Now, look at the set of integers. Complete the table for the closure property if integers under the four operations.
Answers
Answer:
See below.
Step-by-step explanation:
Addition: closed
Example: -5 + 10 = 5, and -5, 10, and 5 are all integers
Subtraction: closed
Example: 10 - 8 = 2, and 10, 8, and 2 are all integers
Multiplication: closed
Example: -4 * 7 = -28, and -4, -7 and -28 are all integers
Division: not closed
Example: 5/2 = 2.5, and 2.5 is not an integer, although 2 and 5 are integers
The set of integers is closed under addition, subtraction, and multiplication because any addition, subtraction, or multiplication of integers always results in an integer.
The set of integers is not closed under division because a division of integers does not always result in an integer.
Related Questions
Find
(1) a + b,
(2) 2a + 3b,
(3) |a|, and |a − b|.
a = 5i + j, b = i − 2j
Answers
Answer:
Step-by-step explanation:
this problem is on vector
given the vectors
a = 5i + j, and
b = i − 2j
1. summation of vector a + b
[tex]= (5i+j)+(i-2j)\\\\=5i+j+i-2j\\\\[/tex]
collect like terms
[tex]=5i+i+j-2j\\\\=6i-j\\\\[/tex]
2. 2a + 3b
[tex]= 2(5i+j)+3(i-2j)\\\\=10i+2j+3i-6j\\\\[/tex]
collecting like terms we have
[tex]=10i+2j+3i-6j\\\\=10i+3i+2j-6j\\\\=13i-4j[/tex]
(3) |a|, and |a − b|.
|a|= |5i+j|
[tex]=\sqrt{5^2+1^2} \\\\=\sqrt{25+1} \\\\=\sqrt{26} \\\\= 5.1[/tex]
also,
[tex]|a - b|= |(5i+j) -(i-2j)| \\\\ a-b= 5i+j -i+2j \\\\ a-b=5i-i+j+2j \\\\a-b= 4i+3j\\\\[/tex]
[tex]|a -b|=\sqrt{4^2+3^2} \\\\|a -b|=\sqrt{16+9} \\\\|a -b|=\sqrt{25} \\\\|a -b|=25[/tex]
Can someone please help the question is below thank you!
Answers
Answer:
you just times the number buy 9 and 3 then divid by 3
Step-by-step explanation:
what is the distance between -11 and 8 on the number line?
Answers
Answer:
= 3
Step-by-step explanation:
| 11-8 |= | 3 |= 3
Select the appropriate response.
An isosceles triangle has vertices at (1,1) and (3, 3). Which of the following could be
the coordinates of the third vertex?
A. (2.1)
B. (3.2)
C. (4,1)
D. (5,1)
Choose
Answers
Answer:
D. (5,1)
Step-by-step explanation:
Because it is an isosceles triangle, the next point we choose must result in two sides with the same length. This means that either the two new sides are equal, or that one of the new sides is equal to the original side. If we wanted both of the new sides to be equal, they would have to be equal distance from the new point and one of the points of the original line. However, none of the options result in both new lines being the same length.
(2,1) would result in one new length being 1 unit long (2-1 x-coordinates) and the other being square root 5 (distance from point 2,1 to point 3,3 minus both coordinates and use Pythagoras). Points 3,2 and 4,1 yield the same result: Length 1=1 unit length 2=square root 5. Length 1 = 3 unit, length 2 = square root 5.
Therefore we are looking for a point which instead yields one length which is the same length as the original. The original length was 2^2 + 2^2 = c^2 = square root 8.
If we try the point 5,1 then we get two lengths of 4 and square root 8, it forms a isosceles triangle whose base line is parallel to the x-axis.
Sorry is my explanation was confusing, it's much easier to try and draw it on a grid and visualize it. Basically the overall idea is to test the side values you get by finding the distance between the points and going with the option which results in two sides with the same length.
Hope this helped!
Answer:
D. (5,1)
Step-by-step explanation: Because it is an isosceles triangle, the next point we choose must result in two sides with the same length. This means that either the two new sides are equal, or that one of the new sides is equal to the original side. If we wanted both of the new sides to be equal, they would have to be equal distance from the new point and one of the points of the original line. However, none of the options result in both new lines being the same length.
(2,1) would result in one new length being 1 unit long (2-1 x-coordinates) and the other being square root 5 (distance from point 2,1 to point 3,3 minus both coordinates and use Pythagoras). Points 3,2 and 4,1 yield the same result: Length 1=1 unit length 2=square root 5. Length 1 = 3 unit, length 2 = square root 5.
Therefore we are looking for a point which instead yields one length which is the same length as the original. The original length was 2^2 + 2^2 = c^2 = square root 8.
If we try the point 5,1 then we get two lengths of 4 and square root 8, it forms a isosceles triangle whose base line is parallel to the x-axis.
Sorry is my explanation was confusing, it's much easier to try and draw it on a grid and visualize it. Basically the overall idea is to test the side values you get by finding the distance between the points and going with the option which results in two sides with the same length.
Find the distance from the point (0, 4, 3) to the plane 5x +1y +2z
Answers
Answer:
distance =
[tex] \sqrt{ \frac{10}{3} } [/tex]
Step-by-step explanation:
Without going through and deriving this (my blackboard doesn't have space and a textbook, teacher, or online tutorial is probably better for that), the equation for the distance from some point on the plane to some point in space is as follows:
[tex]distance = \frac{ax + by + cz - d }{ \sqrt{ {a}^{2} + {b}^{2} + {c}^{2} } } [/tex]
•Note that the d in the equation should actually be D but Brainly doesn't allow me to do uppercase letters on mobile it seems... Anyway, d in the equation represents the value which the equation of the plane is equal to. You only gave the plane equation so I assumed d=0 in my calculations.
•x, y, and z all come from the point which you want to find the distance to. So (x,y,z)=(0,4,3) here.
•a, b, and c all come from the components of the vector normal to the surface. For planes, it simply somes to be the coefficients in front of each part. So (a,b,c)=(5,1,2) here.
With that you just need to plug the information in and simplify for your answer. My work is in the attachment, comment with questions or if anything seems off.
i need help i only got 30 min... 40 points i will give brainliest
Answers
Questions 1, 2, and 5 are correct.
Question 3:
To find the common difference, we can subtract the last two numbers.
60 - 47 = 13
So, the common difference is 13
We can add 13 to each term to get the next term.
8 + 13 = 21
21 + 13 = 34
So, 8, 21, 34, 47, 60
Question 4:
To find the common difference, we can subtract the last two numbers.
8/3 - 2 = 2/3
So, the common difference is 2/3
We can add 2/3 to each term to get the next term.
0 + 2/3 = 2/3
2/3 + 2/3 = 4/3
So, 0, 2/3, 4/3, 2, 8/3
Question 4:
Since we are only given the first and last number, we need to find a number we can subtract that we get -13 at the end. The distance between 3 and -13 is 16. We can divide this by 4 since there are 4 numbers before -13.
16 / 4 = 4
Since the number is going down, the common difference is going to be -4.
Subtract find the next terms.
3 - 4 = -1
-1 - 4 = -5
-5 - 4 = -9
-9 - 4 = -13
So, 3, -1, -5, -9, -13
Best of Luck!
A rectangle has a length of L and a width, W, that is 4 less than 3 times the length. Which expression would give us the correct perimeter?
Answers
Answer:
Length is 4 less than 3
Step-by-step explanation:
Which pair of points has a slope of 4? Question 4 options: (0, 4), (4, 0) (3, 0), (–1, –1) (1, 4), (–1, 4) (0, –3), (1, 1)
Answers
Answer:
(0,-3) and (1,1)
Step-by-step explanation:
In order to have a slope of 4, the y coordinates need to differ by 4, and the x coordinates by 1. This is because slope is equal to rise/run. Rise being difference in y value and run difference in x.
In this pair of coordinates, the y coordinates differ in +4 (-3 and 1) and the x coordinate differs by 1 (0 and 1).
Therefore this is the pair of points with a slope of 4.
Hope this helped!
The pair of points that has a slope of 4 is the coordinate points (0, –3), (1, 1)
The formula for calculating the slope of a line passing through two points is expressed as:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
We need to get which of the coordinates will result in a slope of 4.
Using the coordinate points (0, –3), (1, 1)
[tex]m=\frac{1-(-3)}{1-0}\\m=\frac{1+3}{1}\\m=\frac{4}{1}\\m=4[/tex]
Hence the pair of points that has a slope of 4 is the coordinate points (0, –3), (1, 1)
Learn mroe here: https://brainly.com/question/23935638
Find all values of c such that f is continuous on (-[infinity], [infinity]). f(x) = { 3 - x^2 x less than or equal to c x, x > ca. c = -1 + squareroot 13/2, -1 - squareroot 13/2.b. c = 0. c. c = -1 = squareroot 13/2.d. c = 2.e. c = -1 + squareroot 13/2, 1 - squareroot 13/2.
Answers
Answer:
a) [tex]c=\frac{-1+\sqrt{13}}{2}[/tex] and [tex]c=\frac{-1-\sqrt{13}}{2}[/tex]
Step-by-step explanation:
The idea for the solution of this equation is to find the value of c where both parts of the piecewise-defined function are the same. So we need to take the parts of the function and set them equal to each other, so we get:
[tex]3-x^{2}=x[/tex]
and then solve for x. We move everything to one side of the equation so we get:
[tex]x^{2}+x-3=0[/tex]
and we use the quadratic formula:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
and we substitute:
[tex]x=\frac{-1\pm \sqrt{(1)^2-4(1)(-3)}}{2(1)}[/tex]
and solve
[tex]x=\frac{-1\pm \sqrt{1+12}}{2}[/tex]
[tex]x=\frac{-1\pm \sqrt{13}}{2}[/tex]
so our two answers are:
a) [tex]c=\frac{-1+\sqrt{13}}{2}[/tex] and [tex]c=\frac{-1-\sqrt{13}}{2}[/tex]
I want to bring my grade up so if anyone knows tell me
Answers
Answer:
no
Step-by-step explanation:
You will have more time to do it, but no, try extra credit
Sorry mate hope this helps<3
SOMEONE please help me!!! pls pls pls!!!
Answers
it is true because 14 is 1/14
I’m not understanding this question at all. WILL GIVE BRAINLY!! (6 is not the answer)
Answers
Answer:
-8.
Step-by-step explanation:
Substitute BC with the -4 and 2, as you were given those values to substitute with B and C. Multiply those two values. You get -8.
The manager of a restaurant found that the cost to produce 200 cups of coffee is $65.00 , while the cost to produce 250 cups is $77.50 . Assume the relationship between the cost y to produce x cups of coffee is linear. a. Write a linear equation that expresses the cost, y, in terms of the number of cups of coffee, x. b. How many cups of coffee are produced if the cost of production is $135.00 ?
Answers
Answer:
a). y = 0.25x + 15
b). x = 480 cups
Step-by-step explanation:
(a). Let the equation of the linear function passing through a point (x', y') is,
y - y' = m(x - x')
'm' = slope of the line
b = y-intercept
Two points lying on the linear function will be (200, 65) and (250, 77.5).
Slope of the line 'm' = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]
m = [tex]\frac{77.5-65}{250-200}[/tex]
= [tex]\frac{12.5}{50}[/tex]
= 0.25
Therefore, equation of the line passing through (200, 65) and slope 0.25 will be,
y - 65 = 0.25(x - 200)
y - 65 = 0.25x - 50
y = 0.25x + 15
(b). For y = $135 we have to calculate the number of cups of coffee produced.
135 = 0.25x + 15
0.25x = 135 - 15
0.25x = 120
x = 480 cups
Therefore, 480 cups of coffee will be produced.
given g(x)=x^2 and h(x)= x-3 find (g ∘ h)(x)
Answers
Answer:
(g ∘ h)(x) = x² - 6x + 9Step-by-step explanation:
g(x) = x²
h(x) = x - 3
To find (g ∘ h)(x) substitute h(x) into g(x) that's for every x in g(x) replace it with h(x)
That's
(g ∘ h)(x) = ( x - 3)²
= x² - 3x - 3x + 9
We have the final answer as
(g ∘ h)(x) = x² - 6x + 9Hope this helps you
PLZ HELP ASAP WILL MARK BRAINIEST
Which graph represents the inequality:
x+6<-9??
Answers
I believe the answer is A
Slope intercept Functions
Answers
Y=1/3x-4
11. What is the difference between the weights of planes C and D? Explain how to use mental math to solve. - C: 56,984 D: 79,473 - The difference in weights is ______ pounds. The difference in weights is given by the expression _______ - _______. Compensation can be used to rewrite this so that the second number is the next greater multiple of 1,000. Doing this gives the new expression ______ - ______. The value of this new expression is _____________. (Type whole numbers.)
Answers
Answer:
22,48979,473 - 56,98479,489 - 57,00022,489Step-by-step explanation:
Based on the clues in the problem wording, we assume the numbers given for C and D are the weights of planes, in pounds. For whatever reason, we seem to be interested in the difference of those weights.
The difference in weights is 22,489 pounds.
The difference in weights is given by the expression 79,473 - 56,984.
We can add 16 to both numbers to make the second number a multiple of 1000. To compensate, we also add 16 to the first number.
Doing this gives the new expression 79,489 - 57,000.
The value of this expression is 22,489.
_____
Additional comments
A number of thinking processes are taught for mental math. In this process, you recognize that 984 is near 1000, so you can add a small number to make all the rightmost digits be zeros. That number will have the digits that "make a ten" working from right to left. 4 needs 6 added to make a 10. Adding 6 to 84 makes it 90. Then the 9 needs 1 added to make a 10. Now, we have 984 with 16 added, which makes 1000. Adding that 16 to 79473 to make 79489 completes the transformation we're looking for: 79489 -57000.
Choose the correct solution to the equation.
-3+w=
a. 2
b. Ž
ch
d. None of the Above
Оа
Ob
Ос
Od
Answers
Answer:
Step-by-step explanation: I have no clue
the -3 gets moved to the other side of the = and changes to +3
1w=3
now divide by w on each side
1w/1w = w
3/1 = 3
the answer would be d.
if a point is located on the x-axis , what is the y coordinate?
Answers
0
Step-by-step explanation:
im only saying this because im assuming it is on the line of the axis
Answer:
0
both x and y are zero so the y axis is 0 then the x axis is 0
NEED HELP ASAP!!! Solve 0 = (3x - 4) / 5
Answers
answer: 1.13622
Step by step explanation:
n:
0=(3x-4)/5
0=3x/5-4/5
x=1.3.....
Bill has a container that is shaped like a cube. He uses 125 cubes with a side length of 1 inch to fill the container completely. What is the edge length of the container? *****Hint: 1 inch cubes to fill a container is the volume of the cube Please answer quickly!!! Thank you.
Answers
Answer:
5 inches
Step-by-step explanation:
Given
Length of a cube = 1 inch
Required
Determine the edge length of the cube
If the container can take 125 cubes, then that's the volume
So:
[tex]Volume = 125in^3[/tex]
Volume of a cube is calculated as thus;
[tex]Volume = Length^3[/tex]
This gives;
[tex]Length^3 = 125[/tex]
Take cube root of both sides
[tex]Length = \sqrt[3]{125}[/tex]
[tex]Length = 5[/tex]
Hence, the length is 5 inches
Solve for x 40+5x>95-4x
Answers
Steps to solve:
40 + 5x > 95 - 4x
~Subtract 40 to both sides
5x > 55 - 4x
~Add 4x to both sides
9x > 55
~Divide 9 to both sides
x > 55/9
Best of Luck!
Find the approximate side length of a square game board with an area of 155in2.
Answers
The side of a square is the square root of the area.
Side = sqrt(155)
Side = 12.45 inches. (Round answer as needed)
12. Determine whether the given number belongs
to each set.
te?
Whole
Numbers
Integers
Rational
Numbers
es
- 34
Answers
Answer:
The number -34 belongs to:
✔️Integers and
✔️Rational numbers
Step-by-step explanation:
-34 is an integer because it can written without a fractional or decimal part.
Rational numbers are said to numbers that can actually be expressed as a fraction with integers. They have no fractional part.
For example, −34 is a rational number because it can be written as - 34/1.
-34 can be expressed as -34/17, given an integer.
-34 is NOT a whole number because whole numbers are positive numbers.
If f(x) = 2x + 3 for all values of x, what is the value of f(-3)? A 0 B -3 C 5 D 9
Answers
Answer:
[tex]f(-3)=-3[/tex]
Step-by-step explanation:
[tex]f(x)=2x+3[/tex]
[tex]f(-3)=2(-3)+3[/tex]
[tex]f(-3)=-6+3[/tex]
[tex]f(-3)=-3[/tex]
Hope this helps!
(Please mark Brainliest!)
A triangle has a base of 3 feet and an area of 15 square feet. Find the triangle's height
Answers
Answer:
10 ft
Step-by-step explanation:
The formula for the area of a triangle can be used. Put the known values into the formula and solve for the unknown.
A = (1/2)bh
15 = (1/2)(3)h
h = 15/1.5 = 10
The triangle's height is 10 feet.
Answer:
10
Step-by-step explanation:
A=1/2*b*h
15=1/2*3*h
15=3/2*h
15=3/2h
h=15/(3/2)
h=(15/1)(2/3)
h=30/3
simplify
h=10
how do you turn 372800 into scientific notation
Answers
Answer:
3.78x10^5
Step-by-step explanation:
The supplement of an angle is 42 degrees less than 3 times the complement of the angle. What is the measure of the angle?
Answers
Answer: 24°
Step-by-step explanation:
Given the following :
supplement of an angle is 42 degrees less than 3 times the complement of the angle
Let the angle = θ
Supplement of angle = 180° - θ
Complement of angle = 90° - θ
Supplement of angle is also said to be:
(3 × complement) - 42° = 3(90° - θ) - 42°
= 270° - 3θ - 42° = 228° - 3θ
Hence,
180° - θ = 228° - 3θ
Solve for θ
-θ + 3θ = 228° - 180°
2θ = 48°
θ = 48°/2
θ = 24°
3 pieces of same size can fill a cistern in 90 minutes. how long would 5 pipes takes to fill
Answers
Answer:
i think the answer would be 150. sorry if its wrong
Step-by-step explanation:
90/3*5=
30*5=
150
The sum of two numbers is 190. The sum of their digits is 10.