A triangle has three interior angle measures; x is the largest angle, y is the next largest angle, and z is the smallest angle. The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles. The largest angle is twice the smaller angle plus 20 degrees. The sum of the triangle's interior angles is x + y + z = 180. Which two equations represent the remaining angle relationships? Select each correct answer.
x = 2z + 20
x=2(z+y)−60
x=2z+y−60
x = z + 20
x=60−2(z+y)
Answers
The answer can be seen on the attachment that I have given.
The two equations that represent the remaining angle relationships are (x = 60 - 2(y + z)) and (x = 2z + 20) and this can be determined by using the given data.
Given :
A triangle has three interior angle measures; x is the largest angle, y is the next largest angle, and z is the smallest angle.The measure of the largest angle is 60 degrees less than twice the sum of the measure of the other two angles. The largest angle is twice the smaller angle plus 20 degrees. The sum of the triangle's interior angles is x + y + z = 180.The linear equation that represents the situation "The measure of the largest angle is 60 degrees less than the twice the sum of the measure of the other two angles" is:
x = 60 - 2(y + z) --- (1)
The linear equation that represents the situation "The largest angle is twice the smaller angle plus 20 degrees" is:
x = 2z + 20 --- (2)
Therefore, the correct option is A) and E).
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Related Questions
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.
Answers
Answer:
B,C,D
Step-by-step explanation:
Just answered the question
56 points! Please help
Answers
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
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.
Answers
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
Are two squares with the same side lengths scaled copies of one another? Explain your reasoning.
Answers
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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Use the given conditions to write an equation in point-slope form. Keep parenthesis in point-slope form. slope = -5, passing through (4,-2)
Answers
Answer:
Step-by-step explanation:
y + 2 = -5(x - 4)
y + 2 = -5x + 20
y = -5x + 18
how the number e was discover
Answers
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
Solve the problem
X/5 +4=17
Answers
Answer:
x = 65
Step-by-step explanation:
X/5 +4=17
Subtract 4 from each side
X/5 +4-4=17-4
x/5 = 13
Multiply each side by
x/5 *5 = 13*5
x = 65
Answer:
x=65
Step-by-step explanation:
x/5+4=17
solve for x by simplifying for both sides of the equation, then isolate the variable. x=65
What integer is closest to −7π?
Answers
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.
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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'.
Answers
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 ^-^.
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
Answers
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.
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
Answers
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
Solve the equation x+2/3=18
Answers
Answer: x=52/3
Step-by-step explanation:
x+2/3=18
x=18-2/3 ⇔ subtraction property of equality
x=54/3-2/3 ⇔ convert integer into fraction
x=52/3
Hope this helps!! :)
Answer:
see below
Step-by-step explanation:
( x+2)/3=18
Multiply each side by 3
(x+2)/3 *3 = 18*3
x+2 = 54
Subtract 2
x+2-2 =54-2
x = 52
or if
x+2/3=18
Subtract 2/3
x+2/3 -2/3 = 18-2/3
x = 17 +1 -2/3
x = 17 1/3
If point X is between W and Y then WX + XY = WY.
always
sometimes
never
Answers
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:
What is the area of this irregular figure?
Answers
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
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?
Answers
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:
The average natural gas bill for a random sample of 26 homes in the 19808 zip code during the month of March was $305.30 with a sample standard deviation of $46.50. The critical value for a 95% confidence interval around this sample mean is ________.
Answers
Answer:
2.06
Step-by-step explanation:
The formula for critical value = Margin of Error / Standard Error
Margin of Error = z × Standard deviation/√n
Mean for the month of March = $305.30
Standard deviation = $46.50
n = number of samples = 26 homes
z score for 95% confidence interval = 1.96
= 1.96 × $46.50/√26
= 17.874024556
Standard error = standard deviation/√n
= $46.50/√26
= 9.1194002839
Critical value = Margin of Error/Standard Error
= 17.874024556/9.1194002839
= 2.06
The edge length of a cube with volume 24 cubic units
Answers
Answer:
2∛3 units
Step-by-step explanation:
The volume is the cube of the edge length, so the edge length is the cube root of the volume:
s = ∛V
s = ∛24 = ∛(2³·3)
s = 2∛3
The edge length is 2∛3 ≈ 2.8845 units.
Find a linear inequality with the following solution set. Each grid line represents one unit. [asy] size(200); fill((-5,-3)--(5,2)--(5,5)--(-5,5)--cycle,yellow); real ticklen=3; real tickspace=2; real ticklength=0.1cm; real axisarrowsize=0.14cm; pen axispen=black+1.3bp; real vectorarrowsize=0.2cm; real tickdown=-0.5; real tickdownlength=-0.15inch; real tickdownbase=0.3; real wholetickdown=tickdown; void rr_cartesian_axes(real xleft, real xright, real ybottom, real ytop, real xstep=1, real ystep=1, bool useticks=false, bool complexplane=false, bool usegrid=true) { import graph; real i; if(complexplane) { label("$\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.)
Answers
Make sure you don't put the code, but the url to the image itself. That way, we can try to help you :)
One number is 3/8 of another number. The difference of the two numbers is 4.2. What is the lesser number
Answers
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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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
Answers
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
3. What is the Kinetic Energy of a 100 kg object that is moving with a speed of 12.5 m/s?
Answers
Answer:
7812.5 J
Step-by-step explanation:
Kinetic energy is equal to 1/2 m v^2.
The mass of the object is 100 and the velocity is 12.5 m/s.
Therefore, the kinetic energy is 1/2 (100) (12.5)^2 = 7812.5 J.
Answer:
KE = ½ (100kg) (12.5 m/s)2
KE = ½ (100kg)(156.25)
KE = 7,812.5J
answer ^
Step-by-step explanation:
KE = ½ mv2
KE = ?
m = 100kg
v = 12.5m/s
Can someone help??????
Answers
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
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)
Answers
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
Jo is 5 cm taller than Kathy.Let k=kathy height.Then? = Jo height
Answers
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
"-8 is 12 less than a number."
Answers
Answer:
The answer would be x<4
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.
Answers
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.
Answers
Answer:
A
Step-by-step explanation:
Either a or b could work, but he's a magician so it's probably rigged
For items 21 - 23 determine whether each sequence is arithmetic. if the sequence is arithmetic, then
Answers
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
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.
Answers
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.
What is this answer please help someone
Answers
Answer:
I think the answer is line DE