Can someone help me with this ASAP. Thank You!
1 answer:
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Answer:
<em>Here is the complete question:</em>
The ratio of the number of dogs to the number of cats is 4:5. There are 270 animals on the rescue farm. for each of the following statements, explain whether statements is true or false and why:
a. The number of dogs is 4/5 the number of cats.
b. 4/5 of the pets at the farm are dogs.
c. There are exactly 30 more cats than dogs.
d. There are exactly 30 dogs at the farm.
e. 5/9 of the pets at the farm are cats.
a,c and e are true statements.
Step-by-step explanation:
Let the number of dogs be "d' and number of cats be "c".
According to the question:
⇒ ...equation (i)
Arranging the ratio:
⇒
⇒
⇒ ...equation (ii)
Plugging (ii) in equation (i).
⇒
⇒
⇒
⇒
⇒
⇒
Number of dogs "d" = 120
Number of cats "c" = (270-120) = 150
Lets check each statement:
a.
The number of dogs is 4/5 the number of cats.
⇒
⇒
⇒
Statement is true.
b.
4/5 of the pets at the farm are dogs.
⇒
⇒
Number of dogs = 120
So the above statement is false.
c.
There are exactly 30 more cats than dogs.
⇒
⇒
Statement is true.
d.
There are exactly 30 dogs at the farm.
False, as there are 120 dogs
e.
5/9 of the pets at the farm are cats.
⇒
⇒
Statement is true.
So,
Statement a,c and e are true as we could observe in the explanation.
Answer:
We conclude that the initial value and y-intercept are the same thing on a graph.
Please check the attached graph of the equation y = 2x+1.
Step-by-step explanation:
We know that the initial value on a graph is basically the out-put value y of the point where the line meets or crosses the y-axis.
In other words, the initial value is the y-value or output of the point at x = 0
For example,
Let the equation
y = 2x+1
substitute x = 0
y = 2(0)+1
y = 0+1
y = 1
Thus, the initial value of the equation y = 2x+1 is: y = 1
Please check the attached graph of the equation y = 2x+1.
It is clear from the graph that at x = 0, the value of y = 1.
Thus, at y = 1, the line meets the y-axis.
Hence, the initial value of the line is: y = 1
Similarly, we know that the value of the y-intercept can be determined by setting x = 0 and determining the corresponding value of y.
For example,
Let the equation
y = 2x+1
substitute x = 0
y = 2(0)+1
y = 0+1
y = 1
Thus, the y-intercept of y = 2x+1 is y = 1.
Please check the attached graph of the equation y = 2x+1.
It is clear from the graph that at x = 0, the value of y = 1.
Therefore, the y-intercept of y = 2x+1 is y = 1.
Conclusion:
Therefore, we conclude that the initial value and y-intercept are the same thing on a graph.
Please check the attached graph of the equation y = 2x+1.
