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Anna71 [15]
3 years ago
9

When you eliminate y What is the resulting equation of 2x+y-4=0 and 2x-y-4=0

Mathematics
1 answer:
anastassius [24]3 years ago
6 0
\begin{cases} 2x+y-4=0 \\ 2x-y-4=0\end{cases}\\ + \ \ -------\\ 4x-8=0\\ \\4x=8 \ \ /:4\\ \\x=\frac{8}{4}\\ \\x=2

2x+y-4=0\\ \\ 2*2+y-4=0\\ \\ 4+y -4 =0\\ \\y=0\\ \\\begin{cases} x=2 \\ y=0\end{cases}
 

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What is the square root of m^6?
Nastasia [14]
Answer:
If m is nonnegative (ie not allowed to be negative), then the answer is m^3
If m is allowed to be negative, then the answer is either |m^3| or |m|^3

==============================

Explanation:

There are two ways to get this answer. The quickest is to simply divide the exponent 6 by 2 to get 6/2 = 3. This value of 3 is the final exponent over the base m. Why do we divide by 2? Because the square root is the same as having an exponent of 1/2 = 0.5, so
sqrt(m^6) = (m^6)^(1/2) = m^(6*1/2) = m^(6/2) = m^3
This assumes that m is nonnegative. 

---------------------------

A slightly longer method is to break up the square root into factors of m^2 each and then apply the rule that sqrt(x^2) = x, where x is nonnegative

sqrt(m^6) = sqrt(m^2*m^2*m^2)
sqrt(m^6) = sqrt(m^2)*sqrt(m^2)*sqrt(m^2)
sqrt(m^6) = m*m*m
sqrt(m^6) = m^3
where m is nonnegative

------------------------------

If we allow m to be negative, then the final result would be either |m^3| or |m|^3. 

The reason for the absolute value is to ensure that the expression m^3 is nonnegative. Keep in mind that m^6 is always nonnegative, so sqrt(m^6) is also always nonnegative. In order for sqrt(m^6) = m^3 to be true, the right side must be nonnegative.

Example: Let's say m = -2
m^6 = (-2)^6 = 64
sqrt(m^6) = sqrt(64) = 8
m^3 = (-2)^3 = -8
Without the absolute value, sqrt(m^6) = m^3 is false when m = -2

4 0
3 years ago
Determine the value for x in the picture below.<br> Please help me
Alex787 [66]

Given:

The figure of a right angle triangle.

A line segment intersect the two sides and parallel to third side of the triangle

To find:

The value of x.

Solution:

According to basic proportionality theorem, if a line segment intersect the two sides and parallel to third side of the triangle, then it divides the two sides proportionally.

Using basic proportionality theorem, we get

\dfrac{8}{20-8}=\dfrac{6}{x}

\dfrac{8}{12}=\dfrac{6}{x}

\dfrac{2}{3}=\dfrac{6}{x}

On cross multiplication, we get

2\times x=6\times 3

2x=18

x=\dfrac{18}{2}

x=9

Therefore, the value of x is 9.

6 0
3 years ago
Soccer balls are on sale at Mr. Hawk's sport store from April to July. Mr. Hawk sells six dozen soccer balls in April. Mr. Hawk'
Alja [10]
1.) In what month did he sell he most soccer balls ?
2.) What is the range of April and July?
3.) What is the some of all the months?

6 0
4 years ago
A small school had 60% boys and the rest are girls if the number of boys is 48 what is the total number of boys and girls all to
Flura [38]

Hey there!

When dealing with percent word problems, the word "is" means equals. Let's see what we can do with your problem.

If the small school had 60% boys, it will have 40% girls. The number of boys <em>is</em> 48, which should equal 60% of the total, which we can model below, with t representing the total number of kids. In decimal form, 60% is 0.6.

0.6t=48

We divide both sides by 0.6.

t=80

Therefore, there are 80 total kids at the school.

We can also check our answer below.

BOYS: 0.6(80)= 48

GIRLS: 0.4(80)=32

48+32=80

I hope that this helps!

5 0
3 years ago
SMART PPL PLEASE HELP ME
MrRa [10]

Answer:

last one (d)

Step-by-step explanation:

adding subtracting or dividing is not how you use a growth factor(what my school calls a percentage in a decimal form).

7 0
3 years ago
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