Answer:
1) We can rewrite the equation as 15=(x-5)^2
2) The solutions to the equation are x=5±15
Suppose I randomly choose 4 distinct integers between 1 and 60. Is it true, or is it not true, that at least 2 of them must differ by no more than 19.
Answer:
It’s true
Step-by-step explanation:
Proof by induction
Let the four chosen numbers be x_1, … x_4 and, without loss of generality, let x_1 < x_2, … < x_4.
For x_1 = 1, the smallest possible choice, let x_2 = x_1 + 20 = 21 be the smallest possible choice that has a difference larger than 19. Likewise, x_3 = x_2 + 20 = x_1 + 40 = 41. Then x_4 has to be at least x_3 + 20 = x_1 + 60 = 61 which is out of range.
For the induction, suppose that x_4(n) = x_1(n) + 60 > 60 and therefore x_4(n) can’t be chosen for a given x_1(n). Then incrementing x_1(n+1) = x_1(n) + 1 would require x_4(n+1) to be at least x_1(n) + 1 + 60 = x_4(n) + 1 > 61, so this is out of range as well.
For another induction, suppose that x_4(n) = x_2(n) + 40 > 60 and therefore x_4(n) can’t be chosen for a given x_2(n). Then incrementing x_2(n+1) = x_2(n) + 1 would require x_4(n+1) to be at least x_2(n+1) + 40 = x_4(n) + 1 > 61, so this is out of range as well.
Likewise, for the induction, suppose that x_4(n) = x_3(n) + 20 > 60 and therefore x_4(n) can’t be chosen for a given x_3(n). Then incrementing x_3(n+1) = x_3(n) + 1 would require x_4(n+1) to be at least x_3(n+1) + 20 = x_4(n) + 1 > 61, so this is out of range as well.
Therefore all choices of x_1, x_2, x_3 with differences greater than 19 leaves no choice of x_4 within range with x_4 > x_3 + 19.
40 is 20 of what number
[tex]\huge\text{Hey there!}[/tex]
[tex]\large\text{40 is 20\% of what time number?}\\\\\\\bullet \large\bold{We\ are\ looking\ for\ your\ UNKNOWN\ number; we\ can\ the\ value}\\\large\bold{is\ \underline{a}\ for\ our\ answer!}\\\bullet\large\bold{REMEMBER: Percentages\ are\ out\ 100\ \& the\ word\ \underline{of}\ means\ \underline{multiply}}[/tex]
[tex]\huge\text{NOW LETS SOLVE FOR YOUR ANSWER!}[/tex]
[tex]\bold{Equation: 20\%\ \times \ a\ =\ 40}\\\\\bold{a = \dfrac{40}{20\%}}}\\\\\bold{20\% = \dfrac{20}{100}\rightarrow 0.2}}}\\\\\bold{Equation: a = \dfrac{40}{0.2}}\\\\\bold{\dfrac{40}{0.2}=200}\\\\\bold{a=200}\\\\\boxed{\boxed{\bold{Answer: 200}}}\huge\checkmark[/tex]
[tex]\large\textsf{Good luck on your assignment and enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Name the property of addition modeled here. If a = b, then a + c = b + c. A. Addition Property of Equality B. Commutative Property of Addition C. Associative Property of Addition D. None of the above I think it is either B or C
Answer: I'm pretty sure it's B
Step-by-step explanation:
Answer:
Do you still need an answer? If so, B!
Step-by-step explanation:
Just by looking at the equation you can see the addition symbols. Since there are also letters, you can use that information to help you solve the answer using the key word: Commutative.
For Example: If Lily needs $40 and she already has $30 how many more dollars does she need?
Answer: m-$30=$40 m=$10
Ursula likes to kayak. She uses the equation y=4x to calculate how far she has traveled, where y represents the number of miles traveled, and x represents the number of hours spent kayaking.
How many hours must Ursula kayak to travel 10.4 miles?
2v+7=3
Help me out
I’m dating vinnie hacker
Answer:
v= -2
Step-by-step explanation:
2v+7=3 ------> 2v = 3 - 7 ----------> 2v = -4 ( divide by 2)
v = -2
5r + 2(3r - 1) = -46
please show the work
Answer:
R = - 4
Step-by-step explanation:
5 r + 6r - 2 = - 46
11 r - 2 = - 46
11 r = - 46 + 2
11 r = - 44
r = - 4
Can someone help me please :)
Step-by-step explanation:
the answer is in the attachment.
Work out the size of angle x
Next to 164 and 90
Answer:
x=106 degrees
Step-by-step explanation:
I'm going to assume that this is a circle since you didn't give it to me
So you want to add 164 and 90 together and subtract the sum by 360
360-(164+90)=106
So you want to use PEMDAS (order of operations) to solve this
so do what's in the perenthesis first so 164+90=254Then you want to subtract 254 from 360 so 360-254=106x=106 degrees
N/-3 - 2 = 8 n=___ help
Answer:
-30
Step-by-step explanation:
[tex]\frac{N}{-3} -2 =8[/tex] ( Add 2 on both sides)
[tex]\frac{N}{-3} = 10[/tex] ( Multiply by -3 on both sides)
[tex]N = -30[/tex]
Verify:
[tex]\frac{-30}{-3} =10[/tex] (Correct)
Answer:
[tex] \frac{n}{ - 3} - 2 = 8 \\ \frac{n}{ - 3} = 8 + 2 \\ = 10 \\ n = 10 \times - 3 \\ n = - 30[/tex]
Cards in a pack are black or red in the ratio
black: red = 2:5
What fraction of the cards are red?
Ovo
Three coins are tossed simultaneously 350 times. The distribution of various outcomes is listed below :Outcome3 Tails2 Tails1 TailNo TailsNo. Of times65 95 110 80 respevtove;y Compute the probability of getting:(i)At least 1tail(ii) Exactly 3 heads
Answer:
(i) [tex]\frac{27}{35}[/tex]
(ii) [tex]\frac{8}{35}[/tex]
Step-by-step explanation:
Probability refers to chances of occurrence of any event.
Probability is calculated by dividing number of favorable outcomes by total number of possible outcomes.
Total number possible of outcomes = 350
(i)
Number of favorable outcomes = [tex]65+95+110=270[/tex]
Probability [tex]=\frac{270}{350}=\frac{27}{35}[/tex]
(ii)
Exactly 3 heads is equivalent to no tails.
Number of favorable outcomes = [tex]80[/tex]
Probability [tex]=\frac{80}{350}=\frac{8}{35}[/tex]
Evaluate (c^-2)^0 where c=4
Answer:
1
Step-by-step explanation:
Any value to the power of 0 is equal to 1.
[tex](c^-^2)^0=(4^-^2)^0=(\frac{1}{16} )^0= 1[/tex]
13. Find AC. PLEASEE I NEED HELP!!!!!
Help me I’ll mark brainliest please
Answer:
I don't know sorry but I really want brainliest
Factor the algebraic expression. 9a+21
Step-by-step explanation:
1. factor 3 out of 9a + 21
answer: 3(3a + 7)
A car is parked 80 feet from the base of a 120-foot building. What is the angle of depression from the top of the building to the car? Round your answer to the nearest degree.
A 48° degrees
B 34° degrees
C 42° degrees
D 56° degrees
A worker on the production line is paid a base salary of $170 per week plus $1.21 for each unit produced. Write an equation to represent his earnings of $491.86 for a week when he produced x units. How many units did he produce? Use pencil and paper. If the worker had produced twice that number of units, what would his earnings have been? Show your work.
Answer:
Part 1)
$170 + $1.21x = $491.86
Part 2)
170 + 1.21x + 491.86
1.21x = 491.86 - 170
1.21 x = 321.86
1.21x/ 1.21 = 321.86/ 1.21
x = 266 units produced
Part 3)
Twice that number of units = 266 x 2 = 532
$170 + ($1.21 x 532) =
$170 + $643.72 = $813.72
Find the 3rd term in the sequence
cell phone provider offers a plan that costs $40 per month plus $0.20 per text message sent or received. A comparable plan costs $70 per month but offers unlimited text messaging.
Answer:
the second one is the better deal
Step-by-step explanation:
plssssssssssssssssss hellllllllllp meeeee
Answer:4b+5=1+5b
Step-by-step explanation: b= 14b I HOPE THIS HELPS AND HAVE A GOOD DAY!!!! And i really do hope this did help.
Evaluate: ab+a^2, if a=937 and b=63
The value of expression ab + a² is, 9,37,000
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The expression is,
⇒ ab + a²
And, a = 937, b = 63
Now, Substitute the value of a and b in expression as,
⇒ ab + a²
⇒ 937 × 63 + 937²
⇒ 937 (63 + 937)
⇒ 937 × 1,000
⇒ 9,37,000
Learn more about the mathematical expression visit:
brainly.com/question/1859113
#SPJ2
HELP PLEASE PLEASE PLEASE
1. A lawncare worker charges $45 per hour of work.
additional fee of $20 for equipment transportation.
A. Write an equation in slope-intercept form for this
situation
B. Il your total bill was S155, how long did the worker fix
your yard?
C. If the lawncare worker works a full 8-hour shift, how
much does he make
Three friends went to Texas Roadhouse for dinner. The total bill was $76.25. They left the server a 20% tip and the Montgomery County tax rate is 9.5%.
Answer:
$68.24
Step-by-step explanation:
Three friends went to Texas Roadhouse for dinner. The total bill was $76.25. They left the server a 20% tip and the Montgomery County tax rate is 9.5%.
Given data
The total bill was $76.25
tip
=20/100*76.25
=0.2*76.25
=15.25
Tax
=9.5/100*76.25
= 0.095*76.25
=$7.24375
In all the bills is 76.25-15.25+7.24375
=61+7.24375
=$68.24
What is the conjugate of the product (2 - i)(1+2i)?
Answer:
4-3i is the answer.......
Explanation
Product
(2-i)(1+2i) = 2+4i-i-2i²
= 2+4i-i+2
= 4+3i
conjugate of 4+3i is 4-3i
The budget for a school dance is 370.00. The band charges $65.00 per hour. What is the maximum number of hours the school can have the band play at the dance?
Evaluate expression below if t=3
2t+7-t+1
Answer:
doo doo fart
Step-by-step explanation:
Answer:
11
Step-by-step explanation:
If g(x)=5/4x-7 what is the value of g(12)
Answer:
g(12) = 8
Step-by-step explanation:
g(x) = 5/4(12) - 7
g(x) = 5 × 3 - 7
g(x) = 15 - 7
g(x) = 8
i hope this helps :)
Ben has $19 to spend. He spent $7.25, including tax, to buy a notebook. He needs to save $2.75 but he wants to buy a snack. If pretzels cost $0.50 per package including tax, what inequality would show the maximum number of packages that Ben can buy?
PLS HELP ASAP:
- what is the INEQUALITY FOR THIS PROBLEM. THAT'S ALL IM ASKING. DON'T SOLVE IT.
Answer:
($19 - $7.25) - $2.75 ÷ (0.50p) ≤ 19
Step-by-step explanation:
First, let's define the variable:
p = pretzel packages
Let's first find out how much money Ben has after buying the notebook.
$19 - $7.25 = $11.75
So, we know that Ben has $11.75 left.
The inequality would be: ($19 - $7.25) - $2.75 ÷ (0.50p) ≤ 19
Help Needed! What is the value of x in the triangle? A. 21 B. 10 C. 7 D. 7√3
Answer:
21
Step-by-step explanation:
Decide which item is the better purchase in each scenario below. In addition, state how much you will save per item. Brayden was looking to purchase apples; 5 lbs for $2.89 or 7 lbs for $3.25
Answer:
7 pounds for 3.25
Step-by-step explanation:
7 pounds of apples is alot for a cheap price like 3.25