suppose Point G represents a duck flying over a Lake, point H and J represent two ducks swimming on the lake. Which is a true statement?
Answers
Answer:
Choice D. There is exactly one plane that contains the three ducks: [tex]\sf G[/tex], [tex]\sf H[/tex], and [tex]\sf J[/tex].
Step-by-step explanation:
The three points [tex]\sf G[/tex], [tex]\sf H[/tex], and [tex]\sf J[/tex] are distinct since each of the three points represents a different duck.
There's only one line through two distinct points in a 2D cartesian plane.
Likewise, given two distinct points ([tex]\sf G[/tex] and [tex]\sf J[/tex]) in a 3D space, there would be only one line two the two points.
Assume that plane [tex]\sf L[/tex] represents the plane that contains the surface of the lake.
A line is in a plane if and only if all points on that line are in the said plane.
Point [tex]\sf G[/tex] is on the line that contains [tex]\sf G\![/tex] and [tex]\sf H[/tex]. However, since point [tex]\!\sf G[/tex] denotes the flying duck, this point would not be in [tex]\sf L[/tex] (the plane that contains the surface of the lake.)
Hence, the line that contains [tex]\sf G\![/tex] and [tex]\sf H\![/tex] would not be in plane [tex]\sf L\![/tex].
Given three distinct points in a 3D space, there would be exactly one plane that contains the three points.
Hence, three points in a 3D space would not be non-coplanar.
In this question, point [tex]\sf G[/tex], [tex]\sf H[/tex], and [tex]\sf J[/tex] are all distinct. Hence, there would be exactly one plane that contains these three points.
Related Questions
Suppose $2000 is invested at 9% interest compounded continuously. How long will it take for the investment to grow to $10,000? Use the model A ( T ) = P e^rt and round to the nearest tenth of a year.
It will take approximately ____ years for the investment to grow to $10,000.
.
Answers
Answer:
7
Step-by-step explanation:
sing the equation > A = Pe^rt
20000 = 10000e^0.1t > 10% = 0.1
2 = e^0.1t
log 2 = log e^0.1t > log to the base e
log 2 = 0.1t * 1 log e to the base e =1
0.6931 = 0.1t
t = 6.931
= 7 years
Hope this helps <3
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11. Which of the following is an example of a rational number?
Answers
16. If there are 15 girls and 45 boys in a class. Then, find the percentage of boys and girls.
Answers
Answer:
25% and 75%
Step-by-step explanation:
15+45=60
girl = [tex]\frac{15}{60} *100[/tex] = 25%
boy = [tex]\frac{45}{60} *100[/tex] = 75%
Graph the equation.
2x + 3y = 12
Answers
x=6 y=0
x=3 y=2
Now plot the graph :)
Which equation has no solution?
4(х + 3) 2x = 6(х + 2)
5 + 2(3 + 2x) = x4 3(х + 1)
5(х + 3) +х= 4(х + 3) + 3
4 + 6(2 + х) = 2(3х + 8)
Answers
Answer:
2? equation does not have a solution
Step-by-step explanation:
Which is the graph of 4x + 2y < 3? On a coordinate plane, a dashed straight line with negative slope goes through (0, 2) and (1, 0). Everything to the right of the line is shaded. On a coordinate plane, a dashed straight line with negative slope goes through (0, 2) and (1, 0). Everything to the left of the line is shaded. On a coordinate plane, a dashed straight line with positive slope goes through (negative 1, 0) and (0, 2). Everything to the left of the line is shaded. On a coordinate plane, a dashed straight line with positive slope goes through (negative 1, 0) and (0, 2). Everything to the right of the line is shaded.
Answers
Answer:
it is a negative slope (going left), dashed and shaded left below the line - the points are not correct.
y<-2x+3/2
-2 = m and the y-intercept is 3/2
Step-by-step explanation:
Answer:
The second graph showing the y-intercept as 2 and the x-intercept as 1 with the left side of the line shaded in red. Ur welcome and have a nice day :3
Step-by-step explanation:
simplify 5 - (3 a + 1) + 2 a
Answers
5-3a-1+2a
Simplify:
4-a
Step-by-step explanation:
5-3a-1+2a
5-1-3a+2a
4-1a
Graph step by step:
f(x)=-2x+1
Answers
Step-by-step explanation:
Root:(1/2, 0)
Domain: x∈R
Range: y∈R
Vertical intercept: (0, 1)
help find the surface area of a cylinder with the height of 9 inches and base radius of 4
Answers
9514 1404 393
Answer:
104π in² ≈ 326.7 in²
Step-by-step explanation:
Put the given numbers in the surface area formula for a cylinder.
SA = 2πr(r +h)
SA = 2π(4 in)(4 in +9 in) = 104π in² ≈ 326.7 in²
Answer:
326.73
Step-by-step explanation:
You just have to plug this into the cylinder surface area formula, which is [tex]A=2\pi rh+2\pi r^{2}[/tex]. So solving this would be [tex]A=2\pi (4) (9) +2\pi (4)^{2}[/tex]. You can simply put that into your calculator, and you'll get 326.72564, which rounds to 326.73. Make sure to read your problem carefully in case it specifies what number to round to though.
You want to buy a $239,000 home. You plan to pay 20% as a down payment, and take out a 30 year loan for
the rest
a) How much is the loan amount going to be?
b) What will your monthly payments be if the interest rate is 5%?
$
c) What will your monthly payments be if the interest rate is 6%?
Submit Question
3
1
O
A
оо
Answers
Answer: a) 191200 b) 557.67 c) 562.98
Step-by-step explanation:
a) 239000 times .8 (aka 80%) = 191200
b) 191200/(12 times 30) = 531.11
531.11 times 1.05 (5%) = 557.667
Round to nearest cent: 557.67
c) 191200/(12 times 30) = 531.11
531.11 times 1.06 (6%) = 562.978
Round to nearest cent: 562.98
The price of an item has been reduced by 65%. The original price was $79. Find the price of the item now.
Answers
Solve for x: (1/3)x = 81
Answers
Answer:
243
Step-by-step explanation:
1 /3 x=81
Step 1: Multiply both sides by 3.
3*( 1 /3 x)=(3)*(81)
x=243
The value of x for the expression (1/3)x = 81 is 243.
What is an algebraic expression?An algebraic expression is consists of variables, numbers with various mathematical operations.
The given expression is,
(1/3)x = 81
To find the value of x,
Solve the expression,
(1/3)x = 81
x = 81 x 3
x = 243
The required value of x is 243.
To know more about Algebraic expression on:
https://brainly.com/question/19245500
#SPJ2
Luc has to read 3 novels and 12 short stories for his literature class. The professor will
choose one reading at random for the final exam. Find the probability that the professor
will choose a novel for the final exam. Express your answer as a) a fraction, and b) as a
decimal.
Show your work.
Help! :)
Answers
Answer:
Fraction: 1/5
Decimal: 0.2
Step-by-step explanation:
A scuba diver is 30 feet below sea level. She then rises 30 feet. What is the scuba
diver's new position?
Answers
Answer:
The scuba diver is at sea level.
Step-by-step explanation:
Hi there!
We're given that the scuba diver is 30 feet below sea level, and then she rises 30 feet.
This means she would be at sea level, not above or below.
You can think of it on a vertical ruler; the scuba diver starts at 0, goes down 30 units and goes back up 30 units. She will end up at 0 again, which in this case is sea level.
I hope this helps!
9. ax + by = (a - b), bx - ay = (a + b)
Answers
Answer: give me brainliest
Step-by-step explanation:
ax+by=a-b
ax=a-b-by
x=a-b-by/a←
bx-ay=a+b
substituting
b(a-b-by/a)-ay=a+b
ab-b²-b²y/a-ay=a+b
ab-b²-b²y-a²y/a=a+b
ab-b²-(b²+a²)y=a²+ab
-(b²+a²)y=a²+ab-ab+b²
(b²+a²)y=-(a²+b²)
y=-(a²+b²)/a²+b²
y=-1←
substituting value of y
x=a-b-b(-1)/a
x=a-b+b/a
x=a/a
x=1
What’s is the length of side b?
Answers
[tex]\\ \sf\longmapsto B^2=H^2-P^2[/tex]
[tex]\\ \sf\longmapsto B^2=45^2-27^2[/tex]
[tex]\\ \sf\longmapsto B^2=2025-729[/tex]
[tex]\\ \sf\longmapsto B^2=1296[/tex]
[tex]\\ \sf\longmapsto B=\sqrt{1296}[/tex]
[tex]\\ \sf\longmapsto B=36[/tex]
Answer:
[tex]\displaystyle 36 = b[/tex]
Step-by-step explanation:
The scale factour is [tex]\displaystyle 4\frac{1}{2},[/tex]so multiply 8 by 4½:
[tex]\displaystyle 36 = [4\frac{1}{2}][8][/tex]
Now, the way you can tell that this is the scale factour is by our MAGIC NUMBER, 10. If you divide both hypotenuses, you will get 4½:
[tex]\displaystyle 4\frac{1}{2} = 45 \div 10[/tex]
From here, you already know you must multiply 8 by this scale factour.
I am delighted to assist you at any time.
A
person that weighs 150 pounds on
Earth will weigh 25 pounds on the Moon.
How much will a 90-pound person weigh
on the Moon?
A. 10 lb
B. 12 lb
C. 15 lb
D. 20 lb
Answers
Answer:
Step-by-step explanation:
Ans:15 lb
A 90-pound person will weigh 15lb as we weigh six times less on the moon than the earth. So to find out simply divide 90 by 6.
can someone help me please
Answers
Step-by-step explanation:
11.
[tex] \frac{x - 4}{ \frac{x}{4} - \frac{4}{x} } [/tex]
[tex] \frac{x - 4}{ \frac{ {x}^{2} }{4x} - \frac{16}{4x} } [/tex]
[tex] \frac{x - 4}{ \frac{ {x}^{2} - 16 }{4x} } [/tex]
[tex] \frac{x - 4}{ \frac{(x + 4)(x - 4)}{4x} } [/tex]
[tex] \frac{4x}{x + 4} [/tex]
12.
[tex] \frac{ \frac{ {x}^{2} - 1 }{x} }{ \frac{(x - 1) {}^{2} }{x} } [/tex]
[tex] \frac{ {x}^{3} - x}{ {x}^{3} - 2 {x}^{2} + x } [/tex]
[tex] \frac{x( {x} - 1)(x + 1) }{x( {x} - 1) {}(x - 1) } [/tex]
[tex] \frac{x + 1}{x - 1} [/tex]
13.
[tex] \frac{ \frac{ {t}^{2} }{ \sqrt{ {t}^{2} + 1} } - \sqrt{ {t}^{2} + 1} }{ {t}^{2} } [/tex]
[tex] \frac{ \frac{ {t}^{2} }{ \sqrt{ {t}^{2} + 1 } } - \frac{ {t}^{2} + 1}{ \sqrt{ {t}^{2} + 1 } } }{ {t}^{2} } [/tex]
[tex] \frac{ \frac{1}{ \sqrt{ {t}^{2} + 1 } } }{ {t}^{2} } [/tex]
[tex] \frac{ - \frac{ \sqrt{ {t}^{2} + 1 } }{ {t}^{2} + 1 } }{ {t}^{2} } [/tex]
[tex] - \frac{ \sqrt{ {t}^{2} + 1} }{ {t}^{2}( {t}^{2} + 1) } [/tex]
14.
[tex] \frac{3x { }^{ \frac{1}{3} } - x {}^{ \frac{ - 2}{3} } }{3x {}^{ - \frac{2}{3} } } [/tex]
[tex] \frac{3x - 1}{3} [/tex]
Find m<1 if m<CUB = 78
Answers
[tex]\\ \sf\longmapsto m<1+m<CUS=m<CUB[/tex]
[tex]\\ \sf\longmapsto m<1+48=78[/tex]
[tex]\\ \sf\longmapsto m<1=78-48[/tex]
[tex]\\ \sf\longmapsto m<1=30[/tex]
Question 8 of 10
What is the sum of the roots of the polynomial shown below?
f(x) = x3 + 2x2 – 118 - 12
Answer here
Answers
Answer: y=x3+2x2−130
Step-by-step explanation:
Hope this helps!
Formula to find perimeter of rectangle
Answers
Hey there!
The formula to find the perimeter of a rectangle is "P=2(l+w)".
Hope this helps!
Have a great day! :)
Answer:
formula to find the perimeter of rectangle is
2(l+b)hope it helps
stay safe healthy and happy.
Please I need help the picture below with the options
Answers
9514 1404 393
Answer:
(B) Function 2
Step-by-step explanation:
We can compute the slope of Function 2 using the slope formula.
m = (y2 -y1)/(x2 -x1) . . . . where x and y are the independent and dependent variables.
m = (0.2 -0.8)/(3 -2) = -0.6
The slope of Function 1 is about ...
-3/7 ≈ -0.43
The slope of Function 2 is more negative.
__
On a graph, the line representing function 2 has a steeper downward slope.
Rewrite x2 − 6x + 7 = 0 in the form (x − a)2 = b, where a and b are integers, to determine the a and b values.
a = 4 and b = 3
a = 3 and b = 2
a = 2 and b = 1
a = 1 and b = 4
Answers
Answer:
a = 3 and b = 2
Step-by-step explanation:
From completion of squares:
[tex] {x}^{2} - 6x + 7 = 0 \\ \{ {x}^{2} - 6x + { (\frac{6}{2} )}^{2} \} + 7 - {( \frac{6}{2}) }^{2} = 0 \\ ( {x}^{2} - 6x + {3}^{2} ) = 2 \\ { \boxed {{(x - 3)}^{2} = 2}}[/tex]
a is 3
b is 2
Answer:
Answer B : a = 3 and b = 2
Step-by-step explanation:
Give man above brainlyiest he deserives it
The midpoint of a segment can be found using the formulas for a directed line segment, x = (x2 – x1) + x1 and y = (y2 – y1) + y1. When using these formulas to find a midpoint, which is true?
Answers
Step-by-step explanation:
Formula for finding midpoint of a line segment :
[tex] (\frac{x1 + x2}{2} , \frac{y1 + y2}{2} )[/tex]
you should have both the points of line segment.Just subtitute points in the formula and determine mid points.
Note: if you have any question about it you can freely ask. Thanks
Math what is the range of the absolute value function
Answers
Answer:
The choose C.
I hope I helped you^_^
Type the correct answer in the box. Round your answer to the nearest hour. A scientist running an experiment starts with 100 bacteria cells. These bacteria double their population every 15 hours. Find how long it takes for the bacteria cells to increase to 300. Use the formula , where is the original number of bacteria cells, is the number after t hours, and d is the time taken to double the number. It takes_____ hours for the number of bacteria to increase to 300.
Answers
Answer:
It takes 45 hours for the bacteria to triple the initial amount
Answer:
45 HOURS IS CORRECT
Step-by-step explanation:
Add the Following Fractions:
\large \frac{7}{16}+\frac{5}{16}=?
a. 80/112
b. 12/32
c. 12/16 = 3/4
d. 35/16
Answers
Answer: C, 3/4 And it's decimal form is 0.75
Step-by-step explanation:
Sugar cookie recipe that makes five dozen cookies calls for 2.5 cups of white sugar how much white sugar should you need to make two dozen cookies
Answers
Answer:
1 cup
Step-by-step explanation:
2.5 cups 5 dozen.
x cups 2 dozen.
what is the factor to turn 5 into 2 ?
5×a = 2
a = 2/5
so, we need to multiply also the cups with that factor to keep the relationship cups and amount of cookies unchanged.
therefore,
2.5 × 2/5 = 5/2 × 2/5 = 1
she needs 1 cup.
4×..., biar jadi 100...
tolong ya kak...
Answers
Answer:
25
Step-by-step explanation:
4×25 =100
____________
Answer:
25
Step-by-step explanation:
4 × 25 = 100
100 ÷ 4 = 25
Hope this help :)
#Semangat_Belajar
Does anyone know this and can help please
Answers
Answer:
[tex]\frac{y^7z^3}{x}[/tex]
Step-by-step explanation:
When variables have negative exponents, switch their positions.
[tex]\frac{x^{-1}y^7}{z^{-3}}=\frac{y^7z^3}{x}[/tex]