The nature of roots of the equation 4x² -4x -19 = 0 is : The roots are real.
Given quadratic equation to us is 4x² -4x -19 = 0.
With respect to Standard form ax² +bx +c = 0 , Discriminant of the quadratic equation is given by b² - 4ac . Here's a table for Nature of Roots .
SI. NO. CONDITION NATURE OF ROOTS
1 Discriminant > 1 Real roots
2 Discriminant = 1 Equal roots
3 Discriminant < 1 Complex roots
Hence here , with respect to Standard form ,
• a = 4 , • b = -4 & •c = -19 .
⇒ Discriminant = b² - 4ac
⇒ Discriminant = (-4)² - 4 (4) (-19)
⇒ Discriminant = 16 + 304
⇒ Discriminant = 320
Hence since Discriminant is Greater than 0 , hence the nature of roots of the quadratic equation is real.
Learn more about the nature of roots here ;
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22
Consider the expression below.
3x - (2y + 2)
Evaluate the expression when x = 0.02, y = 0.1, and z = 0.3.
NEED HELP ASAP HELPING A FRIEND
Answer:
Step-by-step explanation:
So it 22
Answer: 0.007
Step-by-step explanation:
3 drinks and 2 hot dog costs 7.70 and 2 drinks and one hot dog is 4.55 system of equation on drink and one hot dog to the nearest cents
Answer:
Drink = 1.4
Hot dog = 1.75
x + y = 3.15
Step-by-step explanation:
Let drink = x ; hot dog = y
3x + 2y = 7.70 - - (1)
2x + y = 4.55 - - - (2)
From (2)
y = 4.55 - 2x - - - (3)
Put y = 4.55 - 2x in (1)
3x + 2(4.55 - 2x) = 7.70
3x + 9.1 - 4x = 7.70
-x = 7.7 - 9.1
-x = - 1.4
x = 1.4
Put x = 1.4 in (3)
y = 4.55 - 2(1.4)
y = 4.55 - 2.8
y = 1.75
Drink = 1.4
Hot dog = 1.75
x + y = 3.15
Please answer both of you can
I'm so stuck I was taught this 5 months ago I don't remember this lol.
Answer:
C. 24 12/20
Step-by-step explanation:
4 3/4 × 6 4/5
24 3/4 × 4/5
24 12/20
Find a unit vector in the direction of the given vector.
v = 9i − 6j
Given:
The given vector is:
[tex]v=9i-6j[/tex]
To find:
The unit vector in the direction of the given vector.
Solution:
If a vector is [tex]v=ai+bj[/tex], then the unit vector in the direction of the this vector is
[tex]\hat v=\dfrac{v}{|v|}[/tex]
Where, [tex]|v|=\sqrt{a^2+b^2[/tex]
We have,
[tex]v=9i-6j[/tex]
Here, [tex]a=9[/tex] and [tex]b=-6[/tex]. So,
[tex]|v|=\sqrt{9^2+(-6)^2}[/tex]
[tex]|v|=\sqrt{81+36}[/tex]
[tex]|v|=\sqrt{117}[/tex]
[tex]|v|=3\sqrt{13}[/tex]
Now, the unit vector in the direction of the given vector is:
[tex]\hat v=\dfrac{9i-6j}{3\sqrt{13}}[/tex]
[tex]\hat v=\dfrac{9i}{3\sqrt{13}}-\dfrac{6j}{3\sqrt{13}}[/tex]
[tex]\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j[/tex]
Therefore, the required unit vector is [tex]\hat v=\dfrac{3}{\sqrt{13}}i-\dfrac{2}{\sqrt{13}}j[/tex].
PLEASE HELP!!
Also the last option is
4 units left and 3 units down
Answer:
B
Step-by-step explanation:
Yalll listen i was at a party with friends in the ghetto and the ice crean truck came and they had the hot cheetos with cheese and chill poured on it ....it was bussin bussin
Answer:
wowo cool
Step-by-step explanation:
Answer:
sounds cheeesyyy
Step-by-step explanation:
25 points. Need help
Answer:
BD = 21 units
Step-by-step explanation:
By applying mean ratio theorem in the given triangle ABC,
[tex]\frac{AD}{BD}=\frac{BD}{CD}[/tex]
AD × CD = BD²
21 × 21 = BD²
BD² = (21)²
BD = 21
Therefore, measure of segment BD is 21 units.
A surveyor holds a laser range finder 3 feet above the ground and determines that the range finder is 92 feet from a building and 106 feet from the top of the building. What is the height h of the building? Round your answer to the nearest tenth.
Answer:
55.64
Step-by-step explanation:
The range finder is 92 feet from the building and 106 feet from the top of the building i.e. hypotheses
We will use the Pythagorean theorem:
x^2 = 106^2 - 92^2
= 11,236 - 8,464
= 2,772
= √2,772
x = 52.64978632
The height of the building:
h = x + 3
= 52.64978632 + 3
= 55.64978632
or
≈ 55.64 feet
Step-by-step explanation:
the answer to the nearest is 55.64
Plz helpp I’m bad at math
Answer:
40
Step-by-step explanation:
because a straight line is 180 degrees so 140 plus 40 equals 180
Answer:
40
Step-by-step explanation:
straight line is 180 degrees
180=140+x
140+40=180
Each side of a circumscribed equilateral triangle is 16 meters. find the radius if the circle
PLZS HELP NEED BY TODAY!!
Answer:
20°
Step-by-step explanation:
ok so if 40 degrees is on one side its also on the side parallel from it
a straight line = 180 degrees
so 180 - 40 = 140
so 7x =140
we now divide 7 on both sides and get x=20 because the 7 cancels out
180 -40 =140
7x = 140
7x/7 =140/7
x=20
Hope I helped?
pls pleaase pls help marking brainlisr
Answer:
1
Step-by-step explanation:
G varies directly as the square of j and inversely as m. If g=0.05 when j = 0.4 and m=1.6, what is g when j =6 and m=4
Answer: The value of G = 4.5
Step-by-step explanation:
As per given,
[tex]G\propto \dfrac{j^2}{m}[/tex]
When we replace proportional sign with an equal to sign, we get
[tex]G=k\dfrac{j^2}{m}[/tex], where k = constant
If G=0.05 when j = 0.4 and m=1.6, then
[tex]0.05=k\dfrac{0.4^2}{1.6}\\\\ 0.05=k(0.1)\\\\ k=0.5[/tex]
Now,
[tex]G=0.5\dfrac{j^2}{m}\\\\\Rightarrow\ G=0.5\dfrac{6^2}{4}\\\\\Rightarrow\ G=4.5[/tex]
hence, when j =6 and m=4, the value of G = 4.5
Can someone please help me?
Answer:
scalene
Step-by-step explanation:
I need this done, please
pls help figure out part c, part e, and part f
Help plsssssss:)))))))
Answer:
x = -14
Steps:
Rewrite the equation as -8 = 6+x
Then move all terms not containing x to the right side of the equation.
x = -8-6
Afterwords subtrack.
x = -14.
hope this helps :)
Find the derivative of
y= 1/(3x^3)
Answer:
[tex]\displaystyle y' = \frac{-1}{x^4}[/tex]
General Formulas and Concepts:
Calculus
Differentiation
DerivativesDerivative NotationDerivative Property [Multiplied Constant]: [tex]\displaystyle \frac{d}{dx} [cf(x)] = c \cdot f'(x)[/tex]
Basic Power Rule:
f(x) = cxⁿf’(x) = c·nxⁿ⁻¹Step-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle y = \frac{1}{3x^3}[/tex]
Step 2: Differentiate
Rewrite: [tex]\displaystyle y = \frac{x^{-3}}{3}[/tex]Derivative Property [Multiplied Constant]: [tex]\displaystyle y' = \frac{1}{3} \frac{d}{dx}[x^{-3}][/tex]Basic Power Rule: [tex]\displaystyle y' = \frac{1}{3}(-3x^{-4})[/tex]Simplify: [tex]\displaystyle y' = \frac{-1}{x^4}[/tex]Topic: AP Calculus AB/BC (Calculus I/I + II)
Unit: Differentiation
What is the difference in a SSS Postulate (side-side-side) and SAS Postulate (Side-angle-side)? How do i know which one its going to be? Thanks!!!
The population of bacteria doubles every 6 hours. By how much will it grow in three days. Write the equation
Answer:
Step-by-step explanation:
let x be the population
so we have ,
2x= 6h
?= 3 days or 3×24h
by cross multiplication we have
2x× 72h= 6h×?
?= 2x×72/6 = 24x
So, in three days the bacteria will b 24 times current population.
Is 8 a solution to the equation 3(x-6)=3x/4?
Explain your answer
I need help on 13 and 14, you will get 25 points with brainlyist!!!
Answer:
14 is C and 13 is also C
Step-by-step explanation:
so 14 and 13 a both C
mark brainliest or give 1 heart and 5 stars or maybe both
Which expression represents the perimeter of the figure below? *
2x + 4 y
w + 2x + 4y
w + x + y
2w + 2x + 4y
Step-by-step explanation:
Perimeter of figure =
[tex]w + x + x + y + y + y + y \\ = 1 \times w + 2 \times x + 4 \times y \\ = w + 2x + 4y[/tex]
Simplify 15.6 divided by negative 3..
Answer:
-5.2
Step-by-step explanation:
15.6 ÷ (-3) = -5.2
53+2444= ??????? HELP I D K THE ANSWER
Answer:
2497
Step-by-step explanation:
Answer:
2497
Step-by-step explanation:
53 + 2444
= 0053 + 2444
= 2497
This is for now I need help pls !!!!!!!
I don’t even understand the question please help
Pls help ASAP I DONT have time
Answer:
B: y = 3x + 6
Which of the following statements are true?
A) 3 lbs of sugar is sugar is required to make 60 muffins.
B) 120 lbs of sugar is required to make 6 muffins.
C) 0 lbs of sugars required to make 0 muffins.
D) The maximum number of muffins that can be made is 220
Answer:
C
Step-by-step explanation:
Because 0 lbs of sugar is required to make 0 muffins
I hope this is right