Answers
Are they divisible by 3?
Add the digits of 45. 4 + 5 = 9. Since 9 is divisible by 3, 45 is divisible by 3.
Add the digits of 567. 5+6+7 = 18. Since 18 is divisible by 3, 567 is divisible by 3.
Now we divide the numerator and denominator by 3.
45/3 = 15
567/3 = 189
We have this now:
45/567 = 15/189
We need to try to reduce it more.
15 is divisible by 3 and 5.
189 is divisible by 3.
15/3 = 5
189/3 = 63
45/567 = 15/189 = 5/63
5 is prime and divisible only by 1 and 5.
63 is not divisible by 5.
The fraction cannot be reduced any more.
Answer: 5/63
Related Questions
1) Write the sum or difference in the standard form a + bi. (2 points)
( 7 + 5i) - ( -9 + i)
a) 16+4i
b) -16-4i
c) 16-4i
d) -2+6i
2) Write the product in standard form. (2 points)
( 7 + 7i)( 6 + 7i)
a) -7 + 91i
b) 49i2 + 91i + 42
c) 91 - 7i
d) -7 - 91i
3) Find the product of the complex number and its conjugate. (2 points)
1 + 3i
a) 1 + 9i
b) 10
c) -8
d) 1-9i
4) Write the expression in standard form. (2 points)
three divided by quantity three minus twelve i.
a) - one divided by seventeen. + four divided by seventeen. i
b) one divided by seventeen. - four divided by seventeen. i
c) - one divided by seventeen. - four divided by seventeen. i
d) one divided by seventeen. + four divided by seventeen. i
5) Find the real numbers x and y that make the equation true. (2 points)
5 + yi = x + 3i
Answers
1)
[tex]( 7 + 5i) - ( -9 + i)=7+5i+9-i=(7+9)+(5i-i)=16+4i[/tex]
2)
Distribute 7+7i over 6 and 7i:
[tex]( 7 + 7i)( 6 + 7i)=( 7 + 7i)\cdot6+( 7 + 7i)\cdot7i=42+42i+49i+49i^2[/tex]
collecting similar terms, and substituting [tex]i^2[/tex] with -1 we have:
42+91i-49=-7+91 i
3)
The conjugate of a complex number a+bi is a-bi;
the conjugate of 1+3i is 1-3i.
Thus, using the difference of squares formula we have
[tex](1+3i)(1-3i)=1^2-(3i)^2=1-9i^2=1-9(-1)=1+9=10[/tex]
4)
To write a rational expression ( with a complex number in the denominator) in the standard form, we multiply by the conjugate of the denominator both the numerator and the denominator:
[tex]\displaystyle{ \frac{3}{3-12i}= \frac{3(3+12i)}{(3-12i)(3+12i)}= \frac{9+36i}{3^2-(12i)^2} [/tex]
[tex]=\displaystyle{ \frac{9+36i}{9+144}= \frac{9+36i}{153}= \frac{9}{153}+ \frac{36}{153}i [/tex]
simplifying by 9, the complex number is finally written as
[tex]\displaystyle{ \frac{1}{17}+ \frac{4}{17}i [/tex]
5)
2 complex numbers a+bi, and c+di are equal only if a=c, and b=d. (Where a, b, c, d are real numbers.)
Thus, x=5, and y=3 is the solution to the equation.
Answers:
1) A
2) A
3) B
4) D
5) (x, y) =( 5, 3)
the total points scored in a basketball game can be calculated using the expression 3c - 3 if c = 41, how many points total were scored
Answers
Answer:
its actually 126
Step-by-step explanation:
The total points scored in the basketball game is 120 points.
Explanation:To find the total points scored in a basketball game, we can use the expression 3c - 3. Given that c is equal to 41, we can substitute this value into the expression to calculate the total points.
So, 3c - 3 = 3(41) - 3 = 123 - 3 = 120.
Therefore, a total of 120 points were scored in the basketball game.
the table represent a linear function
X Y
-2 -2
-1 1
0 4
1 7
2 10
what is the slope of the function?
-3
-2
3
4
Answers
Answer:
The answer is 3.
Step-by-step explanation:
In order to determine the slope of the function, we have to know about linear function.
In any linear function, we can get its slope using two pairs of coordinates that belong to the linear function.
m=Slope of the linear function.
P1=(x1,y1)=First pair of coordinate.
P2=(x2,y2)=Second pair of coordinate.
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this case, we have many pairs of coordinates, so we choose two of them:
[tex]P_1=(-1,1)\\P_2=(0,4)[/tex]
Then, we replace them in the slope formula:
[tex]m=\frac{4-1}{0-(-1)}=\frac{3}{1}=3[/tex]
Finally, the slope of the function is 3.
Find the equation of the line that is perpendicular to the line 3x-y=-4 and contains the point (-2,4)
Answers
- 3x - 3x
-------------------
y = -3x - 4
Slope: -3
Opposite Reciprocal Slope: 1/3
Given: (-2,4)
Point Slope Form: y - y₁ = m(x - x₁)
y - 4 = 1/3(x + 2)
y - 4 = 1/3x + 2/3
+ 4 + 4
-----------------------------
y = 1/3x + 14/3
Is 1.34 a non-terminating decimal
Answers
Use the converse of the pythagorean theorem to determine whether the triangle with the given vertices is a right triangle. (2, 1)(6, 4), (–4, 9)
Answers
let : A(2, 1) , B(6, 4) , C(–4, 9)
calculate : AB , AC, BC
AB = √((6-2)² + (4-1)²) = √25 = 5
AC= √((-4-2)² + (9-1)²) = √100 = 10
BC= √((-4-6)² + (9-4)²) = √125
by pythagorean theorem : BC² = AC² + AB²
the triangle is rectangle in : A
A restaurant bill before tax is 65.50.if the sales tax is 8% and the a 18% tip is added what is the total cost
Answers
$65.50 + $5.24 (8%tax ) = $70.74
$70.74 + $12.73 (18%) = $83.47
You have 6 green marbles, 23 blue marbles, and 18 red marbles. what is the probability of choosing a red marble. express your answer as a fraction in lowest terms.
Answers
two cruise ships are sailing towards each other from caribbean islands that are 264 km apart, one ship travels 4 km/h faster than the other. if they both started at the same time. and meet after 6h. how fast is the other ship travelling?
Answers
The slower ship is traveling at a speed of 21 km/h, while the faster ship is traveling at a speed of 25 km/h.
Explanation:This is a mathematics problem that involves solving for unknown speeds with the given conditions. Lets assume the speed of the slower ship is x km/h. Thus, the speed of the faster ship is x+4 km/h. They are moving towards each other, thus their combined speed is (x+x+4) km/h. As speed is distance over time, we can set up the equation: (2x+4)*6 = 264. Solving this equation, we end up with x=21 km/h as the speed of the slower ship, and hence the speed of the faster ship is 25 km/h.
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When constructing inscribed polygons and parallel lines, how are the steps different?
A.) A protractor is used to take measurements.
B.) Four right angles are created.
C.) A compass is used to copy an angle.
D.) There are no differences.
Answers
The answer is C.
hope this helps:D
plz give me brainiest
How do i factor -1/2 out of -1/2x + 6
Answers
-1/2(x - 12)
multiply -2 to the 6 so that when you multiply -1/2 into the expression it will turn into positive 6
hope this helps
A shop makes $37.50 for selling 15 calendars. If the shop wants to make $2450, how many calendars does it need to sell?
Answers
37.50/15=$2.5 per calendar
Next find the amount of calendars by dividing the amount the shop wants to sell by the price per calendar.
2450/2.5=980 calendars
The shop needs to sell 980 calendars to make $2450.
To find out how many calendars the shop needs to sell to make $2450, we first determine the price per calendar by dividing the total amount made from selling a batch of calendars by the number of calendars in that batch. The shop makes $37.50 from selling 15 calendars, so each calendar is sold for $37.50 / 15 = $2.50. To reach the goal of $2450, we need to calculate the number of calendars by dividing the target amount by the price per calendar.
$2450 / $2.50 = 980 calendars
what is the sum of the measures of interior angles of a 15-sides polygon
Answers
sum = (n-2)180
= (15-2)180 = 13×180 = 2340°
Answer:
2340
Step-by-step explanation:
A P E X
The length of a rectangle is 3 meters less than twice the width. if the area of the rectangle is 527 square meters, find the dimensions.
Answers
Answer:
w=17
l=31
Step-by-step explanation:
correct
What is the definition of proof in geometry
Answers
Which statement is true about the difference 2√7-√28
Answers
2*sqrt(7) - sqrt(28) = 2*sqrt(7) - sqrt(4*7)
2*sqrt(7) - sqrt(28) = 2*sqrt(7) - sqrt(4)*sqrt(7)
2*sqrt(7) - sqrt(28) = 2*sqrt(7) - 2*sqrt(7)
2*sqrt(7) - sqrt(28) = (2-2)*sqrt(7)
2*sqrt(7) - sqrt(28) = (0)*sqrt(7)
2*sqrt(7) - sqrt(28) = 0
So the whole complicated expression simplifies to 0 (zero)
This is because sqrt(28) = 2*sqrt(7) when you simplify sqrt(28)
Side Note: "sqrt" is shorthand for "square root"
A circle and a square have the same area. find the length of the diagonal of the square divided by the radius of the circle.
Answers
Let us say that the square have edge = sqrt(pi), then its area is pi since A = edge^2, and therefore the diagonal is pi*sqrt(2).
Meanwhile the circle of radius 1 has area pi since area of circle is A = pi *radius^2.
Therefore we get that the diagonal of the square divided by the radius is:
diagonal / radius = pi*sqrt(2) / 1 = pi*sqrt(2)
An office uses 478 pounds of paper in one week. The paper comes in packages that hold 18 pounds of paper each. How many packages of paper does the office use each week?
Answers
The office uses 26 and a half package of papers.
What is division?Division is the process of splitting a number or an amount into equal parts.
Given that, An office uses 478 pounds of paper in one week. The paper comes in packages that hold 18 pounds of paper each.
To find the number of packages of paper, the office use each week, we will divide the total paper used in one week to paper in 1 package
Therefore, the number of packages of paper, the office use each week = 478 / 18 = 26.5
That means they are using 26 package plus a half package in one week.
Hence, The office uses 26 and a half package of papers.
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A girl takes 6 hours to ride 38.4 kilometers what is her speed
Answers
F= 9/5C + 32, solve for F please.
Answers
A number sentence is said to be true if both numerical expressions are
Answers
JIMMMMMMMMMMMMMMMM :)
Answers
------------------------------------------------
Plug x = -2 into f(x) to get:
f(x) = 9*x + 7
f(-2) = 9*(-2) + 7
f(-2) = -18 + 7
f(-2) = -11
Do the same for g(x):
g(x) = 5^x
g(-2) = 5^(-2)
g(-2) = 0.04
----------------------------------------
Plug x = -1 into f(x) to get:
f(x) = 9*x + 7
f(-1) = 9*(-1) + 7
f(-1) = -9 + 7
f(-1) = -2
Do the same for g(x):
g(x) = 5^x
g(-1) = 5^(-1)
g(-1) = 0.2
----------------------------------------
Plug x = 0 into f(x) to get:
f(x) = 9*x + 7
f(0) = 9*(0) + 7
f(0) = 0 + 7
f(0) = 7
Do the same for g(x):
g(x) = 5^x
g(0) = 5^(0)
g(0) = 1
----------------------------------------
Plug x = 1 into f(x) to get:
f(x) = 9*x + 7
f(1) = 9*(1) + 7
f(1) = 9 + 7
f(1) = 16
Do the same for g(x):
g(x) = 5^x
g(1) = 5^(1)
g(1) = 5
----------------------------------------
Plug x = 2 into f(x) to get:
f(x) = 9*x + 7
f(2) = 9*(2) + 7
f(2) = 18 + 7
f(2) = 25
Do the same for g(x):
g(x) = 5^x
g(2) = 5^(2)
g(2) = 25
----------------------------------------
Write each of the results into the table (again see attached)
In the last row of that table, we have x = 2 lead to f(x) = 25 and g(x) = 25
So f(x) = g(x) has the solution of x = 2
The solution is x = 2 and not x = 25
25 is the output f(x) and g(x) value. It is not the x value.
Answer: choice C) x = 2
-2 1/5
7 1
16 5
25 25
x = 25
(I'm guessing your suppose to find a common answer)
hope this helps
What is the area of the polygon below
Answers
2+1/6y=3x+4 solve for y
Answers
Answer y=18x+12
× 6y throughout
12y + 1 = 18xy + 24y
Send 12y to the other side
12y + 18xy = 1
Y is common
y (12 + 18x) = 1
y = 1/ (12 + 18x)
Hope it helped!
Reflection : Across the line y = 1
Answers
Reflecting across y = 1 means each point's position stays the same horizontally but mirrors vertically across the line.
When reflecting a point or shape across a line, y = 1,
it means that each point is mirrored on the other side of the line while maintaining the same distance from the line.
Here, the line y = 1 acts as a "mirror" or "axis of reflection."
To reflect a point (x, y) across the line y = 1, follow these steps:
Find the vertical distance between the point and the line y = 1. Let's call this distance "d."
If the point is above the line (y > 1), then d = y - 1.
If the point is below the line (y < 1), then d = 1 - y.
Move the point to the same vertical distance on the other side of the line y = 1.
If the point was above the line (y > 1), the new reflected point will be (x, 1 + d).
If the point was below the line (y < 1), the new reflected point will be (x, 1 - d).
Keep in mind that the x-coordinate remains the same in both cases since the line of reflection is vertical (parallel to the y-axis).
By repeating these steps for all points in a shape, obtain the reflection of the entire shape across the line y = 1.
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Which does not describe the same situation?
Answers
Answer:
4. Option 3rd.
Step-by-step explanation:
In this question, three options are given.
We need to describe the same situation.
First option: y = 3 + 6x
this equation represent the equation of a line. In that line all the points are related with each other with same relation.
So, this equation describe the same situation.
Second equation:
y is two more than six times x.
We write this situation in equation form.
y = 6x + 2
this is also describe the same situation.
Third option:
this table shows the x-y relation table.
Here no two points are describe the same situation.
So, option 3rd doesn't describe same situation.
Question 5:
Please share the options
Answer:
Step-by-step explanation:
It is A
A pool is filled at a rate of 105 gal/min. What is the rate in mL per second?
Answers
(There are 3785.41 mL in a gallon.)
There are 60 seconds in minute. Therefore, if we divided the gallon per minute by 60, we can get the answer.
105/60
=1.75 gallon per second
1.75*3785.41
=6624.4675 mL per second
Hope this helps.
-Benjamin
Cynthia besch wants to buy a rug for a room that is 18 ft wide and 30 ft long. she wants to leave a uniform strip of floor around the rug. she can afford to buy 220 square feet of carpeting. what dimensions should the rugâ have?
Answers
How to find the domain of a composite function?
Answers
Prove that acceleration is perpendicular to velocity