a. Yes, it is possible for a line (y = mx + b) that passes through the origin (0, 0) to pass through no other rational points. An example of such a line is y = sqrt(2)x. This line passes through the origin (0,0), but the y-coordinate will only be a rational number if the x-coordinate is also a rational number and a perfect square.
b. Yes, it is possible for a line to pass through no rational points. An example of such a line is y = sqrt(2)x + sqrt(3). This line will never pass through any rational points because the y-coordinate will only be a rational number if both x and b are rational numbers and perfect squares, which is not possible in this case.
What is the solution to this system of equations?
-3x + 4y = 24
y = 3/4x+6
No solution
(-3,3)
(4,6)
Infinitely many
Equations now take the shape:
[1] 3x - 4y = 24
[2] 3x + 4y = 6
What number is infinitely many solutions?Some equations have infinitely many solutions. In these equations, any value for the variable makes the equation true. You can tell that an equation has infinitely many solutions if you try to solve the equation and get a variable or a number equal to itself. Combine like terms 2x and 2x.As an example, consider 3x + 5 = 3x - 5. This equation has no solution. There is no value that will ever satisfy this type of equation infinitely many. (mathematics) Having a quantity or cardinality that is infinite or unbounded“No solution” means that there is no value, not even 0, which would satisfy the equation. Also, be careful not to make the mistake of thinking that the equation 4 = 5 means that 4 and 5 are values for x that are solutions.To learn more about infinitely many solutions refers to:
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Ax+By=C
y + 6 = -2 (x + 1) Whats the-answer for the question
The answer for y + 6 = -2 (x + 1) the equation in the general form is y - 2x = -8.
What is equation?
Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.
The equation is represented in the general form Ax+By=C.
The given equation is -
y + 6 = -2 (x + 1)
Simplify further -
y + 6 = -2 (x + 1)
y + 6 = -2x -2
y - 2x = -2 - 6
y - 2x = -8
Therefore, the equation is y - 2x = -8.
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12
R
T
37
35
Enter the ratio equivalent to tan(R).
>S
Answer:
[tex]\frac{35}{12}[/tex]
Step-by-step explanation:
The tangent of an acute angle in a right triangle is defined as the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
D
7. Solve the system:
f(x)=(x-3)² +1
g(x)=-3x+10
Answer: (0,10) and (3,1)
Step-by-step explanation:
Before I solve the system, I am going to rewrite it to make it easier for me to understand it.
[tex]y=(x-3)^2+1\\y=-3x+10[/tex]
Notice that f(x) and g(x) have been changed into y. The reason is because f(x) and g(x) are the same and stand for y, but we only use f and g to distinguish between the 2 equations. We can use equal values to solve.
[tex](x-3)^2+1=-3x+10[/tex] [exponent]
[tex]x^2-6x+9+1=-3x+10[/tex] [add both sides by 3x]
[tex]x^2-3x+10=10[/tex] [subtract both sides by 10]
[tex]x^2-3x=0[/tex] [factor]
[tex]x(x-3)=0[/tex]
Notice that x=0 and x-3=0. This means the solutions are x=0 and x=3.
To find the actual full solution, we have to plug those points back into the original equations.
[tex]-3(0)+10=0+10=10\\-3(3)+10=-9+10=1[/tex]
Therefore, the solutions to this system are (0,10) and (3,1).
please answer i need
Answer:A
Step-by-step explanation:
To which subset of real numbers does the following number belong? Square Root Of 54
A.
whole numbers, natrual numbers, integers
B.
whole numbers, integers, rational numbers
C.
irrational numbers
D.
rational numbers
The number √ 54 is an irrational number.
What is Rational number?A number which can be written in the form of fraction p / q , where q is non zero, are called Rational numbers.
Given that;
The number is,
⇒ √54
Now,
⇒ √ 54 = 7.348469...
Hence, By definition of an irrational number,
It is an Irrational number.
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A spinner with 4 equal sections is spun 20 times. The frequency of spinning each color is recorded in the table below.
Outcome | Frequency
Pink | 6
White | 3
Blue | 7
Orange | 4
What statement best compares the theoretical and experimental probability of landing on pink?
A. The theoretical probability of landing on pink is one fifth, and the experimental probability is 50%.
B. The theoretical probability of landing on pink is one fourth, and the experimental probability is 50%.
C. The theoretical probability of landing on pink is one fifth, and the experimental probability is 30%.
D. The theoretical probability of landing on pink is one fourth, and the experimental probability is 30%.
The theoretical probability of landing on pink is 3/10, and the experimental probability is 30%. Therefore, option D is the correct answer.
What is the probability?Probability can be defined as the ratio of the number of favourable outcomes to the total number of outcomes of an event.
We know that, probability of an event = Number of favourable outcomes/Total number of outcomes
Given that, a spinner with 4 equal sections is spun 20 times.
The frequency of spinning each color is recorded in the table below.
Outcome Frequency
Pink 6
White 3
Blue 7
Orange 4
Probability of landing on color pink is 6/20
= 3/10
= 3/10 ×100
= 30%
Therefore, option D is the correct answer.
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The value Q of a material is directly proportional to the square of its weight W. If a material weighing 20 kg is worth 500,find: (a)the value of a material weighing 5 kg (b)the value of a material weighing 50 kg (c)the weight of a material worth 720.
(a) the value of a material weighing 5 kg is 31.25
(b)the value of a material weighing 50 kg is 3125
(c) the weight of a material worth 720 is 24 kg
How to determine the value of the material?
Variation is a relation between a set of values of one variable and a set of values of other variables
If the value Q of a material is directly proportional to the square of its weight W. We can write:
Q α W²
Q = kW² (where k is constant of proportionality)
If a material weighing 20 kg is worth 500, we have:
Q = kW²
500 = k × 20²
500 = 400k
k = 500/400
k = 5/4
k = 1.25
(a)the value of a material weighing 5 kg
Q = kW²
Q = 1.25 × 5² = 31.25
(b)the value of a material weighing 50 kg
Q = kW²
Q = 1.25 × 50² = 3125
(c)the weight of a material worth 720
Q = kW²
720 = 1.25 × W²
W² = 720/1.25
W² = 576
W = √576
W = 24 kg
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Find GH in each trapezoid.
Since the midsegment of each trapezoid is parallel to each base and is half, it has a GH value of 0.85.
what is trapezium ?Having at least one pair of parallel sides, a trapezoid is a quadrilateral in American and Canadian English. In the UK and other nations that speak English, it is referred as as the Trapezium. A trapezoid is a convex quadrilateral according to Euclidean geometry. Its parallel sides make up the trapezoid's base. The trapezoid, a convex quadrilateral, is defined by an identical pair of opposite sides that are parallel to one another. On paper, the two-dimensional trapezoid shape seems like a table. The term "quadrilateral" in Euclidean geometry refers to a polygon with four sides and four vertices.
given
A trapezoid's midsegment runs parallel to each base and is half as long as all of the bases combined.
1/2 * 3x - 6 = 2x
3x - 6 = 4x
= -6 = 7x
x = 0.85
Since the midsegment of each trapezoid is parallel to each base and is half, it has a GH value of 0.85.
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grapg the line 2/3 passing through (-4,1)
The equation of the line with a slope of 2/3 passing through (-4, 1) is y = (2/3)x + 11/3
What is an equation?An equation is an expression relating two or more numbers and variables.
The slope - intercept form of a linear equation is:
y = mx + b
Where m is the rate of change(slope) and b is the y intercept.
The equation of a line passing through (x₁, y₁) with a slope of m is given by:
y - y₁ = m(x - x₁)
The line has a slope of 2/3 and pass through point (-4, 1). Hence:
y - 1 = (2/3)(x - (-4))
y - 1 = (2/3)(x + 4)
y = (2/3)x + 11/3
The equation of the line is y = (2/3)x + 11/3
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11) A plane travels 160 miles on a bearing of 327°. It then changes direction and travels 205 miles on a
bearing of 311°. How far is the plane from its original position?
2051/
2051/2 miles,The plane is travelling in a different direction from its original position, and the distance from the original position can be calculated by using the Law of Cosines.
How far is the plane from its original position?The plane's displacement from its original position can be calculated by finding the magnitude of the vector sum of the two displacements.The first displacement can be calculated using the magnitude of the vector, the bearing, and the formula for the magnitude of a vector in polar coordinates. The magnitude of the vector is equal to the distance traveled (160 miles) multiplied by the cosine of the bearing (327°). Therefore, the magnitude of the first displacement is 149.9 miles.The second displacement can be calculated in the same manner. The magnitude of the vector is equal to the distance traveled (205 miles) multiplied by the cosine of the bearing (311°). Therefore, the magnitude of the second displacement is 176.7 miles.The vector sum of the two displacements can be found by adding their respective x-components and y-components. The x-component of the first displacement is negative 149.9 miles, and the y-component is 131.8 miles. The x-component of the second displacement is negative 176.7 miles, and the y-component is 114.2 miles. The x-component of the vector sum is −326.6 miles, and the y-component is 246 miles.This problem is an example of vector addition. Vector addition is a mathematical process used to calculate the resultant displacement of two or more vector quantities. It is the process of combining two or more vectors to produce a vector that points in the same direction as the total of the individual vectors. In this case, we can use vector addition to find the distance from the plane's original position.
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(Slope MC)
A linear relationship is given in the table.
x-2 -1 0 1 2
y -18 -12 -6 0 6
What is the slope of the relationship?
0-6
-1/6
1/6
6
The given linear relationship slope of the line is D) 6.
What is slope?
An indication of how steep a line is is its slope. When calculating slope mathematically, "rise over run" is used (change in y divided by change in x). The ratio of how much y grows as x grows by a certain amount is known as the slope of a line. A line's slope, or the amount by which y rises as x rises, indicates how steep a line is. The slope is constant (the same) along the line.
Here from given tables lets take any two points to find slope, then
[tex](x_1,y_1)=(0,-6) and (x_2,y_2)=(1,0)[/tex]
Now using slope formula [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex] then
=> m = [tex]\frac{0-(-6)}{1-0}[/tex]
=> m =[tex]\frac{6}{1}[/tex]
=> m = 6.
Hence the slope of the given table is D)6.
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according to money magazine, maryland had the highest mean annual household income of any state in at (time website). assume that annual household income in maryland follows a normal distribution with a mean of and standard deviation of .
The probability of getting a household income of $75,000 in Maryland is 0.3989.
The normal distribution formula is given by:
P(x) = 1/√(2πσ^2) * e^[-(x-μ)^2 / (2σ^2)]
Where,
P(x) - Probability of getting a household income of x
μ - Mean annual household income in Maryland
σ - Standard deviation of annual household income in Maryland
Assuming that the mean annual household income in Maryland is $75,000 and the standard deviation is $10,000, the probability of getting a household income of $75,000 can be calculated using the formula given above.
P(75000) = 1/√(2π10000^2) * e^[-(75000-75000)^2 / (2*10000^2)]
= 0.3989 * e^(0)
= 0.3989
Therefore, the probability of getting a household income of $75,000 in Maryland is 0.3989.
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Complete the table.
Distance
(ft)
0
EN R
2
37
2
2π
Height
(ft)
a
b
с
d
e
The complete distance in feet on the table are a=6, b=7, c=8, d=7, and e=6.
What is revolution?In mathematics, a revolution is a full rotation, or a full 360-degree turn. The item starts and ends in the same location during a 360-degree revolution.
The circumference of the wheel is equal to the length of a full revolution, or 2*pi*radius. The whole rotation of the wheel is 360 degrees.
The eight of the point is 6 feet, and the wheel's radius is 1 feet.
The point will be in its initial position, which is 6 feet high.
The height will thus be a = 6 + 0 = 6 ft.
The point will reach half the whole height of the wheel, or 2 feet, when the distance travelled is pi/2.
Height of b = 6 + 1 = 7 feet will result.
The point will be at the top of the wheel, which is 2 feet higher than the lower point of the wheel, when the distance travelled equals pi.
The height will thus be c = 6 + 2 = 8 ft.
The point will be half the whole height of the wheel, or 2 feet, when the distance travelled is 3 pi/2.
The height will thus be d = 6 + 1 = 7 ft.
The point will be in its initial position, which is 6 feet high, when the distance travelled is 2 pi.
The height will thus be e = 6 + 0 = 6 ft.
Hence, the complete distance in feet on the table are a=6, b=7, c=8, d=7, and e=6.
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Which equation represents a linear function?
A y=1/4x
B y= |x|
C y= x exponent 2
D y= -3x exponent 3
So on solving the provided question, we can say that y= |x| makes a starlight line, this equation is a linear function.
What is linear function ?Two distinct but related concepts are referred to as linear functions in mathematics. A polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line. Any function that depicts a straight line on a coordinate plane is said to be linear. For instance, y = 3x - 2 is a linear function since it depicts a straight line on the coordinate plane. f(x) = 3x - 2 can be used to represent the function since f(x) can be linked to y.
equation represents a linear function is that polynomial function of degree 0 or 1 is a linear function in calculus and related subjects if its graph is a straight line.
so, here y= |x| makes a starlight line, this equation is a linear function.
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What are the slopes of the point o,2 1 , -1
The slope of the line that goes through the points (0, 2) and (1, -1) is -3.
What is the slope of the line?
The slope of a line is a number that describes the steepness of a line and the direction it is heading. It is also known as the "rise over run" or the "rate of change" of a line. The slope of a line is typically represented by the letter "m" and is found using the formula:
slope = (y2 - y1) / (x2 - x1)
To find the slope of a line, you need two points on the line (x1, y1) and (x2, y2) and substitute their coordinates into the slope formula.
To find the slope of a line, we use the formula:
slope = (y2 - y1) / (x2 - x1)
In this case, we have two points: (0, 2) and (1, -1). To find the slope between these two points, we can substitute their coordinates into the slope formula:
slope = (-1 - 2) / (1 - 0)
slope = -3
Hence, the slope of the line that goes through the points (0, 2) and (1, -1) is -3.
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Aaron works at a garden center where he plants
flowers. It takes him 3 1/2 hours to plant 21 flowers.
How many plants can he plant in 1 hour?
The number of flowers that can be planted in 1 hour is 6 flowers.
What is cross-multiplication?To solve equations or determine the value of a variable, cross multiplication is employed in mathematical operations. In this procedure, the numerator of one side is multiplied by the denominator of the other side.
Given that the time required to plant trees is:
3. 5 hours = 21 flowers
Convert 3.5 hours into minutes.
3 hours 60 = 180 minutes,
Additional half hour can be represented as: 1/2 hours 60 = 30 minutes.
Total hours is 180 + 30 = 210 minutes.
So it takes, 210 minutes to plant 21 flowers.
The time taken to plant flowers in 60 minutes is:
[tex]x = \frac{(21)(60)}{210} \\\\x=6[/tex]
Hence, the number of plants that can be planted in 1 hour is 6 flowers.
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5. 5(x + 10) + x
A. 6x + 15
B.5x + 15
C.6x + 50
D.4x – 50
Answer: C
Step-by-step explanation:
Graph the trapezoid A(6,5), B(8,-2), C(-4,-2), D(-2,5)
The trapezoid is a form of quadrilateral that has at least one parallel sides. The trapezoid here is given by the mentioned coordinates.
What is a point?A point is a dot on a sheet of paper or in a plane. There are no lengths, widths, or heights in a point. It establishes a plane's position or location.
What are coordinates?It is possible to find any point in a 2D plane or 3D space using coordinates, which are ordered pairs of points. You may have observed the use of grids in mathematics.
Select a point on the graph according to the given coordinates. Connect all the points on the graph using a line segment. The shape formed by joining all the points together is knows as a trapezoid.
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plisss can you solve this for me
i got nothin
like what?
The scatter plot shows the average monthly temperature, x , and a family's monthly heating cost, y , for 24 different months.
1. y = -1.15x + 102.8 is the equation of the line of best fit.
2. Using the line of best fit's equation, the estimated price is: $62.55.
What are Equations?A mathematical statement that has a "equal to" symbol between two expressions with equal values is called an 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.
We have LHS = RHS (left hand side = right hand side) in every mathematical equation.
To determine the value of an unknown variable that represents an unknown quantity, equations can be solved.
A statement is not an equation if it has no "equal to" sign.
According to our question-
1. Making use of the two points (20, 80) and (72, 20)
Slope (m) is equal to change in y/change in x, or (80 - 20)/(20 - 72) = 60/-52.
Slope is -1.15 meters.
Change y - b = m to m = -3 and (a, b) = (72, 20). (x - a)
y - 20 = -1.15(x - 72) (x - 72)
y - 20 = -1.15x + 82.8
y = -1.15x + 82.8 + 20
y = -1.15x + 102.8
The best line of fit is the equation y = -1.15x + 102.8.
2. To calculate the monthly heating expense, y, for a month with an average temperature of 35°F (x), enter x = 35 into the formula: y = -1.15x + 102.8.
y = -1.15(35) + 102.8
y = 62.55
The estimated monthly expenditure is $62.55.
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Find the equation of a line that passes through (1,8) and is parallel to the graph of y=2x+3. Write the equation in slope-intercept form, if possible.
Therefore , the solution to the given problem of equation comes out to be y = 2x + 4.
Describe the equation.A proclamation of the equivalency of two expressions is an algebraic equation, which is calculated by performing the algebraic of addition, removal, multiplication, division, raising to a power, or extracting a root to a collection of variables. Examples include (y4x2 + 2xy - y)/(x - 1) = 12 and x3 + 1.
Here,
It is important to remember that parallel lines have the same slopes before trying to determine this line's equation.
As a result, we can predict that the new line will have a slope of 2 because the previous line has a slope of 2.
Now that we have that knowledge, we can utilize it to find the equation using point-slope form and the supplied point.
y - y1 = m(x - x1) (x - x1)
y - 8 = 2(x - 2) (x - 2)
y - 8 = 2x - 4
y = 2x + 4
Therefore , the solution to the given problem of equation comes out to be y = 2x + 4.
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7X+2Y=-14 FIND THE X INTRERCEPT AND THE Y INTERCEPT
Answer:
x-intercept = -2; y-intercept = -7
Step-by-step explanation:
4. In a class of 26 students, 18 of the students have a pet. Of
the pet owners, 12 prefer dogs to cats. Of the 8 non-pet
owners, 3 prefer dogs to cats. What is the probability of
selecting a student from the class who is a pet owner or
prefers cats to dogs?
The probability of selecting a student from the class who is a pet owner or prefers cats to dogs is; 0.4
What is the probability of selection?In probability, If events A and B are not mutually exclusive, then the probability of A or B is expressed as;
p(A or B) = p(A) * p(B).
Total number of students = 26
Total number of students that are pet owners = 18
Total number of students that prefers cats to dogs = 26 - (8 + 3) = 15
Thus;
P(pet owner) = 18/26
P(prefers cats to dogs) = 15/26
P(Pet owner or prefers cats to dogs) = (18/26) * (15/26)
= 0.4
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(URGENT) Which pair of functions are inverses of each other?
The requried pair of functions which are inverse of each other is f(x) = 13x - 7 and g(x) = x + 7 / 13.
Functions are the relationship between sets of values. e g y=f(x), for every value of x there is its exists in a set of y. x is the independent variable while Y is the dependent variable.
Here,
(A)
Given function,
f(x) = x / 3 + 10
Its inverse function is given as,
f(x) - 10 = x/3
x = 3(f(x) - 10)
change x = g(x) and f(x) = x
g(x) = 3[x - 10]
Similarly,
Inversfunciton,
B. g(x) = 9/x - 5
C. g(x) = x + 7 / 13
D. g(x) = x³/4
Thus, the requried pair of functions which are inverse of each other is f(x) = 13x - 7 and g(x) = x + 7 / 13.
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I NEED HELP ASAP RN!
Answer:
TQN
Step-by-step explanation:
Classify the triangle by its sides and angles.
Am I right???
Please help!
Draw a graph of the signed area represented by the integral and compute it using geometry. (Use symbolic notation and fractions where needed.)
The integral represents a graph of the signed area, and the geometry is calculated. The area is found to be 100 units².
A plane that is created when two perpendicular coordinate axes cross each other is known as a cartesian plane. Everywhere in the Cartesian plane, the functions define the boundaries of regions with regular geometrical patterns. The right triangle and other regular regions are good examples of how the area of a region may be computed using the geometry of the region.
The given function is [tex]\int\limits^{10}_{-10} {|x|} \, dx[/tex]. The function of this integrand is defined as f(x)=|x| with -10 ≤ x ≤ 10. Now, the graph is drawn for this function.
From the graph, we can tell the base and height of the two right-angle triangles are 10 units and 10 units. Then, the area is,
[tex]\begin{aligned}A&=2\left(\frac{1}{2}\times b\times h\right)\\&=2\times \frac{1}{2}\times 10 \times 10\\&=\mathrm{100\;{units}^2}\end{aligned}[/tex]
The area can also be calculated by solving the integrals,
[tex]\begin{aligned}\int\limits^{10}_{-10} {|x|} \, dx &=\int\limits^0_{-10} {-x} \, dx +\int\limits^{10}_0 {x} \, dx\\&=\left[\frac{x^2}{2}\right]^{0}_{-10} +\left[\frac{x^2}{2}\right]^{10}_{0}\\&=\frac{1}{2}(100+100)\\&=\mathrm{100\;units^2}\\\end{aligned}[/tex]
The required answer is 100 units².
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a smothie recipe calls for 2 1/4 cups of frozen mango. If the recipe serves two. ow many cups of frozen mango is needed to serve one?
1.125 cups of frozen mango is needed to serve one
A smoothie recipe contains 2 1/4 cups of frozen mango
This recipe can serve a total number of two people
The first step is to change the mixed fraction to an improper fraction
2 1/4
9/4
The number of cups of frozen mango needed to serve one person is
9/4 ÷ 2
9/4 × 1/2
= 9/8
= 1.125
Hence the number of cups of frozen mango required to serve one person is 1.125
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A car travels 60 miles with a constant speed of 57 mph and then another 60 miles with 40 mph. How long
does it take for the car to travel the first 60 miles?
t₁ =
What time is required to travel the second 60 miles?
Units hrs
t₂ =
Units hrs
What is the average speed of the car for the entire trip?
The average speed, v =
Units mph
Answer:
Step-by-step explanation:
t1= 60/57
t2=60/40=1.5
v= (57+40)/2= 48.5