the point equidistant from the points (0, 0, 0), (0, 4, 0), (3, 0, 0), and (2, 2, -3) are (1/2, 1, 3/2).
What do you understand by equidistant points?Equidistant is a synonym for "equally distant," which is the state of two points being at the same distance from one another. Equidistant implies at the same distance from a location. The term "equidistant" is commonly used in reference to circles, perpendicular bisectors, parallel lines, and other geometrical concepts .Equidistant refers to the relationship between two or more objects or points that are situated at the same distance from one another. A point is considered to be equidistant from two other points when they are both located at the same distance from it. In the middle of the two starting points is a midway. The distance formula or the halfway formula can be used to demonstrate this.
Equation of sphere passes through origin is given by
x2 + y2 + z2 + ax + by+ cz =0
Given, it also passes through (1,0,0), (0,2,0),(0,0,3)
1+ a = 0, a = -1
4+2b =0, b=-2
And, 9+3c = 0, c= -3
The equation of the sphere becomes x2 +y2+ z2 -x -2y -3z = 0
Comparing with x2 +y2+ z2+ 2gx +2fy +2kz +C =0
Therefore the point that is equidistant from all the given points will be the centre of the sphere passing through all these points.
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Louis makes a model of a plane.
The wingspan of the model is 50 centimetres.
The wingspan of the real plane is 80 metres.
(a) Work out the scale of the model.
Give your answer in the form 1: n
50180
The length of the real plane is 72 metres.
(b) Work out the length of the model.
Give your answer in centimetres.
The sum of two numbers is 88. If one number is 4 more than half the other number, determine the two numbers by setting up a linear equation.
a. 44
b. 56
c. 61.3
d. 126
e. 138
f. 176
The two numbers by setting up a linear equation are 56 and 32
What are linear equations?Linear equations are equations that have constant average rates of change.
Note that the constant average rates of change can also be regarded as the slope or the gradient
How to determine the two numbers by setting up a linear equation?Let the two numbers be x and y
Where
y = 4 + 1/2x
So, we have
x + y = 88
Substitute y = 4 + 1/2x in x + y = 88
x + 4 + 1/2x = 88
Evaluate
1.5x = 84
Divide by 1.5
x = 56
Substitute x = 56 in y = 4 + 1/2x
y = 4 + 1/2 * 56
Evaluate
y = 32
Hence, the two numbers by setting up a linear equation are 56 and 32
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what is the perimeter of a triangle with the points (-9,4) (7,4) and (7, -8)
[tex]~\hfill \stackrel{\textit{\large distance between 2 points}}{d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}}~\hfill~ \\\\[-0.35em] ~\dotfill\\\\ A(\stackrel{x_1}{-9}~,~\stackrel{y_1}{4})\qquad B(\stackrel{x_2}{7}~,~\stackrel{y_2}{4}) ~\hfill AB=\sqrt{(~~ 7- (-9)~~)^2 + (~~ 4- 4~~)^2} \\\\\\ ~\hfill AB=\sqrt{( 16)^2 + ( 0)^2}\implies \boxed{AB=16} \\\\\\ B(\stackrel{x_1}{7}~,~\stackrel{y_1}{4})\qquad C(\stackrel{x_2}{7}~,~\stackrel{y_2}{-8}) ~\hfill BC=\sqrt{(~~ 7- 7~~)^2 + (~~ -8- 4~~)^2}[/tex]
[tex]~\hfill BC=\sqrt{( 0)^2 + ( -12)^2}\implies \boxed{BC=12} \\\\\\ C(\stackrel{x_1}{7}~,~\stackrel{y_1}{-8})\qquad A(\stackrel{x_2}{-9}~,~\stackrel{y_2}{4}) ~\hfill CA=\sqrt{(~~ -9- 7~~)^2 + (~~ 4- (-8)~~)^2} \\\\\\ ~\hfill CA=\sqrt{( -16)^2 + (12)^2}\implies CA=\sqrt{400}\implies \boxed{CA=20} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{Perimeter}{16~~ + ~~12~~ + ~~20\implies \text{\LARGE 48}}[/tex]
solve the equation x/3-6=5
Answer: x= 33
Step-by-step explanation: hope this helps!!!
what is 20 divided by 5 times 20 plus 10
Answer:
Step-by-step explanation:
20 divided by 5x20+10=90
Answer:
90
Step-by-step explanation:
this is easiest if you know your order of operations PEMDAS so there are no parenthesis or exponents so next is multiplication and division. so 20/5= 4 then 4*20 is 80 and 80+10=90.
here's an easy way to remember PEMDAS
Please Excuse My Dear Aunt Sally
Is 0. 19
a rational or irrational? Explain
Answer:
It's rational, because it can be converted into a reasonable fraction.
➯ Hope this helps!
I need help , please quickly!
Choose the associated property
The Associative property is not displayed by any of the given equations.
The associative property of several binary operations in mathematics states that the outcome will not change if the parenthesis in an expression are rearranged.
The order in which the operations are carried out within an expression that has two or more instances of the same associative operator in a row doesn't matter as long as the order of the operands is left untouched.
Examples of associative property :
[tex]{\displaystyle {\begin{aligned}(7+8)+1&=7+(8+1)=9\,\\5\times (3\times 7)&=(5\times 3)\times 7=24.\end{aligned}}}[/tex]
The parentheses were rearranged on each line, but the expression values were left alone. It can be argued that "addition and multiplication of real numbers are associative operations" because this is true for addition and multiplication of all real numbers.
Here 8=8+0 displays additive identity property.
10×1=10 displays multiplicative identity
5+0=5 displays displays additive identity property.
[tex]5\times \frac{1}{5}=1[/tex] displays multiplicative inverse property.
[tex]3+\frac{3}{4} =3+\frac{3}{4}[/tex] displays reflexive property.
Hence no equation displays associative property.
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in triangle abc, angle b is 120∘ . it contains bisectors aa1, bb1 and cc1. prove that the angle a1b1c1 is 90∘
The triangle formed by the feet of angle bisectors of a triangle with a single angle measure of 120° is the Right Triangle.
What is a triangle?A triangle is a three-edged polygon with three vertices. It is a fundamental shape in geometry. Triangle ABC denotes a triangle with vertices A, B, and C. In Euclidean geometry, any three non-collinear points define a unique triangle and, by extension, a unique plane.So,
In triangle ABC, ∠A = 120°.
Let AD, BE, and CF be the respective angle bisectors of A, B, and C.AC in ABD is the exterior angles bisector (as DAC=CAX=60°).BE is the internal angle bisector that meets at E. E is the ex-center of ABCD.As a result, DE is the exterior angle bisector of ABCD.
Then, ADE=EDC, and ADC=2ADE.Similarly, for the ABC, F is ex-center because AB is the exterior angle bisector and CF is the interior angle bisector.
As a result, DF is the exterior angle bisector.
∠ADF = ∠FDB, ∠BDA = 2∠ADFBC is a straight line.
∠BDA+∠ADC=180°2∠ADF+2∠ADE=180°∠ADF+∠ADE=90°So, DEF is the right triangle.
As a result, the triangle formed by the feet of angle bisectors of a triangle with a single angle measure of 120° is the Right Triangle.
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The correct form of the question is given below:
Prove in any ΔABC, if one angle is 120°, the Δ formed by the feet of the angle bisectors is right-angled.
If 3 books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that:________
The probability that:
a dictionary is selected = [tex]\frac{1}{9}[/tex]two novels and a book of novels is selected = [tex]\frac{5}{14}[/tex]What is probability?Probability refers to the possibility of the occurrence of an event.
P(E) = probability of occurrence of an event E = [tex]\frac{Number Of Favourable Outcomes}{Total Number Of Outcomes}[/tex]
Now,
(a) Total number of books = 5 + 3 + 1 = 9
Probability of getting a dictionary = [tex]\frac{1}{9}[/tex]
(b) Number of ways to select 3 books out of 9 books = [tex]\binom{9}{3}[/tex] = [tex]\frac{9!}{3!(6!)} = \frac{9\times\ 8 \times 7}{6}[/tex] = 84
Number of ways to select 1 out of 3 books of poems = [tex]\binom{3}{1} = \frac{3!}{2!}[/tex] = 3
Number of ways to select 2 out of 5 novels = [tex]\binom{5}{2} = \frac{5!}{2! 3!} = \frac{5\times 4}{2} = 10[/tex]
Thus, the probability of getting 2 novels and 1 book of poem = [tex]\frac{3\times10}{84} = \frac{10}{28} = \frac{5}{14}[/tex]
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(COMPLETE QUESTION:
If three books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that (a) a dictionary is selected? (b) 2 novels and 1 book of poems are selected?)
In maryland, the sales tax is 6%. what is the tax, in dollars and cents on a 32.74 purchase( round to the nearest cent) Show your work
The tax on the product will be $1.964.
How to compute the value?It should be noted that from the information, the sales tax is 6% and the price of the product is $32.74.
Therefore, the value of the tax will be:.
Tax percentage × Price
= 6% × $32.74
= 0.06 × $32.74
= $1.9643
Therefore, the tax on the product will be $1.964.
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Values that are perfect squares? Which ones are
1. 64
2. 32
3. 18
4. 100
Answer:
64,100
Step-by-step explanation:
64,100are the values that are perfect square
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Find the 59th term of the arithmetic sequence 29, 37, 45, ...
Answer:
AP = 29,37,45,...
d= t2-t1
=37-29
=8
n=59
t59=?
tn=a+(n-1)d
t59=29+(59-1)8
t59=28+58×8
t59=28 + 464
t59=492
Step-by-step explanation:
please mark it brainliest and thank it please
F(x)=-6x-3 if the input is -8, what is the output
Answer:
F(x) = -6x - 3
F(x) = -6(-8) - 3
F(x) = 48 - 3
F(x) = 45
five times square of a number is equal to 45
Answer:
x can be -3, or +3
Step-by-step explanation:
The equation would be
5[tex]x^{2}[/tex] = 45
Divide both sides by 5
[tex]x^{2}[/tex] = 9
Take the square root of both sides
x = ± 3
What is the absolute value of Point B labelled on the number line?
A number line with point A at coordinate negative 2.2, point B at coordinate negative 1.6, and point C at coordinate 1.2.
Drag and drop the answer into the box to match the correct statement.
Answer:
1.6
Step-by-step explanation:
| -1.6 | = 1.6
Natalie combines 8.54 liters of red paint with 8.31 liters of blue paint to make purple paint. She pours the paint equally into 2 containers, and has 1.13 liters of paint left over. How many liters of paint are in each container?
7.86 liters of purple paint in each container.
Given data from the given problem:volume of red paint is 8.54 liters.
volume of blue paint is 8.31 liters.
Number of container taken is 2 container.
Paint left after equally poured in 2 container.
and we have to find how many liters of paint are in each container.
Volume of RED Paint + Volume of BLUE Paint = Volume of PURPLE Paint
8.54 liters + 8.31 liters = 16.85 liters.
(16.85/2) - (1.13/2) = 15.72/2
=7.86 liters
7.86 liters of purple paint in each container.
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A bike wheel.
The weight of a full steel bead tire is approximately 800 grams, while a lighter wheel weighs only 700 grams. What is the weight of each tire in pounds? There are 453.592 grams in one pound. Round answers to 2 decimal places.
Answer: BABABAB
Step-by-step explanation:
BHBAHBABAHBABHABHBAHBABHABHBAbhaBHBA
you bought a pair of jeans for $42.95 and a sweater for $36.99 . what was the cash price including a 5% sales tax?
Answer:
Step-by-step explanation:
jeans $42.95
sweater + $36.99
total = $69.94
tax + 5% ($3.497 round to nearest hundredth ($3.50))
total with tax = 73.44
hope this helped!!!! let me know if you need anymore help with this :) have a good day!
with show work needed. a and b.
a)
Solution,
Given,
Cost for 1 pen = $ 1.50
= 1.50×100 cents
= 150 cents
Cost for 1 ruler = 80 cents
No. of Pens needed to be bought = x
No. of rulers needed to be bought = x+10
Now,
Cost for x pens = x×150 cents
= 150x cents
Cost for (x+10) rulers = (x+10)×80 cents
= 80x cents+800 cents
Then,
Total cost = 150x cents+(80x cents+800 cents)
= 150x cents+80x cents+800 cents
= 230x cents+800 cents
= $(230x ÷ 100)+$(800 ÷ 100)
= $2.3x + $8
Therefore,Louise spent $2.3x and $8 as total amount
b)
Sorry,I dont know inequality
A football team has attempted 6 running plays. The change in field position resulting from each play is shown in the table. What is the average change in field position per running play?
–6 yards per play
–1 yard per play
0 yards per play
1 yard per play
Answer:
-1 yard per play
play 6 - play 3=0
play 2 - play 4=0
play 1 - play 5 = -6
hope it helped
Can someone help me with this problem? Thank you!
Answer:
122 degrees
Step-by-step explanation:
43 + 15 = 58 - 180 = 122
two ships leave a harbor at the same time. the first ship heads north at 20 miles per hour, and the second ship heads west at 15 miles per hour. write an expression that gives the distance d between the ships after t hours.
The expression that gives the distance, d, between the ships after t hours is d = 25t
Calculating DistanceFrom the question, we are to write an expression that gives the distance, d, between the ships after t hours
First, we will determine the distance the ships have traveled after t hours
Using the formula,
Distance = Speed × Time
Thus,
The first ship would have traveled
20 × t miles
= 20t miles
The second ship would have traveled
15 × t miles
= 15t miles
Using the Pythagorean theorem,
The distance, d, between the ships after t hours is
d² = (20t)² + (15t)²
d² = 400t² + 225t²
d² = 625t²
d = √(625t²)
d = 25t miles
Hence, the expression that gives the distance, d, between the ships after t hours is d = 25t
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E=mo^2 solve for m ...............................................
The expression for m from the given equation is m = E/o^2
Subject of formulaThe subject of formula is a way of representing a variable with another variable
Given the equation
E = mo^2
We are to make m the subject of the formula. To do that, we will divide both sides of the equation by o^2 to have:
E/o^2 = mo^2/o^2
E/o^2 = m
Swap
m = E/o^2
Hence the expression for m from the given equation is m = E/o^2
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ROUND off the answers using the rules for approximate numbers.
Problems: 97.83 - 4.378 + 5.92
and 1,342.8+ 85.32 + 173.54 + 16
The value of the numbers given will be:
1. 108
2. 1618
How to calculate the values?1. The expression given will be calculated as:
= 97.83 - 4.378 + 5.92
= 98 + 4 + 6
= 108
2. 1,342.8+ 85.32 + 173.54 + 16
= 1343 + 85 + 174 + 16
= 1618
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Harry drove for 3 hours on the freeway, then decreased his speed by 20 miles per hour and drove for 6 more hours on a country road. If his total trip was 483 miles, then what was his speed on the freeway?
Harry's speed on the freeway is 67 miles per hour
Time Harry drove on freeway = 3 hours
Time Harry drove on country road = 6 hours
Total distance covered by him = 483 miles
Let his speed be x miles per hour
Formula to be used:
Speed*Time = Distance
Therefore, the distance covered by him on the freeway = 3x -----(1)
Distance covered by him on country road = 6(x - 20)------(2)
Formulating the equations using (1) and (2)
3x + 6(x-20) = 483
3x + 6x - 120 = 483
9x = 603
x = 67 miles per hour
So, his speed on the freeway is 67 miles per hour and on the country road it is 47 miles per hour
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What is the probability of rolling either a 5 or a 6 using a normal six-sided die?
1/3 is the probability of rolling either a 5 or a 6 using a normal six-sided die.
Define probability?Probability can be defined as the ratio between the number of favorable outcomes and the total number of outcomes of an event.
Given:
Six-sided dice rolled once
Let n be the number of outcomes
let x be the number of favorable outcomes
We know that,
[tex]Probability=\frac{x}{n}[/tex]
When the six-sided dice roll, The possible outcomes are,
[tex]\{1,\;2,\;3,\;4,\;5,\;6\}[/tex]
Therefore,
[tex]Number\;of\;outcomes,\;n=6[/tex]
[tex]Probability\;rolling\;5\;is\;\frac{1}{6}[/tex]
[tex]Probability\;rolling\;6\;is\;\frac{1}{6}[/tex]
Therefore, Probability of rolling either 5 or 6 is,
[tex]P(5\;or\;6)=\frac{1}{6} +\frac{1}{6}[/tex]
[tex]P(5\;or\;6)=\frac{2}{6}[/tex]
[tex]P(5\;or\;6)=\frac{1}{3}[/tex]
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Matter is in a liquid state when its temperature is between its melting point and its boiling point. Suppose that some substance has a melting point of -48.39°C and a
boiling point of 313.31°C. What is the range of temperatures in degrees Fahrenheit for which this substance is not in a liquid state? (Hint: C=5/9(F-32)) Express the range
as an inequality
Let x represent the temperature in degrees Fahrenheit. What is the range of temperatures for which this substance is not in a liquid state?
(Type an inequality or a compound inequality. Simplify your answer. Use integers or decimals for any numbers in the expression Round to three decimal places as needed)
[tex]Answer:\ -55.102^0F\leq t^0\leq 595.958^0F[/tex]
Step-by-step explanation:
[tex]\displaystyle\\C^0=\frac{5}{9} (F^0-32^0)\\[/tex]
Let's multiply both parts of the equation by 9/5:
[tex]\displaystyle\\\frac{9}{5} C^0=F^0-32^0\\\\\frac{9}{5} C^0+32^0=F^0-32^0+32^0\\\\\frac{9}{5} C^0+32^0=F^0\\\\Thus,\\\\F^0=1.8C^0+32^0[/tex]
[tex]t=-48.39^0C\\Hence,\\t^0(F)=1.8(-48.39^0)+32^0\\t^0(F)=-87.102^0+32^0\\t^0(F)=-55.102^0[/tex]
[tex]t=313,31^0C\\Hence,\\t^0(F)=1.8(313,31^0)+32^0\\t^0(F)=563.958^0+32^0\\t^0(F)=595.958^0[/tex]
[tex]Thus,\\-55.102^0F\leq t^0\leq 595.958^0F[/tex]
the number of hours it takes for ice to melt varies inversely with the air temperature. suppose a block of ice melts in 2 hours when the temperature is 65 degrees celsius.
The value of the constant of variation is 130
What is constant of variation?Constant of variation can be defined as the ratio between two variables in an inverse variation on a direct variation.
In direct variation equations = k and y = kx, In inverse variation equations xy = k and y = , k is the constant of variation.From the information given, we have that;
The number of hours is x
The temperature is y
x α 1/ y
x = k/y
k = xy
Substitute the values
k = 2 × 65
k= 130
Thus, the value of the constant of variation is 130
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The complete question:
the number of hours it takes for a block of ice to melt varies inversely as the temperature. If it takes 2 hours for a square inch of ice to melt at 65 degrees find the constant of variation
Lashonna passed back 140 papers, if these papers were in stacks of 28 how many stacks of papers did lashonna pass back
By unitary method we can say that number of stacks of papers Lashona will pass back from 140 if each stack conatins 28 papers is 5.
According to the given question.
Total number of papers Lashonna passed back = 140
And one stack is made up of 28 papers.
As we know that, the unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Therefore,
By unitary method number of stacks of papers would be made from 140 if each stack conatins 28 papers
= 140/28
= 5
Hence, by unitary method we can say that number of stacks of papers Lashona will pass back from 140 if each stack conatins 28 papers is 5.
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Read following problem. Identify what you need to know. Then use the information in the problem to solve. Show your work.
R S is the midsegment of trapezoid M N O P . What is the length of RS ?
A 14 units B 19 units C 23 units D 26 units
Answer:
ssdf
Step-by-step explanation:
dbd beddbees sveveusbs wie eje edidjebebe djebejdjebe ejd s