Use the discriminant to describe the roots of each equation. Then select the best description.
7x² + 1 = 5x
Answers
Answer:
Imaginary roots
Step-by-step explanation:
The discriminant of a quadratic in standard form [tex]ax^2+bx+c[/tex] is given by [tex]b^2-4ac[/tex].
Given [tex]7x^2+1=5x[/tex], subtract 5x from both sides so that the quadratic is in standard form:
[tex]7x^2-5x+1=0[/tex]
Now assign variables:
[tex]a\implies 7[/tex] [tex]b\implies -5[/tex] [tex]c\implies 1[/tex]The discriminant is therefore [tex](-5)^2-4(7)(1)=25-28=\textbf{-3}[/tex].
What does this tell us about the roots?
Recall that the discriminant is what is under the radical in the quadratic formula. The quadratic formula is used to find the solutions of a quadratic. Therefore, the solutions of this quadratic would be equal to [tex]\frac{-b\pm \sqrt{-3}}{2a}[/tex] for some [tex]b[/tex] and [tex]a[/tex]. Since the number under the radical is negative, there are no real roots to the quadratic (whenever the discriminant is negative, the are zero real solutions to the quadratic). Therefore, the quadratic has imaginary roots.
Related Questions
Find the value of x.
A. 85
B. 131
C. 73
D. 95
Answers
Answer:
b
Step-by-step explanation:
The value of x 85.
What is the arc of the circle?The arc period of a circle can be calculated with the radius and relevant perspective using the arc period method.
⇒angle= arc/radius
⇒ 107°=arc/7
⇒ arc =1o7°*7
⇒arc=107π/180° *7
⇒arc = 85
Learn more about circle here:-brainly.com/question/24375372
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The football coach randomly selected 10 players and timed how long each player took to perform a certain drill. The result has a sample mean of 9.48 minutes and sample standard deviation of 2.14 minutes. Round answers to two decimals. The 95% confidence interval for the mean time for all players is : __________
Answers
Answer:
The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).
Step-by-step explanation:
We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.
The first step to solve this problem is finding how many degrees of freedom,which is the sample size subtracted by 1. So
df = 10 - 1 = 9
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622.
The margin of error is:
[tex]M = T\frac{s}{\sqrt{n}} = 2.2622\frac{2.14}{\sqrt{10}} = 1.53[/tex]
In which s is the standard deviation of the sample and n is the size of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 9.48 - 1.53 = 7.95 minutes.
The upper end of the interval is the sample mean added to M. So it is 9.48 + 1.53 = 11.01 minutes.
The 95% confidence interval for the mean time for all players, in minutes, is: (7.95, 11.01).
You decide to go on a 4 day backpacking trip. The first day you walk 8 miles at northeast, on the second day, you walk 4 miles at eastsouth, and on the third day you walk 3 miles at southwest. On the fourth day you need to head straight back to your car. How far do you have to walk, and in what direction
Answers
Answer:5
Step-by-step explanation:
Where the above parameters are given, you need to walk a distance of approximately √41 miles back to your car.
How to compute the aboveTo calculate the total distance you need to walk, you can use the Pythagorean theorem since you have a right triangle formed by the north and east displacements.
Distance = √((Distance north)² + (Distance east)²)
= √((5 miles)² + (4 miles)²)
= √(25 miles + 16 miles)
= √41 miles
Hence, you need to walk a distance of approximately √41 miles back to your car.
As for the direction, based on the net displacements, you are 5 miles north and 4 miles east of your car, so the direction would be a combination of north and east, often referred to as northeast.
Learn more about distance at:
https://brainly.com/question/26046491
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Assuming that a 330-foot tall giant redwood grows vertically, if I walk a certain distance from the
tree and measure the angle of elevation to the top of the tree to be 69°, how far from the base of the
tree am I?
Round your answer to four decimal places.
I am about Number
feet away from the base of the tree.
Answers
9514 1404 393
Answer:
126.6751 feet
Step-by-step explanation:
The tangent relation can be helpful.
Tan = Opposite/Adjacent
tan(69°) = (330 ft)/(distance to base)
distance to base = (330 ft)/tan(69°) ≈ 126.6751 ft
_____
Comment on precision
It would make more sense to round to 4 significant figures. The value of a unit in the fourth decimal place is 0.0001 feet = 0.0012 inches, somewhat less than the thickness of a human hair. We know of no technology that will make a measurement of that distance to that accuracy.
n a history class there are 88 history majors and 88 non-history majors. 44 students are randomly selected to present a topic. What is the probability that at least 22 of the 44 students selected are non-history majors
Answers
Answer:
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
Step-by-step explanation:
The students are chosen without replacement from the sample, which means that the hypergeometric distribution is used to solve this question. We are working also with a sample with more than 10 history majors and 10 non-history majors, which mean that the normal approximation can be used to solve this question.
Hypergeometric distribution:
The probability of x successes is given by the following formula:
[tex]P(X = x) = h(x,N,n,k) = \frac{C_{k,x}*C_{N-k,n-x}}{C_{N,n}}[/tex]
In which:
x is the number of successes.
N is the size of the population.
n is the size of the sample.
k is the total number of desired outcomes.
Combinations formula:
[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Approximation:
We have to use the mean and the standard deviation of the hypergeometric distribution, that is:
[tex]\mu = \frac{nk}{N}[/tex]
[tex]\sigma = \sqrt{\frac{nk(N-k)(N-n)}{N^2(N-1)}}[/tex]
In this question:
88 + 88 = 176 students, which means that [tex]N = 176[/tex]
88 non-history majors, which means that [tex]k = 88[/tex]
44 students are selected, which means that [tex]n = 44[/tex]
Mean and standard deviation:
[tex]\mu = \frac{44*88}{176} = 22[/tex]
[tex]\sigma = \sqrt{\frac{44*88*(176-88)*(176-44)}{176^2(175-1)}} = 2.88[/tex]
What is the probability that at least 22 of the 44 students selected are non-history majors?
Using continuity correction, as the hypergeometric distribution is discrete and the normal is continuous, this is [tex]P(X \geq 22 - 0.5) = P(X \geq 21.5)[/tex], which is 1 subtracted by the p-value of Z when X = 21.5. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{21.5 - 22}{2.88}[/tex]
[tex]Z = -0.17[/tex]
[tex]Z = -0.17[/tex] has a p-value of 0.4325
1 - 0.4325 = 0.5675
0.5675 = 56.75% probability that at least 22 of the 44 students selected are non-history majors.
help me please i’ll give brainliest the
Answers
Answer:
y=-1/2x+-1
Step-by-step explanation:
try desmos with this equation.
y=mx+b
m=the slope which is -1/2. It goes down 1 it is negative because it is going down, and to the right 2.
b=y-intercept meaning the point which the line crosses the line y .-1
Which ordered pair would form a proportional
relationship with the points in the graph?
O (44)
O (69)
O (9,6)
O (8,5)
Answers
6,9
8,9
lvnununuunkmviodjoifmvujibg ibzf
r
Answers
Answer:
speaking giberish
Step-by-step explanation:
cos it is just a word that is rare
Find the length of BC
Answers
Since this is a right triangle, we can use one of the three main trigonometric functions: sine, cosine or tangent.
Remember: SOH-CAH-TOA
Looking from the given angle, we want to find the opposite side and we know the hypotenuse. Therefore, we should use sine.
sin(51) = BC / 58
BC = 58 x sin(51)
BC = 45.1 units
Hope this helps!
Step-by-step explanation:
Hey there!
From the above given figure;
Angle CAB = 51°
AB = 58
Taking Angle CAB as reference angle we get;
Perpendicular (p) = BC= ?
Hypotenuse (h) = 58
Now;
Taking the ratio of sin we get;
[tex] \sin( \alpha ) = \frac{p}{h} [/tex]
[tex] \sin(51) = \frac{bc}{58} [/tex]
Simplify it;
0.7771459*58 = BC
Therefore, BC = 45.0744.
Hope it helps!
A population of deer in Florida grows according to a logistic model, with r = 0.17 and K = 10,000. At what population size is the per capita population growth rate the highest? Group of answer choices N = 1000 N = 5000 N = 8000 N = 10000
Answers
Answer:
N = 1000
Step-by-step explanation:
The population growth of species per capita of any geographical can be computed by using the formula:
[tex]\dfrac{dN}{dT}=rN (1 - \dfrac{N}{K})[/tex]
here;
N = population chance
T = time taken
K = carrying capacity
r = the constant exponential growth rate
From the given equation, we can posit that the value of r will be the greatest at the time the value of dN is highest:
As such, when the population chance = 1000
[tex]\dfrac{dN}{dT}=0.17 * 1000 (1 - \dfrac{1000}{10000})[/tex]
[tex]\dfrac{dN}{dT}=0.17 * 1000 (0.9)[/tex]
[tex]\dfrac{dN}{dT}= 153[/tex]
At N = 5000;
[tex]\dfrac{dN}{dT}= 85[/tex]
At N= 8000;
[tex]\dfrac{dN}{dT}= 34[/tex]
At N = 10000
[tex]\dfrac{dN}{dT}= 0[/tex]
Một đài khí tượng thủy văn muốn xem xét khả năng dự báo thời tiết của mình. Từ số liệu thống kê chỉ ra rằng: xác suất dự báo có nắng trong ngày không mưa là 0,95; có nắng trong ngày mưa là 0,8; xác suất một ngày sẽ không mưa là 0,6. a. Tính xác suất dự báo ngày sẽ có nắng. b. Biết đã có dự báo là ngày có nắng, tính xác suất để ngày đó là ngày không mưa.
Answers
Answer:
ask in English then I can help u
Find the integer pair that has the given product and sum. The product is 28 The sum is 11
Answers
Answer:
7 and 4
Step-by-step explanation:
when you multiply 7×4 the answer is 28 and when you add them the answer is 11.
I hope this helps
Answer:
4 and 7
Step-by-step explanation:
xy = 28 ..........1
x + y = 11........2
x = 11 - y.........3
substitute 3 in 1:
(11 - y)*y = 28
-y² + 11y - 28 = 0
y² - 11y + 28 = 0
( y - 7)( y - 4) = 0
y = 7 or y = 4
subs in 2:
x = 4 or x = 7
pairs: (4 ; 7) and (7 ; 4)
9.
How many years will it take to earn N8100
simple interest on N180000 at 9% per annum?what the answer?
Answers
9514 1404 393
Answer:
1/2 year
Step-by-step explanation:
Put the numbers into the interest formula and solve for t.
I = Prt
8100 = 180000(0.09)t
t = 8100/16200 = 1/2
It will take 1/2 year to earn N8100 in interest at 9%.
Write an algebraic expression that represents three less than the square of a number k.
Answers
Answer:
2k-3
Step-by-step explanation:
the square of k is k times k so 2k (two times k) and less than three means minus three.
The width of a rectangle is 9 less than twice its length. If the area of the rectangle is 129cm^2. What is the length of the diagonal? Give your answer to 2 decimal places.
Answers
==========================================================
Explanation:
L = x = length of the rectangleW = 2x-9 = width of the rectangle, since its 9 less than twice the lengtharea of rectangle = L*W = 129
L*W = 129
x*(2x-9) = 129
2x^2-9x = 129
2x^2-9x-129 = 0
Apply the quadratic formula. We'll use a = 2, b = -9, c = -129.
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-9)\pm\sqrt{(-9)^2-4(2)(-129)}}{2(2)}\\\\x = \frac{9\pm\sqrt{1113}}{4}\\\\x \approx \frac{9\pm33.36165464}{4}\\\\x \approx \frac{9+33.36165464}{4}\ \text{ or } \ x \approx \frac{9-33.36165464}{4}\\\\x \approx \frac{42.36165464}{4}\ \text{ or } \ x \approx \frac{-24.36165462}{4}\\\\x \approx 10.59041366\ \text{ or } \ x \approx -6.09041364\\\\[/tex]
We ignore the negative solution because a negative length makes no sense.
The length is approximately L = 10.5904 cm.
The width is 2L-9 = 2*10.5904-9 = 12.1808 cm approximately.
As a quick check,
L*W = 10.5904*12.1808 = 128.99954432
which isn't too far off from 129. We have rounding error which is why we don't perfectly land on the target area value. If you wanted to get closer to the value 129, then use more decimal digits in the approximations of L and W.
----------------------------
If you draw a diagonal in the rectangle, then you form two identical or congruent right triangles.
Focusing on one of those triangles, we have
a = 10.5904b = 12.1808c = unknown hypotenuse = diagonal lengthApply the pythagorean theorem
a^2+b^2 = c^2
c = sqrt( a^2 + b^2 )
c = sqrt( (10.5904)^2 + (12.1808)^2 )
c = 16.1408940520653
c = 16.14
The diagonal is roughly 16.14 cm long.
tìm cực trị của hàm số z(x,y)=x^{3}+y^{3}+3xy-30
Answers
Answer:
Hence, MEAN OF FIRST FIVE COMPOSITE NOS IS 7.5
Will give Brainliest!
Find the period and amplitude of the function.
y = -4cos(4/3 x)
Give the exact values, not decimal approximations.
Answers
Answer:
y = d + a · cos(bx - c) ⇒ y = -4cos(4/3x)
a = -4b = 4/3c = 0d = 0Amplitude = |a| = |-4| = 4
Period = [tex]\frac{2\pi }{b} =\frac{2\pi }{\frac{4}{3} } =2\pi *\frac{3}{4} =\frac{3}{2} \pi[/tex]
I want to know how to solve this equation
Answers
Answer:
one property of log is that if the log expressions have the same base (in this case, 2), then you can multiply the added logs.
The answer would then be D
Find y when x = 22, if y varies directly as x,
and y = 42 when x = 5.
Answers
Answer:
184.8
Step-by-step explanation:
y =kx
k=y/x
k=42/5=8.4
y=8.4*22
A pool has some initial amount of water in it. Then it starts being filled so the water level rises at a rate of 666 centimeters per minute. After 202020 minutes, the water level is 220220220 centimeters.
Graph the relationship between the pool's water level (in centimeters) and time (in minutes).
Answers
I cant graph it on here but. if your graph goes by 10 then the slope should increase by 666 every minute on the x line
Answer:
The answer is in the screenshot
Step-by-step explanation:
PLEASE GIVE BRAINLIEST
please help me bro pleaseeeeeee a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold
Answers
Answer:
325 pencils, 650 markers, 975 pens.
Select all the terms that can be combined with 5.
4b
14a
100
3a’2
Answers
Jessica combines 1/3 cups of blue paint and 1/2 cups of red paint.
Answers
There is more red paint
There is now 5/6 of a cup of paint if they are mixed
IF YOU DONT ANSWER THIS AND GET IT RIGHT YOUR MOM IS PREGO WITH YOUR KID a store sells pencils pens and markers that sells two times as many markers as pencils and three times as many pens as pencils is the store sells a total of 1950 pencils and pens and markers in a week how many of each were sold
Answers
Answer:
Pencils = 325 ; Pens = 975 ; Markers = 650
Step-by-step explanation:
Let :
Number of Pencils = x
Number of pens = y
Number of markers = z
2 times as many markers as pencils
z = 2x
3 times as many pens as pencils
y = 3x
x + y + z = 1950
Write z and y in terms of x in the equation :
x + 3x + 2x = 1950
6x = 1950
Divide both sides by 6
6x / 6 = 1950 / 6
x = 325
Number of pencils = 325
Pens = 3 * 325 = 975
Markers = 2 * 325 = 650
Pencils = 325 ; Pens = 975 ; Markers = 650
In a group of 50 students, 12 play basketball and volleyball
, 9 play volleyball
and soccer, 8 play basketball and play soccer, and 4 play all 3 sports.
Altogether, 21 play basketball, 22 play volleyball, and 19 play soccer. How
many of the 50 students don't play any of the 3 sports?
Answers
Answer:
17 don't play any
Step-by-step explanation:
12+9+8+4=33
33-50=17
In 10 words or fewer, what is the square root of -9?
Type answer here...
What is the square root of -9
Answers
Answer:
no solution
Step-by-step explanation:
a negative number cannot be square rooted
Answer:
"not possible". no such thing as a negative squared number
Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9
New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1
Use a 0.05 significance level to test the claim that the volumes of Bubbly Beverage filled by the old machine vary more than the volumes of juice filled by the new machine.
Answers
Answer:
We Reject the Null, H0 and conclude that the volume of juice filled by old machine varies more than volume filled by new machine
Step-by-step explanation:
Given the data:
Old machine: 8.2, 8.0, 7.9, 7.9, 8.5, 7.9, 8.1,8.1, 8.2, 7.9
Sample size, n = 10
Using calculator :
s1² = 0.37889.
New machine: 8.0, 8.1, 8.0, 8.1, 7.9, 8.0, 7.9, 8.0, 8.1
Sample size, n = 9
s2² = 0.006111
Hypothesis :
H0 : s1² = s2²
H1 : s1² > s2²
New machine :
s2² = 0.006111 ; n = 9
Using the Ftest :
Ftest statistic = larger sample variance / smaller sample variance
Ftest statistic = 0.37889 / 0.006111
Ftest statistic = 62.0
Decision region :
Reject H0 ; If Test statistic > Critical value
The FCritical value at 0.05
DFnumerator = 10 - 1 = 9
DFdenominator = 9 - 1 = 8
Fcritical(0.05, 9, 8) = 3.388
Since 62 > 3.388 ; Reject H0 and conclude that volume filled by old machine varies more than volume filled by new machine
Assume that x and y are both differentiable functions of t. Find dx/dt when x=11 and dy/dt=-4 for the equation xy=99 .
Answers
Differentiating both sides of
xy = 99
with respect to t yields
x dy/dt + y dx/dt = 0
When x = 11, we have
11y = 99 ==> y = 9
and we're given that dy/dt = -4 at this point, which means
11 (-4) + 9 dx/dt = 0 ==> dx/dt = 44/9
The perimeter of the figure below is 107.5 in. Find the length of the missing side
Answers
9514 1404 393
Answer:
7.3 in
Step-by-step explanation:
The sum of the lengths of the sides shown is 100.2 in, so the missing length is ...
107.5 -100.2 = 7.3 . . . inches
Which of the following could NOT be the value of a correlation coefficient?
Select one:
a. 0.98
b.-0.76
c. -1.00
d. 1.34
Answers
Answer:
1.34 cannot be a correlation coefficient
Step-by-step explanation:
The correlation coefficient must be between (and can include) -1 to 1
1.34 is not between -1 and 1
