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3 years ago

How many solutions are there for 5x=10

Mathematics

1 answer:

3241004551 [841]3 years ago

7 0

Answer:e

Step-by-step explanation:

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Please help me!!!!!

denpristay [2]

Answer: see proof below

Step-by-step explanation:

Given: A + B + C = π → A = π - (B + C)

→ B = π - (A + C)

→ C = π - (A + B)

Use Sum to Product Identity: sin A - sin B = 2 cos [(A + B)/2] · sin [(A - B)/2]

Use the following Cofunction Identity: cos (π/2 - A) = sin A

Proof LHS → RHS:

LHS: sin A - sin B + sin C

= (sin A - sin B) + sin C

$\text{Sum to Product:}\quad 2\cos \bigg(\dfrac{A+B}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)$

$\text{Given:}\qquad 2\cos \bigg(\dfrac{\pi -(B+C)}{2}+\dfrac{B}{2}}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\\\\\\.\qquad \qquad =2\cos \bigg(\dfrac{\pi -C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)$

$.\qquad \qquad =2\cos \bigg(\dfrac{\pi}{2} -\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)$

$\text{Cofunction:} \qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\cdot \sin \bigg(\dfrac{A-B}{2}\bigg)+2\cos \bigg(\dfrac{C}2{}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)$

$\text{Factor:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{C}{2}\bigg)\bigg]$

$\text{Given:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi -(A+B)}{2}\bigg)\bigg]\\\\\\.\qquad \qquad =2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\cos \bigg(\dfrac{\pi}{2} -\dfrac{(A+B)}{2}\bigg)\bigg]$

$\text{Cofunction:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ \sin \bigg(\dfrac{A-B}{2}\bigg)+\sin \bigg(\dfrac{A+B}{2}\bigg)\bigg]$

$\text{Sum to Product:}\qquad 2\sin \bigg(\dfrac{C}{2}\bigg)\bigg[ 2\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\bigg]\\\\\\.\qquad \qquad \qquad \qquad =4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)$

$\text{LHS = RHS:}\quad 4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)=4\sin \bigg(\dfrac{A}{2}\bigg)\cdot \cos \bigg(\dfrac{B}{2}\bigg)\cdot \sin \bigg(\dfrac{C}{2}\bigg)\quad \checkmark$

6 0

3 years ago

Identify the slope of the line for the equation y= -2/3× + 1/3

natita [175]

Answer:

$\textbf{The slope of the parallel line is given by $ \frac{-2}{3} $}\\$

Step-by-step explanation:

$\textup{The slope of any two parallel lines are equal and they only differ in their $y- intercepts$. }\\\textup{Given $y = \frac{-2}{3}x + \frac{1}{3} $}\\\textup{This is comparable to $y = mx + c$, where $m$ is the slope of that line.}\\\textup{Therefore, the slope of the given line and any line parallel to it is $ \frac{-2}{3}$.}$

7 0

3 years ago

Which box-and-whisker plot represents this data: 6, 9, 13, 13, 18, 20, 22, 25, 26, 28, 30, 30 ?

BaLLatris [955]

do you want me to make you a box and whisker plot if so then here

7 0

3 years ago

What is the exact volume of a sphere with a diameter of 18 cm? ______ cm3

madam [21]

The formula to find the volume of a sphere is: V= $\frac{4}{3} \pi r^{3}$
Since the diameter is 18 cm, so the radius is equal to r=18/2 = 9
Now we replace r by it's value, so we get:
$\frac{4}{3} \pi 9^{3}$
$\frac{4}{3} \pi 729$
$972 \pi$
And we get approximately $3053.63 cm^{3}$
Hope this Helps :D

4 0

3 years ago

A rectangle has a perimeter 90 cm and length 37 cm. What is it’s width

Tresset [83]

Answer:

8cm

Step-by-step explanation:

5 0

3 years ago

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