Answer:
Center is (3,4)
Radius is √55 which is approximately 7.42
Step-by-step explanation:
First, recall the equation for a circle. The equation for a circle is given by:
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Where (h,k) is the center and r is the radius.
We have the equation:
[tex]x^2+y^2-6x-8y-30=0[/tex]
Thus, we want to turn this into the circle equation.
To do so, we need to complete the square.
First, put all the x-terms together and all the y-terms together. Also, add 30 to both sides:
[tex](x^2-6x)+(y^2-8y)-30=0\\(x^2-6x)+(y^2-8y)=30[/tex]
Now, complete the square for both of the variables. Recall how to complete the square. If we have:
[tex]x^2+bx[/tex]
We divide b by 2 and then square it. Then we will have a perfect square trinomial. To keep things balanced, we must also subtract what we added.
Thus, for the first term:
[tex](x^2-6x)\\=(x^2-6x+9)-9\\(x-3)^2-9[/tex]
And for the second term:
[tex](y^2-8y)\\=(y^2-8y+16)-16\\=(y-4)^2-16[/tex]
Replace the two terms:
[tex]((x-3)^2-9)+((y-4)^2-16)=30[/tex]
Simplify. Add -9 and -16:
[tex](x-3)^2+(y-4)^2-25=30[/tex]
Add 25 to both sides:
[tex](x-3)^2+(y-4)^2=55[/tex]
This is now in the form of the circle equation.
Thus, the center is (3,4).
And the radius is √55 which is approximately 7.42
Answer:
to be honest I'm not sure
We started with five gallons of an orange drink that was 90% water and 10% syrup. We added 1 gallon of concentrate and ended up with a resulting mixture that was 86% water and 14% syrup. Determine what percent of the concentrate was water and what percent was syrup.
Answer:
The gallon of concentrate was 66% water and 34% syrup.
Step-by-step explanation:
- The first thing is to know how much water and how much syrup have the 5 gallons.
90% water and 10% syrup.
- If we have 5 gallons with the same percentages then:
Where X is the percentage that we do not know.
(90 + 90 + 90+ 90 + 90 + X) / 6 = 86
(90 + 90 + 90+ 90 + 90 + X) = 516
X = 66
The answer is 66% water in the gallon added.
A professor would like to test the hypothesis that the average number of minutes that a student needs to complete a statistics exam is equal to 45 minutes. The correct hypothesis statement would be
Answer:
H0 : u = 45
H : u not equal to 45
This is because the topic of claim or contention is that the average minutes a student need to complete the statistics exam is 45mins
Which statements are correct? Check all that apply.
point F → point F'
parallelogram DEFG → parallelogram G'F'E'D'
Point D of the pre-image corresponds to point D' of the image.
ED of the pre-image corresponds to G'F' of the image.
Parallelogram DEFG maps to parallelogram D'E'F'G'.
Answer:
a c e
Step-by-step explanation:
just did it
Answer:
A. Point F → point F'
C. Point D of the pre-image corresponds to point D' of the image.
E. Parallelogram DEFG maps to parallelogram D'E'F'G'.
Step-by-step explanation: This is the correct answer on Edge 2021, just did the assignment. Hope this helps ^-^.
Find a linear inequality with the following solution set. Each grid line represents one unit. [asy] size(200); fill((-5,-3)--(5,2)--(5,5)--(-5,5)--cycle,yellow); real ticklen=3; real tickspace=2; real ticklength=0.1cm; real axisarrowsize=0.14cm; pen axispen=black+1.3bp; real vectorarrowsize=0.2cm; real tickdown=-0.5; real tickdownlength=-0.15inch; real tickdownbase=0.3; real wholetickdown=tickdown; void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) { import graph; real i; if(complexplane) { label("$\textnormal{Re}$",(xright,0),SE); label("$\textnormal{Im}$",(0,ytop),NW); } else { label("$x$",(xright+0.4,-0.5)); label("$y$",(-0.5,ytop+0.2)); } ylimits(ybottom,ytop); xlimits( xleft, xright); real[] TicksArrx,TicksArry; for(i=xleft+xstep; i 0.1) { TicksArrx.push(i); } } for(i=ybottom+ystep; i 0.1) { TicksArry.push(i); } } if(usegrid) { xaxis(BottomTop(extend=false), Ticks("%", TicksArrx ,pTick=gray(0.1),extend=true),p=invisible);//,above=true); yaxis(LeftRight(extend=false),Ticks("%", TicksArry ,pTick=gray(0.1),extend=true), p=invisible);//,Arrows); } if(useticks) { xequals(0, ymin=ybottom, ymax=ytop, p=black, Ticks("%",TicksArry , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize)); yequals(0, xmin=xleft, xmax=xright, p=black, Ticks("%",TicksArrx , pTick=black+0.8bp,Size=ticklength), above=true, Arrows(size=axisarrowsize)); } else { xequals(0, ymin=ybottom, ymax=ytop, p=axispen, above=true, Arrows(size=axisarrowsize)); yequals(0, xmin=xleft, xmax=xright, p=axispen, above=true, Arrows(size=axisarrowsize)); } }; draw((-5,-3)--(5,2),dashed+red, Arrows(size=axisarrowsize)); rr_cartesian_axes(-5,5,-5,5); for( int i = -4; i 0$ or $ax+by+c\geq0$ where $a,$ $b,$ and $c$ are integers with no common factor greater than 1.)
Make sure you don't put the code, but the url to the image itself. That way, we can try to help you :)
What is the area of this irregular figure?
Answer:
hey man if you figure this out comment back bc i need to know also. sorry and thanks!
Step-by-step explanation:
Answer:
A=192cm^2
Step-by-step explanation: Cut the shape. You now have Shape A and B.
Shape A is 8x8=64cm.
Shape B is 16x8=128cm
128cm+64cm= 192^2
Are two squares with the same side lengths scaled copies of one another? Explain your reasoning.
Answer:
Yes.
Step-by-step explanation:
Two squares with the same side lengths will always be a scale copy. Every side is equal because all sides are the same length if it wasn't that way it would be a rectangle or trapezoid.
A rectangle whose all sides are equal is called a square. The two squares with the same length side will be lengths scaled copies of one another.
What is a square?A rectangle whose all sides are equal is called a square.
A square is always a rectangle, parallelogram, and a quadrilateral but its reverse statement may or may not be true.(ie it is not always necessary that a rectangle is a square or a parallelogram is a square).
As it is known that two squares are always similar to each other which is because all the angles of a square are always 90°. Therefore, any two squares are always similar to each other.
Now, as it is given that the two square have the same length sides. Therefore, the two squares with the same length side will be lengths scaled copies of one another. This is because all the sides are equal and all the angles are equal.
Hence, the two squares with the same length side will be lengths scaled copies of one another.
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What integer is closest to −7π?
Answer:
[tex]\Huge \boxed{-22}[/tex]
[tex]\rule[225]{225}{2}[/tex]
Step-by-step explanation:
[tex]-7\pi[/tex]
We can take pi as 22/7.
[tex]\Longrightarrow \displaystyle \ \ -7 \times \frac{22}{7}[/tex]
[tex]\Longrightarrow \displaystyle \ \ 22 \times \frac{7}{-7}[/tex]
[tex]\Longrightarrow \displaystyle \ \ 22 \times -1[/tex]
[tex]\Longrightarrow \displaystyle \ \ -22[/tex]
[tex]\rule[225]{225}{2}[/tex]
The integer closet to -7π is -22.
What is integer?An integer is a number that includes both negative and positive numbers, including zero, and does not have a decimal or fractional component. Examples of integers include: -5, 0, 1, 5, 8, 97, and 3,043. Z is a set of integers that includes the following:
Positive figures: If a number is greater than zero, it is positive. Example: 1, 2, 3 . . .
Negative Counts: If a number is less than zero, it is negative. Example: -1, -2, -3 . . .
Zero cannot be thought of as either a negative or a positive number. It's a complete number.
Given -7π
the value of π in fraction form is 22/7
substitute the value of π
-7π = -7 x 22/7
-7π = -22
Hence, -22 is integer is closest to −7π.
Learn more about integer;
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What is the solution to this system of equations using the linear combination method?
4x + y = 5
3x + y = 8
(0, – 3)
(-3, 17)
(0,5)
(2, -3)
Answer:
My answer is (-3, 17).
Step-by-step explanation:
You will use minus sign for the equation in other to eliminate one of the letters and use the other one to find the one eliminated later...Which means that 4x+y=5 (-) 3x+y=8..... the minus sign will eliminate +y and +y in each equation because the "+y" in the second equation will be turned to -y because + times(×) - will give us minus sign so the "y" will be eliminated to give space for the 'x" .After the x has been found which is x=-3 then you will substitute x=-3 into the any equation and then you will also find the "y" which is y=17.....Thank you
Simplify the equation 4x+3y=2x
Answer:
2x=3y or x= -3y/2 and y =2/-3y
Step-by-step explanation:
4x-2x=-3y
2x=-3y
Answer:
Two options:
2x + 3y = 0
or
2x =-3y
Step-by-step explanation:
4x + 3y = 2x
4x - 2x + 3y = 0
2x + 3y = 0
2x = -3y
Think about what you learned about New Netherland. Which of these statements are true? Check all the statements that correctly describe New Netherland. A. People immediately began to settle New Netherland in great numbers. B. Settlers in New Netherland were often from many different countries. C. New Netherland grew slowly. Early colonists were most interested in the fur trade.
Answer:
B,C,D
Step-by-step explanation:
Just answered the question
One number is 3/8 of another number. The difference of the two numbers is 4.2. What is the lesser number
Answer:
2.52.
Step-by-step explanation:
If one number is x then the other = 3x/8.
Also x - 3x / 8 = 4.2
x - 0.375 x = 4.2
0.625x = 4.2
x = 4.2 / 0.625
x = 6.72.
So the lesser number is 6.72 * 0.375 = 2.52.
The lesser number is 2.52
If that one number is x, then we can agree that the other number is 3x/8.
Again, we are told that the difference between both is 4.2. Which means
x - (3x / 8) = 4.2
(8x - 3x)/8 = 4.2
8x - 3x = 8 * 4.2
5x = 33.6
x = 33.6/5
x = 6.72.
This means that the lesser number is 6.72 * 0.375 = 2.52.
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how the number e was discover
Answer:
It was that great mathematician Leonhard Euler who discovered the number e and calculated its value to 23 decimal places. It is often called Euler's number and, like pi, is a transcendental number (this means it is not the root of any algebraic equation with integer coefficients
A survey of 116 law firms in a country found that the average hourly billing rate for partners was $578.
a. all people in the country.
b. the law firms that were surveyed.
c. all partners.
d. all law firms in the country.
Complete Question
The complete question is shown on the first uploaded image
Answer:
a
The correct option is d
b
The correct option is b
Step-by-step explanation:
From the question we are told that
The sample size is [tex]n = 116[/tex]
The mean is [tex]\= x = \$578[/tex]
Generally the population is all law firms in the country because it is the entire pool from which a statistical sample is drawn
The sample are the law firm that where surveyed because it is the statistical sample is drawn from the population
The edge length of a cube with volume 24 cubic units
Answer:
2∛3 units
Step-by-step explanation:
The volume is the cube of the edge length, so the edge length is the cube root of the volume:
s = ∛V
s = ∛24 = ∛(2³·3)
s = 2∛3
The edge length is 2∛3 ≈ 2.8845 units.
For items 21 - 23 determine whether each sequence is arithmetic. if the sequence is arithmetic, then
Answer:
see below
Step-by-step explanation:
To be arithmetic we have to add the same term each time
1,1,2,3,5,8
1+1 =2 2+1 = 3 3+1 = 4 so it is not arithmetic
20,17,14,11,8,....
Add -3
20+-3 =17 17+-3 = 14 14+-3 = 11 11+-3 = 8
This is an arithmetic sequence
The common difference is -3
The explicit formula is
an = a1+ d(n-1) where d is the common difference and a1 is the first term
an = 20 -3( n-1)
The recursive formula is
an = an-1 + d where an-1 is the previous term and d is the common difference
an = an-1 -3
3,7,11, 15
Add 4
3+4=7 7+4=11 11+4=15
This is an arithmetic sequence
The common difference is 4
The explicit formula is
an = a1+ d(n-1) where d is the common difference and a1 is the first term
an = 3 +4( n-1)
The recursive formula is
an = an-1 + d where an-1 is the previous term and d is the common difference
an = an-1 +4
What is this answer please help someone
Answer:
I think the answer is line DE
Can someone help??????
Answer:
$159.5
Step-by-step explanation:
the price should be increased by 5%.
which means the old price would be 95% of the new price.
168×95=15960
15960÷100=159.6
If point X is between W and Y then WX + XY = WY.
always
sometimes
never
Answer:
Always
Step-by-step explanation:
lets say WY = 8
WX = 2
hope this helps
XY = 6
WX(2) + XY(6) = 8
Answer:
always
Step-by-step explanation:
The data represents the body mass index (BMI) values for 20 females. Construct a frequency distribution beginning with a lower class limit of 15.0 and use a class width of 6.0. 17.7. 33.5. 26.6 24.7
28.8. 23.8. 18.3. 22.1
19.2. 22.6. 22.7. 38.9
27.3. 44.9. 32.2. 23.9
Kindly note that the data supplied is not up to 20. Hence, the answer will be based on the number of data given.
Answer:
Step-by-step explanation:
Given the following data:
BMI of 20 females :
17.7. 33.5. 26.6 24.7
28.8. 23.8. 18.3. 22.1
19.2. 22.6. 22.7. 38.9
27.3. 44.9. 32.2. 23.9
Lower class limit (LCL) = 15.0
Class width = 6.0
Class_interval_____frequency
15.0 - 20.9 _________3
21.0 - 26.9 _________7
27.0 - 32.9 _________3
33.0 - 38.9 _________2
39.0 - 44.9 _________1
A magician flips a coin 8 times producing heads each time. Is there statistical significance to say that the coin is somehow rigged?
A. Yes, because the results are unlikely to happen by chance.
B. No, because the results are unlikely to happen by chance.
C. Yes, because the results are likely to happen by chance.
D. No, because the results are likely to happen by chance.
Answer:
A
Step-by-step explanation:
Either a or b could work, but he's a magician so it's probably rigged
John left his house in Irvine at 8:20 AM to drive to a meeting in Los Angeles, 45 miles away. He arrived at the meeting at 9:50 AM. At 5:30 PM, he left the meeting and drove home. He arrived home at 7:45 PM.
Megan wants to order team t-shirts at $4.50 each, but she doesn’t want to spend more than $65 total. If the t-shirt company charges a one-time fee of $10 for logo application, how many t-shirts can she buy without spending more than $65? What will x represent in the equation?
the cost of the t-shirts
the number of t-shirts
the total cost
Megan’s cost
x will equal her total cost and the most she can spend on shirts without going over $65 is $63.
Sorry if it is wrong
what is the square root of 27
The answer is:
5.19615
Find an equation of the tangent plane to the surface at the point . Question 14 options: a) b) c) d) e)
This question is incomplete, the complete question is;
Find an equation of the tangent plane to the surface z=1y²−1x² at the point (-4, 3, -7).
z = .....................
Note: Your answer should be an expression of x and y; e.g. 3x - 4y + 6.
Answer:
Z = 8x + 6y + 7
Step-by-step explanation:
Given that z = 1y² - 1x²
with points (-4, 3, -7)
so
Z = y² - x²
Equation of tangent plane to the surface Z = f(x,y) at the points ( x₀,y₀,z₀) is
Z - Z₀ = fx (x₀,y₀)(x-x₀) + fy (x₀y₀)(y-y₀)
therefore
Z = f(x,y) = y² - x²
fx = -2x, fx (-4, 3, -7) = -2(-4) = 8
fy = -2y, fy ( -4, 3, -7 ) = 6
Z + 7 = 8(x+4) + 6(y-3)
Z + 7 = 8x + 32 + 6y - 18
Z + 7 = 8x + 32 + 6y - 18
Z + 7 = 8x + 6y + 14
Z = 8x + 6y + 14 - 7
Z = 8x + 6y + 7
There were 326 people at a matinee performance
of a play. For the evening performance, 486
people attended. Which is the most reasonable
estimate for the total number of people that saw
the show?
A. 700
B. 800
C. 900
D. 1,000
Answer:
B. 800
Step-by-step explanation:
Its b because we estimate that 326 is about 300 and 486 is about 500 and if we add tha together we get 800.
solve for h.
please help<3
Answer:
h=2A/a+b
Step-by-step explanation:
Distribute the terms
Divide by two
Isolate h
That would be the steps
swame and luigi were printing calendars swame used 21/2 cartridge, while luigi used 1 3/4 ink cartridges. how many more ink cartridges swame used than luigi?
Well i don't know if its correct but i hope it will help 8.78
On March 24, 1989, the Exxon Valdez oil tanker ran aground and leaked millions of gallons of oil into Prince William Sound. The spill covered approximately 11,000 square miles of ocean. The oil spread out in a circular pattern and the radius increased by 0.10 mph. Use π = 3.14. At this rate, how many hours did it take for oil to cover the area?
Answer:
592 hours
Step-by-step explanation:
Given
[tex]Area = 11000m^2[/tex]
[tex]Radius = 0.10m/h[/tex]
Required
Determine the time taken to cover the area
Since, the oil formed a circular pattern; the question will be answered using area of a circle
[tex]Area = \pi r^2[/tex]
Let t represent the time take to cover 11000m²;
The relationship between these parameters is:
[tex]11000 = \pi * (0.10t)^2[/tex]
Substitute 3.14 for π
[tex]11000 = 3.14 * (0.10t)^2[/tex]
Divide both sides by 3.14
[tex]\frac{11000}{3.14} = \frac{3.14 * (0.10t)^2}{3.14}[/tex]
[tex]\frac{11000}{3.14} =(0.10t)^2[/tex]
[tex]3503.18471338 = (0.10t)^2[/tex]
Take square root of both sides
[tex]\sqrt{3503.18471338} = \sqrt{(0.10t)^2}[/tex]
[tex]\sqrt{3503.18471338} = 0.10t[/tex]
[tex]59.1877074516 = 0.10t[/tex]
Divide both sides by 0.10
[tex]\frac{59.1877074516}{0.10} = \frac{0.10t}{0.10}[/tex]
[tex]\frac{59.1877074516}{0.10} = t[/tex]
[tex]591.877074516 = t[/tex]
[tex]t = 591.877074516[/tex]
[tex]t = 592\ hours[/tex] (Approximated)
Hence, it'll take approximately 592 hours to cover the given area
Answer: B
592 hours
Step-by-step explanation:
56 points! Please help
Answer:
Segment bisector: JK
MN= 52
Step-by-step explanation:
The segment bisector basically means the point where the line is cut in half. If you study the figure, you can see the two small red lines intersecting The longer line. This means that the two small black segments are equal to each other. With this in mind, we now know that the segment bisector is line JK.
To find the length of MN, study the figure again. You can see that we are given the value of one line segment that is half the length of MN. So all we need to do is multiply that value by 2:
[tex]26*2=52[/tex]
The length of line segment MN is 52.
:Done
Answer:
MN = 52
Step-by-step explanation:
bisector is just a half of its length
looking through the graph
MN = 26 * 2 (just multiply ot by 2)
MN = 52
Jo is 5 cm taller than Kathy.Let k=kathy height.Then? = Jo height
Answer:
5+k
Step-by-step explanation:
Since k is Kathy's height and we know Jo is 5+ cm than Kathy. That makes Jo = 5+k