By the fundamental theorem of algebra, we can write the given quadratic in terms of its roots a and b as
3x ² - 5x + k = 3 (x - a) (x - b)
and upon expanding, we have
3x ² - 5x + k = 3x ² - (a + b) x + ab
Two polynomials are equivalent if their coefficients are equal, so
a + b = 5
ab = k
We're given that |a - b| = 2. If we assume a > b (that is, a is the larger root) then |a - b| = a - b = 2, or b = a - 2. Substitute this for b in the first equation above and solve for a :
a + (a - 2) = 5
2a - 2 = 5
2a = 7
a = 7/2
Solve for b :
b = 7/2 - 2
b = 3/2
Solve for k :
k = 7/2 × 3/2 = 21/4
Find the Mean Absolute Deviation: (MAD)
10, 9, 3, 8, 10.
Answer: Hey there !! The answer is 2.
Step-by-step explanation:
The mean absolute deviation of a dataset is the average distance between each data point and the mean.
The absolute mean deviation is 2.
What is mean absolute deviation?The mean absolute deviation of a dataset is the average distance between each data point and the mean.
We have,
10, 9, 3, 8, 10
We first find the mean of 10, 9, 3, 8, 10
Mean = (10 + 9 + 3 + 8 + 10) / 5
Mean = 40 /5 = 8
Data sets
10 | 10 - 8 | 2
9 | 9 - 8 | 1
3 | 3 - 8 | 5
8 | 8 - 8 | 0
10 | 10 - 8 | 2
Mean absolute deviation
= (2 + 1 + 5 + 0 + 2) / 5
= 10 / 5
= 2
Thus the absolute mean deviation is 2.
Learn more about absolute mean deviation here:
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Find the 11th term in the following geometric sequence.
-5,-10,-20,-40
Please answer thank u ASAP.
Answer:
a?
Step-by-step explanation:
Gina needs to buy a bathroom mirror that is 3 feet wide and 6 feet long. If the mirror sells for $3.00 per square foot, what will the total cost of the mirror be?
Answer:
$54
Step-by-step explanation:
beacuse 6x3=18 and 18x3=54 so your answer will be $54
sorry if im wrong mark me brainliest if im right
Please help
❤️❤️❤️❤️❤️❤️❤️❤️
Thanks besties
Answer:
62.33 degrees Fahrenheit.
Anytime bestie <3
Two of the angles in a triangle measure 90 degrees and 7 degrees what is the measure of the third angle
Answer:
The third angle would be 83 degrees.
Step-by-step explanation:
Seeing that every triangle's angles will always add up to 180 degrees, we would do the following:
180-90=90
90-7=83 degrees.
Starting point (1, 4) Show me the new coordinates of the point (1, 4) after it is:
Reflected over the line y = x.
Reflected over the line y = −x.
Rotated through 90°clockwise about the origin.
Rotated through 90°counterclockwise about the origin
Step-by-step explanation:
Reflected over the line y=x is (4,1)
Reflected over the line y=-x is (-4,-1)
Rotated through 90 clockwise about the origin is (4,-1)
Rotated through 90 counterclockwise about the origin is(-4,1)
A taxi driver wrote a formula to represent the mileage and fee for his last customer. He wrote the equation 3.00 + 0.50 m = 9.50, where m represents the number of miles traveled.
Which statement shows the meaning of the driver’s equation? Select two options.
Three dollars added to $0.50 is the same as $9.50.
Three dollars plus $0.50 times the number of miles is equal to nine dollars and fifty cents.
Three dollars more than the quotient of $0.50 and the number of miles is nine dollars and fifty cents.
The product of the number of miles and the sum of $3 and $0.50 is equal to $9.50.
The sum of three dollars and the product of 50 cents times the number of miles is nine dollars and fifty cents.
the last option i believe. sorry if it's wrong
Answer:
It’s B and E
Step-by-step explanation:
Three dollars plus $0.50 times the number of miles is equal to nine dollars and fifty cents.
The sum of three dollars and the product of 50 cents times the number of miles is nine dollars and fifty cents.
Q: Find six rational numbers between 3 and 4 .
Answer:
Six rational numbers between 3 and 4 are 3.1, 3.2, 3.3, 3.4, 3.5 and 3.6.
Answer:
six rational numbers between 3 and 4 are 227 , 237 , 247 , 257 , 267 , 277
What is the solution set for this inequality?
-8x + 32 -16
x < 6
x > 6
x > -2
x < -2
Answer:
x>-2
Step-by-step explanation:
-8x+32-16<0
-8x<16
divide both sides by -8
x>-2
that's because when you divide by a negative your inequality sign changes
Solve the equation by completing the square. Round your solutions to the nearest hundredth if necessary. x^2+2x=5
Answer: The correct answers are -3.45 and 1.45
Step-by-step explanation: The only problem you had was you rounded it to the tenths place instead of the hundredths place.
Sorry for getting back to you late.
please help and putting the steps would help
Answer:
x = 8
Step-by-step explanation:
These angles provided are alternate interior angles. That means they are congruent (equal). All you need to do now is answer the equation "8x-4 = 60".
From that you can see that x is 8.
Answer:
the angles are alternate interior angle pair, they are equal
8x - 4 = 608x = 64x = 8Using the Zero Factor Property, solve (2x + 1)(x - 6) = 0.
Answer:
1 2/3 or 1.67
Step-by-step explanation:
(2x+1)+(x-6)=0
Remove parenthesis.
2x+1+x-6=0
Rearrange to make life temporarily easier.
2x+x+1-6=0
Now combine like terms.
3x-5=0
Add 5 to cancel it out.
3x-5=0
+5 +5
3x=5
Divide 3 from both sides to cancel that out.
3x=5
/3 /3
x=5/3 or 1 2/3
So the answer is 1 2/3 or 1.67
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hope it helps
A CD has a diamter of 4.75 inches, Find the circumference, Use calculator pi or 3.14. Round to the nearest hundredth, if necessary.
WILL GIVE BRAINLIEST!!!
Answer:
15 in.
Step-by-step explanation:
6. cory gets paid every two weeks. he works 40 hours per week at $7.75 per hour. cory has the following deductions: 8% for medical insurance, 12% for federal and state taxes, and 10% for retirement. cory's net pay will be $________.
Answer:
$434
Step-by-step explanation:
Gross Pay
$7.75 per hour40 hours per weekPay received every 2 weeks⇒ Total gross pay = 7.75 × 40 × 2 = $620
Deductions
Medical insurance = 8%Taxes = 12%Retirement = 10%⇒ Total deductions = 8% + 12% + 10% = 30%
Net Pay
Net Pay = Total Gross Pay - Total deductions
= $620 - (30% of $620)
= $620 - (0.3 × $620)
= $620 - $186
= $434
Therefore, Cory's net pay will be $434.
PA = 0.5 PB = 0.3 and p A and b equals 0.15 what is p A or b
Answer:
P(A) = 0.2, P(B) = 0.5, P(A\B) = 0.3:
P(A\B) = P(A and B) P(B)
0.3 = P(A and B) 0.5
0.15 P(A and B)
P(A and B) = 0.15
B. P(A or B) = P(A) + P(B) - P(A and B)
0.2 + 0.5 - 0.15
0.70 - 0.15 = 0.55
Answer right and you get brainliest
What is the area
Local versus absolute extrema. If you recall from single-variable calculus (calculus I), if a function has only one critical point, and that critical point is a local maximum (or say local minimum), then that critical point is the global/absolute maximum (or say global/absolute minnimum). This fails spectacularly in higher dimensions (and thereís a famous example of a mistake in a mathematical physics paper because this fact was not properly appreciated.) You will compute a simple example in this problem. Let f(x; y) = e 3x + y 3 3yex . (a) Find all critical points for this function; in so doing you will see there is only one. (b) Verify this critical point is a local minimum. (c) Show this is not the absolute minimum by Önding values of f(x; y) that are lower than the value at this critical point. We suggest looking at values f(0; y) for suitably chosen y
Answer:
Step-by-step explanation:
Given that:
a)
[tex]f(x,y) = e^{3x} + y^3 - 3ye^x \\ \\ \implies \dfrac{\partial f}{\partial x} = 0 = 3e^{3x} -3y e^x = 0 \\ \\ e^{2x}= y \\ \\ \\ \implies \dfrac{\partial f}{\partial y } = 0 = 3y^2 -3e^x = 0 \\ \\ y^2 = e^x[/tex]
[tex]\text{Now; to determine the critical point:}[/tex]- [tex]f_x = 0 ; \ \ \ \ \ f_y =0[/tex]
[tex]\implies e^{2x} = y^4 = y \\ \\ \implies y = 0 \& y =1 \\ \\ since y \ne 0 , \ \ y = 1, \ \ x= 0\\\text{Hence, the only possible critical point= }(0,1)[/tex]
b)
[tex]\delta = f_xx, s = f_{xy}, t = f_{yy} \\ \\ . \ \ \ \ \ \ \ \ D = rt-s^2 \\ \\ i) Suppose D >0 ,\ \ \ r> 0 \ \text{then f is minima} \\ \\ ii) Suppose \ D >0 ,\ \ \ r< 0 \ \text{then f is mixima} \\ \\ iii) \text{Suppose D} < 0 \text{, then f is a saddle point} \\ \\ iv) Suppose \ D = 0 \ \ No \ conclusion[/tex]
[tex]Thus \ at (0,1) \\ \\ \delta = f_{xx} = ge^{3x}\implies \delta (0,1) = 6 \\ \\ S = f_{xy} = -3e^x \\ \\ \implies S_{(0,1)} = -3 \\ \\ t = f_{yy} = 6y \\ \\[/tex]
[tex]\implies t_{0,1} = 6[/tex]
[tex]Now; D = rt - s^2 \\ \\ = (6)(6) -(-3)^2[/tex]
[tex]= 36 - 9 \\ \\ = 27 > 0 \\ \\ r>0[/tex]
[tex]\text{Hence, the critical point} \ (0,1) \ \text{appears to be the local minima}[/tex]
c)
[tex]\text{Suppose we chose x = 0 and y = -3.4} \\ \\ \text{Then, we have:} \\ \\ f(0,-3.4) = 1+ (-3.4)^3 + 3(3.4) \\ \\ = -28.104 < -1[/tex]
[tex]\text{However, if f (0,1) = 1 +1 -3 = -1 \\ \\ f(0,-3.4) = -28.104} < -1} \\ \\ \text{This explains that} -1 \text{is not an absolute minimum value of f(x,y)}[/tex]
Which expression represents the distance between the two numbers on the
number line?
a. -1 + 2.5
b. -1 -2.5
c. 12.5 - (-1)
d. 12.5 -11
Answer:
B.
Step-by-step explanation:
........................
Suppose that the height (in centimeters) of a candle is a linear function and the amount of time (in hours) it has been burning. After 9 hours of buring, a candle has a hight of 22.2 centimeters. After 23 hours of burning, it's heigh is 16.8 centimeters. What is the height of candle after 19 hour
Answer: cockme
Step-by-step explanation:
cockme
tony completes one lap of a track every 20 seconds. diana completes one lap of the same track every 55 seconds. suppose tony and diana start at the starting line at the same time. how many seconds will it be before they cross the starting line at the same time again?
Answer:
220 seconds.
Step-by-step explanation:
55, 110, 165, 220.
20,40,60,80,100,120,140,160,180,200,220.
Both have 220 in common so will cross at 220 seconds at the same time.
How many people ordered beer?
*it is not 15
Answer:
18 people ordered beer.
Step-by-step explanation:
15 + 3 = 18 people
Answer:
18
Step-by-step explanation:
Add the 15 as well as the three people who purchased both wine and beer. The total for beer purchases would be 18.
BRAINLIEST FOR CORRECT ANSWER, IM FAILING SCHOOL AND NEED HELP ASAP. EVEN OFFICIAL HELP COUNTS
Answer:
80
Step-by-step explanation:
sorry if wrong
An experiment examined the impact of THC (the active ingredient in marijuana) on various physiological and psychological variables. The study recruited a sample of 18 young adults who were habitual marijuana smokers. Subjects came to the lab 3 times, each time smoking a different marijuana cigarette: one with 3.9% THC, one with 1.8% THC, and one with no THC (a placebo). The order of the conditions was randomized in a double-blind design. At the start of each session, no subject reported being "high." After smoking the cigarette, participants rated how "high" they felt, using a positive continuous scale (0 representing not at all "high"). For the placebo condition, participants reported a mean "high" feeling of 11.3, with a standard deviation of 15.5. A 95% confidence interval for the population mean feeling of "high" after smoking a placebo marijuana cigarette is
Answer:
OOO
Step-by-step explanation:
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Can somebody please help me with this question?
To find how many degrees a polygon's angles add up to, use the formula (n - 2) · 180, where n = the number of angles. So, since this polygon has 5 angles (it's a pentagon)
(5-2) · 180 = 3 · 180 = 540.
Now, all we have to do is add up all of the angles:
75 + 126 + 126 + 81 + c = 540
c = 132
The population of a city decreases by 4% per year. If this year's population is 171,000, what will next year's population be, to the nearest individual?
one of the fastest times for 1,500-meter race is 3 minutes and 34 seconds. How many seconds is this time?
Answer:
214 seconds
Step-by-step explanation:
3 times 60 is 180. 180 plus 34 is 214.
Find the range for the data. 1480, 1375, 1285, 1740, 1195, 1785, 1710, 1725, 1355, 1890, 1455
Answer:
The range of the data value is 695.
Step-by-step explanation:
Please mark me brainlliest!
Answer:
695
Step-by-step explanation:
Range is the difference between the largest and smallest value.
1480, 1375, 1285, 1740, 1195, 1785, 1710, 1725, 1355, 1890, 1455
1890 - 1195
695
C(4,4)
D(-8,0
B(6, -2)
A(-6, -6)
Answer:
I don't know how to do it the subject