The sum of the squares of three consecutive odd number 11, 13, 15 is 515.
What are consecutive numbers ?
Numbers that follow each other continuously in the order from smallest to largest are called consecutive numbers. For example: 1, 2, 3, 4, 5, 6, and so on are consecutive numbers.
Let the second number = x.
so the first number = x-2
the third number = x + 2
according to the question, the sum of the squares of the numbers = 515
so the formula is:
x² + (x-2)² + (x + 2)² = 515
(a-b)² = a² + b² - 2ab
and,
(a+b)² = a² + b² + 2ab
So, let’s apply these to our equation:
x² + x² + 2² -2*2x + x² + 2² + 2*2x = 515
There are three x² and 2*2 = 4 and 2*2x = 4x. Let’s apply all that to the equation,
3x² + 4 - 4x + 4 + 4x = 515
there is a -4x and a +4x, -4x + 4x = 0, so let’s remove that.
3x² + 4 + 4 = 515
3x² + 8 = 515
3x² = 515 - 8
3x² = 507
x² = 507/3
x² = 169
x = √169
√169 (square root(169)) = 13
x = 13
if x = 13, then the first number = 13–2 = 11 and the third number = 13 + 2 = 15
Hence , the sum of the squares of three consecutive odd number 11, 13, 15 is 515.
11*11 + 13*13 + 15*15 = 515
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A number x is rounded to 1 decimal place and its 3.7
write down the error interval for x
The error interval for x would be (3.65, 3.75), indicating that the true value of x lies within this range.
Given that a number x is rounded to 1 decimal place and its 3.7.
We need to find the error of the interval for x,
To determine the error interval for the rounded number 3.7, we need to consider the possible range of values that could have been rounded to 3.7 when rounded to 1 decimal place.
When rounding to 1 decimal place, we look at the digit immediately to the right of the decimal point. If this digit is 5 or greater, we round up. If it is less than 5, we round down.
In this case, 3.7 is the rounded value, which means the original number could have been rounded up from a value greater than or equal to 3.65 or rounded down from a value less than 3.75.
Therefore, the error interval for x would be (3.65, 3.75).
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Help please due today!!
Your goal is to have $200,000 in a 401K that is compounded continuously in order to retire. If you invest $9,500 for fifty years at a rate of 7%, will you reach your goal?
Answer:
Yes
Step-by-step explanation:
You will get $279,841.74 in that 50 years.
HELLLPPP!!!
What is the equation of the parabola with focus(1, 1/2)
and directrix y = 3?
A. Y=x^2+17x-1
B. Y=-3/16x^2
C. Y=1/5x^2+2/5x+31/20
D. Y=-3/5x^2-14/31x+71/16
Given:
Focus of a parabola = [tex]\left(1,\dfrac{1}{2}\right)[/tex]
Directrix: [tex]y=3[/tex]
To find:
The equation of the parabola.
Solution:
The equation of a vertical parabola is:
[tex]y-k=\dfrac{1}{4a}(x-h)^2[/tex] ...(A)
Where, [tex](h,k)[/tex] is center, [tex](h,k+a)[/tex] is focus and [tex]y=k-a[/tex] is the directrix.
On comparing the focus, we get
[tex](h,k+a)=\left(1,\dfrac{1}{2}\right)[/tex]
[tex]h=1[/tex]
[tex]k+a=\dfrac{1}{2}[/tex] ...(i)
On comparing the directrix, we get
[tex]k-a=3[/tex] ...(ii)
Adding (i) and (ii), we get
[tex]2k=\dfrac{7}{2}[/tex]
[tex]k=\dfrac{7}{4}[/tex]
Putting [tex]k=\dfrac{7}{4}[/tex] is (i), we get
[tex]\dfrac{7}{4}+a=\dfrac{1}{2}[/tex]
[tex]a=\dfrac{1}{2}-\dfrac{7}{4}[/tex]
[tex]a=\dfrac{-5}{4}[/tex]
Putting [tex]a=\dfrac{-5}{4},h=1,k=\dfrac{7}{4}[/tex] in (A), we get
[tex]y-\dfrac{7}{4}=\dfrac{1}{4\times \dfrac{-5}{4}}(x-1)^2[/tex]
[tex]y-\dfrac{7}{4}=\dfrac{-1}{5}(x^2-2x+1)[/tex]
[tex]y-\dfrac{7}{4}=-\dfrac{1}{5}(x^2)-\dfrac{1}{5}(-2x)-\dfrac{1}{5}(1)[/tex]
[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x-\dfrac{1}{5}+\dfrac{7}{4}[/tex]
On further simplification, we get
[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{35-4}{20}[/tex]
[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex]
Therefore, the equation of the parabola is [tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex].
Note: Option C is correct but the leading coefficient should be negative.
For 0 ≤ ϴ < 2π, how many solutions are there to tan(StartFraction theta Over 2 EndFraction) = sin(ϴ)? Note: Do not include values that are undefined for tan or sin(ϴ).
Answer:
3 solutions:
[tex]\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}} [/tex]
Step-by-step explanation:
So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is [tex]tan(\frac{\theta}{2})[/tex] so let's focus on that part of the equation first.
We know that:
[tex]tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}[/tex]
therefore:
[tex]cos(\frac{\theta}{2})\neq0[/tex]
so we need to find the angles that will make the cos function equal to zero. So we get:
[tex]cos(\frac{\theta}{2})=0[/tex]
[tex]\frac{\theta}{2}=cos^{-1}(0)[/tex]
[tex]\frac{\theta}{2}=\frac{\pi}{2}+\pi n[/tex]
or
[tex] \theta=\pi+2\pi n[/tex]
we can now start plugging values in for n:
[tex] \theta=\pi+2\pi (0)=\pi[/tex]
if we plugged any value greater than 0, we would end up with an angle that is greater than [tex]2\pi[/tex] so, that's the only angle we cannot include in our answer set, so:
[tex]\theta\neq \pi[/tex]
having said this, we can now start solving the equation:
[tex]tan(\frac{\theta}{2})=sin(\theta)[/tex]
we can start solving this equation by using the half angle formula, such a formula tells us the following:
[tex]tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}[/tex]
so we can substitute it into our equation:
[tex]\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)[/tex]
we can now multiply both sides of the equation by [tex]sin(\theta)[/tex]
so we get:
[tex]1-cos(\theta)=sin^{2}(\theta)[/tex]
we can use the pythagorean identity to rewrite [tex]sin^{2}(\theta)[/tex] in terms of cos:
[tex]sin^{2}(\theta)=1-cos^{2}(\theta)[/tex]
so we get:
[tex]1-cos(\theta)=1-cos^{2}(\theta)[/tex]
we can subtract a 1 from both sides of the equation so we end up with:
[tex]-cos(\theta)=-cos^{2}(\theta)[/tex]
and we can now add [tex]cos^{2}(\theta)[/tex]
to both sides of the equation so we get:
[tex]cos^{2}(\theta)-cos(\theta)=0[/tex]
and we can solve this equation by factoring. We can factor [tex]cos(\theta)[/tex] to get:
[tex]cos(\theta)(cos(\theta)-1)=0[/tex]
and we can use the zero product property to solve this, so we get two equations:
Equation 1:
[tex]cos(\theta)=0[/tex]
[tex]\theta=cos^{-1}(0)[/tex]
[tex]\theta={\frac{\pi}{2}, \frac{3\pi}{2}}[/tex]
Equation 2:
[tex]cos(\theta)-1=0[/tex]
we add a 1 to both sides of the equation so we get:
[tex]cos(\theta)=1[/tex]
[tex]\theta=cos^{-1}(1)[/tex]
[tex]\theta=0[/tex]
so we end up with three answers to this equation:
[tex]\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}} [/tex]
Answer:
its D. 3
Step-by-step explanation:
for speed runners
If you were to flip a coin 500 times, how many times would you
theoretically expect the coin to land on heads?
Answer and Step-by-step explanation:
Theoretically, we should expect the coin to flip 250, or very close to 250 times, and land on heads.
This is because the probability of getting heads is [tex]\frac{1}{2}[/tex], or 50%.
There is a 50% chance of landing heads or tails, so that means it would land 250 times on heads out of 500 flips of the coin.
#teamtrees #PAW (Plant And Water)
Answer:
250 times
Step-by-step explanation:
The coins has the heads or tails, with two options there is a 50% probability of landing on heads or tails.
500 x 50% = 250 times
SOME PLEASE HURRY AND ANSWER ASAP
Step-by-step explanation:
A=s2
100=5×5
100/25=25x/25
x=4
Solve for angle G. Type just the number. Round to the nearest degree (whole
number) *G
(1,-6,); (9,-8)
Slope
Best answer =branniest
Two paths each 2m wide run across the middle of a rectangular field. If the area of the cross path is 196m and its lenght is 60m, find its breadth
Answer:
d=2m
area(A)=196m
l=60m
now,
A=d(l+b-d)
196=2(60+b-2)
196=2(58+b)
196=116+2b
2b=196-116
2b=80
b=40m
Whats the Area of a circle with a radius of 2.6? use 3.141592654 for pie
Answer:
16.33628179866692
Step-by-step explanation:
I dont know how far you wanted me to round so you will have to do that part
HALPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP. Please no links :P
Answer:
it will be x < 2
Step-by-step explanation:
Because the circle means greater than or less than. And if the circle isn't fillied up it means it is greater than or equal to or less thanor equal to.
IM SO TIRED CAN SUM1 HELP PLS.
Answer:
a. $250
b. 50x + 200
Step-by-step explanation:
a. For the first month, you have to account for the cost to start which is $200, and the adition of the $50 for each month.
b. the 200 is only a one time fee so you add it on to months(x)
Answer:
a. 250$
b. 200+50x
Step-by-step explanation:
#1 What is the total cost to use the cell phone plan for one month?
GIVEN:
Startup price=$200
Charge per month=50$
SOLVE:
The total cost for one month will be the startup price+ charging price for one month.
200+50=250$
#2 What is the total cost for x months?
The total cost for x months will be the startup price+charging price for x months.
200+50x
Hope this helps!! :)
Please let me know if you have any questions
Geometry pls help me need help
PLEASE HELP ASAP PLZ
ALSO IF ANY ACTUAL HUMANS R SERING THIS PLZ ANSWER BC I TRIED ASKING AND THIS IS MY 6TH TIME AND I GOT SPAMMED BY BOTS SO IF UR A HUMAN PLZ ANSWER I WILL GIVE BRAINLIES
also plz don’t answer if ur gonna put down random things
Answer:
Step-by-step explanation:
I have 5min can sb help please
Answer:
Use M a t h W a y
Step-by-step explanation:
it all together
Laurence is saving money for a set of speakers. He has $230 dollars in his savings right now. He just got a part-time job at Kroger and can increase his savings account by 20.6% each week. Write an equation to represent the amount of money
in his account, y after x weeks.
What’s the equation
Answer:
The equation of the line is;
y = 0.8x + 1
Step-by-step explanation:
Here, we want to get the equation of the line
The general equation of a straight line is;
y = mx + b
m
is the slope and b is the y-intercept
The y-intercept is simply the point on the y-axis where the line crosses the y-axis
we have this point at (0,1)
so we have;
y = mx + 1
to get m, we get any other point on the line and substitute its coordinates before we solve for m
we can identify the point (-2.5, -1)
substituting the coordinates
-1 = -2.5(m) + 1
-2.5m = -1-1
-2.5m = -2
m= 2/2.5
m= 0.8
so we have the equation of the line as;
y = 0.8x + 1
In the equation, y = mx + b, what does the "b" represent? *
Helppppp!!
In DEF e = 100 inches f = 740 inches and angle D = 159°. Find the area of DEF to the nearest square inch
Answer:
13260 square inches
Step-by-step explanation:
In DEF e = 100 inches f = 740 inches and angle D = 159°. Find the area of DEF to the nearest square inch
The formula to solve the above question is
1/2absinθ
a = 100 inches
b = 740 inches
θ = 159°
The area of the triangle =
1/2 × 100 × 740 × sin 159°
= 13259.61 square inches
Approximately = 13260 square inches
Therefore, the area of DEF = 13260 square inches
Find the supplementary angle.
Answer:
x=146 degrees
Step-by-step explanation:
A supplementary angle is the conrisponding angle that adds to the other angle so it is 180. So 180-34= 146
In ΔFGH, the measure of ∠H=90°, the measure of ∠F=44°, and GH = 14 feet. Find the length of HF to the nearest tenth of a foot.
Answer: 14.5 feet
Step-by-step explanation: that’s he correct answer delta math gave me AFTER I got it wrong
Answer:
14.5
Step-by-step explanation:
for brainiest :):):):):):):)
*easy*
Answer:
8. 12 in
9. 30 ft
10. 87.92 in
Step-by-step explanation:
Answer:
12in, 30ft, 87.92in
Step-by-step explanation:
question 8: 24/2 = 12in
question 9: 15(2) = 30ft
question 10:
C = 2πr
C =2(3.14)(14)
C= 87.92in
im not good at percentages
Answer:
D. 16
Step-by-step explanation:
You first need to find the total percentage who liked vanilla, then subtract it from the total percentage of chocolate.
To find the total of those who liked vanilla you would have to add the given percentages and then subtract that from 100.
Chocolate: 42%
Strawberry: 18%
Coffee: 14%
Vanilla: x
42 + 18 = 60 + 14 = 74%
100 - 74 = x
Vanilla = x = 26%
To find how many more like chocolate than vanilla, you would subtract the two percentages.
Chocolate: 42%
Vanilla: 26%
42 - 26 = 16
Marcos and his sister Yvette record their age each year in an annual scrapbook.
The table below shows their recorded ages for the past three years.
Which equation correctly shows the relationship between Marcos's age, m, and
Yvette's age, y?
Marcos
Yvette
10
4
11
5
12
6
4 O y = 7
O y = m + 6
O y = 6m
O y = m - 6
Answer:
It’s b
Step-by-step explanation:
Just think
1. Li rolls a special dice that has 12 sides labeled 1 through 12, then flips a penny. What is the probability, written as a simplified fraction, that she rolls a multiple of 3 and flips tails? 2. A bag contains 5 red marbles, 6 green marbles, and 3 blue marbles. If Cymra draws a marble, puts it back in the bag, then draws another marble, write a multiplication problem you would use to find the probability that both marbles drawn will be red. 3. If Cole flips a coin three times, what is the probability that he will flip three tails in a row? 4. Based on collected data from the past 5 basketball practices, Linda has a 32% for making her free throws. If she shoots 175 more times, how many will she expect to make based on her percentage? !!! DUE IN 18 MINS !!!
Answer:
1. The probability that she throws a multiple of 3 and flips tails is 1/6
2. The probability that Cymra draws a red marble put it back and draws a red marble again is 25/196
3. The probability that Cole flips three tails in a row, P(3T) is 1/8
4. The number of shots Linda is expected to make if she takes 175 shots is 56
Step-by-step explanation:
1. The number of sides on the special die Li rolls = 12 sides
The numbers on the die are 1 through 12
The number of faces on the penny = 2 (heads and tails)
The number of multiples of 3 on the die = 3, 6, 9, and 12 = 4
The probability that she throws a multiple of 3, P(3) = 4/12 = 1/3
The probability that she flips tails rather than heads = 1/2
∴ The probability that she throws a multiple of 3 and flips tails = 1/3 × 1/2 = 1/6
2. The number red marbles in the bag = 5
The number green marbles in the bag = 6
The number blue marbles in the bag = 3
The total number of marbles in the bag = 5 + 6 + 3 = 14
The probability that Cymra draws a red marble put it back and draws a red marble again is given as follows;
The probability with replacement of picking two red marbles = 5/14 × 5/14 = 25/196
3. The probability that Cole flips three tails in a row P(3T) = (1/2)×(1/2)×(1/2) = 1/8
The probability that Cole flips three tails in a row, P(3T) = 1/8
4. The percentage of times Linda makes her free throws in the past 5 basketball practices = 32%
The number of shots she is expected to make if she takes 175 shots = 175 × 32/100 = 56.
marking brianliest pls help
Answer:
117.3
Step-by-step explanation:
7*4=117.29=117.3
Here is an expression. Evaluate the expression: *
3.4 + 4
Answer:
the answer would be 3.4 + 4 = 7.4 .
Answer:
the answer would be 3.4 + 4 = 7.4 .
Step-by-step explanation:
Jonathan is preparing for a triathlon he biked 3.5 miles on Thursday and 4.25 miles on Friday on Saturday he biked 12 miles how much farther did he bike on Saturday than he did on Thursday and Friday combined
Answer: 4.25 miles
Step-by-step explanation:
The distance he biked on Thursday and Friday combined is:
= 3.5 + 4.25
= 7.75 miles
On Saturday he biked 12 miles. The number of miles he biked over Thursday and Friday is:
= 12 - 7.75
= 4.25 miles
Lexi Chappell
Pythagorean Theorem (No Diagram)
Apr 22, 5:26:21 PM
?
One of the legs of a right triangle measures 8 cm and the other leg measures 12 cm.
Find the measure of the hypotenuse. If necessary, round to the nearest tenth.
Answer:
cm
Submit Answer
attempt 1 out of 2
BULLY
HOD