Answer:
S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }
Step-by-step explanation:
Remember that the distance between two points (a, b) and (c, d) is given by:
[tex]distance = \sqrt{(a - c)^2 + (b - d)^2}[/tex]
So, here we have that the distance between the point (x, y) and the origin, (0, 0) must have a magnitude of 5 units, then we want to solve:
[tex]5 = \sqrt{(x - 0)^2 + (y - 0)^2} \\5 = \sqrt{x^2 + y^2}[/tex]
If we square both sides, we get
[tex]5^2 = (\sqrt{x^2 + y^2} )^2\\25 = x^2 + y^2[/tex]
Now we want to find all the points (x, y) that meet this condition, suc that:
x ∈ Z
y ∈ Z
So both x and y must be integers.
So here we can just play with different values of x and y.
For example, if we define:
x = 0 we get:
25 = 0^2 + y^2
25 = y^2
√25 = y
Then we can have y = 5 or y = -5
from this we got two points:
(0, 5) and (0, - 5)
if x = 1 we have:
25 = 1^2 + y^2
25 - 1 = y^2
24 = y^2
There is no integer such that its square is equal to 24, so we can stop here.
if x = 2 or - 2, we have:
25 = 2^2 + y^2
25 = 4 + y^2
25 -4 = 21 = y^2
Again, there is no integer such that its square is equal to 21, so we can stop here.
if x = +3 or -3, we have:
25 = 3^2 + y^2
25 = 9 + y^2
25 - 9 = 16 = y^2
√16 = y
then we can have y = 4 or y = -4
from this we got four points:
(3, 4)
(-3, 4)
(3, -4)
(-3, -4)
And for symmetry, if x = 4 or -4 we have the points:
(-4, 3)
(4, 3)
(-4, -3)
(4, -3)
finally, again for symmetry, if we take x = 5 or x = -5 we have the points:
(5,0)
(-5, 0)
Concluding, the set of all possible values (x, y) is:
S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }
I need help asap!!!! 13 points
If IK is the whole length of the line segment, then IJ + JK = IK.
IJ + JK = IK
(3x - 5) + (2x - 1) = (3x + 2)
3x + 2x - 5 - 1 = 3x + 2
5x - 6 = 3x + 2
2x - 6 = 2
2x = 8
x = 4
Now that we know the value of x, we can plug this value back into the expression for JK and evaluate.
JK = 2x - 1
JK = 2(4) - 1
JK = 8 - 1
JK = 7
Hope this helps!
What is the area of this tile?
Use inch or inch^2 for this problem.
Answer:
24 in^2
Step-by-step explanation:
To get the area of a triangle, multiply the base and height, then divide by 2.
Base=6
Height=8
6*8/2=48/2=24
24 in^2
Answer:
24 inch^2
Step-by-step explanation:
6 times 8 equals 48
Divide that by 2 and get 24
Area of Triangle is A=1/2bh
Can I get Brainliest, please!
A cyclist travels 8 km from home to the park. She leaves home at 10:15 and arrives at the park at 10:30. What is her average speed in km/h?
Answer:
speed = 32km/hr
Step-by-step explanation:
Time
10:15 to 10:30 = 1/4 hr
speed = distance/time
speed = 8 / (1/4)
speed = 32km/hr
Total health care costs in the United States in 2016 was $1.7 trillion. he US population was 290.9 million. What was the average amount spent per person on health care?
Answer:
$5,843.9
Step-by-step explanation:
2016
Total health care cost in US = $1.7 trillion
= $1,700,000,000,000
Population in US = 290.9 million.
= 290,900,000
Average amount spent per person on health care = Total health care cost in US / Population in US
= 1,700,000,000,000 / 290,900,000
= $5843.9326228944
Approximately,
$5,843.9
To the nearest whole number
= $5,844
Write the equations of two lines passing through (4,8)
Answer:
Two lines that pass through the point (4, 8) are y = 3·x - 4 and y = -5·x + 28
Step-by-step explanation:
The equation of two lines that passes through the point (4, 8) are found using the general form of a straight line equation, y = m·x + c, where;
m = The slope of the line
c = The y-intercept
Therefore, two distinct line pass through a given point if they have a different slope, m, and a different y-intercept, c, as follows;
Fot the given point, the x-value = 4, and the y-value = 8, we get;
8 = m₁·4 + c₁...Line 1 and
8 = m₂·4 + c₂...Line 2
m₁ ≠ m₂
If we set m₁ = 3, for line 1, we get;
8 = 3 × 4 + c₁ = 8 = 12 + c₁
∴ c₁ = 8 - 12 = -4
c₁ = -4
The equation for Line 1 for all x and y-values, where, m₁ = 3, c₁ = -4, becomes;
y = 3·x - 4
The equation for Line 2 where m₂ = -5 for example, we have;
8 = -5 × 4 + c₂
∴ c₂ = 8 + 5 × 4 = 28
c₂ = 28
The general form for the equation for Line 2 becomes;
y = -5·x + 28
Therefore;
The equation of the two formed lines that pass through the point (4, 8) are;
y = 3·x - 4 and y = -5·x + 28
what is the effect on the graph of f(x) if it is changed to f(x)+7, f(x+7) or 7f(x)
Answer:
it changed to f(x)+7 because it has an asymptote of 7
Help ASAP please!!!!!!!!!
Answer:
1/4
Step-by-step explanation:
pitches >3
pitches=4,5
P=(15+10)/(15+20+40+15+10)=1/4
PLEASE help me! 50 Points
What is the Inverse of
Answer:
hmm what could it be I DNT kno
a shop sells three types of boots (football, rugby and hiking) sales are usually in the ratio 6:2:3
last month 24 pairs of football boots were sold
how many boots altogether were sold last month
Answer:
44
Step-by-step explanation:
divide 24 by 6 then multiply it by all the number then add it all
please make me brainliest
The first file is the question, 2nd is the answer choices; this question has stumped me.
Answer:
ans: option b
Step-by-step explanation:
remember that,
For matrix addition or subtraction of two or more matrices must have same order and only operation done with corresponding elements,
if you find helpful make it brainlist
Which of the following functions represent exponential decay and has a y-
intercept of 2?
O y = {(0.85)*
O y = (2)*+2
O y = 4 (2)*
O y = 2(3)*
Answer:
Non of the given options
A function that represent an exponential decay and 2 as the y-intercept is y = 0.85ˣ + 1
Step-by-step explanation:
An exponential decay function is a function that reduces in magnitude at a constant percentage rate, r (< 1)
An exponential decay can be represented by the formula, y = a·(1 - r)ˣ
Therefore, the growth factor, (1 - r) = b is less than 1 for an exponential decay
Therefore the function that represent an exponential decay is y = 0.85ˣ, while a function that represent an exponential decay and has a y-intercept of 2 is y = 0.85ˣ + 1. therefore, non of the options
13. Jimmy is writing a paper for one of his classes. The paper has to be 3,000 words
long, and so far he has written 696 words. If he only has 6 more days to write
his paper and wants to write the same number of words each day, then how
many words must he write per day to finish the paper?
Answer:
384 words per day
Step-by-step explanation:
If he already wrote 696 words out of 3,000 words, then he has another 2,304 words left to write. To know how many words he needs to write each day for the next 6 days, then we need to divide 2,304 words by 6. The quotient thus becomes 384 words.
Answer:
384 words per day
Step-by-step explanation:
3000-696=2304
So 2304 divided by 6 =348
72 x 24 in algorithm
The spinner depicted is a fair spinner. The spinner is least likely to land on which number?
A 1
B 2
C 3
D It is impossible to tell.
Answer:
d
Step-by-step explanation:
it is impossible to tell since no numbers were given nor signs were offered to help us know whether we are dealing with additon , subtraction , multiplication or division
Find the surface area of a cylinder with a height of 7 feet and base radius of 4 feet. ,_____ square feet
Answer:
276.32
Like I have explained in a prev. Question of yours.
Answer:
The surface area of cylinder is 276.32 feet²
hope it helps
have a nice day
Solve 17 and 18 please.
Answer:
Step-by-step explanation:
17.
sin20° = [tex]\frac{1}{x}[/tex]
x = 1 ÷ sin20°
x ≈ 2.9238
cos20° = [tex]\frac{x}{y}[/tex]
y = x ÷ cos20°
y ≈ 2.9238 ÷ cos20° ≈ 3.11
18.
x = 2√3 ≈ 3.46
y = √3 ≈ 1.732
help mee
x=
a.8
b. 9
c. 10
Answer:
A
Step-by-step explanation:
The formula is 5*x=4*10. Then simplify to 5*x=40. Divide both sides by 5. x=8
Rewrite the following quadratic function in vertex form. Then, determine if it has a maximum or minimum and say what that value is.
y = -x 2 + 6x + 5
HELP PLEASE!!!!!!
Answer:
-(x-3)²+14
maximum
(3,14)
Step-by-step explanation:
y= -x²+6x+5
y-5= -x²+6x
y-5= -(x²-6x)
complete the square
y-14= -(x²-6x+9)
x²-6x-9= -(x-3)²
y-14= -(x-3)²
y= -(x-3)²+14
maximum because a is negative
vertex is (3,14)
differentiate between interest and interest rate
Answer:
Interest:Interest is the cost of borrowing money, and the money you earn from your savings.
Interest rateInterest rates indicate this cost or return as a percentage of the amount you are borrowing or lending (since you are “lending” your savings to the bank)
❤◍ jess bregoli ◍❤#keep learning!!
pls ans this
its urgent
Explain two procedures that you can use to draw two adjacent complementary angles. Then draw a pair of adjacent complementary angles so that one angle has a measure of 30°.
Answer:
Complementary angle of 30° is 60°.
Step-by-step explanation:
The complementary angles are the angles whose sum is 90.
If one angle is x then the other angle is 90 - x, they both are complementary to each other.
One angle is 30°, so the other angle is 90° - 30° = 60°
if you can bake 14 cupcakes in one hour how long will it take to bake 126 cupcakes?
Answer:
9 hours
Step-by-step explanation:
126 dived by 14 is 9, so it will take 9 hours to bake 126 cupcakes.
Answer: It will take maybe 9 hours
hope this helps :)
Step-by-step explanation:
Someone please help me It’s getting late and it’s due tomorrow
Explain why the equation
1- x= 5(x - 4) - 6x has no solution.
Answer:
After the distribution of the 5 and the addition of x to both sides, the x variable is cancelled out leaving 1 = - 20.
This statement is false. Hence, no solution
Step-by-step explanation:
1 - x = 5(x - 4) - 6x (Distribute 5)
1 - x = 5x - 20 - 6x (Combine like terms)
1 - x = -x - 20 add x to both sides
1 = - 20 False
How would you describe the channel of distribution for Coke using the BreakMate?
Answer:
Yes
Step-by-step explanation:
1. What
2. Even if that's an actual question, it doesnt make any sense
3. What
4. Even if that's an actual question, it's not math related
5. What
Please help and thank you
a. Label another angle whose measure is 76º.
b. Explain how you know this angle has the same measure.
Answer:
Angle QRS
Step-by-step explanation:
because PQ is parallel to RS, angles PQR and QRS are alternate interior angles so theyre equal
The graphs below have the same shape. What is the equation of the blue graph ?
Answer:
A G(x) = (x - 5)²
Step-by-step explanation:
Plug in x = 5 into the given choices
only G(x) = (x - 5)² correctly returns G(5) = 0
Find the next three terms of the sequence 3,9,27,81,...
Answer:
243, 729, 2187
Step-by-step explanation:
Multiply the previous with 3
It's Geometric sequence
Brainliest please~
With three people living together, how will the rent and other expenses be split?
Answer:
Everything will be split in threes. You can do this by either multiplying the cost by 1/3 or dividing by 3.
Step-by-step explanation:
Solve for x
-6/5x-4=-46
Answer:
x = 35
Step-by-step explanation:
-6/5x-4=-46
Add 4 to each side
-6/5x-4+4=-46+4
-6/5x=-42
Multiply each side by -5/6 to isolate x
-5/6 * -6/5x=-42 * -5/6
x = 35
Answer:
x = 35
Step-by-step explanation:
-6 / 5x - 4 = - 46
Add 4 to each side
- 6 / 5 x - 4 + 4 = - 46 + 4
- 6 / 5 x = - 42
To find x, multiply 42 by 5 and then divide by 6.
x = 42 × 5 / 6
x = 7 × 5
x = 35
and angle is 21 more than twice its complement find it
Answer:
angle = 67°
Step-by-step explanation:
let
a = angle in degrees
(90-a) = complement
given
a = 2(90-a)+21
Solve for a
a = 180 - 2a + 21
3a = 201
a = 67°
