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7nadin3 [17]
3 years ago
14

One side of a kite is 6 cm less than 4 times the length of another. The perimeter of the kite is 68 cm. Find the length of each

side of the kite.
Mathematics
1 answer:
strojnjashka [21]3 years ago
3 0
Perimeter:

p = 2b + 2h = 68

b = 4h - 6 (per problem statement)

substituting for b in the perimeter equation:

p = 2(4h - 6) + 2h = 68

(2)(4h) - (2)(6) + 2h = 68

8h - 12 + 2h = 68

10h - 12 = 68

10h = 68 + 12

10h = 80

h = 80/10

h = 8

b = 4(8) - 6 = 32 - 6 = 26

p = 2(26) + 2(8)

p = 52 + 16 = 68 . . . [OK]


b = 26 cm
h = 8 cm

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Step-by-step explanation:

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8 0
3 years ago
How many pounds of a 15% copper alloy must be mixed with 700lb of a 30% copper alloy to maybe a 25.5% copper alloy
lisov135 [29]

Answer:

300\; \rm lb.

Step-by-step explanation:

Let x represent the mass (in pounds) of that 15\% copper alloy required, such that the final mixture would contain 25.5\% copper by mass.

Consider: if x pounds of that 15\% copper alloy is mixed with 700 pounds that 30\% copper alloy, what would be the mass of copper in the mixture?

  • Mass of copper in x pounds of that 15\% copper alloy: (0.15\, x)\; \rm lb.
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Therefore, the mixture would contain (210 + 0.15\, x) \; \rm lb of copper.

The mass of that mixture would be (700 + x)\; \rm lb. The mass fraction of copper in that mixture would be:

\displaystyle \frac{(210 + 0.15\, x)\; \rm lb}{(700 + x)\; \rm lb} \times 100\%.

This ratio is supposed to be equal to 25.5\%. These two pieces of equations combine to give an equation about x:

\displaystyle \frac{(210 + 0.15\, x)\; \rm lb}{(700 + x)\; \rm lb} \times 100\% = 25.5\%.

\displaystyle \frac{210 + 0.15\, x}{700 + x} = 0.255.

Simplify and solve for x:

210 + 0.15\, x= 0.255\, (700 + x).

(0.255 - 0.15)\, x= 210 - 0.255 \times 700.

\displaystyle x = \frac{210 - 0.255 \times 700}{0.255 - 0.15} = 300.

Therefore, 300\; \rm lb of that 15\% alloy would be required.

4 0
3 years ago
You measure 22 textbooks' weights, and find they have a mean weight of 64 ounces. Assume the population standard deviation is 5.
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Answer:

Step-by-step explanation:

We want to determine a 90% confidence interval for the true population mean textbook weight.

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Standard deviation, s = 5.1 ounces

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We will apply the formula

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It becomes

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= 64 ± 1.645 × 1.087

= 64 ± 1.788

The lower end of the confidence interval is 64 - 1.788 = 62.21 ounces

The upper end of the confidence interval is 64 + 1.788 = 65.79 ounces

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3 0
3 years ago
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Answer:

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Step-by-step explanation:

You are referring to

11 {}^{6}

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