There are between 60 and 100 children at the sunny side holiday camp. When the children are put into pairs, there is 1 child lef
1 answer:
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<u>Answer:</u>
There are two approaches to solving the equation -3x + 10 = 4x - 20. The value of x after solving in both methods is 4.2857.
<u>Solution:</u>
Given, equation is -3x + 10 = 4x – 20.
We have to solve the given equation in two methods, now let us see the first method.
<u><em>1st method ⇒ by subtracting 4x from both sides.</em></u>
Then, -3x + 10 = 4x – 20 ⇒ -3x + 10 – 4x = 4x – 20 – 4x ⇒ -3x – 4x = -20 – 10 ⇒ -7x = -30 ⇒ 7x = 30
Then, x =
Now, let us use the 2nd method.
<em><u>2nd method ⇒ by adding 3x on both sides.</u></em>
Then, -3x + 10 = 4x – 20 ⇒ -3x + 10 + 3x = 4x – 20 + 3x
⇒ 10 + 20 = 4x + 3x
⇒ 7x = 30
⇒ x =
Hence, the value of x after solving in both methods is = 4.2857.
Answer:
(D)The midpoint of both diagonals is (4 and one-half, 5 and one-half), the slope of RP is 7, and the slope of SQ is Negative one-sevenths.
Step-by-step explanation:
- Point P is at (4, 2),
- Point Q is at (8, 5),
- Point R is at (5, 9), and
- Point S is at (1, 6)
Midpoint of SQ
Midpoint of PR
Now, we have established that the midpoints (point of bisection) are at the same point.
Two lines are perpendicular if the slope of one is the negative reciprocal of the other.
In option D
- Slope of RP =7
- Slope of SQ
Therefore, lines RP and SQ are perpendicular.
Option D is the correct option.
1)Define the variables you will use in your model.
Let
x------->total pounds of the fruit
y-------> the total number of granola bars
TC----> total cost
Tf------> total cost of the fruit
Tg----> total cost of the granola bars
2) Write an inequality representing the total cost of your purchase. (3 points)
a. Each pound of fruit costs $4. Write an expression that shows the total cost of the fruit. Use the variable you identified in question 1
Tf=4*x
b. Each granola bar costs $1. Write an expression that shows the total cost of the granola bars. Use the variable you identified in question 1.
Tg=1*y--------> Tg=y
c. Combine the expressions from parts a and b to write an expression for the total cost. Then use this expression to write an inequality that compares the total cost with the amount you have to spend.
TC=Tf+Tg
TC=4*x+y
inequality------->
3. Write the inequality that models the number of granola bars you need to buy.
You need at least 10 granola bars
so
4. Describe in words what each of your inequalities means
inequality 1
the total cost of fruits plus the total cost of granola bars must be less than or equal to 48 dollars
inequality 2
5. Graph your system of inequalities.
using a graph tool
see the attached figure
6. Identify one point on the graph that represents a viable solution to the problem, and then identify one point that does not represent a viable solution.
Let
A-------> one point on the graph that represents a viable solution
B-------> one point on the graph that does not represent a viable solution
A(4,20)
x=4-------> total pounds of the fruit
y=20------> the total number of granola bars
check point A
substitute the values of x and y in the inequality 1
-------> is ok
substitute the values of x and y in the inequality 2
--------> is ok
the point A represents a viable solution, because satisfies both inequalities
B(10,30)
x=10-------> total pounds of the fruit
y=30------> the total number of granola bars
check point B
substitute the values of x and y in the inequality 1
-------> is not a viable solution
substitute the values of x and y in the inequality 2
--------> is ok
the point B is not a viable solution because does not satisfy the inequality 1
