The system of equations involving x + y = -6 and 2x - y = 3 has the solution x = -1 and y = -5.
A system of linear equations is a set of two or more equations which includes common variables. To solve system of equations, we must find the value of the unknown variables used in the equations that must satisfy both equations.
There are three methods that can be used to solve system of linear equations.
1. Elimination
2. Substitution
3. Graphing
Using substitution method, given two linear equations in x and y,
x + y = -6 (equation 1)
2x - y = 3 (equation 2)
Express y in terms of x in one of the equations,
x + y = -6 (equation 1)
y = -x - 6
and then substitute it in the 2nd equation.
2x - y = 3 (equation 2)
2x - (-x - 6) = 3
2x + x + 6 = 3
3x = 3 - 6
3x = -3
x = -1
Substituting the value of x in the equation of y,
y = -x - 6
y = -(-1) - 6
y = 1 - 6
y = -5
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Members of a sports club are junior, adult
or senior.
80 of these members were asked whether
they prefer tea, coffee or hot chocolate.
25 members are senior, of which 13
prefer coffee.
10 juniors prefer tea.
There are no adult members who prefer
hot chocolate.
2 out of the 18 juniors prefer coffee.
4 out of the 28 members who prefer tea
are seniors.
What fraction of members in the club
prefer hot chocolate?
Give your answer as a fraction in its
simplest form.
Fraction of members in the club that prefer hot chocolate = [tex]\frac{7}{40}[/tex]
It's Given that :
A sports club has 80 participants.
Senior Members = 25
Junior Members = 18
Adult Members = 80 - (25 + 18) = 80 - 43 = 37
JUNIOR MEMBERS :
Prefers tea = 10
Prefers Coffee = 2
Prefers hot chocolate = 18 - (10 + 2) = 18 - 12 = 6
SENIOR MEMBERS :
Prefers tea = 4
Prefers coffee = 13
Prefers hot chocolate = 25 - (4 + 13) = 25 - 17 = 8
ADULT MEMBERS :
Prefers tea = 28 - (10 + 4) = 28 - 14 = 14
Prefers coffee = 37 - 14 = 23
Prefers hot chocolate = 0 (none)
Calculation of Fraction of members in the club that prefer hot chocolate = 8 + 6 = 14 members out of 80 members
= [tex]\frac{14}{80} = \frac{7}{40}[/tex]
Therefore 7 / 40 of members prefer hot chocolate.
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Which expression is equivalent to −30+(−40)+(−70) ?
−(30−40)+(−70)
negative open parenthesis 30 minus 40 close parenthesis plus open parenthesis negative 70 close parenthesis
30 + 40 + 70
30 + 40 + 70
−30+(−70)+(−40)
negative 30 plus open parenthesis negative 70 close parenthesis plus open parenthesis negative 40 close parenthesis
−30−(40−70)
The answer choice which correctly represents an equivalent expression to that which is given as in the task content is; −30 + (−70) + (−40).
Which expression is equivalent to that which is as given in the task content?It follows from the task content that the expression whose equivalent is to be determined is; −30 + (−40) + (−70).
Therefore, since it follows from the associative property of addition that;
a + b + c = a + c + b.
Therefore, same can be said for the expression as given in the task content where;
-30 + (-40) + (-70) = -30 + (-70) + (-40).
Ultimately, the required equivalent expression is; −30+(−70)+(−40); negative 30 plus open parenthesis negative 70 close parenthesis plus open parenthesis negative 40 close parenthesis
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Find the missing terms in the sequence.
4, 6, 10, 16, 24, 34, __, 60, 76, __, 114
Enter the two missing terms with only a comma between them.
Answer:
46, 94
Step-by-step explanation:
hope this works for you :)
Ava and Wyatt are reading the same book. At the beginning of the month, Ava was on
page 10 and Wyatt was on page 30. Ava will read 20 pages per day and Wyatt will
read 15 pages per day. Let A represent the page of the book that Ava is on at the end
of t days into the month, and let W represent the page of the book that Wyatt is on at
the end of t days into the month. Graph each function and determine after how many
days, t, Ava and Wyatt will be on the same page of the book.
Ava and Wyatt will take 4 days to be on the same page of the book.
X-values must be chosen and entered into the equation in order to graph a function. You will obtain a y-value once those values have been entered into the equation. A single point's coordinates are made up of its x and y values.
From the given question we can get:
A = 10 ₊ 20t
W = 30 ₊ 15t
Graph the each function to get the number of days.
A function can only be graphed if X-values are selected and put into the equation. Once those values are introduced into the equation, a y-value will be produced. The values of x and y are the coordinates of a single point.
Hence we get the number of days as 4. and the graph is attached below.
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the function g is defined as followed
g(x)=2x^2-7
if the graph of g is translated vertically downward by 3 units, it becomes the graph of a
function h
FIND THE EXPRESSION FOR h(x)
(If you know how to answer these questions please help with the next 2 or three I will post afterwards)
Since the graph of g is translated vertically downward by 3 units, the graph of function h is equal to h(x) = 2x² - 10.
The types of transformation.In Mathematics, there are different types of transformation and these include the following:
ReflectionRotationTranslationDilationWhat is a translation?A translation can be defined as a type of transformation which moves every point of the object in the same direction, as well as for the same distance.
Since the graph of g is translated vertically downward by 3 units, the graph of function h would be represented by the following expression:
Note: g(x) = 2x² - 7
h(x) = g(x) - 3.
h(x) = 2x² - 7 - 3.
h(x) = 2x² - 10.
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Help please I will give brainliest
Answer:
For sure, A and C. However, I cannot fully read the last one.
Step-by-step explanation:
Be sure to mark me Brainliest!
A jug contains 3/4 pints of orange juice. After you pour 5/8 of a pint into a glass, how much is left in the jug?
Answer:
1/8
Step-by-step explanation:
each side of the base of a right octagonal prism is 7 in. long. the altitude of the prism measures 12 in. find the lateral area.
The lateral area of right octagonal prism = 672 in^2.
Which octagonal prism is appropriate?An example of a prismatic uniform polyhedron is the octagonal prism, or op. There are 2 octagons as well as 8 squares in it. Each vertex connects two squares and one octagon. As the name implies, it is an octagonal-based prism.
Describe a 3D figure.Three-dimensional geometry is a solid figure, item, or shape comprising three dimensions—length, breadth, as well as height.. Three-dimensional structures have height, which is equivalent to thickness or depth, unlike two-dimensional shapes.
According to the given data:Solve for lateral surface area:
altitude = 12
base = 7
AL=8ah
Putting the value we get:
AL=8 * 12 * 7
Al = 672 in^2
the lateral area of right octagonal prism = 672 in^2.
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a basket contains 3 types of fruit. The apples weigh 4/9 kilogram, the oranges weigh 1/6 kilogram, and the pears weigh 5/18 kilogram. What is the total weight of the fruit in this basket?
A) 10/33
B)15/18
C)8/9
Pls help I’ll give Brainliest
Answer: I hope this helps.
Step-by-step explanation:
According to government tests, a late model hybrid car gets 45 miles per gallon of gas. If gasoline sells
at $3.20 per gallon, how many miles will the car travel on $20.00 of gas?
A janitor had 2/3 of a spray bottle of cleaning solution. He used 1/6 of a solution of the day .How much does a bottle did he use?
Answer:
3/6
Step-by-step explanation:
2/3 = 4/6
(multiply 2 by 2 = 4, multiply 3 by 2 = 6)
4/6 - 1/6 = 3/6
Answer:
2x2/3x2-1/6
4/6-1/6=3/6=1/2
he used half for the day
hope this helps or may also he correct •-•
Find the Error A large box of spaghetti noodles contains 3 pounds and costs $2.40. A student said the unit cost is $1.20 per pound. Complete the statement to explain why the student was incorrect and find the correct answer.
Answer:
1.25 a pound
Step-by-step explanation:
if it was 1.20 per pound it would be less money
You play a game on your phone. For every correct move you make, you receive 50 points. For every second that it takes you to complete the game, you lose 3 points. You complete the game in 2 minutes 24 seconds using 35 correct moves. What is your score?
You get 1750 points from the 35 correct moves (35 x 50) and you get -432 points from time taken (144 x -3) therefore you end the game with 1318 points.
1318 Points.
7:40pm------What is 89 minutes more? (What time will it be?)
The current time is 08 : 09 pm
How to determine the current time?The given parameters are
Time = 7 : 40 pm
Minutes added = 89 minutes
The current time is calculated as
Current time = Time + Minutes added
So, we have
Current time = 7 : 40 pm + 89 minutes
Evaluate the sum
Current time = 7 : 129 pm
Rewrite properly as
Current time = 08 : 09 pm
Hence, the current time is 08 : 09 pm
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AB=2x+7,AC=7x-3,BC=4x-2
The value of x on the line segment is 8
How to determine the value of x?The given parameters are:
AB = 2x + 7
AC = 7x - 3
BC = 4x - 2
The above means that the point B is on the line segment AC
So, we have:
AC = AB + BC
This gives
2x + 7 + 4x - 2 = 7x - 3
Evaluate the like terms
-x = -8
Divide both sides by -1
x = 8
Hence, the value of x on the line segment is 8
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Help I will Mark A Brainlist !!!! Its A Math Question Find the length of a.
Thank you ao much !!! I hope you have a good day!
Answer: a=2√5
Step-by-step explanation:
We have a right-angled isosceles triangle
Hence, a=2√5
Marco earns a commission rate of 6% for
the first $6,500 ins sales and 9% on sales
over $6,500. Find the total graduated
commission on sales of $10,500.
Total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.
As given in the question,
Macro earns commission rate of 6% for the first $6500
And 9% on sales over $6500
Out of $10,500
For first $6500 Commission =(6500 × 6)/ 100
= $390
For $ (10,500 - 6,500 = 4000) commission = (4000 × 9)/ 100
= $360
Total graduated commission on sales of $10,500 = $( 390 + 360)
= $750
Therefore, total graduated commission earned by Macro on sales of $10,500 with the rate of 6% on the first $6500 and 9% on sales over $6500 is equal to $750.
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Mai-Lin measures her heart rate whenever she exercises and tries to make sure that she is staying in her target heart rate zone. The American Heart Association suggests a target heart rate of T=0.75(220-a), where T is a person's target heart rate and a is his or her age.
b. If Mai-Lin's target heart rate is 153, then how old is she? What property justifies your calculation?
When Mai-Lin's target heart rate is 153, then her age is 16 years.
How to illustrate the function?From the information, the The American Heart Association suggests a target heart rate of T=0.75(220-a),
where T = person's target heart rate
a = his or her age.
Therefore, when the heart rate is 153, the age will be:
T = 0.75(220 - a)
153 = 165 - 0.75a
0.75a = 165 - 153
0.75a = 12
Divide
a = 12/0.75
a = 16
The person's age is 16 years.
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a radioactive substance decays exponentially. a scientist begins with 180 milligrams of a radioactive substance. after 33 hours, 90 mg of the substance remains. how many milligrams will remain after 43 hours?
The radioactive substance remaining after 43 hours is: 62.7273 mg by unitary method.
What is unitary method?A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.
Now,
Given that 180 mg is present at t = 0 hours.
After t = 33 hours, substance left = 90mg
By unitary method, after = 1 hour, substance left = [tex]180-\frac{90}{33}=180 -\frac{30}{11}[/tex]mg
The substance left after t = 43 hours = [tex]180 - \frac{30\times43}{11}= 180 - \frac{1290}{11}=180 - 117=62.7273mg[/tex]
Hence, The radioactive substance remaining after 43 hours is: 62.7273 mg by unitary method.
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Figure B is a dilated image of figure A. What is the scale factor?
PLS HELP ASAP!!!! WILL GIVE BRAINIEST!!!!!! 100 POINTS!!!!!
SEE ATTACHED PIC
Answer:
y-coordinate
Step-by-step explanation:
x-intercepts lie on the x-axis. On the x-axis, y=0 while the x value is changing.
Answer: Set the Y equal to zero and solve for x
Step-by-step explanation:
Harry tosses a nickel 4 times. The probability that he gets at least as many heads as tails is.
The vertices of ABCDE are A(-6, 0), B(-3, 0), C(0, -3), D(-3, -6), and E(-6, -3). Find the vertices
of the image after a translation using the rule (x,y) → (x + 9, y - 6) and a dilation with a scale
factor of 1/3 centered at the origin.
The coordinates of the image of the vertices of the polygon are A''(x, y) = (1, - 2), B''(x, y) = (2, - 2), C''(x, y) = (0, - 1), D''(x, y) = (- 1, - 2) and E''(x, y) = (- 2, - 1).
What are the images of the vertices of a polygon by using rigid transformations?
Rigid transformations are transformations applied on geometric loci such that Euclidean distances in such constructions are conserved. Translations and dilations are common examples of rigid transformations.
If we know that A(x, y) = (- 6, 0), B(x, y) = (- 3, 0), C(x, y) = (0, - 3), D(x, y) = (- 3, - 6) and E(x, y) = (- 6, - 3), then the coordinates of the image are determined below:
Translation
A'(x, y) = (- 6, 0) + (9, - 6)
A'(x, y) = (3, - 6)
B'(x, y) = (- 3, 0) + (9, - 6)
B'(x, y) = (6, - 6)
C'(x, y) = (0, - 3) + (9, - 6)
C'(x, y) = (9, - 9)
D'(x, y) = (- 3, - 6) + (9, - 6)
D'(x, y) = (6, - 12)
Dilation
A''(x, y) = (1 / 3) · (3, - 6)
A''(x, y) = (1, - 2)
B''(x, y) = (1 / 3) · (6, - 6)
B''(x, y) = (2, - 2)
C''(x, y) = (1 / 3) · (0, - 3)
C''(x, y) = (0, - 1)
D''(x, y) = (1 / 3) · (- 3, - 6)
D''(x, y) = (- 1, - 2)
E''(x, y) = (1 / 3) · (- 6, - 3)
E''(x, y) = (- 2, - 1)
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Choose the correct statement.
-2 < -3
1 = -1
5 > -6
The answer is only 1
proof let a be a square matrix of order n. (a)show that is symmetric. (b)show that is skew-symmetric. (c)prove that a can be written as the sum of a symmetric matrix b and a skew-symmetric matrix c, a
(a)Symmetric matrix -
Let matrix A be of order 3×3 =
[tex]\left[\begin{array}{ccc}1&3&8\\3&8&-4\\8&-4&6\end{array}\right][/tex]
So, the transpose of A will be -
A' =
[tex]\left[\begin{array}{ccc}1&3&8\\3&8&-4\\8&-4&6\end{array}\right][/tex]
So, we can say that A=A'. So, it is symmetric.
(b) Skew - symmetric matrix -
Let us consider a matrix B =
[tex]\left[\begin{array}{ccc}0&-6&4\\-6&0&7\\4&7&0\end{array}\right][/tex]
matrix B is said to be skew-symmetric if aij =−aji.
(B' =−B)
B' =
[tex]\left[\begin{array}{ccc}0&6&-4\\6&0&-7\\-4&-7&0\end{array}\right][/tex]
(c) A + A′ is a symmetric matrix for any square matrix A with real number entries, whereas A - A′ is a skew-symmetric matrix.
Proof: If B = A + A', then B ′ = (A + A ) ′
(A + B)′ = A′ + B′, thus = A′ + (A′)′
(as (A′)′ =A) = A′ + A
= B (because B + A = B + A′)
B = A+A′ is a symmetric matrix as a result.
Let C now equal A-A′.
Why does C' equal (A-A′)′=(A′)′?
= A′ - A (Why?)
=- (A - A′) = - C
A - A′ is a skew-symmetric matrix as a result.
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Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
(14+3)(2
x 6)
Answer: 204
Step-by-step explanation:
(14+3)(2 x 6)=
(17)(2 x 6)=
(17)(12)=
17*12=
17*(10+2)=
17*10+17*2=
170+34=204
Answer:204
Step-by-step explanation:
The temperature in California was 105 on Thursday. The temperature in the North Pole was -20. What is the difference between the two temperatures.
Answer:
125
Step-by-step explanation:
105 - (-20) = 105 + 20 = 125
four less than the product of 2 and a number g
The expression that represents the statement "four less than the product of 2 and a number g" is 2 g - 4.
We are given a statement:
four less than the product of 2 and a number g
We need to form an expression to represent that statement.
An expression is a combination of variables and constants by using the various operations of mathematics like addition, subtraction, division and multiplication.
So, first we will find the product of 2 and a number g.
This is:
2 × g = 2 g
Now, we will subtract 4 from the expression:
2 g - 4
Therefore, the expression that represents the given statement "four less than the product of 2 and a number g" is 2 g - 4.
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The fairs train ride covers a distance of 3 miles in 20 minutes what is the speed for the ride in miles per minute
Answer:
0.15 miles per minute or 9 miles per hour
Step-by-step explanation: