The price of an item has been reduced by $2.27 . The new sale price is $37.37 . What was the original price?
To find the original price, you need to add the reduced price to the amount reduced.
Let's let x be the original price.
x - 2.27 = 37.37
Then, to isolate x, we add 2.27 to both sides of the equation.
x = 37.37 + 2.27
x = 39.64
Therefore, the original price of the item was $39.64.
For each ordered pair, determine whether it is a solution to the system of equations.
-14x + 2y = -6
y = 7x - 3
x,y
(-1,7) yes or no
(0,-3) yes or no
(2,-4) yes or no
(2,11) yes or no
To determine whether each ordered pair is a solution to the system of equations, we need to substitute the values of x and y into the equations and see if both equations hold true.
For the first ordered pair (-1, 7):
-14(-1) + 2(7) = -6 is true.
7 = 7(-1) - 3 simplifies to 7 = -10, which is not true.
Therefore, (-1, 7) is not a solution to the system of equations.
For the second ordered pair (0, -3):
-14(0) + 2(-3) = -6 simplifies to -6 = -6, which is true.
-3 = 7(0) - 3 simplifies to -3 = -3, which is true.
Therefore, (0, -3) is a solution to the system of equations.
For the third ordered pair (2, -4):
-14(2) + 2(-4) = -6 simplifies to -6 = -6, which is true.
-4 = 7(2) - 3 simplifies to -4 = 11, which is not true.
Therefore, (2, -4) is not a solution to the system of equations.
For the fourth ordered pair (2, 11):
-14(2) + 2(11) = -6 simplifies to -6 = -6, which is true.
11 = 7(2) - 3 simplifies to 11 = 11, which is true.
Therefore, (2, 11) is a solution to the system of equations.
In summary:
(-1, 7) is not a solution.
(0, -3) is a solution.
(2, -4) is not a solution.
(2, 11) is a solution.
Complete the parts below. Write your answers as whole numbers or fractions in simplest form.
(a)Susan makes fruit salad using a ratio of 2 blueberries to 10 strawberries. Give two different unit rates using this relationship.
One unit rate:
(Choose one)
for each
(Choose one)
Another unit rate:
(Choose one)
for each
(Choose one)
(b)How many blueberries are needed if 15 strawberries are used?
(a) Two different unit rates using the given ratio of 2 blueberries to 10 strawberries are:
Unit rate 1:
2 blueberries for each 10 strawberries
Unit rate 2:
1 blueberry for each 5 strawberries
(b) To find how many blueberries are needed if 15 strawberries are used, we can set up a proportion using the given ratio:
2 blueberries / 10 strawberries = x blueberries / 15 strawberries
Cross-multiplying, we get:
10 * x blueberries = 2 * 15 strawberries
10x = 30
Dividing both sides by 10, we find:
x = 3
Therefore, if 15 strawberries are used, 3 blueberries are needed.
___
Find two consecutive whole numbers that |97 lies between.
To find two consecutive whole numbers between which 97 lies, we can consider that the number 97 lies between two consecutive whole numbers, n and n+1.
Since 97 is smaller than n+1, we can conclude that n+1 is the greater number of the two.
To determine n and n+1, we can set up the following inequality:
n < 97 < n+1
From this inequality, we can see that n must be smaller than 97, and n+1 must be larger than 97.
To find the appropriate values for n and n+1, we can start by selecting the whole number that is smaller than 97. In this case, n would be 96, as it is the whole number that is less than 97.
The two consecutive whole numbers that 97 lies between are 96 and 97.
Graph the inequality below on the number line.
x < with a line below it -6
To graph the inequality x ≤ -6 on a number line, we would draw a closed dot on the number -6 and extend a solid line to the left.
The graph would look like this:
<------------●-------------------
At the point -6, there is a closed dot, indicating that -6 is included in the solution set. The solid line indicates that all values less than -6 are also included in the solution set.
Shown below are the scatter plots for four data sets.
Answer the questions that follow.
y1234567891011x12345678910110
y1234567891011x12345678910110
y1234567891011x12345678910110
y1234567891011x12345678910110
Figure 1 Figure 2 Figure 3 Figure 4
(a) Which data set appears to show a nonlinear relationship between its two variables?
(Choose one)
(b) Which data set appears to show a positive linear relationship between its two variables?
(Choose one)
(c) Which data set appears to show a negative linear relationship between its two variables?
(Choose one)
(d) Which data set appears to show no relationship between its two variables?
(Choose one)