Explanation: I would use the substitution method for this system
because one of the variables, x, is already isolated in the first equation.
Since our first equation states that x = 12 - y, 12 - y can be substituted
in for x in the second equation which becomes 2(12 - y) + 3y = 29.
Now we can solve this equation by first distributing the 2
through the parentheses to get 24 - 2y + 3y = 29 and you
should be able to easily finish solving from here to get y = 5.
Now substitute a 5 back in for the first equation to get
x = 12 - (5) or x = 7 which means that our solution is (7, 5).
Insert the missing number.
4
6 9 14
23
40
?
138
266
Answer: The missing number is 73
Step-by-step explanation:
Given:
4, 6, 9, 14, 23, 40, ?, 138, 266
Solve:
First, we try arithmetic patterns.
6 - 4 = 2
9 - 6 = 3
14 - 9 = 5
23 - 14 = 9
40 - 23 = 17
Clearly, there aren't arithmetic patterns.
Then, try through multiplication, exponents, and combination.
Finally, the pattern is multiplied by 2 on each number, then subtract 2 starting with 4 and add 1 for each increasing number.
4×2-2=6
6×2-3=9
9×2-4=14
As it goes on, the missing number would be:
40×2-7=73
Hope this helps!! :)
Please let me know if you have any questions
At a Noodle & Company restaurant, the probability that a customer will order a nonalcoholic beverage is . 43. Find the probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.
Answer:
0.8716 = 87.16% probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.
Step-by-step explanation:
For each customer, there are only two possible outcomes. Either they order a nonalcoholic beverage, or they order an alcoholic beverage. The probability of a customer ordering a nonalcoholic beverage is independent of any other customer, which means that the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
In which [tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by the following formula.
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
And p is the probability of X happening.
At a Noodle & Company restaurant, the probability that a customer will order a nonalcoholic beverage is 0.43.
This means that [tex]p = 0.43[/tex]
Find the probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.
This is:
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)[/tex]
In which
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{7,0}.(0.43)^{0}.(0.57)^{7} = 0.0195[/tex]
[tex]P(X = 1) = C_{7,1}.(0.43)^{1}.(0.57)^{6} = 0.1032[/tex]
[tex]P(X = 2) = C_{7,2}.(0.43)^{2}.(0.57)^{5} = 0.2336[/tex]
[tex]P(X = 3) = C_{7,3}.(0.43)^{3}.(0.57)^{4} = 0.2937[/tex]
[tex]P(X = 4) = C_{7,4}.(0.43)^{4}.(0.57)^{3} = 0.2216[/tex]
Then
[tex]P(X < 5) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) = 0.0195 + 0.1032 + 0.2336 + 0.2937 + 0.2216 = 0.8716[/tex]
0.8716 = 87.16% probability that in a sample of 7 customers, fewer that 5 will order a nonalcoholic beverage.
Write a function rule for the table. (Help please)
is it a,b,c or d
1. A football goal post casts a shadow 120 inches long. You are 5 feet 6 inches tall and cast a shadow 16.5 inches long. Find the height of the goal post in feet. Round your answer to the nearest whole number.
Answer:
40 feets
Step-by-step explanation:
Given that :
Person's height = 5feet 6 inches ;
Person's height in inches ;
1 foot = 12 inches ;
5 feets = (12 * 5) = 60 inches
Person's height = 60 + 6 = 66 inches
Height of person's shadow = 16.5 inches
Height of post shadow = 120 inches
Height of goal post = x
(Height of goal post / height of post shadow) = (person's height / person's shadow)
x / 120 = 66 / 16.5
Cross multiply :
16.5x = 120 * 66
16.5x = 7920
x = 7920 / 16.5
x = 480 inches
To feets ;
1 foot = 12 inches
480 inches = 480/12 feets = 40 feets
Is the answer option b?
Answer:
yes, it is B
Step-by-step explanation:
every input value of x has an unique result value y.
there are no 2 values for x that produce the same result value y.
and there are no multiple result values possible for a subject x value.
bottom line, yes, it is a function, and a 1:1 function at that.
what is the area of the composite shape?
Answer:
the ...ha answer is =99 in.^3
Find the missing side. Round your answer to the nearest tenth.
PLEASE HURRY!!
Answer:
x = 9.4m
Hope this helps...Have a good day!!
Given the center and radius, find equation of the circle
Answer:
[tex]{ \sf{ {(x - 2)}^{2} + {(y + 8)}^{2} = 4}}[/tex]
Answer:
Center is (2, -8) and radius =2
h = 2 and k = -8
Filling in this equation:
(x -h)² + (y -k)² = radius² we get:
(x - 2)^2 + (y--8)^2 = 2^2 which equals
(x-2)^2 + (y +8)^2 = 4
Source: http://www.1728.org/circleqn.htm
Step-by-step explanation:
Question 13 (5 points)
m_1 = (4x + 9)º and m_2 = (x - 14)° in the given figure. Find x.
Answer:
x=19°
Step-by-step explanation:
Line n and l form a right angle. We know that because line m and l are parallel to each other and line n crosses through them as a vertical line.
Right angles always add up to 90°.
So, Angle 1 add Angle 2 equals 90°.
4x+9+x-14=90°
Collect the like terms:
Like terms are terms with the same variables and powers.
4x+x=5x
9-14= -5
Form an equation:
5x-5=90°
Do inverse operations to isolate x.
90+5=95°
95÷5=19° (We divide by 5 because, in algebra, when a number is next to a letter, it means times, so we have to do the opposite and divide).
So, x=19°
Hope this helps :)
how to arrange four 3's to produce 33?
Answer:
[tex]3^{3} + 3 + 3 = 33[/tex]
Step-by-step explanation:
A train is exactly 24km from Smalltown at 7:00p.m. It travels toward Smalltown at a constant rate of 90km per hour. At what time does the train reach Smalltown?
Answer:
7:16 P.M.
Step-by-step explanation:
24/90=4/15. There are 60 minutes in an hour, so we have 240/15=16.
Z= a/m, for a
It a literal equation
Answer:
a = zm
Step-by-step explanation:
z = a/m for a
Multiply all sides by m
zm = a or a = zm
Example:
2 = 6/3
in this case, z = 2, a = 6, and m = 3
We would multiply z(2) and m(3) to get a(6)
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
At a particular school, all students participate in at least one out of three activities: debate, music, and community service. 3 students do all three activities, 21 students do two or more activities, half of all students participate in music, and the ratio of participants in debate, music, and community service, respectively, is $5:4:3$. What is the total number of students at the school
Answer:
48
Step-by-step explanation:
The given parameters are;
The activities in which the students of the school participate = 1) Debate, 2) Music, and 3) Community services
The number of students that do all three activities = 3
The number of students that do two or more activities = 21
The number of the students that participate in music = Half of the students
The ratio of the students that take part in debate, music, and community service = 5 : 4 : 3
Let x represent a common number factor of participants in each of the given three activities, we have;
5·x participate in debate, A
4·x participate in music, B
3·x participate in community service, C
We get;
The sum of the students in the school = A∪B∪C = A + B + C - A∩B - A∩C - B∩C + A∩B∩C
Given that the number of students that do two or ore activities = 21, we have;
(A∩B)∪(A∩C)∪(B∩C) = 21
However, we have;
(A∩B)∪(A∩C)∪(B∩C) = (A∩B) + (A∩C) + (B∩C) - A∩B∩C - B∩A∩C - C∩B∩A + A∩B∩C
∴ 21 = (A∩B) + (A∩C) + (B∩C) - 3 - 3 - 3 + 3
(A∩B) + (A∩C) + (B∩C) = 21 + 3 + 3 + 3 - 3 = 21 + 6 = 27
∴ -(A∩B) - (A∩C) - (B∩C) = -27
Therefore;
A + B + C - A∩B - A∩C - B∩C + A∩B∩C = 5·x + 4·x + 3·x - 27 + 3
5·x + 4·x + 3·x - 27 + 3 = 12·x - 24
The total number of students = A∪B∪C = 12·x - 24
The number of students participating in music, B = 4·x = Half the total number of students = (12·x - 24)/2
∴ 4·x = (12·x - 24)/2
8·x = 12·x - 24
12·x - 8·x = 24
4·x = 24
x = 24/4 = 6
The total number of students at the school = 12·x - 24 = 12 × 6 - 24 = 48
Please explain how you got the answer!
Answer:
One of the scenarios:
Reflection over y-axis, then Translation 1 unit right and 9 units downSimplify the given expression below:
(1 + 3) + (2 - 5i)
Answer:
6 -5i
Step-by-step explanation:
(1 + 3) + (2 - 5i)
Combine like terms
1+3+2 -5i
6 -5i
1. Suppose A = { 1, 3, 5, 7, 9, 11 , 13} and B = {2, 3, 5, 7, 11, 13}. Find the value of A U B .
2. suppose c: {prime numbers less than or equal to 20}. find n(C)
3. Suppose A = { 2, 3, 4, 5, 6, 7, 9, 12} , B = {2, 12, x, 9} and B is a subset of A. What possible values could x have?
help
Problem 1
Answer: {1, 2, 3, 5, 7, 9, 11, 13}-----------------------
Explanation:
The notation A U B means we're applying a union between A and B. This will form a larger set in which items from A or B are thrown into A U B. Think of "union" as in getting married, and person A's stuff is combined with person B's stuff to form a larger set. Any duplicates are tossed. It's often helpful to sort from smallest to largest.
==========================================================
Problem 2
Answer: 8-----------------------
Explanation:
Set C is defined as the set of prime numbers less than or equal to 20. The roster form is C = {2,3,5,7,11,13,17,19} which basically lists every item that fits the description earlier. Note how the value 1 is not prime, so it's not in the set C.
From here, we simply count out the values in set C to find there are 8 values. Therefore, n(C) = 8.
============================================================
Problem 3
Answer: 3, 4, 5, 6, 7-----------------------
Explanation:
Let's consider a real world example of set vs subset. Consider the set of all animals and consider the subset of all dogs. Let's say
A = all animals
B = all dogs
We can see that set A is clearly larger than B. Also, any member of set B is also in set A, but not the other way around. In other words, if something is a dog, then they are also an animal. However, this doesn't work the other way around. For instance, we could have a cat in set A that wouldn't be in set B.
Let's return to the problem at hand. Since B is a subset of A, this must mean everything in B = {2,12,x,9} is found in set A. Sure enough, the 2, 12 and 9 are all in set A. The x must also be a value in set A so we could have
x = 3
x = 4
x = 5
x = 6
x = 7
as our possible answers. I'm not listing x = 2, x = 9 or x = 12 as they have been taken care of. I'm assuming that your teacher wants {2,12,x,9} to list unique items (ie it's after the duplicates are tossed out).
A transformation of AKLM results in AK'L'M'.
Which transformation maps the pre-image to the image?
O dilation
O translation
O reflection
O rotation
K
K
M
M
The transformation that maps the pre-image to the image is given as follows:
Dilation.
How to identify the transformation?The four types of transformation listed in this problem cause these following changes:
Translation: only the position of the figure changes, the orientation, the inclination and the side lengths remain constant.Reflection: The orientation of the figure changes.Rotation: The inclination of the figure changes.Dilation: The side lengths of the figure change, while the angle measures remain constant.From the image, we get that the side lengths were doubled, while the angle measures remained constant, meaning that the transformation is a dilation and the first option is the correct option.
More can be learned about transformations at https://brainly.com/question/28792248
#SPJ1
Answer:
dilation
Step-by-step explanation:
took the test
If l || m, classify the marked angle pair and give their relationship, then solve for x.
Answer:
14. x=16, 15. x=9
Step-by-step explanation:
14.
4x+4=7x-44 by alternate exterior angles
3x=48
x=16
15.
15x-26=12x+1 by alternate exterior angles
3x=27
x=9
Goalie is determined using the formula A = 60 a equals 60 left-parenthesis StartFraction g Over t EndFraction right-parenthesis.. In
Answer:
g = At/60
Step-by-step explanation:
A = 60(g/t)
To solve for 'g'
Open the bracket
A = 60g/t
Multiply both sides by t
At = 60g
Divide both sides by 60
At/60 = 60g/60
At/60 = g
7. solve for x!
please help
(3x/6) + 2 = 8
=> 3x/6 = 8 - 2
=> 3x/6 = 6
=> 3x = 6 × 6
=> 3x = 36
=> x = 36/3
=> x = 12
Answer:
x=12
Step-by-step explanation:
3x/6+2=8
3x/6=8-2
=6
3x/6(6)=6(6)
3x=36
x=12
150 students
110 studied mathematies
95 studied physics
question 1
-The students took mathematics and physics.
the students took math and physics = 55
Which of the following options correctly represents the complete factored
form of the polynomial F(x) = x^4 +5x2 +4
Answer:
(x-5)(x+2)(x+4)
Step-by-step explanation:
I just did It
If there are 3 people splitting a paycheck of 89 how much would each have to pay
Answer:
Around 29.67 each.
Step-by-step explanation:
The bill is being split amongst 3 people. Therefore, we must divide the total price by 3:
[tex]\frac{89}{3}[/tex]
=29.66666667
=29.67
Answer:
3÷89 it would be 36.55 each has to pay on bills
Find the value of x in the figure.
X= _
Answer:
x=35
Step-by-step explanation:
For a polygon with n sides, the sum of its interior angles is equal to
(n-2) * 180
Here, there are 6 sides, so the sum of this polygon's interior angles is equal to (6-2)* 180 = 720
Therefore, the sum of the interior angles is 720. We can add them up to get
(4x-5) + 117 + (3x-3) + (3x+6) + 118 + 4x-3
= 14x +230 = 720
subtract 230 from both sides to isolate the x and its coefficint
14x = 490
divide both sides by 14 to get x
x=35
Use the point slope formula…
Answer:
y = 3x + 7
Step-by-step explanation:
When lines are parallel, the slope is the same but the y-intercept is not
The blue line is the graph for y = 3x + 2
The slope for the line is 3/1
So the slope for the line containing (-2,1) should be 3/1
I plotted (-2,1) and used the Rise/Sun (3/1) to find a point on the y-axis, the teal point.
I graphed the line in yellow
In y=mx + b, b = 7, and mx = 3x
So the equation is y = 3x + 7
If my answer is incorrect, pls correct me!
If you like my answer and explanation, mark me as brainliest!
-Chetan K
By which angle must turn about point A in the clockwise direction so that it coincides with ?
https://cdn.ple.platoweb.com/EdAssets/6168ddce5d8545b692cd00c2eaaf2f05?ts=635385675311870000
A. 90°
B. 180°
C. 270°
D. 360°
When a line is rotated, it is rotated about a fixed point to its new position. Line AB must turn 180 degrees about point A to coincide with line AE.
The complete question is that we determine the angle which AB will turn to, about point A to align with AE (see attachment for the figure)
Line AB and AE form a straight line. This means that the angle between these two lines on either side of point A is [tex]180^o[/tex]
So for line AB to coincides with line AE, the line AB must turn 180 degrees about point A.
Hence, option (B) is correct.
Read more about rotation of points at:
https://brainly.com/question/22363471
given m||n, find the value of x
By using the corresponding angles theorem we can see that (6x - 5)° and (x - 25)° are supplementary angles, so they add up to 180°.
This means that:
(6x - 5) + (x - 25) = 180
7x - 30 = 180
7x = 210
x = 30
If you want to find the exact values of the angles, just plug x = 30 into the angle values! :)
A box contains 9 balls written B,E,R,N,H,E,A,R,T. Two balls are drawn at random without replacement. what is the probability of getting both balls written with R ?
Answer:
How many balls have “R” written on them initially? We can see this is 2.
How many balls are there initially? This is 9.
As a result, the probability of initially drawing a ball with an R on it is 2/9, as out of the 9 possible draws we could make, 2 of them result in a ball with R on it.
How many balls have “R” written on them now? We can see this is 1, since we just drew one ball with R on it and didn’t replace.
How many balls are there in total right now? This is 8, because we took away one.
As a result, the probability of drawing a ball with an R on it after having already done so is 1/8, as out of the 8 possible draws we could make, 1 results in a ball with R on it.
We then multiply these two values (2/9)*(1/8) = 2/72, which is our probability.
Another way to think about this is that there are 72 possible combinations of balls that we could draw, counting each ball uniquely. This is because of our denominator, since 8*9=72. Out of those 72 outcomes that could possibly happen, 2 outcomes will result in both balls being written with R.
Step-by-step explanation:
find the value of the trigonometric ratio. make sure to simplify if its needed.
Answer:
12/5
Step-by-step explanation:
Tan Z
= opposite/adjacent
= 24/10
= 12/5
Answered by GAUTHMATH
plz plz plz help me solving this question
Perimeter: 19 cm ( I added 5.5+7.5+6)
The length of each side of the square: 8 cm
We know that the area is 64 cm2
A=a*a (length times length) We get 8 (because we know the times tables)
Volume: 100
Answer:
3.950121805833336 ≈ 4 m
Step-by-step explanation:
The area of a circle is calculated using this formula: A= πr². Since we know the area of the circle is 154 we have all the values we need to solve this problem.
154 = πr²
√154 = πr
12.40967... = πr
12.40967.../π = r
3.950121805833336 = r
3.950121805833336 ≈ 4 meters
