All categories

3 years ago

Solve for a.

Mathematics

2 answers:

FinnZ [79.3K]3 years ago

8 0

Answer:

iii) a=3b/2

Step-by-step explanation:

7a-2b= 5a+b

7a-5a=2b+b

2a=3b

a=3b/2

pychu [463]3 years ago

8 0

Answer:

$\large\boxed{a=\dfrac{3b}{2}=\dfrac{3}{2}b=1.5b}$

Step-by-step explanation:

$7a-2b=5a+b\qquad\text{add}\ 2b\ \text{to both sides}\\\\7a-2b+2b=5a+b+2b\\\\7a=5a+3b\qquad\text{subtract}\ 5a\ \text{from both sides}\\\\7a-5a=5a-5a+3b\\\\2a=3b\qquad\text{divide both sides by 2}\\\\\dfrac{2a}{2}=\dfrac{3b}{2}\\\\a=\dfrac{3b}{2}$

You might be interested in

Suppose you pay a dollar to roll two dice. if you roll 5 or a 6 you Get your dollar back +2 more just like it the goal will be t

LiRa [457]

Answer:

(a)$67

(b)You are expected to win 56 Times

(c)You are expected to lose 44 Times

Step-by-step explanation:

The sample space for the event of rolling two dice is presented below

$(1,1), (2,1), (3,1), (4,1), (5,1), (6,1)\\(1,2), (2,2), (3,2), (4,2), (5,2), (6,2)\\(1,3), (2,3), (3,3), (4,3), (5,3), (6,3)\\(1,4), (2,4), (3,4), (4,4), (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)$

Total number of outcomes =36

The event of rolling a 5 or a 6 are:

$(5,1), (6,1)\\ (5,2), (6,2)\\( (5,3), (6,3)\\ (5,4), (6,4)\\(1,5), (2,5), (3,5), (4,5), (5,5), (6,5)\\(1,6), (2,6), (3,6), (4,6), (5,6), (6,6)$

Number of outcomes =20

Therefore:

P(rolling a 5 or a 6) $=\dfrac{20}{36}$

The probability distribution of this event is given as follows.

$\left|\begin{array}{c|c|c}$Amount Won(x)&-\$1&\$2\\&\\P(x)&\dfrac{16}{36}&\dfrac{20}{36}\end{array}\right|$

First, we determine the expected Value of this event.

Expected Value

$=(-\$1\times \frac{16}{36})+ (\$2\times \frac{20}{36})\\=\$0.67$

Therefore, if the game is played 100 times,

Expected Profit =$0.67 X 100 =$67

If you play the game 100 times, you can expect to win $67.

(b)

Probability of Winning $=\dfrac{20}{36}$

If the game is played 100 times

Number of times expected to win

$=\dfrac{20}{36} \times 100\\=56$ times$

Therefore, number of times expected to loose

= 100-56

=44 times

8 0

3 years ago

4. Write the equation in point-slope form. (-6, -2) and m = 3

yKpoI14uk [10]

Y+2=3(x+6) is your answer.

5 0

2 years ago

What is 20% of 1630?

sveticcg [70]

20% = 0.20.2 * 1630 = 326

4 0

3 years ago

Read 2 more answers

The area of triangle ABC is 50 square units. What is the length of CD?

My name is Ann [436]

The triangle spilts into two 45-45-90 triangle. Because of that, the short leg and long leg with be the same length. It gives the hypotenuse, 10. Divided 10 by √2 which is 5 √2. The length of CD is 5 √2

7 0

2 years ago

What is the expression

timofeeve [1]

$-9r^2-2r+r^2+r=(-9r^2+r^2)+(-2r+r)=-8r^2-r\to B.$

7 0

3 years ago