Step-by-step explanation:
As we know, for any function domain is referred to as the set of input values that can be taken for an independent variable in the given function. Range of a function is defined as the set of output values generated for the domain (input values) of the function. In the case of a step function, for each value of x, f(x) takes the value of the greatest integer, less than or equal to x. For example:
[-2.19] = -3
[3.67] = 3
[-0.83] = -1
The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.
This can be generalized as given below:
[x] = -2, -2 ≤ x < -1
[x] = -1, -1 ≤ x < 0
[x] = 0, 0 ≤ x < 1
[x] = 1, 1 ≤ x < 2
How can you rewrite the number 1 as 10 to a power?
How can you rewrite the number 1 as 2 to a power?
Answer:
To rewrite 1 as 10 to power, you'd write 10^0 (ten to the power of zero).
Any non-zero number with the power of zero equals one. You might be wondering why, so to prove this theorem...
2^1
-----
2^1
Since the numbers are the same on the numerator and denominator, we can agree that the fraction above is equal to 1, yes? It is also equal to...
2^1-1
...because of the quotient rule. And what does 1-1 equal? 0. So you'd get
2^0
This is known as the "zero-exponent rule!"
Hope this helped.
Step-by-step explanation:
20 POINTS+BRAINLIEST 8TH GRADE MATH: estimating integers between square roots
repost because the file wouldn't upload
Answer:
Q1: C
Q2: F
Q3: C
Step-by-step explanation:
Question 7:
100(3+0.2)^2 -24
According to
P arenthesis
E xponents
M ultiplication
D ivision
A ddition
S ubtraction
We must do the parenthesis first.
100 ( 3 . 2 ) ^ 2 - 24 =
Then exponent
100 * 10 . 24 - 24 =
then multiplication
1024 - 24 =
and finally subtraction
1000 (Option C)
________________________________________________________
Question 8:
Sqrt 50 = 7.07
Sqrt 60 = 7.75
7.07 + 7.75
14.81, which is between 14 and 15, answer choice F
________________________________________________________
Question 9:
A = 13
B = 13
C = 25+36 = 7.81
D = 13
Answer is C, which is the only one which is between positive integers 7 and 8.
Answer:
7) C. 1000
8) F. 14 and 15
9) C. [tex]\sf \sqrt{5^2 + 6^2}[/tex]
Explanation:
7.
⇒ 100(3 + 0.2)² - 24
⇒ 100(3.2)² - 24
⇒ 100(10.24) - 24
⇒ 1024- 24
⇒ 1000
8.
⇒ √50 + √60
⇒ [tex]\sf \sqrt{2 \ \times \ 5^2} + \sqrt{2^2\:\times\: 15}[/tex]
⇒ [tex]\sf 5\sqrt{2 } + 2\sqrt{ 15}[/tex]
⇒ 7.071 + 7.745966
⇒ 14.817
So, it lies between 14 and 15.
9.
A, B, D when simplified gives 11 as an answer.
When simplify C,
[tex]\sf \sqrt{5^2 + 6^2}[/tex]
[tex]\sf \sqrt{25 + 36}[/tex]
[tex]\sf \sqrt{61}[/tex]
[tex]\sf 7.8102396[/tex]
This value lies between 7 and 8.
So far this year, Adam has played 30 games of chess and has only won 6 of them. What is the minimum number of additional games he must play, given that he is sure to lose at least one-third of them, so that for the year he will have won more games than he lost?
A) 24
B) 57
C) 87
D) It is not possible for Adam to do this.
The correct answer is B) 57, but not sure how?
Answer:
Step-by-step explanation:Yikes. Just so we’re all clear—this is not a real SAT question.
So far, Adam’s record is 6 wins/30 games. If he plays x more games, his record will be:
image
You find the minimum x such that the fraction is greater than ½, which would mean he won more than ½ of his games.
Let’s do some math!
image
So if he plays 54 more games, and wins 2/3 of them, he’ll have the same number of wins as losses. Check on that to make sure: He’ll have played 30 + 54 = 84 games, and won 6 + (2/3)54 = 42 of them. Yep, that works.
Now here is where it gets tricky (and why this question is not SAT-caliber). Remember that he’s losing 1/3 of his games. If his 52nd, 53rd, and 54th additional games were win, win, loss, then he would have had, very briefly, a winning record after his 53rd additional game.
His 55th additional game is another chance at a winning record. If he loses that game, then he’ll win the next two, and have a winning record for sure by the 57th additional game. From there, if he continues winning 2/3 of his games, he’ll have a winning record forever.
Simplify -15- |-7.5|
Answer:
-22.5
Step-by-step explanation:
-15- |-7.5|
after taking the absolute value off, -7.5 would become positive 7.5. But then the negative outside the absolute value makes it negative again.
-15-7.5
=-22.5
The simplified expression -15 - |-7.5| is equal to -22.5.
To simplify the expression -15 - |-7.5|, we'll follow these steps:
Evaluate the absolute value: |-7.5|.
The absolute value of a number is its distance from zero on the number line. In this case, |-7.5| is equal to 7.5 because 7.5 units away from zero.
Substitute the absolute value into the expression:
-15 - 7.5.
Perform the subtraction:
-15 - 7.5 = -22.5.
Therefore, the simplified expression -15 - |-7.5| is equal to -22.5.
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a two digit number has three times as many tens than ones. The difference between the number and twice the reversed number is 15.Find the number
olution
verified
Verified by Toppr
Let the one's digit be y and tens digit be x,
Number = 10x + y
Then,x=3y⋯(i)
Reversed number = 10y + x
A.t.Q :- (10x+y)−(10y+x)=36 Put x = 3y in eq. (i)
⇒9x−9y=36
⇒x−y=4⋯(ii)
⇒3y−y=4
∴2y=4 x=3y ∴x=6
y=2
∴ Number = 62
MORE HELP PLEASE :D :D :D
Answer:
11. When 3 students are working, they each need to plant 36 trees. So the club must plant 36*3 = 108 trees total. The equation would be t = 108/s, and the constant of proportionality is 108.
12. The constant of proportionality represents the number of trees the club needs to plant regardless of the number of participants.
PLEASE HELP!!!!!!!! ASAP
A circle has a radius of 5 inches. A semicircle has a radius of 10 inches. How do the areas compare?
1. The circle has twice the area of the semicircle.
2. The semicircle has four times the area of the circle.
3. The semicircle has twice the area of the circle.
4. The areas are equal.
Question #2
A circle has a diameter of 6 cm. What is its area?
1. 37.68 cm 2
2. 9.42 cm 2
3. 28.26 cm 2
4. 18.84 cm 2
Answer: #1) 3. The semicircle has twice the area of the circle
#2) 3. 28.26 cm
Step-by-step explanation:
#1) The formula for area of circle is A=πr².
First, plugging in the radius for the circle, A=π(5)², we get an area of about 78.54 inches².
Plugging in the radius for the semicircle, A=π(10)², which is equal to 314.159.... However, since it is a SEMI-circle, we will divide this value by 2 to give us an area of about 157.08 inches².
Comparing the two areas, we see the semicircle has twice the area of the circle as 78.54 x 2 = 157.08.
#2) Again use the area of circle formula, A=πr². The radius is half the diameter, so half of 6cm=3cm, meaning r=3. plug it in.
A= π(3)²
A= 28.27 cm²
11. VANISHING POINT:
The vanishing point of the picture is represented by point B.
a. The measure of ∠ ABD is 6.2 times greater than the measure of ∠ CBD. Find the measure of ∠ CBD.
b. ∠ FBE and ∠ EBD are congruent. Find the measure of ∠ FBE
Answer:
awnser B and fbe is 55
Step-by-step explanation:
the entire picture is 180 so cut in half there for 90 ok abfe is 90 so bigger section is always 55 and smaller is 35 ok
If the measure of ∠ABD is 6.2 times greater than the measure of ∠CBD=25° and if ∠ FBE and ∠ EBD are congruent then ∠ FBE =65°.
Given that the measure of ∠ ABD is 6.2 times greater than the measure of ∠ CBD and ∠ FBE and ∠ EBD are congruent.
We are required to find the measure of ∠ CBD and ∠ FBE.
∠ABD=6.2*∠CBD--------1
∠ABD+∠CBD=180°
6.2 ∠CBD+∠CBD=180 (From equation 1)
7.2 ∠CBD=180
∠CBD=180/7.2
∠CBD=25°
∠ABD=6.2*25
=155°
∠ABD=90+∠EBD
155=90+∠EBD
∠EBD=155-90
∠EBD=65°
Because ∠ FBE and ∠ EBD are congruent, ∠ FBE =65°.
Hence if the measure of ∠ABD is 6.2 times greater than the measure of ∠CBD=25° and if ∠ FBE and ∠ EBD are congruent then ∠ FBE =65°.
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Manu borrowed Rupees 8500 at the rate of 5% interest per annum for 150 days. Find the interest and amount he paid
Answer:
See below
Step-by-step explanation:
5% interest = .05 :
8500 x .05 x 150days /365 days/year = R 174 .66 = interest......
then amount to be paid = 8500+ 174.66 = R 8674.66
HEEEELLLLLLLPPPPPPPP
The hexagon PQRSTU is plotted on a coordinate plane with vertices P(–1, 0), Q(–1, 3), R(1, 4), S(2, 5), T(4, 4), and U(4, 0). What is the hexagon's perimeter?
15.8 units
14.4 units
17.8 units
12.0 units
help quick ples
What is the range of possible sizes for side x?
Answer: 0.5 < x < 16.5.
Step-by-step explanation: Two sides of triangle: 8.0 units and 8.5 units
Measure of third side = x
According to the triangle's inequality,
Sum of any two sides > third side. (i)
Difference between the sides < third side. (ii)
If x is the third side, then
x < 8+8.5 [Using (i)]
i.e. x< 16.5
Also, x > 8.5-8 [Using (ii)]
i.e. x> 0.5
Hence, Range of possible sizes for side x would be 0.5 < x < 16.5.
The range of possible sizes for side x is,
⇒ 0.5 < x < 16.5
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Two sides of the triangle are 8.5 and 8.
Now, The range of possible sizes for side x is,
⇒ x < 8.5 + 8
⇒ x < 16.5
⇒ x > 8.5 - 8
⇒ x > 0.5
Thus, The range of possible sizes for side x is,
⇒ 0.5 < x < 16.5
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factor the following expression. 3x^3-12x^2-2x-8
Polynomials are mathematical expressions made up of many terms.
To simplify a polynomial as much as possible, you must group all the like terms and rearrange them from higher to lower power.
3x³ - 12x² - 2x-8The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of any constant term is 0. The derivative of axⁿ it's naxⁿ⁻¹.
3 × 3x³⁻¹ + 2(-12)x²⁻¹ - 2x¹⁻¹Multiply 3 x 3.
9x³⁻¹ + 2(-12)x²⁻¹ - 2x¹⁻¹Subtract 1 from 3.
9x² + 2(-12)x²⁻¹ - 2x¹⁻¹Multiply 2 by −12.
9x² - 24x²⁻¹ - 2x¹⁻¹Subtract 1 from 2 and subtract 1 from 1.
9x² - 24x¹ - 2x⁰For any term t, t¹ = t.
9x² - 24x - 2x⁰For any term t except 0, t⁰=1.
9x² - 24x - 2Answer: The solution of the polynomial 3x³ - 12x² - 2x-8 is 9x² - 24x - 2.
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Please Helpppp meeeeee! I really need it!!!
Which of the following can be directly measured using a ruler?
A. Distance between the earth and the moon
B. Distance between two cities
C. Width of a window frame
D. Height of a mountain
Answer:
C
Step-by-step explanation:
windows arent that big compared to 2 cities, distance between the and moon, or a height of a mountain. so i think C is the only reasonable answer
HELP ASAP!!! 99 ASSIGNMENTS TO GO!!!! 25 POINTS!!!!
Answer:
1. Ratio
2. Unit Rate
3. Scale Drawing
4. Similar Figures
5. US Customary System
6. Rate
7. Scale
Step-by-step explanation:
Most of them are just definitions
20 POINTS+BRAINLIEST 8TH GRADE MATH PART 4: Imaginary operations- please explain how you came to the answer because this doesn't make sense
20 POINTS+BRAINLIEST 8TH GRADE MATH PART 2: number sequence
please explain the steps in simple language and as always any answers for the sake of points will be reported :))
Answer:
64
Explanation:
Sequence: -27, -8, -1, 0, 1, 8, 27,...
Identify the type of sequence. Looking at the sequence, it appears it is a cubic sequence with a formula: x³
Shown truth:
(-3)³ = -27(-2)³ = -8(-1)³ = -1(0)³ = 0(1)³ = 1(2)³ = 8(3)³ = 27Next number in this sequence:
(4)³ = 64Select each expression that is equivalent to 3(n + 6). Select all that apply. (ANSWER ASAP)
A.
3n + 6
B.
2(n + 6) + (n + 6)
C.
2(n + 6) + n
D.
3n + 18
E.
2n + 2 + n + 4
Answer:
Step-by-step explanation:
This expression involves the distributive property. In the distributive property, there is a number followed by an equation in parenthesis.
3(n+6)
To simplify it, you have to multiply the first number by each number in the parenthesis, separately:
3(n+6)
3n + 3(6) or 3xn + 3x6 (same thing)
3n+18
Finally, we can check the other 4 choices to double check.
A. 3n+6 (wrong)
B. 2(n+6) + (n+6)=
2xn + 2x6 + n + 6
2n + 12 + n + 6
combine like terms, or all the terms that are the same. start with the Ns, then the numbers:
2n+n + 12+6
3n+18
C. 2(n+6)+n= 2n+2(6) +n = 2n+12+n= 2n+n+12= 3n+12
D.3n+18
E. 2n+2+n+4= 2n+n+2+4= 3n+6
Answer= B and D
hope this helps :))
Answer: 3n+18 bcz of the distributive property
Step-by-step explanation:
b & d
There are 12 different cookies on a plate. Aiden will choose 3 of these cookies to pack in his lunch. How many different groups of cookies can he choose from 12?
A) 220
B) 320
C) 420
D) 440
I know the correct answer is A) 220, but I am not sure why?
Answer: 4
Step-by-step explanation: 3%12=4
PLEASE PLEASE PLEASE HELP ME ASAP!!!
The table completing the proof is:
Statements Reasons
Draw segments UT Construction.
[tex]\overline {UT}[/tex] ≅ [tex]\overline {UT}[/tex] This is reflexive property.
[tex]\overline{BT}[/tex] ≅ [tex]\overline {EU}[/tex] Given
[tex]\overline {BU}[/tex] ≅ [tex]\overline {ET}[/tex] Given
ΔUBT ≅ ΔUET SAS congruency
∠B ≅ ∠E Proof
We have,
From the figure,
Step 1:
Draw segments UT.
Construction.
Step 2:
UT ≅ UT
This is reflexive property.
Step 3:
BT ≅ EU
Given
Step 4:
BU ≅ ET
Given
Step 5:
ΔUBT ≅ ΔUET
This is due to SAS.
Side-Angle-Side (SAS) Congruence.
The two sides and the included angle of one triangle are equal to the corresponding two sides and included angle of another triangle.
Step 6:
∠B ≅ ∠E
Thus,
Statements Reasons
Draw segments UT Construction.
[tex]\overline {UT}[/tex] ≅ [tex]\overline {UT}[/tex] This is reflexive property.
[tex]\overline{BT}[/tex] ≅ [tex]\overline {EU}[/tex] Given
[tex]\overline {BU}[/tex] ≅ [tex]\overline {ET}[/tex] Given
ΔUBT ≅ ΔUET SAS congruency
∠B ≅ ∠E Proof
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Which of the following is a line segment as shown in the drawing?
Answers:
- DH is correct because a line is connecting the two points D and H as shown in the image, forming a line segment.
- ED is correct because a line is connecting the two points D and E, forming another line segment, as shown in the drawing.
- EH is incorrect because in the drawing shown, there is no line connecting the two points E and H, so there would be no line segment formed between these two points.
- CD is correct because there is another line connecting the two points C and D, forming another line segment in the drawing.
Therefore, lines DH, ED, and CD are all line segments.
Ten points QRSTUVWXY and Z are equally and consecutively spaced on a circle.
What is the size, in degrees, of the angle ∠QTW?
The size of ∠QTW in degrees is 72°. See the explanation below. This is based on the concept of opposite sides in a quadrilateral.
What is the logic leading to the above result?QSUWY which is a pentagon is regular that mean:
∠QYW = 108°
The quadrilateral QTWY is a cyclic one. This means that we can apply the rule that states that opposites sides must add up to 180°
Thus, ∠QTW =
180 - 108
= 72°
What is a quadrilateral?A closed quadrilateral has four sides, four vertices, and four angles. It is a form of polygon.
In order to create it, four non-collinear points are joined. Quadrilaterals always have a total internal angle of 360 degrees.
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Full Question:
See the attached image for missing details.
Q1 Write the number in expanded form for the significant digits ( as fractions)
117.000
20.018
13.265
3.4000
0.8100
Q2 - Write the difference in place value of the underlined digits
ex . 12.352 - 2 in the ones place is 1000x bigger than the 2 in the thousandths place
1568.156 ( both of the 5s are underlined)
03.3000 ( both of the 3s are underlined)
5164.66 ( both of the 6s are underlined
9.09 ( the 9s r underlined)
To write in expanded form is to simply mean writing each number into its place value.
in a three digit number, the sum of the digits in the units and the hundreds positions is equal to the number of tens. One more than three times the units igt is the hundreds digit. If there are 9 tens in the original number, find its reverse
Separate the rational from irrational
Answer:
101 squared not rational
-25 squared is rational
pi or any number times pi is not rational
Step-by-step explanation:
Michael is baking cookies. His cookie recipe calls for 3/4 cups sugar and makes 24 cookies. If he wants to scale the recipe to make exactly 18 cookies, how many cups of sugar will he need? Express your answer as a mixed number.
[tex]\begin{array}{ccll} \stackrel{cups}{sugar}&cookies\\ \cline{1-2} \frac{3}{4}&24\\[1em] x&18 \end{array}\implies \cfrac{ ~~ \frac{3}{4} ~~ }{x}~~ = ~~\cfrac{24}{18}\implies \cfrac{ ~~ \frac{3}{4} ~~ }{\frac{x}{1}}~~ = ~~\cfrac{4}{3}\implies \cfrac{3}{4}\cdot \cfrac{1}{x}=\cfrac{4}{3} \\\\\\ \cfrac{3}{4x}=\cfrac{4}{3}\implies 9=16x\implies \cfrac{9}{16}=x[/tex]
now, the fraction is not an improper one, thus we can't quite put it in a mixed format, unless you count 0 as its whole, then I guess we can say is [tex]0\frac{9}{16}=x[/tex]
Answer:
9/16
Step-by-step explanation:
24/6=4
18/6=3
(3/4)x(3/4)=9/16
A spinner has numbers 1-10, all evenly spaced, is spun twice. What is the probability that the second spin lands on a space adjacent to the space where the first spin landed?
Answer:
.20 or 20%
Step-by-step explanation:
100 possible sets of two spin combos
20 result in the desired 'next-door ' combo
20/100 = .20 or 20 %
HELP PLEASE!!!!!!!!!!!!!!!!!!!!!!!!!!!
Instructions
For this option, you will work individually.
Part 1: Collect Data
In order to complete your assignment, you will need to collect some data.
The first five data points have been provided for you.
Age
(years) Number of U.S. States Named in 60 Seconds
5 7
15 42
25 49
35 35
65 50
Take a survey of at least five more people. You need a watch, stopwatch, or timer.
First, record the age of the person you are surveying.
Next, ask the person to name as many U.S. states as possible in 60 seconds. Keep a count, and watch your timer. Record each person’s data next to his or her age.
Repeat this with at least five people, and be sure to survey a range of ages, from young to old.
Part 2: Organize Your Data
Create a table of values using the age and number of U.S. states named in 60 seconds.
A graph is provided with the first five points plotted. Use your table to add your five data points to the scatter plot.
You may create a new graph from scratch, containing all 10 points, print the sample graph and add your data, or save the sample as an image and use a drawing program to add your data to the image. If you choose to print and draw by hand, you need to be able to scan and upload your work at the end of the project.
A coordinate plane is shown. The x axis is labeled age in years and the y axis is labeled number of U.S. States named in 60 seconds. Five data points are already plotted on the graph. These points are located at 5 comma 7, 15 comma 42, 25 comma 49, 35 comma 35, and 65 comma 50.
Draw a line of best fit through your scatter plot. Draw by hand on your printed graph or use a drawing program on your computer to create the line.
Part 3: Drawing Conclusions
How did you decide where to place your line of best fit? Describe your reasoning.
Based on your data, describe the relationship between age and the number of U.S. states a person can name in 60 seconds.
Do you see any areas in your data or points that could be considered clusters or outliers? Explain your answer in complete sentences.
find data points or make up 5 new subjects first
linda 34 y/o, 50 states
bob 65, 47 states
sarah 12, 14 states
terry 23, 28 states
cindy 46, 41 states
plot these points along with the others then draw a line from (0,0) to the top of the x y plane passing through as many point as possible
create a table of values for this information afterward
6. The perimeter of the figure below is equal to 150 cm. What is the length of the longest
side of the polygon? Use mathematics to explain how you determined your answer.
Use words, symbols, or both in your explanation. **SHOW WORK!!!**
x
x+6
x+4
x+5
x+8
x+1
LONGEST SIDE:__________
Answer: 29 centimeters long
Step-by-step explanation: What you want to do in this kind of situation is to combine all like terms. After, you would get 6x + 24 = 150. What you would do here is to get 6x by itself by subtracting 24 on both sides. Now 6x = 126, to isolate the variable you divide 6 on both sides to get x = 21. However, the questions is asking for the longest side and you know that x + 8 will be the greatest out of all. So, x = 21 + 8 equals 29 centimeters. I hope this helps, please give me a brainlest! :)
I'm not good at this kind of meth :C
Is Figure B a scale copy of Figure A?