Step-by-step explanation:
the simplest way for me is
1. to convert both terms into full fractions (not mixed numbers).
2. then to bring both fractions to the same denominator.
3. and then do the actual calculation.
and if needed, we can
4. then convert the result back into mixed numbers.
1.
15 1/2 = (15×2 + 1)/2 = 31/2
1 11/20 = (1×20 + 11)/20 = 31/20
2.
we need to convert 31/2 into a fraction .../20, so that we can actually combine it with the 31/20.
how do we get from 2 to 20 ? by multiplying by 10.
in order to keep the value of the fraction unchanged, we need to do the same multiplication also to the numerator :
31/2 × 10/10 = 310/20
3.
310/20 + 31/20 = 341/20
4.
341/20 = (17×20 + 1)/20 = 17 1/20
to get this you do an integer division and note the remainder.
341/20 = 17 remainder 1
The vertice of a rectangle are located at the coordinate (1, 4), (1, 7), (3, 7), and (3, 4)
An enclosed 2-D shape called a rectangle has four sides, four corners, and four right angles (90°). A rectangle has equal and parallel opposite sides.
What is a rectangle?Four sides, four corners, and four 90° right angles make up the closed, 2-D shape of a rectangle. A rectangle has parallel, equal sides on either side. Rectangles are two-dimensional shapes, and as such, they have length and breadth as their defining characteristics.Rectangles are quadrilaterals having four right angles in the Euclidean plane of geometry. It can alternatively be described as a parallelogram with a right angle, an equiangular quadrilateral, or a group of triangles with equal angles. A square is a rectangle that has four equal sides.A rectangle is a parallelogram with all its inside angles being .The main distinction between a square and a rectangle is that a square has equal lengths on each of its sides, but a rectangle has equal lengths on each of its opposite sides.Completed question :
Please answer fast The vertices of a rectangle are located at the coordinates (1, 4), (1, 5), (6, 5),
1
,
4
,
1
,
5
,
6
,
5
,
and (6, 4)
6
,
4
.
Find the length of the sides of the rectangle and its perimeter.
Given data :
Horizontal sides
There are two x-values present : 1 and 6
Find the difference
6 - 1 = 5
The horizontal sides of the rectangle are 5 units long
Vertical sides
Two y-values are present : 4 and 5
Find the difference
5 - 4 = 1
The vertical sides of the rectangle are 1 unit long
Perimeter
2(Horizontal side + Vertical side)
2(5 + 1)
2(6)
12
The perimeter of the rectangle is 12 units
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Natasha has 1/5 of her action figures left over after she donates some of them. She wants to share her remaining action figures with 3 of her friends. What fraction of the original action figures will Natasha and her 3 friends each receive?
The fraction of the original action figures will Natasha and her 3 friends each receive is (1/15).
What is a fraction?A fraction is written in the form of a numerator and a denominator where the denominator is greater that the numerator.
Example: 1/2, 1/3 is a fraction.
We have,
Total number of action figures = x
Number of action figures left = (1/5)x
The number of action figures received by each friend.
= (1/5)x ÷ 3
= (1/15)x
Thus,
Each friend received (1/15) of the original action figures.
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which angles are coterminal with an angle measure of 2pi/3
The resulting angle of 4 π / 3 is positive and coterminal with - 2π / 3
What are coterminal angles ?
Coterminal angles are the angles that have the identical initial facet and share the terminal aspects. these angles occupy the usual function, though their values are one of a kind. they are at the same sides, within the identical quadrant and their vertices are same. while the angles are moved clockwise or anticlockwise the terminal aspects coincide at the identical attitude.
Given angles measure of -2 pi / 3
So we have to add 2π to - 2 π / 3
- 2π / 3 + 2 π
= 2π - 2π / 3
= 6 π - 2 π / 3
= 4π / 3
The resulting angle of 4 π / 3 is positive and coterminal with - 2π / 3
Therefore, The resulting angle of 4 π / 3 is positive and coterminal with
- 2π / 3
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The acceleration due to gravity on the surface of planet x is 19. 6 meters per second squared. If an object on the surface of this planet weighs 980 newtons, the mass of the object is.
Answer:
m = 50kg
Step-by-step explanation:
First, you have to know that mass is an indicator of the amount of matter that makes up a body. Its unit in the International System is the kilogram (kg).
The mass of an object will always be the same, no matter where it is located.
On the other side, bodies are subjected to the action of forces, such as the force of gravity or electromagnetic forces.
So, weight is the action exerted by the force of gravity on the body. That is, weight is a measure of how much force gravity exerts on the mass of an object.
The weight of an object is measured in Newton (N) and will vary according to the force of gravity that acts on it.
The expression for the calculation of the weight is:
P= m×g
where:
P is the weight of a body.m is its mass.g is the gravity or acceleration with which bodies fall.In this case, you know that:
P= 980 N
m= ?
g= 19.6 [tex]\frac{m}{s^{2} }[/tex]
Replacing in the expression for the calculation of the weight:
980 N= m× 19.6 [tex]\frac{m}{s^{2} }[/tex]
Solving:
[tex]\frac{980N}{19.6\frac{m}{s^{2} } }[/tex]
m=50 kg
Three forces are acting on the ring in the dlagram.
128 N
128 N
30.0°
64 N
The net force and magnitude is 54°. The solution has been obtained by using trigonometry.
What is trigonometry?
The primary objective of the branch of mathematics known as "trigonometry" is the study of the sides, angles, and connections of the right-angle triangle.
We are given that three forces are acting on the ring.
So,
A = -128 N + 64 N
A = -64 N
[tex]A_{x}[/tex] = A cos θ[tex]_{A}[/tex]
[tex]A_{x}[/tex] = (-64 N) (cos 180°)
[tex]A_{x}[/tex] = -64 N
[tex]A_{y}[/tex] = A sin θ[tex]_{A}[/tex]
[tex]A_{y}[/tex] = (-64 N) (sin 180°)
[tex]A_{y}[/tex] = 0 N
B[tex]_{x}[/tex] = B cos θ[tex]_{B}[/tex]
B[tex]_{x}[/tex] = (128 N) (cos 30°)
B[tex]_{x}[/tex] = 111 N
B[tex]_{y}[/tex] = B sin θ[tex]_{B}[/tex]
B[tex]_{y}[/tex] = (128 N) (sin 30°)
B[tex]_{y}[/tex] = 64 N
R[tex]_{x}[/tex] = A[tex]_{x}[/tex] + B[tex]_{x}[/tex]
R[tex]_{x}[/tex] = -64 N + 111 N
R[tex]_{x}[/tex] = 47 N
R[tex]_{y}[/tex] = A[tex]_{y}[/tex] + B[tex]_{y}[/tex]
R[tex]_{y}[/tex] = 0 N + 64 N
R[tex]_{y}[/tex] = 64 N
[tex]R = \sqrt{R_{x}^{2} +R_{y}^{2} }[/tex]
[tex]R = \sqrt{(47 N)^{2} +(64 N)^{2} }[/tex]
R = 79 N
θ = [tex]tan^{-1}(\frac{R_{y} }{R_{x}} )[/tex]
θ = [tex]tan^{-1}(\frac{64 }{47} )[/tex]
θ = 54°
Hence, the net force and magnitude is 54°.
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Since, the question is incomplete, the complete question has been attached below
I NEED HELP ASAP what is 4 2/3 divided by 2 1/6?
Answer choices:
- 10 1/9
- 2 2/13
- 1 1/13
- 2 1/13
Answer:
4 2/3 ÷ 2 1/6 is equal to 2 2/13.
Step-by-step explanation:
When dividing 2 1/6 from 4 2/3, you will get 2 2/13 or 2.15.
solve for x, leave answers in simplest radical form.
The value of x from pythagoras theorem we get as 32.45
What is Right Angle triangle ?A right triangle, also known as a right-angled triangle, right-perpendicular triangle, orthogonal triangle, or previously rectangled triangle, is a triangle with one right angle, or two perpendicular sides. The foundation of trigonometry is the relationship between the sides and various angles of the right triangle.
A right triangle's three sides are related in Euclidean geometry by the Pythagorean theorem, also known as Pythagoras' theorem. According to this statement, the areas of the squares on the other two sides add up to the size of the square whose side is the hypotenuse.
Let the length of the perpendicular be y , the length of the 3rd side be z
Using Pythagoras Theorem :
x² - y² = 27² , ............(i)
x² + z² = (27 +9)² = 36² .......(ii)
y² - z² = 9² ................(iii)
Adding equation (i), (ii) and (iii) we get ,
2x² = 27²+36² + 9²
⇒x = 32.45
The value of x from pythagoras theorem we get as 32.45.
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maximum discount product sql
The result of this operation can then be used to calculate the maximum discount available for each product.
The formula to find the maximum discount product in SQL is:
MAX(Discount) = MAX(Price)-MIN(Price);
This formula calculates the maximum discount available on a product by subtracting the minimum price of the product from the maximum price. This can be used to determine the best value for money for a product by comparing the discount with the prices of other products.
For example, if the minimum price of a product is $100 and the maximum price is $200, the maximum discount available for that would be $100. This could be used to compare the discount of this The result of this operation can then be used to calculate the maximum discount available for each product. to the discounts of other products and find out which one gives the best value for money.
This formula can be implemented in SQL by using the MAX() and MIN() aggregate functions to find the maximum and minimum prices for each product. The result of this operation can then be used to calculate the maximum discount available for each product.
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A scale drawing of a public park shows the length of the
entrance as 7. 9 inches. The drawing has a scale of 1 inch =
4 feet. What is the actual length of the park entrance
The height of the Public Park entreence in smaller scale is 7.9 inches
The actual height of the Park entrence is 7.9*48 = 379.2 inches = 31 feet 7.2 inches
What is Unitary method ?The unitary approach is a strategy for problem-solving that involves first determining the value of a single unit, then multiplying that value to determine the required value.
Direct Variation
When there is a direct variation, an increase or decrease in one quantity will result in an equivalent rise or fall in the other. For instance, a rise in the quantity of commodities will result in higher costs.
Indirect Variation
A change in one quantity will directly affect a change in another, known as a direct variation. A rise in the quantity of goods, for instance, will result in higher costs.
In the scale 1 inch = 4 feet= 4*12 = 48 inches
The height of the Public Park entreence in smaller scale is 7.9 inches
The actual height of the Park entrence is 7.9*48 = 379.2 inches = 31 feet 7.2 inches
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29 x 64 standard edition
Answer: 29x64=1856
Step-by-step explanation:
Answer:
29 x 64 = 1856
Step-by-step explanation:
Step 1: First we set up our equation like this:
6 4
x 2 9
Step 2: Multiply
4 x 9 = 36. Put 6 below the line and 3 as a reminder on top:
3
6 4
x 2 9
_______
6
Step 3: Multiply again...
9 x 6 = 54. Take 54 and add 3 from the previous step to get 57. Enter 57 at the bottom:
6 4
x 2 9
________
5 7 6
Step 4: Add 0
Enter a 0 at the bottom right as a place holder, because you now move over one digit:
6 4
x 2 9
________
5 7 6
+ 0
Step 5: Multiply again. (Sheesh)
2 x 4 = 8. Put 8 below the line and 0 as a reminder on top:
0
6 4
x 2 9
________
5 7 6
+ 8 0
Step 6: Multiply (Last time)
2 x 6 = 12. Take 12 and add 0 from the previous step to get 12. Enter 12 at the bottom:
6 4
x 2 9
________
5 7 6
+ 1 2 8 0
Step 7: Add to get answer
Add up the bottom two numbers (576 + 1280 = 1856) to get the answer:
6 4
x 2 9
________
5 7 6
+ 1 2 8 0
________
= 1 8 5 6
The bottom line is the answer. Therefore, 64 times 29 equals:
1856
In 2010, nominal GDP was approximately $14. 5 trillion; in 2011, it was approximately $15. 1 trillion. Calculate the percentage change in GDP over this time period:
The percentage change in GDP over the time period from 2010 to 2011 was 4.14%. This means that the nominal GDP increased by 4.14% during this time period.
To calculate the percentage change in Gross Domestic Product (GDP) over the time period from 2010 to 2011, we can use the following formula:
Percentage change = (GDP in 2011 - GDP in 2010) / GDP in 2010 * 100%
Substituting the values, we get:
Percentage change = ($15.1 trillion - $14.5 trillion) / $14.5 trillion * 100% = $0.6 trillion / $14.5 trillion * 100% = 4.14%
So, the percentage change in GDP over the time period from 2010 to 2011 was 4.14%. This means that the nominal GDP increased by 4.14% during this time period.
In conclusion, the percentage change in Gross Domestic Product (GDP) over the time period from 2010 to 2011 was 4.14%, which means that the nominal GDP increased by 4.14% during this time period.
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-7 1/7*(3 2/5)+ 6 3/5*(-7 1/7)
Answer:
-71.4285714286Y
Step-by-step explanation:
-7 1/7*(3 2/5)+ 6 3/5*(-7 1/7) = 71.4285714286Y or shorter 71.42
Line D has a slope of 7/4. Line E is perpendicular to line D, what is the slope of line E
Answer:
Step-by-step explanation:
If the slope of line d is -7/4, then the slope of a perpendicular is 4/7.
Given a slope, to find the slope of a perpendicular, flip the fraction and change the sign.
Flip -7/4 to get -4/7. Then change the sign of -4/7 to get 4/7.
Answer: 4/7
How to Calculate the Value of Pi? (Pi Formula)
The pi is a ratio and is obtained from a circle. If the diameter and the circumference of a circle are known, the value of pi will be as π = Circumference/ Diameter.
Define ratio?A ratio in mathematics represents the number of times one number contains another. If a bowl of fruit contains eight oranges and six lemons, the orange-to-lemon ratio is eight to six. Similarly, the lemon-to-orange ratio is 6:8, and the orange-to-fruit ratio is 8:14.Ratio is a direct borrowing from the Latin word. In Latin, ratio could mean anything from "reason" to "calculation" to "proportion," and it was the latter meaning that was used to create the mathematical and English ratios.The first term in a ratio is referred to as the antecedent, and the second term is referred to as the consequent.To learn more about ratio refer to:
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A three-column table is given.
What is the value of C in the table?
18
24
27
71
Answer:
C
Step-by-step explanation:
8 : 10 = 18
12 : 15 = 27
36 : 45 = 81
what does y equal to
x+2y=3
Answer:
1 3
y = - ----- x + -----
2 2
Step-by-step explanation:
x + 2y = 3
-x -x
--------------------
2y = -x + 3
÷2 ÷2 ÷2
--------------------
1 3
y = - ----- x + -----
2 2
I hope this helps!
A scatter plot is shown on the coordinate plane.
100 POINTS, HELP ASAP, WILL GIVE BRAINLEIST.
Which two points would a line of fit go through to best fit the data?
(1, 10) and (10, 1)
(1, 7) and (2, 6)
(3, 7) and (7, 4)
(3, 8) and (6, 6)
Answer:D
Step-by-step explanation:
the dots are forming a mixed up line going across the plot. D best fits the line.
when u, v are nonzero vectors, then span{u, v} contains the line through u and the origin, as well as the line through v and the origin. T/F
True, The span of {u, v} contains both the line through u and the origin, as well as the line through v and the origin.
The span of a set of vectors is defined as the set of all linear combinations of those vectors. When u and v are nonzero vectors, the span of {u, v} is a two-dimensional subspace of the vector space that contains both u and v, and any linear combination of u and v.
Since u and v are nonzero vectors, the lines through the origin and u, and through the origin and v, are non-degenerate lines in the vector space. Therefore, these lines are contained within the span of {u, v}.
In other words, if we take any scalar multiples of u and v, such as au and bv, where a and b are scalars, the sum au + bv will be a linear combination of u and v and therefore will also be contained within the span of {u, v}.
Therefore, the span of {u, v} contains both the line through u and the origin, as well as the line through v and the origin.
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Show that ¬ (p ↔ q) and p ↔¬q are logically equivalent.?
¬ (p ↔ q) and p ↔¬q are proved to be logically equivalent.
Explain the term contrapositive law?According to the law of contrapositive, the initial assertion is accurate if and only if the contrapositive is accurate. The original assertion is untrue if indeed the contrapositive is false. A conditional assertion that could or might dependent on another is a contrapositive.The given statement are-
¬ (p ↔ q) and p ↔¬q
To prove these are logically equivalent, use contrapositive law
¬(p↔q) = ¬[(p∧q) ∨ (¬p∧¬q)]
¬(p↔q) = (p∧¬q) ∨ (¬p∧q)
And,
p↔¬q = (p∧¬q) ∨(¬p∧¬(¬q))
p↔¬q = (p∧¬q) ∨(¬p∧ q)
Thus, ¬ (p ↔ q) and p ↔¬q are proved to be logically equivalent.
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What is the probability of rolling a die 2 times and then rolling 2 odd numbers in a row
The probability of rolling a die 2 times and then rolling 2 odd numbers in a row is 1/4
How to determine the probabilityWhen rolling a fair six-sided die, each outcome has an equal chance of happening, so the probability of rolling an odd number is 1/2 i.e. 3 out of 6
The probability of rolling two odd numbers in a row is then
(1/2) * (1/2) = 1/4.
This means that, the probability of rolling a die two times and then rolling 2 odd numbers in a row is 1/4
Therefore, the probability of rolling a die 2 times and then rolling 2 odd numbers in a row is 1/4
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The sum of three consecutive numbers is 42. What are the three numbers?
Answer:
Step-by-step explanation:
Here's a step-by-step explanation to find the three consecutive numbers whose sum is 42:
Let's call the smallest of the three numbers "x".
Since they are consecutive numbers, we can represent the next two numbers as x+1 and x+2.
The sum of these three numbers can be represented as x + (x + 1) + (x + 2) = 42.
Simplifying this equation, we get 3x + 3 = 42.
Subtracting 3 from both sides, we get 3x = 39.
Dividing both sides by 3, we get x = 13.
So, the three consecutive numbers are 13, 14, and 15.
Please help me with this math problem
The probability of event A is [tex]P(A)=\frac{7}{18}\\[/tex],
The probability of event B is [tex]\\P(B)=\frac{1}{2}[/tex]
What is Probability?
Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
The sample space of rolling two dice has 36 possible outcomes. Remember that the "sample space" is a set which contains all possible outcomes.
(1,1) (2,1) (3,1) (4,1) (5,1) (6,1)
(1,2) (2,2) (3,2) (4,2) (5,2) (6,2)
(1,3) (2,3) (3,3) (4,3) (5,3) (6,3)
(1,4) (2,4) (3,4) (4,4) (5,4) (6,4)
(1,5) (2,5) (3,5) (4,5) (5,5) (6,5)
(1,6) (2,6) (3,6) (4,6) (5,6) (6,6)
Using these probabilities, you can answer your questions:
A: The probability of getting sum of greater number than 7
A={(6,2),(2,6),(3,5),(3,6),(4,4)(4,5)(4,6),(5,3)(5,4)(5,6)(6,3)(6,4)(6,5)(6,6)}
n(A)=14
P(A)=14/36.
P(A)=7/18.
B:Getting Sum of odd numbers.
B={(1,2)(1,4)(1,6)(2,1)(2,3)(2,5)(3,2)(3,4)(3,6)(4,1)(4,3)(4,5)(5,2)(5,4)(5,6)(6,1)(6,3)(6,5)}
n(B)=18
P(B)=18/36.
P(B)=1/2
[tex]P(A)=\frac{7}{18}\\\\P(B)=\frac{1}{2}[/tex]
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A curve is represented by the equation 2y3 + xy - 6x + 3 = 0. Part A: Determine dy dx (10 points) Part B: Evaluate dy at the point (1, 1). (10 points) dx Part C: Determine d°у (10 points) dx2 day Part D: Evaluate at the point (1, 1). (10 points) dx2
The derivative of the equation 2y³ + xy - 6x + 3 at the point (1,1) is 0, and the second derivative is 13.
The derivative of y with respect to x can be calculated by differentiating both sides of the equation with respect to x. This gives us:
[tex]\frac{dy}{dx} = \frac{x}{2y^2} - 5[/tex]
We can evaluate dy/dx at the point (1, 1) by substituting x = 1 and y = 1 into the equation for dy/dx and calculating the result. This gives us:
[tex]\frac{dy}{dx} = \frac{1}{2} - 6 = -5.5[/tex]
The second derivative of y with respect to x can be calculated by differentiating both sides of the equation with respect to x twice. This gives us:
[tex]\frac{d^2y}{dx^2} = -\frac{1}{2y^3}[/tex]
We can evaluate d2y/dx2 at the point (1, 1) by substituting x = 1 and y = 1 into the equation for d2y/dx2 and calculating the result. This gives us:
[tex]\frac{d^2y}{dx^2} = -\frac{1}{2} = -0.5[/tex]
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A bucket is being filled with water at a constant rate. The graph shows the total amount of water in the bucket over a period of 6 minutes.
Bucket Water
Water (gallons)
0
2
3
Time (minutes)
At what rate is water filling the bucket? Enter the answer in the box.
4
gallons per minute
5
The constant rate at which the water is filling the bucket is: 2/5 gallon per minute.
What is the Constant Rate of a Proportional Relationship?The constant rate of a proportional relationship is the ratio of the change in the dependent variable to the change in the independent variable.
It is also called the slope of the line in a graph representing the relationship. It is given as, k = y/x.
From the given graph, we can pick the point on the line, (5, 2), and find the constant rate, which is the rate the water is filling the bucket.
Constant rate = y/x = 2/5 gallon per minute.
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Are the two triangles congruent? What are the missing sides and angles? Write a valid argument with a claim and warrant to explain.
The missing side of the first triangle is 125' and the angle is 20.61°.
the missing side of the second triangle is 117' and the angle is 69.39°.
What are triangles?Having three edges and three vertices, a triangle is a three-sided polygon. The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic. This characteristic is known as the triangle's angle sum property.
Given the two triangles are congruent,
Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. These triangles can be turned, flipped, rotated, and slid to create an identical appearance.
we can compare both the triangles and the remaining dimensions of triangle 1 are side = 125' and angle = 20.61°
and dimensions of second triangle are,
side = 117' and angle = 69.39°
Hence the dimensions of the first triangle, side = 125' and angle = 20.61°,
and for the second triangle, side = 117' and angle = 69.39°.
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Find the measures of an exterior angle and an interior angle given a regular polygon with 3 sides. Round to the nearest tenth, if necessary.
Answer:
Step-by-step explanation:
A regular polygon with 3 sides is an equilateral/equiangular triangle. All the interior angles measure 60 degrees. The exterior angles are supplementary to that (add up to 180) so an exterior angle is 180 - 60 = 120
Which point in the diagram at the right had a distance of sq of 130
Answer:
S
Step-by-step explanation:
the distance formula (Pythagoras on the right-angled triangle of the coordinate differences) says that
sqrt²(130) = 130 = (-5 - x)² + (5 - y)²
let's try Q
130 = (-5 - 5)² + (5 - 2)² = (-10)² + 3² = 100 + 9 = 109
no, wrong.
let's try S
130 = (-5 - 4)² + (5 - -2)² = (-9)² + 7² = 81 + 49 = 130
correct !
1) SOLVE THE SYSTEM OF LINEAR EQUATIONS.
x=y+2
-3x+3y=6
The system has : (___???____)
?- NO SOLUTION; INFINITELY ?- MANE SOLUTIONS;
?- ONE SOLUTION (7,5)
?- ONE SOLUTION (-8,-10)
2) EXPLAIN YOUR CHOICE OF METHOD
The solution to the system is (x, y) = (7, 5).
What is the linear equation?
A linear equation is an equation of a straight line. It is an equation of the form y = mx + b, where m is the slope of the line and b is the y-intercept.
The system has one solution (7,5).
One method to solve the system of linear equations is substitution. From the first equation, x = y + 2. Substituting this into the second equation, we get -3(y + 2) + 3y = 6, which simplifies to -3y - 6 + 3y = 6.
Combining like terms, we get -3y = -6, or y = 2.
Finally, substituting y = 2 back into x = y + 2, we get x = 2 + 2, or x = 4. So, the solution to the system is (x, y) = (7, 5).
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Please help, 20 points
(5)^2/-10 please help