We can tell if a number is rational or irrational by Venn Diagram
Both irrational and rational numbers are exact, yet they have different properties. Any number that can be expressed as P/Q, where P and Q are both integers and Q is more than zero, is considered to be reasonable. Simple fractions, however, cannot be used to express an irrational number. An illustration of a rational number is 2⅔ 3, while an irrational number is √2.
All integers, fractions, and repeating decimals are included in the concept of a rational number. We may represent every rational number as p/q, where p and q are integer numbers.
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Can you help me with this
Answer:
slope = 2
Step-by-step explanation:
calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 1, 0) and (x₂, y₂ ) = (1, 4) ← 2 points on the line
m = [tex]\frac{4-0}{1-(-1)}[/tex] = [tex]\frac{4}{1+1}[/tex] = [tex]\frac{4}{2}[/tex] = 2
Answer: The slope is 2.
Step-by-step explanation: To find the slope of a line, we first need to pick two points on a line. To solve this, I picked points (-2, -2) and (1, 4). The slope is rise over run, so you need to find the rise and run and divide.
We need to go 6 spaces up from (-2, -2) to get to (1, 4). This is our rise. Then, we go 3 spaces to the right. That is our run. 6 / 3 is 2, so that's your slope. Notice that if you cannot divide the rise and run into a whole number, keep it as a fraction instead.
Let me know if this is right! :)
Write an equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5).
y =
The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5) is 2x+y = -2.
The line between these locations' slopes must equal the negative reciprocal of the bisector's slope. It must go through the segment midway.
The slope of the line through the given points :
m = (y2 -y1)/(x2 -x1) = (5 -(-1))/(4 -(-8)) = 6/12 = 1/2
Then, The slope of the required bisector: m = -1/(1/2) = -2
The midpoint of the given segment:
((-8, -1) +(4, 5))/2 = (-8+4, -1+5)/2 = (-4, 4)/2 = (-2, 2)
Then the point-slope form of the equation of the bisector:
y -y1 = m(x -x1)
y -2 = -2(x -(-2))
y = -2x -4 +2
y = -2x -2 . . . . . . . slope-intercept form equation
2x +y = -2 . . . . . . .standard form equation
Thus, The equation of the perpendicular bisector of the segment with the endpoints (-8,-1) and (4,5) is 2x+y = -2.
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Ellie bought snacks for her team's practice. She bought a bag of oranges for
$2. 66 and a 5-pack of juice bottles. The total cost before tax was $7. 46. Write
and solve an equation which can be used to determine j, how much each
bottle of juice costs?
The linear equation for jj is ($7.46 - $2.66) / 5 and the cost of each bottle of juice is $0.96.
What in mathematics is a linear equation?
A linear equation is a first-order (linear) term plus a constant in the algebraic form y=mx+b, where m is the slope and b is the y-intercept.
Sometimes, the aforementioned is referred to as a "linear equation of two variables," where x and y are the variables.
The first step to take in order to determine jj, is to determine the total cost of the 5-pack of juice bottles.
Cost of the 5-pack of juice bottles = Total cost before tax - cost of the bag of oranges
Cost of the 5-pack of juice bottles = $7.46 - $2.66 = $4.80
The second step is to determine the cost of each bottle of juice
The cost of each bottle of juice = Cost of the 5-pack of juice bottles / total number of bottles
$4.80 / 5
= $0.96
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9. The expression (xn)(x5)3 is equivalent to x30. What is the value of n?
Answer: N= x24 over 3
Step-by-step explanation:
Olivia owns a pastry shop, and needs to fill an order for 700 cupcakes
She already has 15 cupcakes made, and she can make 137 cupcakes
hour. How many hours does Olivia need to fill the order?
Olivia needs
more hours.
Answer:
5 hours
Step-by-step explanation:
Olivia needs to make 700 - 15 = <<700-15=685>>685 cupcakes.
So she needs to work for 685 / 137 = <<685/137=5>>5 hours
which answer is this
A.43
B.38
C.61
D.81
ine segment SU is dilated to create S'U' using point Q as the center of dilation. The scale factor of the dilation is
The scale factor of the dilation is 2. An expansion happens when the scaling factor's absolute value exceeds one.
What does a scale factor mean when defining dilation?The scale factor is defined as the proportion of the new image's size to that of the previous image. A fixed location in the plane serves as the center of dilatation. The scale factor and the center of dilation are used to determine the dilation transformation. The image stretches if the scaling factor is greater than 1.
As per the rule of scale factor
Q'U'/QU = SF
SF= Scale factor
= (5+5)/5= Scale factor
= 10/5= 2
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Identify all of the necessary assumptions for a significance test for comparing dependent means.
>Categorical Data
>At least 15 successes and 15 failures in both groups
>Quantitative Data
>Random Samples or Random application of treatments
>n is greater than or equal to 30 OR Population of Differences could be Normally distributed.
>Both sample sizes are greater than 30 or Both population distributions could be Normally Distributed
The correct answer will be:
Quantitative data, both sample sizes are greater than 30 or Both population distributions could be Normally Distributed, Random Samples or Random application of treatments
There should be just one group for each subject. The observations in each category are unrelated to one another. There were no notable outliers in any category.
The following are the presumptions for a percentage significance test: Data come from a random sample [Sample is large enough, which is presumed to be true when. It should be noted that both quantitative and categorical data can be subjected to a significance test for a proportion.
Most parametric tests begin with the underlying presumption of population distribution. The ratio scale or interval scale measurements, easy random extraction, normal distribution of the data, a sufficient sample size, and homogeneity of variance are all prerequisites for performing the t-test.
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In our class there are 40 boys. 22 students are girls write a ratio comparing girls to boys
Answer:
Its 22:40
Step-by-step explanation:
Answer: 22:40
Pretty simple
Step-by-step explanation:
The sum of two consecutive even numbers is 34. What numbers is it
Answer:
16 and 18
16 + 18 = 34 .......... .....
Question 22 This question has two parts. First, answer Part A. Then, answer Part B. Part A STATE YOUR ASSUMPTION Liling is making a quilt. She starts with two small squares of material and cuts them along the diagonal. Then she arranges the four resulting triangles to make a large square quilt block. She wants the large quilt block to have an area of 36 square inches. A. What side lengths should Liling use for the two small squares of material? Explain. Round to the nearest tenth, if necessary. In. ; For the block to have an area of 36 square inches, each side must be V2 in. Or about inches. By the inches. This means the hypotenuse of each small right triangle is V2 inches 45°-45°-90° Triangle Theorem, the sides of these triangles measure Part B Do b. Explain any assumption that you make to answer part a. Next Question Check Answer Privacy and Cookies | Terms of Use | Minimum Requirements Platform Status 2021 McGraw-Hill Education. All Rights Reserved.
Blank space 1: 3
Blank space 2: 4.242
Blank space 3: 6
Blank space 4: 6
Blank space 5: 3
This can be solved using triangle theorem.
What is triangle theorem?The first theorem, a triangle's three inner angles can be added up to 180 degrees. According to this theorem, if ABC is a triangle, then ∠A + ∠B + ∠C = 180°.The second theorem states that an isosceles triangle's base angles are congruent or that its opposing sides' angles are also equal in size.The third theorem states that the total of the equivalent internal angles is equal to the size of the exterior angle of a triangle.Given that,
Liling is making a quilt. She starts with two small squares of material and cuts them along the diagonal.
The bigger square = 36 sq. in.
Then the side of the bigger square = √36 inch = 6 inch
Next, The side of the bigger square = Diagonal of the smaller square
Let the side of the smaller square = a (let)
Diagonal (smaller square): a√2 = 6 inch
so, a = 3√2 inch
Thus, a = 3 x 1.414 = 4.242
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The complete question is as follows:
What is the reflection of point 2/3 about y-axis?
When reflected in the y-axis, the image of the point (2/3) is (-2/3).
The sign of the x coordinate changes when a point is mirrored on the y-axis.
When a figure is built around a single point known as the point of reflection or the figure's centre, a reflection point results. There is an exact opposite point on the other side of each point in the figure. The shape and dimensions of the figure remain unchanged underneath the point of reflection.
The y-coordinate stays the same when a point is reflected across the y-axis, but the x-coordinate is assumed to be the additive inverse. Point (x, y) is reflected across the y-axis as (-x, y).
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Uncle Drew scored 28 points in 5 5/6 minutes during a game of basketball. How many points did he average per minute during that 5 5/6 minutes?
Answer:
He scored an average of 4.8 points per minute.
A triangle has sides with lengths of 12 feet, 16 feet, and 18 feet. Is it a right triangle?
Answer:
Step-by-step explanation: If the sides are a,b,c (in ascending order) and c squared = the sum of the squares of a and b, then it's a right triangle.
Answer:
No, it is not a right triangle.
Step-by-step explanation:
Right triangle fulfill the pythagorean theorem:
[tex]a^2+ b^2 = c^2[/tex]
Where, c is the hypothenuse or the longest side, and b and a are the remaining two sides.
[tex]12^{2} = 144\\16^2 = 256\\256 + 144 = 400\\\sqrt {400} = 20 \neq 18[/tex]
The graph of y = x2 has been translated 7 units to the left. The equation of the resulting parabola is _____.
The equation of the parabola after the translation is:
g(x) = (x - 7)^2
What is the equation for the resulting parabola?We know that we start with a parabola of the form:
y = x^2
Now we know that the parabola has been translated 7 units to the left.
Remember tht for a general function y = f(x), a horizontal translation of N units is written as:
g(x) = f(x + N)
If N > 0, the translation is to the left.if N <0, the translation is to the right.So a translation of 7 units to the left is written as:
g(x) =f(x - 7)
g(x) = (x - 7)^2
That is the equation of the parabola after the translation.
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Hannah either walks or cycles to school. The probability that she walks to school is 0.75 If she walks, the probability that she is late is 0.6 If she cycles, the probability that she is late is 0.2 Work out the probability that on any one day Hannah will not be late for school.
If Hanna is walking there is a 0.4 chance of not being late. 0.75 x 0.4 = 0.3 probability of not being late.
If Hanna cycles there is a chance of 0.8 of not being late. 0.6 x 0.8 = 0.48.
0.48 + 0.3 = 0.78.
In other words, there is a 78% probability of her not being late.
Find the volume of the cone either enter an exact anwer in term of pi or ue 3. 14. For pie. R= 5 l=6
The volume of the cone is 50π cubic units .
What is a cone ?A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the apex or vertex. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base that is in a plane that does not contain the apex.
A cone has a circular base.
A cone has no edges, one face, and one vertex.
The length of the line segment from a cone's apex to any point around the circle of the cone's base is known as the slant height of the cone.
A right circular cone is a cone with its apex perpendicular to the base of the cone and directly above it.
An oblique cone is one that doesn't have its apex precisely over the base's circle.
Radius of the cone = 5
Height of the cone is 6
Volume of the cone = [tex]\frac{1}{3}\pi r^{2} h[/tex] = [tex]\frac{1}{3}\pi *5^{2}* 6 = 50\pi[/tex] cubic units.
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Write the equation of the line that passes through the points (6, 1) and
(6, -8). Put your answer in fully simplified point-slope form, unless it
is a vertical or horizontal line.
something noteworthy is that the x-coordinate is the same for each point, so Check the picture below.
How do you find mass using FG?
To find the mass of an object, one can use the formula (Force x Distance) / Gravitational Constant (FG). This formula involves multiplying the force applied to an object by the distance it moves, and then dividing the result by the gravitational constant (FG). The resulting number is the mass of the object in kilograms.
Mass can be found by using the formula (Force x Distance) / Gravitational Constant (FG).
For example, if a force of 10N is applied to an object that is moving 2 meters, the mass of the object can be calculated as follows:
Mass = (10 N x 2 m) / FG
Mass = 20 / 9.8
Mass = 2.04 kg
Finding mass using the force-distance formula (FG) is a simple process. To use it, one needs to know the force applied to an object, the distance it moves, and the gravitational constant (FG). The force and distance values can be measured or calculated depending on the situation. The gravitational constant is a fixed number and is equal to 9.8 m/s2. To calculate the mass, one needs to take the force multiplied by the distance and then divide it by the gravitational constant (FG). The resulting number is the mass of the object in kilograms. This formula is useful for calculating the mass of objects in a variety of situations. It is also useful for verifying the mass of an object that has already been measured.
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1. You may get up to 35 gallons of gas at a time at the gas station. What inequality is that?
The inequality is x ≤ 35, where x represents the amount of gas in gallons.
This question means by the statement that we have been given that the number of gallons cannot exceed 35 so it actually means that they are either 35 or less than 35. so will use < = sign to come up with this equation.
You can have up to 35 gallons of gas at a time at the gas station. The inequality x ≤ 35 represents the fact that x (the amount of gas in gallons) is less than or equal to 35.
This means that the equation will be x≤35
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Tanner has $4.60 in nickels and quarters. If he has 14 more nickels than quarters, how many of each coin does he have?
quarters
nickels
The number of coins of nickels and quarters will be 27 and 13, respectively.
What is the solution to the equation?The allocation of weights to the important variables that produce the calculation's optimum is referred to as a direct consequence.
Tanner has $4.60 in nickels and quarters. If he has 14 more nickels than quarters.
Let 'x' be the number of nickels and 'y' be the number of quarters. Then the equations are given as,
x = y + 14 ....1
0.05x + 0.25y = 4.60 ....2
From equations 1 and 2, then we have
0.05(y + 14) + 0.25y = 1
0.05y + 0.70 + 0.25y = 4.60
0.30y = 3.9
y = 13
Then the value of 'x' is given as,
x = 13 + 14
x = 27
The number of coins of nickels and quarters will be 27 and 13, respectively.
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Aisha bought 15 apples and oranges for $9.00. each orange costs $0.50, and each apple costs $0.65. let x represent the number of oranges and y represent the number of apples. which system can be used to find the number of apples and oranges aisha bought? x y = 15. 0.5 x 0.65 y = 9.00 x = y. 0.5 x 0.65 y = 9.00 x y = 9. 0.5 x 0.65 y = 15.00 x = y. 0.5 x 0.65 y = 15.00
Both (x + y = 15) and (0.5x + 0.65y = 9.00) make up the equation system.
What is 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.
The statement is not an equation if there is no "equal to" sign in it
According to our question-
x is the quantity of oranges.
y is the quantity of apples.
Oranges plus apples equal 15, or x plus y equals 15, so Aisha purchased 15 pieces of fruit.
Apples cost $0.65 and oranges cost $0.50. The fruit cost Aisha $9.00.
0.5x (the total cost of the oranges) + 0.65y (the total cost of the apples) equals 9.00 (the total cost of the fruit).
x + y = 15
0.5x + 0.65y = 9.00
As a result, the system of equations is (0.5x + 0.65y = 9.00) and (x + y = 15).
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Activity 1: Keep Trying
Direction: Read, understand, analyze the given problem and solve it by applying the suggested
steps. Write your answer on the box provided.
1. Esther gave birth to a new-born baby weighing 5 kg at birth. Her friend told her that
the monthly average weight gained by a baby is 2 kg. If the rate of increase of the baby's
weight every month is constant, what is the weight of the baby after five months?
Perlom
Solution
Step 5
ernalia
Step 1
Step 2
Step 4
Step 3
nent anar
lia
The weight of the baby after five months is 15 Kg.
Step 1:
Given:
New-born baby weight = 5kg
Monthly average weight gained = 2kg
To find:
The weight of the baby after 5 months.
Average Weight of Baby:
Birth weight is the weight of the baby at birth. [1] The average birth weight of babies of European descent is 3.5 kilograms, with a normal range of 2.5 to 4.5 kilograms (5.5 to 9.9 pounds). On average, South Asian and Chinese babies weigh about 3.26 kg. The prevalence of low birth weight infants decreased slightly from 7.9% (1970) to 6.8% (1980), then increased slightly to 8.3% (2006) and is currently at 8.2% (2016).
Step 2:
Represent the unknown.
Let x-the number of months .
Let y-weight of the baby after 5 months.
Step 3:
Formulate the equation.
The mathematical equation is:
5+2x = y
Step 4:
Solve the equation.
5+2x = y
5+2(5) = y
5+10 = y
y = 15
Thus, the baby weight is 15kg after 5 months.
Step 5:
Using the equation 5+2x=y.
5+2x = y
5+2(5) = 15
5+10 = 15
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Marissa is skateboarding on a straight stretch of sidewalk. In 3.0 minutes, she travels 486 meters. What is the magnitude of her velocity during this stretch?
Marissa velocity while skateboarding is 162 meters per minute
What is an equation?An equation is used to show the relationship between numbers and variables.
Velocity is the ratio of displacement to time taken. It is a vector quantity (has magnitude and direction) and it is given by:
Velocity = displacement / time
Marissa travels 486 meters in 3 minutes, hence:
Velocity = displacement / time
Velocity = 486 m / 3 min = 162 meters per minute
The velocity is 162 meters per minute
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Answer: The correct answer is 2.7m/s
Step-by-step explanation:
I took the test
HELP!!! Find the inverse of the matrix..
Answer:
The matrix does not have an inverse (D)
Step-by-step explanation:
The matrix is singular, therefore doesn't have an inverse
The diameter of a circle is 34 inches.What is the area of the circle in square inches?Use 3.14 as pi
Answer: 907.46 inches squared
Step-by-step explanation:
The formula for the area of the circle is:
[tex]A = \pi r^{2}[/tex]
In this question, pi is 3.14. The radius of a circle is half of its diameter. So:
[tex]\frac{34}{2} =17[/tex]
Plug these values into the equation:
[tex]A = (3.14)(17)^2[/tex]
Simplify:
[tex]A = 907.46[/tex]
The area of the circle is 907.46 inches squared.
Study the example showing a function. Then solve
problems 1-6.
Example
The table and graph show the
relationship between the length
of the sides of a square, in feet, and
the perimeter of the square in feet.
Side Length (input) 1 2 3 4 S
Perimeter (output) 4
812 16 20
The relationship is a function because
there is only one output value for
each input value.
Perimeter (output)
20
18
16
14
12
10
8
6
4
2
Perimeters of Squares
0 1 2 3 4 5 6 7 8 9
Side Length (input)
1 Describe the relationship between the input and output
values in the example.
2 Can you represent the function in the example with an
equation? If so, what equation can you write? If not,
why not?
Vocabulary
function a rule that
The relationship between the input and output is that the perimeter of a square is always equal to four times the length of one of its sides.
What is the perimeter of square?The perimeter of a square is the total distance around the outside of the square. It is the sum of the lengths of all four sides. To find the perimeter of a square, you simply multiply the length of one side by four, since all sides of a square are equal in length. The formula is P=4S
1.The relationship established between (side length of the square) and output (perimeter of the square) represent that A square's perimeter is always equal to 4 times one of its sides.
2.Yes, the function can be represented with an equation. The equation would be:
Perimeter = 4 × Side Length.
Side Length (input) 1 2 3 4 5
Perimeter (output) 4 8 12 16 20
This equation states that the perimeter of a square is equal to four times the length of one of its sides.
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Classify each transformation by its properties.
The classification of the transformations based on the properties are presented as follows;
[tex]\begin{array}{|c|c|c|} & \mathbf{Preserves \ length} & \mathbf{Does \ not \ preserve \ lengths} \\\mathbf{Preserves \ angle \ measure} & Reflection\ Rotation &Translation \ followed \ by \ dilation \\&&Dilation \ with \ K > 1\\\mathbf{Does \ not \ preserve \ angle \ meas} & & \\\end{matrix}[/tex]
What are the different transformation effects?The transformations that preserves the lengths of the original figure or pre-image and also preserves the angle measure is a rigid transformation.
Rigid transformations includes; Reflections, rotations, and translations
Transformations that preserves the angle of measure but in which the lengths of the preimage is not preserved are non-rigid transformations
Non rigid transformations includes; Dilation with a scale factor
Transformations that does not preserve the angle measure includes; Shear transformation
A translation and a dilation transformation does not preserve the lengths of the original figure.
The classification of the transformations based on their properties are therefore presented as follows;
[tex]{}[/tex] Preserves lengths Does not preserve lengths
Preserves Reflection [tex]{}[/tex] Translation followed by dilation
angle measure Rotation [tex]{}[/tex] with k > 1
[tex]{}[/tex] Dilation with k > 1
Does not
Preserve angle
measure
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What is the median? Help please
Answer:
-65
Step-by-step explanation:
Median = middle number
-76, -74, -67, -65, -63, -58, -48
out of the numbers I am shown, from the photo, I would say "-65" is the answer, but if there is another number I'm missing, add it to the row of numbers above and add the two numbers together and divide by 2
I hope this helps!
A particle moves along the x-axis so that at time
t
≥
0
t≥0 its position is given by
x
(
t
)
=
t
3
−
6
t
2
−
29.
x(t)=t
3
−6t
2
−29. Determine the total distance traveled by the particle from
0
≤
t
≤
7.
0≤t≤7.
The total distance traveled from 0 ≤ t ≤ 7, considering the position function x(t) = t³ - 6t² - 29, is given as follows:
288.75 units.
How to obtain the total distance traveled?The position function for this problem is defined as follows:
x(t) = t³ - 6t² - 29.
The total distance traveled over an interval [a,b] is given by the definite integral of the function x(t) over the interval from x = a to x = b.
The definite integral in this problem is calculated as follows:
I = 0.25t^4 - 2t³ - 29t, from t = 0 to t = 7.
Applying the Fundamental Theorem of Calculus, the total distance is calculated as follows:
I = 0.25(7)^4 - 2(7)³ - 29(7) - (0.25(0)^4 - 2(0)³ - 29(0))
I = 288.75 units.
(which is the absolute value of the result of the definite integral).
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