Answer:
Solution: x=5, y=4
Step-by-step explanation:
System of Equations
We need to solve:
- 5x + 9y = 11
x - 3y = - 7
There are several ways to solve a system of linear equations. We'll take advantage of the second equation since it has the x with coefficient 1 and solve it for x:
x = - 7 + 3y
Now replace it into the first equation:
- 5(- 7 + 3y) + 9y = 11
Operate:
35 - 15y + 9y = 11
Simplify:
35 - 6y = 11
Rearrange:
- 6y = 11 - 35 = -24
Solve:
y = -24 / -6
y = 4
Finally, since
x = - 7 + 3y
x = - 7 + 3*4
x = - 7 + 12
x = 5
Solution: x=5, y=4
Suppose we want to choose 5 colors, without replacement, from 16 distinct colors.
Complete question is;
Suppose we want to choose 5 colors, without replacement, from 16 distinct colors.
A) How many ways can this be done, if the order of the choices is taken into consideration?
B) How many ways can this be done, if the order of the choices is not taken into consideration?
Answer:
A) 524160 ways
B) 4368 ways
Step-by-step explanation:
A) If the order of choices is taken into consideration, then it is a Permutation problem.
Formula for Permutation is;
P(n, r) = n!/(n - r)!
In the question, n = 16 and r = 5
Thus;
P(16, 5) = 16!/(16 - 5)!
P(16, 5) = 524160
B) If the order of choices is not taken into consideration, then it becomes a Permutation problem.
Formula for Combination is;
C(n, r) = n!/((r! × (n - r)!)
C(16, 5) = 16!/((5! × (16 - 5)!)
C(16, 5) = 4368
The terminal side of angle θ intersects the unit circle in the first quadrant at (925,y). What are the exact values of sinθ and cosθ?
Correct question is;
The terminal side of angle θ intersects the unit circle in the first quadrant at (9/25,y). What are the exact values of sinθ and cosθ?
Answer:
sinθ = (√544)/25) and cosθ = 9/25
Step-by-step explanation:
We are given that (9/25,y) lies on the unit circle. Thus, from general representation of equation of a circle, we can write that;
(9/25)² + y² = 1²
y² = 1 - (9/25)²
y² = (625 - 81)/25²
y² = 544/25²
y = ±(√544)/25
We are told the point is in the first quadrant and so we will choose the positive value of y = (√544)/25.
Therefore, the terminal side of the angle θ intersects the unit circle at [9/25, (√544)/25)]
In unit circle geometry, cosθ = x, while sinθ = y.
Thus; sinθ = (√544)/25) and cosθ = 9/25
The exact value of [tex]sin\theta[/tex] and [tex]cos\theta[/tex] is [tex]cos\theta = \frac{9}{25} , sin\theta = \frac{\sqrt{544} }{25}[/tex] and this can be determined by forming the equation of circle.
Given :
The terminal side of angle [tex]\theta[/tex] intersect at unit circle ([tex]\frac{9}{25}, y[/tex]).
From general representation of equation of circle , we can write
[tex]x^{2} + y^{2} = a^{2}\\[/tex]
[tex](\frac{9^{2} }{25^{2} })[/tex] + [tex]y^{2} = 1^{2}[/tex]
[tex]y^{2} = 1 - \frac{81}{625}[/tex]
[tex]y^{2} = \frac{625-81}{625}[/tex]
[tex]y^{2}=\frac{544}{625}[/tex]
Taking square root both sides
[tex]y= \frac{\sqrt{544} }{\sqrt{625} }[/tex]
[tex]y = \frac{\sqrt{544} }{25}[/tex]
We are taking only because point lies in first quadrant.
The terminal side of angel [tex]\theta[/tex] unit circle in first quadrant at [tex](\frac{9}{25} , \frac{\sqrt{544} }{25})[/tex]
In unit circle
[tex]x = cos\theta , y = sin\theta[/tex]
[tex]\rm cos\theta = \frac{9}{25} , sin\theta = \frac{\sqrt{544} }{25}[/tex].
For more information click on the link gives below
https://brainly.com/question/23841023
7. The population of Canada is about 37.59 million. How is this number written in scientific
notation?
(Please hurry)
Answer:
3.759*10^7
Step-by-step explanation:
Question 3: Determine the missing base in the equation problem below. 75eight = 23 base
Answer:
29
Step-by-step explanation:
Given the expression [tex]75_8 = 23_x[/tex] where x is the unknown base:
[tex]75_8 = 23_x\\7\times8^1 +5\times8^0 = 2\times x^1+3 \times x^0\\56+5 = 2x+3\\61 = 2x+3\\2x = 61-3\\2x = 58\\x = 58/2\\x = 29[/tex]
Hence the missing base is 29
Troy and Lisa were shopping for school supplies. Each purchased different quantities of the same notebook and thumb drive. Troy bought five notebooks and five thumb drives for $110. Lisa bought three notebooks and five thumb drives for $102. Find the cost of each notebook and each thumb drive.
Answer:
Notebooks cost $4
Thumb drives cost $18
Step-by-step explanation:
x=$ for notebooks
y=$ for thumb drives
5x + 5y = 110 ----> for Troy
3x + 5y = 102 ----> for Lisa
Use subtraction to find x.
(5x + 5y = 110)
-(3x + 5y = 102)
_____________
2x + 0y = 8
2x = 8
x=4
Sub 4 for x into 5x + 5y = 110
20 + 5y = 110
-20 -20
___________
5y = 90
y=18
Notebooks cost $4
Thumb drives cost $18
wha is 3 3/5 *(-8 1/3)=
Answer: -24/5
3 3/5*(-8 1/3)=-24/5
Kai needs a car to get to work and school. He's decided on a used car with a cost of $12,000. According to his budget he can afford to pay up to $300 per month and car payments. Which loan offer is best for Kai?
Answer:
The answer is Offer 3 because it has the lowest total loan cost of the offers with a monthly payment in his budget
Answer: c, offer 3
Step-by-step explanation: just did the quiz
List coordinates for A' if A(2,3) is rotated 180°.
a
(2, -3)
b
(-2, -3)
c
(-3, -2)
d
(-3, 2)
If 10x - 2 represents the time Anna and Tamara leave tonight and 4x - 9 represents
the time Anna and Tamara would leave in the morning, write an algebraic
expression that represents the difference in the time between leaving at night and
leaving in the morning.
Time
✓ Check
Answer:
6x + 7
Step-by-step explanation:
Given parameters:
Time Anna and Tamara leaves tonight = 10x - 2
Time Anna and Tamara leaves in the morning = 4x - 9
Unknown:
An algebraic expression that represents the difference in time between leaving at night and leaving in the morning = ?
Solution:
The algebraic expression is given as:
= (10x - 2) - (4x - 9)
= 10x -2 -4x + 9
= 10x -4x -2 + 9
= 6x + 7
The algebraic expression for the time difference is 6x + 7
ax+by=c
solve for equation for y
Answer:
[tex]y=\frac{c}{b}-\frac{ax}{b}[/tex]
Step-by-step explanation:
[tex]ax+by=c\\ax+by-ax=c-ax\\by=c-ax\\by/b=(c-ax)/b\\y=\frac{c-ax}{b} \\y=\frac{c}{b}-\frac{ax}{b}[/tex]
is y=0.18.x proportional
Answer:
-50/9 is the answer i think
Challenge An arts academy requires there to be 3 teachers for every 51 students and 5 tutors for
every 55 students. How many students does the academy have per teacher? Per tutor? How many
tutors does the academy need if it has 88 students?
The academy has students per teacher.
Miss Johnson walks at a rate of 2 miles
per hour.
x = hour
y = miles walked
what is the constant of proportionality and equation?
Answer:
The constant of proportionality is 2 it is y=2x
Step-by-step explanation:
Each time the number goes up it goes up by two i hope this helps have a nice day
PLEASE HELP ASAP!)Carter graphs the equivalent ratios shown in the table. If one of the ordered pairs Carter graphs is (4,2), which other ordered pairs does he graph? Check all that apply.
Answer:
(8,4)
(16,8)
Step-by-step explanation:
The table is given which shows the number of yellow tiles and red tiles.
The first row in the table shows that if there are 4 red tiles then there will be 2 yellow tiles. This relation can be defined as the number of red tile will always be double the amount of number of yellows tiles. Carter graphs this point as (4,2) where number of red tiles are plotted on x axis and number of yellow tile are plotted on y axis.
Consider the second row of the table. Number of red tiles is 8 while number of yellow tiles is 4, so the point he plots on the graph is (8,4)
Similarly, other points are (12,6) and (16,8)
Each of the letters of the word MISSISSIPPI are written on separate pieces of paper that are then folded, put in a hat, and mixed thoroughly. One piece of paper is chosen (without looking) from the hat. What is the probability it is an I? *
2/5
1/3
4/11
1/4
Answer:1/4
Step-by-step explanation:
Which of the values from the set (-7, -6, -2, 0, 1, 3) satisfy the inequality-5x + 5< 25
Answer: -2, 0, 1, 3
Step-by-step explanation:
when you multiply -7 and -6 by -5 than add 5 you get a higher number than 25.
when you multiply -2, 0, 1 And 3 by -5 than add 5 you get a lower number than 25.
7(3-x) ≤ 5x-15 solve for x
Answer:
x≥3
Step-by-step explanation:
6 ≤ -3x + 12
can somone solve this for me *correctly* ill give u brainlest only if ur right
Answer:
x ≤ 2
Step-by-step explanation:
-3x+12≥6
-3x≥6
3x≤6
x ≤ 2
Answer:
x ≤ 2 is the correct answer!
Step-by-step explanation:
Hope this helps!
Given (-1, -8) & m=2
write the corresponding equation in SLOPE-INTERCEPT FORM (No caps, no spaces)
Answer:
y=2x+15
Step-by-step explanation:
just count from (-1,8) to get y intercept
what is 936,292 rounded to the nearest thousand
Answer:
936,000
Step-by-step explanation:
936,292 rounded to the nearest 1,000 is 936,000 as 292 is less than 500, you have to round down, to get 936,000.
Create 3 equivalent ratios for 5:7
Answer:
10:14
15:21
20:28
Step-by-step explanation:
Which statement describes how to determine if a relation given in a table is a function? OIf none of the output values are repeated, the relation is a function. Olf none of the input values are repeated, the relation is a function. If any of the input values are equal to the output values, the relation is a function. f all the output values are paired with the same input value. the relation is a function.
Answer: if none of the input values are repeated the real action is a function
Step-by-step explanation:
Answer:
B.
Step-by-step explanation:
If none of the input values are repeated, the relation is a function.
i dont know how to explain but edge 2020/2021
i need help asap please
Answer: The answer is 0.00065
Step-by-step explanation: Cuz I am good at math.
Of the 52 cards in the deck, four are aces and others (kings, queens, jacks, and tens) are worth 10 points each. The dealer has a blackjack if one card is an ace and the other is worth 10 points; it doesn't matter which card is face up and which card is face down. How many different blackjack hands are there?
Answer:
64 different black jack hands
Step-by-step explanation:
there are 4 aces in a deck, and you can score a blackjack if any of these 4 aces is paired with any of the 16 different cards that are worth 10 points. Total number of different blackjack combinations = 4 aces x 16 different tens = 64.
Even though the number of possible blackjack hands might seem large, the possibilities of actually getting one are really low:
possibility of getting 1 ace = 4/52 = 1/13
possibility of getting 1 ten = 16/51
possibility of getting a blackjack = 16 / 663
if you start with the 10 first the odds are the same:
possibility of getting 1 ten = 16/52 = 4/13
possibility of getting 1 ace = 4/51
possibility of getting a blackjack = 16 / 663
The square root of 1000 is between
A.498 and 502
B.98 and 102
C.48 and 52
D.28 and 32
Answer:
D
the square root of 1000 is 31.6227766017
Step-by-step explanation:
BRANIEST
PLEASE HELP!!!!!! PLEASE
Please help with this problem thank you.
-8 + n = 62 What is n?
Answer:
n = 70
Step-by-step explanation:
-8 + n = 62
n = 70
(i need this ASAP)
Which of the following is an
arithmetic sequence?
A 1, 3, 6, 10, 15, …
B −8, −11, −14, −17, −20, …
C 48, 24, 12, 6, 3, …
D 1, 12, 123, 1234, 12345, …
Answer:
A
Step-by-step explanation:
is there a need for explanation
9(k+12)+4k2 when k= 3 the 2 is small
Answer:
the answer is 4k^2+9k+108
Step-by-step explanation:
Answer:
171
Step-by-step explanation:
When you say "the 2 is small" I think you mean it's an exponent so the equation would look like....
[tex]9(k+12) + 4k^{2}[/tex]
if k=3 we would replace all the k's with 3.
9(3+12) + 4(3)²
9(15) + 4(9)
135 + 36
171
So the answer would be 171
Hope that helps and have a great day!
4 x 234567890123456789
Answer:
Step-by-step explanation:
9.3827156E17 the awnser
Answer:
pop smoke ting go skrdraaaa pop. po pop pop popskibbydo pop pah
