Using the graph as your guide, complete the following statement.
The discriminant of the function is
Answers
Answer:
Using the graph as your guide, complete the following statement.
The discriminant of the function is
Step-by-step explanation: Remember a parable of the form f(x) = a[tex]a x^{2} + bx + c[/tex], satisfy:
(1) has only one root if and only if [tex] b^2 - 4ac = 0[\tex]
(2) has two real roots if and only if [tex] b^2 - 4ac > 0[\tex]
(3) has two complex roots if and only if [tex] b^2 - 4ac < 0[\tex].
The number b^2 - 4ac is called the discriminant of the parable f(x).
From the graph we can see that the parable has only one root approx in x =1. Thus from point (1) we can conclude that the discriminant should be zero.
PD: a root of a polynomial f(x) is a number a such thast f(a) =0.
The answer is A.
Answer: The answer is A because the vertex lies on the x axis which makes it zero.
Answer= A
Related Questions
Sadie has a cousin Nanette in Germany. Both families recently bought new cars and the two girls are comparing how fuel efficient the two cars are. Sadie tells Nanette that her family’s car is getting 42 miles per gallon. Nanette has no idea how that compares to her family’s car because in Germany mileage is measured differently. She tells Sadie that her family’s car uses 6 liters per 100 km. Which car is more fuel efficient? Please explain everything
Answers
Sadie’s family’s car is slightly more fuel efficient than Nanette’s family’s car.
Answer:
Sadie's car is more fuel efficient.
Step-by-step explanation:
Consider the provided information.
For comparison both quantity should be same. So convert miles per gallon into kilometers per liter.
Sadie tells her family's car is getting 42 miles per gallon.
To convert miles per gallon into liters per km use the formula:
1 miles per gallon = 0.425144 kilometers per liter
Multiply both the sides by 42.
1×42 miles per gallon = 0.425144×42 kilometers per liter
42 miles per gallon = 17.856 kilometers per liter
That means Sadie's car millage is 17.856 kilometer per liter.
Nanette tells Sadie that her family’s car uses 6 liters per 100 km.
6 Liters = 100 km
Divide both sides by 6.
1 Liters = 16.66..
That means Nanette's car millage is approximately 16.67 kilometer per liter.
Hence, Sadie's car is more fuel efficient.
Two minor league baseball players got a total of 390 hits. Washington had 16 more hits than Sanchez. Find the number of hits for each player.
Washington had
hits. Sanchez had
hits.
Answers
Answer:
Sanchez had 179 hits, while Washington had 211 hits. Hope this helps!
Final answer:
To solve the problem, we set up two equations: W = S + 16 and W + S = 390. By substituting the first equation into the second, we found that Sanchez had 187 hits, and Washington had 203 hits.
Explanation:
The question involves determining the number of hits for each player given the total number of hits and the difference in hits between the two players. We can set up a system of equations to solve for the number of hits for each player. Let's denote the number of hits by Washington as W and the number of hits by Sanchez as S.
According to the problem, we have two relationships:
Washington had 16 more hits than Sanchez: W = S + 16
The total number of hits is 390: W + S = 390
We can substitute the first equation into the second to solve for S.
S + (S + 16) = 390
S + S = 390 - 16
2S = 374
S = 374 / 2
S = 187
Now we plug the value of S back into the first equation to solve for W:
W = 187 + 16
W = 203
Therefore, Washington had 203 hits and Sanchez had 187 hits.
What is the difference between a day and a line segment
Answers
Hello!
I do believe you meant to say:
"What is the difference between a ray and a line segment?"
The difference between a ray and a line segment is:
A ray has one endpoint and continues in one direction. a ray is infinite
A line segment has two endpoints. a line segment is finite
I hope this helps, and have a nice day!
42 students arrived at the school dance after it started. in all 78 students attended. write and solve an equation to find how many students arrived at the dance before it started. plz help right when you see it!!!
Answers
Answer:
The answer is 36
Step-by-step explanation:
we know 42 students arrived after the dance started and 78 arrived in total. You have to subtract 42 from 78. how I remember this: part+part=whole whole-part=part
Using the numbers -4, 10, 8, 2, -3, -5, create two expressions that
equal 6.
Answers
The two expressions should be [tex]-4 \div 2 + 8 = 6\ and\ (10 \times -3) \div -5 = 6[/tex].
Given that,
The numbers are -4, 10, 8, 2, -3, -5.We need to develop two expressions that are equivalent to 6.Based on the above information, the calculation is as follows:
[tex]-4 \div 2 + 8 = 6\[/tex]
6 = 6
And,
[tex](10 \times -3) \div -5 = 6[/tex]
6 = 6
Therefore we can conclude that the two expressions should be [tex]-4 \div 2 + 8 = 6\ and\ (10 \times -3) \div -5 = 6[/tex].
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Two expressions using the given numbers that equal 6 are: Expression 1: 10 - 2 - (-3) + (-5) and Expression 2: 10 - 2 + 8 - (-4) - 5. The calculations are done using the order of operations (PEMDAS).
Explanation:The task is to create two mathematical expressions using the numbers -4, 10, 8, 2, -3, and -5, which result in 6. We can accomplish this by utilizing basic arithmetic operations such as addition, subtraction, multiplication, or division. The important thing is making sure all operations adhere to the Order of Operations, also known as PEMDAS (Parentheses, Exponents, Multiplication and Division, and Addition and Subtraction). Here are the two ways you could form expressions:
Expression 1: 10 - 2 - (-3) + (-5). The calculation goes as follow: 10 minus 2 equals 8, then we subtract -3 which is the same as adding 3, so 8 plus 3 equals 11, and finally we subtract 5 to get 6.Expression 2: 10 - 2 + 8 - (-4) - 5. Similarly, you calculate 10 minus 2 equals 8, plus 8 equals 16, add -4 (which is the same as subtracting 4) results in 12, and subtracting 5 gives us 6.Learn more about Mathematical Expressions here:https://brainly.com/question/30350742
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On the surface, it seems easy. Can you think of the integers for x, y, and z so that x³+y³+z³=8? Sure. One answer is x = 1, y = -1, and z = 2. But what about the integers for x, y, and z so that x³+y³+z³=42?
That turned out to be much harder—as in, no one was able to solve for those integers for 65 years until a supercomputer finally came up with the solution to 42. (For the record: x = -80538738812075974, y = 80435758145817515, and z = 12602123297335631. Obviously.)
Answers
Answer:
Well ,lets see∉ if you add theose numbers togetherФ it maybe it he answe ris 4=67 *64 ---4 67x54 5xe4t4 6xStep-by-step
Answer:
if i see them it my be 5x6x7=76 6(*)665_+65x673 then add those toether then sub em 56-78-463=738
Step-by-step explanation:
simplify by distributing and combining like terms
Answers
Answer: -9x + 24
Step-by-step explanation:
To do this, we need to multiply each term by -3
So -3(3x -8) turns into
-9x + 24
That’s the answer!
Factor -4x + 24 - 4x^2
Answers
Answer:
- 4(x + 3)(x - 2)
Step-by-step explanation:
Given
- 4x + 24 - 4x² ← rewrite in standard form, that is
- 4x² - 4x + 24 ← factor out - 4 from each term
= - 4(x² + x - 6) ← factorise the quadratic
Consider the factors of the constant term (- 6) which sum to give the coefficient of the x- term (+ 1)
The factors are + 3 and - 2, since
3 × - 2 = - 6 and 3 - 2 = + 1, hence
x² + x - 6 = (x + 3)(x - 2), and
4x² - 4x + 24 = - 4(x + 3)(x - 2)
A single little brown bat can eat up to 1,000 mosquitoes in a single hour.express in scientific notation how many mosquitoes a little brown bat might eat in 10.5
Answers
Answer: 1.05 ·10⁴ mosquitoes
Step-by-step explanation:
1,000mosquitoes/hour x 10.5hours =10,500 mosquitoes
Now you have to move decimal point as many space as needed left so that the number is less than ten.
10,500 ↪ 1.0500 because I moved decimal point 4 spaces, its 10⁴
Answer: 1.05 ·10⁴ mosquitoes
[tex]\textit{\textbf{Spymore}}[/tex]
The sum of Chris and Mike’s scores on a math quiz is 39. Mike’s score is twice the sum of Chris’ score and 3. Find each student’s quiz score.
Answers
Answer: c=11, m=28
Step-by-step explanation:
c= Chris's score
m= Mike's score
c+m=39 we know from the equation that their scores
add up to 39, so this equation is a good starting
point.
c+2(c+3)=39 we also know that Mike's score is twice the sum of Chris's
score and 3 so we can substitute that in for his score.
now we can solve.
c+2c+6=39 distribute
3c+6=39 combine like terms
-6 -6
3c=33 addition property of equality
÷3 ÷3
c=11 multiplication property of equality
Now that we know Chris's score, we simply substitute that number in in our simple equation for earlier to find Mike's score.
11+m=39 substituted in 11 for c
-11 -11
m=28 addition property of equality
There you go! Don't worry, I had a lot of trouble with these types of problems too. That's why I'm so good at them now Hope this helps!
BRAINLIEST PLUS 100 POINTS
Please show full working out and draw a neat diagram for question five and also note that this is trigonometry
Correct answers only please ;)
Thank you in advance :)
Answers
The exact answer is 4√2 + 4
The decimal answer is 9.6568 ( round the answer as needed.)
See the attached picture:
solve for b a + b/c = pq
Answers
Answer:
b = c(pq - a)
Step-by-step explanation:
All we need to do is isolate (solve for) the variable b
a + b/c = pq
Subtract a from both sides
b/c = pq - a
Multiply by c on both sides
b = c(pq - a)
Answer:
b = c(pq - a)
Step-by-step explanation:
Based on the example above, identify the first operation needed to solve the following equation.
4m/3 = 8
Answers
Answer:
See below.
Step-by-step explanation:
I can't see any example but what I would do is first multiply both sides by 3.
4m/3 = 8
4m/3 * 3 = 8 * 3
4m = 24.
The first operation in solving the equation 4m/3 = 8 is multiplying both sides of the equation by 3, which eliminates the fraction and isolates the variable 'm'. After further simplification, the solution to the equation is m = 6.
Explanation:To solve the equation 4m/3 = 8, the first operation we need to perform is to isolate the variable on one side of the equation. We can do this by multiplying both sides of the equation by 3. This cancels out the fraction on the left side, allowing us to solve for 'm'.
In step by step:
Multiply both sides of the equation by 3: (4m/3) * 3 = 8 * 3.This simplifies to 4m = 24.Finally, we divide both sides by 4 to solve for 'm': m = 24/4.m = 6.So, "the solution to the equation is m = 6".
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7. Find the product (3x + 2)(4x2 – 5x + 7).
Answers
Answer:
12x³ - 7x² + 11x + 14
Step-by-step explanation:
Each term in the second factor is multiplied by each term in the first factor, that is
3x(4x² - 5x + 7) + 2(4x² - 5x + 7) ← distribute both parenthesis
= 12x³ - 15x² + 21x + 8x² - 10x + 14 ← collect like terms
= 12x³ - 7x² + 11x + 14
The age of a woman is 4 times the age of her daughter. 5 yrs hence,the age of the woman will be 3 times the age of her daughter. Find the present age of the daughter in yrs.
Answers
Answer:
10
Step-by-step explanation:
If W is the present age of the woman and D is the present age of the daughter, then:
W = 4D
W + 5 = 3(D + 5)
Substituting the first equation into the second:
4D + 5 = 3(D + 5)
4D + 5 = 3D + 15
D = 10
The daughter is 10 years old.
Solve the inequality for x 24x > 18(4x – 6) – 30
Answers
Answer:
The required solution is: [tex]x<\frac{23}{8}[/tex] or x<2.875 or [tex]\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\frac{23}{8}\right)\end{bmatrix}[/tex]
Step-by-step explanation:
Consider the provided inequity.
[tex]24x>18(4x-6)-30[/tex]
We need to solve the above inequity of x.
Open the parentheses.
[tex]24x>18\times 4x-18\times 6-30[/tex]
[tex]24x>72x-108-30[/tex]
[tex]24x>72x-138[/tex]
Subtract 72x from both sides.
[tex]24x-72x>72x-138-72x\\-48x>-138[/tex]
Multiply both sides by -1 and reverse the inequality.
[tex]\left(-48x\right)\left(-1\right)<\left(-138\right)\left(-1\right)[/tex]
[tex]48x<138[/tex]
Divide both side by 48.
[tex]x<\frac{23}{8}[/tex]
Hence, the required solution is: [tex]x<\frac{23}{8}[/tex] or x<2.875 or [tex]\mathrm{Interval\:Notation:}&\:\left(-\infty \:,\:\frac{23}{8}\right)\end{bmatrix}[/tex]
Find the value of x if R is the midpoint of QS QR=5x-7 and QS=96
Answers
Answer: The required value of x is 11.
Step-by-step explanation: Given that R is the midpoint of the line segment QS, where
QR=5x-7 and QS=96.
We are to find the value of x.
Since the point R is the midpoint of the segment QS, so we must have
[tex]QR=SR=\dfrac{1}{2}QR\\\\\\\Rightarrow QR=\dfrac{1}{2}QS\\\\\\\Rightarrow 5x-7==\dfrac{1}{2}\times96\\\\\Rightarrow 5x-7=48\\\\\Rightarrow 5x=48+7\\\\\Rightarrow 5x=55\\\\\Righatrrow x=\dfrac{55}{5}\\\\\Rightarrow x=11.[/tex]
Thus, the required value of x is 11.
If R is the midpoint of QS, then x = 11.
We have,
If R is the midpoint of QS, then QR is equal in length to RS.
Therefore:
QR = RS
Given that QR = 5x - 7 and QS = 96, we can set up an equation:
5x - 7 = QS/2
Now, plug in the value of QS:
5x - 7 = 96/2
5x - 7 = 48
Add 7 to both sides:
5x = 48 + 7
5x = 55
Now, divide both sides by 5 to isolate x:
x = 55 / 5
x = 11
So, the correct value of x is 11.
Thus,
If R is the midpoint of QS, then x = 11.
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The volume of air inside a rubber ball with radius r can be found using the function V(r) = four-thirds pi r cubed. What does V and five-sevenths represent?
the radius of the rubber ball when the volume equals five-sevenths cubic feet
the volume of the rubber ball when the radius equals five-sevenths feet
that the volume of the rubber ball is 5 cubic feet when the radius is 7 feet
that the volume of the rubber ball is 7 cubic feet when the radius is 5 feet
Answers
Answer: v[5/7] represents the volume of air inside a rubber ball with radius 5/7 units, such that
Step-by-step explanation:
Given: The volume of air inside a rubber ball with radius r can be found using the function.
Here volume is a dependent variable on radius (independent variable).
Therefore, the value of v[5/7] represents the volume of air inside a rubber ball with radius 5/7 units.
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Answer:
we know that
The volume of a sphere (rubber ball) is equal to
V = 4/3pi r^3
where r is the radius of the sphere (rubber ball)
The volume in function notation is equal to
V(r) = pi r^3
in this problem we have
V(5/7)
that means
The radius of the rubber ball is 5/7 ft and the volume of the rubber ball is V(5/7) ft^3
therefore, the answer is the option B
the volume of the rubber ball when the radius equals 5/7 feet
Plz help me show the work plz
Answers
Answer:
all work is shown and pictured
I need help with this
Answers
#3 is 40 degrees Clockwise.
what does x equal and explain how
Answers
Answer:
x = 32Step-by-step explanation:
[tex]\dfrac{x}{8}+2=6\qquad\text{subtract 2 from both sides}\\\\\dfrac{x}{8}+2-2=6-2\\\\\dfrac{x}{8}=4\qquad\text{multiply both sides by 8}\\\\8\!\!\!\!\diagup^1\cdot\dfrac{x}{8\!\!\!\!\diagup_1}=(8)(4)\\\\x=32[/tex]
Solve this equation use pemdas 4x(5+8•2)
Answers
Answer:84
Step-by-step explanation:
p = perentsis acccording to pemdas you have to multiply then 8x2 =16 +5=21
21 x4 = 84
4. Which of the two figures below has the lesser volume?
5. Which of the two figures below has the greater volume?
Answers
Answer:
cylinder has greater volume
Fourteen is 20% of
please help me in need
Answers
Answer:
14 / .20 = x
.20 x = 14
x = 14 / .20
x = 70
DOUBLE - CHECK
20 % of 70 = .20 * 70 = 14
Step-by-step explanation:
Add the following
(This is just a filler so i can post this)
Answers
Answer:
9/10
Step-by-step explanation:
You find the lowest common denominator which is 56 and then, you multiply each numerator by the opposite denominator (3 times 7 and 3 times 8) after that you should get 5 45/50 then you simplify it to get 9/10
Find the distance between the points (-5, 0) and (-4,1).
01
O2
02.12
Answers
Answer:
[tex]\sqrt{2}[/tex] ≈ 1.414
Step-by-step explanation:
Calculate the distance d using the distance firmula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (- 5, 0) and (x₂, y₂ ) = (- 4, 1)
d = [tex]\sqrt{(-4+5)^2+(1-0)^2}[/tex]
= [tex]\sqrt{1^2+1^2}[/tex]
= [tex]\sqrt{2}[/tex] ≈ 1.414 ( to 3 dec. places )
what is 2 + 2 - 4 + 1500 x 2 - 300 - 2700 equal to?
Answers
2+2-4+3000-2700 and do it from left the right, the answer is 300
Use A=12bh to find the height of a triangle that has an area of 180 in^2 and a base of 20 in.
Answers
Answer:
18 in
Step-by-step explanation:
A=1/2 bh
180 = (20* h)/2
180*2 = 20*h
(180*2)/20 = h
360/20 = h
18 in = h
b. You used 13 gallons when you traveled 342 miles. How many miles did you
travel per gallon?
Answers
Answer:
26.307 miles per gallon
Step-by-step explanation:
Divide the miles traveled by the number of gallons used.
In this case, divide 342 by 13 to get the answer of 26.307 miles per gallon.
If the outliers are not included in the data set below, what is the mean of the data set?
42, 43, 46, 48, 57, 60, 96, 59, 38, 68, 29 (2 points)
a 47
b 48
c 49
d 52
Answers
The mean of the given data set, after removing the outlier, is 49.
Explanation:To determine the mean of a data set, outliers (extremely high or low values) must first be identified and removed. Looking at the given data set: 42, 43, 46, 48, 57, 60, 96, 59, 38, 68, 29; the number 96 is an outlier as it is remarkably higher than the other values.
After removing the outlier, the rest of the data set becomes: 42, 43, 46, 48, 57, 60, 59, 38, 68, 29.
To find the mean (average), sum all these numbers and divide by the count of numbers. The total sum of these numbers is 490, and there are 10 numbers. Therefore, the mean is 49 (490 divided by 10).
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The mean of the data set after removing the outliers is c. 49
How to determine the mean if the outliers are not includedFrom the question, we have the following parameters that can be used in our computation:
The data set
Where, we have
42, 43, 46, 48, 57, 60, 96, 59, 38, 68, 29
The outlier in the data set is 96
If we remove them, we will have the following data set:
42, 43, 46, 48, 57, 60, 59, 38, 68 and 29
The mean of this data set is calculated as follows:
mean = (42 + 43 + 46 + 48 + 57 + 60 + 59 + 38 + 68 + 29) / 10 = 49
Hence, the mean without outliers is 49
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