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3 years ago

8

Paco needs at least 3/8 yard of twine to build a model ship. How much twine should he buy? 3/10 yard, 1/4 yard, 3/5 yard or 1/8

yard? Please explain why.

1 answer:

trasher [3.6K]3 years ago

7 0

He should buy 3/5 yard because even if he used 3/8 yard twine he would still have twine leftover.

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In six grade class the ratio of boys to girls is 3 to 2 how many boys and how many girls could there be in this class is there m

vivado [14]

If we take ratio of3:2 many possible answers are possible. Moreover if you give me a total of how many students are there in total then i may give you a fixed no.
Without any fixed no. Ration can be anything like
30:20
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4 years ago

A rectangular field is 75 yards wide and 105 yards long

nika2105 [10]

Answer:

width = 72 yards

length = 108 yards

Step-by-step explanation:

Given:

Width = 75 yards
Length = 105 yards

<u>Area of the field</u> with the given values:

$\begin{aligned}\textsf{Area of a rectangle}&=\sf width \times length\\& = \sf 75 \times 105\\& = \sf 7875\:\: yd^2\end{aligned}$

To maintain the <u>same perimeter</u>, but <u>change the area</u>, either:

decrease the width and increase the length by the same amount, or
increase the width and decrease the length by the same amount.

In geometry, length pertains to the <u>longest side</u> of the rectangle while width is the <u>shorter side</u>. Therefore, we should choose:

decrease the <u>width</u> and increase the <u>length</u> by the <u>same amount</u>.

<u>Define the variables</u>:

Let x = the amount by which to decrease/increase the width and length.

Therefore:

$\implies \sf width \times length < 7875\:\:yd^2$

$\implies (75-x)(105+x) < 7875$

Solve the inequality:

$\begin{aligned}(75-x)(105+x) & < 7875\\7875-30x-x^2 & < 7875\\-x^2-30x & < 0\\-x(x+30) & < 0\\x(x+30) & > 0\\\implies x & > 0 \:\: \textsf{ or }\:\:x < - 30\end{aligned}$

Therefore, as distance is positive only and the maximum width is 75 yd (since we are subtracting from the original width):

$\begin{cases}\textsf{width} = 75 - x\\\textsf{length} = 105 + x\end{cases}$

$\textsf{where } 0 < x < 75$

Therefore, to find the width and length of another rectangular field that has the same perimeter but a smaller area than the first field, simply substitute a value of x from the restricted interval into the found expressions for width and length:

<u>Example 1</u>:

Let x = 3

⇒ Width = 75 - 3 = 72 yd

⇒ Length = 105 + 3 = 108 yd

⇒ Perimeter = 2(72 + 108) = 360 yd

⇒ Area = 72 × 108 = 7776 yd²

<u>Example 2</u>:

Let x = 74

⇒ Width = 75 - 74 = 1 yd

⇒ Length = 105 + 74 = 179 yd

⇒ Perimeter = 2(1 + 179) = 360 yd

⇒ Area = 1 × 179 = 179 yd²

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4 years ago

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3 years ago

Phil’s age is 7 years more than times Peter’s age. Also, 4 times Phil’s age is 2 years less than twice Peter’s age. If x is Pete

Alchen [17]

Answer:

simultaneous equations

Step-by-step explanation:

phils age =7x

Peter age=x

scenario 2

phils age = 4(7x)

Peter age= 2x-2

$7x + x = 4(7x) + 2x - 2$

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3 years ago