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3 years ago

Mateo started with more

Mathematics

1 answer:

NemiM [27]3 years ago

4 0

Answer:

y > 75

Step-by-step explanation:

Given that:

Starting number of boxes = > 100

Number of boxes sold = 25

Number of boxes left after selling 25

Let the number of boxes left = y

y = starting number of boxes - Numbe rof boxes sold

y = 100 - 25

y = 75

Since the starting number of boxes is more than 100

Then, y should also be more than 75

y > 75

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A farmer harvests 15 cucumbers for every 45 carrots. Which of the following ratios represents the ratio of cucumbers to carrots,

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15 cucumbers to 45 carrots...

so the ratio of cucumbers to carrots is : 15/45 which reduces to 1/3 <==

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Which angle is coterminal to a 185° angle?

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The area of the rhombus is 540 cm2; the length of one of its diagonals is 4.5 dm. What is the distance between the point of inte

malfutka [58]

1. The area of the rhombus can be found by the formula

$A=\dfrac{d_1\cdot d_2}{2},$ where $d_1,\ d_2$ are rhombus's diagonals.

Note that $d_1=4.5\ dm=45\ cm,$ then

$540=\dfrac{45\cdot d_2}{2},\\ \\540\cdot 2=45d_2,\\ \\d_2=24\ cm.$

2. The diagonals of rhombus are perpendicular and are bisectors of each other. Then the triangle formed with halfs of diagonals is right triangles with legs

$\dfrac{d_1}{2}=22.5\ cm,\ \dfrac{d_2}{2}=12\ cm.$

The hypotenuse of this triangle is the rhombus's side. By the Pythagorean theorem

$\text{rhombus's side}^2=(22.5)^2+12^2=506.25+144=650.25,\\ \\\text{rhombus's side}=25.5\ cm.$

3. The distance between the point of intersection of the diagonals and the side of the rhombus is the height of right triangle considered above.

Use twice the Pythagorean theorem to find this height:

$\left\{\begin{array}{l}x^2+h^2=12^2\\(25.5-x)^2+h^2=22.5^2,\end{array}\right.$

where x is projection of leg 12 cm and h is height.

Subtract the first equation from the second:

$(25.5-x)^2+h^2-x^2-h^2=22.5^2-12^2,\\ \\650.25-51x=506.25-144,\\ \\51x=650.25-362.25=288,\\ \\x=\dfrac{96}{17}\ cm.$

Then

$h^2=144-\left(\dfrac{96}{17}\right)^2=144-\dfrac{9216}{289}=\dfrac{32400}{289},\\ \\h=\dfrac{180}{17}\ cm.$

Answer: $h=\dfrac{180}{17}\ cm.$

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Answer:

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Step-by-step explanation:

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