Answer:
For a single digit in base 8, we need up to three digits in base 2. For two digits in base 8, we need 4, 5, or 6 digits in base 2. For three digits in base 8, we need 7, 8, or 9 digits in base 2.
Step-by-step explanation:
Answer:
Base = 2
Step-by-step explanation:
2⁸
Here 2 is the base and 8 is the exponent
If a is a non-zero constant, determine the vertex of y = -3(x + a)^2 - 6
Answer:
Vertex is (-a, -6), where a ≠ 0.
General Formulas and Concepts:
Algebra I
Coordinates (x, y)QuadraticsAlgebra II
Vertex Form: y = a(bx - h)² + k
a is the vertical scale factorb is the horizontal scale factor(h, k) is the vertexStep-by-step explanation:
Step 1: Define
y = -3(x + a)² - 6
↓ Identify variables
a = -3
b = 1
(h, k) = (-a, -6)
Evaluate the following expression. You should do this problem without a
calculator.
In e^e
A. 0
B. e^e
C. 1
D. e
Answer:ln is called the natural log, or log to the base e. ln can also be written as
So, we can write the given expression as
The property of logs is:
This mean if the number a is raised to log whose base is the same as the number a itself, then the answer will be equal to the argument of the log which is x.
In the given case, the number e and the base of log are the same. So the answer of the expression will be the argument of log which is 6.
so, we can write
Thus, the correct answer is option D
Step-by-step explanation:
If a firm uses x units of input in process A, it produces 32x3/2 units of output. In the alternative process B, the same input produces 4x3 units of output. For what levels of input does process A produce more than process B?
Answer:
The outcomes produced by A would be greater than B. A further explanation is provided below.
Step-by-step explanation:
Given:
In process A,
Produced units = [tex]32x^{1.5}[/tex]
In process B,
Produced units = [tex]4x^3[/tex]
If the outcomes are equivalent then,
⇒ [tex]32x^{1.5}=4x^3[/tex]
⇒ [tex]x^{1.5} = 8[/tex]
By taking log both sides, we get
⇒ [tex]log \ 8= 1.5 \ log \ x[/tex]
⇒ [tex]x=3.99[/tex]
Please help if can and show work
Answer:
Step-by-step explanation:
4x³ - 4x + 3 is divided by (2x-1)
Complete question:
4x³ - 4x + 3 is divided by (2x - 1). Find the quotient and the remainder
Answer:
The quotient = 2x² + x - ³/₂ and the remainder = ³/₂
Step-by-step explanation:
Given function;
4x³ - 4x + 3 divided by (2x-1)
Use long division method to obtain the remainder and the quotient.
2x² + x - ³/₂
-----------------------
2x - 1 √4x³ - 4x + 3
- (4x³ - 2x²)
----------------------------
2x² - 4x + 3
- ( 2x² - x)
-----------------------------
-3x + 3
-(-3x + ³/₂)
----------------------------
³/₂
Therefore, the quotient = 2x² + x - ³/₂ and the remainder = ³/₂
Are holidays a proper subset of the calendar year?
Select the correct answer below:
No, holidays are only a subset of the calendar year.
Yes, holidays are a proper subset but not a subset of the calendar year.
Yes, holidays are a subset and proper subset of the calendar year.
No, holidays are not a subset or proper subset of the calendar year.
Answer: Choice C
Yes, holidays are a subset and proper subset of the calendar year.
=========================================================
Explanation:
The set of days in the calendar year spans from Jan 1st to Dec 31st.
The set of holidays is a small subset of the previous set mentioned. Any holiday is found on the calendar, but not every day on the calendar is a holiday.
------------
Here's another example of a subset
A = set of all animals
B = set of dogs
Set B is a subset of set A because any dog is an animal. In other words, any individual in set B is also in set A, but not the other way around.
------------
Going back to the calendar example, the set of holidays is a subset and it's also a proper subset of all the days in the year. We say that set B is a proper subset of set A if B has less items in it compared to A.
If we had these two sets
A = {1,2,3,4,5,6}
B = {1,2,3}
We can see that B is a proper subset of set A since everything in B is found in A, and B is smaller than A. The only time we have a subset and not a proper subset is when we talk about the set itself. Any set is a subset of itself (not a proper subset of itself).
The True statement is
Yes, holidays are a subset and proper subset of the calendar year.
What is Set?Sets are represented as a collection of well-defined objects or elements that are consistent from one person to the next. A capital letter represents a set. The cardinal number of a set is the number of items in a finite set.
The order of a set determines the number of elements in the set. It refers to the size of a set. The order of the set is often referred to as the cardinality.
The set of days in the calendar year spans from Jan 1st to Dec 31st.
The set of holidays is a subset of the previously described set. Any holiday can be found on the calendar, however not every day is a holiday.
let Set B is a Proper subset of set A if it contains fewer elements than A.
So, A = {1,2,3,4,5,6}
B = {1,2,3}
We can see that B is a proper subset of set A since everything in B is found in A, and B is smaller than A.
So, holidays are a subset and proper subset of the calendar year.
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Sara can weed a garden in 30 minutes. When her brother Hamdan helps her, they can weed the same garden in 20 minutes. How long would it take Hamdan to weed the garden if he
worked by himself?
a. Write an expression for Hamdan's rate, using n for the number of hours he would take to
weed the garden by himself.
b. Write an equation to show the amount of work completed when they work together.
c. How long would it take Hamdan to weed the garden by himself?
Answer:
Let's define:
S as the rate at which Sara can weed a garden.
We know that:
S*30min = 1 garden
And let's define H as the rate at which Hamdan can weed a garden, we know that when they work together, they can complete the job in 20 minutes, then
(S + H)*20min = 1 garden
a) Here we get:
H*n = 1 garden
where n is the number of hours that he would take (note that in two previous equations we have minutes, so we need to use a change of units)
b) The equation is
(S + H)*20min = 1 garden
c) ok, we know two things:
(S + H)*20min = 1 garden
S*30min = 1 garden
first, let's convert both times to hours:
60 min = 1 hour
then:
30 min = (30/60) hours = 0.5 hours
20 min = (20/60) hours = 0.33 hours
Then the equations become:
(S + H)*0.33 hours = 1 garden
S*0.5 hours = 1 garden
Le's solve the second equation for S:
S = (1 garden /0,5 hours) = 2 gardens/hour.
Now we can replace this in the other equation to get:
(2 garden/hour + H)*0.33 hours = 1 garden
2 garden/hour + H = (1 garden)/(0.33 hours) = 3 gardens/ hour
H = 3 gardens/hour - 2 gardens/hour = 1 gardens/hour
This means that the rate of Hamdan is 1 gardens/hour, so he can weed a garden in one hour.
Then:
(1 garden/hour)*n = 1 garden
n = ( 1 garden)/((1 garden/hour)) = 1 hour
D R с C The diagram shows two squares ABCD and PQRS. Given that AB-12 cm, calculate (1) the perimeter of PORS. the area of AORS.
the diagram isn't available.Please fix that
The city of Plainview is building a new sports complex. The complex includes eight baseball fields, four soccer fields, and three buildings that have concessions and restrooms. Arrange the structures in the sports complex using translations, reflections, and rotations so that the final arrangement satisfies each of these criteria:
All the fields and buildings fit on the provided lot.
Each field is adjacent to at least one building for ease of access.
Two or more fields can be adjacent, but no two fields should share the same boundary (e.g., a sideline or a fence.)
For safety reasons, no baseball field should have an outfield (the curved edge) pointed at the side (the straight edges) of another baseball field.
Answer:
See explanation
Step-by-step explanation:
(Please Find Diagram in the attachment)⇒Answer Drawing is Given There
According to the question,
Given that, The city of Plainview is building a new sports complex. The complex includes eight baseball fields, four soccer fields, and three buildings that have concessions and restrooms. Now, Arrange the structures in the sports complex using translations, reflections, and rotations so that the final arrangement satisfies each of these criteria: All the fields and buildings fit on the provided lot.Each field is adjacent to at least one building for ease of access.Two or more fields can be adjacent, but no two fields should share the same boundary (e.g., a sideline or a fence.) For safety reasons, no baseball field should have an outfield (the curved edge) pointed at the side (the straight edges) of another baseball fieldThe area of a rectangle is given as x^2+ 5x+6. Which expression represents either the
length or width of the rectangle?
a) (x-3)
b) (x + 6)
c) (x + 1)
d) (x+3)
Answer:
d) x + 3
Step-by-step explanation:
= x² + 5x + 6
Factorise :-
= x² + 2x + 3x + 6
= x(x + 2) + 3(x + 2)
= (x + 2)(x + 3) [Taking common]
Here we are getting (x + 3) as a factor of x² + 5x + 6 which will be either length or the width
Which of the following graphs is described by the function given below?
y = 2x2 + 6x + 3
Answer: Graph A
Step-by-step explanation:
Sum of two digit number is9.When we interchange the digits it is found that the resulting new number becomes twice the other number. What are the numbers
Answer:
4 and 5
Step-by-step explanation:
Let the numbers be x and y
If their sum is 9, hence;
x + y = 9 ....1
When reversed
10y+x = 2(10x+y)
10y+x = 20x + 2y
10y - 2y = 20x - x
8y = 19x
y = 10x/8 ...2
Substitute equation 2 into 1;
From 1;
x+y = 9
x +(10x/8) = 9
18x/8 = 9
18x = 72
x = 72/18
x = 4
Since x+y =9
y = 9-x
y =9-4
y = 5
Hence the numbers are 4 and 5
Find three solutions of the equation.
y = -2x - 1
Step-by-step explanation:
three solutions of the equation:
y = -2x - 1
=>
1) (0, -1)
2) (1, -3)
3) ( -1, 1)
The graphs of g(x) = x³- ax² + 6 and h(x) = 2x² + bx + 3 touch when x = 1. Therefore, the tangent to
the curve of g at x = 1 is also the tangent to the curve of h at x = 1.
Determine the coordinates of this point of contact of the two graphs.
Answer:
[tex](1,\, 10)[/tex].
Step-by-step explanation:
Differentiate each function to find an expression for its gradient (slope of the tangent line) with respect to [tex]x[/tex]. Make use of the power rule to find the following:
[tex]g^\prime(x) = 3\, x^2 - 2\, a\, x[/tex].
[tex]h^\prime(x) = 2\, (2\, x) + b = 4\, x + b[/tex].
The question states that the graphs of [tex]g(x)[/tex] and [tex]h(x)[/tex] touch at [tex]x = 1[/tex], such that [tex]g^\prime(1) = h^\prime(1)[/tex]. Therefore:
[tex]3 - 2\, a = 4 + b[/tex].
On the other hand, since the graph of [tex]g(x)[/tex] and [tex]h(x)[/tex] coincide at [tex]x = 1[/tex], [tex]g(1) = h(1)[/tex] (otherwise, the two graphs would not even touch at that point.) Therefore:
[tex]1 - a + 6 = 2 + b + 3[/tex].
Solve this system of two equations for [tex]a[/tex] and [tex]b[/tex]:
[tex]\begin{aligned}& a + b = 2 \\ & 2\, a + b = -1\end{aligned}[/tex].
Therefore, [tex]a = -3[/tex] whereas [tex]b = 5[/tex].
Substitute these two values back into the expression for [tex]g(x)[/tex] and [tex]h(x)[/tex]:
[tex]g(x) = x^3 + 3\, x^2 + 6[/tex].
[tex]h(x) = 2\, x^2 + 5\, x + 3[/tex].
Evaluate either expression at [tex]x = 1[/tex] to find the [tex]y[/tex]-coordinate of the intersection. For example, [tex]g(1) = 1 + 3 + 6 = 10[/tex]. Similarly, [tex]h(1) = 2 + 5 + 3 = 10[/tex].
Therefore, the intersection of these two graphs would be at [tex](1,\, 10)[/tex].
please help 20 pnts!!
Answer:
[tex]m^{\frac{1}{2} }[/tex] . [tex]n^{\frac{1}{2} }[/tex]
Step-by-step explanation:
Using the rules of exponents/ radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
[tex]\sqrt{a}[/tex] = [tex]a^{\frac{1}{2} }[/tex]
Given
[tex]\sqrt{mn}[/tex]
= [tex]\sqrt{m}[/tex] × [tex]\sqrt{n}[/tex]
= [tex]m^{\frac{1}{2} }[/tex] . [tex]n^{\frac{1}{2} }[/tex]
Answer:
[tex] {(mn)}^{ \frac{1}{2} } \\ {m}^{ \frac{1}{2} } {n}^{ \frac{1}{2} } [/tex]
Lauren, Shannon, and Maddie all work at a restaurant. Lauren earned $11.00 less than 3 times the amount Maddie earned. Shannon earned $9.00 more than 2 times the amount Maddie earned. If Lauren and Shannon both earned the same amount of money, how much money, m, did Maddie earn?
Which equation below correctly represents the situation above?
A.
3m - 9 = 2m + 11
B.
3m - 11 = 2m + 9
C.
3m + 2m + 11 = 9
D.
4 × 11 + 2 × 9 = m
Answer:
B.
3m - 11 = 2m + 9
Amount Maddie earns = m = $20
Step-by-step explanation:
Let
Amount Maddie earns = m
Amount Lauren earns = 3m - 11
Amount Shannon earns = 2m + 9
If Lauren and Shannon both earned the same amount of money, how much money, m, did Maddie earn?
Amount Lauren earns = Amount Shannon earns
3m - 11 = 2m + 9
Collect like terms
3m - 2m = 9 + 11
m = 20
Amount Maddie earns = m = $20
B.
3m - 11 = 2m + 9
Please help me with this question.
Answer:
Step-by-step explanation:
736
I will give branliest if it let's me! Please help! I'll give 5 star rating, thanks and 40+ points!
Answer:
B
Step-by-step explanation:
These are corresponding angles if i remember correctly.
Answer:
Supplementary
Step-by-step explanation:
The angles add up to 180 degrees
I need help in this zzzzzzz
Answer:
[tex]7[/tex]
Solution:
This is a linear function. This means means that r is our rate of change.
To find r recal following formula
[tex]r=\frac{\Delta y}{\Delta x} = \frac{y_2-y_1}{x_2-x_1}[/tex]
Since this is a linear function we can choose any two points. I will choose the first two for simplicity
[tex]\Displaystyle \therefore r = \frac{42-14}{6-2}=\frac{28}{4}=7[/tex]
Question 1 of 10
Which of the following is equal to the rational expression when x#5?
x² - 25
X-5
A. x + 5
B. X-5
1
C
x+5
O D. X+5
X-5
SUBMIT
Answer:
A. x + 5
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsFactoringStep-by-step explanation:
Step 1: Define
Identify
[tex]\displaystyle \frac{x^2 - 25}{x - 5}[/tex]
Step 2: Simplify
Factor: [tex]\displaystyle \frac{(x - 5)(x + 5)}{x - 5}[/tex]Divide: [tex]\displaystyle x + 5[/tex]You can identify sample spaces for compound events using organized lists, tables, and tree diagrams. Which of the three methods do you find easiest to use? Which method is the most helpful? Why? Use the Internet or another resource to find the definition of the Fundamental Counting Principle. What does this principle state? How can the principle be used to help you identify a sample space for a compound event? What are the limitations of using the Fundamental Counting Principle when determining the probability of an outcome? Support your answers with an example.
The fundamental counting principle is used to count the total number of possible outcomes that are in a situation.
What does the fundamental counting principle state?The fundamental counting principle states that if there are n ways of doing something, as well as m ways of doing another thing, then there are n×m ways to perform both of these actions.
The Fundamental Counting Principle helps when determining the sample space of probability as it figures out the total number of ways the combination of events can occur. Therefore, it is used as a guide when determining the sample space of a probability.
Lastly, the limitation is that the Fundamental Counting Principle is that it assumes that each basic event is equally probable, which does not necessarily have to be true.
Learn more about counting principle on:
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Answer:
The fundamental counting principle is used to count the total number of possible outcomes that are in a situation
Step-by-step explanation:
Please help!! Thank you if you do!!
What is the domain of y= log 5x
Answer:
all positive real numbers, (0, ∞)
Step-by-step explanation:
The log function is not defined for 0 or for negative numbers.
The domain of the log function is all positive real numbers.
Answer: all positive real numbers
Which could be the missing data item for the given set of data if the median of the complete data set is 65?
66, 43, 35, 78, 74, 37, 65, 66, 76, 78, 80, 43, 56, 60
A. 71
B. 75
C. 69
D. 50
Answer:
B.) 75
Step-by-step explanation:
Answer: B 75
Step-by-step explanation:
i WILL mark brainliest !!!!
John had a total of $150. He purchased a DVD box set which costs $50 as well as a single DVD. He is left with $75. Which equation could be used to find the cost p of the DVD?
a. 150 + 50 + p = 75
b. 150 + 50 + 75 = p
c. 150 − 50 + 75 = p
d. 50 + p + 75 = 150
ps: absurd answers will be reported !!
Answer:
please mark as brilliant
Find the area of this circle in square centimeters. Use 3.14 for π . Round to 2 decimal places if necessary. Enter only the number π
Answer:
113.04 is the answer
Step-by-step explanation:
Use the formula for finding the area of a circle.
Area= pi times radius to the second power.
First you had to divide your diameter by 2 to get 6. Then 6 squared, to get 36. Then finally 36x3.14.
Need help!!! Please explain!!!
Which is the graph of f(x) = (2) -x
Answer:
In other words y = 2-x
Put in some values of x and see which graph matches the given ys.
The last graph
Answer:
b
Step-by-step explanation:
Find the distance between the points (1,5) and (3,0). Round your answer to the nearest tenth.
Answer:
5.4 units
Step-by-step explanation:
Hi there!
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] where two given points are [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex]
Plug in the given points (1,5) and (3,0)
[tex]d=\sqrt{(3-1)^2+(0-5)^2}\\d=\sqrt{(2)^2+(-5)^2}\\d=\sqrt{4+25}\\d=\sqrt{29}\\d=5.4[/tex]
Therefore, the distance between the two points when rounded to the nearest tenth is 5.4 units.
I hope this helps!
If this trapezoid is moved through the
translation (x+3, y-2), what will the
coordinates of C'be?
5
00
NO
A
D
1
-7 -6 -5
4
-3
1
2
3
4
-2 -1 0
-1
C' = (1, [?])
-2
Given:
The rule of translation is:
[tex](x+3,y-2)[/tex]
The trapezoid ABCD on the graph.
To find:
The coordinates of the point C'.
Solution:
From the given graph, it is clear that the coordinates of point C are (-2,4).
The rule of translation is:
[tex](x,y)\to (x+3,y-2)[/tex]
Using this rule of translation, we get
[tex]C(-2,4)\to C'(-2+3,4-2)[/tex]
[tex]C(-2,4)\to C'(1,2)[/tex]
Therefore, the coordinates of the point C' are (1,2).