Answer:
S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }
Step-by-step explanation:
Remember that the distance between two points (a, b) and (c, d) is given by:
[tex]distance = \sqrt{(a - c)^2 + (b - d)^2}[/tex]
So, here we have that the distance between the point (x, y) and the origin, (0, 0) must have a magnitude of 5 units, then we want to solve:
[tex]5 = \sqrt{(x - 0)^2 + (y - 0)^2} \\5 = \sqrt{x^2 + y^2}[/tex]
If we square both sides, we get
[tex]5^2 = (\sqrt{x^2 + y^2} )^2\\25 = x^2 + y^2[/tex]
Now we want to find all the points (x, y) that meet this condition, suc that:
x ∈ Z
y ∈ Z
So both x and y must be integers.
So here we can just play with different values of x and y.
For example, if we define:
x = 0 we get:
25 = 0^2 + y^2
25 = y^2
√25 = y
Then we can have y = 5 or y = -5
from this we got two points:
(0, 5) and (0, - 5)
if x = 1 we have:
25 = 1^2 + y^2
25 - 1 = y^2
24 = y^2
There is no integer such that its square is equal to 24, so we can stop here.
if x = 2 or - 2, we have:
25 = 2^2 + y^2
25 = 4 + y^2
25 -4 = 21 = y^2
Again, there is no integer such that its square is equal to 21, so we can stop here.
if x = +3 or -3, we have:
25 = 3^2 + y^2
25 = 9 + y^2
25 - 9 = 16 = y^2
√16 = y
then we can have y = 4 or y = -4
from this we got four points:
(3, 4)
(-3, 4)
(3, -4)
(-3, -4)
And for symmetry, if x = 4 or -4 we have the points:
(-4, 3)
(4, 3)
(-4, -3)
(4, -3)
finally, again for symmetry, if we take x = 5 or x = -5 we have the points:
(5,0)
(-5, 0)
Concluding, the set of all possible values (x, y) is:
S = {(0, 5), (0, - 5), (3, 4), (3, -4), (-3, 4), (-3, -4), (4, 3), (4, -3), (-4, 3), (-4, -3), (5,0), (-5, 0) }
Figure PQRS is a parallelogram. The expressions represent the measures of the angles in degrees.
Parallelogram P Q R S is shown. Angle Q is (20 + 2 x) degrees and angle R is (6x) degrees.
What is the value of x?
5
10
20
25
Given:
In parallelogram PQRS, [tex]m\angle Q=(20+2x)^\circ,\ m\angle R=6x^\circ[/tex].
To find:
The value of x.
Solution:
In a parallelogram, the consecutive interior angles are supplementary angles.
In parallelogram PQRS,
[tex]m\angle Q+m\angle R=180^\circ[/tex] (Supplementary angles)
[tex](20+2x)^\circ+(6x)^\circ=180^\circ[/tex]
[tex](20+8x)^\circ=180^\circ[/tex]
[tex]20+8x=180[/tex]
Subtracting 20 from both sides, we get
[tex]8x=180-20[/tex]
[tex]8x=160[/tex]
Divide both sides by 8.
[tex]\dfrac{8x}{8}=\dfrac{160}{8}[/tex]
[tex]x=20[/tex]
Therefore, the correct option is C.
Answer:
c
Step-by-step explanation:
Aere are two squares. A and B.
A
B
The length of each side of square B is 4 cm greater than the length of each side of square A.
The area of square B is 70 cm² greater than the area of square A.
Find the area of square B.
Give your answer correct to 3 significant figures.
You must show all your working.
Answer:
116 cm²
Step-by-step explanation:
a = side length of A
b = side length of B
b = a + 4
b² = a² + 70
(a+4)² = a² + 70
a² + 8a + 16 = a² + 70
8a + 16 = 70
8a = 54
a = 54/8 = 27/4 = 6.75
b² = a² + 70 = 6.75² + 70 = 45.5625 + 70 =
= 115.5625 ≈ 116 cm²
our does your teacher mean 3 significant figures after the decimal point ? then it would be
115.563 cm²
Hello! I wanted answer with explanation
If you didn't understand what question in the screen I can't tell you...
Question: In an election, there are a total of 80,000 voters and there are two candidates A and B. 80% of the voters go for the polls and out of which 60% vote for A. How many voters does B get?
I hope you answer...
Thank you!
Need help with this question
Answer:
B.
Step-by-step explanation:
you know that (a+b+c)/d is the same as a/d + b/d + c/d.
and (a×b)/(c×d) is the same as (a/c)×(b/d).
and the powers of variables subtract when the variables are divided, and the powers add when the variables are multiplied.
14a⁸y³ / 7a⁴y
14/7 = 2
a⁸/a⁴ = a⁴
y³/y = y²
=> 2a⁴y² is the first part. that eliminates already all other answer options. only B can be right.
but let's practice and look at the second part :
-7a⁴y⁵ / 7a⁴y
-7/7 = -1
a⁴/a⁴ = 1
y⁵/y = y⁴
=> -y⁴ is the second part. B is still confirmed.
the third part :
28a¹²y² / 7a⁴y
28/7 = 4
a¹²/a⁴ = a⁸
y²/y = y
=> + 4a⁸y is the third part. B confirmed.
Find the squares of a+3b
Answer:
3ab
Step-by-step explanation:
because it is answer
Triangle ABC is similar to triangle DEF. Find the measure of side EF. Round your
answer to the nearest tenth.
B
50
F
D
41
HELP PLEASEEEE
Answer:
83.5units
Step-by-step explanation:
Find the diagram attached
Since both triangles are similar, then;
AB/DB = BC/EF
11/54 = 17/EF
Cross multiply
11EF = 17 * 54
11EF = 918
EF = 918/11
EF = 83.5
Hence the length of EF to the nearest tenth is 83.5units
what is the simplist form of 240/1000
Divide by 100 to reduce it to 24/100
Now divide by 4 to get 6/25
The simplest form is 6/25
Area of base=
A)8 square units
B)6 square units
C)12 square units
Answer:
its 8
Step-by-step explanation:
4 times 2 is 8 and you cant get 6 or 12
Answer:
A
Step-by-step explanation:
Area of base = length x width = 4 * 2 = 8 square units
A number line is shown below. The
numbers 0 and 1 are marked on the line, as are two
other numbers a and b.
Which of the following numbers is negative? Choose
all that apply.
a-b
ab
-b
ab + 1
Answer:
-b
Step-by-step explanation:
1 is b and a negative sign shows that the number is a negative in -b there is a negative sign and b = 1 so this -b shows the number -1
The equation |x-3| = 4 has what solutions?
Answer:
x-3=4
x=4+3
X=7
or
x-3=-4
x=-4+3
x=-1
-1 and 7
Step-by-step explanation:
Any equation within the | | notation is an absolute value, where the the value of the equation can only be positive.
So within the notation, we have two possibilities to the solution, a positive and negative value.
In other words, |4| = 4 and |-4| = 4
Hence, we only need to substitute x with an appropriate integer to satisfy the answer.
|x - 3| = 4
substitute x = 7
|7 - 3| = 4
|4| = 4
substitute x = -1
|-1 - 3| = 4
|-4| = 4
Therefore the solutions to x is x = 7 and x = -1.
Determine the value of x.
A right triangle has 2 sides with a length of 6 centimeters. The length of the hypotenuse is x centimeters.
Answer:
6^2 + 6^2 = 72 sqrt(72) = 8.49
Step-by-step explanation:
use pythagorean therom a^2 + b^2 = c^2
where c is the hyp.
Answer: 6 sqrt 2
Step-by-step explanation:
can someone help please
Answer:
3a. (i). Sequence [tex]V_{n}[/tex] is in Arithematic
(ii). Sequence [tex]W_{n}[/tex] is in Geometric
3b. 2520 Sum of First 20 Arithmetic Sequence
3c. 98292 Sum of First 13 Geometric Sequence
Step-by-step explanation:
According to the Question,
3a. (i) Arithmetic Sequence ([tex]V_{n}[/tex]) = 12 , 24 , 36 , 48 .....
it is a sequence of numbers such that the difference between the consecutive terms is same. example → 24+12=12 , 36-24=12 , 48-36=12 ∵Common Difference=12
(ii) Geometric Sequence ([tex]W_{n}[/tex]) = 12 , 24 , 48 , 96 .....
A geometric series is a series for which the ratio of each two consecutive terms is a constant function. example → 24/12= 2 , 48/24= 2 , 96/48= 2 ∵Common Ratio=2
3b. Sum of first 20 terms of Arithematic sequence, [tex]S_{n}=\frac{n}{2}[2a + (n-1) d][/tex]
(Where, a=first term of sequence , n= number of term & d=common difference)
[tex]S_{n}[/tex]=10[2×12 + 19×12]
[tex]S_{n}[/tex] =10×252 ⇔ 2520
3c. Sum Of First 13 term of a geometric sequence, [tex]S_{n}= \frac{a(r^{n}-1) }{r-1}[/tex]
(Where, a=first term of sequence , n= number of term & r= common ratio)
[tex]S_{n}[/tex]=12([tex]2^{13}[/tex]-1) / 2-1
[tex]S_{n}[/tex]=12×8191 ⇔ 98292
I really need help with this question as fast as possible
Answer:
-1625
Step-by-step explanation:
→ (-125) × 5 + (-125) × 8
Taking (-125) as in common,
→ (-125) × (8 + 5)
→ (-125) × 13
→ -1625
7.80/hour=________ cents/minute?
Answer: 0.13 cents per minute.
Step-by-step explanation:
7.80 divided by 60(min per hour.)= .13 cents.
Which row in the table is the closest to the actual solution?
Answer:
0.8
Step-by-step explanation: 6 22 6 06
I plotted both sides of the equation using DEMOS graphing calculator and located the intersection at (0.779, 2.135) I found that easier than finding the delta difference of both sides of the equation for the table or solving for x.
Write this number in scientific rotation. 1,490,000.
Answer and explain.
Answer:
4.9 x 10^5
Step-by-step explanation:
the answer is 4.9 x 10^5
Amber works as a waitress at a restaurant. She earns an hourly wage and also earns tips. One night, she worked 6 hours and earned a total of $69.20, which included tips of $15.50. Explain how the equation 6w + 15.5 = 69.2 represents this situation. Then, calculate Amber’s hourly wage.
Answer:
Hey there!
The given equation helps us understand the relationship between Amber's tips earned and the money she earned through her hourly wage. This information will add up to equal a grand total of $69.20.
We know that Amber earns $15.50 in tips during her 6 hour shift. Therefore, this is not considered part of her wage. This would be one of the constants of our equation.
We also know that Amber earns a fixed hourly wage, but we don't know what this wage is. We need to find w.
[tex]6w+15.5=\$69.20[/tex]
Subtract 15.5 from both sides of the equation (and get rid of the currency symbol).
[tex]6w=69.20-15.5\\6w=53.7[/tex]
Divide both sides of the equation by 6.
[tex]\displaystyle \frac{6w}{6}=\frac{53.7}{6}\\\\w=8.95[/tex]
Therefore, Amber's hourly wage is $8.95.
Manipulate the radius of the sphere, setting it to different values. In the table below, record each radius you chose and the exact volume of the sphere (in terms of π). Also calculate the decimal value of each volume, and verify that it matches the volume displayed by the tool. (You might see some discrepancies in the tool due to rounding of decimals.)
Answer:
641654654
Step-by-step explanation:
Answer:
1) r=9 v=972
2) r=6 v=288
3) r=12 v=2,304
Step-by-step explanation:
Sample Answer on edmentum
The radius of the circle is 7 cm. What is the area of the shaded part? Use π = 227
Answer:
227 * 7^2
Put into calculator
Step-by-step explanation:
Area of a circle is pi * r^2 (pi times radius squared)
Just put the numbers in
227 * 7^2
Put into calculator and there you go
m∠RST =______because they are __________ (Fill in the blanks)
Answer:
∠RST = ∠SRU because they are alternate angles.
Step-by-step explanation:
Hope it helps .
What 2 numbers add to get -9 and multiply to get -30?
Answer:
[tex]y_{1}=-\frac{9}{2}-\frac{\sqrt{201}}{2}[/tex] or [tex]y_{2}=-\frac{9}{2}+\frac{\sqrt{201}}{2}[/tex]
[tex]x_{1}=-\frac{9}{2}-\frac{\sqrt{201}}{2}[/tex] or [tex]x_{2}=-\frac{9}{2}+\frac{\sqrt{201}}{2}[/tex]
Step-by-step explanation:
Let be x the first number and y the second number.
So we have:
[tex]x+y=-9[/tex] (1)
[tex]x*y=-30[/tex] (2)
Solve x from equation 1 and put it into equation 2
[tex]x=-9-y[/tex]
[tex](-9-y)*y=-30[/tex]
[tex]-9y-y^{2}=-30[/tex]
[tex]y^{2}+9y-30=0[/tex]
Solving this quadratic equation and put it on the equation (1) the solutions will be:
[tex]y_{1}=-\frac{9}{2}-\frac{\sqrt{201}}{2}[/tex] or [tex]y_{2}=-\frac{9}{2}+\frac{\sqrt{201}}{2}[/tex]
[tex]x_{1}=-\frac{9}{2}-\frac{\sqrt{201}}{2}[/tex] or [tex]x_{2}=-\frac{9}{2}+\frac{\sqrt{201}}{2}[/tex]
I hope it helps you!
A line has the equation 3x–4y–12=0 what is the slope of this line
Answer:
The slope of this line is 3/4.
Step-by-step explanation:
Solving this equation 3x–4y–12=0 for y puts the equation into the form
y = mx + b, where m is the slope of the line.
One way of solving for 4y here is to add 4y to both sides, obtaining:
3x - 12 = 4y
Dividing all three terms by 4 yields
y = (3/4)x - 3
The slope of this line is 3/4.
A used automobile dealership recently reduced the price of a used compact car by %. If the price of the car before discount was $, find the discount and the new price.
Answer:
$1674
$16926
Step-by-step explanation:
A used automobile dealership recently reduced the price of a used compact car by 9%. If the price of the car before the discount was $18,600, find the discount and the new price?
Discount = percentage discount x original price
0.09 x $18,600 = $1674
New price = original price - discount
$18,600 - $1674 = $16926
The points A, B, C and D lie on a circle centre O.
Angle AOB = 90° angle COD= 50° and angle BCD= 1239
The line DT is a tangent to the circle at D.
Find
(a) angle OCD
The measure of angle OCD from the given figure is 58°.
Given that, the points A, B, C and D lie on a circle Centre O.
What is the circle?A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) on the plane. The fixed point is called the origin or center of the circle and the fixed distance of the points from the origin is called the radius.
Here, OC and OB are radius of a circle, then BOC is isosceles triangle
Now, ∠BOC+∠OBC+∠OCB=180°
50°+∠OBC+∠OBC=180°
⇒ 2∠OBC=130°
⇒ ∠OBC=65°
Here, ∠OCD=∠BCD-65°
⇒ x=123-65=58°
Hence, the measure of angle OCD from the given figure is 58°.
To learn more about the circle visit:
https://brainly.com/question/11833983.
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Which steps can be done to both sides of the equation to determine the value of x ?
3.2.2 - 9.6 = 38.4
A. subtract 9.6, then multiply by 3.2.
B. Add 9.6, then multiply by 3.2.
C. Add 9.6, then divide by 3.2.
D. Subtract 9.6, then divide by 3.2.
Answer:
C. Add 9.6, then divide by 3.2.
Step-by-step explanation:
[tex]3.2x−9.6=38.4[/tex]
[tex]3.2x=38.4+9.6[/tex]
[tex]3.2x=48[/tex]
[tex]x = \frac{48}{3.2} [/tex][tex]x = 15[/tex]
Hope it is helpful...Please help me !!!
What is the image of (-8,-1) after a reflection over the line y = -x?
Answer:
Step-by-step explanation:
Reflection of (-8 , -1) over y = -x is (-1 , 8)
Image of (x , y) over the line y = -x is (y, -x)
Answer:
reflection on the y axis (x,y)=(-x,y)
(-8,-1)=(8,-1)
Step-by-step explanation:
hope this is helpful
Brian spends 3 5 of his wages on rent and 1 3 on food. If he makes £735 per week, how much money does he have left?
Answer :
Brian has $49 left.
Step by step explanation :
Step 1 : Find how much money Brian spends on rent and food.
First question we should be asking is what is 3/5 of 735?
Let's find that.
[tex]\frac{3}{5}[/tex] * [tex]\frac{735}{1}[/tex]
= [tex]\frac{(3)(735)}{(5)(1)}[/tex]
= [tex]\frac{2205}{5}[/tex]
= 441
We know Brian spends $441 on rent. Now we find how much he spends on food.
[tex]\frac{1}{3} * \frac{735}{1}[/tex]
= [tex]\frac{(1)(735)}{(3)(1)}[/tex]
= [tex]\frac{735}{3}[/tex]
= 245
Brian spends $245 on food.
Step 2 : Add what he spends on rent and food together.
$441 + $245 = $686
Step 3 : To find out how much money Brian has left, we subtract $686 from $735.
$735 - $686 = $49
Conclusion : Brian has $49 left.
Hope this helps, please mark brainliest if possible. Have a nice day.
John is buying new shoes. He finds the shoes he wants on sale for 30%, and the original price is $88. How much will he pay for the shoes?
Answer:
61.6 dollars
Step-by-step explanation:
So, lets go over what we know:
The shows orginally cost 88 dollars.
They are 30% less than that.
This basically means that the shoes will cost 70 percent of their orginal price.
We can basically find the new cost by multiplying the 88 dollars by the 70 percent.
Or, multiplying 88 by 0.7, which is the decimal form of 70%.
88*0.7=61.6
How did I get this?
Multiply 80 by 0.7:
7*8=56
We have 0.7 so it = 5.6
However, it's tens place is 80, not 8, so it will be = 56
It is the same thing in the ones place, however it is 8 not 80, so it will be 0.7*8
= 5.6
56+5.6=61.6
So 61.6 is our answer.
Hope this helps!
Answer:
$61.60
Step-by-step explanation:
the other answer is correct.
just to add some explanation about the % considerations.
we know $88 is 100%
in order to get any other % value, we need to divide the original value by 100 (that gives us 1%), and then multiply with the number of % we want to have - in our example 70, as the discount is 30% (so the remaining part is 70% of the original price).
so, in order to get 70% we actually have to do the above things and divide by 100 and multiply by 70.
70% = (100% / 100) × 70 = 100% × 70 / 100
70 / 100 = 0.7 (that is how answer 1 actually got that multiplication factor)
70% = 100% × 0.7
70% = $88 × 0.7 = $61.60
If a,b, and c are three different numbers, which of the following equations has no solutions?
A. ax= bx+c
B. ax+b=ax+c
C. ax+b=ax+b
Answer:
C
Step-by-step explanation:
if you divide both sides by ax+b you get 1=1 which is not a solution for x.
DEF is a dilation image of ABC. What is the scale factor?
2
1/2
1/4
2/3
Answer:
Option (2)
Step-by-step explanation:
ΔDEF is a dilation image of ΔABC.
Rule for the dilation,
Scale factor = [tex]\frac{\text{Length of one side of the image triangle}}{\text{Length of one side of the original triangle}}[/tex]
= [tex]\frac{DE}{AB}[/tex]
= [tex]\frac{4}{8}[/tex]
= [tex]\frac{1}{2}[/tex]
Therefore, scale factor by which ΔABC is dilated is [tex]\frac{1}{2}[/tex].
Option (2) will be the correct option.