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2 years ago

What is the value of x? Enter your answer in the box. __ cm

Mathematics

2 answers:

nasty-shy [4]2 years ago

7 0

Answer:

You need to add a picture

Step-by-step explanation:

dolphi86 [110]2 years ago

7 0

65447 6yr5euot5 two-wheeler

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Item 7

Mariulka [41]

Answer:

$A = 74.7^\circ$

$B = 42.5^\circ$

$C = 62.8^\circ$

Step-by-step explanation:

Given

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

Required

The measure of each angle

First, we calculate the length of the three sides of the triangle.

This is calculated using distance formula

$d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

For AB

$A = (-1,2) \to (x_1,y_1)$

$B = (2,8) \to (x_2,y_2)$

$d = \sqrt{(-1 - 2)^2 + (2 - 8)^2$

$d = \sqrt{(-3)^2 + (-6)^2$

$d = \sqrt{45$

So:

$AB = \sqrt{45$

For BC

$B = (2,8) \to (x_2,y_2)$

$C = (4,1) \to (x_3,y_3)$

$BC = \sqrt{(2 - 4)^2 + (8 - 1)^2$

$BC = \sqrt{(-2)^2 + (7)^2$

$BC = \sqrt{53$

For AC

$A = (-1,2) \to (x_1,y_1)$

$C = (4,1) \to (x_3,y_3)$

$AC = \sqrt{(-1 - 4)^2 + (2 - 1)^2$

$AC = \sqrt{(-5)^2 + (1)^2$

$AC = \sqrt{26$

So, we have:

$AB = \sqrt{45$

$BC = \sqrt{53$

$AC = \sqrt{26$

By representation

$AB \to c$

$BC \to a$

$AC \to b$

So, we have:

$a = \sqrt{53$

$b = \sqrt{26$

$c = \sqrt{45$

By cosine laws, the angles are calculated using:

$a^2 = b^2 + c^2 -2bc \cos A$

$b^2 = a^2 + c^2 -2ac \cos B$

$c^2 = a^2 + b^2 -2ab\ cos C$

$a^2 = b^2 + c^2 -2bc \cos A$

$(\sqrt{53})^2 = (\sqrt{26})^2 +(\sqrt{45})^2 - 2 * (\sqrt{26}) +(\sqrt{45}) * \cos A$

$53 = 26 +45 - 2 * 34.21 * \cos A$

$53 = 26 +45 - 68.42 * \cos A$

Collect like terms

$53 - 26 -45 = - 68.42 * \cos A$

$-18 = - 68.42 * \cos A$

Solve for $\cos A$

$\cos A =\frac{-18}{-68.42}$

$\cos A =0.2631$

Take arc cos of both sides

$A =\cos^{-1}(0.2631)$

$A = 74.7^\circ$

$b^2 = a^2 + c^2 -2ac \cos B$

$(\sqrt{26})^2 = (\sqrt{53})^2 +(\sqrt{45})^2 - 2 * (\sqrt{53}) +(\sqrt{45}) * \cos B$

$26 = 53 +45 -97.67 * \cos B$

Collect like terms

$26 - 53 -45= -97.67 * \cos B$

$-72= -97.67 * \cos B$

Solve for $\cos B$

$\cos B = \frac{-72}{-97.67}$

$\cos B = 0.7372$

Take arc cos of both sides

$B = \cos^{-1}(0.7372)$

$B = 42.5^\circ$

For the third angle, we use:

$A + B + C = 180$ --- angles in a triangle

Make C the subject

$C = 180 - A -B$

$C = 180 - 74.7 -42.5$

$C = 62.8^\circ$

8 0

2 years ago

What is the sum of 1 1/2 and 2/3

prisoha [69]

$1\dfrac{1}{2}+\dfrac{2}{3}=1+\dfrac{1\cdot3}{2\cdot3}+\dfrac{2\cdot2}{3\cdot2}=1+\dfrac{3}{6}+\dfrac{4}{6}=1+\dfrac{3+4}{6}=1+\dfrac{7}{6}=1+1\dfrac{1}{6}=2\dfrac{1}{6}\\\\Answer:\ \boxed{1\dfrac{1}{2}+\dfrac{2}{3}=2\dfrac{1}{6}}$

6 0

3 years ago

Read 2 more answers

If Josie wants to buy cupcakes and cookies for a party with a budget of

kolezko [41]

Answer:

50 cupcakes, 150 cookies

Step-by-step explanation:

3 0

3 years ago

Can anyone explain how to solve this?

eduard

I’m not 100 percent sure someone can comment on this and confirm but when it’s written like a fraction it means division. If they gave you the meaning of each variable (the letters) multiply each variable by each coefficient (the number next to the variable). Multiply all of those. Then divide it by the product of 4 and the variable

Hope this helped!

8 0

3 years ago

write an enaquality that expresses the reason the lengths 5 feet , 10 feet and 20 feet could not make a triangle. explain how th

NikAS [45]

For any triangle, the 2 shortest sides added together have to be longer than the longest sides.

short side (10) + short side (5) needs to be greater than (>) longest side (20)

10 + 5 > 20

15 > 20

This inequality is incorrect, so the lengths cannot make a triangle.

Hope this helps :)

7 0

3 years ago