All categories

3 years ago

How do you solve for a: 4b = 2a - t

Mathematics

1 answer:

mihalych1998 [28]3 years ago

6 0

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

a=t2−ba=t2-b

You might be interested in

let sin(θ) =3/5 and tan(y) =12/5 both angels comes from 2 different right trianglesa)find the third side of the two tringles b)

statuscvo [17]

In a right triangle, we haev some trigonometric relationships between the sides and angles. Given an angle, the ratio between the opposite side to the angle by the hypotenuse is the sine of this angle, therefore, the following statement

$\sin (\theta)=\frac{3}{5}$

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

$5^2+12^2=h^2$

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

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

To calculate the sine and cosine of the sum

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

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

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

4 0

1 year ago

Your checking account balance is $225. You received a “bounced” check and your bank has charged you a penalty fee of $35. What p

Eduardwww [97]

Answer: 15.56%

Step-by-step explanation:

Given : Your checking account balance is $225.

i.e. Account balance= $225

You received a “bounced” check and your bank has charged you a penalty fee of $35.

i.e.Penalty fee= $35

Now, the percent of your balance the penalty cost :-

$\dfrac{\text{Penalty fee}}{\text{Account balance}}\times100\\\\=\dfrac{35}{225}\times100=15.5555555556\approx15.56\%$

Hence, the penalty cost 15.56% of your balance .

4 0

4 years ago

There are 5 appetizers to choose from, 10 main courses to choose from, and 2 desserts to choose from. if you pick 1 appetizer, 1

storchak [24]

Since there are 5 appetizers and 10 main courses, that already gives us 50 options. For each appetizer, you can pair it with ten different courses. That means for each appetizer, 10 options are possible. 10*5=50, so if there were only appetizers and courses, there'd be 50 choices. But there are also desserts. That gives us 2 times the possibilities (since for each previous possibility, you have two options for dessert). 2*50=100. There are 100 options.

5 0

3 years ago

The problem (5x² + 10x — 15) ÷ (x + 5) can be done using synthetic division as it is.

denis23 [38]

True or false it will be true

4 0

3 years ago

HEB sells mangos for $2.50 each. Costco Sells them for $1.75 each but has a

Gnoma [55]

Answer:

$20.833

Step-by-step explanation:

HEB:

Total cost = 2.50m

Costco:

Total cost = 50 + 1.75m

Where,

m = number of mangoes

HEB = Costco

2.50m = 50 + 1.75m

2.50m - 1.75m = 50

O.75m = 50

m = 50 / 0.75

= $20.833

6 0

3 years ago