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2 years ago

Determine if a triangle can be formed with 40 given sides. Show your calculations to support your yes or no answer.

Mathematics

1 answer:

Tanzania [10]2 years ago

5 0

If sum of 2 shorter sides > longest side , then a triangle can be formed.
9.) 6 + 8 = 14 > 10; yes
10.) 7 + 8 = 15 > 10; yes
11.) 75 + 25 = 100 = 100; no
12.) 1 + 1 = 2 = 2; no

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Step-by-step explanation:

If the dog has 5 to start with and the cat gives him 4.5 more, the dog would end up with 9.5

5.0+4.5=9.5

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<img src="https://tex.z-dn.net/?f=%20-%206.2%20%5E%7B0.1x%7D%20%20%3D%20%20-%20100" id="TexFormula1" title=" - 6.2 ^{0.1x} = -

Anna71 [15]

Answer:

$x=25.24$

Step-by-step explanation:

To find the value of $x$ , we are solving the exponential equation $-6.2^{0.1x} =-100$ using logarithms.

Let's solve it step-by-step

Step 1. Divide both sides of the equation by -1 to get rid of the negative signs:

$-6.2^{0.1x} =-100$

$\frac{-6.2^{0.1x}}{-1} =\frac{-100}{-1}$

$6.2^{0.1x} =100$

Step 2. Take natural logarithm to bot sides of the equation:

$ln(6.2^{0.1x)}=ln(100)$

Step 3. Use the power rule for logarithms: $ln(a^{x} )=xln(a)$

For our equation: $a=6.2$ and $x=0.1x$

$ln(6.2^{0.1x)}=ln(100)$

$0.1xln(6.2)=ln(100)$

Step 4. Divide both sides of the equation by $0.1ln(6.2)$

$0.1xln(6.2)=ln(100)$

$\frac{0.1xln(6.2)}{0.1ln(6.2)} =\frac{ln(100)}{0.1ln(6.2)}$

$x=\frac{ln(100)}{0.1ln(6.2)}$

$x=25.24$

We can conclude that the value of x in our exponential equation is approximately 25.24.

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2 years ago

A narrow rectangular banner is 5 inches wide. It is 6 times as long as it is wide. what is the area ?

butalik [34]

Answer: 30

6 times larger than the width = that's 5×6=30.

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Which of the following is not a correct factorization of the binomial 10x2 + 40x ?

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B. To be careful, use brackets: 10(1*2) + 4x which will be 20 + 40x or as you have it, 10*2 + 40x.

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