a. The expression y=5x represent the number of small marbles she has.
b. The expression z=3x+2 represents the number of large marbles she has.
c. Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Step-by-step explanation:
a. Let x represent the number of medium marbles Amy has. Write an algebraic expression to represent the number of small marbles she has.
Medium marbles = x
Let,
Small marbles = y
According to given statement;
She has five times as many small marbles as medium marbles.
y = 5x Eqn 1
The expression y=5x represent the number of small marbles she has.
b. Write an algebraic expression to represent the number of large marbles she has.
Let,
Large marbles = z
The number of large marbles is two more than three times the number of medium marbles.
z = 3x+2 Eqn 2
The expression z=3x+2 represents the number of large marbles she has.
c. If Amy has a total of 560 marbles, how many of each size does she have?
x+y+z= 560 Eqn 3
Putting value of y and z from Eqn 1 and 2 in Eqn 3
Dividing both sides by 9
Putting x=62 in Eqn 1
Putting x=62 in Eqn 2
Amy has 310 small marbles, 62 medium marbles and 188 large marbles.
Keywords: linear equation, substitution method
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Answer:
Solving the inequality 
we get 
The graph of the inequality is shown in figure attached.
Step-by-step explanation:
We need to Solve each compound inequality
Solving the inequalities
For solving compound inequalities we solve both inequalities simultaneously and find the value of m.
For solving 5+m > 4, we subtract 5 from both sides.
While solving 7m < -35, we divide both sides by 7 to get value of m
Applying these functions we get:
So, solving the inequality we get
The graph of the inequality is shown in figure attached.
Answer:
Step-by-step explanation:
this is a question about two similar triangles , one is from Amelia , the other is the tree.
1.5/4 = x/12
solve for x
4.5 = x
the tree is 4.5 meters tall
Answer:
f(x) has three real roots and two imaginary roots.
Step-by-step explanation:
Given that three roots of a fifth degree polynomial function f(x) are -2,2 and (4+i).
Now we need to find about which of the given statements describes the number and nature of all roots for this function.
We know that imaginary roots always occur in conjugate pairs.
So if (4+i) is root then (4-i) must also be the root.
So now we have total 4 roots
-2, 2, (4+i) and (4-i).
Degree of the polynomial is 5 so that means 1 root is still remaining. It can't be imaginary as that must be in pairs
So that means 5th root is real.
Hence correct choice is :
f(x) has three real roots and two imaginary roots.
Answer:
-98
Step-by-step explanation:
