The remainder when [tex]5^{400}[/tex] is divided by 19, the remainder is 17.
Remainder
The Remainder is the value left after the division. If a number (dividend) is not completely divisible by another number (divisor) then we are left with a value once the division is done. This value is called the remainder.
We can write,
[tex]5^{400} = (5^4)^{100} = 625^{100}[/tex]
We know that,
19*33 = 627
Hence, we can write 625 as 627 - 2
It will become,
[tex]\frac{(627-2)^{100}}{19}=\frac{(-2)^{100}}{19}[/tex]
We know that, even power of any number and its negative counterpart will be same.
Hence, we can write,
[tex]\frac{(-2)^{100}}{19}=\frac{(2)^{100}}{19} = \frac{2*2^{99}}{19}[/tex]
We know that 99 = 11*9
Hence, we can write,
[tex]\frac{2*({2^9})^{11}}{19} =\frac{2*512^{11}}{19}[/tex]
We know that,
19*27 = 513
Hence, we can write, 512 as 513 - 1
[tex]\frac{2*(513-1)^{11}}{19}=\frac{2(-1)^{11}}{19}[/tex]
2*(-1)/19 = -2/19
It means the remainder will be 19 - 2 = 17.
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Use elimination to solve for x and y: 2x-y =18
-2x-9y=2
Answer:
2x-y=18
-2x-9y=2
cancel 2x
add equation:
-y+(-9y)=20
-10y=20
y=-20/10
y = -2
input y in any equation:
2x-(-2)=18
2x+2=18
2x=18-2
2x=16
x= 8
At the beginning of spring, Khalil planted a small sunflower in his backyard. When it was first planted, the sunflower was 5 inches tall. The sunflower then began to grow at a rate of 1 inch per week. How tall would the sunflower be after 6 weeks? How tall would the sunflower be after w weeks?
The sunflower would be 11 inches tall after 6 weeks and it would be (5+w) inches tall after w weeks .
In the question ,
it is given that
the height of the sunflower when it was planted = 5 inches
rate of growth of sunflower = 1 inch per week
let y represents the height of the sunflower after x weeks .
So , According to the question , the equation becomes
y = 5 + 1*x
to find the height after 6 weeks , substitute x=6
we get ,
y = 5 + 1(6)
y=5+6
y=11
height after 6 weeks will be 11 inches .
to find the height after w weeks , substitute x=w
we get ,
y = 5 + 1(w)
y=5+w
sunflower will be (5+w) inches tall
Therefore , the sunflower would be 11 inches tall after 6 weeks and it would be (5+w) inches tall after w weeks .
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Which of the following best describes the graph below?
A. It is not a function.
B. It is a one-to-one function.
C. It is a many-to-one function.
D. It is a function, but it is not one-to-one.
The correct option B. It is a one-to-one function; for the given graph.
What is termed as the one-to-one function?Each element of one set, say Set (A), is mapped with such a unique element of another set, say Set (B), where A as well as B are two different sets. It can also be written 1-1. In terms of function, if f(x) = f(y) implies that x = y, after which f is one to one.An injective function is a one-to-one function that maps each element of one set to each element of some other set.For the given question;
As, in the given graph for the function, for each value of the domain (the value of x), there is only one value of range (y).
Thus, the given graph shows the one-to-one function.
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Write down the order of rotational symmetry of this regular heptagon.
The order of the rotational pentagon is 6.
What is order of a polygon?The amount of times a form may be turned in a full circle without losing its appearance is known as its order of rotational symmetry. The only time the triangle appears the same after being rotated a full 360 degrees is when it returns to its original beginning position. It only has one rotational symmetry order, which is the initial position. A form can only have one rotational symmetry order.
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Rationalizing factor of cube root 5
Answer:
You cube your answer that is the numerator and denominatorFind the Area of the figure below, composed of a square and four semicircles. Rounded to the nearest tenths place
The Area of the figure ,composing of a square and four semicircles is 832.7 sq. units
The Length of the side of the square is 18 units which is also the diameter of the semicircle.
So, The Area of square is Length * Length = 18*18 = 324 sq. units
Now, the radius of semicircle = 0.5(diameter)= (0.5)*18 = 9 units
The area of semicircle = half of area of circle = (0.5)3.14(radius)(radius)
The area of one semicircle = (0.5)3.14(9)(9)
The area of one semicircle = 127.17
The Total area of figure consists of 4 semicircles and one square
So, Total area = 4(area of 1 semicircle) + area of square
Total area = 4(127.17) + 324
Total area = 832.68 sq. units
rounding off the total area = 832.7 sq. units
Therefore, the total area of the given figure is 832.7 sq. units.
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Determine whether the graph represents a linear or non linear function and explain
Answer:
Non-linear
Step-by-step explanation:
Because the line is not straight.
The quarterly dividend for Tiffany, a jewelry company, was $0.12
during the second quarter of 2008. What was the annual divider
for 2,000 shares?
Answer:
$960
Step-by-step explanation:
Quarterly Dividend Per Share = $0.12
Quarterly Dividend For 2000 shares = 0.12 x 2000 = $240
Since there are 4 quarters in a year, yearly dividend for 2000 shares at $0.12 per share
= $240 x 4 = $960
Help 5 star and thanks to the best answer
The value of the smiley face provided in the question is 908.
What is the value of the smiley face ?The first step is to determine the value of each of the shapes.
The value of the rectangle would be determined first. Using the third given equation, let r represent the value of one rectangle.
(4 x r) + (2 x r) - (3 x r) = 15
4r + 2r - 3r = 15
3r = 15
r = 15 / 3 r
r = 5
The next step is to determine the value of the triangle. The second equation would be used. Let t represent the value of the triangle.
(3 x 5) + (4 x t) = 47
15 + 4t = 47
4t = 47 - 15
4t = 32
t = 32 / 4
t = 8
Finally, the value of the star would be determined. Let the value of the star be represented with s. Using the first equation:
5 + (3 x 8) - s = 17
5 + 24 - s = 17
29 - s = 17
s = 29 - 17
s = 12
Now, the value of the smiley face can be determined:
12 x (8 + 12 - 5) + 8(8 . 12 - 5)
12 x (15) + 8(91)
180 + 728 = 908.
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Sam creates a dot pattern using a rule. He starts with 2 dots and adds 2 dots for each term. The dot pattern continues for 50 terms. The first four terms in his dot pattern are shown below.
Answer:
That means the sum of the first 99 positive integers is 49(100) + 50 = 4900 + 50 = 4950. 2.
Augustina has 2 posters with length x inches.
One poster has a width of x + 5 inches, and
the other has a width of x + 7 inches. Write an
expression to represent the area of wall that the
posters will cover.
Answer:
2x² + 12x
Step-by-step explanation:
Area of rectangle:Area of rectangle = length * width
Poster 1:
length = x inches
widht = (x + 5) inches
Area of poster 1 = x * (x + 5)
= x*x + x*5 {Distributive property}
= x² + 5x square inches
Poster 2:
length = x inches
width = (x + 7) inches
Area of poster =x *(x+ 7)
= x*x + x*7
= x² + 7x
Area of wall = area of poster1 + area of poster 2
= x²+ 5x + x² + 7x
= x² + x² + 5x + 7x {Combine like terms}
= 2x² + 12x
Answer:
[tex]2x^2+12x[/tex]
Step-by-step explanation:
Dimensions of Poster 1:
Length = x inchesWidth = (x + 5) inchesDimensions of Poster 2:
Length = x inchesWidth = (x + 7) inchesThe posters can be modeled as rectangles.
[tex]\boxed{\textsf{Area of a rectangle}=\sf length \times width}[/tex]
Therefore, the expressions for the area of each poster are:
[tex]\implies \textsf{Area of Poster 1}=x(x+5)[/tex]
[tex]\implies \textsf{Area of Poster 2}=x(x+7)[/tex]
Therefore, the expression that represents the area of the wall that the posters will cover is the sum of the expressions of the areas of the individual posters:
[tex]\begin{aligned}\textsf{Area of wall posters will cover}&=\textsf{Area of Poster 1}+\textsf{Area of Poster 2}\\& = x(x+5)+x(x+7)\\&=x^2+5x+x^2+7x\\&=x^2+x^2+5x+7x\\&=2x^2+12x\end{aligned}[/tex]
-5 + |1 - 8n| > 58
MUST SHOW EQUATION
The value of the inequality is n > 7. 75
What are inequalities?Inequalities are simply defined as mathematical relations that makes an unequal or unbalanced comparison between two elements or numbers and even for known mathematical expressions
They are frequently used in comparing two or more numbers on the number line and this is carried out on the basis of their magnitude or size.
What is absolute value?Absolute value can be defined as the value of a number irrespective of its direction from zero on the number line.
The absolute value of a number must take the positive sign.
It is represented with the symbol '| |'
Given the inequality:
-5 + |1 - 8n| > 58
find the absolute value
-5 + 1 + 8n > 58
collect like terms
8n > 58 + 4
8n > 62
Make 'n' the subject of formula by dividing both sides by 8
8n/8 > 62/8
n > 7. 75
Hence, the value is n > 7. 75
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Solve for x
2x = -21
Give your answer as an
improper fraction in its simplest
form.
Answer: x = -21/2
Step-by-step explanation:
2x/2 = -21/2
x = -21/2
Divide both sides by 2.
-21 is not divisible by 2, so -21/2 is improper in simplest form.
What is the result of converting 0.5 cups to fluid ounces? (Remember that 1
cup = 8 fluid ounces.)
O A. 16 fluid ounces
OB. 2 fluid ounces
OC. 4 fluid ounces
O D. 8 fluid ounces
SUBT
the time it takes me to wash the dishes is uniformly distributed between 12 minutes and 20 minutes. what is the probability that washing dishes tonight will take me between 14 and 16 minutes?
The probability that washing dishes will take time between 14 and 16 minutes is equal to 25%.
This type of probabilty can be termed a uniform probability in which all the outcomes or results are equally likely.
The lower limit can be represented as a and in this problem is 12 minutes and the upper limit can be considered b and in this problem is 20 minutes.
The equation to find probability, in this case, can be given as:
P ( c ≤ X ≤ d ) = d - c / b - a
Here c = 14 and d = 16 as we have to find the probability that washing dishes will take between 14 and 16 minutes.
Therefore;
P ( 14 ≤ X ≤ 16 ) = 16 - 14 / 20 - 12 = 2 / 8 = 0.25
Converting it into percentage:
0.25 = 0.25 × 100 = 25%
Therefore, the probability that washing dishes will take her between 14 and 16 minutes is calculated to be 25%.
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£N is shared between three people in the ratio 2:3:7 The largest share is £540 more than the smallest share. Calculate the value of N.
If £N is shared between three people in the ratio 2:3:7 The largest share is £540 more than the smallest share. the value of N is 1296.
Value of NLet x represent the sharing unit
Hence,
2x :3x :7x
so
7x = 2x + 540
7x - 2x = 540
5x =540
Divide both side by 5x
x = 540/5
x = 108
Sharing unit
2x = 2 ×108
= 216
3x = 3 × 108
= 324
7x = 7 × 108
= 756
Value of N = 216 + 324 +756
Value of N = 1296
Therefore we can conclude that the value of N is 1296.
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Introduction: Drag the concepts more commonly associated with each type of economy to the correct column. More public property Command economies Mixed market economies More private property Greater chance for higher income Larger wealth gap Less chance for higher income Smaller wealth gap
Command Economies -More Public Property, Smaller Wealth Gap ,Less chance for higher income
Mixed Market Economies- Larger Wealth Gap, Greater chance for
higher income, More private property
What is Meant by Economy?Economy: An economy encompasses all of the activities related to the production, consumption, and trade of goods and services in an entity, whether the entity is a nation or a small town. No two economies are identical. Each is formed according to its own resources, culture, laws, history, and geography
Command Economies Mixed Market Economies
More Public Property Larger Wealth Gap
Smaller Wealth Gap Greater chance for higher income
Less chance for higher income More private property
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Answer:
in the picture
Step-by-step explanation:
Please answer the question
For given functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x², f(x) - g(x) = 5x² + 2x - 13
In this question, we have been given two functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x²
We need to find f(x) - g(x)
We need to subtract function g(x) from function f(x)
= f(x) - g(x)
= 3x² - 8 - (5 - 2x - 2x²)
= 3x² - 8 - 5 + 2x + 2x²
= 3x² + 2x² + 2x - 8 - 5
= (3 + 2)x² + 2x - (8 + 5)
= 5x² + 2x - 13
Therefore, for given functions f(x) = 3x² - 8 and g(x)=5 - 2x - 2x², f(x) - g(x) = 5x² + 2x - 13
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The lengths of the four sides of a quadrilateral (in feet) are consecutive even integers. If the perimeter is 9292 feet, find the value of the longest of the four side lengths.
The longest side of a quadrilateral with length of consecutive even integers is 26 feet.
How to find the side of a quadrilateral?The lengths of the four sides of a quadrilateral (in feet) are consecutive even integers.
A quadrilateral is a polygon with 4 sides.
Therefore, the sides are consecutive even numbers.
Hence,
smallest side = x
Therefore, perimeter is the sum of the whole sides of the quadrilateral.
x + x + 2 + x + 4 + x + 6 = 92
4x + 12 = 92
4x = 92 - 12
4x = 80
x = 80 / 4
x = 20
Therefore, the longest side of the quadrilateral is 20 + 6 = 26 ft.
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Find the solutions to x² = 12. O A. x = +2√/6 OB. x = +2√3 O C. x = +6√2 O D. x = ±3√2
The solution for the expression x² = 12 will be x = ±2√3.
The expression is given in the form of square of a variable x which is equal to 12. This expression does not form a perfect square as the constant term is not a perfect square number. A perfect square is a number which is expressed as the square of whole number, or a number multiplied by itself twice. Here, we are given that x² = 12. We take square root of the expression on both the sides then,
√x² = √12
x = √(2×2×3)
x = ±2√3
We use the sign '±' because any number which when expressed in variable form comes out of the square root then it can be positive or negative,
Thus, the value of x is ±2√3.
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Write and solve multiplication equations
We need to solve the s varibale for the given equation:
[tex]\begin{gathered} s-12=20 \\ Add\text{ both sides 12} \\ s-12+12=20+12 \\ s=32 \end{gathered}[/tex]Hence, s=32
Brian is driving to Miami. Suppose that the distance to his destination (in miles) is a linear function of his total driving time (in minutes). Brian has 69 miles to his destination after 15 minutes of driving, and he has 58.8 miles to his destination after 27 minutes of driving. How many miles will he have to his destination after 41 minutes of driving?
Brian will have 46.90 miles to his destination after 41 minutes of driving.
In the question ,
it is given that
Brian has 69 miles left to his destination after 15 minutes of driving
let x denotes the driving time ( in minutes)
and y denote the remaining distance ( in miles )
so the point is represented by (15,69)
and given that
Brian has 58.8 miles to his destination after 27 minutes of driving
so the second point is (27,58.8).
Since the relationship is given to be linear , hence it will represent a line .
the equation of line passing through the two points (15,69) and (27,58.8) is given by
(y-69)=(58.8-69)/(27-15) * (x-15)
y-69 = -10.2/12 * (x-15)
y-69 = -0.85(x-15)
y-69= -0.85x+12.75
y = -0.85x + 81.75
So , the linear relationship between remining distance and driving time is given by y = -0.85x + 81.75 .
to find miles will he have to his destination after 41 minutes of driving
Substituting x=41 we get
y = -0.85(41) + 81.75
y = -34.85 + 81.75
y = 46.90 .
Therefore , Brian will have 46.90 miles to his destination after 41 minutes of driving.
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Find the domain of the graphed function.
OA. -9≤x≤ 5
OB. 0≤x≤ 10
OC. x20
-10
D. x is all real numbers.
10-
-10-
PLEASE HURRY
The domain of the graphed function is option (D)
What is the domain of a graphed function?
In mathematics, the domain of a function is the set of inputs that the function accepts. It is also known as dom(f) or dom f, where f is the function.
The domain of the graphed function is option (D) x is all real numbers.
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The arithemetic mean of 3,15, and my number is 40. What is my number?
_
Average of given n numbers X1,X2,.........,Xn is x= £xi/n
Let the my number be x
Given:- The average of 3,15,x is 40
£xi/n =40
3+15+x/3=40
Multiplying 3 both side
18+x=120
x=120-18
x=102
Hence, my number is 102
8th grade Mathematics
According to the trend line equations, which plants are growing at the same rate per day?
1 and 2
1 and 4
2 and 3
2 and 4
I appreciate you answers so much!
Have a great day! :)
The plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 [tex]y = \frac{3}{2}x+1[/tex] i.e because they have same slope(rate of change )
What is rate of change ?The pace at which one quantity changes in relation to another quantity is known as the rate of change function. Simply said, the rate of change is calculated by dividing the amount of change in one item by the equal amount of change in another.
The plant are growing at the same rate per day is given by equation 1[tex]y=\frac{3}{2}x +\frac{3}{2}[/tex] and equation 4 i.e [tex]y = \frac{3}{2}x+1[/tex]
because they have same slope(rate of change )
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Find the odd one out
7142
2168
3248
7426
3211
8547
9455
9273
The area of a rectangle ABCD is 9cm².
Show that x² + 5x = 3
We can show that x² + 5x = 3 given the dimensions of the rectangle that has an area of 9 cm² as explained below.
How to Find the Area of a Rectangle?To find the area of a rectangle, use the formula given below:
Area of a rectangle = (length)(width).
Given the parameters:
Area of rectangle ABCD = 9 cm²Length of the rectangle = BC = (x + 3) cmWidth of the rectangle = AB = (x + 2) cmTo show that x² + 5x = 3, plug in the values into the formula for the area of a rectangle:
(x + 3)(x + 2) = 9
Apply the distributive property of equality
x(x + 2) + 3(x + 2) = 9
x² + 2x + 3x + 6 = 9
Combine like terms:
x² + 5x + 6 = 9
Add -6 to both sides of the equation
x² + 5x + 6 - 6 = 9 - 6 [subtraction property of equality]
x² + 5x = 3
Thus, if the area of the rectangle with the given dimensions is 9 cm², then we can show that, x² + 5x = 3 as explained above.
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Stephanie ran 5 3/4 miles in one hour if she ran at the same pace how far would she be able to run in 2.5 hours
Answer:
14.375 or 14 3/8
Step-by-step explanation:
5.75*2.5=answer
Answer 5 3/4
Step by step explanation:
So her speed is 5 3/4 mph.
So you just calculate 5 3/4 x 2.5 and you get 14 3/8
I hope this helps
a. If p is an even number, then p + 12 is even.
Answer:
True???
Step-by-step explanation:
Is this a true or false question?
P+12=even number
Examples...
12+12=24
16+12=28
66+12=78
Answer:
YES
Step-by-step explanation:
even + even = even
always and forever
Find the coordinates of the midpoint M
(-3, 2) and K(9, 2)
Answer:
(3,2)
Step-by-step explanation:
since -3 + 9 =6
6 ÷ 2 =3
2 + 2 = 4
4 ÷ 2 = 2
therefore (3,2)