
Have a nice day, fam. Spread The Love.
How Roses Got Their Thorns.
Many years ago ,in the land of Lucia, there was a beautiful queen named —————. Queen —————lived in a century old castle surrounded by a forest on the north side,a maze on the east side, a fountain on the west side and a rose garden on the south side. Her private living quarters had a large window facing the south. Each morning she would start her day by opening her window to the sweet aroma coming from her rose garden. She had a special servant whose only job was to care for her roses. Queen ———- rose garden was her favorite place and every day she would spend time there relaxing and caring for her lovely blooms. Her garden was world famous and people came from miles around to visit and enjoy their beauty and lovely fragrance.
One day she notice there were fewer blooms than usual and she became concerned. She thought her servant was not doing his job,so she obtained a new gardener. The blooms continued to disappear and then she noticed that plants were starting to disappear. Finally, she had some of her servants start guarding the roses. They discovered that the visitors were picking and digging up her roses. She loved sharing the beauty of her garden with her subjects but she had to find a way to protect her roses . Several attempts were tried to protect the. She had a fence built,but the people knocked it down. She had a wall built but they climbed over it. She put guards around but the guards could not be everywhere and the people continued to take her roses . Finally, she sought the advice the local wizard . His solution was to put a curse on the roses. Queen———-agreed to a curse as long as it did not affect the aroma or the beauty of them Beginning that day the loveliest of flowers started growing thorns and still do. P
Answer:
Queen Marie Antoinette
Help with 2 3 4 and 5 please!
Answer:
Number 2 is A
Number 3 is (5, -4)
Number 4 is (5, -4)
Number 5 is (4, 2)
Step-by-step explanation:
Answer:
B, maybe (5,-4), (5,-4), (4,2)
Step-by-step explanation:
Translate just means to move, and vertex T just means the dot labeled "T". Move just that point three to he left and two to the right is (-5,0). I would give (5,-4) as the answer for three, but I'm not too sure and don't wanna spread false information... onto number 4. (3,1) and the form is (x,y) Right is positive, so ADD 2 to 3. Down is negative, so SUBTRACT 5 to 1. You now have (5,-4). 2 multiplied by 2 is 4 and 1 multiplied by 2 is 2. (4,2)
I need help with this question ( see image). Please show workings.
Answer:
14) (C) 8√2 km
15) (C) 225°
Exercise 15.17 (D) 8.7 km
Step-by-step explanation:
14)
d² = 8² + 8² = 64 + 64 = 128
d = √128 = 8√2 km
15) 180° + 45° = 225°
Exercise 15.17
QR² = 10² - 5² = 100 - 25 = 75
QR = √75 = 5√3 = 8.7 km
Answer:
Kofi, the building and the tree form an isosceles right triangle KTB.
Refer to picture
15.15The distance KB is the hypotenuse and its length is:
KB = √8² + 8² = √64 + 64 = √128 = 8√2Correct choice is C
15.16The angles at vertices K and B equal to 45° as opposite sides are equal.
TB is a vertical line which makes angle 180°.
Add 45° to get a required bearing:
180°+ 45° = 225°Correct choice is C
15.17P, Q and R form a right triangle with PR as hypotenuse.
RQ is the missing leg and its length is:
RQ = √PR² - PQ² = √10² - 5² = √100-25 = √75 = 8.7 (rounded)Correct choice is D
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Answer:
Step-by-step explanation:
Angle x is what I call "point to point" with the angle that measures 95 degrees. Because of this, they are vertical (the vertex of an angle makes a "v"; hence, the reason I call them point to point). Vertical angles are congruent. That means that they have the same measure. If x is vertical to an angle that measures 95 degrees, then x also measures 95 degrees.
Answer:
x is 95 degrees.
Step-by-step explanation: