A linear function has a constant rate of change, which means that the change in the value of y is proportional to the change in the value of x. This means that if we plot the points (x,y) for a linear function, they will fall on a straight line.
To determine which of the tables represents a linear function, we can calculate the rate of change between the points. If the rate of change is the same for all pairs of points, then the table represents a linear function.
For the first table:
Rate of change between (−2,4) and (−1,1) = (1−4)/(−1−(−2)) = −3
Rate of change between (−1,1) and (0,−2) = (−2−1)/(0−(−1)) = −3
Rate of change between (0,−2) and (1,−5) = (−5−(−2))/(1−0) = −3
Rate of change between (1,−5) and (2,−8) = (−8−(−5))/(2−1) = −3
Since the rate of change is constant (equal to −3) for all pairs of points, the first table represents a linear function.
For the second table:
Rate of change between (−2,4) and (−1,1) = (1−4)/(−1−(−2)) = −3
Rate of change between (−1,1) and (0,0) = (0−1)/(0−(−1)) = 1
Rate of change between (0,0) and (1,1) = (1−0)/(1−0) = 1
Rate of change between (1,1) and (2,4) = (4−1)/(2−1) = 3
Since the rate of change is not constant (it changes from −3 to 1 to 3), the second table does not represent a linear function.
For the third table:
Rate of change between (2,−2) and (2,−1) is undefined since x does not change.
Rate of change between (2,−1) and (0,0) = (0−(−1))/(0−2) = 0.5
Rate of change between (0,0) and (2,2) = (2−0)/(2−0) = 1
Rate of change between (2,2) and (2,−2) is undefined since x does not change.
Since the rate of change is not constant (it changes from undefined to 0.5 to 1 to undefined), the third table does not represent a linear function.
For the fourth table:
Rate of change between (0,−2) and (1,1) = (1−(−2))/(1−0) = 3
Rate of change between (1,1) and (2,0) = (0−1)/(2−1) = −1
Rate of change between (2,0) and (3,1) = (1−0)/(3−2) = 1
Rate of change between (3,1) and (4,−2) = (−2−1)/(4−3) = −3
Since the rate of change is not constant (it changes from 3 to −1 to 1 to −3), the fourth table does not represent a linear function.
Therefore, the only table that represents a linear function is the first one.
The largest Hmong population
per capita in the United States is in St. Paul,
Minnesota, where about 10% are Hmong americans How can this percent be written
as a fraction in simplest form?
Expressing the given percentage as a fraction is; 1/10
How to convert percentage to fractions?To change a percent to a fraction, put the percentage over 100 (after removing the % sign) and simplify if necessary. For example, to convert 17% to a fraction, put 17 over 100, like this: 17/100.
Now, we are told that the largest Hmong population per capita in the United States is in St. Paul, Minnesota, where about 10% are Hmong Americans.
Thus, expressing this as a fraction gives us;
10/100 = 1/10
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What is the solution to the equation 21⁄2 + x = 31⁄2? Record your answer on the
grid. Then fill in the bubbles.
Answer: To find the solution to the equation 21/2 + x = 31/2, we need to isolate x on one side of the equation. Subtracting 21/2 from both sides gives us:
x = 31/2 - 21/2
Combining the fractions on the right side gives us:
x = 10/2
Dividing the numerator by the denominator gives us:
x = 5
So the solution to the equation 21/2 + x = 31/2 is x = 5. To fill in the bubbles on the grid, you would need to write the number 5 in the appropriate row and fill in the corresponding bubbles to indicate the digits of the number.
Step-by-step explanation:
A mother is 5 times as old as her daughter. In 6 years, the mother will be 3 times as old as her daughter. How old is each now?
The age of the mother and the daughter currently would be = 30 and 6 years respectively.
How to calculate the age of the daughter and mother?The previous age of the mother(M) = 5D
Where D = daughter
Let the current age of the mother after 6 years ;
M + 6 = 3( D+6)
substitute 5D for M
5D + 6 = 3( D+6)
5D + 6 = 3D+ 18
5D-3D = 18-6
2D = 12
D= 12/2
D = 6 years
Therefore the current age of the mother= 5×6= 30 years
and daughter = 6 years.
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Please help
Solve for x
[tex] \sf 36 \degree = 3x[/tex]
These angles are equal because they are vertically opposite to each other...[tex] \sf36 \div 3 = 3x \div 3 \\ \tt \: x = 12[/tex]
Does anybody understand this question? Please explain how you solved it Thank you
If you are told that a 20 kilogram object is raised by 10 meters, you know that Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a the force of gravity on the object is 20 kilograms. b the mass of the object is 20 kilograms. с the force of gravity on the object is 10 meters. d the mass of the object is 10 meters. e the acceleration of the object is 200 kilogram-meters.
If you are told that a 20 kilogram object is raised by 10 meters, you know that (b) the mass of the object is 20 kilograms.
The force of gravity, also known as gravitational force, is the force that attracts two objects with mass towards each other.
AS we all know that Mass refers to the amount of matter an object contains, and is measured in kilograms. Weight, on the other hand, refers to the force of gravity on an object, and is measured in newtons.
Now, let's look at the options provided.
Option b states that the mass of the object is 20 kilograms, which is correct. This means that the object contains 20 kilograms of matter, regardless of its location or gravitational force acting on it.
In conclusion, we can determine from the given information that the mass of the object is 20 kilograms. However, we cannot determine the force of gravity acting on the object without additional information.
To calculate the force of gravity on an object, we can use the formula
Fg = mg,
where Fg is the force of gravity, m is the mass of the object, and g is the acceleration due to gravity (approximately 9.81 m/s² on Earth).
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A recent survey found that 75% of households had internet access and 80% of households had cable television. Also, it was reported that 70% of the households in the survey had both Internet and cable television. Determine the probability that a rabdomly selected household in the survey had either internet access or cable.
The required probability of the randomly selected households either having internet access or cable television is equal to 0.85.
Let us consider 'A' represents the number of house hold has internet access.
And 'B' represents the number of house hold has cable television.
P(A) = 75%
= 0.75
P(B) = 80%
= 0.80
Number of household has both internet access and cable television
= P( A∩B)
= 70%
= 0.70
Probability of randomly selected household either with internet access or cable are P( A∪B) :
P( A∪B) = P(A) + P(B) - P( A∩B)
Substitute the value we get,
⇒ P( A∪B) = 0.75 + 0.80 - 0.70
⇒ P( A∪B) = 0.85
Therefore, the probability of household having either internet access or cable television is equal to 0.85.
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Dawson simplifies the equation 4y-3=4(y + 1) and says it has no solution. Is dawson correct?
Let's start by substituting the right-hand side of the equation into the left-hand side:
What does the math equation mean?
Two expressions are combined by the equal sign to form a mathematical statement known as an equation. For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.
4y - 3 = 4(y + 1)
4y - 3 = 4y + 4
Now, we can isolate y by subtracting 4y from both sides:
0 = y + 4
-4 = y
So, there is a solution to the equation: y = -4. This means that Dawson is incorrect in saying that the equation has no solution.
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Which pair of measurements is not equivalent?
O 25 g. 25,000 kg
O 16 g, 16,000 mg
O 140 mg, 0.14 g
O 5 kg. 5,000 g
The pair of measurements that is not equivalent is 25 g and 25,000 kg. Option A.
What is a unit of measurement?Unit of measurement is defined as every entity having its measures in dimensions, weight, and time. Such as for length we have a meter, for liquid we have liters, and so on.
Here,
The pair of measurements that is not equivalent is 25 g and 25,000 kg.
25 g is a relatively small amount of mass, while 25,000 kg is a very large amount of mass. Therefore, these two measurements are not equivalent.
The other pairs of measurements are equivalent because they involve conversions between different units of the same base unit. For example:
16 g and 16,000 mg, 1 g = 1,000 mg, so 16 g = 16,000 mg
140 mg and 0.14 g, 1 g = 1,000 mg, so 0.14 g = 140 mg
5 kg and 5,000 g, 1 kg = 1,000 g, so 5 kg = 5,000 g
Thus, the pair of measurements that is not equivalent is 25 g and 25,000 kg. Option A.
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HELP !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! NOW PLEASE YOU GET 25 POINTS
Which are the solutions to the following inequality?
−2(4y+4)+5y≤−35
Answer:
y ≥ 9
Step-by-step explanation:
−2(4y+4)+5y ≤ −35
-8y - 8 + 5y ≤ -35
-3y - 8 ≤ -35
-3y ≤ -27
y ≥ 9
Select the correct answer. Which expression is equivalent to ³√27x + ³√x, if x # 0?
A. 4³√x
B. ³√28x
C. 3³√x
D. 4³√x²
Expression is equivalent to ³√27x + ³√x, if x # 0, The correct answer is A. 4³√x.
To find the equivalent expression, we can factor out the common term of ³√x from both terms in the original expression:
³√27x + ³√x = ³√x(³√27 + 1)
Next, we can simplify the term ³√27 by finding the cube root of 27, which is 3:
³√x(3 + 1) = ³√x(4)
Finally, we can simplify the expression by multiplying ³√x and 4:
³√x(4) = 4³√x
Therefore, the equivalent expression is 4³√x, or answer choice A.
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A group of statements that executes as a single unit is a(n) ____.
a. module
b. unit
c. bunch
d. block
The term that describes a group of statements that executes as a single unit is a "block". A block of code is a program that is grouped together and treated as a single unit. So, the correct option is D.
In computer programming, a block is a group of statements or declarations that are enclosed within a set of curly braces ({ }). The block serves as a single unit that is executed together. Blocks are used to organize code and to apply control structures, such as loops and conditional statements, to multiple statements.
A block can contain any number of statements, which can include variable declarations, function calls, loops, conditional statements, and other constructs. The statements within a block are executed in sequence, one after another, unless a control statement is encountered that alters the normal sequence of execution.
For example, a while loop in Java consists of a block of code that is executed repeatedly while a certain condition is true:
while (condition) {
// block of code to be executed while condition is true
}
In this example, the block of code inside the curly braces will be executed repeatedly while the condition specified in the while statement is true. The block can contain any number of statements, and these statements will be executed each time the loop iterates.
Another common use of blocks is to define functions or methods. A function or method is a block of code that can be called from other parts of the program, and can take inputs (arguments) and return outputs. For example, in Python, a function can be defined as follows:
def function(argument1, argument2):
# block of code to be executed in the function
return result
In this example, the block of code enclosed within the function definition is executed when the function is called. The function can take inputs (argument1 and argument2), which can be used within the function, and it can return a result using the return statement.
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It takes 2 ounces of paint to completely cover all 6 sides of a rectangular prism box which holds 15 cups of sugar. Double the dimensions of the box. Approximately how much paint would be needed to cover the box? How much sugar would it hold?
The amount of paint needed if the dimensions are doubled is; 8 ounces.
The quantity of sugar which the rectangular prism would hold if the dimensions are doubled is; 120 cups of sugar.
What quantity of sugar would the prism hold when the dimensions are doubled?Recall,
Area of a rectangular prism = 2 (lw + lh + wh) and
Volume of a rectangular prism = l × w × h.
Hence, when the dimensions are doubled;
New Area = 2 × 4 (lw + lh + wh) = 4 × initial area.
Therefore, the quantity of paint needed is; 4 × 2 ounces = 8 ounces of paint.
Also, when the dimensions are doubled;
New Volume = 2l × 2w × 2h = 8 lwh.
New Volume = 8 × initial volume = 8 × 15 cups = 120 cups of sugar.
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A number is chosen at random from the first 100 positive integers. Find the probability that the number is either even or a perfect square. 11/20 1/20 3/5.
The probability that the number is either even or a perfect square is [tex]\frac{3}{5}[/tex]
Probability refers to potential.This branch of mathematics deals with the occurrence of a random event. The value's range is 0 to 1. Probability is a concept in mathematics that helps predict the likelihood of certain events. Probability generally refers to the degree to which something is likely to occur..we will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a certain event will occur.
Total Number of Outcome = 100
Number of even numbers = 50
Number of perfect square = 10
[tex]Probability \:=\:\frac{Number\: of\: favourable\:outcome\:}{Number\: of\: total\:outcome\:}[/tex]
[tex]Probability=\frac{50}{100} +\frac{10}{100} = \frac{60}{100} =\frac{3}{5}[/tex]
Therefore, the probability that the number is either even or a perfect square is [tex]\frac{3}{5}[/tex]
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Karen is replacing the carpet in her living room that measures 18 feet by 24 feet. The carpet she wants to install costs $24.99 per square meter (taxes included). If she can not order less than a full square meter of carpet, A) How much carpet should she order? B) How much will the carpet cost?
Karen should order 41 square meters of carpet, and the cost will be $1,024.59 (taxes included).
Describe Algebraic Expression?An algebraic expression is a mathematical phrase that consists of variables, numbers, and mathematical operations such as addition, subtraction, multiplication, and division. It is a combination of constants, variables, and operators that represent a value or a relationship between values.
For example, "3x + 5" is an algebraic expression where "3" and "5" are constants, "x" is a variable, and "+" is an operator. The expression can be evaluated by substituting a value for "x" and performing the necessary operations.
Algebraic expressions can also be simplified by combining like terms and using the rules of arithmetic to simplify the expression. For instance, the expression "2x + 3x" can be simplified to "5x" by adding the coefficients of the like terms "x".
Algebraic expressions are used extensively in algebra to represent equations and relationships between variables. They are also used in a wide range of mathematical and scientific applications, including physics, engineering, and finance.
To calculate the amount of carpet Karen needs to order, we first need to convert the measurements of her living room from feet to meters:
Length: 18 feet = 5.4864 meters (rounded to four decimal places)
Width: 24 feet = 7.3152 meters (rounded to four decimal places)
To find the area of the living room in square meters, we multiply these two values:
Area: 5.4864 meters x 7.3152 meters = 40.0637 square meters (rounded to four decimal places)
Since Karen can only order full square meters of carpet, she should order 41 square meters (to be safe).
To calculate the cost of the carpet, we simply multiply the area by the cost per square meter:
Cost: 41 square meters x $24.99/square meter = $1,024.59
So Karen should order 41 square meters of carpet, and the cost will be $1,024.59 (taxes included).
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The amount of water consumed per week by Montana residences is normally distributed with an unknown mean and a standard deviation of 10 gallons. A simple random sample of ten residences has a mean value of gallons. The city of Bozeman claim that the average water consumed in the state of Montana is not 125 gallons. (a) State the null and alternative hypothesis.
The null hypothesis, denoted by H0, represents the status quo or the default assumption. In this case, the null hypothesis is that the average water consumption in Montana residences is 125 gallons per week.
The alternative hypothesis, denoted by Ha, is the hypothesis that the researcher is trying to prove. In this case, the alternative hypothesis is that the average water consumption in Montana residences is not equal to 125 gallons per week.
So, the null and alternative hypotheses for this problem are:
H0: μ = 125 (where μ is the population mean water consumption in Montana residences)
Ha: μ ≠ 125 (where μ is the population mean water consumption in Montana residences)
Note that the alternative hypothesis is a two-tailed hypothesis since we are testing whether the population mean is not equal to 125, which could mean it is either greater or less than 125.
How do you find the center of a triangle?
Answer:
Step-by-step explanation:
There are several ways to find the center of a triangle:
The Centroid: The centroid is a point that divides each median of the triangle into two equal parts. It is the average of the vertices of the triangle. To find the centroid, you simply average the x-coordinates and the y-coordinates of the vertices:
G = (x1 + x2 + x3)/3, (y1 + y2 + y3)/3
where (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the vertices of the triangle.
The Circumcenter: The circumcenter is the center of the circle that passes through all three vertices of the triangle. To find the circumcenter, you need to find the midpoint of each side of the triangle and then draw perpendicular bisectors to each side. The point where the perpendicular bisectors intersect is the circumcenter.
The Orthocenter: The orthocenter is the point where the altitudes of the triangle intersect. The altitudes are the perpendicular lines from each vertex to the line that contains the opposite side. To find the orthocenter, you need to find the equations of the altitudes and then solve for the point where they intersect.
Note: If the triangle is an equilateral triangle, then the circumcenter and the centroid are the same. If the triangle is a right triangle, then the orthocenter and the circumcenter are the same.
Algebra:
Kapil's age is m years. What is his grandfather's age if he is 10 years more than thrice Kapil's age?
The grandfather's age if he is 10 years more than thrice Kapil's age is
3x +10.
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Kapil's age is m years.
His Grandfather is 10 years more than thrice Kapil's age.
Thrice Kapil's age = 3x
and, 10 years more than thrice Kapil's age = 3x + 10
Then, the age of Grandfather is
= 3x+ 10
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A closed half-plane is the solution of a linear inequality that comes close to the boundary line.
O True
O False
Answer:false
Step-by-step explanation:
2.
REASONING Write an equation in slope-intercept form of the line that passes
through the point (8, 2) and is parallel to the graph of the equation y = 4x - 3.
y
Grade 8: MRL CC 2022 Chapter 4>Section 4.7: Wri
Y
Answer:
y=4x-30
Step-by-step explanation:
9. Johnny found a fraction equivalent to the
one shown by the point on the number
line. Which fraction could Johnny have
found? Explain. 4.FR.1.3
A
B
0
1.
1
8
2/8
3
8
4 ÷ 2
8÷2
482/23
because
1. because 4
||
58 114
1
4
1
618
+710
8
1
The equivalent fraction to the given fraction is 1/2. Therefore, option C is the correct answer.
What is an equivalent fraction?Equivalent fractions are two or more fractions that are all equal even though they different numerators and denominators.
On the number line, the fraction marked is 3/6.
Here, divide both numerator and denominator by 3
We get (3÷3)/(6÷3)
= 1/2
Therefore, option C is the correct answer.
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"Your question is incomplete, probably the complete question/missing part is:"
Johnny found a fraction equivalent to the one shown by the point on the number line. Which fraction could he have found?
A) 1/4
B) 1/3
C) 1/2
D) 2/3
The difference between Monica’s age and her father’s age is 32 years.16 years ago her father was 9 times as old as Monica. Find Monica’s age and her father’s age
Monica's age is 20 years and her father's age is 52
What is Simultaneous equation?Simultaneous equations are two or more algebraic equations that share variables e.g. x and y . They are called simultaneous equations because the equations are solved at the same time. For example, below are some simultaneous equations: 2x + 4y = 14 4x − 4y = 4.
Represent Monica's age by x and her father's age by y
y -x = 32 equation 1
y-16= 9(x-16)
= y-16 = 9x -144
y-9x = -144+16
y - 9x = -128 equation 2
subtract equation 2 from 1
-x-( -9x )= 32-(-128)
8x = 160
x = 160/8
x = 20
substitute 20 for x in equation 1
y = 32+x
y = 32+20
y = 52
Therefore Monica's age is 20 and her father's age is 52
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W^3- w^2+9w=9 find the zero
The zeroes of the equation is 0, 1 and 9.
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
w³ -w² + 9w= 9
Now. solving for 'w'
w(w² - w + 9)=9
so, either w= 9 or w² - w + 9 = 9
w= 9 or w² - w = 0
w= 9 or w(w-1) = 0
w= 9 or w= 0, w= 1
So, the zeroes are 0, 1 and 9.
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Compare / Contrast Exponential Equations
1.) 2 (1/5)x-5
2.) y=4x
The functions y = 2 (1/5)^x - 5 and y = 4^x are compared as follows
y = 2 (1/5)^x - 5 y = 4^x
Initial value: 2 1
base function: 1/5 = decay function 4 = growth function
Translation: 5 units down no transformation
What is a decay function?
A decay function is a mathematical function used in various fields such as physics, engineering, economics, and machine learning, to model the reduction or decline of a value over time.
It is a type of function that decreases at a rate proportional to its current value, so that it approaches zero as time progresses.
Decay function are exponential functions with the base function as
0 < k < 1This is the opposite of growth function which has values greater than 1
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A factory has production lines A and B producing cookies. The two production lines produce 7280 cookies in total each day. If production line A produces 8% more cookies than production line B, find the difference of the numbers of cookies produced by production lines A and B in a day.
please tell me the whole process， thank you
The difference of the numbers of cookies produced by production lines A and B in a day is 280 cookies.
What are equations?When two algebraic expressions are equated, a mathematical statement is called an algebraic equation. P = 0 or P = Q, where P and Q are polynomials, are the generic forms of algebraic equations. One variable only algebraic equations are referred to as univariate equations, while multiple variable algebraic equations are referred to as multivariate equations. A balanced equation in algebra is a given. Because of this, the right side of the equation will equal the left side.
Let the cookies produced by production line A = x.
Let the cookies produced by production line B = y.
Given that, the two production lines produce 7280 cookies in total each day.
x + y = 7280
Also, production line A produces 8% more cookies than production line B.
x = y + y(8/100)
x = y + 0.08y
x = 1.08y
The system of equations thus are:
x = 1.08y
x + y = 7280
Substitute the value of x in equation 2:
x + y = 7280
1.08y + y = 7280
2.08y = 7280
y = 3500
Substitute the value of y in equation 2:
x + y = 7280
x + 3500 = 7280
x = 3780
The difference between the cookies produced is:
D = x - y
D = 3780 - 3500
D = 280
Hence, the difference of the numbers of cookies produced by production lines A and B in a day is 280 cookies.
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The Function G Is Defined And Differentiable On The Closed Interval [-7,5] And Satisfies G(0)=5. The Graph Of Y = G(X), The Derivative Of G, Consist A Semicircle And Three Line Segments, As Shown In The Figure Above. (A) Find G(3) And G(-2). (B) Find The X-Coordinate Of Each Point Of Inflection Of The Graph Of Y =G(X) On The Interval -7 < X < 5. Explain
The graph of y = G(x) consists of a semicircle and three line segments. The function G is defined and differentiable on the closed interval [-7, 5] and satisfies G(0) = 5.
A) G(3) = 4.5 and G(-2) = 4
B) The x-coordinates of the points of inflection are x = -3, x = 0 and x = 4. This is because the graph has three separate linear segments, each with a point of inflection at the junction between them.
The graph of y = G(x) consists of a semicircle and three line segments. The function G is defined and differentiable on the closed interval [-7, 5] and satisfies G(0) = 5.
A) To find G(3) and G(-2), we need to identify the y-coordinate of each point on the graph. The y-coordinate of G(3) is 4.5 and the y-coordinate of G(-2) is 4.
B) To find the x-coordinates of each point of inflection of the graph of y = G(x) on the interval -7 < x < 5, we need to identify the points where the graph changes direction. These points are located at the junction between each of the three linear segments. Therefore, the x-coordinates of the points of inflection are x = -3, x = 0 and x = 4.
the complete question is :
The Function G Is Defined And Differentiable On The Closed Interval [-7,5] And Satisfies G(0)=5. The Graph Of Y = G(X), The Derivative Of G, Consist A Semicircle And Three Line Segments, As Shown In The Figure Above. (A) Find G(3) And G(-2). (B) Find The X-Coordinate Of Each Point Of Inflection Of The Graph Of Y =G(X) On The Interval -7 < X < 5. Explain your reasoning.
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Find X.
to
37°
39°
30°
Answer:123 degrees west
Step-by-step explanation: ngl i need them points but the degrees add up to 123 sine the is a prime number
can somebody help me here
After multiplying and adding given equations, new equations are
3x² + 2xy - 8y² = -273 and 4x - 2y = -32 respectively.
Solutions of the equations are x = -5 and y = 6.
What is linear equation?A linear equation is an equation in which the greatest power of a variable is always 1. Also called the 1 degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. where x is a variable, A is a coefficient, and B is a constant.
Given equations,
a) x + 2y = 7
b) 3x - 4y = -39
Multiplying both equations
(x + 2y)(3x - 4y) = (7)(-39)
Using Foil method (a+b)(c+d) = ac + ad + bc + bd
3x² - 4xy + 6xy - 8y² = -273
3x² + 2xy - 8y² = -273
Which is a new equation.
Adding both equations
(x + 2y)+(3x - 4y) = (7)+(-39)
Adding like terms, we get
4x - 2y = -32
Solving the equations (a) and (b)
a) x + 2y = 7
x = 7 - 2y
Substituting x in terms of y in equation (b)
b) 3x - 4y = -39
3(7 - 2y) - 4y = -39
21 - 6y - 4y = -39
-10y = -60
y = 6
then x = 7 - 2(6)
⇒ x = - 5
Hence, x = -5 and y = 6 are solutions of given equations.
3x² + 2xy - 8y² = -273 is the equation, after multiplying both equations.
4x - 2y = -32 is equation after both equations are added.
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Pls helppppp its math and its pretty hard
A maintenance worker needs to wax a restaurant floor shaped like the image shown. A six-sided figure. There is a horizontal base of 35 feet then another horizontal base below it of 20 feet. The longest side is to the right and is 40 feet. The top is 30 feet. There is a perpendicular from the vertex of the top to the first base of 35 that is labeled 15 feet. If the wax cost $1.38 a square foot, how much will the wax cost to cover the floor? $1,224.75 $1,569.75 $2,104.50 $2,449.50
The total cost of wax to cover the floor is
B. $1569.75How to find the cost that will cover the floorThe area for of the floor is calculated and multiplied by the unit cost $1.38 to get the total cost
The floor is segmented and the area calculated and added together at last
1. Area of rectangle joining the right triangle
= 15 * (30 - 20)
= 150 square feet
2. Area of right triangle
= 1/2 * 15 * (35 - 10)
= 187.5 square feet
3. Area of the large rectangle
= 40 * 20
= 800 square feet
total area = 800 + 187.5 + 150 = 1137.5
cost of wax to cover the floor
= total area * unit cost
= 1137.5 * 1.35
= $1569.75
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complete question: image is attached
Answer:
The correct answer is B.
Step-by-step explanation:
I literally just took the test.
Exit Topic 8: MathXL for School: Topic Review
Triangle KLM has KL=30, KM = 25, and LM = 22. What is the area of the triangle?
The area of AKLM is about
The area of the triangle is given by Heron's formula A = 269.99 units² which is approximately 270 units²
What is Heron's formula?Heron's formula is used to calculate the area of a triangle in terms of the lengths of its sides. If a, b, and c are the lengths of the sides, then the area of the triangle is
Area of Triangle A = √ [ s(s - a) (s - b) (s - c) ]
where s is half the perimeter, or (a + b + c) / 2
Given data ,
Let the triangle be represented as ΔKLM
Now , the measure of side KL , a = 30
The measure of side KM , b = 25
The measure of side LM , c = 22
From Heron's formula , the half the perimeter s = (a + b + c) / 2
Substituting the values in the equation , we get
s = ( 30 + 25 + 22 ) / 2
s = 38.5
Now , Area of Triangle A = √ [ s(s - a) (s - b) (s - c) ]
Substituting the values in the equation , we get
Area of Triangle A = √ [ 38.5 ( 38.5 - 30 ) ( 38.5 - 25 ) ( 38.5 - 22 ) ]
On simplifying the equation , we get
Area of Triangle A = √ [ 38.5 ( 8.5 ) ( 13.5 ) ( 16.5 ) ]
Area of Triangle A = √ ( 72,894.9375 )
On further simplification , we get
Area of Triangle A = 269.99 units² ≈ 270 units²
Hence , the area of triangle is 270 units²
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