Answer:
1. x² + y² + 8x - 14y - 35 = 0
2. x² + y² - 2x - 8y - 47 = 0
3. x² + y² - 4x - 2y - 116 = 0
4. x² + y² + 2x + 4y - 20 = 0
5. x² + y² - 4x - 8y - 52 = 0
Step-by-step explanation:
General equation of a circle is: x² + y² + 2gx + 2fy + c = 0
with center (-g, -f) and radius √(g² + f² - c)
1. From inspection: center (-4, 7) and radius = √100 = 10
Therefore, g = 4 and f = -7
√(4² + (-7)² - c) = 10 ⇒ 65 - c = 100 ⇒ c = -35
So, x² + y² + 8x - 14y - 35 = 0
2. From inspection: center (1, 4) and radius = √64 = 8
Therefore, g = -1 and f = -4
√((-1)² + (-4)² - c) = 8 ⇒ 17 - c = 64 ⇒ c = -47
So, x² + y² - 2x - 8y - 47 = 0
3. From inspection: center (2, 1) and radius = √(11²) = 11
Therefore, g = -2 and f = -1
√((-2)² + (-1)² - c) = 11 ⇒ 5 - c = 121 ⇒ c = -116
So, x² + y² - 4x - 2y - 116 = 0
4. From inspection: center (-1, -2) and radius = √25 = 5
Therefore, g = 1 and f = 2
√(1² + 2² - c) = 5 ⇒ 5 - c = 25 ⇒ c = -20
So, x² + y² + 2x + 4y - 20 = 0
5. From inspection: center (2, 4) and radius = √72
Therefore, g = -2 and f = -4
√((-2)² + (-4)² - c) = √72 ⇒ 20 - c = 72 ⇒ c = -52
So, x² + y² - 4x - 8y - 52 = 0
[tex]n = 20[/tex] , ∑[tex]x = 1570[/tex] , ∑[tex]x^2 = 125696[/tex] , minimum = 60, maximum = 100
Find s. Round your answer to one decimal place.
Estimate s by using the range rule-of-thumb. (If you can explain the range rule of thumb it'll be greatly appreciated).
Answer:
s=10
Step-by-step explanation:
Basically, the range rule-of-thumb is that the range is generally about four times the standard deviation.
First, we find the range:
Range=Maximum-Minimum
Range=100-60
Range=40
Next, divide the range by 4 to get the standard deviation
Range=4(Standard Deviation)
40=4(Standard Deviation)
10=Standard Deviation
Therefore, s=10, which is the standard deviation
Mean:-
[tex]\\ \tt\hookrightarrow \overline{x}=\dfrac{\sum x}{n}=\dfrac{1570}{20}=78.5[/tex]
Standard deviation:-
Two ways are available ,Let's do in both.WAY-1(apply common formula)
[tex]\\ \tt\hookrightarrow \sigma=\sqrt{\dfrac{\sum x^2}{n}-(\overline{x})^2}[/tex]
[tex]\\ \tt\hookrightarrow \sigma=\sqrt{\dfrac{125696}{20}-(78.5)^2}[/tex]
[tex]\\ \tt\hookrightarrow \sigma=\sqrt{6284.8-6162.25}[/tex]
[tex]\\ \tt\hookrightarrow \sigma=\sqrt{122.55}[/tex]
[tex]\\ \tt\hookrightarrow \sigma=11.07=11.1[/tex]
Way-2(Apply range-rule of thumb):-
So the rule basically defines that range is approximately equal to four times of standard deviation.[tex]\\ \tt\hookrightarrow Range=max-min=100-60=40[/tex]
NOW
[tex]\\ \tt\hookrightarrow \sigma \approx \dfrac{Range}{4}[/tex]
[tex]\\ \tt\hookrightarrow \sigma\approx \dfrac{40}{4}[/tex]
[tex]\\ \tt\hookrightarrow \sigma\approx 10[/tex]
Make sure to use approx sign instead of equal to as range -rule of thumb doesn't give accurate standard deviation.I need help answering this question
Answer:
The 2nd option is the correct answer.
since you split 12 pieces with 3 people there is 4 pieces per person.
Find the equation of the exponential function represented by the table below
Answer:
[tex]y=4(4)^x[/tex]
Step-by-step explanation:
Exponential functions are represented in the form [tex]y=a(b)^x[/tex], where a is the initial value and b is the multiplier.
Here, we see that when x = 0, y = 4. This means that 4 is our initial value, or a. You can look at the a variable almost being like the y-intercept of a graph.
Next, we must solve for b. We can do 16 ÷ 4 to find the slope, or multiplier of this function, because 16 is 1 input x-value up from 0. 16 ÷ 4 = 4.
So, we now have all the needed variables, so we plug them into the formula
[tex]y=a(b)^x[/tex]
Which expression is equivalent to the given expression?
7x−3
7x−3x
3−7x
4x−3+3x
3−6+3x
Answer:
4x–3+3x
Step–by–step explanation:
Look at each term as positive or negative. I will use brackets for the sake of clarity, but that is not necessary. Here, that would look like:
[+4x] [–3] [+3x]
Rearrange the terms.
[+4x] [+3x] [–3]
Remove the brackets.
4x +3x –3
Simplify.
7x – 3
Answer:
Option CStep-by-step explanation:
Let's verify all the options.
Option A:
7x - 3x = 7x - 3=> 4x = 7x - 3 (False)Option B:
3 − 7x = 7x - 3=> 3 + 3 = 14x (False)Option C:
4x − 3 + 3x = 7x - 3=> 7x - 3 = 7x - 3 (True)Option D:
3 − 6 + 3x = 7x - 3=> 3x - 3 = 7x - 3=> 3x = 7x (False)We can conclude that option C is correct.
how to tell if a table is a exponential decay function an exponential growth function or neither
Answer:
Exponential function: a*b^x
if B is less than 1, it is a decay function
if B is more than 1, then it is a growth function
if B is 0, then the function neither decreases nor increases
Example 1: 100*0.14^x
The y-intercept is decreasing by 86%
Example 2: 3000*1.14^x
The y-intercept is increasing by 14%
Example 3: 400*0
The y-intercept is neither decreasing nor increasing
Going back to the function, a is the y-intercept, and b is the rate
I hope this will help you, I just started to learn about exponential functions..
The value of 22 to the nearest hundred
Answer:
0
Step-by-step explanation:
Since the tens place is below 5 you would round down to zero. 5 and above round up, four and below round down.
8-1.2y=2 solve the 2 step equation and check the soultion
Answer:
Given :0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3
To Find solve using substitution method
Solution :
0.2x + 0.3y = 1.3
0.4x + 0.5y = 2.3 -2
Substitute the value of x from 1 in 2
0.4(1.3-0.3) +0.5y = 2.3
y = 3
0.2x + 0.3(3) = 1.3
0.2x = 1.3 0.9
X = 1.3-0.9 0.2
x = 2
So, x = 2 and y = 3
Answer:
[tex]y=5[/tex]
Step-by-step explanation:
[tex]8-1.2y=2[/tex]
Subtract 8 from both sides.
[tex]-1.2y=2-8[/tex]
Subtract 8 from 2 to get -6.
[tex]-1.2y=-6[/tex]
Divide both sides by -1.2.
y= [tex]\frac{-6}{-1.2}[/tex]
Expand [tex]\frac{-6}{-1.2}[/tex] by multiplying both numerator and the denominator by 10.
[tex]y=\frac{-60}{-12}[/tex]
Divide -60 by -12 to get 5.
[tex]y=5[/tex]
Hope this helps! Brainliest would be much appreciated! Have a great day! :)
Are the following triangles similar? Justify your reasoning using mathematics.
If UW = 25 - 35 and UY = S, find the value
of s that makes quadrilateral VWXY a
parallelogram.
Answer:
s = 35 unitsStep-by-step explanation:
We know that:
Rectangle = ParallelogramUW = 2s - 35UY = sUW = UYSolution:
2s - 35 = s=> 2s - s = 35=> s = 35 unitsHence, the value of s must be 35 units so that the quadrilateral becomes a parallelogram.
-18 subtracted from - 7
Answer:
[tex]-7-(-18)\\-7+18\\11[/tex]
Step-by-step explanation:
Today only, a sofa is being sold at a 33% discount. The sales price is $603 what was the sales price yesterday
Answer: 801.99
Step-by-step explanation:
603 + Percentage increase =
603 + (33% × 603) =
603 + 33% × 603 =
(1 + 33%) × 603 =
(100% + 33%) × 603 =
133% × 603 =
133 ÷ 100 × 603 =
133 × 603 ÷ 100 =
80,199 ÷ 100 =
801.99
Answer:
$801.99
Step-by-step explanation:
You first make 33% into a decimal which makes .33
Then multiply .33 by $603 which equals $198.99
Lastly add $198.99 to $603 and you get $801.99
help pls ill mark brainliest!!!!!!!!!!!!!!!!!
Any points that are less than 6. So 5, 4, 3, 2, etc.
Answer:
He could've sent 5, 4, 3, or 2 postcards
Step-by-step explanation:
1. Services performed but unbilled and uncollected at July 31 were $1,730.
2. Depreciation on equipment for the month was $180.
3. One-twelfth of the insurance expired.
4. A count shows $330 of cleaning supplies on hand at July 31.
5. Accrued but unpaid employee salaries were $410.
The appropriate journal entries for the transactions are: Debit Accounts receivable $1,730; Credit Sales revenue$1,730.
Journal entriesJuly 31
Debit Accounts receivable $1,730
Credit Sales revenue $1,730
July 31
Debit Depreciation expenses $180
Credit Accumulated depreciation $180
July 31
Debit Insurance expenses xx(1/12)
Credit repaid insurance xx(1/12)
July 31
Debit Supplies expenses $330
Credit Supplies $330
July 31
Debit Salaries wages and expense $410
Credit Salaries and wages payable $410
Inconclusion the appropriate journal entries for the transactions are: Debit Accounts receivable $1,730; Credit Sales revenue$1,730.
Learn more about journal entries here:https://brainly.com/question/14279491
123,456.78901 to ten – thousandths
-
Answer:
123,456.789
Step-by-step explanation:
The ten thousandth place is less than 5.
Answer:
123,456.789
Explanation:
Given: 123,456.789..........the last 3 digit after decimal place is thousands and 1 digit after decimal place is tenths.
Determine if the following system of equations has no solutions, infinitely many solutions or exactly one solution.
x+4y=1
2x+8y=2
Answer:
Infinitely many solutionsStep-by-step explanation:
First, let's organize the equations of the lines into slope-intercept form.
x + 4y = 1=> 4y = -x + 1=> y = -x/4 + 1/4And,
2x + 8y = 2=> 8y = -2x + 2=> y = -2x/8 + 2/8=> y = -x/4 + 1/4Since both the graphs are the same, the two equations have infinitely many solutions.
Which is equivalent to (2^-3)^4?
A. -2^12
B. 1/2^12
C. 1/2^7
D. 2
Answer:
B
Step-by-step explanation:
(2^-3)^4=2^(-12) = 1/(2^12)
Seven decreased by 13
Answer:
13-7
=6
hope it helps you
make me brainliest plz
Answer:
it will be 6
Step-by-step explanation:
decreases by means - soo
13-7=6
A quadrilateral has two angles that measure 135º and 85º. The other two angles are in a
ratio of 2:5. What are the measures of those two angles?
Answer:
40, 100
Step-by-step explanation:
the sum of a quadrilateral is 360, 360 - 135 - 85 =140
140 ÷ 7 × 2 = 40, 140 ÷ 7 × 5 = 100.
3 over 4 of 4 over 5 ?
Answer:
what's the question? it could be both
Red beads come in packages of 10. Blue beads come in packages of 12. Lee wants to buy an equal number of red and blue beads. He thinks he has to buy 10 packages of blue beads and 12 packages of red beads to have the least equal number of each. Is lee correct?
(Needs answer asap)
Please Hurry and Answer this
Answer:
5x + 20 = 5(x+4)
5(2x+8) = 10x + 40
5(x+8) =5 + 5 x 8
Step-by-step explanation:
Portfolio Option 1: Sports Graph
This portfolio problem will have you write. You will turn in a “mathematical paper” of about 1 page of writing. You can use this handout to write rough draft ideas first.
Brainstorm: Which of the above sports do you think the graph could represent? Why?
Brainstorm: What vocabulary and properties of graphs and functions do you see represented in the graph? How did any of those affect your choice for the sport?
Use your brainstorms above to write a 1 page paper that talks about this graph, what sport you believe it could represent, and what properties of functions and graphs support your answer. You can add diagrams as well.
Answer:The graph represent skydiving, Because when you jump out of the plane you have a bunch of speed and when you pull your parachute the speed will drop exceedingly.
Step-by-step explanation:
A cycliest rides at 30 kilometers per hour. how far will travel in 21/2 hours
[tex]\\ \tt\hookrightarrow Speed=Distance/Time[/tex]
[tex]\\ \tt\hookrightarrow Distance=Speed\times Time[/tex]
[tex]\\ \tt\hookrightarrow Distance=30(10.5)[/tex]
[tex]\\ \tt\hookrightarrow Distance=315km[/tex]
Answer:
315 kilometers.Step-by-step explanation:
We know that:
30 kilometers = 1 hourSolution:
30 kilometers = 1 hour=> 30 x 21/2 kilometers = 21/2 hours=> 15 x 21 kilometers = 21/2 hours=> 315 kilometers = 21/2 hoursHence, in 21/2 hours, the cyclist rides 315 kilometers.
You spent $14.80 at a restaurant and want to leave a 15% tip. How much do you leave as a tip?
Answer:
You leave $2.22
Step-by-step explanation:
convert 15% to 0.15
multiply $14.80*0.15
14.80*0.15=2.22
tip:$2.22
Answer:
Step-by-step explanation: in a calculator type in 15%14.80 and it will be 2.22
so ur answer is $2.22
Plz help I can’t figure this out
Answer:
57
Step-by-step explanation:
[tex]9+6 (2^2 +4)\\9+6 (4 +4)\\9+6 *8\\9+48\\57[/tex]
Your answer is 57.
Hope this helps! Brainliest would be much appreciated! Have a great day! :)
Answer:
The answer is 57.
Step-by-step explanation:
[tex]{\tt{\underline{\underline{\pink{SOLUTION:}}}}}[/tex]
To solve the above equation we will follow the BODMAS rule.
[tex]\blue\star[/tex] BODMAS is an order of mathematic operations.[tex]\blue\star[/tex] BODMAS rule is to be followed while solving expressions in mathematics.It stands for :
[tex]\purple\star[/tex] B = bracket[tex]\purple\star[/tex] O = order of power[tex]\purple\star[/tex] D = division[tex]\purple\star[/tex] M = multiplication[tex]\purple\star[/tex] A = addition[tex]\purple\star[/tex] S = subtractionSolving this question by bodmas rule :
[tex]\begin{gathered}\qquad{\sf{ = 9 + 6( {2}^{2} + 4)}}\\\\\qquad{\sf{ = 9 + 6(2 \times 2 + 4)}}\\\\\qquad{\sf{ = 9 + 6(4 + 4)}}\\\\\qquad{\sf{ = 9 + 6(8)}}\\\\\qquad{\sf{ = 9 + 6 \times 8}}\\\\\qquad{\sf{ = 9 + 48}}\\\\\qquad{\sf{ = 57}}\end{gathered}[/tex]
Hence, the answer is 57.
[tex]\rule{300}{2.5}[/tex]
what is the simplification of 1.1
Answer:
1 1/10
Step-by-step explanation:
I hope it's what you wanted
Solve for x.
[tex] \rm \longrightarrow \dfrac{x}{ \sqrt{ {x}^{2} + 1} } = {x}^{4} - x[/tex]
Best answer will be rewarded.
Factorize both sides of the equation:
[tex]\dfrac x{\sqrt{x^2+1}} = x^4 - x[/tex]
[tex]\dfrac x{\sqrt{x^2+1}} = x(x^3-1)[/tex]
[tex]\dfrac x{\sqrt{x^2+1}} - x(x^3-1) = 0[/tex]
[tex]x \left(\dfrac1{\sqrt{x^2+1}} - (x^3 - 1)\right) = 0[/tex]
One immediate solution is then x = 0. This leaves us with
[tex]\dfrac1{\sqrt{x^2+1}} - (x^3 - 1) = 0[/tex]
or as we had earlier,
[tex]\dfrac1{\sqrt{x^2+1}} = x^3 - 1[/tex]
Take the square of both sides:
[tex]\dfrac1{x^2+1} = \left(x^3-1\right)^2[/tex]
[tex]\dfrac1{x^2+1} = x^6 - 2x^3 + 1[/tex]
Turn this into a polynomial equation:
[tex]1 = \left(x^2+1\right) \left(x^6-2x^3+1\right)[/tex]
Expand the right side and make it equal to zero:
[tex]1 = x^8 + x^6 - 2x^5 - 2x^3 + x^2 + 1[/tex]
[tex]0 = x^8 + x^6 - 2x^5 - 2x^3 + x^2[/tex]
Each term in the polynomial has a common factor of x². Factoring this out just gives x = 0 again as a solution.
[tex]0 = x^2 \left(x^6 + x^4 - 2x^3 - 2x + 1\right)[/tex]
[tex]0 = x^6 + x^4 - 2x^3 - 2x + 1[/tex]
You'll need a computer to solve the remain se.xtic equation. Solving over reals, you would find two solutions, x ≈ 0.438 and x ≈ 1.18, but only x ≈ 1.18 is valid.
Answer:
x = 0 and x = 1.181Step-by-step explanation:
Another solution is graphical.
Take either side as a function and find the intersection of the graphs.
Use graphing software to make it much easier.
See below
use words to write this number: 40302010
40,302,010
forty million, three hundred two thousand, ten
The polynomial −2x3 − x2 + 13x in the last line is the result of
Answer:
The Second Option as of 2022
Step-by-step explanation:
subtracting 3x4 + 9x3 + 3x2 from the
dividend and bringing down 13x .
A number decreased by 5 is less than 33.
Step-by-step explanation:
ket the number be x
Decreased by 5 means x-5
Less than 33 means x - 5 < 33
x < 33 + 5
x < 38
