What is equivalent to y-2x=1

Find all angles, 0 ≤C<360 that satisfy the equation below, to the nearest tenth of a degree.

ludmilkaskok [199]

Move all the terms involving the sine to one side, and all the numbers to the other:

$9\sin(c)-2=\sin(c)-7 \iff 8\sin(c) = -5\iff \sin(c)=-\dfrac{5}{8} \iff c = \arcsin\left(-\dfrac{5}{8}\right)\approx 321.3$

7 0

3 years ago

How much water must be evaporated from 130 gallons of a 9% acid solution to make a 12% acid solution?

Bad White [126]

Answer: 33 gallons

Step-by-step explanation:

We initially have 130 gallons of a $9\%$ acid solution and we need to change it to a $12\%$ acid solution, and for that it is necessary to evaporate $n$ gallons of water.

So, this situation can be mathemtically expressed as follows:

$(130)(9\%)=(130-n)(12\%)$

Then:

$(130)(\frac{9}{100})=(130-n)(1\frac{12}{100})$

Isolating $n$ :

$11.7=15.6-0.12 n$

$n=32.5 \approx 33$

Hence, we need to evaporate 33 gallons of water.

6 0

3 years ago

Write two different equations to describe each situation. a) You buy 3 identical shirts and 2 identical pairs of socks and spend

Ronch [10]

Answer:

3x + 2y = 38, 3a + 2b = 38

Step-by-step explanation:

An equation may be defined as a statement that shows two mathematical expressions to be equal. It is to equate one thing to another thing.

In the context, two different equations for the situations are :

i). Let the shirt be represented by x

And the socks be represented by y

Therefore, according to the question,

3x + 2y = 38

ii). Let the shirt be represented by a

And the socks be represented by b

Therefore, according to the question,

3a + 2b = 38

7 0

3 years ago

Simplify and write the answer in exponential form. 3^4 x 3^5 a.) 3^9

givi [52]

Answer:

Step-by-step explanation:

<h3> IN EXPONNETIAL FORM :</h3>

<h3 />

5 0

3 years ago

Given: △ABC, m∠A=60° m∠C=45°, AB=8 Find: Perimeter of △ABC, Area of △ABC . FIRST CORRECT ANSWER GETS POINTS AND BRAINLIEST!!!! T

Ad libitum [116K]

Answer:

Given : In △ABC, m∠A=60°, m∠C=45°,and AB=8 unit

Firstly, find the angles B

Sum of measures of the three angles of any triangle equal to the straight angle, and also expressed as 180 degree

∴m∠A+ m∠B+m∠C=180 ......[1]

Substitute the values of m∠A=60° and m∠C=45° in [1]

$60^{\circ}+ m\angle B+45^{\circ}=180^{\circ}$

$105^{\circ}+ m\angle B=180^{\circ}$

Simplify:

$m\angle B=75^{\circ}$

Now, find the sides of BC

For this, we can use law of sines,

Law of sine rule is an equation relating the lengths of the sides of a triangle to the sines of its angles.

$\frac{\sin A}{BC} = \frac{\sin C}{AB}$

Substitute the values of ∠A=60°, ∠C=45°,and AB=8 unit to find BC.

$\frac{\sin 60^{\circ}}{BC} =\frac{\sin 45^{\circ}}{8}$

then,

$BC = 8 \cdot \frac{\sin 60^{\circ}}{\sin 45^{\circ}}$

$BC=8 \cdot \frac{0.866025405}{0.707106781} =9.798$ unit

Similarly for AC:

$\frac{\sin B}{AC} = \frac{\sin C}{AB}$

Substitute the values of ∠B=75°, ∠C=45°,and AB=8 unit to find AC.

$\frac{\sin 75^{\circ}}{AC} =\frac{\sin 45^{\circ}}{8}$

then,

$AC = 8 \cdot \frac{\sin 75^{\circ}}{\sin 45^{\circ}}$

$AC=8 \cdot \frac{0.96592582628}{0.707106781} =10.9283$ unit

To find the perimeter of triangle ABC;

Perimeter = Sum of the sides of a triangle

i,e

Perimeter of △ABC = AB+BC+AC = 8 +9.798+10.9283 = 28.726 unit.

To find the area(A) of triangle ABC ;

Use the formula:

$A = \frac{1}{2} \times AB \times AC \times \sin A$

Substitute the values in above formula to get area;

$A=\frac{1}{2} \times 8 \times 10.9283 \times \sin 60^{\circ}$

$A = 4 \times 10.9283 \times 0.86602540378$

Simplify:

Area of triangle ABC = 37.856 (approx) square unit

4 0

3 years ago