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blagie [28]
3 years ago
8

The value of X and Y vary directly, and when X= 4 Y equals -10. Find the value of Y when X equals 10.

Mathematics
1 answer:
ziro4ka [17]3 years ago
7 0

y = - 25

since x varies directly with y then we can express the relationship as

x = ky ← k is the constant of variation

to find k use the given condition y = - 10 when x = 4

k = \frac{x}{y} = \frac{4}{-10} = - \frac{2}{5}

hence x = - \frac{2}{5} y

when x = 10

10 = - \frac{2}{5} y

multiply both sides by - 5 and divide both sides by 2 )

- 50 =  2y ⇒ y = - 25


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Determine whether a triangle can be formed with the given side lengths. If so, use Heron's formula to find the area of the trian
marysya [2.9K]

Answer:

a, b, and c can be formed a triangle

The area of the triangle is 13385.87 square units.

Step-by-step explanation:

<em>Let us revise an important fact in any triangle</em>

  • The sum of the lengths of the two shortest side must be greater than the length of the longest side

The length of the sides are a = 240, b = 132, and c = 330

∵ The two shortest sides are a = 240 and b = 132

∵ a + b = 240 + 132 = 372

∵ The longest side is c = 330

∵ 372 > 330

∴ a + b > c

∴ a, b, and c can be formed a triangle

<em>Let us revise the </em><em>Heron's formula</em><em> of the area of the triangle</em>

  • Area = \sqrt{p(p-a)(p-b)(p-c)}, where a, b,c are the lengths of the sides of the triangle, and p=\frac{a+b+c}{2}

∵ p=\frac{240+132+330}{2}=351

∴ Area = \sqrt{351(351-240)(351-132)(351-330)}

∴ Area = \sqrt{351(111)(219)(21)}

∴ Area=13385.87

The area of the triangle is 13385.87 square units.

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3 years ago
Which expressions are equivilant to 6^16?
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The expressions which are equivalent to 6¹⁶ are

(6^{8}) ^{2}

(6^{-2}) ^{\times -8}

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<h3>Equivalent expressions </h3>

From the question, we are to determine which of the given expressions are equivalent to 6¹⁶

From one of the laws of indices, we have that

x^{y\times z} = (x^{y})^{z}

The given expression, 6¹⁶, can be expressed as

6^{8\times 2}

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6^{-2\times -8}

or

6^{-4\times -4}

Then,

6^{8\times 2}= (6^{8}) ^{2}

6^{-2\times -8}= (6^{-2}) ^{\times -8}

6^{-4\times -4}= (6^{-4}) ^{\times -4}

Hence, the expressions which are equivalent to 6¹⁶ are

(6^{8}) ^{2}

(6^{-2}) ^{\times -8}

and (6^{-4}) ^{\times -4}

Learn more on Equivalent expressions here: brainly.com/question/21643960

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Step-by-step explanation:

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maxonik [38]

Answer:

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Step-by-step explanation:

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4x^2 - 4x = 2x - 1

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x - 3/4 = +/- √5 / 4

x  = √5 / 4 + 3/4 ,  -√5 / 4 + 3/4

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4 years ago
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Vanyuwa [196]

Answer:

x = \frac{21}{32}

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21 - 32x = 0 ( subtract 21 from both sides )

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x = \frac{21}{32}

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4 years ago
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