What is the quadrant of 3 1 on a graph?
The point (3,-1) is situated in the fourth quadrant.
Define quadrants.The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes. The intersection of the x-axis (the horizontal number line) and the y-axis in the cartesian system divides the coordinate plane into four equal pieces (the vertical number line). Because each of these four areas occupies a quarter of the entire coordinate plane, they are collectively referred to as quadrants.
Given
Quadrant of (3, -1)
Due to the fact that x is positive and y is negative, the point is situated in the fourth quadrant.
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What is y 2x 5 on a graph?
To see the graph of y = 2x−5 with the points (5/2,0) and (0,−5)
Now, According to the question:
y = 2x - 5 is a line. Determine the two points that this line intersects with the axes then connect these points to graph it.
y = 2x - 5
Take y = 0
then, solve for the abscissa
y = 2x - 5
0 = 2x - 5
2x = 5
x = 5/2
We now have the point (5/2 , 0)
Take x = 0
then, solve for the ordinate
y = 2x - 5
y = 0 -5
y = -5
We now have the point (0 , -5)
We now simply draw a line passing thru the two points (5/2 , 0) and
(0 ,-5)
Kindly see the graph of y = 2x−5 with the points (5/2,0) and (0,−5)
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The following rectangle is formed by four squares as shown below. The perimeter of this rectangle is 30 inches. What is the area of the rectangle?
The area of the rectangle formed by 4 squares is 36 sq inches.
What are the area and perimeter of a rectangle?We know the perimeter of any 2D figure is the sum of the lengths of all the sides except the circle and the area of a rectangle is the product of its length and width.
We know the perimeter of any plane figure is the sum of the lengths of all the sides.
Let each side of this square be 'a'.
∴ (a + a + a + a) + a + (a + a + a + a) + a = 30.
4a + a + 4a + a = 30.
2(4a + a) = 30.
2(5a) = 30.
10a = 30
a = 3.
So, the length of the rectangle is 4a and the width is a.
∴ The area of the rectangle is (4a×a) = 4a².
= 4(3)².
= 4(9).
= 36 sq inches.
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What is the x-coordinate of the ordered pair for the solution of the system of equations {y = −x + 102x + 6y = 8?
The x-coordinate of the ordered pair for the solution of the system of given equations is 10.4.
To find the solution to a system of equations, we need to find the values of the variables that make both equations true at the same time.
In this case, we are looking for the x-coordinate of the solution. To find this, we can solve the system of equations by eliminating one of the variables.
We can start by eliminating y from the equations by substituting the expression for y in the first equation into the second equation:
x + 6(-x + 10) = 8
x - 6x + 60 = 8
-5x + 60 = 8
-5x = -52
x = 10.4
The x-coordinate of the solution is 10.4.
This solution tells us that the x-coordinate of the point where the two lines intersect is 10.4, and the y-coordinate can be found by substituting this value into either of the original equations and solving for y.
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x + 6(-x + 10) = 8
x - 6x + 60 = 8
-5x + 60 = 8
-5x = -52
x = 10.4
The x-coordinate of the solution is 10.4.
This solution tells us that the x-coordinate of the point where the two lines intersect is 10.4, and the y-coordinate can be found by substituting this value into either of the original equations and solving for y.
If the simple interest on $3,000 for 9 years is $1,350, then what is the interest rate?
Answer:
5%
Step-by-step explanation:
To solve this problem, we need to use the formula for simple interest, which is I = PRT, where I is the interest earned, P is the principal amount, R is the interest rate, and T is the length of time the money is invested. We know that I = 1350, P = 3000, and T = 9, so we can rearrange the formula to solve for R: R = I / (P * T) = 1350 / (3000 * 9) = 0.05. Therefore, the interest rate is 5%.
Answer: 5% per year
Step-by-step explanation:
First, take 1350 divided by 3000, then times 100% = 45% for 9 years
Then take 45 divided by 9 = 5% per year
How do you convert this equation into vertex form?
Answer:
Below
Step-by-step explanation:
Filter out the - 2
y = -2 ( x^2 - 5/2 x) - 1 Now 'complete the square'
y = -2 ( x^2 - 5/2x + 25/16) + 50/16 -1 Now simplify:
= -2(x-5/4)^2 + 34/16 This will have vertex at 5/4, 34/16
in a large population, 55% of the people get a physical examination at least once every two years. an srs of 100 people are interviewed and the sample proportion is computed. the mean and standard deviation of the sampling distribution of the sample proportion are
The mean and standard deviation of the sampling distribution of the sample proportion are: (d) 0.55, 0.0497.
What is a sample proportion?In Mathematics and Statistics, a sample proportion can be defined as the proportion of individuals in a sample that have a specified characteristic or trait.
The mean of the sampling distribution of the sample proportion is equal to 0.55. Mathematically, the standard deviation of the sampling distribution of the sample proportion can be calculated by using this formula:
σp = √(p(1 - p)/n)
Substituting the given parameters into the standard deviation formula, we have;
Standard deviation, σp = √(0.55(1 - 0.55)/100)
Standard deviation, σp = √(0.55(0.45)/100)
Standard deviation, σp = 0.002475
Standard deviation, σp = 0.0497
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Complete Question:
In a large population, 55% of the people get a physical examination at least once every two years. An SRS of 100 people are interviewed and the sample proportion is computed.
The mean and standard deviation of the sampling distribution of the sample proportion are:
(a) 55, 4.97.
(b) 0.55, 0.002.
(c) 55, 2.
(d) 0.55, 0.0497.
(e) The standard deviation cannot be determined from the given information.
How do you find the vertical and horizontal asymptotes of a function?
The vertical asymptotes can be simply found by equating the denominator of a function to zero and solving for x, but the vertical asymptotes requires consideration of the highest degrees of x in numerator and denominator.
What is veritcal asymptote?A vertical asymptote is a vertical line that guides the graph of the function but is not part of it. Because it appears at an x-value outside of the function's scope, the graph can never cross it. There may be several vertical asymptotes for a given function.
What is horizontal asymptote?A graph's horizontal asymptote is a horizontal line with the equation y = b, where the graph moves closer to the line as the inputs go closer to 0 or -1.
Find the x values where the function is undef for the purpose of determining a function's vertical asymptotes. Consider the degree of the numerator and the degree of the denominator while looking for a function's horizontal asymptotes. The horizontal asymptote is y = 0 if the degree of the numerator is smaller than the degree of the denominator. There is no horizontal asymptote if the degree of the numerator is higher than the degree of the denominator. The horizontal asymptote is y = the coefficient of the highest-degree term in the numerator divided by the coefficient of the highest-degree term in the denominator if the degree of the numerator and denominator are equal.
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Is (–39, 42) a solution to the equation y = x + 81?
Answer:
Yes
Step-by-step explanation:
Yes because if you insert -39 for x and 42 for y then your equation is:
42 = -39 + 81
If you were to solve this equation it would be true.
What are the roots of 3x² 7x 6?
On solving the provided question we can say that, - the roots of the given equations [tex]3x^2 + 7x - 6[/tex] are - x2/3 and x = -3
What are roots ?
When referring to the values of a variable for which the supplied polynomial equals zero, we use the term "roots of a polynomial." The polynomial p(x) has zero roots if and only if an is its root. By setting each component to 0, you may solve for x to determine the roots, or solutions, of the polynomial equation P(x) = 0. Factoring is used to solve the polynomial equation. Set each component to a value of 0 (2x4), (x-6) or (x+1). Calculate x using the solution.
here,
[tex]3x^2 + 7x - 6[/tex]
(x - 2/3)(x+3)
x = 2/3 and x = -3
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When solving a linear system of equations you are looking for roots of the equation?
When solving a linear system of equations, what you obtain are the roots of the equation.
What is a linear equation?A linear equation is the type of equation in which he highest power of the variable is one. In some cases, we would have a system of linear equations and we have to solve the system.
When we are solving the system of equations, there are various methods that we could use such as;
Substitution methodElimination methodCramer's ruleGraphical methodThe solutions that we obtain from the equation are the root of that equation.
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How much timber would be left if eleven 1.75m lengths are cut from a 22m piece of timber?
Work Shown:
1 piece = 1.75 m
11 pieces = 11*1.75 = 19.25 m
22 m - 19.25 m = 2.75 meters
This ignores the width of the saw blade, while small, it's not infinitely thin.
Please help me with this
Answer:
y = 13z = 14Step-by-step explanation:
You want the values of y and z in the figure showing a triangle with exterior angle 135° opposite remote interior angles (5y+5)° and (4z+9)°, where angle (4z+9)° is adjacent to exterior angle (9y-2)°.
Exterior angleThe exterior angle of a triangle is equal to the sum of the remote interior angles. This can be used to find both y and z.
The lower left interior angle is 180° -135° = 45°, so the right-side exterior angle is ...
(9y -2)° = (5y +5)° +45°
4y = 52 . . . . . . . . . . . . . divide by °, add 2-5y
y = 13 . . . . . . . . . . divide by 4
The lower left exterior angle is ...
135° = (5y +5)° +(4z +9)°
135 = 5(13) +5 +4z +9 . . . . . . . . . divide by °, substitute value of y
56 = 4z . . . . . . . . . . . . . . . . subtract 79
14 = z . . . . . . . . . . . . divide by 4
The values of y and z are 13 and 14, respectively.
What are the SSS SAS and AAS congruence criteria?
The definition of SSS, SAS, and AAS congruency conditions is shown.
SSS condition:
In accordance with the SSS rule, two triangles are considered to be congruent if their corresponding three sides are equal on both triangles.
SAS condition:
The two triangles are congruent if two sides and the included angle of one triangle match those of a second triangle by two sides and the included angle.
AAS condition:
The triangles are said to be congruent when two angles and a non-included side of one triangle match the corresponding angles and sides of another triangle.
Therefore, the definition of SSS, SAS, and AAS congruency conditions is shown.
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What is the volume of this cylinder?
Use
3.14 and round your answer to the nearest hundredth.
6 in
2 in
cubic inches
By using the volume of the cylinder, it can be calculated that
Volume of the cylinder is 75.360 cubic inches
What is volume of a cylinder?
Volume of a cylinder is the total space taken by the cylinder.
If r is the radius of the cylinder and h is the height of the cylinder, then volume of the cylinder is calculated by-
V = [tex]\pi r^2h[/tex]
Here,
Height of the cylinder = 6 inches
Radius of the cylinder = 2 inches
Volume of the cylinder = [tex]3.14 \times 2^2 \times 6[/tex] = 75.360 cubic inches
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Complete Question
A cylinder has a height of 6 inches and a radius of 2 inches. What is its volume? Use a 3.14 and round your answer to the nearest hundredth.
Which types of transformations change the shape of a graph?
Dilation
By maintaining the object's orientation or shape, this type of translation either expands or contracts the object. This is referred to as resizing.
What is Graph Transformation?
A graph can be transformed to produce a different version of the one that came before it. The x-y plane can be used to translate or shift the graphs. In addition to these modifications, they may also be stretched.
Types of Stretching of Graphs
Stretching out VerticallyConsider the case where we need to lengthen a graph by a factor of 2. Next, change the y value. Now, each point of the function F's form (x, y) shifts to the point (x, 2y)*
Stretching out horizontallyAdjust the x value if a graph needs to be stretched horizontally by a factor of two. The point (2x, y) in function F is now the new location for all points with the form (x, y) in function F.
Types of Translation in Graphs
Moving HorizontallyA graph is horizontally translated by moving the base graph to the left or right in relation to the x-axis. Consider that if we want to move a graph horizontally by 1 unit, we would also need to change the x value.
Moving VerticallyA graph's base graph is moved up or down in the y-axis direction when it is vertically translated. Each point on a graph is moved b units vertically to translate the graph in that many directions.
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A car can get 10 miles on 1 1/2 gallons of gas. How many gallons of gas are needed if you need to go 150 miles
22 1/2 because if you see the 150 as 15 an multiply it by 1 1/2 you get 22 1/2
how does a qualitative graph describe the relationship between quantities
As described in Analytical Geometry the relationship between quantities of a qualitative graph are explained below.
What is Analytical Geometry?
The area of algebra known as analytical geometry uses an ordered pair of numbers known as coordinates to determine the position of a point on a plane. It is utilised to model many plane objects, including points, lines, and others. The terms Coordinate geometry and Cartesian geometry are both used to refer to analytical geometry.
Cluster Use functions to model relationships between quantities. Standard Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear).
A linear relationship between two quantities will produce a graph of a straight line. The line represents every possible solution for the range of the function. In order to create the line, we use the function equation and evaluate the range, or output, values based upon several of the domain, or input, values.
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Solve this system of equations by graphing. First graph the equations, and then type the solution.
According to question,
Given data,
2x-3y=-12……… (1)
Y=-5x/3-3……… (2)
3y= -5x-9………… (3)
Solving the equation,
(1) and (3)
5x-3y=-9
2x-3y=-12
To solve both equation
3x=3
x=1
the value of x, putting equation 1
5x-3y= -9
5×1-3y=-9
5-3y=-9
-3y=-9-5
-y=-14
y=14/3
y=4.6
the value of x=1 and y=4.6
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Q-find the greatest common factor.ab4c7,a7b4c.
We know that,
Greatest common factor= the greatest common factor is the greatest factor that divides both numbers.
According to question.
Given data,
Factor of a= a
Factor of b=b× b× b× b
Factor of c=c× c× c× c× c× c× c
Therefore,
Factor of a=a× a× a× a× a ×a ×a
Factor of b4=b ×b ×b× b
Factor of c=c
Greatest common factor=ab4c
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What are the roots of the quadratic equation 2x² 5x 3 0?
The roots of the quadratic equation 2x² + 5x + 3 = 0 are x = -3 and x = -1/2.
To find the roots of a quadratic equation, we must first convert the equation into the standard form ax² + bx + c = 0. In this case, the given equation is already in this form, so we can proceed with solving. To solve, we use the quadratic formula, which is x = (-b ± √(b² - 4ac))/2a.So, we have x = (-5 ± √(25 - 4(2)(3))/2(2). Simplifying, we get x = (-5 ± √(13))/4. The quadratic formula yields the values x = -3 and x = -1/2. Therefore, the roots of the quadratic equation 2x² + 5x + 3 = 0 are x = -3 and x = -1/2.
x = (-5 ± √(25 - 4(2)(3))/2(2)
= (-5 ± √(13))/4
= -3, -1/2
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How do you find the z-score for a sample mean on the distribution of means?
The formula z = (x-μ)/σ allows us to determine the z-score for a sample mean on the distribution of means.
What is a z-score?A Z-score is a metric that quantifies how closely a value relates to the mean of a set of values.
Standard deviations from the mean are used to measure Z-score.
A Z-score of zero means the data point's score is the same as the mean score.
Z-scores are calculated using the formula z = (x-μ)/σ, where x represents the raw score, the population mean, and the population standard deviation.
The z-score is simply the raw scoreless the population means, divided by the population standard deviation, as the calculation demonstrates.
Therefore, the formula z = (x-μ)/σ allows us to determine the z-score for a sample mean on the distribution of means.
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brittany is playing game in which 1 out of 10 players is selected to be a spy. the game claims the selection of a spy is random and all players are equally likely to be selected. brittany has played 7 games and was selected to be a spy in 5 of those games. brittany runs a simulation of 100 trials. in the simulation, she used a random number generator to select 7 digits from 0 to 9 with 0 representing being selected to be a spy and 1 through 9 representing not being selected to be a spy. the frequency of games selected to be a spy in a trial of 7 samples in the simulation is represented by this table. what is the best conclusion for brittany to make based on the data?
The simulation disproves the hypothesis that 1 out of 10 players are arbitrarily chosen to be spies by showing that being selected as a spy in 5 out of 7 games is improbable.
What is meant by probability?A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
The probability is a metric for determining how likely an event is to occur. It gauges the event's degree of certainty. The probability formula is presented as follows:
P(E) = Number of Favorable Outcomes/Number of Total Outcomes.
The frequency is o when the number of agnes chosen to be soy is 5, as shown in the table.
The simulation demonstrates that getting chosen as a spy in 5 out of 7 games is implausible, refuting the claim that 1 out of 10 players is randomly chosen to be a spy.
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How do you do two step inverse operations?
You meaured the width of your front door to be 3 feet and 2 inche. The chair you are trying to through the door meaured to be 20 inche wide. How much wider i the door than the chair
Answer:
1 foot and 4 inches.
Step-by-step explanation:
1 feet = 12 inches
3 feet = 12*3 = 36 inches
Then:
3 feet and 2 inches = 36 + 2 = 38 inches
if the chair measured 20 inches:
36 - 20 = 16 inches
16 inches = 12inches + 4 inches
= 1 foot and 4 inches
the question is in the picture
Answer:
15 weeks
Step-by-step explanation:
read the graph at the number of words correct
those past 15.words count the weeks in the y.axis
What is the x and y intercept of y=3x-15 and is (2,-9) a solution?
Answer: y intercept (0,-15), x intercept (5,0), yes, (2,-9) is a solution
Step-by-step explanation:
the y intercept is when x=0, so plug in 0 for x -> y=3(0)-15
y=-15, y intercept is (0,-15)
the x intercept is when y=0
so plug in 0 for y -> 0=3x-15
then solve for x,
add 15 to both sides -> 15=3x
divide both sides by 3, 5=x
x intercept is (5, 0)
to test if (2, -9) solution, lets plug in 2 for x and see if we get an answer of -9
so y=3(2)-15
y=6-15
y=-9
so yes, (2,-9) is a real solution
What are the roots of the quadratic equation V 2x² 9 9?
The roots of the quadratic equation 2[tex]x^{2}[/tex] -9x +9 =0 are 1.5 and 0.75
given equation
2[tex]x^{2}[/tex] -9x +9 =0
now , we need to find the roots of the above equation
roots = - b ± [tex]\sqrt{b^{2} - 4ac}[/tex] /4a
a = 2
b =-9
c = 9
roots = -(-9) ± [tex]\sqrt{(-9)^{2} - 4(2)(9)}[/tex] / 4(2)
= 9 ± [tex]\sqrt{81-72}[/tex] / 8
= 9 ± [tex]\sqrt{9}[/tex] /8
= 9 ± 3 /8
= 9+3/8 and 9-3/8
= 12/8 and 6/8
= 1.5 and 0.75
The roots of the quadratic equation 2[tex]x^{2}[/tex] -9x +9 =0 are 1.5 and 0.75
In algebra, a quadratic equation (from Latin quadratus 'square') is any equation that can be rearranged in standard form as
a[tex]x^{2}[/tex] +bx +c =0
where x represents an unknown value, and a, b, and c represent known numbers, where a ≠ 0. (If a = 0 and b ≠ 0 then the equation is linear, not quadratic.) The numbers a, b, and c are the coefficients of the equation and may be distinguished by respectively calling them, the quadratic coefficient, the linear coefficient and the constant or free term.
The values of x that satisfy the equation are called solutions of the equation, and roots or zeros of the expression on its left-hand side. A quadratic equation has at most two solutions. If there is only one solution, one says that it is a double root. If all the coefficients are real numbers, there are either two real solutions, or a single real double root, or two complex solutions that are complex conjugates of each other. A quadratic equation always has two roots, if complex roots are included; and a double root is counted for two. A quadratic equation can be factored into an equivalent equation
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Statements and Reasons:
Given: Quadrilateral ABCD with
diagonal AEC bisecting DAB,
BE, DE, and 1 = 2.
Prove: BC = DC.
Quadrilateral ABCD with diagonal AEC bisecting DAB, BE, DE, and 1 = 2 then BC=DC.
What is Quadrilateral?A quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices.
Given that Quadrilateral is ABCD.
diagonal AEC bisecting DAB,
BE, DE, and 1 = 2.
It is clearly given that the diagonals bisects each other.
Which means all the sides of the quadrilateral might be equal which means the quadrilateral may be a square or an rhombus.
Diagonals DAB and AEC are bisecting.
Then the sides BC and DC are equal.
BC=DC.
Hence, if Quadrilateral ABCD with diagonal AEC bisecting DAB,
BE, DE, and 1 = 2 then BC=DC.
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What is the relationship between the volumes of a cylinder and a cone both of which have equal radii and vertical heights?
The relationship between the volumes of a cylinder and a cone both of which have equal radii and vertical heights:
the volume of cone = 1/3 × volume of cylinder
In this question we need to find the relationship between the volumes of a cylinder and a cone both of which have equal radii and vertical heights.
Consider a cylinder with radius r and vertical height h.
We know that the formula for the volume of cylinder.
V1 = π × r² × h ..........(1)
Now consider a cone with radius r and vertical height h.
Using the formula for the volume of cone,
V2 = 1/3 × π × r² × h
From equation (1),
V2 = 1/3 × V1
the volume of cone = 1/3 × the volume of cylinder
Therefore, volume of cone = 1/3 × volume of cylinder
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Simplify (m^4n)^3.
m^12n^3
m^4n^3
m^12n
mn^15
Answer:
Step-by-step explanation:
Simplifying the expression (m^4n)^3 can be done by using the laws of exponents. The first law states that when two terms with identical bases are being multiplied, you add their exponents together. In this case, m is the base and 4n is its exponent; therefore, when we multiply them together three times (or raise to the third power), then our result should be m raised to a power of 12n.