Answer:
Not a Proportional Relationship ; No Constant of Proportionality
Step-by-step explanation:
Consider the first example, 4 hours of parking costs $ 10. From this we can derive the ratio 4 : 10, so that hours parked : fee for parking is a common ratio among the two examples, the other being 5 : 12;
[tex]4 : 10, Simplify\\2 : 5, Take As Fraction,\\Solution; 2 / 5ths\\[/tex]
[tex]5 : 12, Simplify\\( Can't Be Simplified Further ) - Take as Fraction,\\Solution; 5 / 12ths[/tex]
Considering that the fractions when compared are not similar, ( 2 / 5, and 5 / 12 ) they don't have a proportional relationship, and thus have no constant of proportionality
Solution; Not a Proportional Relationship
A tree harvester estimates the trunk of a tree to have a height of about 34 meters and a base diameter of about 0.52 meters. The wood of the tree has a density of about 770 kilograms per cubic meter. Find the mass of the trunk. Round your answer to the nearest hundred.
Answer: 5,559.89 kilograms
Step-by-step explanation:
Hi, to answer this question we have to apply the next formula:
Mass = π/4 (diameter) ^2 (height) (density)
Replacing with the values given and solving for M (mass)
M = π/4 (0.52) ^2 (34) (770) = 5,559.89 kg.
The mass of the trunk is 5,559.89 kilograms
Feel free to ask for more if needed or if you did not understand something.
What is the value of x in the diagram?
Answer:
5
Step-by-step explanation:
Given is a right angled triangle.
Therefore, by Pythagoras theorem:
[tex] {(2x + 3)}^{2} = {x}^{2} + {(2x + 2)}^{2} \\ 4 {x}^{2} + 9 + 12x = {x}^{2} + 4 {x}^{2} + 4 + 8x \\ 9 + 12x = {x}^{2} + 4 + 8x \\ {x}^{2} + 4 + 8x - 12x - 9 = 0 \\ {x}^{2} - 4x - 5 = 0 \\ ({x}^{2} - 4x + 4 )- 4 - 5 = 0 \\ {(x - 2)}^{2} - 9 = 0 \\ {( x - 2)}^{2} = 9 \\ x - 2 = \pm \: \sqrt{9} \\ x - 2 = \pm 3 \\ x = 2 \pm 3 \\ x = 2 + 3 \: \: or \: \: x = 2 - 3 \\ x = 5 \: \: or \: \: x = - 1 \\ \because \: x \: can \: not \: be \: negative \\ \therefore \: x \neq \: - 1 \\ \therefore \: x = 5[/tex]
Use the commutative or associative property to simplify the expression.
1/3(3y)
Answer:
y
Step-by-step explanation:
Associative property is when we change the order of the bracket / can solve any order
So 1/3(3y)
= (1/3x 3)y
= 3/3y
= 1y or simply y
I need help with this math problem.
Answer:
(45,60)
Step-by-step explanation:
in a parallelogram, opposite angles are equal measure
2x-10 = y + 20
angles that lie on the same line add up to 180, since alternate angles of parallel lines and a transversal are equivalent
2x + 10 + 2x - 10 = 180
solving the equation with only Xs
4x = 180
x = 180/4 = 45
plug x = 45 into x and y equation
90-10 = y+ 20
80 = y + 20
y = 80-20 = 60
How do I work out this question (explanation and answer please)
Answer: Each friend will pay £3.75
Step-by-step explanation:
4 friends pay £15, 12 will pay
12/4 x 15 = £45
Each will pay 45/12 = £3.75
Which equation represents the data in this function table?
OA) y = x + 2
OB) x = y + 2
OC) y = 2x
OD) x = 2y
Answer:
c
Step-by-step explanation:
its not too complicated, look
to get from 2 to 5 u gotta multiply by 2
so C is saying that Y equals 2 times X which would be: 4 equals 2 times 2
Or 12 equals 2 times 6
Answer:
C
Step-by-step explanation:
Rise over run is [tex]\frac{12-4}{6-2} = \frac{8}{4}=2[/tex]
so y=2x
you and six friends go to a movie. the tickets cost $7.50 each. you each buy a drink for $2.00 and a box of popcorn for $3.75. write an expression that represents the total amount of money spent. then evaluate the expression.
which linear inequality is represented by the graph?
Answer:
y ≥ [tex]\frac{1}{3}[/tex]x - 1
Step-by-step explanation:
First, determine the slope of the line. We can see that the slope is [tex]\frac{1}{3}[/tex], because the slope has less than 1 y interval per every x interval. This means that the line is less steep. There are only 2 slope choices, [tex]\frac{1}{3}[/tex], -[tex]\frac{1}{3}\\[/tex], and 3. We can tell that the slope is positive, but it must be [tex]\frac{1}{3}\\[/tex] because it is clearly less steep than a 3 slope line.
Now, look at the portion that is shaded. It is above the line, and this means that y is greater than the equation given. We can tell it is greater than or equal to, because the line that represents the equation is shaded as well. If it was only greater than and not equal to, the line would not be shaded.
Hope this helps ! :) Please feel free to ask me any questions!
If the sum of the measure of two angles in a triangle is 101, then the measure
of the third angle must be
Answer:
79 degrees.
Step-by-step explanation:
It is just a rule of trigonometry that all the angles inside ANY triangle will add up to 180 degrees.
There's only 3 possible angles in a triangle, so if you know what the sum of 2 are, its easy to find the last one.
All you have to do is 180 - 101, which equals 79 degrees.
Hope this helped : )
