Answer:
The image of the circle is 9·x² + 9·y² - 42·x + 33·y = 22
Step-by-step explanation:
We convert the equation to the form (x - h)² + (y - k)² = r²
Where:
(h, k) = Coordinates of the center of the circle
We therefore have;
x² + y² - 2·x + 3·y = 8 which gives;
x² - 2·x + 1 - 1 + y² + 3·y + (3/2)² - (3/2)² = 8
(x - 1)² + (y + 3/2)² - 1 - (3/2)² = 8
(x - 1)² + (y + 3/2)² = 8 + 1 + (3/2)² = 45/4
Therefore, the center = (1, -3/2) and the radius = √5 × 3/2
The line joining the centers of the actual (1, -3/2) and reflected circle (h, k) is bisected by the line of reflection, therefore the midpoint of the line is on the line of reflection with coordinates;
Midpoint between (1, -3/2) and (h, k) = [tex]\left (\dfrac{{h - 1}}{2}, \, \dfrac{k - 3/2}{2} \right )[/tex]
Which gives;
y = 2·x - 3 being equivalent to [tex]\dfrac{k - 3/2}{2} = 2\times\dfrac{{h - 1}}{2} - 3[/tex]
Which gives;
4·h -2·k -13 = 0.......(1)
Similarly the slope of the reflecting line is perpendicular to the line joining the centers of the actual and reflected circles
Therefore;
The slope of the line, y = 2·x - 3 = 2, hence we have;
[tex]\dfrac{\left ( \dfrac{k - 3/2}{2} \right ) + 3/2}{\left (\dfrac{{h - 1}}{2}-1 \right )} = \dfrac{1}{2}[/tex]
Which gives;
2·h -4·k -12 = 0.......(2)
Multiplying equation (2) and subtracting from equation (1) gives
4·h -2·k -13 - 2×(2·h -4·k -12) = 0
6·k + 11 = 0
k = -11/6
From which we have;
2·h -4×(-11/6) -12 = 0
Hence;
h = 7/3
Therefore, the center of the reflected circle = (7/3, -11/6)
The equation of the reflected circle is therefore;
(x - 7/3)² + (y + 11/6)² = 45/4
Which gives;
9·x² + 9·y² - 42·x + 33·y - 22 = 0
or x² + y² - 42/9·x + 33/9·y = 22/9.
I will give brainliest answer
Answer:
The answer would be 12.571428571 units or 12.57units.
a box is 24cm by 15cm by 10cm. this box will packed with smaller boxes of paper clips which are 6cm by 3cm by 5cm . what is the largest number of boxes of paper clips that will fit in the bigger box?
Answer:
40 boxes
Step-by-step explanation:
box = 24 x 15 x 10 = 3600 cm
1 paper clip box = 6 x 3 x 5 = 90 cm
3600/90 = 40
so 40 boxes of paper clips will fit
Answer:
40 boxes
box = 24 x 15 x 10 = 3600 cm
A paper clip box = 6 x 3 x 5 = 90 cm
3600/90 = 40
so 40 boxes of paper clips
I really need help on these 2 questions. Please!!!!
Two trains leave the station at the same time, one heading east and the other west. The eastbound train travels at 80 miles per hour. The westbound train
travels at 70 miles per hour. How long will it take for the two trains to be 360 miles apart?
Do not do any rounding.
Answer:
2.4 hours
Step-by-step explanation:
after an hour the distance between them will be 80+70=150 miles
1 hour .......150 m
x hours .......360 m
x*150=360
x=360/150
x=2.4 hours
Answer: 2.4 hours
Step-by-step explanation:
Distance = speed x time
1st train = 80t
2nd train = 70t
80t + 70t = 360
t = 360/150 = 2.4 hours
If ABC is reflecting across the y-axis ,what are the coordinates of c’?
Express the quotient in simplest form.
Answer:
(x-2)
----------------
x^3
Step-by-step explanation:
(x^2 -4) x^3 -x^2 -6x
------------ ÷ ---------------------
x^3 + 7x^2 x^2 +4x -21
Copy dot flip
(x^2 -4) x^2 +4x -21
------------ * ---------------------
x^3 + 7x^2 x^3 -x^2 -6x
Factor
(x-2)(x+2) (x+7)(x-3)
------------ * ---------------------
x^2(x+7) x(x-3)(x+2)
Cancel like terms
(x-2) 1
------------ * ---------------------
x^2 x
(x-2)
----------------
x^3
I’ll mark you brainliest
Answer:
42
Step-by-step explanation:
In a rectangle, the diagonals have the same length. Therefore:
[tex]3x+6=5x-18 \\\\3x+24=5x \\\\ 24=2x \\\\x=12 \\\\BD=5(12)-18=60-18=42[/tex]
Hope this helps!
Answer:
BD = 42
x=12 is found below as a way to find x
We can find 42 by adding together the equations
3x+6 = 5x-18
+18 = 5x(-3x-6)
18 + 6 = 2x
24 = 2x
x= 12
We can then plug in for 5x and 3x
as BD = 5x-18 = 3x+6
5(12) = 60 -18 = 42 and 3(12) =36+6 = 42
To find line BD = 42
Step-by-step explanation:
3x+6= 42
3x = 42-6
3x = 36
x = 12
5x-18 = 60
5x = 60- 18
5x = 42
x=12
Determine whether the proportion is true or false. 6 miles / 30 quarts = 30 miles/ 15 quarts
Answer:
False
Step-by-step explanation:
6 miles / 30 quarts
Divide by 6
1 miles / 5 quarts
30 miles /15 quarts
Divide by 15
2 miles/1 quart
These are not the same so they are not proportional
How many water do you need to mix with 200ml of shampoo? How many water should you mix with 500ml of shampoo? If the correct amount of water is mixed with 400ml of shampoo will the mixture fit in a 2500ml container?
Answer:
200 mL shampoo - 1050 ml water
500 mL shampoo - 2625 mL water
Step-by-step explanation:
1) 400 ml shampoo , should be mixed 2500 - 400 = 2100 mL of water.
2) 400 mL shampoo - 2100 mL water
200 mL shampoo - x mL water
x = 200*2100/400 = 1050 mL water
3) 400 mL shampoo - 2100 mL water
500 mL shampoo - x mL water
x = 500*2100/400 = 2625 mL water
Determine the value of k. answers: A) 18° B) 180° C) 108° D) 97°
Answer:
C) 108°
Step-by-step explanation:
72°+k°=180° (straight line)
Subtract 72° from both sides
k°=108°
Our answer is C)108°.
Value of k = 108°
The correct option is C.
What is exterior angle?Exterior angles are angles that are parallel to the inner angles of a polygon but lie on the outside of it. The measure of an exterior angle is equal to the sum of the two internal opposite angles.
Given,
In a triangle,
Interior angles are
A = 72°,
B = 83° and
C = 25°
exterior angle A = k°
Exterior angle A = Interior angle B + Interior angle C
k = 83° + 25°
k = 108°
Hence, 108° is the value of k.
Learn more about exterior angle here:
brainly.com/question/28835566
#SPJ2
Plz Help!
Hank has cards that are 4 inches by 2 inches. A stack of these cards fits inside the box shown and uses up 8 cubic inches of volume.
L 4 in.
W 2 in.
H 2 in.
Part 1 out of 2
How tall is the stack of cards?
The stack is ___ inch(es) tall.
What is the range of the function shown in this table?
х 3 4 5 6 y 4 4 2 5
Answer:
2,4,5
Step-by-step explanation:
Do not repeat numbers, u need to put them in order from least to greatest, and range is for the y
^ this week, The sparkling water was 4 for $5 , the regular was $1.69
The function ƒ(x) = 4x + 1 is transformed to g(x) = 2x + 1. What type of transformation has occurred? A) Reflection and Vertical Translation B) Rotation C) Reflection D) Rotation and Vertical Translation
Answer:
B) Rotation
Step-by-step explanation:
The only difference between functions f(x) and g(x) is the slope. To get from f(x)=4x+1 to g(x)=2x+1, you would need to rotate slightly clockwise about point (0,1) - the y-intercept. This would make the graph less steep (2x is less steep than 4x) while still retaining the (0,1) y intercept.
Answer:
rotation
Step-by-step explanation:
Triangle JKL has vertex coordinates J(0,-3), K(-1,0), and L(-2,-1). It is reflected across the line y = x. What are the coordinates of J’K’L?
A. J’(0,-3), K’(1,0), L’(2,-1)
B. J’(-3,0), K’(0,-1), L’(-1,-2)
C. J’(3,0), K’(0,1), L’(1,-2)
D. J’(0,3), K’(-1,0), L’(-2,1)
Answer:
B
Step-by-step explanation:
Under a reflection in the line y = x
a point (x, y ) → (y, x ), thus
J(0, - 3 ) → J'(- 3, 0 )
K(- 1, 0 ) → K'(0, - 1 )
L(- 2, - 1 ) → L'(- 1, - 2 )
Answer:
yee its B
Step-by-step explanation:
UGH HELP :(
Use the distributive property to write the expression without parentheses. Then simplify the result, if possible.
5(4x+3)
Answer:
5(4x+3)
5×4x + 5×3
20x+15
Javier constructed a square by drawing two congruent triangles. Which shows one of the triangles he could have used? A triangle with angles 45 degrees, 45 degrees, and 90 degrees. 2 sides are congruent. A triangle with angles 55 degrees, 35 degrees, and 90 degrees. A triangle with angles 65 degrees, 65 degrees, and blank. A triangle with 3 angles of 60 degrees. All sides are congruent.
Answer:
The answer is A triangle with 45 degrees, 45 degrees, and 90 degrees
Step-by-step explanation:
can we use a ruler to measure angles yes or no an why
Answer:
Step-by-step explanation:
No because rulers measure distance not angles. Rulers also do not have all the angles on them as they are not a protractor
Graph the equation by plotting three
points. If all three are correct, the line
will appear.
2y = 3x + 11
Answer:
y=3/2x+11/2
Step-by-step explanation:
divide the whole thing by 2
2y=3x+11 divided by 2 equals
y-3/2x+11/2
then just plug in the 3 points
someone plz help i need it in like 3 minutes
Answer:
B
Step-by-step explanation:
A: -(3/-2)=-(-3/2)=3/2
B:3/-2=-3/2
C:-(-3/2)=3/2
D:-3/-2=3/2
If 1/3 of a gallon of paint covers 1/9 of a gate, then how many gallons of paint are needed to cover the entire gate?
Answer:
3 gallons
Step-by-step explanation:
So just multiply by 9.
You get 3.
Answer:
3 gallons
Step-by-step explanation:
divide 1 / 3 by 1/9
=) 1/3 ÷ 1/9
=)1/3 × 9/1
=)9/3
=)3
therefour your answer is 3 gallons
Please do 1,2,3 for 10 points
Answers:
-218-2please see the attached picture for full solution
Hope it helps
Good luck on your assignment
Answer:
1. -2
2. 18
3. -2
Step-by-step explanation:
In the following explanations "x" is a variable which represents "a number" given in the problems.
1. You can set up a simple equation " x + 7 = 5 " because you are increasing a number to get the answer. From there you can subtract 5-7 and you'll get -2, the answer to the first one.
2. This time the number is decreased by 6, and the answer is 12. Since it's being decreased, you'll set up the equation like this: " x - 6 = 12 ". For this problem you can do 12 + 6 = 18, which is your answer.
3. A number "added" to -3 is -5. The number following 'is' will almost always be the answer you're looking for, so we can do x + (-3) = -5 . From there just add 3 to each side, and you'll get -2 + (-3) = -5.
If you take one thing away from this, let it be the following:
The methods that I used do work, but something I'd suggest trying in the future is carrying over the same number to the other side of the equation.
If you're struggling on these problems, this might help.
The way this works is simple, lets say you have this equation:
x + 5 = 10
The best and most efficient way of solving this problem is by taking a number from one side, and moving it to the other side. It seems confusing at first, but isn't all that hard once you figure it out. So for this problem:
x + 5 = 10
- 5 -5
Now you only have 'x' on the left side of the equation. This is the end goal. Once you get x on one side of the equation, the answer tends to be on the other side.
So:
x + 5 = 10
- 5 -5
x + 0 = 5 <- this is what you want.
x = 5
Hope this helps, and hope you learned more from this then an hour and a half at school :P
help plz!
Find the width of a cereal box that has a volume of 6,860 cm3 and is 35 cm long and 28 cm high.
Answer:
The width is 7 cm
Step-by-step explanation:
The volume of a cereal box is
V = l*w*h
6860 = 35 * w * 28
6860 =980 w
Divide each side by 980
6860/980 = w
7 = w
Answer:
35*28=6,860
980 = 6,860
divide by 980 to both side
_980__ = _6,860_
980 980
x = 7
Step-by-step explanation:
Can anybody tell me the answer to this question in the picture?
Answer:
Option 2
Step-by-step explanation:
Group 2 does have a greater median. And group 1 is less spread out
Function gis transformed to obtain function has shown.
g(x + 2) - 5
Which statement describes how the graph of his different from the graph of g?
A
The graph of h is the graph of g shifted 5 units to the left and 2 units down.
B.
The graph of h is the graph of g shifted 5 units to the right and 2 units up.
The graph of h is the graph of g shifted 2 units to the left and 5 units down.
C.
D.
The graph of h is the graph of g shifted 2 units to the right and 5 units up.
Reset
Next
Answer:
dont get mad if I got it wrong but I think its C
A certain bag of potting soil is 1/4 peat moss, and the rest is dirt. What part is dirt?
1/4
А
B
3/8
3/4
D
7/8
E
1-1/4
Answer:
[tex]D = 1 - \frac{1}{4}[/tex]
[tex]D = \frac{3}{4}[/tex]
Step-by-step explanation:
Given:
1 bag of potting soil
[tex]Peat Moss = \frac{1}{4}[/tex]
Required
What part is dirt?
The whole bag of potting soil is represented as 1;
Let P represent Peat Moss and D represented Dirt; Such that
[tex]P + D = 1[/tex]
Subtract P from both sides
[tex]P - P + D = 1 - P[/tex]
[tex]D = 1 - P[/tex]
Substitute [tex]\frac{1}{4}[/tex] for P
[tex]D = 1 - \frac{1}{4}[/tex]
Take LCM
[tex]D = \frac{4-1}{4}[/tex]
[tex]D = \frac{3}{4}[/tex]
Hence, [tex]1 - \frac{1}{4}[/tex] or [tex]\frac{3}{4}[/tex] of the potting soil is Dirt
x+y= 2
y=-12? + 3
\right.V)
1. In two or more complete sentences, explain how to solve the system of equations algebraically.
2. Solve the system of equations. In your final answer, include all of your work.
Answer:
11
Step-by-step explanation:
11
Find the product:
-2x(-y - 3x + 3)
Answer:
[tex]=2xy+6x^2-6x[/tex]
Step-by-step explanation:
[tex]-2x\left(-y-3x+3\right)\\\mathrm{Distribute\:parentheses}\\=\left(-2x\right)\left(-y\right)+\left(-2x\right)\left(-3x\right)+\left(-2x\right)\cdot \:3\\\mathrm{Apply\:minus-plus\:rules}\\\left(-a\right)\left(-b\right)=ab,\:\:+\left(-a\right)=-a\\=2xy+2\cdot \:3xx-2\cdot \:3x\\\mathrm{Simplify}\:2xy+2\cdot \:3xx-2\cdot \:3x:\quad 2xy+6x^2-6x\\2xy+2\cdot \:3xx-2\cdot \:3x\\2\cdot \:3xx=6x^2\\2\cdot \:3x=6x\\=2xy+6x^2-6x[/tex]
please see the attached picture for full solution
Hope it helps
Good luck on your assignment
How to convert 1/4 to decimal form. How do I start that ? I obviously know it’s .25 but how do I show work ?
Answer:
(1/4 x 1 ) = 0.25
or (1/4) x 1 = 0.25
Step-by-step explanation:
We are doing the opposite to finding 25%
Which is 1/4 of 100%
We do this an opposite (not as inverse)
To find percentage increase as you can compare below.
or as percentage increase
230 x 0.25 (x 100) = 287.50
Even though we are not finding increase for 1/4 by changing it to decimal form, this practice does use the (x1) element in brackets and does identify the distribution.
Answer:
Use a calculator or use long division. See long division below.
Step-by-step explanation:
Use a calculator or use long division.
Long division:
------------------------------
4 | 1
4 does not go into 1, so add a decimal pace to 1.
0.
------------------------------
4 | 1.0
4 goes into 10 2 times.
0.2
------------------------------
4 | 1.0
- 8
--------------
2
There is a remainder, so bring down another 0.
0.2
------------------------------
4 | 1.00
- 8
--------------
20
4 goes into 20 5 times.
0.25
------------------------------
4 | 1.00
- 8
--------------
20
- 20
--------------
0
The remainder is zero.
1/4 = 0.25
What's the largest eight-digit base 2 integer? Express your answer in base 10.
Answer:
[tex]11111111_{2} =255_{10}[/tex]
Step-by-step explanation:
The largest eight-digit base 2 integer is 11111111.
[tex]\begin{array}{rcr}1\times 2^{7} & = & 128\\1\times 2^{6} & = & 64\\1\times 2^{5} & = & 32\\1\times 2^{4} & = & 16\\1\times 2^{3} & = & 8\\1\times 2^{2} & = & 4\\1\times 2^{1} & = & 2\\1\times 2^{0} & = & 1\\\mathbf{11111111_{2}} & = & \mathbf{255_{10}}\\\end{array}[/tex]
Answer:1111111
Step-by-step explanation:
The largest eight-digit base 2 integer is 11111111