Q.22 5.3 Write a system of linear equations that has the ordered pair of (-2,8) as it's solution.
Answers
A system of linear equations that has the ordered pair of (-2,8) as it's solution is Oy - 2x = 12 and x - 2y.
calculation:-
x = -2
for 2y - 4x = 24 plug in x = -2
2y + 8 = 24
Subtract 8 from both sides
2y + 8 - 8 = 24 - 8
2y = 16
divide both sides by 2
2y/2 = 16/2
y = 8
Therefore, the solution to the system of linear equations is:
(x, y) = (-2, 8).
A non-linear equation is such that it does not form a straight line. It looks like a curve in a graph and has a variable slope value. A linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y. The graph of a linear equation always forms a straight line. The definition of a linear equation is an algebraic equation in which each term has an exponent of 1.
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Related Questions
Which property of addition is shown? −3+ 5 = 5 + (−3)
Associative Property
Commutative Property
Distributive Property
Identity Property.
Answers
This is the Commutative Property. It states that when addition takes place, the addends may switch positions with another addend.
The given expression −3+ 5 = 5 + (−3) is showing the commutative Property. The correct option is B.
What is cumulative property?
The cumulative property states that if the position of the numbers when they are in addition is changed then it will not affect the final result of the addition. If altering the operands' order has no effect on the outcome, the binary operation is commutative in mathematics.
The given expression is −3+ 5 = 5 + (−3).
From the cumulative property, the expression can be solved. The two expressions will have the same value but the frame of writing the expression is different.
This is the Commutative Property. It states that when an addition takes place, the addends may switch positions with another added.
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The table below shows the changes in the value of a company's stock over the past four weeks. By how many points would the stock value need to change in Week 5 to return to its value before Week 1? Explain.
Answers
ANSWER:
+ 4 7/8
STEP-BY-STEP EXPLANATION:
Assuming that we start in week 0, with a total of 0 points, we must operate the changes in each week and the value opposite to that result must be the change necessary to return to the original value.
Just like that:
[tex]\begin{gathered} 9\frac{1}{2}+6\frac{5}{8}-12\frac{3}{4}-8\frac{1}{4}=\frac{19}{2}+\frac{53}{8}-\frac{51}{4}-\frac{33}{4}=-\frac{39}{8}=-4\frac{7}{8} \\ -4\frac{7}{8}+4\frac{7}{8}=0 \end{gathered}[/tex]Which means that to return to the initial value, 4 7/8 points must be added
The selling price of a refrigerator, is $548.90. The markup value was 10%. How much was the refrigerator originally?
Answers
Let the original price be p.
Then
p + (10% of p) = 548.90
1.1p = 548.90
p = 548.9 / 1.1 = $499.00
Hence the refrigerator was $499.00 originally
Identify the graphs of y 2|x+2|-6 and y=-2 in the same coordinate plane
Answers
The graphs of the absolute value function y = 2|x + 2| - 6 and the horizontal line y = -2 are given on the image at the end of the answer.
How to build the graphs?The definition of the absolute value function is given as follows:
y = |x - h| + k.
In which the coordinates of the vertex are (h,k), representing the turning point of the graph of the absolute value function, the point in which the function makes the "V".
In this problem, the definition of the function is:
y = 2|x + 2| - 6.
Hence the coordinates of the vertex are:
(-2, -6).
The multiplication by 2 represents a vertical stretch but is not related to the vertex of the function.
y = -2 is a horizontal line, and the graph with these two functions is given by the image at the end of the answer.
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Graph −4 < x < 2 on the number line. Write −4 < x < 2 in interval notation.
Answers
To graph the inequality, we need to take the following steps:
0. Draw a number line.
,1. Draw circles over -4 and 2; in this case the circles are hollow since the inequality only has exact signs.
,2. Join them with a straight line.
With this in mind the graph of the inequality is:
The inequality is written in interval notation as:
[tex](-4,2)[/tex]In Exercises 1 and 2, solve the system using the elimination method.2. x + y - 2 = -22x – y += = 8-x + 2y + 2: = 10
Answers
(1,3,-7)
1) Let's write the following system of linear equations, and then solve them by the elimination method.
The first thing to do is to proceed with the elimination of one variable. In this case, let's chose to start with
x-6y+2z=5 x -2
2x-3y+z=4
3x+4y-z=-2
2x-12y+4z=10
2x-3y+z=4
3x+4y-z=-2
Adding these two equations:
2x-3y+z=4
-2x+12y-4z=-10
----------------------------------
9y -3z =-6
Now getting the other equations, let's eliminate another variable, in this case, "x"
-2x+12y-4z=-10 x 3
3x+4y-z=-2 x 2
Adding them
-6x +36y -12z=-30
6x+8y-2z=-4
----------------------------
0 44y -14z=-34
2) Now that we have a simpler system of two variables "y" and " z" let's operate them. Choosing a factor that we can multiply and cancel out the y variable, in this case, let's pick the Least Common Multiple between 9 and 44 = 396, so let's multiply them by
9y -3z = -6 x 44
44y-14z=-34 x -9
396y -132z = -264
-396y+126z=-306
----------------------------
6z =-42
z=-7
Plugging into the equation 9y -3z =-6
9y-3(-7)=-6
9y +21 =-6
9y=27
y=3
And for x
x-6y+2z=5
x-6(3)+2(-7)=5
x+18-14=5
x+4=5
x=1
3) So the solution for that system is (1, 3, -7).
write a fracción and a decimal for the part of the gris that is shaded.
Answers
The shaded part is 3 column
There are 10 columnn in total.
The number of grids are 100 and shaded grids are 30
Thus the fraction of shaded portion is:
3/10.
The decimal form is 0.3.
What is the value of 0 in the following image
Answers
We will determine the value of theta as follows:
[tex]\begin{gathered} cos(\theta)=\frac{10}{21}\Rightarrow\theta=cos^{-1}(\frac{10}{21}) \\ \\ \Rightarrow\theta\approx61.6 \end{gathered}[/tex]So, the measurement of the angle is approximately 61.6°.
A spinner with 10 equally sized slices is shown below. (2 slices are red, 4 are blue, and 4 are yellow.) The dial is spun and stops on a slice at random. What is the probability that the dial stops on a slice that is not red?Write your answer as a fraction or a whole number.
Answers
We will have the following:
Since there are 8 slices that are not red, the probability will be given by:
[tex]p=\frac{8}{10}\Rightarrow p=\frac{4}{5}\Rightarrow p=0.8[/tex]So, the probability will be of 4/5, that is 80%.
These ordered pairs represent a proportional relationship. Use the interactive and the constant of proportionality to find the missing coordinates for the ordered pairs.
(3, 9), (A, 12), (5, 15), (6, B
Answers
Missing coordinates for the ordered pairs given are A= 4 and B= 18.
What are coordinates ?An integer pair used to define a point's location on a coordinate plane using the horizontal and vertical separations from the two reference axes Coordinates are two numbers (Cartesian coordinates) or, less frequently, a letter and a number that identify a specific location on a grid, also known as a coordinate plane. They are frequently represented by the x-value and y-value pair (x,y). The x (horizontal) and y (vertical) axes are the two axes of a coordinate plane with four quadrants (vertical)
Calculation12/A = 9 / 3
A = 4
Same as above
B/6 = 9/3
B = 18
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Then where dose the two lines intersect needs to be (x,y) pair
Answers
Answer:
The lines are parallel, and therefore, never intersect.
2. The volume of a 3-D shape is 13 cubic feet. The shape is scaled up and the new volume is 832 cubic
feet. What was the scale factor?
Answers
Scale factor of given equation is 64 : 1
What is scale factor ?Scale Factor is used to scale the shape in various dimensions. In Geometry you will learn about different geometric shapes in 2D and 3D. A scale factor is a measure of similar figures that look the same but have different scales or measurements. Suppose two circles are similar but may have different radii. The scale factor indicates how much larger or smaller the figure is than the original figure. Scale allows you to scale the original shape up or down and draw it. The amount by which a shape is magnified or shrunk is called the scale factor. Used when you need to increase the size of 2D shapes such as circles, triangles, squares, and rectangles. Magnification is also well understood from the basic theorem of proportionality.Calculationinitial volume = 13 cubic feet
final volume = 832 cubic feet
scale factor = 832 / 13
= 64 : 1
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Q14.
The diagram shows a solid shape.
The cone has a height of 10 cm.
The volume of the cone is 270π cm³.
The solid shape is made from a hemisphere and a cone.
The radius of the hemisphere is equal to the radius of the base of the cone.
Work out the total volume of the solid shape.
Give your answer in terms of pi.
Answers
The total volume of the solid shape is 756π cm³.
There is a solid shape. The shape is formed by joining a cone with a hemisphere. The radius of the hemisphere is equal to the radius of the base of the cone. The height of the cone is 10 cm. The volume of the cone is 270π cm³. We need to find the total volume of the solid shape. The total volume is the sum of the volumes of the cone and the hemisphere. Let the radius be "r". The volume of the cone is (1/3)πr²h. So, we can find the radius.
270π = (1/3)πr²h
810 = r²*10
r = √81 = 9
The volume of the hemisphere is (2/3)πr³ = (2/3)π9³ = 486π cm³. The total volume of the solid shape is V = 270π +486π = 756π cm³.
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Which angles are coterminal with -6pie/5
Answers
4π/5 and -16π/5 are Coterminal angles with -6π/5
What is Angle?an angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle
Coterminal angles are angles that share the same initial and terminal sides. To find an angle coterminal to another you can do so by simply adding or subtracting any multiple of 360 degrees or 2 pi radians.
The given angle is -6π/5
We need to add 2π for finding coterminal angle
-6π/5+2π
4π/5
We need to subtract 2π for finding coterminal angle
-6π/5-2π
-6π-10π/5
-16π/5
Hence 4π/5 and -16π/5 are Coterminal angles with -6π/5
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Lacy picks blueberries and raspberries from her garden. She has 1/5 as many pounds of blueberries as raspberries. If she picks 1 4/5 pounds more blueberries, she will have an equal weight of berries. let x represent the weight of raspberries. Which equations could be used to find the weight of the blueberries Lacey has?
Chose all correct answers.
A. [tex]\frac{1}{5} x-1\frac{1}{5}=x[/tex]
B. [tex]x-1\frac{4}{5} =\frac{1}{5}x[/tex]
C. [tex]\frac{1}{5}x=x-1\frac{4}{5}[/tex]
D. [tex]x+1\frac{4}{5}=\frac{1}{5}x-1\frac{4}{5}[/tex]
E. [tex]\frac{1}{5}x+1\frac{4}{5}=x[/tex]
F. [tex]x=1\frac{4}{5}(\frac{1}{5}+x)[/tex]
Answers
The equations that could be used to find the weight of the blueberries Lacey has are given as follows:
B. x - 1 and 4/5 = x/5.
C. x/5 = x - 1 and 4/5.
E. x/5 + 1 and 4/5 = x.
How to obtain the equations?The variable that represents the weight of the raspberries is given as follows:
x.
The variable that represents the weight of the blueberries is given as follows:
b.
She has 1/5 as many pounds of blueberries as raspberries, hence:
b = x/5.
If she picks 1 4/5 pounds more blueberries, she will have an equal weight of berries, hence:
b + 1 and 4/5 = x.
x/5 + 1 and 4/5 = x.
Thus the correct options are given as follows:
Option B, as x - 1 and 4/5 = x/5.Option C, as x/5 = x - 1 and 4/5.Option E, as x/5 + 1 and 4/5 = x.More can be learned about a system of equations at https://brainly.com/question/24342899
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Micah has an electricity plan where he is charged a monthly fixed rate of $3.18 and a usage fee of $0.14 per kilowatt-hour. In the equation below, x represents the amount of electricity he used, and y represents the amount Micah was charged for electricity. y = $0.14x + $3.18 If Micah was charged $143.18 for electricity last month, how much electricity did he use? A. 140 kilowatt-hours B. 45 kilowatt-hours C. 1,023 kilowatt-hours D. 1,000 kilowatt-hours Reset Submit
Answers
Answer:
D. 1,000 kilowatt-hours
Step-by-step explanation:
Given:
[tex]y=0.14x+3.18[/tex]
If Micah was charged $143.18, then:
[tex]143.18=0.14x+3.18[/tex]
First, subtract 3.18 from both sides:
[tex]140.00=0.14x[/tex]
Then, divide both sides by 0.14:
[tex]1000=x[/tex]
6x+1.6=58
i dont know the answer to this
Answers
The value of x in the given equation, 6x + 1.6 = 58, is x = 9.4
Determining the value of x in an equationFrom the question, we are to determine the value of x in the given equation.
The given equation is
6x + 1.6 = 58
To determine the value of x in the equation, we will determine the value of the unknown variable.
The unknown variable in the given equation is x.
Thus, we will determine the value of x.
Solving the equation for x
6x + 1.6 = 58
Subtract 1.6 from both sides of the equation
6x + 1.6 - 1.6 = 58 - 1.6
6x = 56.4
Divide both sides of the equation by 6
6x/6 = 56.4/6
x = 9.4
Hence, the equation solved for x gives x = 9.4
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Can someone answer this for me ill give a big reward
Answers
Answer:
carol
Step-by-step explanation:
Beth’s hair can be represented as 1 since everyone else is a fraction of her hair so we just convert the other 2 fractions to make them have the same denominator
4x3/5x3=12/15
2x5/3x5=10/15
10 is less than 12 so carol has the shortest hair
Hopes this helps please mark brainliest
To help visualize, let's say Beth's hair is 15 inches:
Beth = 15"
Abbey = 4/5 * 15" = 12"
Carol = 2/3 * 15" = 10"
Carol has the shortest hair.
2) A recycling center was offering cash for different types of recyclables. For each pound of
paper recycled they offered $0.03, for each pound of aluminum they offered $1.32 and for
each pound of plastic they offered $0.07. Jerry took in 10 pounds of paper, 8 pounds of
aluminum and 7 pounds of plastic. How much money did he earn?
Answers
The money earned by Jerry at the recycling center is $11.35.
According to the question,
We have the following information:
For each pound of paper recycled they offered $0.03, for each pound of aluminum they offered $1.32 and for each pound of plastic they offered $0.07. Jerry took in 10 pounds of paper, 8 pounds of aluminum and 7 pounds of plastic.
Now, we have the following expression when multiplied with the cost of each pound:
10*0.03+8*1.32+7*0.07
Now, we will first use multiplication and then we will use addition:
0.3+10.56+0.49
$11.35
Hence, the money earned by Jerry at the recycling center is $11.35.
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Look at the simultaneous equations below.
x - 6y=10
3y² = 4x + 1
a) Show that 3y² - 24y - 41 0
=
b) Use part a) to solve the simultaneous
equations.
Answers
For x = 200, the equation 3y² - 24y - 410 is satisfied and there two possible solution sets A(66.68, 9.447) and B(1.31, - 1.447) for the given system of equations.
What is a expression? What is a mathematical equation? What is degree of a equation?A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.A mathematical equation is used to equate two expressions.Degree of equation is the highest power of x in the given equation.An equation of second degree is of the form -f(x) = ax² + bx + c
It has two possible roots.Given is are the following equations -
x - 6y=10
3y² = 4x + 1
It is given that -
3y² - 24y - 41 ...Eq[1]
3y² = 4x + 1
y² = (4/3)x + (1/3)
So, we can write -
3{(4/3)x + (1/3)} - 24 × √{(4/3)x + (1/3)} - 410
Refer to the graph [1] attached. We can see that, for x = 200, the equation is fulfilled.
Now, refer to the graph [2] attached. It shows there two possible solution sets.
A(66.68, 9.447)
B(1.31, - 1.447)
Therefore, for x = 200, the equation 3y² - 24y - 410 is satisfied and there two possible solution sets A(66.68, 9.447) and B(1.31, - 1.447) for the given system of equations.
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The local seven digit telephone numbers in city A have 207 as the first three digits. How many different telephone numbers are possible in City A?
Answers
Given:
There are seven total digits.
The first 3 are already selected, so there is a choice for 4 digits.
There are 10 possible choices for each of the other 4 digits, so there are a total of 10×10×10×10 choices. Therefore:
[tex]10\times10\times10\times10=10000[/tex]Answer: 10000
Find the Area of the figure below, composed of a rectangle and one semicircle, with
another semicircle removed. Round to the nearest tenths place.
18
14
:C
PLEASE HELP 10 POINTS !!!!!!!!
Answers
Answer:
112
Step-by-step explanation:
8*14=112
3.14*4²=50.24
50.24/2=25.12
112-25.12+25.12=112
It costs $2 to download a song and $12 to download an entire album. Jorge has $50 to spend on downloading music. Create an inequality that represents the number of songs (s ) and albums (a ) that Jorge could download.
I need a inequality
Answers
The inequality to represent the given situation is 2s+12a≤50.
Given that, it costs $2 to download a song and $12 to download an entire album.
What are inequalities?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Jorge has $50 to spend on downloading music.
Let the number of songs be s and the number of albums be a.
So, inequality to represent the given situation is
2s+12a≤50
Therefore, the inequality to represent the given situation is 2s+12a≤50.
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What is the equation X+y>3 in the slope interceptform (ie y=mx+b)?
Answers
Select the correct answer.Which equation represents the line that is perpendicular to y = 1/4 and passes through (-6,-9)?A. x = -9B. X=-6C. y=-9D. y=-4
Answers
SOLUTIONS
Step-by-step explanation:
y = 1/4 is the equation of a horizontal line parallel to the x- axis.
A line perpendicular to it will be a vertical line parallel to the y- axis with equation
x = c
where c is the value of the x- coordinates the line passes through.
The line passes through (- 6, - 9 ) with equation
x = - 6 →
Option B
Answer:
B
Step-by-step explanation:
y = [tex]\frac{1}{4}[/tex] is the equation of a horizontal line, parallel to the x- axis and passing through all points with a y- coordinate of [tex]\frac{1}{4}[/tex]
A line perpendicular to it will be a vertical line parallel to the y- axis, with equation
x = c ( c is the value of the x- coordinates the line passes through )
the line passes through (- 6, - 9 ) with x- coordinate - 6 , then
x = - 6 ← equation of perpendicular line
jack wants to buy a pair of trousers for $60.When he went to the store he found that the price was marked down by 20%. how much do they cost
Answers
Answer:
$48
no idea how working out would go
Answer: $48
Step-by-step explanation: First convert 20% to a decimal which is 0.2 or 0.20.
Then multiply 60 x 0.20 which equals 12.
Because it is a markdown then you must subtract 12 from 60 which gives you the answer $48.
I hope this helps!! Good Luck!
1/16*1/8 in exponential form
Answers
The exponential form of 1/6 × 1/ 8 = 1/32 = 3.125 × [tex]10^{-5}[/tex]
The given numbers are 1/6 and 1/8
and exponential form means that we would have to write these numbers in such a way that the number can be expressed in the form 10 raised to the power of an integer.
When we solve 1/6
we will get 1/6 = 0.166
and when we solve 1/8 we will get
1/8 = 0.125
thus when we multiply 1/6 × 1/ 8 = 1/32
which when solved will give us
0.03125
this can be expressed as 3.125 × [tex]10^{-5}[/tex]
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Find the slope and y-intercept of the line. Graph the line.
Answers
Answer:
Graphing the equation we have;
Explanation:
Given the equation;
[tex]x+5y=40[/tex]the slope of the line can be derived by expressing the equation in slope-intercept form;
[tex]\begin{gathered} 5y=-x+40 \\ y=-\frac{1}{5}x+\frac{40}{5} \\ y=-\frac{1}{5}x+8 \end{gathered}[/tex]So, the slope and y-intercept are;
[tex]\begin{gathered} \text{slope m = -}\frac{1}{5} \\ y-\text{intercept b = 8} \end{gathered}[/tex]to graph the equation, let us find the x-intercept;
[tex]\begin{gathered} at\text{ y=0;} \\ x+5y=40 \\ x+0=40 \\ x=40 \\ (40,0) \\ at\text{ x=0;} \\ (0,8) \end{gathered}[/tex]Graphing the equation we have;
Other points on the graph includes;
[tex]\begin{gathered} at\text{ x=10}; \\ y=-\frac{1}{5}(10)+8=-2+8=6 \\ (10,6) \\ at\text{ x=20;} \\ y=-\frac{1}{5}(20)+8=-4+8=4 \\ (20,4) \end{gathered}[/tex]Potassium-42 has a half-life of 12.4 hours. How much of a 746-gram sample will be left after 62 hours?
Answers
the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)
Explanation:half life = 12.4 hours
initial amount = 746g
time elapsed = 62 hours
Using the half-life formula:
[tex]\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = amount remaining} \\ N_0\text{ = initial amount = 746g} \\ t\text{ = 62 hours} \\ t_{\frac{1}{2}\text{ }}\text{ = 12.4 hours} \end{gathered}[/tex]Substitute for the values:
[tex]\begin{gathered} N(t)=N_0(\frac{1}{2})^{\frac{t}{t_{_{\frac{1}{2}}}}} \\ N(t)\text{ = }746(\frac{1}{2})^{\frac{62}{12.5}} \\ N(t)\text{ = }746(\frac{1}{2})^5 \\ N(t)\text{ = }746(\frac{1}{2^5}) \end{gathered}[/tex][tex]\begin{gathered} N(t)\text{ = }(\frac{746}{32})^{} \\ N(t)\text{ = }23.3125 \end{gathered}[/tex]Hence, the amount of potassium-42 remaining after 62 hours is approximately 23.31 grams (option B)
There are 6 mice in an attic. Their population is growing at a rate of12% per month.a. Write an exponential growth function to model this situation.
Answers
general equation of a population is
[tex]y=a(1+\frac{b}{100})^x[/tex]where a is the initial population and b the percent of growing
then replacing a=6 and b=12
[tex]y=6(1+\frac{12}{100})^x[/tex]and simplify
[tex]\begin{gathered} y=6(1+0.12)^x \\ y=6(1.12)^x \end{gathered}[/tex]