All categories

3 years ago

Which equation results from adding the equations in this system?

Mathematics

1 answer:

eimsori [14]3 years ago

3 0

Answer: 3x=3

Step-by-step explanation: Let's divide this into parts--

1. Adding the x variables: -2x+5x or 5x-2x = 3x.

2. Adding the y variables: y-y or -y+y = 0. (The negative and the positive y cancel each other out.)

3. Adding the numbers: 8-5 or -5+8 = 3.

Now just put it back into an equation: 3x + 0 = 3.

We don't need to add the 0, so the equation changes into 3x = 3.

You might be interested in

Find the area of the right triangle

xenn [34]

Answer:

Area: 24 sq units

Step-by-step explanation:

Area of a rectangle formula:

A = 0.5bh

Given:

b = 6

h = 8

Work:

A = 0.5bh

A = 0.5(6)(8)

A = 3(8)

A = 24

3 0

2 years ago

Read 2 more answers

Death Valley has an altitude that is below sea level. Which situation describes a hiker in Death Valley who hikes until he reach

Firdavs [7]

Answer: D

Step-by-step explanation:

Think of it logically: A and C are not below sea level so you can cross them out. And B doesn't work because if you decrease -10 by 10 you get -20. So, D is correct.

5 0

3 years ago

Read 2 more answers

Use Euler's formula to find the missing number.

irakobra [83]

The answer is C 16 I believe

6 0

3 years ago

Read 2 more answers

A scientist has a sample of bacteria that initially contains 10 million microbes. They observe the sample and finds that the num

sergiy2304 [10]

Answer:

M(t) = 6.7 * 10⁷ (67 million)

Minutes (t) =55

Step-by-step explanation:

1. Write an exponential equation that represents M, the total number of bacterial microbes in millions, as a function of t, the number of minutes the sample has been observed.

For answering this question, we will use the following formula:

M(t) = B₀ * g ^(t/m), where:

•M(t) represents the total number of bacterial microbes in millions.

• B₀ represents the initial population of bacteria in millions.

• g represents the growth factor.

• t represents the total number of minutes we will observe the bacteria growing.

• m represents the time in minutes it takes to the growth factor g to occur.

2. Then, determine how much time, to the nearest minute, will pass until there are 67 million bacterial microbes.

M(t) = B₀ * g ^(t/m)

Replacing with the values we know:

6.7 * 10⁷ = 10⁷ * 2 ^(t/20)

6.7 = 2 ^(t/20) (Dividing by 10⁷ at both sides)

ln 6.7 = ln 2 ^(t/20)

ln 6.7 = t/20 ln 2

ln 6.7/ ln 2 = t/20

t = ln 6.7/ln 2 * 20

t = 2.74 * 20

t = 54.88

t ≅ 55 (rounding to the nearest minute)

3 0

2 years ago

A perpendicular bisector, , is drawn through point C on .

Liula [17]

Answer:

The x-intercept of CD is B(18/5,0). The point C(32,-71) lies on the line CD.

Step-by-step explanation:

the x-intercept of CD is[ A(3,0) B(18/5,0) C(9,0) D(45/2,0) ] . Point [ A(-52,117) B(-20,57) C(32,-71) D(-54,-128) ] lies on CD.

Given :

CD is perpendicular bisector of AB.

The coordinates of point A are (-3, 2) and the coordinates of point B are (7, 6).

C is the midpoint of AB.

$C=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})=(\frac{7-3}{2},\frac{2+6}{2})=(2,4)$

The coordinates of C are (2,4).

Line AB has a slope of: $m_1=\frac{y_2-y_1}{x_2-x_1}=\frac{6-2}{7-(-3)}=\frac{4}{10}=\frac{2}{5}$

The product of slopes of two perpendicular lines is -1. Since the line CD is perpendicular to AB, therefore the slope of CD : $m_2=-\frac{5}{2}$

The point slope form of a line is given by:

$y-y_1=m(x-x_1)$

The slope of line CD is $-\frac{5}{2}$ and the line passing through the point (2,4), the equation of line CD can be written as:

$y-4=-\frac{5}{2}(x-2)\\y=-\frac{5}{2}x+5+4\\y=-\frac{5}{2}x+9 .... (1)$

The equation of CD is $y=-\frac{5}{2}x+9$

In order to find the x-intercept, put y=0.

$0=-\frac{5}{2}x+9\\\frac{5}{2}x=9\\x=\frac{18}{5}$

Therefore the x-intercept of CD is B(18/5,0).

Put x=-52 in eq(1).

$y=-\frac{5}{2}(-52)+9=139$

Put x=-20 in eq(1).

$y=-\frac{5}{2}(-20)+9=59$

Put x=32 in eq(1)

$y=-\frac{5}{2}(32)+9=-71$

Put x=-54 in eq1).

$y=-\frac{5}{2}(-54)+9=144$

Thus, only point (32,-71) satisfies the equation of CD. Therefore the point C(32,-71) lies on the line CD.

8 0

3 years ago