All categories

3 years ago

(08.03) Consider the following pair of equations:

Mathematics

1 answer:

Luba_88 [7]3 years ago

6 0

Substitution method is used to solve the linear system of equations for one or more variables.

Consider the first equation y = 3x + 3 -----(1)

In equation (1) plug in y=x-1, we get

x -1 = 3x + 3

Add -3x on both side , we get

x-3x -1 = 3x-3x +3

-2x-1=0 + 3

Now add +1 on both sides, we get

-2x-1+1= 3+1

-2x + 0 =4

Now divide both side by -2

-2x/-2= 4/-2

X= -2

Now put x=-2 in the the second equation,

y=x-1

y=(-2)-1

y=-3

Solution(-2,-3)

You might be interested in

If P is the orthocenter of △ABC, AB = 13, BF = 9,and FC = 5.6, find each measure & the perimeter of triangle ABC.

harina [27]

Answer:

$Perimeter = 38.6$

Step-by-step explanation:

Given

$A\ B = 13$

$B\ F = 9$

$F\ C = 5.6$

Required

Calculate the perimeter of A B C

To calculate the perimeter of A B C, we sum up the sides of the triangle

i.e.

$Perimeter = A B + B\ C + A\ C$

AB is given in the question already.

So, we need to calculate B F and F C

To solve for BF, we consider triangle B F C

Using Pythagoras Theorem, we have:

$B\ C^2 = B\ F^2 + F\ C^2$

Substitute values for BF and FC;

$B\ C^2 = 9^2 + 5.6^2$

$B\ C^2 = 81 + 31.36$

$B\ C^2 = 112.36$

$B\ C^2= \sqrt{112.36$

$B\ C = 10.6$

Next, we calculate A C.

To calculate A C, we need to calculate A F, considering triangle B F A

Using Pythagoras Theorem, we have:

$A\ B^2 = B\ F^2 + A\ F^2$

Substitute values for B F and A B;

$13^2 = 9^2 + A\ F^2$

$169= 81 + A\ F^2$

$A\ F^2 = 169 - 81$

$A\ F^2 = 88$

$A\ F = \sqrt{88$

$A\ F = 9.4$

Since F lies on line A C:

$A\ C = A\ F + F\ C$

$A\ C = 9.4 + 5.6$

$A\ C = 15.0$

Recall that:

$Perimeter = A\ B + B\ C + A\ C$

$Perimeter = 13 + 10.6 + 15.0$

$Perimeter = 38.6$

<em>Hence, the perimeter is 38.6</em>

3 0

3 years ago

In a class, there are 20 girls and 10 boys. What is the percentage of the boys?

gayaneshka [121]

Answer:

33.33%

Step-by-step explanation:

Number of boys=10
Number of girls=20
Total number of students=

Number of boys + Number of girls

10+20

Percentage of boys=

10/30×100%

33.33%

4 0

3 years ago

Logan wants to have $130,000 to pay for a surgery on his retractable forearm claws in 30 months. If he can invest money in an ac

dangina [55]

Answer: $107,836.69 or about $107,837 (to the nearest dollar)

Step-by-step explanation:

Formula to the accumulated amount received after investing principal amount (P) at rate of interest (r) compounded monthly for t months :

$A=P(1+\dfrac{r}{12})^{t}$

As per given , A = $130,000

r= 7.5% = 0.075

t= 30 months

Now,

$130000=P(1+\dfrac{0.075}{12})^{30}\\\\\Rightarrow 130000=P(1+0.00625)^{30}\\\\\Rightarrow 130000=P(1.00625)^{30}\\\\\Rightarrow 130000=P \times1.20552661036\\\\\Rightarrow\ P=\dfrac{130000}{1.2055266}=107,836.69$

Hence he need to invest $107,836.69 .

8 0

4 years ago

The sum of eight times a number and seven is twice the number

Dovator [93]

8x7=56

i hope this helps

8 0

3 years ago

What is 42cm per second converted to meters per min

BARSIC [14]

25.2 meters per minute

8 0

3 years ago