Answer:
a) The set of real numbers is the union of the set of Irrational numbers and the set of rational numbers.
b) Real numbers have a lot of properties, one example is that they are closed under a lot of operations, like addition or multiplication.
This means that if we have two real numbers A and B:
A + B is also a real number.
A*B is also a real number.
c) A good way to learn Algebra (or math in general) is:
First, read the textbook, have a general idea of the complete topic, if you don't understand something, keep reading, just take note of all the things you don't understand.
Second, ask the things that you do not fully understand, not shame in it, math has a lot of complex relations that sometimes can be really hard to understand, and there are a lot of cases (at least for me) where one can think that understands very well a topic, but it is wrong, so in order to avoid this, ask everything you can.
Third, do a LOT of exercises, the only way in which you can learn to use your equations and relations is applying them in math problems, and it will also help you to understand the meaning of those equations in a more profound way.
What is the value of 20 + 3 (7 + 4) + 5 + 2 (7 + 9)? PLEASE HELP ASAP
Answer:
90
Step-by-step explanation:
The length of a rectangle is shown below: (look at the picture) If the area of the rectangle to be drawn is 12 square units, where should points C and D be located if they lie vertically below the line that connects B and A, to make this rectangle? C(−2, −1), D(1, −1) C(−2, −4), D(1, −4) C(−2, −2), D(1, −2) C(−2, −5), D(1, −5)
================================================
Explanation:
The distance from B to A, or vice versa, is 3 units. You can count out the spaces between the points, or you could subtract the x coordinate values then use absolute value
|B - A| = |-2-1| = |-3| = 3
or
|A - B| = |1-(-2)| = |1+2| = |3| = 3
Whichever method you prefer, the distance between the two points is 3 units.
----------
The area of the rectangle is 12 square units, and we know one dimension of the rectangle is 3 units. The other dimension must be 12/3 = 4 units.
Point C is directly below point B. Specifically C is 4 units below B.
Start at B(-2,2) and move down 4 units to get to C(-2,-2). Then move to the right 3 units to get to D(1,-2)
Or you could start at A(1,2) and move 4 units down to get to D(1,-2) and then move 3 units to the left to get to C(-2,-2)
Answer:
Answer choice = B - C(−2, −4), D(1, −4)
() and () are inverses of one another and drawn on the same graph with the same scale on both the horizontal and vertical axis. Which of the following would be true?
A.
By reflecting the entire coordinate grid over the line =, () would land on ().
B.
() is the same as (), translated up 3 units.
C.
By rotating () 90° clockwise around the origin you would get ().
D.
By rotating () 180° clockwise around the origin you would get ().
Answer: Option A.
Step-by-step explanation:
We have the functions f(x) and g(x), that are inverses between them.
This means that if:
f(x) = y
then:
g(y) = x.
now, remember that:
When we have a point (x, y), and we reflect it over the line y = x, our new point will be (y, x).
So before we whe had:
f(x) = y.
and now in that same place, we have:
g(y) = x.
So the old graph of f(x) now coincides with the graph of g(x). (And the old graph of g(x) now coincides with the graph of f(x) )
So A is true.
B) This depends on the function:
if we have f(x) = x + 1.5
then f(0) = 1.5
now we want that:
g(1.5) = 0, then we can write:
g(x) = x - 1.5
Now f(x) and g(x) are inverses, and we would have that:
f(x) = g(x) + 3.
So f(x) is g(x) translated up by 3 units, but this is a particular case, not a general one, so B is not always true.
C and D) When we do rotations of 90° or 180°, we are effectively changing the quadrant of our point. so rotations will cause not only changes as the reflection over the x = y line, those will also cause changes in the sign of our variables, so, while for some functions f(x) and g(x) we can have that the rotations will map one into the other, this is not the general case.
What two factors of 24 have a sum of 11
Answer:
8 and 3
Step-by-step explanation:
8+3=11
8*3=24
The function f(x) = –4x2 represents the path of a whale as it surfaces for air and dives again. Select all the observations that are true about the whale’s path.
A. The domain is all real numbers x until the ocean hits the shore.
B. The range is (−∞,−4)
C. There are two points where the whale touches the surface.
D. f is decreasing for the whale's entire path.
E. The point where the whale touches the surface is a maximum.
Answer:
Option (A) and (E)
Step-by-step explanation:
Characteristics of the quadratic function representing the path of a whale as it surfaces for air is,
y = -4x²
1). Since domain of the given function will be all real number x until ocean hits the shore on both the sides of the path.
2). Range of the function will be the value of y from the bottom of the ocean to the surface.
3). Whale will touch the surface of the ocean at one point only.
4). Function 'f' will increase initially upto the surface of the ocean and then it will decrease.
5). Point where the hale touches the surface will be maximum.
Therefore, Options (A) and (E) will be the correct options.
Answer:
The answer is A and E hope this helps
Step-by-step explanation:
. Suppose the coordinate of A is 0 and AR = 5 and AT = 7.
a. What are the possible coordinates of R? Of T
==================================================
Explanation:
If we're on a number line, then R could be at either R = 5 or R = -5. This is so the distance from A to R is 5 units. Distance is never negative. You count out the spaces to get the distance, or use subtraction and absolute value.
Saying "distance from A to R is 5" can be written as AR = 5. Meaning segment AR is 5 units long.
Now if AT = 7, then T could be at 7 or -7 on the number line. The reasoning as similar as to why R could be at -5 or 5.
Which number line represents the solution |2x|-12 =
Answer:
Third option, last one
Step-by-step explanation:
Let's solve for x first.
|2x| - 12 = -2
|2x| = 10
2x = 10 or -2x = 10
x = 5 or x = -5
The number line that represents this is the last one.
Help me pls 15 points
POINTS......!!!!
Please answer!!!
Please state the width (part a)
And length (part b)
Answer:
(a) = 71 cm
(b) = 89 cm
Step-by-step explanation:
(a.)
perimeter of a rectangular field = 324 m
length (l) = 91 m
width (w) = ?
Now,
Perimeter Of Rectangle
= P = 2(l + w)
= 2(91 + w) = 324m
= 182 + 2w = 324m
= 2w = 324 - 182m
= 2w = 142m
= w = 142/2
= w = 71
(b.)
area of rectangular painting = 5696 cm²
width (w) = 64 cm
length (l) = ?
Now,
Area Of Rectangle
A = l × w
= l × 64 = 5696
= l = 5696/64
= l = 89 cm
VERIFICATION:-FOR (a)
= P = 2(l + w)
= P = 2(91 + 71) = 324 cm
FOR (b)
= l × w
A = 89 × 64 = 5696
In a study appearing a Science journal, a research team reports that plants in southern England are flowering earlier in the spring. Records of the first flowering dates for 385 species over a period of 47 years show that flowering has advanced an average of 15 days per decade, an indication of climate warming, according the the authors. What is the population of interest? *
Answer:
Its about plants
Step-by-step explanation:
when factoring 6x^2 -7x-20 by grouping , how should the middle term be rewritten
Answer: -7x should be written as -15x+8x or 8x-15x
===============================================
Explanation:
Multiply the first coefficient 6 and the last term -20 to get -120
We need to find factors of -120 that add to the middle coefficient -7
Through trial and error you should find that
-15 + 8 = -7
-15 * 8 = -120
Therefore, we break the -7x into -15x+8x
----------------------------
Extra info: if you want to fully factor by grouping, then follow these steps
6x^2 - 7x - 20
6x^2 - 15x + 8x - 20 ... break up -7x
(6x^2 - 15x) + (8x - 20) .... group into pairs
3x(2x - 5) + 4(2x - 5) .... factor each group
(3x + 4)(2x - 5) ..... pull out the overall GCF 2x-5
So 6x^2-7x-20 fully factors to (3x+4)(2x-5)
We can check the answer by FOILing out the last expression above to get the original expression back again. The box method works as well. So does the distributive property.
Evaluate : 9⁴xa⁷b⁴/ 3⁵xa⁴b⁴
Answer:
27a³
Step-by-step explanation:
9⁴xa⁷b⁴ / 3⁵xa⁴b⁴
(3²)⁴xa⁷b⁴ / 3⁵xa⁴b⁴
3⁸xa⁷b⁴ / 3⁵xa⁴b⁴
3³a³
27a³
3(3x-2)=39
Solve equation
Over the last three evenings, Lucy received a total of 107 phone calls at the call center. The second evening, she received 3 times as many calls as the third evening. The first evening, she received 7 more calls than the third evening. How many phone calls did she receive each evening?
Answer:
1st evening = 7 + 20 = 27 calls
2nd evening = 3 (20 ) = 60 call
3rd evening = 20 calls
Step-by-step explanation:
total calls for the last three evenings = 107 phone calls
2nd evening = 3x as many calls as the 3rd evening
1st evening = 7 more calls than the 3rd evening.
find:
how many calls did she receive each evening?
let T (total) = 107
let x = 3rd evening.
let 2nd = 3x
let 1st = (7 + x)
T = 1st + 2nd + 3rd
107 = (7 + x) + 3x + x
107 - 7 = 5x
100 = 5x
x = 100 / 5
x = 20
therefore,
1st evening = 7 + 20 = 27 calls
2nd evening = 3 (20 ) = 60 call
3rd evening = 20 calls
Answer:
1st = 27 calls
2nd = 60 call
3rd = 20 calls
Step-by-step explanation:
total calls = 107 phone calls
2nd = 3x
1st = 7 + 3x
T (total) = 107
T = 1st + 2nd + 3rd
107 = (7 + x) + 3x + x
107 - 7 = 5x
100 = 5x
x = 100 / 5
x = 20
so,
1st = 7 + 20 = 27 calls
2nd = 3 (20 ) = 60 call
3rd = 20 calls
How many solutions are there for the system of equations shown on the graph?
Answer:
Hey there!
These lines only intersect at one point, so there is only one solution.
Let me know if this helps :)
Answer:
one solution
Step-by-step explanation:
The solutions are where the graphs intersect
There lines cross at one point (0,3), so there is one solution
Which of the following sets of points are coplanar? I'm not sure what the answer is.
Answer:
The fourth one
Step-by-step explanation:
coplanar means the points on the plane and only B,E,D,C is on the plane
Hence, B,E,D,C is your answer
Jan is painting a square canvas. The length of one side of the canvas is 4 feet. Write an equation to show how to show how to find the area of the canvas
Step-by-step explanation:
It is given that, Jan is painting a square canvas. The length of one side of the canvas is 4 feet.
We need to write an equation to show how to find the area of the canvas.
For a square, all its sides are equal. Let the side is x. The area of a square is given by :
[tex]\text{Area}=\text{side}^2\\\\A=x^2\\\\A=4^2\\\\A=16[/tex]
So, the equation that shows the area of the canvas is [tex]A=x^2[/tex].
A population of bacteria is growing rapidly. The population at any hour, h, can be represented
by the function f(h) = 2 • 4h. What is the population of bacteria after 4 1/2 hours?
Answer:
36
Step-by-step explanation:
Function is:
f(h) = 2*4hAfter 4 1/2 hours, h = 4 1/2 = 4.5
f(4.5) = 2*4*4.5 = 36Answer:
36
Step-by-step explanation:
4×4.5=18
18×2=36
PLEASE HELP !
How many ounces are there is 2.59 gallons of lemonade? (There are quarts in a gallon. ) ounces in a quart and 4 quarts in a gallon .)
Answer:
331.52 oz
Step-by-step explanation:
Google :D
Answer:
a
Step-by-step explanation:
3b^2+6b-28
which of the following describes 3 in the expression above
A. quotient
B. coefficient
C. sum
D. product
Answer:
3 is a coefficient. (Option B)
Step-by-step explanation:
A coefficient in a term is the number placed before the variable. The coefficient multiplies the variable.
In the given expression, 3 would be the coefficient in [tex]3b^2[/tex].
A, C, and D are answers to an expression depending on the expression's operation.
In this case, option B would be the correct answer.
Hope this helps.
Answer:
[tex]\huge \boxed{\mathrm{B. \ coefficient}}[/tex]
Step-by-step explanation:
[tex]3b^2[/tex]
[tex]b^2[/tex] is being multiplied by 3.
A coefficient is a number used to multiply a variable.
when bisecting an angle, one of the steps is to draw an arc centered on a point on a ray of the angle. in particular this angle is to be drawn on the interior of the angle, why must The Arc be drawn in the interior of the angle?
Step-by-step explanation:
The arc drawn must be in the interior side of the angle to be bisected because while constructing the angular bisector, we make an arc cutting both the rays of the angle, so in order to cut the angle in to two equal part, we should make arcs in the interior part of the angle subtended so that it bisects the angle in two equal parts.
5x - 10 less than it equal to 20
given that (y+2) (y+3) and (2y^2+1) are consecutive terms of an arithmetic progression, find the possible value of y
Answer:
-3/2 and 1
Step-by-step explanation:
Given the arithmetic sequence (y+2) (y+3) and (2y²+1), the common difference is gotten by taking the difference in their terms. For example if we have 3 terms T1, T2, T3... the common difference d = T2-T1 = T3-T2
From the sequence given;
T1 = y+2, T2 = y+3 and T3 = 2y²+1
d = y+3-(y+2) = 2y²+1- (y+3)
open the parenthesis
y+3-y-2 = 2y²+1- y-3
1 = 2y²+1- y-3
1 = 2y²- y-2
2y²- y-2-1 = 0
2y²- y-3 =0
Factorize the resulting expression
2y²- y-3 =0
2y²- 2y+3y-3 =0
2y(y-1)+3(y-1) = 0
(2y+3)(y-1) = 0
2y+3 = 0 and y-1 = 0
2y = -3 and y =1
y = -3/2 and 1
Hence the possible values of y are -3/2 and 1
ANSWER PLEASE! Hopefully someone can figure out.
Answer:
B
Step-by-step explanation:
The domain is the input values, that is the x- values
The range is the output, that is the y- values.
Thus using values from table
domain : {- 2, 0, 2 }, range : { - 1, 0, 1 }
Which of the following spreadsheets shows the financial plan with the greatest net cash flow?
a.
A
B
1 Cash Inflows
2 Disposable income
$2,350
3 Interest on deposits
SO
4 Income from investments
$0
5 Total Cash Inflow
$2,350
6
7 Cash outflows
8 Rent
$800
9 Utilities
$235
10 Cable and telephone
$125
11 Groceries
$400
12 Car expenses
$320
13 Recreation
$175
14 Insurance
$200
15 Miscellaneous
$80
16 Total Cash Outflow
$2,335
Answer:
Net Cash-flow = Cash Inflows - Cash Outflows
The net amount of cash that a company has is the difference between the cash coming in(revenue) and the cash going out (expenses).
Spreadsheet 1
= Cash Inflows - Cashflows
= 2,350 - 2,335
= $15
Spreadsheet 2
= Cash Inflows - Cashflows
= 2,270 - 2,260
= $10
Spreadsheet 3
= Cash Inflows - Cashflows
= 2,380 - 2,380
= $0
Spreadsheet 4
= Cash Inflows - Cashflows
= 2,150 - 2,055
= $95
Spreadsheet 4 has the greatest net cash flow at $95.
Answer:The answer is A
A .......... divides a two dimensional shape in two congruent shapes
Answer:
A diagonal. (A rectangle is divided into two triangles by a diagonal, for example.)
Hope this helps!
Find the domain of the relation represented by the list of ordered pairs below (-2,9), (6,-7), (-9,-5), (-12,10)
Domain of the relation → {-12, -9, -2, 6}
Given in the question,
List of ordered pairs,
(-2, 9), (6, -7), (-9, -5), (-12, 10)In a ordered pair (h, k), domain is defined by the x-values and range is defined by the y-values.
Therefore, domain of the relation represented by the ordered pairs will be {-12, -9, -2, 6}
Learn more,
https://brainly.com/question/24212724
Use the frequency distribution shown below to construct an expanded frequency distribution.
High Temperatures (°F)
Class
16-26
27-37
38-48
49-59
60-70
71-81
82-92
Frequency, f
17
45
66
67
82
66
22
Answer and Step-by-step explanation:
The calculation of midpoints, relative frequencies and cumulative frequencies are shown below:-
For Midpoint = [tex]\frac{Lower\ limit\ +\ Upper\ limit}{2}[/tex]
For Relative frequency = [tex]\frac{Frequency}{Total\ number\ of\ frequency}[/tex]
Class Frequency Midpoints Relative Cumulative
frequency frequency
16-26 17 21 0.047 0.047
27-37 45 32 0.123 0.17
38-48 66 43 0.181 0.351
49-59 67 54 0.184 0.535
60-70 82 65 0.225 0.76
71-81 66 76 0.181 0.941
82-92 22 87 0.060 1.001
Total 365
Therefore for computing the cumulative frequency we simply added relative frequency with previous cumulative frequency for class 27-37 and in the same manner of every class.
The rate at which something occurs over a particular period of time or in a given sample:
"An increase in the frequency of accidents due to increased overtime"
GivenUse the frequency distribution shown below to construct an expanded frequency distribution.
The formula to calculate the midpoint and relative frequency are given below.
[tex]\rm Midpoint = \dfrac{Lower \ limit + Upper \ limit }{2}[/tex]
[tex]\rm Relative \ frequency = \dfrac{Frequency}{total \ frequency}[/tex]
The frequency distribution to construct an expanded frequency distribution is given below.
Class Frequency Midpoints Relative frequency Cumulative frequency
16-26 17 21 0.047 0.047
27-37 45 32 0.123 0.17
38-48 66 43 0.181 0.351
49-59 67 54 0.184 0.535
60-70 82 65 0.225 0.76
71-81 66 76 0.181 0.941
82-92 22 87 0.060 1.001
Total 365
To know more about Frequency click the link given below.
https://brainly.com/question/17740069
in the following graph, AABC is congruent to AA'B'C'. A teacher asks a student Janine to state the
translation rule for this transformation janine focuses on point and states that the translation rule is
(x,y) (x-2, y-6). In other words, to shift from the blue to the red triangle, you must shift each point two
units left and six units down
State whether Janine's answer was correct or incorrect. In at least three sentences, support your
response with a brief explanation. Be sure to use the term transformation in your explanation
Answer:
Janine's answer is incorrect.
Step-by-step explanation:
Rigid transformations are methods by which the image of a given figure or object can be produced either by rotation, translation, dilation or reflection.
Since Janine used translation method for the transformation, the dimension of the shape is preserved but not its initial position. To translate AABC to AA'B'C', each point should shift three units left and five units down.
Therefore, the appropriate translation rule is:
(x, y) ⇒ (x + 3, y + 5)
Find x, if 3x − 5(y + x ) ^2 = 16 and 4x + 2(y + x )^ 2 = 30
Answer:
x = 7
Step-by-step explanation:
Start by solving for [tex](y+x)^2[/tex] which is a common expression for both equations. Then in the first equation:
[tex]3\,x5\,(y+x)^2=16\\3x-16=5\,(y+x)^2\\(y+x)^2=\frac{3\,x-16}{5}[/tex]
and in the second equation:
[tex]4\,x+2\,(y+x)^2=30\\2\,(y+x)^2=30-4\,x\\(y+x)^2=15-2\,x[/tex]
Now we make the two [tex](y+x)^2[/tex] expressions equal so we get:
[tex]\frac{3\,x-16}{5} =15-2\,x\\3\,x-16=75-10\,x\\13\,x=75+16\\13\,x=91\\x=7[/tex]