Answers
Answers:
5x^2 + 2 = 4x has no real solutions3x^2 + 24x = -48 has exactly one real solution3(x+5)^2 = -2 has no real solutions4x^2 - 16x = 0 has two real solutions======================================================
Explanation:
We can use the discriminant formula to determine how many (and what type of) roots we have. The term "root" is another word for "solution" or "x intercept". It's the x value that makes y = 0.
Any quadratic is of the form ax^2 + bx + c = 0
The discriminant formula is
d = b^2 - 4ac
which is found underneath the square root in the quadratic formula.
Here are the three possible outcomes
d > 0: we get two different real number solutionsd = 0: we have exactly one real number solutiond < 0: there are no real number solutions (the two solutions are complex or imaginary numbers).With all that in mind, let's find the discriminant of the first equation on the very left.
First we need to get it into standard form ax^2+bx+c = 0
5x^2 + 2 = 4x
5x^2 - 4x + 2 = 0
We see that
a = 5b = -4c = 2Computing the discriminant gets us...
d = b^2 - 4ac
d = (-4)^2 - 4(5)(2)
d = 16 - 40
d = -24
The actual discriminant value itself doesn't matter. All we care about is whether its positive, zero, or negative.
In this case, we get a negative discriminant. So this equation goes to the "no real solutions" column.
-------------------------
Let's move onto the next quadratic
3x^2 + 24x = -48
3x^2 + 24x + 48 = 0
a = 3, b = 24, c = 48
d = b^2 - 4ac
d = 24^2 - 4(3)(48)
d = 0
The discriminant of zero means this equation goes into the "exactly one real solution" category.
-------------------------
For the next equation, we don't need to use the discriminant formula here.
Notice that the right hand side is negative, but the left side is never negative because 3 is positive and (x+5)^2 is never negative. There is no way to have 3(x+5)^2 be negative if we let x be a real number only.
The equation 3(x+5)^2 = -2 goes into "no real solutions" pile.
-------------------------
For the last equation, we have
a = 4, b = -16, c = 0
So,
d = b^2 - 4ac
d = (-16)^2 - 4(4)(0)
d = 256
The result is a positive number, so we have two different solutions.
The discriminant is a perfect square which means we not only have real number solutions, but those solutions are rational numbers. This only works when a,b,c are rational as well.
Related Questions
25 POINTS!!! simplify A=(1/2)(5x-2y)(4x+3y) please help and do step by step
Answers
Answer:
A= 10x^2 + 7/ 2 xy − 3y^2
Step-by-step explanation:
( 1/ 2) (5x−2y))(4x+3y)
= ( 1/ 2(5x−2y)) (4x+3y)
= ( 1/ 2 (5x−2y)) (4x) + ( 1/ 2 (5x−2y)) (3y)
= 10x^2 − 4xy + 15/ 2 xy − 3y^2
= 10x^2 + 7/ 2 xy − 3y^2
James has 16 baloons 1/4 of his balloons are red how many balloons deos he have
Answers
16 balloons
reason :
you're asking how many balloons does he have :>
Answer:
16 balloons
But if your asking how many red balloons, then the answer is 4
Step-by-step explanation:
16 balloons because you asked how many balloons does he have
LCD 7/8 and 1/4
Im stuck
help pls
Answers
Answer:
2
Step-by-step explanation:
It's the lowest common denominator si the answer is 2
Draw a picture or model to show the ratio 8:5 explain how you know your picture shows the ratio.
Answers
Answer:
draw a rectangle with side lengths 8 and 5. the ratio of the side lengths will be 8:5.
A bag contains 15 marbles. The probability of randomly selecting a green marble is One-third. The probability of randomly selecting a green marble, replacing it, and then randomly selecting a red marble is StartFraction 1 over 15 EndFraction. What is the probability of randomly selecting a red marble? StartFraction 1 over 45 EndFraction StartFraction 1 over 5 EndFraction StartFraction 4 over 15 EndFraction Two-fifths.
Answers
The probability of randomly selecting a red marble will be P=1/45
What is probability?
The probability is defined as the chances of happening of any event it is defined as the ratio of required outcomes to the total number.
Now here is the question, it is given that
Total marbles in the bag = 15
probability of randomly selecting a green marble = [tex]\dfrac{1}{3}[/tex]
The probability of randomly selecting a green marble, replacing it, and then randomly selecting a red marble is [tex]\dfrac{1}{15}[/tex]
So, the probability of randomly selecting a red marble will be the product of the two probabilities.
[tex]P= \dfrac{1}{3} \times \dfrac{1}{15}[/tex]
[tex]P=\dfrac{1}{45}[/tex]
Thus the probability of randomly selecting a red marble will be
[tex]P= \dfrac{1}{45}[/tex]
To know more about probability follow
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which is the simplest form of the expresson...
Answers
It is known that the point P(-9,18) belongs to the graph of the function y=k/x. Find k.
Answers
Answer:
[tex]k = (-162)[/tex].
Step-by-step explanation:
A point of the form [tex](x_{0},\, y_{0})[/tex] belongs to the graph of this function, [tex]y = k / x[/tex], if and only if the equation of this function holds after substituting in [tex]x = x_{0}[/tex] and [tex]y = y_{0}[/tex].
The question states that the point [tex](-9,\, 18)[/tex] belongs to the graph of this function. Thus, the equation of this function, [tex]y = k / x[/tex], should hold after substituting in [tex]x = (-9)[/tex] and [tex]y = 18[/tex]:
[tex]y = k / x[/tex].
[tex]18 = k / (-9)[/tex].
Solve this equation for the constant [tex]k[/tex]:
[tex]\begin{aligned}k &= 18 \times (-9) \\ &= (-162)\end{aligned}[/tex].
Thus, [tex]k = (-162)[/tex].
how much money is 1 dollar, 3 quarters, 1 nickel, and 3 pennies
Answers
Answer:
1.83$
Step-by-step explanation:
Your car gets 25 mi/gal around town and 30 mi/gal on the highway.
a. If 50% of the miles you drive are on the highway and 50% are around town, what
is your overall average miles per gallon?
b. If 60% of the miles you drive are on the highway and 40% are around town, what
is your overall average miles per gallon?
need work shown if possible im really confused
Answers
Answer:
Ok so what it is asking on part A is if your driving 50% on the highway which is 30 miles a gallon and 50% on around the town which is 25 miles a gallon then how many miles a gallon are you getting and the answer for that you need to first find what kind of problem it is and in this case you are working with percents so what you first want to do is multiply 50% to both 30 and 25 which will be 15 and 12.5 then add those together to get you answer now do the same for part B but instead of 50% it will be 60% and 40%.
Step-by-step explanation:
glad I could help
I WILL GIVE BRAINLEST IF ANSWER IS CORRECT AND U ARE FIRST!!!!!!!!!!!!!!!!!!!!!!!!!
Sean is raising funds for an event at his school. He has collected $25 each from x
people, and he is still $100 short of his goal.
The expression that gives his goal is _____.
Answers
Answer:
25x-100= a
let a= the amount of money for his goal????
Step-by-step explanation:
A biologist hopes to estimate the proportion of alligators in Florida that are adult. When sampling alligators, the biologist computes the one-proportion Z-interval going from 0.67 to 0.74 at 99% confidence. The margin of error for a 95% confidence interval would be:_____.
Answers
Using the z-distribution, as we are working with a proportion, it is found that the margin of error for a 95% confidence interval would be of 0.0008.
What is a confidence interval of proportions?A confidence interval of proportions is given by:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which:
[tex]\pi[/tex] is the sample proportion.z is the critical value.n is the sample size.The margin of error is given by:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In this problem, we have a 95% confidence level, hence[tex]\alpha = 0.95[/tex], z is the value of Z that has a p-value of [tex]\frac{1+0.95}{2} = 0.975[/tex], so the critical value is z = 1.96.
Considering the 99% confidence interval, which has z = 2.575, the estimate and the sample size are given by:
[tex]\pi = \frac{0.67 + 0.74}{2} = 0.705[/tex]
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.74 - 0.705 = 2.575\sqrt{\frac{0.705(0.295)}{n}}[/tex]
[tex]0.035 = 2.575\sqrt{\frac{0.705(0.295)}{n}}[/tex]
[tex]0.035\sqrt{n} = 2.575\sqrt{0.705(0.295)}[/tex]
[tex]\sqrt{n} = \frac{2.575\sqrt{0.705(0.295)}}{0.035}[/tex]
[tex](\sqrt{n})^2 = \left(\frac{2.575\sqrt{0.705(0.295)}}{0.035}\right)^2[/tex]
[tex]n = 1126[/tex]
Hence, the margin of error is given by:
[tex]M = 1.96\sqrt{\frac{0.705(0.295)}{1126}} = 0.0008[/tex]
More can be learned about the z-distribution at https://brainly.com/question/25890103
Find the equation of a line through (-3,5) and perpendicular to (1,-3) (6,1)
Answers
Step-by-step explanation:
simply use the formula as given in the image
10. Determine whether MN and RS are parallel, perpendicular, or neither. M(-2, 2) N(1.-3) R(-2, 1) S(3,4)
Answers
Answer:
3.4 and 1 - 3
Step-by-step explanation:
The scatterplot shows the relationship between the time a water balloon is filled from a running faucet and the volume of the balloon.
Which transformations would display linearized data? Check all that apply.
ln(Time), ln(Volume)
Time,
Time3, Volume3
Time, log(Volume)
Time3, Volume
Answers
Answer:
a,b,e
Step-by-step explanation:
Answer:
A; B; E
In(Time), In(volume) ; Time,3/volume ; Time^3, Volume
Step-by-step explanation:
PLEASE HELP ME YOU HAVE TO MAKE AN EQUATION LIKE y=mx+b!!!
Answers
Answer:
5. y=-3x-3
6.y=5/3x+5
Step-by-step explanation:
you take the slope of the line and substitute it for x and take the y-intercept and sub it in for b
I hope this is right
In the given figure, x = 30°. What's the property of parallel lines used to find x?
Answers
d = 3xy − y I will MARK BRAINLIESTTTTTTTTTTT ASAP PLEAAAAASSSSSSEEEEEE
Answers
Answer:
Since
3
y
is constant with respect to
x
, the derivative of
3
x
y
with respect to
x
is
3
y
d
d
x
[
x
]
.
3
y
d
d
x
[
x
]
Differentiate using the Power Rule which states that
d
d
x
[
x
n
]
is
n
x
n
−
1
where
n
=
1
.
3
y
⋅
1
Multiply
3
by
1
.
3
y
Step-by-step explanation:
What is x?
5x - 1 = - 8
Answers
Answer:
x = -1.4, -7/5, or -1 2/5 (all same answer, just in different forms)
Step-by-step explanation:
Step 1: Add 1 to both sides.
[tex]5x-1+1=-8+1[/tex] [tex]5x=-7[/tex]Step 2: Divide both sides by 5.
[tex]5x/5=-7/5[/tex] x = -1.4, -7/5, or -1 2/5.Have a lovely rest of your day/night, and good luck with your assignments! ♡
Answer:
x = -7/5 or -1.4
Step-by-step explanation:
Given :-
5x - 1 = -8
To Find :-
x
Solving :-
5x - 1 = -8
5x = -7
x = -7/5 or -1.4
Solution :-
x = -7/5 or -1.4
Can someone help me figure this out
Answers
Answer:
k is 16 so now u would plug it in.
Step-by-step explanation:
3 is 65 and 9 is 65 because they are alternate interior angles
Look at picture need help asap
Answers
Answer:
f^-1 = 3(x + 1)
Step-by-step explanation:
f(x) = (3 - x)/x
y = (3 - x)/x
x = (3 - y)/y
xy = 3 - y
xy + y = 3
y(x + 1) = 3
y = 3/(x + 1)
f^-1 = 3(x + 1)
Please help, I will give brainliest if you are correct
Answers
Answer:
In 24 years there will be 140 foxes
Step-by-step explanation:
Chin was shown the graph of a line that contained point (1, 7). He wrote f(x) = 4x + 3 to correctly represent the line. Which of these equations could represent the same line?
y – 7 = 3(x – 1)
y – 1 = 3(x – 7)
y – 7 = 4(x – 1)
y – 1 = 4(x – 7)
Answers
Answer: it’s the third option
Step-by-step explanation:
Answer:
y – 7 = 4(x – 1)
Step-by-step explanation:
Third option
What’s the scale factor?
Answers
rectangle has sides that are 25 m, 25m, 9m, and 9 m. What is the rectangle’s width?
10pts
68m
9m
25m
18m
Answers
It said the sides are 25m (x2) and 9m(x2). The width of a rectangle are shorter than the length so 9m.
FInd the area of the figures
Answers
Answer:
What is that on
Step-by-step explanation:
Flower pots cost $60.25 each.
Flower pot saucers cost $25 each.
A customer buys 4 of each.
How much change should the customer
receive from $500?
Answers
Answer:
159 dollars
Step-by-step explanation:
Multiply 60.25 and 25 four times and add them. Then subtract it from a 500.
What is the area of the parallelogram?
11 in.
13 in
A. 290 in.^2
B. 286 in.^2
C. 143 in.^2
D. 71.5 in^2
Answers
Marilyn has two credit cards, D and E. Card D has a balance of $691. 64, and Card E has a balance of $1,014. 22. The minimum monthly payment on Card D is 3. 57% of the total balance, and the minimum monthly payment on Card E is 2. 51% of the total balance. How much greater is the minimum payment on Card E than on Card D? a. $18. 85 b. $8. 10 c. $11. 24 d. $0. 77 Please select the best answer from the choices provided A B C D.
Answers
By using basic concept of percentage we got that minimum payment on Card E is 0.77 than on Card D.
What is percentage ?Percentage is a number or ratio expressed as a fraction of 100.
Here given that
Marilyn has two credit cards, D and E. Card D has a balance of $691. 64, and Card E has a balance of $1,014. 22. The minimum monthly payment on Card D is 3. 57% of the total balance, and the minimum monthly payment on Card E is 2. 51% of the total balance
So minimum balance of Card D is 3.57 Percentage of $ 691.64
[tex]=3.54\times\frac{691.64}{100} =24.691548=24.69[/tex]
minimum balance of Card E is 2. 51 Percentage of $1,014. 22.
[tex]=2.51\times\frac{1014.22}{100} =25.456922=25.46[/tex]
Now we can see that minimum balance of Card E is 25.49-24.69=0.77 extra that on D
By using basic concept of percentage we got that minimum payment on Card E is 0.77 than on Card D.
To learn more about Percentage visit : https://brainly.com/question/19247356
help please
i don't understand
Answers
Answer:
I believe it has 9 edges, comment if u need me to explain more
Answer:
6
Hope it helps!
Say you've got a credit score of 750, and you miss one credit card payment will
this impact your credit score MORE or LESS than if your original score was 650?
Why do you think this is the case?
Answers
The higher the score, the greater the decrease will be, since the greater the value of the decreased percentage will be greater too.
PercentagesGiven that you've got a credit score of 750, and you miss one credit card payment, to determine if this will impact your credit score MORE or LESS than if your original score was 650, the following calculation must be performed:
Suppose that a non-payment reduces the value of the score by 5%.100 - 5 = 95750 x 0.95 = 712.5 (-37.5)650 x 0.95 = 617.5 (-32.5)Thus, as can be seen, the higher the score, the greater the decrease will be, since the greater the value of the decreased percentage will be.
Learn more about percentages in https://brainly.com/question/8011401