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2 years ago

the sum of two consecutive integers is -49 write an equation that models this situation and find the values of the two integers

2 answers:

wel2 years ago

8 0

Let n be the 1st number, the 2nd is n+1
But we know that (n) + (n+1) = -49
2n + 1 = - 49
2n = - 49 - 1
2n = -50 and n = - 25 and n+1 = -25 + 1 = -24
the 2 consecutive numbers are - 25 and - 24

hodyreva [135]2 years ago

7 0

Х is the first <span>integer
</span>(x+1) is the second integer

x + x + 1 = -49
2x + 1 = - 49
2x = -49 - 1
2x = -50
x = -25 first integer
-25 + 1 = -24 second integer

Answer: -25 and -24

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I am Lyosha [343]

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Area of given triangle is 939.15cm² and smallest altitude is 30.8cm

<h3>Solution:</h3>

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Heron's formula was founded by hero of Alexandria, for finding the area of triangle in terms of the length of its sides. Heron's formula can be written as:

$\sf{ \pmb { \longrightarrow \: \sqrt{s(s - a)(s - b)(s - c)} }}$

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$\sf \longrightarrow s = \dfrac{a + b + c}{2}$

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$\begin {aligned}\quad & \quad \longmapsto \sf s = \dfrac{a + b + c}{2} \\ & \quad \longmapsto \sf s = \dfrac{35 + 54 + 61}{2} \\ & \quad \longmapsto \sf s = \dfrac{150}{2} \\ & \quad \longmapsto \sf s = 75cm \end{aligned}$

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$\begin{aligned}&:\implies \sf\quad \sf \: A = \sqrt{s(s - a)(s - b)(s - c)} \\ &:\implies \sf\quad \sf \: A = \sqrt{75(75 - 35)(75 - 54)(75 - 61)} \\&:\implies \sf\quad \sf \: A = \sqrt{75 \times 40 \times 21 \times 14} \\ &:\implies \sf\quad \sf \: A = \sqrt{5 \times 5 \times 3 \times 3 \times 2 \times 2 \times 7 \times 7 \times 2 \times 2 \times 5} \\ &:\implies \sf\quad \sf \: A =5 \times 3 \times 2 \times 7 \times 2 \sqrt{5} \\ &:\implies \sf\quad \sf \: A =420 \times 2.23 \\ &:\implies \sf\quad \sf \boxed{ \pmb{ \sf A =939.15 {cm}^{2} }} \end{aligned}$

Also, we have to find the smallest altitude, and the smallest altitude will be on the longest side. So,

$\begin{aligned}&:\implies \sf\quad \sf \: Area =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times b \times h =939.15 \\ &:\implies \sf\quad \sf \: \dfrac{1}{2} \times 61 \times h = 939.15 \\&:\implies \sf\quad \sf \: h =939.15 \times \dfrac{2}{61} \\&:\implies \sf\quad \sf \: h = \dfrac{1818.3}{61} \\ &:\implies \sf\quad \boxed{ \pmb{\sf \: h =30.79 \: (approx)}} \end{aligned}$

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