Find the value of x. If your answer is not an integer, express it in simplest radical form.

Mathematics

1 answer:

LenaWriter [7]3 years ago

5 0

Step-by-step explanation:

$4 \\ {x}^{2} = {16}^{2} + {14}^{2} \\ {x}^{2} = 256 + 196 \\ {x}^{2} = 452 = 2 \sqrt{113} = 21.26$

$5 \\ {x}^{2} = {8}^{2} + {15}^{2} \\ {x}^{2} = 64 + 225 \\ {x}^{2} = 289 \\ x = 17$

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Monica paid sales tax of $2.80 when she bought a new bike helmet. If the sales tax rate was 7%, how much did the store charge fo

larisa [96]

7 % of cost price is 2.80 , What about 1%?

7 = 2.80

1 = x (where x is the price value of 1% in dollars)

We simplify the above equation, so:

7 × x = 2.8 × 1 → 7x = 2.8 → x = 2.8 / 7 → x = 0.4 dollars

We know that 100% represents the whole price,

so if 1% is 0.4 dollars, then 100% will be 0.4 × 100 = 40 dollars

Therefore the store charged $40 dollars for the helmet before tax

5 0

3 years ago

In ΔABC, the lengths of a, b, and c are 22.5 centimeters, 18 centimeters, and 13.6 centimeters, respectively.

Irina-Kira [14]

Given the values of the three sides of the triangle, we can apply the Cosine Law to find the angles of the triangle. Recall that for we can express the value of c through the equation below.

$c^{2} = a^{2} + b^{2} - 2abcosC$

Rearranging this equation, we can find the value ∠C as shown below.

$\cos C = \frac{a^{2}+b^{2}-c^{2}}{2ab}$
$C = cos^{-1} (\frac{a^{2}+b^{2}-c^{2}}{2ab})$

We can apply the same reasoning for finding the value of ∠B as shown.

$B = cos^{-1} (\frac{a^{2}+c^{2}-b^{2}}{2ac})$

Plugging in the values of the sides (see image attached) from the given. It will now be straightforward to compute for ∠B and ∠C.

$C = cos^{-1} (\frac{22.5^{2}+18^{2}-13.6^{2}}{2(22.5)(18)})$
$C \approx 37.19$

$B = cos^{-1} (\frac{22.5^{2}+13.6^{2}-18^{2}}{2(22.5)(13.6)})$
$B \approx 53.13$

Answer: ∠C = 37.19° and ∠B = 53.13°