Answer:
[tex]\sf (x+2)^2+(y-2)^2=2[/tex]
Step-by-step explanation:
If RS is the diameter of the circle, then the midpoint of RS will be the center of the circle.
[tex]\sf midpoint=\left(\dfrac{x_s-x_r}{2}+x_r,\dfrac{y_s-y_r}{2}+y_r \right)[/tex]
[tex]\sf =\left(\dfrac{-1-(-3)}{2}+(-3),\dfrac{3-1}{2}+1 \right)[/tex]
[tex]\sf =(-2, 2)[/tex]
Equation of a circle: [tex]\sf (x-h)^2+(y-k)^2=r^2[/tex]
(where (h, k) is the center and r is the radius)
Substituting found center (-2, 2) into the equation of a circle:
[tex]\sf \implies (x-(-2))^2+(y-2)^2=r^2[/tex]
[tex]\sf \implies (x+2)^2+(y-2)^2=r^2[/tex]
To find [tex]\sf r^2[/tex], simply substitute one of the points into the equation and solve:
[tex]\sf \implies (-3+2)^2+(1-2)^2=r^2[/tex]
[tex]\sf \implies 1+1=r^2[/tex]
[tex]\sf \implies r^2=2[/tex]
Therefore, the equation of the circle is:
[tex]\sf (x+2)^2+(y-2)^2=2[/tex]
Help picture below problem 12
Answer:
78°
Step-by-step explanation:
Angles on a straight line = 180°
AD is the straight line
Angle BFA = 48
Angle CFD = 54
54 + 48 = 102
180 - 102 = 78
Therefore, Angle BFC = 78°
A square with diagonals is shown. The distance from one point to the middle point is 3. The length from the center point to another point is 3.
What is the approximate side length of the square?
3.0 units
3.5 units
4.2 units
4.9 units
Step-by-step explanation:
in a square 2 sides with a diagonal creates a right-angled triangle, with the diagonal being the Hypotenuse (the side opposite of the 90° angle).
the diagonal is 3+3 = 6 units long.
let's call the square side length "s".
then we have via Pythagoras
6² = s² + s² = 2s²
36 = 2s²
18 = s²
s = 4.242640687 ≈ 4.2 units
On the same coordinate plane mark all points (x y) that satisfy the rule y=3x-2 SHOW GRAPH
Answer:
*View the attached graph*
Step-by-step explanation:
Hope it helps!
Find the simple interest on the loan of $2500 for 2 years at 5%.
$
(Simplify your answer. Round to the nearest cent as needed.)
Answer:
Step-by-step explanation:
simple interest=prt
p=principle amount
r=rate
t=time
here p=$2500
r=5 %=0.05
t=2 years
simple interest=2500×2×0.05=$250
The simple interest on the loan of $2500 for 2 years at 5% is $250
How to determine the value?The formula for calculating simple interest is expressed as;
I = PRT/100
Such that the parameters of the formula are;
P is the principal amountI is the simple interestR is the interest rateT is the timeNow, substitute the values, we get;
Simple interest = 2500 × 5 × 2/100
Multiply the values
Simple interest =25, 000/100
Simple interest =$250
Learn about simple interest at: https://brainly.com/question/25793394
#SPJ2
A rectangular container that has a length of 30 cm, a width of 20 cm, and a height of 24 cm is filled with water to a depth of 15 cm. When an additional 6.5 liters of water are poured into the container, some water overflows
Answer:
Step-by-step explanation:
1.1 L
Given:
A rectangular container that has:
a length of 30 cm,
a width of 20 cm, and
a height of 24 cm
It is filled with water to a depth of 15 cm.
When an additional 6.5 L of water are poured into the container, some water overflows.
Question:
How many liters of water overflow the container?
The Process:
Step-1: calculate the volume of rectangular container
The volume of rectangular container is 14,400 cm³, then converted to 14,4 L.
Step-2: calculate the volume of water filled in the container to a depth of 15 cm
The volume of water filled is 9,000³ cm, then converted to 9 L.
Step-3: calculate the volume of water overflow when an additional 6.5 L of water is poured into a container.
The volume of water overflow equals the initial water volume is added to the additional water volume then subtracted by the container volume.
The volume of water overflow =
Thus, the volume of water overflow of the container is 1.1 L.
99 PTS PLS HELP! Data Set 1 has a mean of 152.7 and a MAD of 2.5.
Data Set 2 has a mean of 170.2 and a MAD of 1.7.
What can be concluded about the two distributions?
Select each correct answer.
The means-to-MAD ratio is 10.
The distributions are different.
The distributions are somewhat similar.
The means-to-MAD ratio is 7.
Answer:
the means to and reroof is 10
the distributions are somewhat similar
Step-by-step explanation:
In the game of roulette, a player can place a $7 bet on the number 5 and have a 1/38 probability of winning. If the metal ball lands on , the player gets to keep the $7 paid to play the game and the player is awarded an additional $245. Otherwise, the player is awarded nothing and the casino takes the player's $7. What is the expected value of the game to the player? If you played the game 1000 times, how much would you expect to lose? Question content area bottom Part 1 The expected value is $ -0.37. the player would expect to lose about $
Answer:
973.68 times
Step-by-step explanation:
Since you would expect to win 1 in 38, the amount of times you will win in 1000 times is 1000 / 38 which is 26.32. therefore you would expect to lose 1000 - 26.32 times which is 973.68
The sides of a fair number cube are labeled 1, 2, 3, 4, 5, and 6. What is the theoretical probability that the number cube will land with the number 5 facing up?
Answer:
Probability that the number cube will land with the number 5 facing up
=5/6
Hope this helps, just used my mind
Step-by-step explanation:
Please mark me brainliest if correct
Complete or justify each step. 2(2h + 2)2(3h + 5) - 12 Distributive Property 4h + 4 < 6h-2 Simplify (combine like terms). 4h+ 4- 6h 6h-2-6h - 2h + 4<-2 simplify-2h<-6 simplify h>3
Answer:
7[tex]\geq[/tex][tex]\frac{h}{14}[/tex]
Step-by-step explanation:
Mark brainliest
Find the surface area of the cone. Use 3.14 for it.
The surface area is about in.2.
look at the picture ⬇️⬇️⬇️
This value is approximate since pi = 3.14 is approximate.
=======================================================
Work Shown:
r = radius = diameter/2 = 20/2 = 10 inches
L = slant height = 40 inches
SA = surface area of the cone
[tex]\text{SA} = \pi*r^2 + \pi*r*L\\\\\text{SA} = \pi*10^2 + \pi*10*40\\\\\text{SA} = \pi*100 + \pi*400\\\\\text{SA} = 100\pi + 400\pi\\\\\text{SA} = (100+400)\pi\\\\\text{SA} = 500\pi \text{ ... exact surface area in terms of pi}\\\\\text{SA} \approx 500*3.14\\\\\text{SA} \approx 1570\\\\[/tex]
The surface area of the cone is approximately 1570 square inches.
We can abbreviate "square inches" into [tex]\text{in}^2[/tex]
If you want to get a more accurate surface area value, then use more decimal digits of pi.
how many terms of the geometric progression 6,12,24,......must be taken to get a sum of 49146
Answer:
13
Step-by-step explanation:
the sum to n terms of a geometric sequence is
[tex]S_{n}[/tex] = [tex]\frac{a(r^{n}-1) }{r-1}[/tex]
where a is the first term and r the common ratio
here a = 6 , r = [tex]\frac{12}{6}[/tex] = 2 and [tex]S_{n}[/tex] = 49146 , then
[tex]\frac{6(2^{n}-1) }{2-1}[/tex] = 49146
6([tex]2^{n}[/tex] - 1) = 49146 ( divide both sides by 6 )
[tex]2^{n}[/tex] - 1 = 8191 ( add 1 to both sides )
[tex]2^{n}[/tex] = 8192 ( take log of both sides )
log [tex]2^{n}[/tex] = log 8192 , that is
n log 2 = log 8192 ( divide both sides by log 2 )
n = [tex]\frac{log8192}{log2}[/tex] = 13
[tex]\red{ \underline { \boxed{ \sf{Common \: Ratio,r = \frac{any\:observed\:term}{previous\:term}}}}}[/tex]
[tex]\longrightarrow[/tex][tex]\sf Common \: Ratio,r = \frac{12}{6} [/tex]
[tex]\quad \boxed{\sf {Common \:Ratio,r = 2 }}[/tex]
Now,
[tex]\green{ \underline { \boxed{ \sf{Sum\: of \: G.P. \: to\: n\:term,S_n = \frac{a(r^n-1)}{r-1}}}}}[/tex]
where
a = first termr = common Ration= number of termsPutting Values -
[tex]\begin{gathered}\\\implies\quad \sf 49146 = \frac{6(2^n-1)}{2-1} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf \frac{\cancel{49146}}{\cancel{6}} = \frac{2^n-1}{1} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 8191= \frac{2^n-1}{1} \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n-1 =8191 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n =8191+1 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n =8192 \\\end{gathered} [/tex]
[tex]\begin{gathered}\\\implies\quad \sf 2^n =2^{13}\quad(8192= 2^{13}) \\\end{gathered} [/tex]
Comparing powers on both sides-
[tex]\begin{gathered}\\\implies\quad \boxed{\sf{ n = 13}}\\\end{gathered} [/tex]
[tex]\longrightarrow[/tex]Therefore, to get a sum of 49146 , 13 terms of this G.P. should be taken.
Does x/x+11 simplify to 1/11? Why or why not ?
Answer:
No.
Step-by-step explanation:
Because only x / 11x simplifies to 1 / 11
X and 11 are not the same, therefore you cannot simplify them
6 8/10 + 1 7/10 =
please help meee
Answer:
8.2
Step-by-step explanation:
Hope this helps....
Answer:
The answer is 8 1 / 2
Step-by-step explanation:
See the Image
Option 1 is easier to understand
In circle D with m∠CDE = 118 m∠CDE=118 and CD=4 units, find the length of arc CE. Round to the nearest hundredth.
Answer:
CE ≈ 8.24 units
Step-by-step explanation:
The circumference of a circle is given by the formula ...
C = 2πr
Your circle has a radius CD of 4 units, so its circumference is ...
C = 2π(4 units) = 8π units
__
The arc of interest is 118°. The whole circle is 360°, so the length of the arc is 118/360 times the circumference of the circle:
CE = (118/360)(8π units) ≈ 8.24 units
Ms. Gardner is thinking of a number
The number is even.
It is not divisible by 6
It is not divisible by 7
it is not greater than 81
It is not less than 64
Answer:
74
Step-by-step explanation: 74 is not divisible by 6 or 9not nor 7 and it's less than 81 and greater than 64
An archer releases an arrow with an initial velocity of 20 feet per second at a height of 12 feet. The path the arrow takes can be modeled using the function f(x)=−16x^2+20x+12, where f(x) represents the height, in feet, of the arrow and x represents the time the arrow travels in seconds. What is the maximum height, in feet, reached by the arrow? Round your answer to the nearest hundredth if necessary. Do not include units in your answer.
Answer:
18.25 feetStep-by-step explanation:
The given function is quadratic.
The maximum of the quadratic function is its vertex.
The x-coordinate is determined by x = - b/(2a)
x = - 20/(-16*2) = 5/8Apply the x-value and find the value of f:
f(x) = - 16(5/8)² + 20(5/8) + 12 = 18.25 feetAnswer:
18.25
Step-by-step explanation:
we are given a quadratic function
[tex] f(x) = - 16 {x}^{2} + 20x + 12[/tex]
where:
f(x) represents the heightx represents the timeTo find the maximum value of f(x) in other words, the maximum height, in feet, reached by the arrow.
Differentiate both sides:
[tex] f'(x) = \dfrac{d}{dx}( - 16 {x}^{2} + 20x + 12)[/tex]
with sum differentiation rule, we acquire:
[tex] \displaystyle f'(x) = \frac{d}{dx}( - 16 {x}^{2} )+ \frac{d}{dx} 20x + \frac{d}{dx} 12[/tex]
recall that,
differentiation of a constant is equal to 0[tex] \dfrac{d}{dx} {x}^{n} = n {x}^{n - 1} [/tex]utilizing the rules we acquire:
[tex] \displaystyle f'(x) = - 32 {x}^{} + 20 [/tex]
now equate f'(x) to 0:
[tex] \displaystyle - 32 {x}^{} + 20 = 0[/tex]
solving the equation for x yields:
[tex]x _{max}= \dfrac{5}{8} [/tex]
plug in the maximum value of x into the quadratic function:
[tex]f(x )_{max}= - 16 {( \frac{5}{8} )}^{2} + 20( \frac{5}{8} ) + 12[/tex]
simplify:
[tex]f(x )_{max} = 18.25[/tex]
hence,
The maximum height reached by the arrow is 18.25 feet
find the e measure of the missing angle. round to 2 decimal places
Answer:
theta= 1.085
Step-by-step explanation:
How can I find the value of X?
Answer:
D
Step-by-step explanation:
Remark
The first thing you must do is notice that <D = <BEA. Mark it that way on your diagram.
The Second thing you need to notice is that <BEA and <A are equal because <A and <D are marked as equal.
So both the large triangle and the small one are isosceles. because 2 of the 3 angles are equal.
Now are you ready for this? That means that BA = 10 because BA is opposite one of the 2 equal angles in the small triangle. So now you are ready to set up a proportion.
Proportion
AB / AC = AE/AD
Givens
AB = 10
AC = 18
AE = 8
AD = x + 8
Solution
Substitute the Givens into the Proportion.
10/18 = 8/(x + 8) Cross multiply
10(x + 8) = 8 * 18 Simplify both sides
10x + 80 = 144 Subtract 80 from both sides
10x + 80 - 80 = 144 - 80
10x = 64 Divide by 10
10x/10 = 64/10
Answer: x = 6.4
12.44 = 4x what does x =
4 * x = 12.44
4/4 * x = 12.44 / 4
x = 3.11
Answer:
x = 3.11
Step-by-step explanation:
To find the value of 'x', divide both sides of the equation by 4
12.44 = 4x
[tex]\dfrac{12.44}{4}=\dfrac{4x}{4}\\\\\\3.11=x[/tex]
Find simple interest
Principal=rs 4000
Time :2
rate of interest :10%
Step-by-step explanation:
please mark me as brainlest
Step-by-step explanation:
Simple Interest is calculated using the following formula: SI = P × R × T/100, where P = Principal , T is time and r is interest rate.
So , by the values given
Principal :-rs 4000
Time :-2
rate of interest :- 10%
[tex] \frac{p \times r \times t}{100} [/tex]
[tex] \frac{4000 \times 10 \times 2}{100} [/tex]
[tex] = 800 \: rs[/tex]
What is the value of the
expression? 1 7/8 - 6/4
When rounding to the nearest hunderth, which numbers below will round to 187.55? Select all that apply
A)187.556
B)188.454
C)187.548
D)187.553
E)187.550
Answer:
C, D, E,
Step-by-step explanation:
All of these will round to 187.55
Help help help ASAP help
Answer:
(8, -2)
Step-by-step explanation:
While reflection over x-axis, the x-coordinate remains the same and the y-coordinate changes to it's opposite.
So,
Rx-axis => = (8, -2)
Solve for x 5x + 15 = 28
o
ol
43
5
13
5
O 13
043
Answer:
[tex]\boxed{\sf{x=\dfrac{13}{5}=2.6 }}[/tex]Step-by-step explanation:
To solve for x, you have to isolate it on one side of the equation.
First, subtract by 15 from both sides.
[tex]\sf{5x+15-15=28-15}[/tex]
Solve.
28-15=13
Rewrite the problem down.
5x=13
Divide by 5 from both sides.
[tex]\sf{\dfrac{5x}{5}=\dfrac{13}{5} }[/tex]
Solve.
You can also divide the numbers from left to right.
13/5=2.6
[tex]\boxed{\sf{x=\dfrac{13}{5}=2.6 }}[/tex]
Therefore, the correct answers is x=13/5=2.6.I hope this helps you! Let me know if my answer is wrong or not.
[tex]\rightarrow \sf 5x + 15 = 28[/tex]
[tex]\rightarrow \sf 5x + 15 -15= 28-15[/tex]
[tex]\rightarrow \sf 5x = 13[/tex]
[tex]\rightarrow \sf \dfrac{5x}{5} = \dfrac{13}{5}[/tex]
[tex]\rightarrow \sf x = \dfrac{13}{5}[/tex]
[tex]\rightarrow \sf x = 2\dfrac{3}{5}[/tex]
[tex]\rightarrow \sf x = 2.6[/tex]
Lana used the two blocks pictured in the diagram to build a tower. What is the total volume, in cubic inches, of the tower Lana built?
Answer:
120
Step-by-step explanation: 4x10x2 +2x5x4 =80+40=120 cubic inches
Answer:
Step-by-step explanation:
How could you correctly rewrite the equation 4(10 + 5) = 6 (12 - 2) using the distributive property?
Answer:
40+20 = 72-12 is the simplified version.
Step-by-step explanation:
Your equations
4(10+5) = 6(12-2)
Multiply 4 by 10 and 5 for the "4(10+5)"
Multiply 6 by 12 and -2 for the "6(12-2)"
40+20 = 72-12 is the simplified version.
If you want to solve/verify:
40+20 = 72-12
60 = 60
The nanswer is correct.
Answer:
40 + 20 = 72 - 12
Step-by-step explanation:
The number outside the parenthesis will be multiplied to both numbers inside the parenthesis, making the equation
(4 * 10) + (4 * 5) = (6 * 12) + (6 * (-2))
simplifying the equation...
40 + 20 = 72 - 12
If Ryan does a job in 10 hours and with the help of Chelsea they can do it together in 5 hours, how long would it take Chelsea to do it alone?
It would take her 10 hours. If it is double the time for one person to complete the task versus two, you can guess that the other person takes the same amount of time
PLEASE HELP WILL GIVE BRAINLIEST
Are the ratios 3:4 and 4:3 equivalent??
Answer:
Those ratios are not equivalent
Step-by-step explanation:
3:4 is not the same as 4:3 because 3:4 means 3 out of 4 but 4:3 means 4 out of 3 which means it is more than one while 3:4 is less than one
A store sells a workout outfit that consists of a jacket, a t-shirt, and a pair of shorts. The store purchases the jacket for $34, the t-shirt for $9, and the shorts for $12. The percent of markup is 28%. Find the selling price of the outfit.
PS: include show work please I have to submit this in like 3 hours thankyou
Answer:
The Outfit costs $70.4.
Step-by-step explanation:
Add the selling price together
34 + 9 + 12 = 55
Multiply by the markup (Profit)
100% = 1
28% = 0.28
55 x 1.28 = 70.4