Answer:
5 -3 = 2
3-5 = -2
Step-by-step explanation:
In this question, we want to examine the validity of the statement by the use of an example.
Firstly, we need to understand the meaning of the fact that they are ‘closed’
By saying these numbers are closed under this arithmetic operation i.e subtraction, we directly mean that they obey the closure property.
Now, to obey the closure property means that if we move either way i.e by switching the numbers and performing the same arithmetic operation of subtraction, we are supposed to get same answer.
What this means in terms of examples is as follows;
Consider two positive numbers, 5 and 3
Now we know that 5-3 = 2
To check if the closure property is obeyed, switch the place of the numbers.
This means we would have;
3-5 = -2
We can see that both results are not the same. We can then conclude that the arithmetic operation of subtraction is not closed or does not obey the closure property for positive numbers.
Graph the solution to the following linear inequality in the coordinate plane 5x-y>-3
Answer:
Here's one way to do it
Step-by-step explanation:
1. Solve the inequality for y
5x - y > -3
-y > -5x - 3
y < 5x + 3
2. Plot a few points for the "y =" line
I chose
[tex]\begin{array}{rr}\mathbf{x} & \mathbf{y} \\-2 & -7 \\-1 & -2 \\0 & 3 \\1 & 8 \\2 & 13 \\\end{array}[/tex]
You should get a graph like Fig 1.
3. Draw a straight line through the points
Make it a dashed line because the inequality is "<", to show that points on the line do not satisfy the inequality.
See Fig. 2.
4. Test a point to see if it satisfies the inequality
I like to use the origin,(0,0), for easy calculating.
y < 5x + 3
0 < 0 + 3
0 < 3. TRUE.
The condition is TRUE.
Shade the side of the line that contains the point (the bottom side).
And you're done (See Fig. 3).
3/4 + z = 5/6 what does z equal
Answer:
1/12
Step-by-step explanation:
3/4 + z = 5/6
Subtract 3/4 from each side
3/4 -3/4+ z = 5/6-3/4
z = 5/6 -3/4
Get a common denominator of 12
z = 5/6 *2/2 -3/4 *3/3
z = 10/12 - 9/12
z = 1/12
f(x) = x2. What is g(x)?
Answer:
g(x)=3x(superscript)2
Answer:
g(x) = 3x².
Step-by-step explanation:
In the diagram, we see that the vertex has not been shifted from the origin. The only thing that happened to the graph of f(x) was that it was vertically stretched to become g(x).
Where x = 1, f(x) = 1. Where x = 1, g(x) = 3. That means that the graph of f(x) was multiplied by 3.
So, g(x) = 3x².
Hope this helps!
all integers are whole numbers?true or false
Answer:
that would be false
Step-by-step explanation:
all whole numbers are integers, but not all integers are whole numbers
A building has an entry the shape of a parabolic arch 84 ft high and 42 ft wide at the base, as shown below. A parabola opening down with vertex at the origin is graphed on the coordinate plane. The height of the parabola from top to bottom is 84 feet and its width from left to right is 42 feet. Find an equation for the parabola if the vertex is put at the origin of the coordinate system. (
Answer:
Step-by-step explanation:
Because of the nature of the information we are given, we have no choice but to use the equation
[tex]y=a(x-h)^2+k[/tex]
and solve for a.
We know by the info that the vertex is (0, 84). We also know that if the vertex is at the origin, and that the base is 42 feet wide, it spans 21 feet to the right of the origin and 21 feet to the left of the origin. That means that we have 2 coordinates from which we need to pick one for our x and y in the equation. I don't like negatives, so I am going to choose the coordinate (21, 0) as x and y. Because this parabola opens upside down, as archways of door openings do, our "a" value better come out algebraically as a negative. Let's see...From the vertex we have that h = 0 and k = 84. So filling in:
[tex]0=a(21-0)^2+84[/tex] and simplifying a bit:
0 = 441a + 84 and
-84 = 441a so
[tex]a=-\frac{84}{441}=-\frac{4}{21}[/tex] Good, a is negative. Your equation is, then:
[tex]y=-\frac{4}{21}x^2+84[/tex]
Answer:
x² = -21y
Step-by-step explanation:
THIS IS THE RIGHT ANSWER I TOOK THE TEST
Evaluate the following expression.
10^7 + 9 + 1^3 =
Anjdjdnjadnosepsjkdsksksks
bzjd
1. Find 3 consecutive integers whose sum is 33.
Answer: 10, 11, 12
Step-by-step explanation: Think of the integers like this:
1st integer: x
2nd integer: x+1
3rd integer: x+2
That is necessary because they are consecutive integers. Since the sum is 33, we need to create an equation.
x+x+1+x+2=33.
Simplify:
3x+3=33.
Opposite operations:
3x=-3+33.
To get the 3 close to the 33, we needed to make it negative, which is the opposite operation of the positive 3.
So,
3x=30.
Divide by 3:
x=10.
The first integer, x, equals 10.
To go with the guide that we already created,
1st integer: x=10
2nd integer: x+1=11
3rd integer:x+2=12.
Therefore, the three consecutive integers are 10, 11, and 12.
To check that, add them up. They all equal 33 and they are consecutive, which means this is the right answer!
Answer:
10, 11, 12
Step-by-step explanation:
For problems involving consecutive integers, I like to consider their average value. For three consecutive integers, their average will be the middle one. It will be ...
average = sum / (number of numbers) = 33/3 = 11
The middle number is 11, so the numbers are ...
10, 11, 12
_____
If you want to write an equation, you can let x represent the middle number. Then the other two are x-1 and x+1, and their sum is ...
(x-1) +(x) +(x+1) = 33 = 3x
x = 11 ⇒ x-1 = 10, x+1 = 12
I need help ASAP!
Possible answers are 9, 37, -37, 19, 24, 8, and -24
Answer:
37
Step-by-step explanation:
Hello!
First we add 15 to both sides
[tex]\frac{-5x-10}{5} = -2x + 35[/tex]
Multiply both sides by 5
-5x - 10 = -10x + 175
Add 10 to both sides
-5x = -10x + 185
Add 10x to both sides
5x = 185
Divide both sides by 5
x = 37
The answer is 37
Hope this helps!
[tex]\dfrac{-5x-10}{5}-15=-2x+20\quad|\cdot5\\\\-5x-10-75=-10x+100\\\\-5x+10x=100+10+75\\\\5x=185\quad|:5\\\\\boxed{x=37}[/tex]
f(x) = x^2. What is g(x)?
Convert the mixed number to an improper fraction 1 13/15
━━━━━━━☆☆━━━━━━━
▹ Answer
28/15
▹ Step-by-Step Explanation
[tex]1\frac{13}{15} \\\\1 * 15 = 15\\15 + 13 = 28\\\\\\= \frac{28}{15}[/tex]
Hope this helps!
CloutAnswers ❁
━━━━━━━☆☆━━━━━━━
What is the solution to this system of equations?
5x + 2y = 29
x + 4y= 13
Answer:
x = 4.5
y = 3.25
Step-by-step explanation:
Use elimination
5x + 2y = 29
x + 4y = 13 (-5)
4y(-5) = 13(-5)
2y = 29
-20y = -65
y = 3.25
Sub it back into the equation
5x + 6.50 = 29
5x = 22.5
x = 4.5
can someone please help me I need the answer urgently please
Answer:
Step-by-step explanation:
AB ≅ BC. So, ΔABC is an isosceles triangle
Opposite angles of equal sides are equal.
∠BAC = ∠BCA = x°
In ΔABC,
∠ABC + ∠BAC + ∠BCA = 180 {Angle sum property of triangle}
56 + x + x = 180
56 + 2x = 180
2x = 180 - 56
2x = 124
x = 124/2
x = 62°
∠BAC = ∠BCA = 62°
∠DCF = ∠BCA {Vertically opposite angles}
∠DCF = 62°
CDEF is a parallelogram.
In parallelogram, opposite angles are congruent.
∠DEF = ∠DCF
∠DEF = 62°
In a parallelogram, sum of adjacent angles = 180
∠DEF + ∠CDE = 180
62 + ∠CDE = 180
∠CDE = 180 - 62
∠CDE = 118°
∠CFE = ∠CDE {In parallelogram, opposite angles are congruent}
∠CFE = 118°
Which graph represents a function?
Answer:
The first one is the only function
Step-by-step explanation:
You cannot have points on the same y gridline
If it is a function is has to pass the pencil test
Answer:
[tex]\boxed{Graph A.}[/tex]
Step-by-step explanation:
Hey there!
Well graph A is correct because if you do the vertical line test which decides is the graph is a function or not you can see that all the graph expect A have the vertical line go through 2 points.
Hope this helps :)
* * +:) help .........
1. -11 2.-3
Make sure to simplify the equation..
example: 3(2x - 7) = 6x - 21
because 3 x 2 = 6 and 3 x 7 = 21
It takes Matt 3 minutes to read one page in a book. If he continues to read at the same pace, he can read 15 similar pages in minutes. If the book has 300 pages, it will take him minutes to read it.
Answer:
a)45min
b)900min
Step-by-step explanation:
We were told that it takes Matt 3 minutes to read one page in a book.
It implies that 3minutes = 1page of the book
Then he continues to read at the same pace, he can read 15 similar pages in minutes.
a)Then, he can read 15 similar pages in
15x3 minutes.which is 45minutes.
b)Then if the book has 300 pages, it will take him. 300×3 minutes to read it.which is 900mins
Answer: has anyone seen my dad?
Complete the Magic Square.
Answer:
+5
Step-by-step explanation:
So you can see the 5 pattern, so you add 9+5= 14 which goes in the middle square and 14+5=18 in the left square
Now between 18 and 11 it is 7 so you subtract 7 which equals 4 then - 5= -1 then -5= -6
Answer:
4 5 9
11 6 1
3 7 8
Step-by-step explanation:
In a magic square, all rows, columns, and diagonals have the same sum.
Let's call the cells a - i this way:
a b c
d e f
g h i
Now lets's fill in what we have:
a b 9
11 6 1
g h i
2nd row: 11 + 6 + 1 = 18
3rd column: 9 + 1 + i = 18; i = 8
a b 9
11 6 1
g h 8
Main diagonal: a + 6 + 8 = 18; a = 4
4 b 9
11 6 1
g h 8
1st row: 4 + b + 9 = 18; b = 5
4 5 9
11 6 1
g h 8
1st column: 4 + 11 + g = 18; g = 3
4 5 9
11 6 1
3 h 8
2nd column: 5 + 6 + h = 18; h = 7
4 5 9
11 6 1
3 7 8
The company is building a scale model of the theater’s main show tank for an investor's presentation. Each dimension will be made 16of the original dimension to accommodate the mock-up in the presentation room. What is the volume of the smaller mock-up tank? Hint: You do not divide the volume of the main show tank by 6.
Answer:
see below
Step-by-step explanation:
If the original dimensions of the tank are x, y, and z, the mock dimensions will be 1/6x, 1/6y and 1/6z. The volume of the original tank is x * y * z = xyz whereas the volume of the mock-up tank is 1/6x * 1/6y * 1/6z = 1/216 * xyz. Therefore, we know that the volume of the mock-up tank is 1/216 th of the original tank.
ABC is an equilateral triangle, solve y
Answer:
y is 60⁰
because all sides are equal
Answer:
60 degrees
Step-by-step explanation:
In an equilateral triangle, the angles are equiangluar and the sides are equal.
180 degrees in a triangle/3 sides =
= 60 degrees per side
Cory earns $9.50 per hour for the first 40 hours he works in a week. For any hours over 40 hours per week, his hourly rate is multiplied by 1.5. How much does he earn is he works for 43.5 hours in one week?
Answer:
429.88
Step-by-step explanation:
The first 40 hours is at 9.50
40 *9.50 =380
The remaining hours is at 9.50 * 1.5 or 14.25
43.5 -40 = 3.5
3.5 * 14.25
49.875 = 49.88 ( rounding to the nearest cent)
Add together
380+49.88 =429.88
Jess receives a $15000 salary for working as an engineer. If Jess has to spend $6000 of her salary on expenses each year, then what percent of Jess's money does she have to spend? Round your answer to the nearest whole number if necessary.
Answer:
Jess will have to spend 40% of her salary
Step-by-step explanation:
Jess salary = $15,000
Jess expenses = $6,000
what percent of Jess's money does she have to spend
Percentage of Jess expenses = Jess expenses / Total salary × 100
= 6,000 / 15,000 × 100
= 0.4 × 100
= 40%
Jess will have to spend 40% of her salary
Evaluate 2^2⋅4^3=
Your answer
Answer:
256
Step-by-step explanation:
First, handle the exponent:
2²=4 (2*2=4) and 4³=64 (4*4=16*4=64)
Now multiply those two outcomes:
4*64=256
This equation is also known as 4⁴
If paul puts 300 dollars in a saving account that earns 3% interest how much interest will he earn after 2 years?
Answer:
[tex] \boxed{18 \: dollars}[/tex]Step-by-step explanation:
Principal ( P ) = $ 300
Rate ( R ) = 3%
Time ( T ) = 2 years
Now, let's find the simple Interest:
I = [tex] \mathsf {\frac{PTR}{100} }[/tex]
[tex] \mathsf{ = \frac{300 \times 2 \times 3}{100} }[/tex]
[tex] \mathsf{ = \frac{1800}{100} }[/tex]
[tex] \mathsf{ = 18}[/tex]
Extra information:
Simple Interest
In our daily life when we borrow a sum of money either from a moneylender or from any financial company, we have to pay the money back by adding with extra sum of money. This borrowed money is called principal. The extra money to be paid for the borrowing money is called interest , which is paid after certain duration in certain rate. At last, the borrowed money should be paid back along with interest which is called amount.
Interest is based on three factors : Principal ( P ) , Rate of interest ( R ) and Time ( T ). While computing the interest, the rate must be in percent and time in years.
[tex] \mathsf{ \: simple \: interest \: = \frac{PTR}{100} }[/tex]
On simplifying
[tex] \mathsf{p = \frac{I \times 100}{T \times R} }[/tex]
[tex] \mathsf{t = \frac{I \times 100}{P \times R} }[/tex]
[tex] \mathsf{r = \frac{I \times 100}{P \times T}} [/tex]
And from the definition,
Amount ( A ) = Principal ( P ) + Interest ( I )
Principal ( P ) = Amount ( A ) - Interest ( I )
Interest ( I ) = Amount ( A ) - Principal ( P )
Hope I helped!
Best regards!
Answer:$18
Step-by-step explanation:3% of $300 is $9.$9 is the interest of 1 year so the interest of 2 years is 2 multiplied by 9 which is $18.
What’s the function of the Unit Circle and why is it called the unit Circle?
Answer:
It is a unit of radius that is radius of 1. Thus, the distant to the middle to any edge is always 1.
Step-by-step explanation:
**50 points Once again and brainliest** Please hurry ;w;
Answer:
Part A:
Two types of translation are;
1) Horizontal translation left T(0, 8),
2) Vertical translation T(16, 0)
Part B:
For the horizontal translation transformation, k = 8
For the vertical translation transformation, k = 16
Part C:
For the horizontal translation transformation, the equation is f(x + 8) = g(x)
For the vertical translation transformation, the equation is f(x) + 16 = g(x)
Step-by-step explanation:
Answer:
see below
Step-by-step explanation:
Part A
We can shift f(x) up to g(x)
or we can shift f(x) to the left into g(x)
Part B
y = f(x) + k k > 0 moves it up
f(x) goes from -1 to 17 for a distance of 18 units
We are moving up 18 units
k = 18
y = f(x + k) k> 0 moves it left
We are moving to the left from 0 to -6 units for a distance of 6 units
k = 6
Part C
Up:
g(x) = f(x) +18
Left:
g(x) = f(x+6)
Please answer this question now
Answer:
112°
Step-by-step explanation:
Angle A is an inscribed angle that intercepts arc BCD.
Therefore:
m<A = ½ of arc BCD (Inscribed Angle Theorem)
Arc BCD = BC + CD = 146 + CD
An equation can be written to enable us find the measure of arc CD. See below:
Let x = measure of arc CD
Thus,
129° = ½(146 + x)
Solve for x
129*2 = 146 + x
258 = 146 + x
Subtract 146 from both sides of the equation.
258 - 146 = x
112 = x
x = measure of arc CD = 112°
4 (hx - 1) -3 (x +h) ≡ 5 (x + k)
Work out the value of h and k
H and k are integer constants
Answer:
4hx - 8x - 3h - 4
k = ------------------------
5
8x + 5k + 4
h = ------------------------
4x - 3
Step-by-step explanation:
4 (hx - 1) - 3 (x + h) = 5 (x + k)
4hx - 4 - 3 (x + h) = 5 (x + k)
4hx - 4 - 3x - 3h = 5 (x + k)
4hx - 4 - 3x - 3h = 5x + 5k add 3h both sides
4hx - 4 - 3x - 3h + 3h = 5x + 5k + 3h simplify
4hx - 4 - 3x = 5x + 5k + 3h add 4 both sides
4hx - 4 - 3x + 4 = 5x + 5k + 3h + 4 simplify
4hx - 3x = 5x + 5k + 3h + 4 subtract 5x from both sides
4hx - 3x - 5x = 5x + 5k + 3h + 4 - 5x simplify
4hx - 8x = 5k + 3h + 4
4hx - 8x - 3h - 4 = 5k
4hx - 8x - 3h - 4
k = ------------------------
5
solving for h;
4hx - 3h = 8x + 5k + 4
h(4x - 3) = 8x + 5k + 4
8x + 5k + 4
h = ------------------------
4x - 3
The value of h and k are h = (8x + 5k + 4) / (4x - 3) and k = (4hx - 8x - 3h - 4) / 5 respectively
Given:
4 (hx - 1) -3 (x +h) ≡ 5 (x + k)
open parenthesis
4hx - 4 - 3x - 3h = 5x + 5k
4hx - 4 - 3x - 3h - 5x - 5k = 0
4hx - 8x - 3h - 5k - 4 = 0
For k
4hx - 8x - 3h - 4 = 5k
[tex]k = (4hx - 8x - 3h - 4) / 5[/tex]
For h
4hx - 8x - 3h - 5k - 4 = 0
4hx - 3h = 8x + 5k + 4
h(4x - 3) = 8x + 5k + 4
[tex]h = (8x + 5k + 4) / (4x - 3)[/tex]
Therefore, the value of h and k are h = (8x + 5k + 4) / (4x - 3) and k = (4hx - 8x - 3h - 4) / 5 respectively
Read more:
https://brainly.com/question/21406377
Factor x^4+xy^3+x^3+y^3 completely showing work.
Answer:
Step-by-step explanation:
Hello, please consider the following.
[tex]x^4+xy^3+x^3+y^3\\\\=x^3*x+x*y^3+x^3+y^3\\\\=x(x^3+y^3)+x^3+y^3\\\\\boxed{=(x+1)(x^3+y^3)}\\[/tex]
Thank you
On the coordinate plane below, Point P, is located at (2,-3) and point Q is located at (-4,4). Find the distance between points, P and Q
Answer:
approximately 9.2195
Step-by-step explanation:
We can use Pythagorean theorem
one leg is 7 and the other leg is 6
square them
49 and 36
add
85
square root
approximately 9.2195
A
man paid 15600
for a new
car. He
was given a discount of
7%. Find the marked price
of the car
hope it helps.I was reading the same chapter
On his return trip, Zen descends from the Calloway Peak Summit to an elevation of 2,402.5 feet, arriving at the Flat Rock Junction. So, the elevation at Flat Rock is feet.
Complete question :
Zen is participating in an all-day hike to the Grandfather Mountain Summit on the Blue Ridge Parkway.
Starting at elevation zero, Zen climbs to an elevation of 4,646.4 feet to reach the Cragway Trail. From there, he hikes up another 1,817.6 feet to the Calloway Peak Summit, the highest point on Grandfather Mountain. Based on these numbers, the Calloway Peak Summit is at a height of _____ feet.
On his return trip, Zen descends from the Calloway Peak Summit to an elevation of 2,402.5 feet, arriving at the Flat Rock Junction. So, the elevation at Flat Rock is ______ feet.
Answer:
6,464 Feets; 4,061.5 Feets
Step-by-step explanation:
Given the following:
Starting elevation = 0
Elevation of the Cragway Trail = 4,646.4 feets
Elevation of Cragway Trail to Calloway peak summit = 1,817.6
From Calloway peak summit, Zen descends to an elevation of 2,402.5 Feets (flat Rock junction)
The Calloway Peak Summit is at a height of _____ feet.
Height of Calloway Peak Summit:
(Starting elevation to Cragway trail) + (Cragway trail elevation to Calloway peak Summit)
4,646.4 Feets + 1,817.6 Feets = 6,464 Feets
B) Elevation at Flat Rock Junction:
Height of Calloway peak summit - 2,402.5
(6464 - 2402.5) Feets = 4,061.5 Feets
