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2 years ago

How can you determine if two expressions are equivalent?

Mathematics

1 answer:

Vladimir [108]2 years ago

7 0

Simplify them until they can be simplified no more, then compare both sides.

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Richard and Teo have a combined age of 37. Richard is 4 years older than twice Teo's age. How old are Richard and Teo?

valkas [14]

Answer:

Teo is 11 years old and Richard is 26 years old.

Step-by-step explanation:

Let R be the age of Richard and T be the age of Teo.

First set up the equations:

The combined age of Teo and Richard is 37:

R+T=37

Richard is four years old than twice Teo's age:

R=2T+4

Then, solve the equations:

Substitute (2) to (1) and solve for T:

(2T+4)+T=37

3T=11

T=11

Solve for R using (2):

R=2(11)+4

R=22+4

R=26

5 0

2 years ago

ΔEFG is located at E (0, 0), F (−7, 4), and G (0, 8). Which statement correctly classifies ΔEFG?

MariettaO [177]

Answer:

ΔEFG is an isosceles triangle.

Step-by-step explanation:

Given:

E (0, 0),

F (−7, 4),

G (0, 8)

ΔEFG

Solution:

Distance formula

Distance d = $\sqrt{(x_2-x_1)^2 +( y_2-y_1)^2$

Step 1: Finding the length of EF

By using distance formula,

$EF = \sqrt{(-7 - 0)^2 + (4-0)^2}$

$EF = \sqrt{(49) + (16)}$

$EF = \sqrt{(49) + (16)}\\EF = \sqrt{65}\\$

Step 2: Finding the length of FG

By using distance formula,

$FG = \sqrt{(0-(-7))^2+(8-4)^2}\\FG = \sqrt{(7)^2 +(4)^2}\\FG = \sqrt{49 +16}\\FG = \sqrt{65}$

Step 2: Finding the length of GE

$GE= \sqrt{(0-0)^2 + (0-8)^2}\\\\GE =\sqrt{(-8)^2}\\GE = \sqrt{64}\\GE = 8$

Thus we could see that the sides EF = FG

So it is a isosceles triangle.

6 0

2 years ago

A certain smartphone family plan costs $55 per month plus additional usage costs. If x is the number of cell phone used above th

Marina CMI [18]

First thing to do, is organize in your mind what is asked of the problem. Since the problem talks about total cost, then you are dealing with monetary units of measurement. Next, you investigate on the variables given and what they represent. Looking at the following expressions, I could not immediately get a hint on what these terms stand for. But for letter c, I deduced that that would be the overall equation representing the total cost.

The first term, 0.25x, must be the cost of the phone units purchased under the plan . That means each cellphone unit used costs $0.25 each. The second term, 2y, must be the cost of data used by the plan. So, that means each megabyte used up costs $2. These two costs must be what is referred to by the additional costs. Lastly, the last term, '55'. is the fixed cost when you subscribe to the amount per month. Hence, the equation in letter C represents the total cost per month.

7 0

3 years ago

One leg of a right triangle is 28 inches longer than the other leg, and the hypotenuse is 52 inches. Find the lengths of the leg

katovenus [111]

Step-by-step explanation:

Let x represent the missing sides measurement.

x+x+28=52

combine like terms

2x + 28 = 52

subtract 28 from both sides

2x + 28 = 52

- 28 - 28

2x = 24

divide both sides by 2

x = 12

plug it back in

one leg is 12 inches

the other leg is 40 inches

7 0

2 years ago

What is the domain of the ordered pairs?

BigorU [14]

Answer:

b. {-3, -1, 2}

Step-by-step explanation:

An ordered pair is a pair of elements written as (x, y) where the first element is the input value and the second element is the output value.

The domain is the set of input values (x-values)

The range is the set of output values (y-values)

Therefore, for the given ordered pairs (-1, 0), (2, 4) and (-3, 6)

Domain: {-3, -1, 2}

Range: {0, 4, 6}

3 0

1 year ago