Answer:
D. No. When the discriminant is less than zero, there are no real solutions.
Step-by-step explanation:
We have to notice that quadratic equations are second order polynomials whose standard form is:
[tex]y = a\cdot x^{2}+b\cdot x + c \cdot x[/tex], [tex]\forall \,a,b,c\,\in\,\mathbb{R}[/tex]
The factorized form of this polynomial is:
[tex]y = (x-r_{1})\cdot (x-r_{2})[/tex]
Where [tex]r_{1}[/tex] and [tex]r_{2}[/tex] are the roots of the quadratic equation, which may be real or complex.
If we equalize [tex]y[/tex] to zero and make algebraic handling, we can get the value of each root anatically by the Quadratic Formula:
[tex]r_{1,2} = \frac{-b\pm \sqrt{b^{2}-4\cdot a \cdot c}}{2\cdot a}[/tex]
Where [tex]b^{2}-4\cdot a\cdot c[/tex] is known as the discriminant. Then, we should remember the following rules:
i) If discriminant is greater than zero, then the quadratic equation has two different real roots.
ii) If discriminant is zero, then the quadratic equation has two equal real roots.
iii) If discriminant is less than zero, then the quadratic function has two complex roots.
In consequence, we came to the conclusion that statement is false, as quadratic equation have all roots real or all complex, but not one real and the other complex.
In a nutshell, the correct answer is D.
At Becky's Restaurant, 10 out of 25 customers order wheat rolls. The rest of the customers order cornbread. Which does NOT represent the part of the customers who order wheat rolls
Answer:
C. 25 ÷ 10
Step-by-step explanation:
A. 10/25
B. 2/5
C. 25 ÷ 10
D. 0.4
Total customers at Becky's restaurant = 25
Customers who order wheat rolls = 10
It means 10 out of 25 customers order wheat rolls
That is
10 / 25
Dividing both numerator and denominator by 5
= 2 / 5
2/5 in decimal
= 0.4
The option Which does NOT represent the part of the customers who order wheat rolls
is 25/10
Option C. 25 ÷ 10
Add.
(2x2 - 2x) + (6x – 4)
2x^2 + 4x - 4
..........................
Answer:
x = {-2, -1}
Step-by-step explanation:
Combine like terms: 0 + -2 = -2
x = -2
Simplifying
x = -2
Combine like terms: 0 + -1 = -1
x = -1
Simplifying
x = -1
The area of a rectangular wall of a barn is 252 square feet. Its length is 10 feet longer than twice its width. Find the length and width of the wall of the barn.
Answer: Length = 28 feet and width = 9 feet
Step-by-step explanation:
Let x = width of the wall.
Then, Length of the wall = 10+2x
Since , Area of rectangle = length x width
Then, as per given,
[tex]252= (10+2x)x\\\\\Rightarrow\ 252=10x+2x^2\\\\\Rightarrow\ 2x^2+10x-252=0\\\\\Rightarrow\ x^2+5x-126=0\\\\\Rightarrow\ x^2+14x-9x-126=0\\\\\Rightarrow\ (x+14)-9(x+14)=0\\\\\Rightarrow\ (x+14)(x-9)=0\\\\\Rightarrow\ x=-14 \ or \ x= 9[/tex]
Since width cannot be negative , so x = 9
So width = 9 feet and length = 10+2(9)=10+18 = 28 feet
Hence, length is 28 feet and width is 9 feet of the wall of the barn.
El cubo de la diferencia entre dos números cualquiera
Answer:
El cubo de la diferencia de dos cantidades es igual a la primera cantidad elevada al cubo menos tres veces la primera cantidad elevada al cuadrado por la segunda cantidad más tres veces la primera cantidad por la segundad cantidad al cuadrado menos la segunda cantidad al cubo.
Step-by-step explanation:
Answer:
lo siento, no puedo ayudarte
Step-by-step explanation:
4(-32x+5)-(-33x-26)=
Answer:
-95x+46
Step-by-step explanation:
4(-32x+5)-(-33x-26)=
-128x+20-(-33x-26)=
-128x+20+33x+26
-95x+46
Answer:
-95x-46
Step-by-step explanation:
4(-32x+5)-(-33x-26)=
-128x+20-(-33x-26)=
-128x+20+33x+26
-95x+46
Simplify the expression: 1–7v+7v+9–2
Answer: 8
Step-by-step explanation:
Simplify 7 -(-4) + 3(-6).
0-7
07
-9
9
Rewrite as a simplified fraction.
3.2 = ? 2 is repeating
Answer:
3
.
¯
2
=
29
9
Explanation:
Using the notation of a bar over a set of digits to denote their infinite repetition,
let
x
=
3
.
¯
2
⇒
10
x
=
32
.
¯
2
⇒
10
x
−
x
=
32
.
¯
2
−
3
.
¯
2
=
29
⇒
9
x
=
29
∴
x
=
29
9
This technique works in general. Set
x
as your desired value, multiply by
10
n
where
n
is the number of digits repeating, and then subtract
x
to eliminate the infinitely repeating portion. It then is just a matter of dividing by
10
n
−
1
a
Step-by-step explanation:
x=536/165
you should know what to do since your in this part of the unit
need help please help
Answer:
9 minutes
Step-by-step explanation:
The water volume in pool 1 starts at 50 gallons and increases at 2.3 gallons per minute. An expression for that volume could be ...
v = 50 +2.3t
The water volume in pool 2 starts at 102.2 gallons and decreases at 3.5 gallons per minute. An expression for that volume could be ...
v = 102.2 -3.5t
The volumes will be equal when ...
50 +2.3t = 102.2 -3.5t
5.8t = 52.2 . . . . . . . . . . . subtract 50-3.5t from both sides
t = 52.2/5.8 = 9 . . . . . . . divide by the coefficient of t
After 9 minutes, the pools will contain the same amount of water.
_____
The equation 5.8t = 52.2 tells you the 52.2 gallon difference in volumes is being reduced at the rate of 5.8 gallons per minute. You don't really need the 'v' equations to figure that out.
Point K is on line segment JL. Given JK = 5x + 7, JL = 2x+8, and KL = 4,
determine the numerical length of JL.
Answer:
The numerical length of JL is 6 units
Step-by-step explanation:
Here, we want to determine the numerical length of JL
Mathematically;
JL = JK + KL
2x + 8 = 5x + 7 + 4
2x + 8 = 5x + 11
5x -2x = 8-11
3x = -3
x = -1
But JL = 2x + 8
JL = 2(-1) + 8 = -2 + 8 = 6
please solve for x, and give me an explanation on how you did so? 1/2x-1/3=5/6
=======================================================
Explanation:
Fractions are a pain to deal with, so whenever possible I recommend you eliminate them. With equations like this, you can multiply both sides by the same number to do so. The question is: which number would that be?
If you pick on the LCD, then you'll be able to clear out the fractions. The LCD of 1/2, 1/3, and 5/6 is 6 since the LCM of the denominators is 6.
Multiply both sides by 6 to get
(1/2)x - 1/3 = 5/6
6*[ (1/2)x - 1/3 ] = 6(5/6)
6*(1/2)x - 6*(1/3) = 6(5/6)
3x - 2 = 5
------------
At this point, the fractions are gone. We can now solve like so
3x-2 = 5
3x-2+2 = 5+2 ... adding 2 to both sides
3x = 7
3x/3 = 7/3 .... dividing both sides by 3
x = 7/3
Answer:
x=5/6
Step-by-step explanation:
12x−13=5612x-13=56
Combine 1212 and xx.
x2−13=56x2-13=56
Move all terms not containing xx to the right side of the equation.
Add 1313 to both sides of the equation.
x2=56+13x2=56+13
To write 1313 as a fraction with a common denominator, multiply by 2222.
x2=56+13⋅22x2=56+13⋅22
Write each expression with a common denominator of 66, by multiplying each by an appropriate factor of 11.
Multiply 1313 and 2222.
x2=56+23⋅2x2=56+23⋅2
Multiply 33 by 22.
x2=56+26x2=56+26
Combine the numerators over the common denominator.
x2=5+26x2=5+26
Add 55 and 22.
x2=76x2=76
Multiply both sides of the equation by 22.
2⋅x2=2⋅
Find the LCM of 30, 45, 60 and 90.
Answer:180
Step-by-step explanation:
write in standard form x2 + y = 2x -4
Answer:
y = - x² + 2x - 4
Step-by-step explanation:
The equation of a parabola in standard form is
y = ax² + bx + c ( a ≠ 0 )
Given
x² + y = 2x - 4 ( subtract x² from both sides )
y = - x² + 2x - 4 ← in standard form
How can you approximate the value of VI 30 ?
Answer:
VI is 6
Step-by-step explanation:
Answer:
VI is 6
Step-by-step explanation:
I WILL MARK YOU BRAINLIEST. Xavier decorated his paper with stickers. He put 3 stickers on his paper. Each sticker is 1/8 inches wide and 2/5 inches long. What is the total area, in square inches, of all of the stickers Xavier used?
Answer:
3x1/8x2/5=3/20
Step-by-step explanation:
PLEASE HELP ME! I have de done this 10+ times
Determine intersections and unions of sets using interval notation
Given the sets A and B in interval notation,
A = (-∞, 2) U (2, + ∞) and
B= (-∞, - 1) U (-1, + ∞)
find A n B =
Answer:
Shown in the picture
jacob weights 36.4 pounds and alice. weights 42.275 pounds. how much do they weigh together
Answer:
78.675 pounds
Step-by-step explanation:
36.4 + 42.275 = 78.675 pounds
Answer:
it is 78.675 just round it to the nearest something which would be 78.68
Step-by-step explanation:
just add and round
Translate sentence into an equation. Then ſind each number.
1. Seven more than three times a number is 16.
How to translate it
Answer:
This is the equation
Step-by-step explanation:
7 + 3x = 16
Please mark as brainliest.
Need help i don't understand
Represent the following sentence as an algebraic expression, where "a number" is the letter x.
A number plus 2
Answer:
X+2
Step-by-step explanation:
A number is x plus 2
X+2
A tree that grows 3 feet every 5 years is growing at a rate of ___ feet per year.'
[tex]\bf Step-by-step~explanation:[/tex]
Objective: You need to find the number of feet the tree grows every year (the unit rate).
[tex]\bf Steps:[/tex]
FIrst, we look at what we have now. The tree grows 3 feet every 5 years, so we have to divide 3 by 5 to get the number of feet the tree grows in one year.
[tex]\bf 3~feet~divided~by~5~years~=~Our~final~answer\\\frac{3}{5}=\frac{6}{10}~(multiplied~3~and~5~by~2)\\ \frac{6}{10} =0.6~feet[/tex]
[tex]\large\boxed {\bf Our~final~answer: ~0.6~feet~per~year}[/tex]
[tex]The~tree~grows~at~a~rate~of~0.6~feet~per~year.[/tex]
i need a little help with this equation 15-5+5^2
Answer:
35
Step-by-step explanation:
15-5+(5^2)
10+25
35
Please help! (Will give brainliest answer and hearts) Thank you and have a nice day!
Answer:
W
Step-by-step explanation:
so you go to the right 2 times then you go down 5 and a half times (where the negative numbers are) and then you get the answer here is a picture so you can understand a little better, I hope this helps you :)
Karen sells tickets at a movie theater. Last night she sold 128 tickets for a total of $1108. Adult's tickets cost $10 and children's tickets cost $6. How many of each kind of ticket did Karen sell?
Answer:
Adult's tickets 85
children's tickets 43
Step-by-step explanation:
x + y = 128
10x + 6y = 1108
x = 128 - y
10(128 - y) + 6y = 1108
1280 - 10y + 6y = 1108
1280 - 4y = 1108
-4y = 1108 - 1280
-4y = -172
y = -172/-4
y = 43
x = 128 - y
x = 128 - 43
x = 85
i need an answer and explaination
Antony borrowed 20,000,000 for 7 years his interest rate is 5% how much interest will he pay in all
Answer:
7,000,000
Step-by-step explanation:
[tex]Principal = 20,000,000\\Time =7\:years\\Rate = 5\%\\Simple\:interest =?\\\\Simple\:interest = \frac{Principal\times Rate\times Time}{100} \\\\S.I= \frac{20000000\times 5 \times 7}{100} \\\\S.I==\frac{700000000}{100}\\\\Simple\: interest=7000000[/tex]
The solution is, he will pay 7000000 interest in all.
What is interest?Interest is the price you pay to borrow money or the cost you charge to lend money. Interest is most often reflected as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.
Here, we have,
formula: I = Prt.
here, we have,
given that,
Antony borrowed 20,000,000 for 7 years his interest rate is 5%
i.e. we get,
P= 20,000,000
t = 7
r= 5%
and, we have to find I
so, we have,
I = P r t
=20,000,000*5*7/100
=7000000
Hence, he will pay 7000000 interest in all.
To learn more on interest click:
brainly.com/question/29335425
#SPJ3
What is the slope of a line that passes through 41-50
Answer:
-15/7
Step-by-step explanation:
The formula for slope is y2-y1/x2-x1 so replace the variables with -8-7/3-(-4) and solve which gets you -15/7
The length of a rectangle is 16m greater than the width. If the perimeter of a rectangle is 256m, what is the width of the rectangle?
Answer:
L=16+W
2W+2(16+W)=256
2W+32+2W=256
4W=224
W=56
The figure shown has two parallel lines cut by a transversal: A pair of parallel lines is shown, crossed by a transversal. Angles are identified as 1, 2, 3, 4, 5, 6, 7, and 8. Angles 1-4 are on the top line clockwise from upper left. Angles 5-8 are on the lower line clockwise from upper left. Use the figure to complete the sentence. (4 points) ∠7 and ____ are alternate exterior angles. a ∠2 b ∠1 c ∠5 d ∠8
There are several relationships between angles within a transversal of parallel lines.
The complete statement is (b) ∠7 and ∠1 are alternate exterior angles
From the figure (see attachment), we have the following highlights
Angles 1 and 7 are both exterior anglesAngles 1 and 7 are both alternate anglesThe above highlights mean that:
Angles 7 and 1 are alternate interior angles
Hence, the text that completes the blank is (b) ∠1
Read more about alternate interior angles at:
https://brainly.com/question/15685431
Answer:
b ∠1
Step-by-step explanation:
A researcher randomly selected 30 people to participate in a study to investigate which of two materials, A or B, used in the heels of sneakers will last longer. The researcher is considering two design types for the study.
Design 1: Randomly assign 15 participants to wear sneakers with material A on their left feet and material B on their right feet. The remaining participants will wear sneakers with material B on their left feet and material A on their right feet.
Design 2: Randomly assign 15 participants to wear sneakers with material A on both feet and the remaining participants to wear sneakers with material B on both feet.
Which of the following best describes each design?
Answer:
Design 1
Step-by-step explanation:
Design one would work better because the students get to see both materials (each on one foot) and if they do the same things each day with both feet, they can test how the material works with the activity...If that makes sense
The question is an illustration of a random selection.
The descriptions of the designs are:
Design 1 is a matched pair designDesign 2 is a completely randomized design.Design 1
From the question, we understand that:
15 participants wear material A on the left feet, and material B on the right feet.The other 15 wear material B on the left feet, and material A on the right feet.The above description is a matched pair design, because half of the participants gets randomly assigned to material A and B, while the other half gets automatically assigned to the remaining materials.
Design 2
From the question, we understand that:
15 participants wear material A on both feetThe other 15 wear material B on both feetThe above description is a completely randomized design, because half of the participants gets randomly assigned to material A, while the other half gets randomly assigned to material B.
Read more about random selections at:
https://brainly.com/question/10678373