The required value of a + b = -14.
What is a quadratic equation?The quadratic equation is defined as a function containing the highest power of a variable is two.
The standard quadratic function is given by as f(x) = ax² + b x + c.
The roots of the quadratic equation z² + az + b = 0 are -7 + 2i and -7 - 2i,
As we know that the sum of roots is -b/a for the standard quadratic function.
So the sum of these roots, -7 + 2i + (-7 - 2i) = -14, is equal to -a/2.
Hence, a = -28, and the sum of the coefficients, a + b = -28 + b = -14.
So, a + b = -14.
Learn more about the quadratic function here:
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Final answer:
The sum of the coefficients a and b from the quadratic equation with roots -7 + 2i and -7 - 2i is 67.
Explanation:
The roots of the quadratic equation z2 + az + b = 0 given are -7 + 2i and -7 - 2i. These roots are complex conjugates of each other. According to the properties of quadratics, the sum of the roots (given by -a) is equal to -7 + 2i + (-7 - 2i), which simplifies to -14. Therefore, the coefficient a is 14. To find b, we use the fact that the product of the roots is b. Thus, b equals (-7 + 2i) x (-7 - 2i), which expands to 49 + 4, giving us b = 53. The question asks us for the sum of a and b, which is 14 + 53 = 67.
75 months is how many years
Answer:
75 months is 6.25001 calendar years.
Step-by-step explanation:
Paula leaned a 10 ft ladder against a building as shown below. if Paula wants the top of the ladder to reac
h exactly 5 feet up in the building, what is x the distance between the building and the base of the ladder, in feet?
The distance between the building and the base of the ladder is 5√3 feet.
Step-by-step explanation:
Consider a right angle triangle,
Hypotenuse = Paula leaned a 10 ft ladder against a building.Height = the top of the ladder is exactly 5 feet up in the building.Base = 'x' ft, distance between the building and the base of the ladder.From the Pythagorean theorem,
Base, x = [tex]\sqrt{hypotenuse^{2}-height^{2} }[/tex]
⇒ x = [tex]\sqrt{10^{2} -5^{2} }[/tex]
⇒ x = [tex]\sqrt{100-25}[/tex]
⇒ x = [tex]\sqrt{75}[/tex]
⇒ x = 5√3
The distance between the building and the base of the ladder is 5√3 feet.
Notebooks cost $1.20 each this weekend they will be on sale for $.80 what percentage is the sale
Answer:
33%
Step-by-step explanation:
(1.20-0.80)
=0.40 dollars
(0.40/1.20)x100
0.33x 100
=33%
Hope this helps and can I get a brainliest if you want to. That would be nice thanks!
Thanks if u help and brainly
Answer:
Mode: 33 Mean: 35.5
Step-by-step explanation:
The mode of a data set is the number that appears most often.
So the mode of this set would be 33, since it appears twice.
The mean of a data set is the average of the numbers.
To find the mean (average), add all eight numbers together, then divide by eight...
31 + 29 + 33 + 37 + 43 + 38 + 33 + 40 = 284
284 / 8 = 35.5
So, the mean of the numbers is 35.5!
Joyce is thinking of a 3 - digit number. Her number has the digits 8,4, and 6. To the nearest hundred, it rounds to 600. What is the number?
Answer:
684 :)
Step-by-step explanation:
Joyce's number is 648.
To determine Joyce's number, we need to use the information that it has the digits 8, 4, and 6, and it rounds to 600 to the nearest hundred. Here's how we can approach this:
The number must round to 600, so it must be closer to 600 than to 500 or 700. This means it must be in the range 550 to 649.We need to form numbers using the digits 8, 4, and 6: 486, 468, 846, 864, 684, and 648.Comparing these numbers, only 648 falls within the range of 550 to 649.Therefore, Joyce's number is 648.
i'm too lazy to figure out an equivalent fraction to 12/36
Answer:
1/3
Step-by-step explanation:
12/36
Divide the top and bottom by 12
1/3
What is the average rate of change of f(x) from x = -2 to x= 2?
Answer:
Below.
Step-by-step explanation:
The difference of the f(x) values divided by the difference in the corresponding x values.
That would be (f(2) - f(-2)) / (2 - (-2))
y=-5x - 1 What is the slope?
Answer:
Slope is -5
Step-by-step explanation:
The slope is the number attached to the x.
In this problem: y = -5x - 1, the slope is -5 because it is the number attached to the x
Example: y = -23/5x + 6
In this case, the slope is -23/5 because it is the number attached to the x.
Answer: Slope is -5
why are we still here?
Answer:
like why are we still alive or why are we still on the site?
Step-by-step explanation:
what is 15/21 subtracted by 5/7 equal ?
Answer:
0
Step-by-step explanation:
Step 1: Make common denominators
What is the LCM of 21 and 7: 7
So, we need to convert both fractions into a 21 denominator.
15/21 * 1/1 = 15/21
5/7 * 3/3 = 15/21
Step 2: Subtract the numbers
15/21 - 5/7 is same as 15/21 - 15/21
15/21 - 15/21
0
Answer: 0
Answer:
10 over 7 is the answer
Step-by-step explanation:
Second time asking plz help. Linear or exponential. plz help me :(
Answer:
Exponential
Step-by-step explanation:
The change isn't constant for the volume, so it must be exponential.
Using quadratic regression, the equation is:
[tex]y=\frac{19}{63}x^{2}-\frac{968}{105}x+\frac{3312}{35}[/tex]
Answer:
I agree it's exponential, but it's so much simpler than you guys make it out to be. An easy way to check is to measure the distance in the x and y values to see if they change at a constant rate.
for instance; 1) abs(0-3) =3 95-69= 26
2) abs(3-6) = 3 59-50= 19 ...
It's easier, faster, and less to memorize
not sure how to do thisss,,, help!
Answer:
4 and 13
Step-by-step explanation:
(a)
To evaluate f(3) substitute x = 3 into f(x), that is
f(3) = 3 + 1 = 4
(b)
To evaluate gf(3) substitute f(3) = 4 into g(x), that is
g(4) = 4² - 3 = 16 - 3 = 13
Carson went to pick apples at an orchard.he gave one-third of his apples to his friend Nathan.then he gave one-half of what he had to his friend Nikki.on his way home he dropped one-fourth if what he had left,so that he only had 9 for him and his family.how many apples did Carson pick originally?
Answer:
36 apples
Step-by-step explanation
Step 1 = he dropped 1/4 and was left with 9
Finding 1/3 one third of 9 = 3.
Then 9 +3 = 12
Step 2 He parted with 1/2 and was left with 12
12x2=24
Step 3 He parted with 1/3 and was left with 24
= 12+ 12 + 12 = 36 Where 1/3 of 36 = 24
Answer = 36
Answer:
36
Step-by-step explanation:
Carson had x number of apples to start with.
He gave 1/3 to Nathan. Now Carson has (2/3)x apples left.
He gave 1/2 of what was left to Nikki. Now Carson has (1/2)(2/3)x = (2/6)x = (1/3)x apples.
On the way home, he dropped 1/4, so he has 3/4 of the last amount he had, and the number is 9.
(3/4) * (1/3)x = 9
3/12 x = 9
1/4 x = 9
x = 36
Answer: He picked 36 apples.
Check:
Start with 36 apples.
Give 1/3 to Nathan. Now Carson has 24 apples.
Give 1/2 to Nikki. Now Carson has 12 apples.
Drop 1/4. 1/4 of 12 is 3. 12 - 3 = 9.
Hew only had 9 apples left, so 36 is correct.
what is the volume of a sphere with a radius of 5 meters rounded to the nearest square meter.
560m
314m
340m
524m
Step-by-step explanation:
V = 4/3 π r³
V = 4/3 π (5 m)³
V = 524 m³
Final answer:
The volume of a sphere with a radius of 5 meters rounded to the nearest whole number is 524 cubic meters, calculated using the formula V = (4/3)πr³.
Explanation:
The question is asking for the volume of a sphere with a radius of 5 meters. To find the volume of a sphere, we use the formula V = (4/3)πr³, where V is the volume and r is the radius of the sphere. In this case, the radius r is given as 5 meters.
Plugging in the values, we get:
V = (4/3)π(5³) = (4/3)π(125) = 523.6 cubic meters.
When we round to the nearest whole number, we get 524 cubic meters.
Therefore, the correct answer from the options provided is 524m³.
1458+3. Use multiplication to check answer. Show work?
Answer:
1461
Step-by-step explanation:
1458 + 3 = 1461
1458 + 3
3(486 + 1)
3(487)
1461
Explain why the function represented by the equation y=ax2+bx+c is quadratic only when a≠0.
Answer:
see below
Step-by-step explanation:
y=ax^2+bx+c
Let a=0
y=0*x^2+bx+c
y = bx+c
This is the equation of a line. It is no longer quadratic, but linear. a cannot equal zero
Which is bigger 2/3 1/8 or 3/4
Answer:
3/4
Step-by-step explanation:
2/3= 0.6
1/8= 0.125
3/4= 0.75
I convert the fractions into decimals the decimal with the highest number in the tenths place is the biggest
Hope This Helps!
Answer:
3/4
Step-by-step explanation:
if you convert them all to have the same denominator you find that 3/4 has the biggest numerator.
2/3 = 16/24
1/8 = 3/24
3/4 = 18/24 ← has the greatest numerator so it's the greatest
Anne has duplicates of 125 stamps in her collection. She gives 50 to Sam, Then she divides the remainder among five friends. If two of her friends but there are stamps together how many will they have?
Answer:
This is incomplete you can edit and report this answer as not the answer you was looking for. 125-70 is 55 stamps among 5 friends this is either 11 stamps each but some have two together so if it is an odd number like 13 or 17 together then you type in T = 17 O=55-17= ? and you have your answer for the other three.
Step-by-step explanation:
15) Yanni received her monthly credit card statement in the mail, the summary of which is shown below. When she
calculated the new balance for the month, she arrived at a different amount than the credit card company. What
should be the correct new balance?
SUMMARY
Previous
Balance
$3,589
Payments
Credits
$130.00
Transactions
$275,00
Late
Charge
$0.00
Average
Daily
Balance
$3,558.71
Finance
Charge
$82.28
Days
in Billing
Cycle
Now
Balance
$3,796.28
Minimum
Payment
$100.00
Monthly
Periodic
Rate
1.75%
Total Credit Line
Total Available Credit
$ 10.000.00
$6,203.72
APR
21%
$3,576.28
$3,676.28
B.
C. $3,766.28
D. $3,776.28
Answer:
D. $3,776.28
Step-by-step explanation:
The finance charge should be ...
$3558.71 × 1.75% = $62.28 . . . . . . not $82.28
The new balance should be $20 less than what is shown, so should be ...
$3,776.28
Answer:
I believe the answer is D
Step-by-step explanation:
A bag contains 9 red marbles,5 green marbles, and 6 purple marbles.
What are the odds of picking a red marble?
The odds or probability of picking a red marble from a bag that contains 9 red marbles, 5 green marbles, and 6 purple marbles is 0.45 or 45%.
Probability refers to the chance, likelihood, or odds that an event occurs out of many possible events.
Probability is a value that ranges from 0 to 1, depending on the level of certainty.
The number of red marbles in the bag = 9
The number of green marbles in the bag = 5
The number of purple marbles in the bag = 6
The total number of marbles in the bag = 20 (9 + 5 + 6)
The probability of choosing or picking a red marble = 9/20 = 0.45 or 45%.
Question 2 of 10
2 Points
What is the measure of XYZ?
O A. 1740
O B. 96
O C. 186°
O D. 93°
SUBMIT
Answer:
Question is not clear.
Step-by-step explanation:
But i think so 186degree
Which exponent makes the following statement true?
Answer:
-7
Step-by-step explanation:
8⁷ in the denominator becomes a negative power in the numerator
Eduardo earns a base salary of $30,000 per year and earns $1,875 per car he sells. Which equation can be used to find the number of cars, c, that Eduardo sold in a year he made 46,875 ?
Answer:
The equation is, A =30,000 + 1875n.
He sold 9 cars the year he made that amount of money.
Step-by-step explanation:
Before calculating, let's assign letters to certain variables:-
✓ let "A" be used to represent the total amount earned after adding his base salary to the amount he earned as commission per car he sells.
✓ "P" will be used to represent his base salary (a constant = 30,000)
✓ "n" will represent the number of cars sold within a given year.
✓ "B" will be used to represent his commission per car he sells.
Fixing them into a formula, we have:
A = P + n(B)
Since "P" and "B" are constants of 30000 and 1875 respectively, we substitute the letters for their actual amount in the formula:-
A = 30,000 + n(1875)
A = 30,000 + 1875n +This is now the equation that can be used to calculate the number of cars he sold in the year he earned 46,875).
So, since "A" is now $46,875, we substitute accordingly to find the number of cars he sold in the year he earned such amount.
46,875 = 30,000 + 1875b
1875n = 46,875 - 30,000
1875n = 16875
n = 16875/1875
n = 9 cars
Therefore the equation to be used to determine how many cars he sold when he earned $46,875 is:
A = 30,000 + 1875n
He sold 9 cars the year he earned $46,875.
4x+10>28-2x
What is the solution to the inequality
Answer:
x>3
Step-by-step explanation:
add 2x to both sides and subtract 10 from both sides. Then divide by 6.
Answer:
x>3
Step-by-step explanation:
1- subtract 10 from both sides so (4x+10-10>28-2x-10)
2- Simplify (4x>-2x+18)
3- Add 2x to both sides (4x+2x>-2x+18+2x)
4- Simplify (6x>18)
5- Divide both side by 6 (6x/6>18/6)
6 Simplify which gives you (x>3)
20 POINTS!!! PLEASE ANSWER CORRECTLY!
Olivia is buying juice boxes for a party. She is comparing two brands to determine the best price. A case of All Natural Juice costs $2.80 and has 8 boxes of juice. A case of Just Juice costs $1.98 and has 6 boxes of juice.
(a) What is the unit price (cost per box) for All Natural Juice?
(b) What is the unit price (cost per box) for Just Juice?
(c) She spends $8.40 on several cases of All Natural Juice. She wants to buy the same number of boxes of Just Juice. How many cases of Just Juice will she need to buy?
(d) How much will the cases of Just Juice from problem (c) cost?
Answer:
a) $0.35
b) $0.33
c) 4 cases
d) $7.92
Step-by-step explanation:
a) 2.80/8 = $0.35
b) 1.98/6 = $0.33
c) 8.40/2.4 = 3
3 cases = 3×8 = 24 boxes
24/6 = 6 cases of Just Juice
d) 4 × 1.98 = $7.92
Brisa's kite is flying above a soccer field at the end of 43 m of string. If the angle of elevation to the kite measures 72degree, and Brisa is holding the kite 1.2 m off the ground. How high above the ground is the kite flying? (Round to the nearest meter)
Answer:
The height the kite is flying above the ground level to the nearest meter is 42m.
Step-by-step explanation:
this is not drown to scale:
|\
| \
x | \ 43m
| \
|___\
Angle is 72º
sine = opposite / hypotenuse
sin 72 = x / 43
0.9510565 = x / 43
therefore x = 40.9m
Brisa is holding the kite 1.2 m off the ground, we also need to add 1.2 m to our calculated height of the kite. Thus, the answer is
40.9 m + 1.2 m = 42.1 m to the nearest meter is 42m.
Danna purchased a tv for $200 eight months later the same tv was selling for $160 what was the percent of decrease in the price
Answer: The tv had dropped 20%
Step-by-step explanation: $160 is 80% of $200. So 100%- 80%= 20%
Its 20%................................................. .
-2h - 16=3h - 6. Solve for h
Answer:
H=2
Step-by-step explanation:
-2h - 16=3h - 6
Move the 3h to the left
-5h-16=6
Move the -16 to the right
-5h=10
Now divide both by 5
-h=2
Or
H=2
Hope I Helped
Answer:
H=2
Step-by-step explanation:
H=2
1 point
The volume of a container varies jointly with the square of its radius, r, and its height, h. The
container has a height of 10 centimeters, and radius of 6 centimeters, and a volume of 377 cubic
centimeters. What is the volume of a container with a radius of 4 centimeters and a height of 4
centimeters?
Your answer
Solution:
The volume of a container varies jointly with the square of its radius, r, and its height, h
Therefore,
[tex]v \propto r^2 h\\\\v = k \times r^2h -------- eqn\ 1[/tex]
The container has a height of 10 centimeters, and radius of 6 centimeters, and a volume of 377 cubic centimeters
Substitute v = 377 and h = 10 and r = 6 in eqn 1
[tex]377 = k \times 6^2 \times 10\\\\377 = k \times 360\\\\k = 1.047 \approx 1.05[/tex]
What is the volume of a container with a radius of 4 centimeters and a height of 4 centimeters?
Substitute k = 1.05 and r = 4 and h = 4 in eqn 1
[tex]v = 1.05 \times 4^2 \times 4\\\\v = 1.05 \times 16 \times 4\\\\v = 67.2[/tex]
Thus volume of a container with a radius of 4 centimeters and a height of 4 centimeters is 67.2 cubic centimeter
solve:
(2.5x10^6) x (3x10^6)
(1.1x10^7)/(1.2x10^7)
7.5^12
[tex].916666666666[/tex]