First, let's write the given equation in slope-intercept form: y = mx + b
In slope-intercept form, the slope of the line is m, and the y-intercept is b. The slope is a measure of how steep the graph is at any point and is found by doing rise over run. This means the change in y values divided by the change in x values. Next, y-intercept is just where the graph crosses the y axis.
All we need to do to get the equation in slope-intercept form is to divide each term by 3. This will isolate the y.
As you can see, the slope of the line is 2/3, and the y-intercept is -2.
To graph the line, plot a point at (0,-2). This is the point where the graph crosses the y axis. Then from that point, count up two and right 3. Plot a point here as well. Lastly, connect the two points with a straight line.
See attached picture for the graph.
Answer:
a. Required system of equations is:
c+p = 10
5c+4p = 46
b. 6 cakes were sold
Step-by-step explanation:
Let p be the number of pies and c be the number of cakes.
Then according to given statement " the store sold 10 baked goods"
And
"A cake costs $5 and a pie costs $4"
Using equation 1,
Putting this value of c in equation 2:
Putting p = 4 in equation 1
Hence,
a. Required system of equations is:
c+p = 10
5c+4p = 46
b. 6 cakes were sold
Answer:
For every 15 students scoring in the 60's there were 9 students scoring in the 70's.
Step-by-step explanation:
Your first step would be to rewrite the numbers into an easier to understand form like fractions, 45/3 and 27/3. Then you divide both numbers by 3, so you get comparable numbers. 45/3= 15, 27/3=9.
The answer is: [C]: -0.7, ⅕, 0.35, ⅔ .
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Explanation:
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<span>
Note that in this correct Answer choice "C" given, we have the following arrangement of numbers:
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</span>→ -0.7, ⅕, 0.35, ⅔ ;
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We are asked to find the "Answer choice" (or, perhaps, "Answer choices?") given that show a set of numbers arranged in order from "least to greatest"; that is, starting with a value that is the smallest number in the arrangement, and sequentially progressing, in order from least to greatest, with the largest (greatest) number in the arrangement appearing as the last number in the arrangement.
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Note the EACH of the 4 (four) answer choices given consists of an arrangement with ONLY one negative number, "- 0.7". Only TWO of the answer choices—Choices "B" and "C"—have an arrangement beginning with the number, "-0.7 "; So we can "rule out" the "Answer choices: [A] and [D]".
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Let us examine: Answer choice: [B]: <span>-0.7, 0.35, ⅕, ⅔ ;
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Note: The fraction, "⅕" = "2/10"; or, write as: 0.2 .
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The fraction, "⅔" = 0.6666667 (that is 0.6666... repeating; so we often see a "final decimal point" rounded to "7" at some point.
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Through experience, one will be able to automatically look at these 2 (two) fractions and immediately know their "decimal equivalents".
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Otherwise, one can determine the "decimal form" of these values on a calculator by division:
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→ ⅕ = 1/5 = 1 ÷ 5 = 0.2
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→ ⅔ = 2/3 = 2 ÷ 3 = 0.6666666666666667
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For Answer choice: [B], we have:
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→ -0.7, 0.35, ⅕, ⅔ ;
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→ So, we can "rewrite" the arrangement of "Answer choice [B]" as:
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→ -0.7, 0.35, 0.2, 0.666666667 ;
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→ And we can see that "Answer choice: [B]" is INCORRECT; because
"0.2" (that is, "⅕"), is LESS THAN "0.35". So, "0.35" should not come BEFORE "⅕" in the arrangement that applies correctly to the problem.
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Let us examine: Answer choice: [C]: -0.7, ⅕, 0.35, 0.666666667 .
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→ Remember from our previous— and aforementioned—examination of "Answer Choice: [B]" ; that:
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→ ⅕ = 0.2 ; and:
→ ⅔ = 0.666666667
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So, given:
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→ Answer choice: [C]: -0.7, ⅕, 0.35, ⅔ ;
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→ We can "rewrite" this given "arrangement", substituting our known "decimal values for the fractions:
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→ Answer choice: [C]: -0.7, 0.2, 0.35, 0.666666667 ;
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→ As mentioned above, this sequence starts with "-0.7", which is the ONLY negative number in the sequence; as such, the next positive number is correct. Nonetheless, "0.2" (or, "(⅕") is the next number in the sequence, and is greater than "-0.7". The next number is "0.35. "0.35" is greater than "⅕" (or, "0.2"). Then next number is "(⅔)" (or, "0.666666667").
"(⅔)"; (or, "0.666666667") is greater than 0.35.
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This set of numbers: "-0.7, ⅕, 0.35, ⅔" ; is arranged in order from least to greatest; which is "Answer choice: [C]: -0.7, ⅕, 0.35, ⅔" ; the correct answer.
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