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Schach [20]
3 years ago
9

Solve the system of equations two ways: 3x+y=5 and x-2y=4 A) using substitution B) using elimination

Mathematics
1 answer:
Vedmedyk [2.9K]3 years ago
5 0
A. solve for 1 variable
let's solve for x in 2nd equation
add 2y to both sides
x=2y+4
sub 2y+4 for x in other equation
3(2y+4)+y=5
6y+12+y=5
7y+12=5
minu12 both sides
7y=-7
divide 7
y=-1
sub back
x=2y+4
x=2(-1)+4
x=-2+4
x=2
(2,-1)


B. eliminate
eliminate y's
multiply first equation by 2 and add to first

6x+2y=10
<u>x-2y=4 +</u>
7x+0y=14

7x=14
divide by 7
x=2
sub back
x-2y=4
2-2y=4
minus 2
-2y=2
divide -2
y=-1
(2,-1)



(2,-1) is answer
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Very buys a basket of mangoes that is priced $14 before tax. ​ ​The sales tax is 6%. ​ ​What is the total price Avery pays for t
igor_vitrenko [27]

Answer:

Avery needs to pay $14.84

Step-by-step explanation:

When there's a tax we need to sum the original value of the product with the tax's value. To find the amount of money Avery needs to pay in taxes we can apply a rule of three as shown below:

\frac{14}{x} = \frac{100}{6} \frac{\%}{\%}

Where "x" is the tax value, and $14 represents 100%, since it's the value used to calculate the tax. We have:

x = \frac{14*6}{100}\\x = \frac{84}{100}\\x = 0.84

The value to be paid is the product value plus the tax, therefore:

\text{paid} = 14 + 0.84 = 14.84

Avery needs to pay $14.84

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Evaluate 8^-2 pls only real answers
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10. Two lighthouses are located on a north-south line.
Kamila [148]

The question is an illustration of bearing (i.e. angles) and distance (i.e. lengths)

The distance between both lighthouses is 5783.96 m

I've added an attachment that represents the scenario.

From the attachment, we have:

\mathbf{\angle A = 180^o - 120^o\ 43'}

Convert to degrees

\mathbf{\angle A = 180^o - (120^o +\frac{43}{60}^o)}

\mathbf{\angle A = 180^o - (120^o +0.717^o)}

\mathbf{\angle A = 180^o - (120.717^o)}

\mathbf{\angle A = 59.283^o}

\mathbf{\angle B = 39^o43'}

Convert to degrees

\mathbf{\angle B = 39^o + \frac{43}{60}^o}

\mathbf{\angle B = 39^o + 0.717^o}

\mathbf{\angle B = 39.717^o}

So, the measure of angle S is:

\mathbf{\angle S = 180 - \angle A - \angle B} ---- Sum of angles in a triangle

\mathbf{\angle S = 180 - 59.283 - 39.717}

\mathbf{\angle S = 81}

The required distance is distance AB

This is calculated using the following sine formula:

\mathbf{\frac{AB}{\sin(S)} = \frac{AS}{\sin(B)} }

Where:

\mathbf{AS = 3742}

So, we have:

\mathbf{\frac{AB}{\sin(81)} = \frac{3742}{\sin(39.717)}}

Make AB the subject

\mathbf{AB= \frac{3742}{\sin(39.717)} \times \sin(81)}

\mathbf{AB= 5783.96}

Hence, the distance between both lighthouses is 5783.96 m

Read more about bearing and distance at:

brainly.com/question/19017345

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2 years ago
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