How many solutions does the following equation have? 60z+50-97z=-37z+4960z+50−97z=−37z+49

For each system of equations, drag the true statement about its solution set to the box under the system?

natta225 [31]

Answer:

y = 4x + 2

y = 2(2x - 1)

Zero solutions.

4x + 2 can never be equal to 4x - 2

y = 3x - 4

y = 2x + 2

One solution

3x - 4 = 2x + 2 has one solution

Step-by-step explanation:

* Lets explain how to solve the problem

- The system of equation has zero number of solution if the coefficients

of x and y are the same and the numerical terms are different

- The system of equation has infinity many solutions if the

coefficients of x and y are the same and the numerical terms

are the same

- The system of equation has one solution if at least one of the

coefficient of x and y are different

* Lets solve the problem

∵ y = 4x + 2 ⇒ (1)

∵ y = 2(2x - 1) ⇒ (2)

- Lets simplify equation (2) by multiplying the bracket by 2

∴ y = 4x - 2

- The two equations have same coefficient of y and x and different

numerical terms

∴ They have zero equation

y = 4x + 2

y = 2(2x - 1)

Zero solutions.

4x + 2 can never be equal to 4x - 2

∵ y = 3x - 4 ⇒ (1)

∵ y = 2x + 2 ⇒ (2)

- The coefficients of x and y are different, then there is one solution

- Equate equations (1) and (2)

∴ 3x - 4 = 2x + 2

- Subtract 2x from both sides

∴ x - 4 = 2

- Add 4 to both sides

∴ x = 6

- Substitute the value of x in equation (1) or (2) to find y

∴ y = 2(6) + 2

∴ y = 12 + 2 = 14

∴ y = 14

∴ The solution is (6 , 14)

y = 3x - 4

y = 2x + 2

One solution

3x - 4 = 2x + 2 has one solution

3 0

2 years ago

a model car is one tenth of the size of the real car the models measures 42cm longs what the length of length of the real car

trapecia [35]

Just multiply 42 by 10 and that gives you 420 , so the real car has a length of 420cm or 4.2 metres :)

8 0

2 years ago

Read 2 more answers

A coin has a radius of 10 mm. How long will it take the coin to roll through the given angle measure at the given angular veloci

Gemiola [76]

Answer:

t = 1.57 sec

distance, d = 98.65 mm

Step-by-step explanation:

Given an angle of 540°

At 6 revolutions per second, which is the angular velocity.

Radius, r = 10 mm

We are asked to find the time and the distance.

To find the time, let's use the formula:

$\theta = a*t$

Where $\theta$ = angle in radians.

Converting 540° to radians, we have:

$\theta = 540 * \frac{\pi}{180} = 9.42 rad$

Therefore, from the formula, let's find t.

$\theta = a*t$

$9.42 = 6 * t$

$t = \frac{9.42}{6} = 1.57$

time = 1.57

To find the distance, we have:

$\frac{1.57 * 360}{360} = \frac{d}{2 \pi r}$

$\frac{1.57 * 360}{360} = \frac{d}{2\pi 10}$

$1.57 = \frac{d}{20\pi}$

$d = 20 \pi *1.57$

d = 98.65 mm

Therefore, the time is 1.57 seconds and the distance is 98.65 mm

8 0

2 years ago

Chapter 7 of the Jiuzhang suanshu presents a problem of two linear equations involving acres of land and their respective prices

djyliett [7]

Answer: 33.041666

Step-by-step explanation:

Given: The translated equation : $300x+y = 10000$

To find the value of x if y = 87.5, we need to substitute the value of y in the given translated equation, we will get

$300x+87.5 = 10000$

Subtract 87.5 from both the sides , we get

$300x=9912.5$

Now, divide 300 on both the sides, we get

$x=\frac{9912.5}{300}\\\\\Rightarrow x=33.041666666$

3 1

2 years ago

Read 2 more answers

The bottom of a large theater screen is 3ft above your eye level and the top of the acreen is 10ft above your eye level. Assume

Anna71 [15]

As usual, draw a diagram. You can easily see that if you are x away from the wall,

the angle of elevation of the bottom of the screen (A) is 

cotA = x/3 
A = arccot(x/3) 

angle B to the top is 

cotB = x/10 
B = arccot(x/10) 

So, since θ = B-A 
dθ/dt = dB/dt - dA/dt 
= -3/(x^2+9) + 10/(x^2+100) 
= 7(x^2-30)/((x^2+9)(x^2+100)) 

so, at x=30 
dθ/dt = 203/30300

5 0

2 years ago