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3 years ago

Which equation results from isolating a radical term and squaring both sides of the equation for the equation

Mathematics

1 answer:

astraxan [27]3 years ago

8 0

Answer:

$c - 2 = 25 + 10 \sqrt c + c$

Step-by-step explanation:

Given

$\sqrt{c-2} - \sqrt c = 5$

Required

Isolate radical, then square both sides

We have:

$\sqrt{c-2} - \sqrt c = 5$

Isolate radical

$\sqrt{c - 2} = 5 + \sqrt c$

Square both sides

$(\sqrt{c - 2})^2 = (5 + \sqrt c)^2$

$c - 2 = 25 + 2 * 5 * \sqrt c + c$

$c - 2 = 25 + 10 \sqrt c + c$

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A collection of coins consists of nickels, dimes, and quarters. There are three fewer quarters than nickels and six more dimes t

weeeeeb [17]

Answer:

You have 15 dimes. You have 9 quarters. You have 12 nickels

Step-by-step explanation:

lets set some variables:

let "n" = the number of nickels

let "d" = the number of dimes

let "q" = the number of quarters

So, the total amount of money you have should be: $4.35 = 0.25q + 0.10d + 0.05n

Now let's look at the relationships between the coins:

"There are three fewer quarters than nickels": n - 3 = q

"six more dimes than quarters": q + 6 = d

So now you have three equations with three variables, all you need to do is solve.

$\left \{ {{4.35 = 0.25q + 0.10d + 0.05n} \atop {n - 3 = q}} \atop {q + 6 = d}}\right.$

first, you can substitute "n-3" for "q" (according to the 2nd equation) in the 1st and 3rd equation, you get:

$\left \{ {{4.35=0.25(n-3)+0.10d+0.05n} \atop {(n-3)+6=d}} \right.$

You now only have two equations and two variables.

Simplify:

$\left \{ {{4.35=0.25n-0.75+0.10d+0.05n} \atop {n+3=d}} \right.$

$\left \{ {{4.35=0.30n-0.75+0.10d} \atop {n+3=d}} \right.$

Now substitute "n+3" for "d" (according to the 2nd equation) in the 1st equation:

4.35=0.30n-0.75+0.10(n+3)

simplify:

4.35=0.30n-0.75+0.10n+0.30

4.35=0.40n-0.45

4.35+0.45=0.40n

4.80=0.40n

n=12

You have 12 nickels. Now sub "n" back into your equations to find the number of dimes and quarters:

n - 3 = q

12 - 3 = q

q = 9

You have 9 quarters.

q + 6 = d

9 + 6 = d

d = 15

You have 15 dimes.

3 0

3 years ago

In the triangle below, what is the measure of A?<br> ОА. 180°<br> Ос. 30°<br> ор. 90°

ICE Princess25 [194]

Answer:

60°

Step-by-step explanation:

Total angle measurement for a triangle is 180°

Equilateral triangle measures 60 on all angles. (60 + 60 + 60 = 180°)

This triangle is equilateral so it's angle is 60°.

Why is it equilateral? Because all sides of the triangle are equal (10 on all sides).

Hope this helps

3 0

3 years ago

Write an inequality for the graph

natima [27]

The open circle means the inequality will be greater than or equal to (≥) or less than or equal to (≤).
A closed circle means the inequality will be greater than (>) or less than (<)

An arrow pointing right to increasingly positive values means the inequality is getting greater (> or ≥)
A narrowing pointing left to increasingly negative values means the inequality is getting lesser (< or ≤)

So for this graph with an open circle and rightward pointing arrow, “x” will be some number on the number line greater than the first point of -38:
x > -38

6 0

3 years ago

Imani is selling T-shirts for a student council fund-raiser. She spent $100 on

Kruka [31]

Answer:

Step-by-step explanation:

the domain is gonna be ur x values and ur range is gonna be ur r(x) values

the domain has to do with the number of t-shirts.....and it can range from 0 to 25.......so it would be written as : [0,25]...include the brackets....not parenthesis...or all whole numbers from 0 to 25

the range has to do with the money made....and it can range from : -100 to 200....so it would be written as : [ -100,200] ..use brackets and not parenthesis.

3 0

3 years ago

What is the value of <img src="https://tex.z-dn.net/?f=%5Cfrac%7B81%5E4%7D%7B3%5E5%7D" id="TexFormula1" title="\frac{81^4}{3^5}"

IRISSAK [1]

Answer: $3^1^1\\$