Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]6x^2-8x+k=0\\\\\text{We compute the discriminant.}\\\\\Delta = b^2-4ac=8^2-4*6*k=8*8-8*3*k=8*(8-3k)[/tex]
And the we know that if the discriminant is
***** [tex]\Delta[/tex] < 0, meaning 8-3k<0, meaning
[tex]\boxed{k>\dfrac{8}{3}}[/tex]
then, there is no real solution.
***** [tex]\Delta = 0[/tex], meaning
[tex]\boxed{k=\dfrac{8}{3}}[/tex]
There is 1 solution.
***** [tex]\Delta[/tex] > 0, meaning
[tex]\boxed{k<\dfrac{8}{3}}[/tex]
There are 2 solutions.
Thank you
PS: To give more details...
[tex]8-3k=0\\\\\text{Add 3k}\\\\8=3k\\\\\text{Divide by 3}\\\\k=\dfrac{8}{3}[/tex]
What is the formula for a^3-b^3??
Answer:
[tex]\boxed{\mathrm{view \ explanation}}[/tex]
Step-by-step explanation:
The difference of two cubes formula is given as:
[tex]a^3-b^3 =(a-b)(a^2 +ab+b^2)[/tex]
Step-by-step explanation:
[tex] {(a - b)}^{3} = {(a - b)}^{2} (a - b)[/tex]
[tex] {a}^{3} - 3{a}^{2} b + 3a {b}^{2} - {b}^{3} = {(a - b)}^{2} (a - b)[/tex]
[tex] {a}^{3} - {b}^{3} + 3ab(a - b)= {(a - b)}^{2} (a - b)[/tex]
[tex] {a}^{3} - {b}^{3}= {(a - b)}^{2} (a - b) + 3ab(a - b)[/tex]
[tex] {a}^{3} - {b}^{3} = (a - b)(( {a}^{2} - 2ab + {b}^{2} ) - 3ab)[/tex]
[tex] {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )[/tex]
please help ASAP!! question is in the image below
Answer:
(a) ∠EFH = 68°
(b) ∠EGF = 21°
Step-by-step explanation:
(a) The given parameters are;
The diameter of the circle = Segment [tex]\overline{EG}[/tex]
Arc [tex]m\widehat{FG}[/tex] = 138°
∠GFH = 22°
∠ EFG = (Angle subtended by the diameter EG at the center)
Arc mEG = 180° (Arc subtended by the diameter of a circle = 180°)
∠ EFG is subtended by the diameter EG at the center
∴ ∠ EFG = 90° (Angle at the center = 2 times angle at the circumference)
∠EFG = ∠EFH + ∠GFH (Angle addition postulate)
∴ ∠EFH = ∠EFG - ∠GFH = 90° - 22° = 68°
∠EFH = 68°
(b) ∠EGF
Arc GH = 44°
Arc mFE + Arc [tex]m\widehat{FG}[/tex] + Arc mEHG = 360 (Sum of angles at the center of a circle)
Arc mFE = 360 - ( Arc [tex]m\widehat{FG}[/tex] + Arc mEHG )
Arc mFE = 360 - 180 - 138 = 42°
∠EGF = Arc mFE/2 (Angle at the center = 2 times angle at the circumference)
∠EGF = 42/2 = 21°
∠EGF = 21°
i give you 5 stars please help
Answer:
C....................
Answer:
(C) [tex]x=4[/tex]
Step-by-step explanation:
A line will be parallel to the y-axis if It’s x never changes.
In A, x is always being -y, so that’s going to change all the time.
In B, x is always becoming y, so that is changing too.
In C, x is always being 4, so this never changes.
In D, x is always 4 times y, so this changes.
Hope this helped!
(6e−3f−4)⋅2= what is the answer for this?
Answer:
12e-6f-8 is the answer
Step-by-step explanation:
did work on peice of paper
Answer:
12e - 6f - 8
Step-by-step explanation:
By using the distributive property,, the answer is
(6e x 2) - (3f x 2) - (4 x 2)
12e - 6f - 8
Quadratic and Ratios...
Answer:
x=0
Step-by-step explanation:
in the quadratic formula to only have one solution
[tex]b^{2} -4ac=0[/tex] for [tex]ax^2+bx+c=0[/tex]
so we have
[tex]ax^2+b=c[/tex]
[tex]ax^2+(b-c)=0[/tex]
if we insert in the formula we have
[tex]0^2-4(a)(b-c)=0\\\\-4ab+4ac=0\\\\4ac=4ab\\\\\frac{4ac}{4a} = \frac{4ab}{4a}\\\\c=b[/tex]
[tex]ax^2+b=c\\\\ax^2=b-b\\\\ax^2=0[/tex] since a≠0
[tex]\frac{ax^2}{a}=\frac{0}{a} \\\\x^2=0\\\\x=0[/tex]
What is the value of 12^0?
Answer:
1
Step-by-step explanation:
Anything real number (except 0) to the zeroth power would be 1.
Therefore, 12 to the zeroth power would also be 1.
[tex]12^0=1[/tex]
Answer:
As you know everynumber raised to 0 is always 1 even if its x or infinity so the answer will be 12^0 will be 1
Step-by-step explanation:
any and every number raised to 0 is 1
Intersecting chords form a pair of supplementary, vertical angles. True or false.
Answer:
its false
Step-by-step explanation:
Answer:
The answer is false
Step-by-step explanation:
Tony knew there was a solution to his math problem in one of four textbooks. He got some information from his classmates about it: Andy: "The solution is in either book 1 or 2"; Billy: "The solution is in either book 3 or 4"; Charlie: "The solution is in book 4"; Danny: "There is no solution in book 3". Emily helped Tony by saying that only one of his classmates was right, and the other three were mistaken. Which book has the solution in it?
Answer:
Charlie is the right person.
Step-by-step explanation:
The right person is Charlie because he was sure of what he was saying. Others were not sure making them mention two textbooks while Danny didn't answer the question Tony asked because he was talking about the one that doesn't have the solution.
what is the answer to (3^2-8) +4=
Answer:
5
Step-by-step explanation:
Answer:
5 is the answer to the question.
Step-by-step explanation:
(3² - 8) + 4
= (3×3×3 - 8) + 4
= (9 - 8) + 4
= 1 - 4
= 5
need help with this one
Answer:
At x intercept, x = 0
2.8(0)+5.7y+5.8=0
y=-5.8/5.7
=-1.02
At y intercept, y=0
2.8x+5.7(0)+5.8=0
x=-5.8/2.8
=-2.07
Answer:
X ans y intercepts are
xintercept (s) : (-2.0,0) you can roud if necessary
y intercept(s) : (0,-1.01754385) you can round if nessecary
Step-by-step explanation:
to find the [tex]x[/tex] and [tex]y[/tex] intercepts simply plug in [tex]o[/tex] to replace [tex]x[/tex] then when you solve for [tex]x[/tex] plug in [tex]x[/tex]to solve for [tex]y[/tex]
3 x 19 x 14 + 18 ÷ 2
Answer:
807Step-by-step explanation:
[tex]3 \times 19 \times 14 + 18 \div 2 \\ PEDMAS \\ (3 \times 19 \times 14 )+ 9 \\ = 798 + 9 \\ [/tex]
[tex] = 807[/tex]
Answer:
408
Step-by-step explanation:
3x19= 57
57x14= 798
798 + 18= 816
816/ 2= 408
can someone please help me
Answer:
y=3
Step-by-step explanation:
7y-(5y+4)=10
7y-5y+4=10
-4 -4
7y-5y=6
2y=6
÷2 ÷2
y=3
Please solve, will give BRAINLIST!!
Answer:
x = 19 1/3
Step-by-step explanation:
6/14 = 7/(x-3)
Using cross products
6 * (x-3) = 7*14
6x -18 = 98
Add 18 to each side
6x-18+18 =98+18
6x = 116
Divide each side by 6
6x/6 = 116/6
x =58/3
x = 19 1/3
Answer= 58/3
Step by Step
Step 1: Cross-multiply.
6*(x−3)=(7)*(14)
6x−18=98
Step 2: Add 18 to both sides.
6x−18+18=98+18
6x=116
Step 3: Divide both sides by 6.
6x /6 = 116 /6
x= 58 /3
ASAP!!!!!!!!! PLEASE help me with this question! This is really urgent! No nonsense answers please.
Answer:
Option (2)
Step-by-step explanation:
In the given circle,
[tex]m(\widehat{CBD})+m(\widehat{CED})[/tex] = 360°
Therefore, 212° + [tex]m(\widehat{CED})[/tex] = 360°
[tex]m(\widehat{CED})=360-212[/tex]
= 148°
Tangent - chord theorem states,
"Angle between a chord and tangent measure the half of the angle measure of the intercepted minor arc."
m∠ACD = [tex]\frac{1}{2}(\widehat{CED})[/tex]
= [tex]\frac{1}{2}(148)[/tex]
= 74°
Therefore, measure of ∠ACD is half the measure of arc CD or 74°.
Option (2) will be the correct option.
for which values of x is A U B = Ø
Answer:
The first: 2 < x < 3Step-by-step explanation:
[tex]3x+4\geq13\\\\3x\geq9\\\\x\geq3\\\\A=\big<3\,,\ \infty)[/tex] [tex]\frac12x+3\leq4\\\\\frac12x\leq1\\\\x\leq2\\\\B=(-\infty\,,\ 2\big>[/tex]
[tex]A\cup B\not=\varnothing\quad for\ all\ x\in(-\infty\,, 2\big>\cup\big<3\,,\ \infty)[/tex]
so:
[tex]A\cup B=\varnothing\quad for\ x\in(\,2\,,\ 3\,)[/tex]
Answer:hi, the answer would be (a) or 2<x<3 hope this helps :)
Step-by-step explanation: i just took the test got em all correct
Roselyn is driving to visit her family, which lives 150150150 kilometers away. Her average speed is 606060 kilometers per hour. The car's tank has 202020 liters of fuel at the beginning of the drive, and its fuel efficiency is 666 kilometers per liter. Fuel costs 0.600.600, point, 60 dollars per liter.
Answer:
see explanation (please confirm if I read you problem correctly)
Step-by-step explanation:
150 kilometers
60 kph
tank is 20 liters
6 km/l
150/6 = 25 liters needed
$60/l
you will need to get 5 more liters of fuel
total cost 25 x .60 = $15
Answer:
AHHHHH I think its two hours
Step-by-step explanation:
she...? can drive 120 Kilometers before she runs out of fuel since the car's tank has 20 liters of fuel at the beginning of the drive, and its fuel efficiency is 6 kilometers per liter. and that means she can drive 2 hours
Melissa the trainer has two solo workout plans that she offers her clients: Plan A and Plan B. Each client does either one or the other (not both). On Wednesday there were 5 clients who did Plan A and 3 who did Plan B. On Thursday there were 2 clients who did Plan A and 12 who did Plan B. Melissa trained her Wednesday clients for a total of 7 hours and her Thursday clients for a total of 19 hours. How long does each of the workout plans last? LengthofeachPlanAworkout:hour(s) LengthofeachPlanBworkout:hour(s)
Let Length of each Plan A workout be [tex] a[/tex]
and Length of each Plan B workout be $b$
on Wednesday,
$5a+3b=7$
$2a+12b=19$
multiply equation one by $4$ and subtract equation two from it
to get,
$18a=9$ or $a=\frac12$
substitute $a$ in eq 2. to get $b$, $12b=18\implies b=\frac32$
NEED ANSWER ASAP!! PLEASE!!! The length of a rectangle is 1 foot more than twice the width. Write an expression that represents the length.
Answer:
The expressión that represents the length:
a = 2w + 1
a = length of the rectangle
w = width of the rectangle
A, B, C, D, E, F, ... 2, 3, 5, 7, 11, 13, ... what number is the letter Z replaced with?
Answer:
Z=101
Step-by-step explanation:
A=2
B=3
C=5
D=7
E=11
F=13
From the above illustration, it can be deduced that A to Z represent prime numbers in ascending order.
Prime numbers are natural numbers that are greater than 1 and are only divisible by 1 and itself.
Therefore,
G=17
H=19
I=23
J=29
K=31
L=37
M=41
N=43
O=47
P=53
Q=59
R=61
S=67
T=71
U=73
V=79
W=83
X=89
Y=97
Z=101
PLEASE HELP WITH ALL PLEASE WILL MAKR BRAINLIEST, THANK YOU AND THESE POINTS
Answer/Step-by-step Explanation:
12. A. (1,299 + 3,563) ÷ 22 = 221
4,862 ÷ 22 = 221
221 = 221 (TRUE)
B. 16*(132 + 34)*12 = 32,872
16*166*12 = 32,872
31,872 = 32,872 (NOT TRUE)
C. (65 + 78)*(45 - 29) = 2,188
143*16 = 2,188
2,288 = 2,188 (NOT TRUE)
D. (1,444 - 349) ÷ (457 - 238) = 6
1,095 ÷ 219 = 6
5 = 6 (NOT TRUE)
The answer is A.
13. Let the missing number = X
Thus,
i. 25*(157 + x) = 8,850
[tex] 157 + x = \frac{8850}{25} [/tex]
[tex] 157 + x = 354 [/tex]
[tex] x = 354 - 157 [/tex]
[tex] x = 197 [/tex]
ii. x ÷ (453 - 425) = 135
x ÷ (28) = 135
x = 135*28
x = 3,780
14. (56 + 69) * (268 - 137)
125*131 = 256
15. 9,144 ÷ (2,784 - 2,784)
9,144 ÷ 0 = cannot divide
16. (72 + 126) ÷ (687 - 654)
198 ÷ 33 = 6
17. 22*(562 + 733)
22*1,295 = 28,490
18. Let the missing number be x
48*(x - 239) = 4,272
[tex] x - 239 = \frac{4,272}{48} [/tex]
[tex] x - 239 = 89 [/tex]
[tex] x = 89 + 239 [/tex]
[tex] x = 328 [/tex]
The missing number is 328.
19. (794 + 718) ÷ (68 - 41)
1,512 ÷ 27 = 56
20. (58*89) + (192 ÷ 16)
5,162 + 12 = 5,174
what is .6239 as fraction?
Answer:
.6239 as a fraction is 6239/10000.
Meredith has $630,000 she wants to save. If the FDIC insurance limit per
depositor, per bank, is $250,000, which of these ways of distributing her
money between three banks will guarantee that all of her money is insured?
A. $200,000 in bank A, $200,000 in bank B, $230,000 in bank C
B. $200,000 in bank A, $170,000 in bank B, $260,000 in bank C
C. $160,000 in bank A, $180,000 in bank B, $290,000 in bank C
D. $160,000 in bank A, $200,000 in bank B, $270,000 in bank C
you
Answer:
$200,000 in bank A, $200,000 in bank B, $230,000 in bank C
Step-by-step explanation:
Meredith has $630,000
Limit per depositor, per bank, is $250,000
She needs to distribute her money between three Banks to guarantee that her money is insured.
A. $200,000 in bank A, $200,000 in bank B, $230,000 in bank C
It can be seen in A that her deposit per bank deposit didn't exceed the $250,000 limit in the three Banks.
B. $200,000 in bank A, $170,000 in bank B, $260,000 in bank C
Here, her deposit in bank C exceeds $250,000, so there is no guarantee for insurance in bank C
C. $160,000 in bank A, $180,000 in bank B, $290,000 in bank C
Her deposit in bank C is $290,000 which exceeds the $250,000 limit. Therefore, no guarantee for insurance of her money in bank C
D. $160,000 in bank A, $200,000 in bank B, $270,000 in bank C
you
Also, her deposit in bank C exceeds $250,000, so there is no guarantee for insurance in bank C
The way her money can be distributed between three Banks and guarantee insurance is
A. $200,000 in bank A, $200,000 in bank B, $230,000 in bank C.
That way, her deposit per bank is less than the $250,000 limit
Maria had 600 coins in her wallet, but now she has 30 left of coins. What percentage of the 600 money does he have left?
Answer:5
Step-by-step explanation:30/600×100
Answer:
5%Step-by-step explanation:
[tex]\frac{30}{600} \times 100\\\\= \frac{3000}{600}\\ \\= 5\%[/tex]
A students wants to report on the number of movies her friends watch each week. The collected date are below:
0, 0, 1, 1, 2, 2, 2, 14
which measure of center is most appropriate for this situation and what's its value?
A.) Median; 1.5
B.) Median; 3
C.) Mean; 1.5
D.) Mean; 3
Answer:
A.) median; 1.5
Step-by-step explanation:
Hello!
The median is the number that is in the middle when the numbers are listed from least to greatest
0, 0, 1, 1, 2, 2, 2, 14
We can take one from both sides till there are one or two numbers left
0, 1, 1, 2, 2, 2
1, 1, 2, 2
1, 2
If there are two numbers left we add them then divide by 2 to get the median
1 + 2 = 3
3 / 2 = 1.5
The answer is A.) median; 1.5
Hope this helps!
Enter the values needed to find the length CB
Answer:
[tex]6b[/tex]
Step-by-step explanation:
We know that the distance formula is [tex]\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]. We already have the x values, which are [tex]5a[/tex] and [tex]-a[/tex], subtracting [tex]-a[/tex] from 5a gets us [tex]6a[/tex].
Same concept for the y values, let's subtract the first y value from the second.
The second y value is [tex]b[/tex], while the first is [tex]-5b[/tex]
[tex]b - (-5b) = b + 5b = 6b[/tex]
Hope this helped!
Answer:
6b is your answer!
Step-by-step explanation:
I wish ALL ACELLUS USERS LUCK
6) By which least number should each of the following numbers be divided to make them perfect squares?
a) 3920
3920|2
1960|2
980|2
490|2
245|5
49|7
7|7
1
[tex]3920=2^4\cdot5\cdot7^2=(2^2)^2\cdot5\cdot7^2[/tex]
It's 5
solve the equation 3), x=???? Please help me!!!
Answer:
x = {π/4, 7π/6, 5π/4, 11π/6} +2kπ . . . for any integer k
Step-by-step explanation:
[tex]\dfrac{\sin^3{x}}{1+\cos{x}}+\dfrac{\cos^3{x}}{1+\sin{x}}=\cos{2x}+2\cos{x}-1\\\\\dfrac{\sin{x}(1-\cos^2{x})}{1+\cos{x}}+\dfrac{\cos{x}(1-\sin^2{x})}{1+\sin{x}}=\cos^2{x}-\sin^2{x}+2\cos{x}-1\\\\\sin{x}(1-\cos{x})+\cos{x}(1-\sin{x})=\cos^2{x}-\sin^2{x}+2\cos{x}-1\\\\\sin{x}+\cos{x}-2\sin{x}\cos{x}=2\cos{x}-2\sin^2{x}\qquad\text{use $1=s^2+c^2$}\\\\\sin{x}+2\sin^2{x}-\cos{x}-2\sin{x}\cos{x}=0\\\\\sin{x}(1+2\sin{x})-\cos{x}(1+2\sin{x})=0\\\\(\sin{x}-\cos{x})(1+2\sin{x})=0[/tex]
This will have solutions where the factors are zero.
sin(x) -cos(x) = 0
Dividing by cos(x), we have ...
tan(x) -1 = 0
x = arctan(1) = π/4, 5π/4
1 +2sin(x) = 0
sin(x) = -1/2
x = arcsin(-1/2) = 7π/6, 11π/6
The four solutions in the interval [0, 2π] are x = {π/4, 7π/6, 5π/4, 11π/6}. Solutions repeat every 2π radians.
_____
Additional comment
We have made use of the factoring of the difference of squares:
(1 -a^2) = (1 -a)(1 +a)
and we have made use of the cosine double angle identity:
cos(2x) = cos(x)^2 -sin(x)^2
The "Pythagorean" identity for sine and cosine was used several times:
1 = sin(x)^2 +cos(x)^2
Answer ASAP THANKKK YOUUUUU
Answer:
D. 40
Step-by-step explanation:
Interquartile range is the difference between the upper quartile value (Q3) and the lower quartile value (Q1).
In a box plot, Q1 is located at the beginning of the edge of the rectangular box from our left, while the Q3 is located at the end of the edge of the rectangular box to our right.
Interquartile range for City A = 70 - 40 = 30
Interquartile range for City B = 80 - 40
Therefore, city B has greater variability. The interquartile range is 40.
f(x) [tex]\sqrt{x-9}[/tex] ; g(x) = 8x - 13 Find f(g(x)).
Answer:
f(g(x)) = [tex]\sqrt{8x-22}[/tex]
Step-by-step explanation:
Substitute x = g(x) into f(x), that is
f(g(x))
= f(8x - 13)
= [tex]\sqrt{8x-13-9}[/tex]
= [tex]\sqrt{8x-22}[/tex]
At 11,560 feet above sea level, Climax, Colorado, is the highest town in the united States. The lowest town in Calipatria, California, at 185 feet below sea level. Express both of these distance as integers and tell which is closer to sea level. How much closer to sea level is the town that is closer?
Answer:
Climax: 11,560. Calipatria: 185 Calipatra is closer by 11,375ft
Step-by-step explanation:
Climax is 11,560ft above sea level, which means it is 11,560ft away from sea level. Calipatria 185ft away from sea level by the same logic. The one whih is closer to sea level would be the smaller number, which would be 185, and how much closer would be 11,560-185= 11,560.
If you're wondering why the 185 isn't negative, it's because the question is asking how far away from zero the numbers are, so you would take the absolute value of -185 which would be 185.
