If two or more points are collinear they lie on the same plane.
What are collinear points?Collinear points are points that lie on the same straight line. In other words, if three or more points are collinear, they can be connected by a straight line.
Collinear points are important in geometry and are used in many geometric proofs and constructions. The concept of collinearity is also used in other fields, such as physics and engineering, where it is used to describe the motion of objects along a straight line or to define the direction of forces acting on an object.
Given data ,
Let the points be represented as A , B and C
Now , when A , B and C are lying on the same line , we say the points are collinear or collinear points
So , If two or more points are collinear they lie on the same plane.
Hence , the collinear points are solved
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A solution containing 30 percent juice is mixed with a solution containing 10 percent juice to make 100 gallons of a 12 percent juice mixture. how much of the 30 percent juice solution was used
10 gallons of 30% juice was mixed with 90 gallons of 10% juice to make 100 gallons of 12% juice.
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Let x represent the amount of 30% juice and y represent the amount of 10% juice, hence:
x + y = 100 (1)
Also:
0.3x + 0.1y = 0.12(100) (2)
From eqn 1 and 2:
x = 10, y = 90
10 gallons of 30% juice was mixed with 90 gallons of 10% juice to make 100 gallons of 12% juice.
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Irina rode her bike to work at an average speed of 16 miles per hour. It started to rain, so she got a ride home along the same route in her coworker’s car at an average speed of 27 miles per hour. If Irina’s ride home in the car took 24 minutes (0.4 of an hour), how many hours was her bike ride to work, to the nearest tenth of an hour?
Answer:
0.7 an hour .
Step-by-step explanation:
What is the equation of a line that passes through the point (2, 7) and is perpendicular to the line whose equation is y=x4+5 ? Enter your answer in the box.
What is the simplest form of
What is the side length b in the triangle below
Answer:
Option B : 16
Step-by-step explanation:
Refer the attached file
Given :
In ΔABC , AB = b , BC = 12 , AC= 20
To Find : value of b i.e. Length of AB
Solution:
Since we are given a right angles triangle so we can use Pythagoras theorem i.e.
[tex](Hypotenuse)^{2} =(Perpendicular)^{2} +(Base)^{2} [/tex] ---(a)
Now in a given triangle AB is Perpendicular , BC is Base and AC is Hypotenuse.
So, putting values in (a)
[tex](AC)^{2} =(AB)^{2} +(BC)^{2} [/tex]
[tex](20)^{2} =(b)^{2} +(12)^{2} [/tex]
[tex]400 =(AB)^{2} +144 [/tex]
[tex]400-144 =(b)^{2} [/tex]
[tex]256 =(b)^{2} [/tex]
[tex]\sqrt{256} =b[/tex]
[tex]16=b[/tex]
Thus the value of b is 6
Hence Option B is correct.
Which value of x makes the numerical sentence true? 25^ 1/2 × 5 ^–3 = 5 ^x
A sample of n = 9 scores is obtained from a population with m = 70 and s = 18. if the sample mean is m = 76, then what is the z-score for the sample mean?
What is 0.125 written as a fraction in simplest form?
Transitive property: if 3x plus y equals 7 and 7 equals 5x minus 2y then
Transitive property states that if x = y and y = z then x = z.
3x + y = 7 and 7 = 5x - 2y
Using the transitive property we get,
3x + y = 5x - 2y.
What is transitive property?It states that if x, y and z are the three quantities, and if x is related to y by a rule, and y is related to z by the same rule, then we can say x is related to z by the same rule.
Example:
x + 1 = 2 and 2 = x + 9 then x + 1 = x + 9
We have,
3x + y = 7 and 7 = 5x - 2y
Using transitive property we can say that,
3x + y = 5x - 2y
Thus using the transitive property we have,
3x + y = 5x - 2y.
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Convert 5460 feet per minute to miles per hour. Round to the nearest whole number
A $360,000 building is depreciated by its owner. the value y of the building after x months is: y = 360,000 – 1,500 x. how many months will it take until it is completely depreciated
To find when the building will be completely depreciated, you solve for x in the equation y = 360,000 - 1,500x by setting y to 0. The solution is x = 240, meaning the building will be totally depreciated after 240 months or 20 years.
Explanation:In this case, you are looking to find the value of x (the number of months) when the value of the building (y) becomes 0. The equation given is y = 360,000 - 1,500x. Set y = 0 and solve for x
First, replace y with 0 in the given equation: 0 = 360,000 - 1,500x. Next, move the term with x to the other side by adding 1,500x to both sides, which gives: 1,500x = 360,000.Finally, solve for x by dividing both sides of the equation by 1,500. This gives you: x = 360,000 / 1,500 = 240.So, the building will be completely depreciated after 240 months or 20 years.
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find the value of v......
What is the value of x? Answer it as a decimal
Ali,s dod weighs 8 times as many as her cat.Together, the two pets weigh 54 pounds.HOW much does Ali's dog weigh
What is the square root of 9/36 as a fraction?
Which symbol creates a true sentence when x equals 3?
8•3-4x_7(10-x)
A.<
B.=
C.>
The sides of an equilateral triangle are increasing at a rate of 10 cm/min. at what rate is the area of the triangle increasing when the sides are 30 cm long?
Option 1: $30 per month and $100 membership fee. Option 2: $25 per month and $150 membership fee.
Michael is trying to determine which tennis club to join. If Michael chooses option 2, for which month will his total cost for option 2 be less than his total cost for option 1? A) month 8 B) month 9 C) month 10 D) month 11
Let us say that m is the number of months. So that the equations for option 1 (O1) and option 2 (O2) are:
O1 = 30 m + 100
O2 = 25 m + 150
TO determine this, we equate O1 and O2 so that:
30 m + 100 = 25 m + 150
5 m = 50
m = 10
So at the 10th month, the cost for both options are equal. So we select month 11.
Answer:
D) month 11
URGENT NEEDS TO ME SUBMITTED BY MIDNIGHT!! The ratio of girls to boys in Mr. Hansen’s class is 4:5. The ratio of girls to boys in Ms. Luna’s class is 8:10. Which equation correctly compares these ratios?
4:5 ≡ 8: 10 is the correct way to compares these ratios.
What are equivalent?
" Equivalent means when two or more things have same value but different expression."
According to the question,
Ratio of girls to boys in Mr. Hansen's class = 4 : 5
Ratio of girls to boys in Ms. Luna's class = 8 : 10
Compare both the ratio's we get,
As
[tex]\frac{8}{10} =\frac{2}{2} * \frac{4}{5}[/tex]
Therefore,
4 : 5 ≡ 8 : 10
Hence, 4:5 ≡ 8: 10 is the correct way to compares these ratios.
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A computer password consists of 3 letters followed by two digits. none of the letters or digits repeat. how many different passwords can be created
Answer:
67,600
Step-by-step explanation:
find the greatest common factor of 15x^2y^3 and -20x^3yz
The greatest common factor of [tex]\(15x^2y^3\)[/tex] and [tex]\(-20x^3yz\)[/tex] is [tex]\(5x^2y\)[/tex].
To find the greatest common factor (GCF) of [tex]\(15x^2y^3\)[/tex] and [tex]\(-20x^3yz\)[/tex], we need to identify the highest power of each common factor that both terms share.
List the prime factors of each term:
[tex]\(15x^2y^3 = 3 \times 5 \times x^2 \times y^3\)[/tex]
[tex]\(-20x^3yz = -1 \times 2 \times 2 \times 5 \times x^3 \times y \times z\)[/tex]
Identify the common factors:
Common factors: [tex]\(5\), \(x^2\), \(y\)[/tex]
Find the lowest exponent for each common factor:
For (5), it appears in both terms, so we use the smaller exponent, which is [tex]\(5^1\)[/tex].
For [tex]\(x^2\)[/tex], it appears in both terms, so we use the smaller exponent, which is [tex]\(x^2\)[/tex].
For (y), it appears in both terms, so we use the smaller exponent, which is [tex]\(y^1\)[/tex].
Multiply the common factors:
[tex]\(GCF = 5 \times x^2 \times y = 5x^2y\).[/tex]
So, the greatest common factor of [tex]\(15x^2y^3\)[/tex] and [tex]\(-20x^3yz\)[/tex] is [tex]\(5x^2y\)[/tex].
If f(x)=x^2+3x+5 what is f(3+h) ?
Use the conversion factor 4 quarts / 1 gallon to convert 5.25 gallons to quarts
Answer: 21 quarts
Step-by-step explanation: In this problem, we are asked to convert 5.25 gallons into quarts. To convert gallons into quarts, we use the conversion factor for gallons and quarts.
Conversion factor ⇒ 4 quarts = 1 gallon
Next, notice that we are going from a larger unit "gallons" to a smaller unit "quarts" and when we go from a larger unit to a smaller unit we multiply.
We will multiply 5.25 by the conversion factor which is 4 to get 21 quarts.
Therefore, 5.25 gallons is equal to 21 quarts.
help me with algebra 2 homework
I need help with a math question on my quick check. 0.24 x 13 A. 3.12 B. 4.62 C. 4.12 D. 3.10
This problem is simply a multiplication problem. All we have to do in this case is to multiply 0.24 by 13, or the other way around multiply 13 by 0.24. We can do this in the calculator which gives us:
13 x 0.24 = 3.12
Answer:
A. 3.12
Show that each property of matrices is true for all 2 by 2 matrices scalar distributive
20 points! If u can provide an explanation that would be great if not just tell me how certain that's the answer. Thanks a bunch
Which of the following expressions is a polynomial?
4a3+3a2+5a-9
32
y-3
x2-4x-2
When given the coordinates of the vertices of a triangle, can the slope formula be used to determine whether the triangle is a right triangle? if so, how?
What is (-3+2i)(-6-8i)