David went to the store and bought 3 candy bars for $2 each. David also bought 3 sodas. If he spent a total of $15, how much did
2 answers:
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A equation to represent this situation is:
Now we have to find x.
Step 1: Subtract 0.5x from both sides.
<span><span><span><span>0.75x</span>+7.5</span>−<span>0.5x</span></span>=<span><span><span>0.5x</span>+10</span>−<span>0.5x</span></span></span><span><span><span>0.25x</span>+7.5</span>=10
</span>Step 2: Subtract 7.5 from both sides.
0.25x+7.5−7.5=10−7.50.25x=2.5
Step 3: Divide both sides by 0.25.
<span><span><span>0.25x/</span>0.25</span>=<span>2.5/<span>0.25
</span></span></span>Answer:
<span>x=<span>10</span></span>
They will cost the same after 10 rides.
Now we have to find x.
Step 1: Subtract 0.5x from both sides.
<span><span><span><span>0.75x</span>+7.5</span>−<span>0.5x</span></span>=<span><span><span>0.5x</span>+10</span>−<span>0.5x</span></span></span><span><span><span>0.25x</span>+7.5</span>=10
</span>Step 2: Subtract 7.5 from both sides.
0.25x+7.5−7.5=10−7.50.25x=2.5
Step 3: Divide both sides by 0.25.
<span><span><span>0.25x/</span>0.25</span>=<span>2.5/<span>0.25
</span></span></span>Answer:
<span>x=<span>10</span></span>
They will cost the same after 10 rides.
Answer:
11700 mm²
Step-by-step explanation:
A rectangle is a quadrilateral with two equal, opposite and parallel sides. Each of the angles in a rectangle is 90°.
The horizontal distance of the rectangle = r + r + r + r = 4r
The vertical distance = r + h + r = 2r + h
Where h is the distance between the midpoint of the 2 up circles and the midpoint of the down circle.
Using Pythagoras:
(2r)² = h² + r²
h² + r² = 4r²
h² = 3r²
h = √3r²
h = r√3
Vertical distance = 2r + h = 2r + r√3
Area of rectangle = vertical distance * horizontal distance
Area = 4r * (2r + r√3) = 8r² + 4r²√3 = 4r²(2 + √3)
Substituting:
Area = 4r²(2 + √3) = 4(28²)(2 + √3) = 11703.711 mm²
Area = 11700 mm² to 3 s.f
Answers:
- b = -19
- b = -11
- b = -9
- b = 19
- b = 11
- b = 9
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Explanation:
Here are all the ways to multiply to 18 when using integers only:
- -1*(-18) = 18
- -2*(-9) = 18
- -3*(-6) = 18
- 1*18 = 18
- 2*9 = 18
- 3*6 = 18
Sum each pair of factors to find out a possible value of b.
- -1 + (-18) = -19
- -2 + (-9) = -11
- -3 + (-6) = -9
- 1 + 18 = 19
- 2 + 9 = 11
- 3 + 6 = 9
Therefore, the possible values of b are
- b = -19
- b = -11
- b = -9
- b = 19
- b = 11
- b = 9
which are the final answers.
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An example:
Let's say b = 11. This would mean becomes
It would factor to since it was stated earlier that:
2+9 = 11
2 * 9 = 18
You can use the FOIL rule, distributive property, or the box method to confirm that is a true equation for all real numbers x.
This same idea applies for the other values of b.
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If you're curious why this works, consider multiplying the two factors (x+p) and (x+q)
Use the FOIL rule to get
The middle term has the components add to the coefficient, while those same two components multiply to get the last term. This is why when factoring we're looking for two numbers that multiply to 18, and also add to the value of b (which in the case of the last example was 11).