To prove that (m + dk) mod d = m mod d, we can use the definition of the modulo operation and properties of integers.
Explanation:To prove that (m + dk) mod d = m mod d, we can use the definition of the modulo operation and properties of integers. Let's assume that m and d are integers, d > 0, and k is an integer.
Start with the left-hand side: (m + dk) mod d.Using the distributive property, we can rewrite (m + dk) as m mod d + (dk mod d).Since any number mod d is less than d, (dk mod d) is equivalent to 0.Therefore, (m + dk) mod d simplifies to m mod d + 0, which is equal to m mod d.Since the left-hand side is equal to the right-hand side, we have proved that (m + dk) mod d = m mod d.Learn more about Modulo operation here:https://brainly.com/question/30264682
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If two angles are adjacent and supplementary, then they are examples of the _____ Postulate.
Linear pair Postulate. Two angles are a linear pair if the angles are adjacent and the two unshared rays form a line. Below is an example of a linear pair: The linear pair postulate states that two angles that form a linear pair are supplementary.
Let f(x) = x + 8 and g(x) = x2 − 6x − 7. find f(g(2)). −7 −3 10 33 open study
Mia is standing 210 yd from a radio tower. The angle of elevation from where she is standing on the ground to the top of the tower is 11°. How tall is the radio tower?
What is the radius of a circle with an area of 32.1 sq ft
Factor this expression completely and then place the factors in the proper location on the grid. Note: Place factors alphabetically in the grid! ab + 4 + a + 4b
Answer:
The required form of the given expression is : (a + 4)(b + 1)
Step-by-step explanation:
The given expression is : ab + 4 + a + 4b
We need to factor he given expression and arrange the factors in the alphabetic order.
To find the factors of the given expression, we need to use the concept of algebra :
ab + 4 + a+ 4b
First rearranging the terms in order to form the factors :
= ab + 4b + 4 + a
= b(a + 4) + 1(4 + a)
= b(a + 4) + 1(a + 4)
= (b + 1)(a + 4)
Now, the factors in the alphabetic order :
= (a + 4)(b + 1)
Hence, the required form of the given expression is : (a + 4)(b + 1)
The radius of a circle is 6 feet. What is the area of the circle?
A. 6π
B. 12π
C. 18π
D. 36π
What value completes the square for the expression?
x2 - 18x
A. 9
B. -9
C. 81
D. -81
To complete the square for the expression x^2 - 18x, add 81 to become a perfect square trinomial in the form (x - 9)^2.
Explanation:To complete the square for the expression x^2 - 18x, we need to add a constant term to the expression in such a way that it can be factored as a perfect square trinomial. First, we take half of the coefficient of the linear term and square it:
Half of -18 is -9, and when we square it we get 81. Therefore, adding 81 to the expression gives us x^2 - 18x + 81. This can be factored as (x - 9)^2. So the value that completes the square is 81.
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How would you graph a point at -5?
A: Put a point 5 units to the right of zero.
B: Put a point at zero.
C: Put a point 5 units to the left of zero.
Answer:
C: Put a point 5 units to the left of zero.
Step-by-step explanation:
Which logarithmic graph can be used to approximate the value of y in the equation 3^y = 7? 20 POINTS
Answer with explanation:
The exponential function is
[tex]3^y=7\\\\ \text{taking log on both sides}\\\\y\log3=\log7\\\\y=\frac{\log7}{\log3}\\\\y=\log_{3}7\\\\y=\frac{0.8450}{0.477}\\\\y=1.77[/tex]
It is equation of a line, parallel to X axis.
Drawn the graph of the function , which cuts the y axis at ,(1.77,0).
None of the curve matches with the given Options.
Martha can complete 15 activities a day at summer camp. She can choose between crafts or sport
Variable 1: X= number of craft activities
Variable 2: Y= number of sports activities
Equation: X + Y=15
One person can do a certain job in fifteen minutes, and another person can do the same job in thirty minutes. How many minutes will it take them to do the job together?
Find the volume of a rectangular prism if the length is 4x, the width is 2x, and the height is x3 + 3x + 6. Use the formula
V = l ⋅ w ⋅ h, where l is length, w is width, and h is height, to find the volume.
6x5 + 18x3 + 36x2
6x6 + 18x3 + 36x2
8x5 + 24x3 + 48x2
8x6 + 24x3 + 48x2
Answer:
option C is correct
[tex]8x^5+24x^3+48x^2[/tex]
Step-by-step explanation:
As per the statement:
The length(l), width(w) and height(h) of the rectangular prism are:
l = 4x
w = 2x
[tex]h = x^3+3x+6[/tex]
We have to find volume.
Use the formula:
[tex]V = lwh[/tex]
Substitute the given values we have;
[tex]V = 4x \cdot 2x \cdot (x^2+3x+6)[/tex]
⇒[tex]V = 8x^2 \cdot (x^3+3x+6)[/tex]
Using distributive property, [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]
then;
[tex]V = 8x^5+24x^3+48x^2[/tex]
Therefore, the volume of the rectangular prism is, [tex]8x^5+24x^3+48x^2[/tex]
Since the population size is always larger than the sample size, then the sample statistic:
Which of the following is the definition of term? A. an ordered set of numbers B. an element in a sequence C. a sequence in which terms are given by multiplying the previous term by a common ratio D. a sequence in which terms are not given by multiplying the previous term by a common ratio
Which line is parallel to 4x + 2y = 0?
A. y=2x+3
B. -1/2×+3
C. y=-2x+3
D. y=1/2x+3
Given: WA = NO, WS = NT, W = N.
A)SSS
B) SAS
C) ASA
D)AAS
Answer with explanation:
It is given that ,
In two triangles, ΔWAS and ΔNOT
1. WA = NO
2. W S = NT
3. ∠W=∠N
≡ΔWAS ≅ ΔNOT
The Angle is included between two sides .
So,these two triangles are congruent by ,SAS.
Option B:→ S AS
What methods can be used to rewrite square trinomials and difference of squares binomials as separate factors?
Final answer:
Square trinomials and difference of squares binomials can be rewritten into separate factors using methods such as completing the square, the difference of squares method, and factoring by grouping.
Explanation:
Completing the square method: Rewrite square trinomials by completing the square to factor them into separate factors. For example, [tex]x^2 + 6x + 9[/tex] can be written as (x + 3)(x + 3).
Difference of squares method: Rewrite binomials with a difference of squares by factoring them into separate factors. For instance, [tex]x^2 - 4[/tex] can be expressed as (x + 2)(x - 2).
Factoring by grouping: For more complex trinomials, you can use the method of factoring by grouping to rewrite them as separate factors.
Sally found that a solution of x = 2 was extraneous for her function. What would be a possible denominator in Sally's function?
4x + 8
2x + 12
x^2 − 4
x^2 − 16
Answer:
[tex]x^2-4[/tex]
Step-by-step explanation:
Sally found that a solution of x = 2 was extraneous for her function.
Extraneous solution is a solution that makes the denominator 0
Possible denominator are given . LEts plug in 2 for x and check which option gives us 0
[tex]4x+8=4(2)+8= 16[/tex]
[tex]2x+12=2(2)+12=4+12= 16[/tex]
[tex]x^2-4= (2)^2-4= 4-4=0[/tex]
[tex]x^2-16= (2)^2-16= 4-16= 12[/tex]
[tex]x^2-4[/tex] gives us 0 when we plug in 2 for x.
So x=2 was extraneous solution for [tex]x^2-4[/tex]
(06.02 LC)
What is most likely the line of best fit for this scatter plot?
Line A
Line B
Line C
Line D
PLEASEEE help shape equation puzzle
Which of the following quadrilaterals have diagonals that are perpendicular to each other? Check all that apply.
A. Rectangle
B. Square
C. Parallelogram
D. Rhombus
Answer:
B. Square
D. Rhombus
Step-by-step explanation:
If you take a rhombus ABCD, its all sides are congruent. Lets take E as the point where the diagonals of a rhombus meet. Now it is known fact that the point where diagonals meet, they bisect each other.
Since, for sides, AB , CD,AD and CB are congruent
For diagonals, AC = BD
As E is the bisecting point for diagonals,
AE = EC and ED = EB
Now by SSS postulate, we can prove that all four triangles formed by rhombus are congruent
ΔAED , ΔBEC , ΔEDC and ΔAEB are congruent
Now the angles
∠AED, ∠AEB, ∠CED and ∠CEB are congruent as well,
So, we know that sum of interior angles of any quadrilateral is 360°
So each angle is 360/4 = 90°
This calculation is valid for square as well.
Answer:
B and D
Step-by-step explanation:
cya
4x + 5 - 2x + 1 = 2x - 5
What is the rational number equivalent to 1 point 28 with a bar over 28? 1 and 6 over 97 1 and 28 over 99 1 and 8 over 33 1 and 5 over 16
Answer: The answer is [tex]1\dfrac{28}{99}.[/tex] .
Step-by-step explanation: The given rational number is
[tex]R=1.\bar{28}.[/tex]
We are to select the correct expression from the options that is equivalent to the given rational number.
Let us consider that
[tex]x=1.\bar{28}\\\\\Rightarrow x=1.28\bar{28}\\\\\Rightarrow 100\times x=100\times 1.28\bar{28}\\\\\Rightarrow 100x=128.\bar{28}\\\\\Rightarrow 100x=128+.\bar{28}\\\\\Rightarrow 100x=127+x\\\\\Rightarrow 100x-x=127\\\\\Rightarrow 99x=127\\\\\Rightarrow x=\dfrac{127}{99}\\\\\Rightarrow x=1\dfrac{28}{99}.[/tex]
Thus, the correct option is [tex]1\dfrac{28}{99}.[/tex]
CAN SOMEBODY PLEASE HELP ME? I will mark you as a BRAINLIST!!!
George plans to cover his circular pool for the upcoming winter season. The pool has a diameter of 20 feet and extends 12 inches beyond the edge of the pool. A rope runs along the edge of the cover to secure it in place.
a.
What is the area of the pool cover?
b.
What is the length of the rope?
so use a basic formula here:
area of a circle = πr²
and the circumference of a circle = πd
a)
therefore the area of the pool cover is π multiplied by the radius² (which is the diameter of the pool cover plus the extra 12 inches divided by two, so the radius is 21/2 or 10.5) is 346.36(to two decimal places.)
b)
Using the same diameter, we can work out the length of the rope by multiplying the diameter (10.5) by π, which is 32.99 (to two decimal places).
The domain of the following relation R {(6, −2), (1, 2), (−3, −4), (−3, 2)} is
{−3, −3, 1, 6}
{−4, −2, 2, 2}
{−4, −2, 2}
{−3, 1, 6}
Answer:
Option 4th is correct
the domain of the following relation R is:
[tex]\{-3, 1, 6\}[/tex]
Step-by-step explanation:
Domain is the set of all values of x-coordinates where function is defined.
Given the Relation:
[tex]R = \{(6, -2), (1, 2), (-3, -4), (-3, 2)\}[/tex]
The ordered pairs are in the form of (x, y)
Domain = Set of all values of x.
In the given relation:
x-values = { 6, 1, -3}
⇒[tex]\text{Domain} = \{-3, 1, 6\}[/tex]
therefore, the domain of the following relation R is:
[tex]\{-3, 1, 6\}[/tex]
Which three lengths could be the lengths of the sides of a triangle? 9 cm, 22 cm, 11 cm10 cm, 15 cm, 24 cm12 cm, 5 cm, 17 cm21 cm, 7 cm, 6 cm
Answer: 10, 15, 24 is your answer
Step-by-step explanation:
Determine the exact value of
sin(−135)°.
Identify the reference angle, Theta
Theta=?
We will see that the exact value is √2/2 = 0.707, and the reference angle is 45°.
How to determine the reference angle?
We know that for any angle θ we have that:
sin(θ) = sin(θ + n*360°)
Where n is an integer value.
To find the reference angle of a given angle θ, we just need to find a value of n such that:
0 ≤ θ + n*360° ≤ 360°
So we can write our angle in the normal range.
in this case, our angle is -135°
Then we can write:
0 ≤ -135° + n*360° ≤ 360°
Is immediate to notice that we must take n = 1
0 ≤ -135° + 1*360° ≤ 360°
0 ≤ -135° + 1*360° ≤ 360°
0 ≤ 225° ≤ 360°
Now we know that θ = 225°.
Ok, this lies on the third quadrant, when an angle lies on the third quadrant, to get the reference angle you just need to subtract 180°.
We will get:
225° - 180° = 45°
So the reference angle is 45°.
Finally, to get the exact value we use:
sin (-135°) = sin(225°) = cos(45°) = √2/2 = 0.707
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find the surface area of each figure to the nearest tenth. show your work, please!
A. The figure given in A is a square pyramid and the formula for the surface area of this figure is:
A = l w + l sqrt [(w/2)^2 + h^2] + w sqrt [(l/2)^2 + h^2]
where l and w are the lengths of the base and h is the height of the pyramid. Since the base is square, so:
l = w = 16 in
h = 15 in
Substituting:
A = 16 * 16 + 16 sqrt [(16/2)^2 +15^2] + 16 sqrt [(16/2)^2 + 15^2]
A = 256 + 272 + 272
A = 800 in^2
B. We are given a cone, the formula for surface area is:
A = πr (r + h^2 + r^2)
where h is the height = 8 in and r is the radius = 3 in
Substituting:
A = π * 3 (3 + sqrt (8^2 + 3^2))
A = 34.63π in^2 = 108.80 in^2
The graph below shows four straight lines, P, Q, R, and S: graph of line P going through ordered pairs negative 2, negative 5 and 0, 3. Graph of line Q going through ordered pairs negative 1, negative 2 and 1, 6. Graph of line R going through ordered pairs negative 1, negative 4 and 1, 4. Graph of line S going through ordered pairs 0, negative 3 and 2, 5 Which line is represented by the function f(x) = 4x - 3?
You are given the graph of four straight lines, P, Q, R, and S. You are asked to find which line corresponds to the function of f(x) = 4x - 3. The easiest way to answer this is to plug in the values of the coordiante points used for each graph.
f(x) = 4x - 3 = y
y = 4x - 3
for graph of line S we have the coordinates (0, -3) and (2, 5)
(0, -3)
-3 = 4(0) - 3
-3 = -3
(2,5)
5 = 4(2) - 3
5 = 8 - 3
5 = 5
So the answer is the graph of line S.