Answer:
b
Step-by-step explanation:
B: Every plane contains at least three points that do not lie on the same line
To answer this question, we will have to state the 5 axioms of Euclidean geometry and they are;
1. A straight line could be drawn between any two points; This means that as long as there is no obstacle between the two points, then we can say that it is possible to draw a straight line between both points. However, if there is an obstacle between the two points, then it is not possible to draw a straight line.
2. Any straight line that is terminated could still be extended indefinitely; A line segment may be bound by an endpoint, but a straight line is not bounded by any endpoint and as a result, it can be extended indefinitely in both directions.
3. A circle could be drawn with any given center point and any given radius; If for example we use a line segment bounded by two end points. If we use one of these 2 endpoints to be the centre of a circle and make the radius of the circle to be equal to the length of the line segment earlier used as an example, it means if we draw a circle, it will have a diameter that is twice the length of that same line segment.
4. All right angles are definitely equal; A right angle always has a measurement of 90°. This means that regardless of its' orientation, it will still remain 90°.
5. For any given point that is not on a given line, there will be exactly one line passing through the point that would not meet that same given line; This implies that two lines will be parallel to each other if they intersect a third line with the interior angle between them being 180°.
Looking at the given options in the question, the only one that doesn't correspond to any of these 5 axioms I have stated would be option B.
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A bus averages 4 miles per hour faster than a motorcycle. If the bus travels 180 miles in the same time it takes the motorcycle to travel 156 miles, then what is the speed of each?
Set up equations:
(1) speedbus = speedbike+4
(2) speedbus/speedbike = 180/156
plug (2) into (1)
speedbike * 180/156 = speedbike + 4
(solve for speedbike)
speedbike = 4 / (180/156-1) = 26 mph
--> speedbus = 26+4 = 30mph
Please help...
If g(x) = x2 + 2, find g(3).
A: 9
B: 8
C: 11
D: 6
As the [tex] g(x)=x^{2}+2[/tex]
To find the value of g(3) we have to put the value of [tex]x[/tex] equal to 3 everywhere in g([tex]x[/tex])
Therefore [tex] g(3)=(3)^2+2[/tex]
on solving the equation
[tex]g(3) = 9+2 [/tex]
[tex] g(3) = 11 [/tex]
Hence g(3) =11 is the answer
Hope this will help
Find the value of k if it is known that the line y=kx+2 goes through point P (−7, 12)
Hey there!!
What is slope-intercept form ?
Ans :- y = mx + b
Where ' m ' is the slope and ' b ' is the y-intercept.
Equation given :- y = kx + 2
Now, we know k is m or the slope and 2 y-intercept.
y-intercept can be given as a coordinate.
Hence, y - intercept 2 can be written as ( 0 , 2 )
Now we have 2 coordinates, ( 0 , 2 ) and ( -7 , 12 )
How do we find slopes ?
Ans :- Slope = [tex]\frac{y2- y1 }{x2-x1}[/tex]
Plugging in the values :
Slope = [tex]\frac{12-2}{-7-0}[/tex]
Slope = [tex]\frac{-10}{7}[/tex]
Hence, the value of 'k' is [tex]\frac{-10}{7}[/tex]
Hope my answer helps!
Answer:
k = -10/7
Step-by-step explanation:
1. Plug in (x,y)
2. You would get -7k+2=12
3. If you solve for k, you would get:
-7k = 10
k= -10/7
Hope this helped some people, and have a great day!
How to solve this for x ?
[tex]4+\dfrac{3}{5}\left(15+2x\right)=25\\\\\dfrac{3}{5}\left(15+2x\right)=21\\\\15+2x=35\\\\2x=20\\\\x=10[/tex]
10 times as much as 2000 is 1/10 of
The hard drive on your computer has a capacity of 160 gigabytes (GB). You have used 122 GB. You want to save some home videos to your hard drive. What are the possible sizes of the home video collection you can save? If u represents the amount of space used, write an inequality that determines a, the amount of space available.
To determine the size of the home video collection one can save, subtract the used space (122 GB) from the total hard drive capacity (160 GB). The remaining space is 38 GB, which is the maximum size for the home videos that can be saved. The inequality representing the available space in terms of 'a' is: a ≤ 38 GB.
Explanation:The subject of this question is a practical application of mathematics related to computer storage space.
If the computer's hard drive has a total capacity of 160 GB and you have already used 122 GB, we can determine the remaining available space with a simple subtraction: 160 GB - 122 GB = 38 GB.
So, the size of the home video collection that you can save cannot exceed 38 GB.
To represent this as an inequality where u is the amount used, and a is the amount available, we can write:
u + a ≤ 160 GB
Since you've used 122 GB already, the inequality in terms of a alone is:
a ≤ 160 GB - 122 GB
a ≤ 38 GB
This inequality states that the amount of additional data (home videos) you can save, denoted as a, should be less than or equal to 38 GB, which is the available space remaining on your hard drive.
Final answer:
To determine the available space on your hard drive, subtract the amount used from the total capacity. The possible sizes of the home video collection you can save range from 0GB to a maximum of 38GB. The inequality a ≤ 38GB represents the amount of space available.
Explanation:
To determine the amount of space available, you subtract the amount of space used from the total capacity. In this case, the total capacity is 160GB and the amount used is 122GB, so the amount of space available is 160GB - 122GB = 38GB.
Therefore, the possible sizes of the home video collection you can save range from 0GB (if you don't save any videos) up to a maximum of 38GB (if you save videos that take up the entire available space).
The inequality that represents this is: a ≤ 38GB, where 'a' represents the amount of space available.
what is the solution of 7k+2=4k-10?
Use one of the reasons from the box to justify each step.
You may use a reason more than once.
k=-4
7k+2=4K-10
+10 +10
7k+12=4K
-7k -7k
12=-3k
Divide both sides by -3
K=-4
The solution is k = -4.
To solve the linear equation 7k+2=4k-10, we need to isolate the variable k on one side of the equation. Here are the steps to simplify the equation and find the value of k:
Subtract 4k from both sides to eliminate the variable from the right side of the equation: 7k - 4k + 2 = 4k - 4k - 10, which simplifies to 3k + 2 = -10.
Subtract 2 from both sides to eliminate the constant term from the left side of the equation: 3k + 2 - 2 = -10 - 2, which simplifies to 3k = -12.
Divide both sides by 3 to solve for k: 3k / 3 = -12 / 3, which simplifies to k = -4.
Now we need to check the solution by substituting k = -4 back into the original equation to verify that it holds true:
7(-4) + 2 = 4(-4) - 10
-28 + 2 = -16 - 10
-26 = -26
The left and right sides of the equation are equal, confirming that k = -4 is the correct solution. Thus, the steps are justified and the solution is reasonable
If f(x)=6x+7 and g(x)=x^2-4 find value of g(-4t)
The final value of g(-4t) is [tex]16t^2 - 4.[/tex]
To find the value of g(-4t) with [tex]g(x) = x^2 - 4[/tex], substitute -4t into the function
The task is to find the value of g(-4t) when given that [tex]g(x) = x^2 - 4.[/tex]
To solve this, we simply replace x with -4t in the function g(x).
So, [tex]g(-4t) = (-4t)^2 - 4.[/tex]
Squaring -4t gives us [tex]16t^2[/tex], so the expression simplifies to [tex]16t^2 - 4.[/tex]
The final value of g(-4t) is [tex]16t^2 - 4.[/tex]
The values are: f(-3) = -11, f(m) = 6m + 7, f(r-2) = 6r - 5, g(5) = 21, and g(a) + 9 = a^2 + 5.
f(-3): Replace x with -3 in f(x) = 6x + 7Complete question is:
If f(x)=6x+7 and g(x)=x^2-4, find each value.
1.) f(-3)
2.) f(m)
3.) f(r-2)
4.) g(5)
5.) g(a)+9
How do I solve?
Which expression is equivalent to ^3 square root 343 x^9 v^12 z^6?
[tex]\sqrt[3]{343x^9v^{12}z^6}=\sqrt[3]{343}\cdot\sqrt[3]{x^{3\cdot3}}\cdot\sqrt[3]{v^{4\cdot3}}\cdot\sqrt[3]{z^{2\cdot3}}\\\\=\sqrt[3]{7^3}\cdot\sqrt[3]{(x^3)^3}\cdot\sqrt[3]{(v^4)^3}\cdot\sqrt[3]{(z^2)^3}=7x^3v^4z^2\\\\Used:\\\\\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\(a^n)^m=a^{nm}\\\\\sqrt[n]{a^n}=a[/tex]
The cube root of 343 is 7, x^9 is x^3, v^12 is v^4, and z^6 is z^2. So the equivalent expression to the cube root of [tex]343x^9v^12z^6[/tex] is 7x^3v^4z^2.
Explanation:The expression is asking for the cube root of each term. The cube root of 343 is 7 because [tex]7*7*7[/tex]equals to 343. The cube root of x^9 is x^3 because 3*3 equals to 9. Similarly, cube root of v^12 is v^4 because 4*3 equals 12, and cube root of z^6 is z^2 because 2*3 equals 6.
So the equivalent expression is [tex]7x^3v^4z^2.[/tex]
Remember, when dealing with cubic roots and exponential terms, we divide the exponent by 3.
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Alice and Carl each have the same number of marbles. Alice puts her marbles into groups of four with none left over. Carl puts his marbles into groups of 10 with none left over. What is the LEAST total number of marbles that Alice and Carl can each have?
Hey
Since there is none left over for both groups of 10 and 4, the number of marbles must be an LCM of 10 and 4, which is 20. Check: 20/10=2 groups of 10, 20/4=5 groups of 4. Thus the LEAST number of marbles each has must be 20, while multiples of 20 are possibilities, such as 40, 60, 80,100, ..
goodluck
What is the slope of a line parallel to a line with a slope of -1/6
As the slope of parallel lines are equL therefore slope of required line is -1/6
Answer: The answer is -1/6
Step-by-step explanation:
The other person was right and I happened to get an A<3
is the difference of two positive rational number always positive? Explain
NO, the difference between two positive rational numbers is not always positive.
A rational number is any number that can be expressed as a fraction of two different integers and these integers in their fractional form are not equal to zero.
Now, let assume the two positive numbers are 8 and 12. In rational positive
number, the numbers will be: [tex]\mathbf{\dfrac{8}{1}}[/tex] and [tex]\mathbf{\dfrac{12}{1}}[/tex]
The difference between these two rational numbers will not be positive because 12 is a larger number than 8.
[tex]\mathbf{=\dfrac{8}{1}-\dfrac{12}{1}}[/tex]
= -4
Therefore, the difference between two positive rational numbers is not always positive.
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Ameena's boat travels 35 miles per hour. The best fishing spot in the lake is 27 miles away from her starting point. If she drives her boat for 2/3 of an hour, will she make it to the best fishing spot on the lake?
Answer: No, she will not make it tot he best fishing spot on the lake.
Step-by-step explanation:
Since we have given that
Distance between the starting point and the best fishing spot = 27 miles
Speed at which Ameena drives = 35 miles per hour
Time she takes to drive her boat is given by
[tex]\frac{2}{3}\text{ of an hour}[/tex]
As we know that ,
[tex]Distance=Speed\times time\\\\Distance=35\times \frac{2}{3}\\\\Distance=\frac{70}{3}\\\\Distance=23.33\text{ miles}[/tex]
But we have given that the best fishing spot in the lake is 27 miles away from her starting point ,
[tex]\text{And with this speed in }\frac{2}{3}\text{ of an hour he reached only }23.33 \text{ miles. }[/tex]
So,
No, she will not make it tot he best fishing spot on the lake.
No, she will not
Find how far Ameena's boat will have traveled at two thirds of an hour.
(35 miles per hour) (2/3 of an hour)= 23.33 miles
Ameena's boat will have traveled just over 23 miles. She will not have reached the best fishing spot which will still be approximately another 4 miles away.
To find how far Ameena's boat has traveled you multiplied the speed by the time, but since time is now the unknown variable, divide the distance by the speed
27 miles divided by 35 miles per hour to get 0.77 hours
What is the conversion for hours to minutes?
0.77 = 46.2 minutes
Given the perimeter of a square, find the length of one side using the appropriate formula.
A square closet with a perimeter of 16 ft.
Answer:
f
Step-by-step explanation:7574
Aleta went to dinner. the bill was 36. she gave the waiter a 15% tip. what was the total ammount Aleta spend on the food and the tip
To calculate the total amount Aleta spent, including the tip, multiply the bill ($36) by the tip percentage (15%) to get the tip amount ($5.40) and add it to the bill to get the total cost ($41.40).
The question asks us to calculate the total amount Aleta spent on dinner including a 15% tip. To find the tip amount, we multiply the bill by the tip percentage in decimal form. The bill is $36, so we calculate 15% of $36 as follows:
0.15 × $36 = $5.40
The total cost of the meal including the tip is $36 (the original bill) + $5.40 (the tip) = $41.40.
In a science experiment, the temperature of a substance is changed from 42 °F to −54 °F at an average rate of −12 degrees per hour. Over how many hours does the change take place?
A 8 hours B
1
8
hour
C −8 hours D 1 hour
Remark
There are a couple of ways to do this. The easiest is to take the number of degrees between 42 and - 54 and divide by 12.
Method
the number of degrees is abs(42) + abs(-54) = 42 + 54 = 96
Now divide by 12
Hours = 96 / 12 = 8 hours. I think the answer is A.
Answer:
Its 8hrs
Step-by-step explanation:
Bruce has a 16 ounces bottle of water that is 1/2 full. He drinks 1/5 of the water left in the bottle. How many ounces of water are left in the bottle
Answer:
6.4 oz are left.
Step-by-step explanation:
Start with the bottle being half full.
A bottle that is half full when it started with 16 oz is 1/2 16 oz = 8 oz
If he drinks 1/5 of the remaining amount, it means that he has 4/5 left.
4/5 * 8 = 32/5 = 6.4 oz or 6 oz and 2/5 of an ounce.
Answer:
6.4 oz are left
Step-by-step explanation:
The bake star bakery uses 2 1/4 cups of raisins to make 4 servings of trail mix. How many cups of raisins are in each serving?
let's firstly convert the mixed fraction to improper fraction, and then divide it by 4 to see what our quotient is.
[tex]\bf \stackrel{mixed}{2\frac{1}{4}}\implies \cfrac{2\cdot 4+1}{4}\implies \stackrel{improper}{\cfrac{9}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{9}{4}\div 4\implies \cfrac{9}{4}\div \cfrac{4}{1}\implies \cfrac{9}{4}\cdot \cfrac{1}{4}\implies \cfrac{9}{16}[/tex]
Answer:
[tex]\frac{9}{16}[/tex] cups of raisins are in each serving
Step-by-step explanation:
Unit rate defined as the rates are expressed as a quantity as 1 such as 2 meter per seconds or 4 miles per hour.
As per the statement:
The bake star bakery uses 2 1/4 cups of raisins to make 4 servings of trail mix.
⇒Cup of raisins = [tex]2\frac{1}{4} = \frac{9}{4}[/tex] and number of serving = 4
We have to find the cups of raisins are in each serving
Then by definition of unit rate we have;
[tex]\text{unit rate per serving} = \frac{\frac{9}{4} }{4} = \frac{9}{16}[/tex] cups of raisins
therefore, [tex]\frac{9}{16}[/tex] cups of raisins are in each serving
Donte and Trista both bought the same three-ring binder for $5. Donte lives in Arizona and pays 5.6% in sales tax, while Trista lives in New Jersey and pays 7% in sales tax. How much more did Trista pay in sales tax than Donte?
Sales tax paid by Donte = [tex]\frac{5.6}{100} (5)[/tex]
= 0.28
Sales tax paid by Trista = [tex]\frac{7}{100} (5)[/tex]
= 0.35
The extra tax paid by Trista = 0.35 - 0.28 = 0.07.
Hence, Trista paid $0.07 more than Donte.
Solve for Y2: m= y2-y1 over x2-x1
y2 = m(x2-x1) + y1
Hope this helps :)
Use properties of addition and subtraction to evaluate the expression.
−38−11−22
Enter your answer in the box.
Answer:
-71
Step-by-step explanation:
Make t the subject of the formula
v = u + 5t
[tex]v = u + 5t\\\\5t=v-u\\\\t=\dfrac{v-u}{5}[/tex]
To make t the subject of the formula v = u + 5t, subtract u from both sides and divide by 5.
Explanation:To make t the subject of the formula v = u + 5t, we need to isolate t on one side of the equation.
First, subtract u from both sides of the equation: v - u = 5t.
Then, divide both sides of the equation by 5: (v - u)/5 = t.
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Two numbers have a sum of 21. one number is 7 more than the other . find the numbers
Answer: 14
Reasoning behind it: If you take 21 and subtract it by 7, you get 14. You can check this answer by doing this:
14+7=21.
Hope this helped!!!
Find the slope of a line that is perpendicular to the line 4x + 3y - 15 = 0.
I need help in this . Just ignore that equation in top of the problem
what is the interquartile range of this set of data 5, 5, 6, 7, 9, 11, 14, 17, 21, 23
Answer:
11.00
Step-by-step explanation:
To calculate the interquartile range of the data:
5, 5, 6, 7, 9, 11, 14, 17, 21, 23
To calculate the interquartile range we need to lower quartile [tex](X_L)[/tex] and upper quartile [tex](U_L)[/tex].
The lower interquartile [tex](X_L)[/tex] of the data set is: 6.
The upperquartile [tex](U_L)[/tex] of the data set is: 17.
Therefore, the interquartile range is: [tex](X_U-X_L)=(17-6)=11[/tex].
Answer:
11
Step-by-step explanation:
here is a easer way to explain you need the highest aand lowest number so thats 5 and 23 23-5=18 5 6 7 9 11 14 17 21 18=108 108/10=10.8 now you round the 8 and its 11
What is the permitter in simplest terms
3x+1+3x+1+2x+2x or 2(3x+1+2x)
10x+2
Your cousin gave you $9 to buy a present with. This covered 3/5 of the cost. How much did the present cost?
If the $9 is 3/5 of the amount of the present, then it will be 9 divided by 0.60, which is 15. You can check this by putting in 15 times 0.60, which is 9
0.1875 rounded to the nearest hundredth
To round the number 0.1875 to the nearest hundredth, you look at the thousandths place. As the digit (5) is 5 or more, we round up, giving us 0.19.
When rounding a decimal number to the nearest hundredth, you need to look at the digit in the thousandth place.
The number 0.1875 has a 5 in the thousandths place.
In rounding, if the digit immediately after the place we're rounding to is 5 or larger, we round up, otherwise we round down. Hence, 0.1875 rounded to the nearest hundredth becomes 0.19.
To clarify, 0.1875 is between 0.18 and 0.19, but is closer to 0.19 because of the 5 in the thousandths place prompting the round up.
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There are 8 people who are attending a speed dating event. Each person has the chance to spend 5 minutes on a speed date, getting to know all of the other people at the event. How many unique speed dates will there be? Please help!!!
i think there should be 8 factorial. that is, 8 times 7 times 6 times 5 times 4...
There will be 28 unique speed dates in total.
Explanation:In this speed dating event, there are 8 people who each have the chance to go on a speed date with every other person at the event. Since there are 8 people, there will be 8 - 1 = 7 speed dates for each person.
To find the total number of unique speed dates, we can use the formula n * (n - 1) / 2, where n is the number of people. Plugging in 8 for n, we get (8 * 7) / 2 = 28. So, there will be 28 unique speed dates in total.
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