Taking into account the definition of a system of linear equations, a small pizza and a regular pizza cost £7 and £11 respectively.
System of linear equationsA system of linear equations is a set of two or more equations of the first degree, in which two or more unknowns are related.
Solving a system of equations consists of finding the value of each unknown so that all the equations of the system are satisfied. This mieans thar systems of linear equations have as a solution set all ordered pairs (x, y) that satisfy the equation, where x and y are real numbers.
This caseIn this case, a system of linear equations must be proposed taking into account that:
"r" is the cost of a regular pizza."s" is the cost of a small pizza.You know:
2 regular pizzas and 3 small pizzas cost £43.8 regular pizzas and 9 small pizzas cost £151.The system of equations to be solved is
2r + 3s= 43
8r + 9s= 151
Of the several methods to solve a system of equations. it is decided to solve it using the substitution method, which consists of clearing one of the two variables in one of the equations of the system and substituting its value in the other equation.
In this case, isolating the variable "r" from the first equation:
2r= 43 - 3s
r= (43 -3s)÷2
r= 43/2 - 3/2s
Replacing this expression in the second equation:
8×(43/2 - 3/2s) + 9s= 151
Solving:
8×43/2 - 8×3/2s + 9s= 151
172 -12s + 9s= 151
-12s + 9s= 151 - 172
-3s= -21
s= (-21)÷ (-3)
s= 7
Remembering that r=43/2 - 3/2s you get:
r=43/2 - 3/2×7
r= 11
Finally, a small pizza cost £7 and a regular pizza cost £11.
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2 questions standard algorithm division WRITE ON PAPER OR USE DIGITAL NOTEPAD
50 POINTS
lol its easy 2 questions
Answer:
Step-by-step explanation:
Write an equation that represents the line.
Use exact numbers.
[tex]\displaystyle\\Answer:\ \frac{7}{5}x +\frac{34}{5}[/tex]
Step-by-step explanation:
[tex]\displaystyle\\(-7,-3)\ \ \ \ (-2,4)\\\\\frac{x-x_1}{x_2-x_1}=\frac{y-y_1}{y_2-y_1} \\\\x_1=-7\ \ \ \ \ x_2=-2\ \ \ \ y_1=-3\ \ \ \ \ y_2=4\\\\\frac{x-(-7)}{-2-(-7)} =\frac{y-(-3)}{4-(-3)}\\\\\frac{x+7}{-2+7}=\frac{y+3}{4+3} \\\\\frac{x+7}{5} =\frac{y+3}{7} \\\\[/tex]
Multiply both parts of the equation by 7:
[tex]\displaystyle\\7(\frac{x+7}{5} )=y+3\\\\7(\frac{1}{5} x+\frac{7}{5} )=y+3\\\\\frac{7}{5}x +\frac{49}{5} =y+3\\\\\frac{7}{5}x +\frac{49}{5} -3=y+3-3\\\\\frac{7}{5}x +\frac{49}{5}-3=y\\\\\frac{7}{5}x +\frac{49-3(5)}{5} =y\\\\\frac{7}{5}x +\frac{49-15}{5} =y\\\\\frac{7}{5}x +\frac{34}{5} =y\\\\So,\ y=\frac{7}{5}x +\frac{34}{5}[/tex]
A local news station wants to find out opinions on the economy for their next broadcast. Which of the following describes how they could do this? Select all that apply.
Ask specific people's opinions on the economy
Ask a randomly selected people's opinions on the economy
Ask the members of the local news station about their opinions on the economy.
Ask every person that works in town opinions about their own economic impact
Ask the entire community opinions about their own economic impact
The ways that describes how they could gather the opinions include:
Ask a randomly selected people's opinions on the economy Ask the members of the local news station about their opinions on the economy.How will the opinion be illustrated?From the information, the local news station wants to find out opinions on the economy for their next broadcast.
It should be noted that in this case, a sample will be used and not the entire population. Therefore, they can ask randomly selected people's opinions on the economy as well as the members of the local news station about their opinions on the economy.
Therefore, the correct options are A and B.
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help, please! 25 points! :)
The properties of the function are:
Its shape is an absolute functionIt has a domain of all real valuesIt has a range of real values greater than or equal to 0Vertex at (0, 0)How to make a table of values for the following equationThe absolute value equation of the function is given as
y = |x|
On the incomplete table of values, we do not have any x values
So, we can make use of any x value
To do this, we make use of the following x values
x = -3, -1, 0, 1 and 3
Next, we substitute x = -3, -1, 0, 1 and 3 in the equation y = |x|
So, we have:
y = |-3| = 3
y = |-1| = 1
y = |0| = 0
y = |1| = 1
y = |3| = 3
When represented on a table of values, we have
x | y
-3 | 3
-1 | 1
0 | 0
1 | 1
3 | 3
How to make the graph the equationNext, we plot the graph of the absolute value equation
See attachment for the graph of the absolute value equation
From the graph of the absolute value equation, we have the following properties:
Domain: All set of real valuesRange: All set of real values greater than or equal to 0Vertex: (0, 0)Shape: Absolute value equationRead more about absolute value equation at
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a + 1/4 = -6
Please help explain it to me I just want to understand it. I learned it today.
Answer: a = 6 and 1/4
Step-by-step explanation:
you subtract the 1/4 to the other side and theres your answer
PLEASE HELP will give BRAINLIEST
What is the domain for the exponential function f (x) = –4log(x + 2)?
Answer:
The domain for this function is all real numbers greater than -2.
An apartment building owner charges $905 to each apartment for rent month if the building is currently renting 64 apartments how much money does the building owner collect in each month?
Answer: 57920 per month
Step-by-step explanation: 905 x 64 = 57920
if RS = ST and ST = 2UV then RS = 2UV
It is true given the above logical analysis to state that RS = 2UV. This is known as a conditional statement also known as an If-then-statement.
What is a conditional statement?A conditional statement (also known as an If-Then Statement) is a statement that begins with a hypothesis and ends with a conclusion.
A conditional statement can also be defined as "If this happens, then that will happen." A conditional statement's hypothesis is the first, or "if" element. While the "Then" is the Conclusion.
Hence, the hypothesis from the above statement is:
IF RS = ST and ST = 2UV [Hypothesis]
Then RS = 2UV [Conclusion]
Put differently we can say
A → B and B→C; then
A → C.
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There will be 4 floats in a parade. the parade organizers are trying to determine the order in which the floats should appear. how many different orders are possible?
Using permutation, there are a total of 24 different orders possible.
If there are a total of 4 floats in a parade then the number of possible orders = 4!
If we further calculate it we will get,
4 x 3 x 2 x 1 = 24
So there are a total of 24 possible orders in which the floats should appear.
The concept used here is the number of arrangements and the technical term used for it in mathematics is a permutation. A permutation is a mathematical calculation that involves finding the number of ways a particular set can be arranged.
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A soccer team played 24 games and won 16.
What is the ratio of the number of wins to the number of losses?
Answer: 8:16
24(games)-16(wins)=8. 8=the losses
Step-by-step explanation:
What is the least common multiple of 32, 48, and 16?
The least common multiple of 32, 48, and 16 is 96
How to calculate the least common multiple ?The first step is to get the prime factors of each number
The prime factors of 32 are 2, 2, 2, 2 and 2.
The prime factors of 48 are 2, 2, 2, 2 and 3
The prime factors of 16 are 2,2,2 and 2
The least common multiple of 32, 48 and 16 can be calculated as follows
2 × 2 × 2 × 2 × 2 × 3
= 32 × 3
= 96
Hence the least common multiple of 32, 48, and 16 is 96
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A
X -2
y
C
4
-1
1
−2
10. Construct an exponential equation for the data presented in the table.
y = 2 (1)x
y = 1. (2)x
y = 2.(x) ¹
y = 1. (x)²
B
0
1
D
1
2
2
4
Answer:
b
Step-by-step explanation:
put -2 on x and you will get a value of 1/4
(can use other number on table too but must got the same value of y)
example: use -1 for x and the answer must be 1/2
SOLVE FOR X.
PLS HURRY
In this question we have 3 lines, where 2 parallel lines intersect the other.
Now, because the 2 lines are parallel, their corresponding angles are congruent. Therfore, we can derive the equation:
[tex]2x-43 = x+9[/tex]
First, we need to move 43 to the right side.[tex]2x = x+9+43[/tex]
Next, we add 9 and 43.[tex]2x = x+52[/tex]
Then, we move x to the left side.[tex]2x-x = 52[/tex]
Finally, we subtract the left side.
[tex]x = 52[/tex]
Area of the shaded part
In the picture, there is a square and a shaded region inside the square. The shaded portion has a 13.76 square meter area.
Given that,
In the picture, there is a square and a shaded region inside the square.
We have to find the shaded portion area.
The side of the square is 8cm.
Now,
First we see the unshaded region on the square is there are 4 unshaded regions.
In the figure u can see there is a unshaded region we named that has tile 1, tile2, tile 3, and tile 4.
If we restock them we can see that we got a circle with that 4 tiles.
Now, the side is 8 cm then the 1 tile will be of 4 cm.
So, the radius of the circle is 4 cm.
In the other picture we can see that the area of the shaded region is equal to area of square- area of circle.
Area of the shaded region =s²-πr²
Area of the shaded region =8²-π(4)²
Area of the shaded region =64-π(16)
Area of the shaded region =64-16π
Area of the shaded region =64-16(3.14)
Area of the shaded region =64-50.24
Area of the shaded region =13.76
Therefore, The shaded portion has a 13.76 square metre area.
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The radius of a sphere is 14 cm. The cost of
painting the surface of sphere is ₹25 per
square cm. If the radius of sphere is increased
by 10%, then the cost of painting is increased
by 20%. What is the percentage increase in
the total cost of painting per square cm?
(a) 54.27%
(b) 20.3%
(d) 45.2%
(c) 2.58%
The total cost of painting per cm will be 45.2% i.e. option(d).
Total cost of painting = Rate × Surface area of sphere
We know the radius is increases by 10%.
Thus, the Surface area will change by 21%
using formula a + b + (a × b)/ 100
The total change in cost of painting will be
= 20+21 +(20x21)/100
= 45.2%.
What is surface area?
The total area of all faces (or surfaces) on a 3D form is the surface area. For example:
There are six rectangular faces of a cuboid.
Add the areas of each of the cuboid's six faces to determine its surface area.
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One gram of protein contains 4 calories. One gram of fiber contains 2 calories. A protein bar has 80 calories from p grams of protein and f grams of fiber.
The equation 4p+2f=80 represents the relationship between these quantities.
Which pair of values could be the number of grams of protein and fiber in the protein bar?
Pairs of values that could be the number of grams of protein and fiber in the protein bar are:
10 grams of protein and 20 grams of fiber. That is, (10, 20)
and
15 grams of protein and 10 grams of fiber. That is, (15, 10)
Calculating value pairsFrom the question, we are to determine the pair of values that could be the number of grams of protein and fiber in the protein bar
From the given information,
The protein has 80 calories from p grams of protein and f grams of fiber
and
The equation that represents the relationship is
4p + 2f = 80
To determine the pair of values, we can determine the values of f for certain values of p
When p = 10
4p + 2f = 80
4(10) + 2f = 80
40 + 2f = 80
2f = 80 - 40
2f = 40
f = 40/2
f = 20
A pair of values is 10 grams of protein and 20 grams of fiber.
When p = 15
4p + 2f = 80
4(15) + 2f = 80
60 + 2f = 80
2f = 80 - 60
2f = 20
f = 20/2
f = 10
Thus,
Another pair of values is 15 grams of protein and 10 grams of fiber.
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Which relation is also a function?
Answer:
answer is D prettyy sure
what is the sqr of 7-2sqrtof10
It is to be noted that the square root of 7-2√10 is √5-√2. See the explanation below.
What is the square of a number?It is to be noted that square root, in mathematics, refers to a factor of a number which when multiplied by itself, results in the original number. For example, both 3 and –3 are square roots of 9.
Hence the solution to the above expression or problem is given as stated below:
7-2√10 = 5 + 2 - 2 2√10
= (√5)² + (√2)² - 2(√5)(√2)
Hence
7-2√10 = (√5 - √2)²
√(7-2√10) = √5 - √2
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Which factor do 9x2 + 24x + 16 and 9x2 - 16 have in common?
O 3x-4
0 3x + 16
O 3x + 4
9x²
Answer:
3x + 4
.................
The factor 3x + 4 have common in both the given expressions.
What is common factor?A whole number that is a factor of two or more numbers is referred to as a common factor. The largest factor that will divide into two or more numbers is known as the highest common factor (HCF). The smallest multiple shared by two or more numbers is known as the lowest common multiple (LCM).
The given expressions are,
[tex]9x^2 + 24x + 16, 9x^2 - 16[/tex]
The expression [tex]9x^2 + 24x + 16[/tex] is of the form [tex](a + b)^2[/tex]
where [tex]a = 3x , b = 4[/tex]
Therefore, [tex]9x^2 + 24x + 16 = (3x + 4)^2.[/tex]
The expression [tex]9x^2 - 16[/tex] is of the form [tex]a^2 - b^2[/tex].
It can be written as, [tex]a^2 - b^2 = (a - b)(a + b)[/tex]
Here, [tex]a = 3x , b = 4[/tex]
Therefore,
[tex]9x^2 - 16 = (3x - 4)(3x + 4)[/tex]
So, in both the expressions the factor (3x + 4) is common.
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Which statement explains why one source is the most reliable? The Squawkbook post is the most reliable source because ConcernedCitizen was at the meeting. The Local Reader article is the most reliable source because it shows a photograph of the lots. The Squawkbook post is the most reliable source because it provides the author’s opinion of the council. The Local Reader article is the most reliable source because the author offers a neutral reporting of facts.
HELP PLEASE
The statement that explains why one source is the most reliable is D. The Local Reader article is the most reliable source because the author offers a neutral reporting of facts.
What are reliable sources?Reliable sources are necessary for reliable information. A trustworthy source will offer a "complete, well-reasoned hypothesis, argument, etc. based on substantial evidence," according to UGA Libraries.
Scholarly, peer-reviewed articles and books are examples of widely regarded sources. trade publications, professional books, etc.
It should be noted that a reliable source should be based in facts and should not be biased.
Therefore, the correct option is D.
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A dieter loses a total of 24 pounds over 6 months. The dieter uses the expression -24/6 to represent the average weight loss each month. which expression is equivalent to the expression the dieter uses?
The equivalent expression to the dieter's expression which is given as -24/6 is equal to -(24/6).
What are the three fractional signs?Every fraction has three signs: one for the numerator, one for the denominator, and one for the overall fraction.
A fraction can have what kind of sign?The fraction will always be negative if one of the numerators or denominators is negative and the other is positive.
It is given that a dieter loses 24 pounds in 6 months.
The dieter represents the average monthly weight loss with the expression -24/6.
We know that,
The negative sign in numerator can be assigned to the overall fraction.
So, we can write the expression (-24)/6 as -(24/6).
Therefore, the expression that is equivalent to the expression the dieter uses is -(24/6).
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WILL GIVE BRAINLIST TO BEST ANSWER
Determine if the sequence is arithmetic. If it is, find the common difference, the 21st term, the explicit rule, the recursive rule, and the three terms in the sequence after the last one given.
-3, 6, -12, 24,…
Answer:
This sequence is geometric with common ratio -2.
Solve the equation.
p - 132 = 7, p = ______
Answer:
139
Step-by-step explanation:
Add 132 to both sides, so it will cancel out on the left side and you are left with only p.
[tex]p - 132 + 132 = 7 +132\\p = 139[/tex]
Consider the following graph of g(x). Write a formula for g(x) that describes the transformations performed on the basic function.
The formula for function g(x) that describes the transformations performed on the basic function f(x) = |x| is g(x) = - ( |x| + 4 )
As per the question statement, we are given a basic function f(x) = |x| and we are supposed to find the formula for function g(x) that describes the transformations performed on the basic function f(x) = |x|.
Solution is as follows:
Reflected about X - axis and translated 4 units down to X - axis.
Basic function y = |x| - 2
Transformed function g(x) = - ( |x| + 4 )
Reflected across y = -2
Function: A mathematical phrase, rule, or law that establishes the link between an independent variable and a dependent variable (the dependent variable).To learn more about functions, click on the link given below:
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For which value of x is 12/x not a rational number
0
0.1
2
-1/2
Because we can't divide by zero, the correct option is x = 0.
For which value of x the quotient is not a rational number?
Here we have the quotient:
12/x
We want to find a value of x such that it is not a rational number, where a rational number is any number that can be written as the quotient of two integers.
Here is a trick, remember that we can't divide by 0, so if we choose x = 0, technically we can't take the quotient, so in that case we wouldn't have a rational number.
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Compare problems 1 and 2. What similarities do you see? What differences do you
notice?
(Algebra/geometry terms)
In the picture there are 2 problems. The similarity is they two have to find 2 question. The difference is given question are different.
Given that,
In the picture there are 2 problems.
We have to find the difference and similarities of question in the picture.
The similarities are they 2 are word problems.
Another similarity is they two have to find 2 question.
1. How much money for 10 days and How many days to collect the money $1.05?
2.How much gallon of water need for 50 minutes and How much time take to fill the pool?
Another similarity is they two have to justified the answer in a mathematical model.
Now,
The difference is,
First question has given sisters and money problem where as the second has given pool and gallon water problem.
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Let f(p) be the average number of days a house stays on the market before being sold for price p in $1,000s. Which statement best describes the meaning of f(150)? (2 points)
This is the average number of days the house stayed on the market before being sold for $150,000.
The house sold on the market for $150,000 and stayed on the market for an average of 150 days before being sold.
The house sold for $150,000.
The house stayed on the market for an average of 150 days before being sold.
A statement which best describes the meaning of function f(150) is that: A. This is the average number of days the house stayed on the market before being sold for $150,000.
What is the average rate of change?The average rate of change can be defined as a type of function that is used for describing the average rate at which a quantity either decreases or increases with respect to another quantity.
What is a function?A function simply refers to a mathematical expression which is used to define and represent the relationship that exists between two or more variables. This ultimately implies that, a function is typically used for mapping an input variable (x-value) to an output variable (y-value or f(x)).
In this scenario, the function f(150) can be evaluated as follows:
Function f(150) = 150 × p
Function f(150) = 150 × $1,000.
Function f(150) = $150,000
Therefore, the function f(150) simply means the average number of days this house stayed on the market before it was then sold for $150,000.
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13y-5=9y+27
What is y?
Answer:
y=8
Step-by-step explanation:
Jake, Aliya and Lucy each vegetable patch. Jake's vegetable patch has a m², of h. Aliya's vegetable patch has a m², of 3h + 7. Lucy's vegetable patch has a m², of 5h. In total, their vegetable patch an area greater than 79 Write and solve an inequality possible values of h
The most appropriate choice for Linear Inequation and area will be given by-
value of h > 8.
What is Linear Inequation and area?
Linear Inequation involves comparision between two values with the help of <, >, [tex]\leq[/tex], [tex]\geq[/tex].
Area of a 2D shape is the total space taken by that shape.
Here ,
Area of vegetable patch of Jake = [tex]h[/tex] [tex]m^{2}[/tex]
Area of vegetable patch of Aliya = ([tex]3h + 7[/tex]) [tex]m^{2}[/tex]
Area of vegetable patch of Lucy = [tex]5h[/tex] [tex]m^{2}[/tex]
Total area of vegetable patch of Jake, Aliya and Lucy
= [tex](h + 3h+7+5h)[/tex] [tex]m^{2}[/tex]
= [tex](9h+7)[/tex] [tex]m^{2}[/tex]
By the problem,
[tex]9h + 7 > 79\\9h > 79 - 7\\9h > 72\\h > \frac{72}{9}\\ h > 8[/tex]
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If the right triangle BAR were rotated 90° clockwise about Point B to what location would point A be relocated
Using rotation rules, considering the 90º clockwise rotation, the coordinates of point A are given as follows:
(-2,0).
What is the rule for a 90º clockwise rotation at a point other than the origin?The origin has coordinates (0,0), hence the rule for a 90º clockwise rotation about the origin is:
(x,y) -> (y, -x).
Considering a point (xP, yP) as reference, the rule for the coordinates of the vertices after the rotation is given as follows:
(x,y) -> (y - yP, -x + xP).
For this problem, point B is the reference point, hence the reference coordinates are as follows:
xP = 2, yP = 1.
Then the rule is:
(x, y) -> (y - 1, -x + 2).
Point A is located at:
x = -2, y = -1.
After the rotation, the coordinates will be given as follows:
(x, y) -> (-1 - 1, -2 + 2) = (-2,0).
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