Answer:
Step-by-step explanation:
c2+2c+4
(c+2)^2
^ is the exponent
Help me please I’m dying
Answer:
[tex]\boxed{x = 2+2\sqrt{6} ~~or~~x = 2 - 2 \sqrt{6} }[/tex]
.
Step-by-step explanation:
To find x, use pythagoras form
[tex]c^2 = a^2 + b^2[/tex]
[tex](x + 4)^2 = x^2 + (x + 1)^2[/tex]
[tex]x^2 + 8x + 16 = x^2 + x^2 + 2x + 1[/tex]
[tex]2x^2 + 2x + 1 - x^2 - 8x - 16 = 0[/tex]
[tex]x^2 - 6x - 15 = 0[/tex]
[tex]x^2 - 6x = 15[/tex]
[tex](x - 3)^2 - 9 = 15[/tex]
[tex](x - 3)^2 = 15 + 9[/tex]
[tex](x - 3)^2 = 24[/tex]
[tex]x - 2 = \pm \sqrt{24}[/tex]
[tex]x = 2 \pm 2\sqrt{6}[/tex]
.
[tex]x_1 = 2 + 2\sqrt{6}[/tex]
[tex]x_2 = 2 - 2\sqrt{6}[/tex]
.
Happy to help :)
n/ 39 = 8/13
Please select the best answer from the choices provided.
A: n = 32
B: n = 2 2/3
C: n = 24
D: n = 63 3/8
Answer:
24 is the correct answer
A group of friends ordered two pizzas, one with pepperoni and one with mushrooms and green peppers. A plain pizza costs $9. Each topping costs $1. How much did the two pizzas cost?
A.
Answer:
21$
Step-by-step explanation:
2 pizzas =18 plus 3 toppings which equals 21$
I will mark BRAINLIEST pls I need to turn this in soon !!!!!
5. Use the race times to calculate the mean time for each team. Show your work
Red:
Yellow:
Blue:
6. How do the tree teams rank based on mean times? List them in order from fastest to slowest, and explain your ranking
7. How do the three teams rank based on median times? Explain your ranking
8. What statistic should you use if you wish to compare the spreads? Explain your answer
9. The interquartile range for the red teams race time is 5 seconds. Find the IQR for the yellow and blue teams.
10. What do the interquartile ranges (IQRs) tell you about how the teams race ? Explain your thinking.
11. Now that you’ve analyzed the data, it’s time to make a decision.who do you think will win the strict meet describe how you think each team will do, explain your reasoning.
Red:
Yellow:
Blue:
here is your answer pls check it
Answer:
5. Use the race times to calculate the mean time for each team. Show your work. (3 points: 1 point for each team)
Red
45.6
Yellow
47
Blue
42.8
6. How do the three teams rank based on mean times? List them in order from fastest to slowest, and explain your ranking. (1 point)
From fastest to slowest the teams rank
Red
Yellow
Blue
7. How do the three teams rank based on median times? Explain your ranking. (1 point)
Based on median times the teams rank from fastest to slowest
Red and yellow tie for the first place
Blue
8. What statistic should you use if you wish to compare the spreads? Explain your reasoning. (1 point)
The interquartile range would be the best option for measuring the spread of these statistics.
Step-by-step explanation:
Sorry, this is the best I can do I need help with the rest of the questions.
In this problem you will use undetermined coefficients to solve the nonhomogeneous equation y′′+4y′+3y=8te^−t+6e^−t−(9t+6)
with initial values y(0)=2andy′(0)=2.
We're given the ODE,
y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) - (9t + 6)
(where I denote exp(x) = eˣ )
First determine the characteristic solution:
y'' + 4y' + 3y = 0
has characteristic equation
r ² + 4r + 3 = (r + 1) (r + 3) = 0
with roots at r = -1 and r = -3, so the characteristic solution is
y = C₁ exp(-t ) + C₂ exp(-3t )
For the non-homogeneous equation, assume two ansatz solutions
y₁ = (at ² + bt + c) exp(-t )
and
y₂ = at + b
• y'' + 4y' + 3y = 8t exp(-t ) + 6 exp(-t ) … … … [1]
Compute the derivatives of y₁ :
y₁ = (at ² + bt + c) exp(-t )
y₁' = (2at + b) exp(-t ) - (at ² + bt + c) exp(-t )
… = (-at ² + (2a - b) t + b - c) exp(-t )
y₁'' = (-2at + 2a - b) exp(-t ) - (-at ² + (2a - b) t + b - c) exp(-t )
… = (at ² + (b - 4a) t + 2a - 2b + c) exp(-t )
Substitute them into the ODE [1] to get
→ [(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c)] exp(-t ) = 8t exp(-t ) + 6 exp(-t )
(at ² + (b - 4a) t + 2a - 2b + c) + 4 (-at ² + (2a - b) t + b - c) + 3 (at ² + bt + c) = 8t + 6
4at + 2a + 2b = 8t + 6
→ 4a = 8 and 2a + 2b = 6
→ a = 2 and b = 1
→ y₁ = (2t ² + t ) exp(-t )
(Note that we don't find out anything about c, but that's okay since it would have gotten absorbed into the first characteristic solution exp(-t ) anyway.)
• y'' + 4y' + 3y = -(9t + 6) … … … [2]
Compute the derivatives of y₂ :
y₂ = at + b
y₂' = a
y₂'' = 0
Substitute these into [2] :
4a + 3 (at + b) = -9t - 6
3at + 4a + 3b = -9t - 6
→ 3a = -9 and 4a + 3b = -6
→ a = -3 and b = 2
→ y₂ = -3t + 2
Then the general solution to the original ODE is
y(t) = C₁ exp(-t ) + C₂ exp(-3t ) + (2t ² + t ) exp(-t ) - 3t + 2
Use the initial conditions y (0) = 2 and y' (0) = 2 to solve for C₁ and C₂ :
y (0) = C₁ + C₂ + 2 = 2
→ C₁ + C₂ = 0 … … … [3]
y'(t) = -C₁ exp(-t ) - 3C₂ exp(-3t ) + (-2t ² + 3t + 1) exp(-t ) - 3
y' (0) = -C₁ - 3C₂ + 1 - 3 = 2
→ C₁ + 3C₂ = -4 … … … [4]
Solve equations [3] and [4] to get C₁ = 2 and C₂ = -2. Then the particular solution to the initial value problem is
y(t) = -2 exp(-3t ) + (2t ² + t + 2) exp(-t ) - 3t + 2
A person saving for retirement makes an initial deposit of $1,000 to a bank account earning interest at a rate of 3% per year compounded monthly, and each month she adds an additional $200 to the account For each nonnegative integer n, let An be the amount in the account at the end of n months. Find a recurrence relation relating Ak to Ak-1. Use iteration to find an explicit formula for An.
Answer:
Step-by-step explanation:
(a)
From the given information:
Let An denote the amount in the account at the end of n month
Thus,
[tex]A_o[/tex] =1000
After the first month ends, interest = [tex]=A_o \times \dfrac{3}{100} \times \dfrac{1}{12}[/tex]
= [tex]0.0025A_o[/tex]
Additional deposit = $200
Now,
[tex]A_1 = A_o + 0.0025A_o + 200[/tex]
[tex]=1.0025A_o + 200 --- eqn(1)[/tex]
Interest after 2nd month, = [tex]A_1 \times \dfrac{3}{100} \times \dfrac{1}{2}[/tex]
Additional deposit = $200
[tex]A_2 = A_1 + 0.0025A_1 + 200[/tex]
[tex]=1.0025A_1 + 200 --- eqn(2)[/tex]
Thus:
[tex]A_n = 1.0025A_{n-1} +200[/tex]
(b)
From above;
[tex]A_1 = 1.0025A_ 0+ 200[/tex]
Thus;
[tex]A _2 = 1.0025A_ 1+ 200[/tex]
[tex]A_2 = 1.0025( 1.0025A_ 0+ 200)+ 200[/tex]
[tex]A_2 = 1.0025^2A_o +200 ( 1+1.0025)[/tex]
[tex]A _3 = 1.0025A_ 2+ 200[/tex]
[tex]A _3 = 1.0025( 1.0025^2A_o +200 ( 1+1.0025))+ 200[/tex]
[tex]A _3 = 11.0025^3A_o +200 ( 1+1.0025 + 1.0025^2)[/tex]
To continuity...
[tex]A_n = 1.0025^n A_o + 200 (1+1.0025 +1.0025^2 +...+ 1.0025^{n-1} ) ---- (3)[/tex]
Thus, we have a geometric term [tex]1 + 1.0025 +1.0025^2 +...+ 1.0025^{n-1}[/tex]
where:
a = 1 (first term)
r = 1.0025>1 (common ratio)
Thus;
[tex]1 + 1.0025 +1.0025^2 +...+ 1.0025^{n-1} = \dfrac{a(r^n -1)}{r-1}[/tex]
[tex]= \dfrac{1(1.0025^n -1)}{1.0025-1}[/tex]
[tex]= 400(1.0025^n -1)[/tex]
From equation(3)
[tex]A_n = (1.0025^n \times 1000) + 80000(1.0025^n -1)[/tex]
[tex]A_n = 1.0025^n \times 81000-80000[/tex]
If the total value of the coins is 36¢, what are the missing coins?
we need a better explaination
triangle ABC has veritices A(-2,3), B(0,3), and C (-1,-1). Find the coordinates of the image after a reflection over the x-axis.
Answer:
A' = (-2, -3)
B' = (0, -3)
C' = (-1, 1)
I did this on edg
Step-by-step explanation:
Since it's a reflection over the x axis, the x coordinates will stay the same while the y coordinates will be opposite of what they are.
After reflected: A'(-2,-3), B'(0,-3), C'(-1,1)
Evaluate
f(x)=5x-3
f(5) =
f(x)=5x-3
use the substitution method
f(5)=(5)(5)-3
multiply the parentheses first
using: PEDMAS
P=Parentheses
E= Exponents
D=Division
M=Multiplication
A= Addition
S=Subtraction
(5)(5)=25
25-3
=22
answer:
f(5)=22
If PQ=12, QR=20, PS=12, and SR=20, then QS=
Answer:
QS=23.32
Step-by-step explanation:
by Pythagorean theoremh square is equal to p square + b square
so h=√12×12+20×20h=√144+400h=√544h=23.32Buddy mark me as a brainlist
Helpppppppppp meeeee ASAP
option c is the answer....
Consider drawing two cards, without replacement, from a standard deck of 52 cards. That means we are drawing the first card, leaving it out, and then drawing the second card.what is the probability that both cards selected for black?
Given:
Two cards are drawn from a standard deck of 52 cards without replacement.
To find:
The probability that both cards selected for black.
Solution:
We know that,
Total number of cards = 52
Total number of red cards = 26
Total number of black cards = 26
[tex]\text{Probability}=\dfrac{\text{Favorable outcomes}}{\text{Total outcomes}}[/tex]
Probability of selecting first black card is
[tex]\text{Probability}=\dfrac{26}{52}[/tex]
[tex]\text{Probability}=\dfrac{1}{2}[/tex]
Number of remaining total cards = 52-1 = 51
Number of remaining black cards = 26-1 = 25
Probability of selecting second black card is
[tex]\text{Probability}=\dfrac{25}{51}[/tex]
So, the probability that both cards selected for black is
[tex]\text{Probability}=\dfrac{1}{2}\times \dfrac{25}{51}[/tex]
[tex]\text{Probability}=\dfrac{25}{102}[/tex]
Therefore, the required probability is [tex]\dfrac{25}{102}[/tex].
The elves are loading all of the toys from Santa's workshop to the sleighs. They filled 2 small sleighs and 9 big sleighs with 241 toys. Later, they filled 14 small sleighs and 13 big sleighs with 437 toys. How many toys can fit on each type of sleigh?
Answer:
2*9=18 14*13=182 18+182=200
Step-by-step explanation:
well you multiply 2 times 9 and you get 18 and then you multiply 14 times 13 and you get 182 and then you 18+182 and that will give you 382.
How much money will i get in 5.4 hours if i get $4 per 6 hours
Answer:
3 dollars and 60 cents
Step-by-step explanation:
Wrote a linear function f with the values f(-4)=0 and f(4)=2
Answer:
y = (1/4)x + 1
Step-by-step explanation:
The points mentioned are (-4,0) and (4,2).
We can find the slope m:
(2-0)/(4-(-4)) = 2/8 = 1/4
We now have the equation y = (1/4)x + b
Now we must find the y-intercept.
Plugging in the first point:
0 = (1/4)*(-4) + b
0 = -1 + b
1 = b
y = (1/4)x + 1
Company a charges 60$ plus 0.15 per mile company b charges 25$ per day or portion of a day .Jason has determined that it will cost him less to rent a car from company a for a weekend trip .is Jason's conclusion accurate?
Answer:
No
Step-by-step explanation:
A: C = 60 + 0.15m (C is total cost and m is no. of miles)
B: C = 25d (d is no. of days)
For a weekend trip, there are 2 days.
This means that the cost for B is 2*$25, which is $50.
It doesn't matter how many miles are driven for A because the cost will always be at least $60.
This means that B is cheaper and that Jason is inaccurate.
6) A climber is on a hike. After 2 hours she is at an altitude of 400 feet. After 6 hours, she is at an
altitude of 700 feet. What is her rate of change?
Answer:
Her rate of change is 75 ft/h
Step-by-step explanation:
Rate of Change
It measures how one quantity varies with respect to another. The second variable usually is the time.
The climber is hiking. We are given two points of her progress: At 2 hours, she is at 400 ft. This corresponds to the point (2,400).
At 6 hours, she is at 700 ft. This is the point (6,700)
The rate of change is the slope between these two points or the quotient of the variations of each variable:
[tex]\displaystyle m=\frac{700\ ft-400\ ft}{6\ h-2\ h}[/tex]
[tex]\displaystyle m=\frac{300\ ft}{4\ h}[/tex]
[tex]m=75\ ft/h[/tex]
Her rate of change is 75 ft/h
Is this correct if not correct me
Dawn purchased 6 quarts of motor oil for $14.12. What is the Unit Price per quart rounded to
the nearest cent?
Answer:
$2.35 per quart (rounded to nearest cent)
Step-by-step explanation:
6 quarts --- $14.12
1 quart --- [tex]\frac{1}{6}[/tex] × $14.12 = $2.35 (rounded to nearest cent)
Find the unknown of the following
Step-by-step explanation:
For 4.
4b + 2b + 3b = 180°< Sum of angles of triangle >
9b = 180°
b = 180° / 9
b = 20°
4b = 4* 20° = 80°
2b = 2* 20° = 40°
3b = 3 * 20° = 60°
For 5.
x = 64° + 45° <Exterior angle of a triangle is equal to the sum of two opposite interior angles>
x = 109°
Hope it helps :)
Given the vectors u and v.
On a coordinate plane, vector u has origin (0, 0) and terminal point (7, 8). Vector v has origin (0, 0) and terminal point (negative 3, 5).
What is u · v?
19
59
61
160
Answer:
A. 19
Step-by-step explanation:
edge 2020
The dot product of the vector u and v is 19 if option (A) is correct.
What is a vector?It is defined as the quantity that has magnitude as well as direction also the vector always follows the sum triangle law.
We have:
On a coordinate plane, vector u has an origin (0, 0) and terminal point (7, 8). Vector v has origin (0, 0) and terminal point (negative 3, 5).
Vector u = <(7-0, (8-0)> = <7, 8>
Siimilarly, v = <-3, 5>
u · v = (7×(-3)) + (8×5) = -21 + 40 = 19
Thus, the dot product of the vector u and v is 19 if option (A) is correct.
Learn more about the vector here:
brainly.com/question/8607618
#SPJ2
(-2/3)+3/4 Please help
Answer:
-17\12
Step-by-step explanation:
(b) Mrs. Young calculates that 5 nights will cost $1350. What is the percent error in Mrs. Young’s calculation? Round to the nearest percent. Show your work
Answer:
5 x 13,50= 6,750
Step-by-step explanation:
5,400 is the answer of the persentage. I subtracted 6,750 from 1350 and got 6,750
Cost of 1 night:-
[tex]\\ \sf\longmapsto \dfrac{1350}{5}[/tex]
[tex]\\ \sf\longmapsto \dfrac{270}{1}[/tex]
[tex]\\ \sf\longmapsto 270[/tex]
I need help with these too questions
Number 1
Number 2
Answer:
Step-by-step explanation:
-6n + 2.9 = 11
subtract 2.9 from both sides
-6n = 8.1
divide both sides by -6
n = -1.35
2/3n - 3 = 8
add 3 to both sides
2/3n = 11
multiply both sides by 3
2n = 33
divide both sides by 2
n = 16.5
hope this helps <3
Answer:
left side:
-6n = 11 - 2.9
-6n = 8.1
n = - 8.1/6
n = - 1.35
right side:
2/3 n = 8 + 3
2/3 n = 11
n = 33/2
n = 16.5
Solve the system of equations using the elimination method.
(8x +11y = 37
8x+y=7
Carle is cutting pieces of string that are exactly inches long. How many pieces can she cut from a ball of string that has 100 feet?
Answer:
Carle is cutting pieces of string that are exactly 24 3/8 inches long. How many pieces can she cut from a ball of string that has 100 feet? 1 foot= 12 inches. A) 49 pieces.Oct 14, 2016
Step-by-step explanation:
Can someone help with these two problems ?
Answer:
1. 6 cookies 2. 5/12 of the pan is left
Step-by-step explanation:
42/2=21
21(2/3)= 14
14-8=6
6 cookies were left
1/4+1/3= 3/12+4/12=7/12
5/12 of the pan is left
Answer:
1/2x42 = 21
42-21= 21x1/3= 7
21-7= 14
14-8= 6
santa got 6 cookies
2.85 tons when rounded to the nearest hundreds
Answer:
0
Step-by-step explanation:
Find an equation of the line that passes through the point (23, 22) and is
parallel to 2x=3-5y
Answer:
The equation of the line is y= -2/5x+156/5
Step-by-step explanation:
y=mx+b
m= -2/5 ( 23,22)
y-y=m(x-x¹)
y-22=-2/5(x-23)
y-22=-2/5x+46/5
+22 +22
y= -2/5x+156/5
1)A student earned a grade of 80% on a math test that had 60 problems. How many
problems on this test did the student answer correctly?
Answer:
48
Step-by-step explanation:
80% = .8
60 x .8 = 48
Answer: 48
Step-by-step explanation:
80% of 60 or 80/100 x 60 = 48