Ezra works two summer jobs to save for a laptop that costs at least $1100. He charges $15/hr to mow lawns and $10/hr to walk dog
s. Recall the inequality that represents this situation: 15x+10y>110 . Is (60, 20) a solution? How do you know? What does this point represent?
2 answers:
Begin by disregarding the inequality symbol and substituting it with an '=' sign. After that, determine the x- and y-intercepts.
15x + 10y = 1,100
x-intercept:
15x + 0 = 1,100
x = 1,100/15 = 73.33
y-intercept:
0 + 10y = 1,100
y = 1,100/10 = 110
Now, plot the points (73.33,0) and (0,110). Given that the inequality symbol is ≥, representing equality, connect these points using a solid line.
Next, let's identify a point on the graph, for instance, the origin (0,0). Use this point in the equation.
15x + 10y ≥ 1,100
15(0) + 10(0)? 1,100
0? 1,100
0 < 1,100
This makes the ≥ statement false. As a result, the alternate area defined by the line is the solution. Consequently, shade that region. The resulting graph is displayed in the attached image.
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762,508 expressed in expanded form with exponents is:
Solution:
We need to write 762,508 using expanded notation with exponents.
Expanded form indicates how to represent numbers to highlight the individual digit values.
Displaying 762508 in Expanded format
Let's determine the positional values of each digit:
The concept of place value signifies the worth assigned to each digit based on its location.
For 7, the place value is 700,000
In 762508, the digit 7 is located in the hundred-thousands position.
For 6, the place value is 60,000
In 762508, the digit 6 occupies the ten-thousands position.
For 2, the place value is 2,000
In 762508, 2 is in the thousands position.
For 5, the place value is 500
In 762508, 5 is placed in the hundreds position.
For 0, the place value is 0 x 10 = 0
In 762508, 0 is found in the tens position.
For 8, the place value is 8
In 762508, 8 is positioned in the units place.
Thus, the expanded form is:
700,000 + 60,000 + 2,000 + 500 + 0 + 8
Expressed with exponents, it can be written as: