Six cell phones weigh 46.2 ounces. Fourteen cell phones weigh 107.8 ounces. This relationship is an example of a proportional re
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Answer:
C. and
Step-by-step explanation:
The proportion between these fractions is true. Multiply 4/10 (numerator and denominator) by 2.5 to get 10/25. This is the only correct option.
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<span><u><em>Answer:</em></u>
Each will have passed 17 tests and it will take 3 weeks.
<u><em>Explanation: </em></u>
Let x be the number of weeks.
The number of tests <u>Travis</u> passes to begin with is 11.
We then add 2 tests per week, or 2x to that, giving us:
11+2x.
The number of tests <u>Jenifer</u> has passed to begin with is 2.
We then add 5 tests per week, or 5x to that, giving us:
2+5x.
<u>Setting these equal, we have: </u>
11+2x=2+5x.
<u>Subtract 2x from each side: </u>
11+2x-2x=2+5x-2x;
11=2+3x.
<u>Subtract 2 from each side: </u>
11-2=2+3x-2;
9=3x.
<u>Divide both sides by 3:</u>
</span>
<span>;
3=x.
It will take <u>3 weeks</u>.
In 3 weeks,
Travis will have passed:
11+2*3 = 11+6 = 17 tests.
Jenifer will have passed the same number, since she catches up with him at this point.</span>
Each will have passed 17 tests and it will take 3 weeks.
<u><em>Explanation: </em></u>
Let x be the number of weeks.
The number of tests <u>Travis</u> passes to begin with is 11.
We then add 2 tests per week, or 2x to that, giving us:
11+2x.
The number of tests <u>Jenifer</u> has passed to begin with is 2.
We then add 5 tests per week, or 5x to that, giving us:
2+5x.
<u>Setting these equal, we have: </u>
11+2x=2+5x.
<u>Subtract 2x from each side: </u>
11+2x-2x=2+5x-2x;
11=2+3x.
<u>Subtract 2 from each side: </u>
11-2=2+3x-2;
9=3x.
<u>Divide both sides by 3:</u>
</span>
3=x.
It will take <u>3 weeks</u>.
In 3 weeks,
Travis will have passed:
11+2*3 = 11+6 = 17 tests.
Jenifer will have passed the same number, since she catches up with him at this point.</span>
Answer:
The difference in the areas of the cross section is 32 m²
Step-by-step explanation:
The given parameters are;
The height of the rectangular pyramid = 8 meters
The length of the base of the pyramid = 7 meters
The width of the base of the pyramid = 15 meters
Whereby triangular cross sections are formed through the vertex and perpendicular to the base, and to each other, we have;
The sides of the two triangles consists of the following;
1) Two slant height of the pyramid each
2) The two perpendicular lines joining the midpoints of the opposite sides of the base of the pyramid with length equal to the length of the adjacent side to the sides from which they are drawn which are 15 meters and 7 meters
3) The two lines and the corresponding slant height form triangles cross section which are perpendicular to each other.
the slant height, , is given as follows;
= √(8² + (15/2)²) ≈ 10.966
For the triangular cross section with base = 15 m
The area of the cross section = 1/2 × Base₁₅ × Height = 1/2 × 15 m × 8 m = 60 m²
For the triangular cross section with base = 7 m
The area of the cross section = 1/2 × Base₇ × Height = 1/2 × 7 m × 8 m = 28 m²
The difference in the areas of the cross section = 60 m² - 28 m² = 32 m².
