Which of the following is a valld conclusion for the quadratic equation?
x2 - 6x+8=0
OX-3 = 0 and x+ 5 = 0
Ox+ 4 = 0 and x + 2 = 0
O x-4 = 0 and x + 2 = 0
O x-4 = 0 and x - 2 = 0
Answers
Answer:
[tex]x-4=0\: and\: x-2=0[/tex]
Step-by-step explanation:
[tex]x^{2} -6x+8-0[/tex]
[tex]x^{2} -4x-2x+8-0[/tex]
[tex]x(x-4)-2(x-4)=0[/tex]
[tex](x-4)(x-2)=0[/tex]
[tex]x-4=0[/tex] and [tex]x-2=0[/tex]
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The valid conclusions for the quadratic equation x² - 6x + 8 = 0 are:
x - 4 = 0 and x - 2 = 0
Option D is the correct answer.
We have,
Quadratic equation x² - 6x + 8 = 0.
Now,
To solve the quadratic equation x² - 6x + 8 = 0, we can use the quadratic formula, which states that:
x = (-b ± √(b² - 4ac)) / (2a)
where a, b, and c are the coefficients of the quadratic equation.
In this case,
a = 1, b = -6, and c = 8.
Substituting these values into the quadratic formula, we get:
x = (-(-6) ± √((-6)² - 4(1)(8))) / (2(1))
x = (6 ± √(36 - 32)) / 2
x = (6 ± √(4)) / 2
x = (6 + 2) / 2 or x = (6 - 2) / 2
x = 4 or x = 2
Therefore,
The valid conclusions for the quadratic equation x² - 6x + 8 = 0 are:
x - 4 = 0 and x - 2 = 0
because the roots of the equation are x = 4 and x = 2,
which can be written in factored form as (x - 4)(x - 2) = 0.
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Related Questions
For each of the following angles, assume that the terminal ray of the angle opens up in the counter-clockwise direction. A circle with a radius 7 cm long is centered at Angle A's vertex, and Angle A subtends an arc length of 9.8 cm along this circle. The subtended arc is how many times as long as the circle's radius
Answers
9514 1404 393
Answer:
1.4
Step-by-step explanation:
We want to find the multiplier n such that ...
arc length = n × radius
n = arc length / radius = (9.8 cm)/(7 cm)
n = 1.4
The subtended arc is 1.4 times as long as the circle's radius.
A general wishes to draw up his 7500 soldiers in the form of a square. After arranging, he found out that some of them are left out. How many soldiers were left out ?
Answers
If you want to form a square of 7500 soldiers, the side of the square must be [tex]\sqrt{7500}\approx86.6[/tex] soliders.
But since you cannot have 0.6 solider, the general needs to find the closest perfect square to the number 7500 which is less than 7500.
That number is 7396 which when square rooted gives 86 soliders on the side.
Subtract 7396 from 7500 and get how many soliders were left out,
[tex]7500-7396=\boxed{104}[/tex]
Hope this helps :)
I need step by step solution.
Answers
Answer: it is an exponential decay function
Step-by-step explanation:
Since 0.3 is less than 1 then increasing the value of the x will lead to the decrease of the value function y
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25. Use the equation P(AUB)=P(A) + P(B) - P(ANB), where A and B are any events, to compute the probability that the number drawn is prime or greater than 12.
The probability that the number drawn is prime or greater than 12 is : ___________
Answers
Answer:
17/25
Step-by-step explanation:
The equation for the probability of two events that are not mutually exclusive is:
p(A ∨ B) = p(A) + p(B) - p(A ∧ B)
A = the number is prime
B = the number is prime
The numbers are:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
Here are the 8 prime numbers that satisfy event A:
3, 5, 7, 11, 13, 17, 19, 23
p(A) = 8/25
Here are the 13 numbers that are greater than 12 that satisfy event B:
13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25
p(B) = 13/25
Here are the 4 numbers that satisfy both event A and event B:
13, 17, 19, 23
p(A ∧ B) = 4/25
p(A ∨ B) = p(A) + p(B) - p(A ∧ B)
p(A ∨ B) = 8/25 + 13/25 - 4/25
p(A ∨ B) = 17/25
The probability that the number drawn is prime or greater than 12 = [tex]\frac{18}{25}[/tex]
What is probability?"Probability is a branch of mathematics which deals with finding out the likelihood of the occurrence of an event."
Formula of the probability of an event A is:P(A) = n(A)/n(S)
where, n(A) is the number of favorable outcomes, n(S) is the total number of events in the sample space.
For given question,
In a lottery game, a single ball is drawn at random from a container that contains 25 identical balls numbered from 1 through 25.
n(S) = 25
Let event A: the number drawn is prime
The prime numbers from 1 to 25 are:
2, 3, 5, 7, 11, 13, 17, 19, 23
So, n(A) = 9
The probability that the number drawn is prime,
[tex]P(A)=\frac{n(A)}{n(S)}\\\\ P(A)=\frac{9}{25}[/tex]
Let event B: the number drawn is greater than 12
So, n(B) = 13
The probability that the number drawn is greater than 12,
[tex]P(B)=\frac{n(B)}{n(S)}\\\\ P(B)=\frac{13}{25}[/tex]
The number drawn is prime as well as greater than 12.
Such numbers are : 13, 17, 19, 23
n(A ∩ B) = 4
So, the probability that the number drawn is prime as well as greater than 12,
[tex]P(A\cap B)=\frac{n(A\cap B)}{n(s)}\\\\ P(A\cap B)=\frac{4}{25}[/tex]
Using the equation P(AUB) = P(A) + P(B) - P(A ∩ B) to find the probability that the number drawn is prime or greater than 12,
[tex]\Rightarrow P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\\Rightarrow P(A\cup B)=\frac{9}{25}+ \frac{13}{25} -\frac{4}{25} \\\\\Rightarrow P(A\cup B)=\frac{9+13-4}{25}\\\\ \Rightarrow P(A\cup B)=\frac{18}{25}[/tex]
Therefore, the probability that the number drawn is prime or greater than 12 = [tex]\frac{18}{25}[/tex]
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how many 50 cents coins are there in $10:50
Answers
Question:- how many 50 cents coins are there in $10.50
Answer:-
Total amount-> $ 10.50
So amount in cents
$ 1 is equal to 100 cents
$10.50 is equal to 1050 cents
According to the question
[tex]Number \: of \: the \: 50 \: cents= \frac{ Total \: cents}{ 50 \: cents } \\ [/tex]
[tex]Number \: of \: the \: 50 \: cents = \frac{1050}{50} \\ Number \: of \: the \: 50 \: cents = 21 \: [/tex]
What type of polynomial is: sqrt 7x^4 - x^3
Answers
Answer:
Quartic cause highest degree is 4
which is larger 1 1/2 or 1 15/16
Answers
Hi there!
»»————- ★ ————-««
I believe your answer is:
1 (15/16)
»»————- ★ ————-««
Here’s why:
⸻⸻⸻⸻
[tex]\boxed{\text{Converting the Fractions...}}\\\\\rightarrow \frac{1}{2}=\frac{1*8}{2*8}= \boxed{\frac{8}{16}}\\\\\text{We would only compare the fractions because we have the same whole number.}\\\\\frac{8}{16} <\frac{15}{16}\\\\\text{Therefore:}\\\\\boxed{1\frac{15}{16} >1\frac{1}{2}}[/tex]
⸻⸻⸻⸻
»»————- ★ ————-««
Hope this helps you. I apologize if it’s incorrect.
Find F(-3).
F(x) = 2x^2- 5x-8
Answers
Answer:
25
Step-by-step explanation:
F(x) = 2x^2- 5x-8
Let x=-3
f(-3) = 2 (-3)^2 -5(-3) -8
=2(9) +15 -8
=18+15-8
=25
A person of height 2m observes the angle of elevations of the top of a Pole 62m height which is in front of him and finds it to be 45. find the distance between the person end the pole .
Answers
Explanation:
distance from pole to person = adjacent
Height of pole = opposite
Angle(theta) = 45°
We can use tan(theta) = opp/adj to figure out the distance.
tan(45°) = 62/adj
1 = 62/adj
adj = 62m
Thus, adj = distance = 62m
-4x+3x+2x+x=17
x-4x+3x+2x=13
2x+x-4x+3x=9
3x+2x+x-4x=1
Answers
Answer:
x= 8,5
x=0
X= 2
x= -2
Step-by-step explanation:
apter 3 If a driver uses of a tank of gas every day, what fraction of a tank will he use in a) 3 days? b) 1 week? 21
Answers
You need to re copy and paste it, I can’t see the full possible answers/question.
a can do a piece of work in 10 days and B can do in 15 days in how many days would they finish the work if they do it
Answers
A can do a piece of work in 10 days and B can do it 15 days. If both of them are working together, half of the work can be finished in?
Here we find,LCM of 10 and 15 is 30.
A can do ( 1 /10 th ) of the work in one day Or, ( 3/30th ).B can do ( 1/15th ) of the work in one day ( or 2/30th ).Working together, A and B can do
= (3/30) + (2/30) = 5/30= 1/6 th of the work in one day.So, they would require 30/5 or 6 days to complete the task.
Factor the following
9t^2-42t+49
Answers
Answer:
(3t -7)²
Step-by-step explanation:
We know that the square of a binomial is ...
(a -b)² = a² -2ab +b²
So, when we see the first and last terms are both perfect squares, we suspect that the trinomial is a perfect square trinomial.
9t² = (3t)²
49 = 7²
-42t = -2(3t)(7) . . . . confirming we have a perfect square
The factorization is ...
(3t -7)²
express 6.25 as a fraction and find the square root as a decimal
Answers
Answer:
There are several ways to find this. For example:
√
6.25
=
√
6
+
1
4
=
√
25
4
=
√
25
√
4
=
5
2
=
2.5
√
6.25
=
√
625
100
=
√
625
√
100
=
25
10
=
2.5
The price of a car has been reduced from $16,500 to $11,055. What is the percentage decrease of the price of the car?
Answers
Answer:
33%
Step-by-step explanation:
$16,500-$11,055= $5,445
$5,445÷$16,500= 0.33 which in percentage format is 33%
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if chaka,ada and ese are to share 120 oranges with the ratio of 1:2:3 respectively. How many oranges does ada have?.
Answers
Answer:
40
Step-by-step explanation:
1+2+3=6
1/6×120=20
2/6×120=40
3/6×120=60
Use the diagram to answer the question below.
Name a point not on line AC
Answers
Answer:
It can be the point E or the point D
the perimeter of a square room is 48m,how much square carpet is requried to cover it ?
Answers
Answer:
144
Step-by-step explanation:
perimeter of square=48 ( formula= 4*a )
a= 48/4
= 12
area= a*a
=12*12
=144
8th grade math
A box of chocolates contains 3 milk chocolates 2 dark chocolates, and 1 white chocolate You randomly select and eat three chocolates What is the probability that the first piece is milk chocolate, the second is dark chocolate, and the third is white chocolate
Answers
Answer:
10 Milk chocolates
8 dark chocolates
6 white chocolates
24 TOTAL
\frac{10}{24} Probability that Hanissa choose a milk chocolate
Now, since she has already eaten one chocolate, then what's left is 23 chocolates.
So, since the second one should be a white chocolate and there are 6 of them, then
\frac{6}{23} - probability of choosing a white chocolate.
Then, multiply,
( \frac{10}{24} )( \frac{6}{23} )= \frac{60}{552} or \frac{5}{46}
Answer: 5/46 or 10.87%
Step-by-step explanation:
Answer: there is 1/2 chance of your first being milk chocolate, 1/3 chance your second will be drake and 1/6 chance it will be white chocolate
Step-by-step explanation:
Hi! I'd appreciate if you could help me on this question.
Liam is buying bottles of soda in packages that contain 8 bottles each. If the total number of sodas Liam bough t was between 45 and 50, how many did he buy? Explain your answer.
Answers
Answer:
48
Step-by-step explanation:
We need to find the multiples of 8
8,16,24,32,40,48
48 is between 45 and 50 so he must have bought 48
Answer:
6 bottles
Step-by-step explanation:
For this question we need to know the multiple of 8 which are:
8 x 1 = 8
8 x 2 = 16
8 x 3 = 24
8 x 4 = 32
8 x 5 = 40
8 x 6 = 48
8 x 7 = 56
There is only one multiple, which is greater than 45 but less than 50, which is 8x6 l.
This means he bought 6 bottles.
Answered by g a u t h m a t h
Previous studies suggest that use of nicotine-replacement therapies and antidepressants can help people stop smoking. The New England Journal of Medicine published the results of a double-blind, placebo-controlled experiment to study the effect of nicotine patches and the antidepressant bupropion on quitting smoking. The target for quitting smoking was the 8th day of the experiment.
In this experiment researchers randomly assigned smokers to treatments. Of the 162 smokers taking a placebo, 28 stopped smoking by the 8th day. Of the 272 smokers taking only the antidepressant buproprion, 82 stopped smoking by the 8th day.
Calculate the 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment). (The standard error is about 0.0407. Use critical value z = 2.576.)
( ), ( )
Round your answer to three decimal places. Put lower bound in the first box and upper bound in the second box.
Answers
Using the z-distribution, it is found that the 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).
What is a t-distribution confidence interval?The confidence interval is:
[tex]\overline{x} \pm zs[/tex]
In which:
[tex]\overline{x}[/tex] is the sample mean.z is the critical value.s is the standard error.In this problem, we are given that z = 2.576, s = 0.0407. The sample mean is the difference of the proportions, hence:
[tex]\overline{x} = \frac{28}{162} - \frac{82}{272} = -0.129[/tex]
Then, the bounds of the interval are given by:
[tex]\overline{x} - zs = -0.129 - 2.576(0.0407) = -0.234[/tex]
[tex]\overline{x} + zs = -0.129 + 2.576(0.0407) = -0.024[/tex]
The 99% confidence interval to estimate the treatment effect of buproprion (placebo-treatment) is (-0.234, -0.024).
More can be learned about the z-distribution at https://brainly.com/question/25890103
HLP HLP 10 10 10 HLP HLP HLP
W
Answers
Answer:
A. 6²¹
Step-by-step explanation:
When you have a number raised to the power in that form, you have to multiply the powers:
(6⁷)³
7×3 = 21
(6⁷)³ = 6²¹
Answer:
A. 6 raise to 21
Step-by-step explanation:
its a formula if:
a raise to m whole raise to n = a raise to m×n
so here
6 raise to 7 × 3
that is 6 to the power of 21
Write the equation of the line that passes through the points (- 4, - 3) and (3, - 5) . Put your answer in fully reduced slope intercept form, unless it is a vertical or horizontal line
Help:(
Answers
Answer:
y = (-2/7)x - (29/7)
Step-by-step explanation:
Find all real zeros of the function y = 2x - 4.
a.
2
C.
-4
b. 2, -4
d. -2
Answers
Answer:
x = 2
Step-by-step explanation:
To find the zeroes of the function, substitite 0 for y.
0 = 2x - 4
~Add 4 to both sides
4 = 2x
~Divide 2 to both sides
2 = x
Best of Luck!
This table gives a few (x,y) pairs of a line in the coordinate plane.
Answers
Answer:
The x-intercept of the line will be (10, 0)
Step-by-step explanation:
start from -12
get to -2...
-12 + (10) = -2
-2 + (10) = 8
therefore, the x-intercept is (10, 0)
Q4.A/Find the linearization L(x, y) of the function f(x, y) = (x + y + 2)² at p. = (1,2)
Answers
Answer:
Find the linearization L(x,y) of the function at each point. f(x,y) = x2 + y2 + 1 a. (4,0) b. (2,0) a. L(x,y) = Find the linearization L(x,y,z) of the function f(x,y,z) = 1x2 + y2 +z2 at the points (7,0,0), (3,4,0), and (4,4,7). The linearization of f(x,y,z) at (7,0,0) is L(x,y,z)= (Type an exact answer, using radicals as needed.)
How to find Joint and Combined variation?
Answers
Answer:
W is multiplied by 8
Step-by-step explanation:
If W varies jointly with x, y, and z, we can say that
W = k (xyz), with k being a constant for our original equation. We are asked what will happen to W if x, y, and z are each doubled. To figure this out, we can go back to our equation,
W = k (xyz)
First, we can double x, meaning that we multiply it by 2. Doing this, we get
W = k (2x * y * z)
Then, we can double y and z in a similar fashion, resulting in
W = k (2x * 2y * 2z)
W = 8 * k (xyz)
The new W, after all the doubling, is equal to 8 * k * x * y * z. The old W is equal to k * x * y * z. It can be determined that the new W is equal to 8 * the old W, so W is multiplied by 8
a clock hand rotated from 12 to 6 this is
Answers
Answer:
If it's the hour hand, 1/4 of a day or 6 hours have passed. If it's the minute hand, 1/48 of a day or 30 minutes have passed.
Step-by-step explanation:
BRAINLIEST, PLEASE!
What is p (call a person from school)
Answers
Answer:
.53
Step-by-step explanation:
P(person from school) = number of people from school/ total
= 16/30
= 8/15
=.5333333
Rounding to 2 decimal places
=.53
Answer:
0.53
Step-by-step explanation:
so the possible outcomes are 30, and the favorable outcomes are 16
the fraction is 16/30
16/30 ≈ 0.53
If my answer is incorrect, pls correct me!
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-Chetan K
Write expression for the sum x and 6
Answers
Answer:
X+6
Step-by-step explanation:
Sum means Addition.
Because the sum means the answer of an addition equation
