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2 years ago

- 8.3 + 11.7 + x = 0 p;lssssss helppp

Mathematics

1 answer:

Ierofanga [76]2 years ago

4 0

Answer:

X = -3.4

I found that the answer should be -3.4 because I just did 11.7 - -8.3 which equals 3.4 so i just changed it so it would be a negative number.

Step-by-step explanation:

11.7 + -8.3 + -3.4

the answer is then 0 so x = -3.4

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Joel wanted his mom to buy a super-sized box of his favorite cereal, but his mom didn't think it would fit in her cupboard. The

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<h3><u>Given</u>:-</h3>

Volume 6,900 cm^3
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<h3><u>Solution</u>:-</h3>

$\\\diamond{\underline{\underline{\sf {\;\; Calculating\; Height\; of \; box :-}}}}\\$

$\\ \pink \star \: \: {\underline{\boxed {\bf{ Volume_{ \red{ \{Rectangle \}}} \: = l \times w \times h }}} }\; \red\bigstar \\$

Where,

» l denotes Length
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$\\ \sf \implies \: {Volume_{ \red{ \{Rectangle \}}} \: = l \times w \times h} \\$

$\\ \sf \implies \: { 6,900 \: = \: 23 \: \times \: 10 \: \times h} \\$

$\\ \sf \implies \: { 6,900 \: = \: 230 \: \times \: h} \\$

$\\ \sf \implies \: { \: h \: = \: \frac{6900}{230} \: } \\$

$\\ \sf \implies \: { \: h \: = \: 30 \: {cm }^{3} \: } \\$

$\\ \implies{\underline{\boxed{\frak { Height = 30 \: cm^3 }}}} \; \purple\bigstar \: \\$

$\\\qquad \rule{120pt}{3pt}\\$

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Describes the following triangle

To find the missing length x, we could use the Pythagorean Theorem. The sum of the squares of the legs is equal to the square of the hypotenuse. From this, we have the following equation

$x^2+3^2=5^2$

Solving for x, we have

$\begin{gathered} x^2+3^2=5^2 \\ x^2+9=25 \\ x^2=25-9 \\ x^2=16 \\ x=\sqrt[]{16} \\ x=4 \end{gathered}$

The missing length of the first triangle is equal to 4.

For the other triangle, instead of a sine we have a tangent relation. Given an angle in a right triangle, its tanget is equal to the ratio between the opposite side and adjacent side.The following expression

$\tan (y)=\frac{12}{5}$

Describes the following triangle

Using the Pythagorean Theorem again, we have

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Solving for h, we have

$\begin{gathered} 5^2+12^2=h^2 \\ 25+144=h^2 \\ 169=h^2 \\ h=\sqrt[]{169} \\ h=13 \end{gathered}$

The missing side measure is equal to 13.

Now that we have all sides of both triangles, we can construct any trigonometric relation for those angles.

The sine is the ratio between the opposite side and the hypotenuse, and the cosine is the ratio between the adjacent side and the hypotenuse, therefore, we have the following relations for our angles

$\begin{gathered} \sin (\theta)=\frac{3}{5} \\ \cos (\theta)=\frac{4}{5} \\ \sin (y)=\frac{12}{13} \\ \cos (y)=\frac{5}{13} \end{gathered}$

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$\begin{gathered} \sin (\theta+y) \\ \cos (\theta+y) \end{gathered}$

We can use the following identities

$\begin{gathered} \sin (A+B)=\sin A\cos B+\cos A\sin B \\ \cos (A+B)=\cos A\cos B-\sin A\sin B \end{gathered}$

Using those identities in our problem, we're going to have

$\begin{gathered} \sin (\theta+y)=\sin \theta\cos y+\cos \theta\sin y=\frac{3}{5}\cdot\frac{5}{13}+\frac{4}{5}\cdot\frac{12}{13}=\frac{63}{65} \\ \cos (\theta+y)=\cos \theta\cos y-\sin \theta\sin y=\frac{4}{5}\cdot\frac{5}{13}-\frac{3}{5}\cdot\frac{12}{13}=-\frac{16}{65} \end{gathered}$

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