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vaieri [72.5K]
3 years ago
11

Suppose a system of two linear equations has one solution. What must be true about the graphs of the two equations?

Mathematics
2 answers:
Neporo4naja [7]3 years ago
3 0

Answer:

They intersect at one point.

Step-by-step explanation:

If a system of two linear equations has one solution then the two lines intersect at one point. The solution is the point of intersection.

adell [148]3 years ago
3 0
They intersect at one point
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What are the solutions to the following system of equations? y = x2 + 3x − 7 3x − y = −2 (2 points) (3, 11) and (−3, −7) (11, 3)
Minchanka [31]
ANSWER

(3, 11) and (−3, −7)


EXPLANATION

The given system of equations are:


y =  {x}^{2}  + 3x - 7

and

3x - y =  - 2

or

y = 3x  + 2


We equate the two equations to obtain,



{x}^{2}  + 3x - 7 = 3x + 2

We rewrite in standard quadratic form to obtain,

{x}^{2}  + 3x  - 3x - 7 - 2 = 0


This simplifies to

{x}^{2}- 9= 0


We solve for x to obtain,


{x}^{2}  = 9

x =  \pm \sqrt{9}

x =  \pm 3

x = 3 \: or \: x =  - 3

When
x = 3

y = 3(3) + 2 = 11

When x=-3,

y = 3(  - 3) + 2 =  - 7


Therefore the solution for the system is (3, 11) and (−3, −7).
7 0
3 years ago
Read 2 more answers
Which table represents the graph of a logarithmic function in the form y=log3x when b>1?
alex41 [277]

Answer:

<u><em>The satisfied table of the given function</em></u>y = log_{b} (x)<u><em></em></u>

<em>x                    1/8            1/4             1/2              1             2</em>

<em>y                    -3                 -2            -1               0               1</em>

<em></em>

Step-by-step explanation:

<u><em>Explanation</em></u> :-

Given logarithmic function y = log_{b} (x)   if b >1

Given first table

i)

put x = \frac{1}{8}     given b > 1 so we can choose b = 2

y = log_{2} (\frac{1}{8} )

y = log_{2} (2^{-3}  )

we will apply logarithmic formula

log x ⁿ = n log (x)

y = log_{2} (2^{-3}  ) = -3 log_{2} (2) = -3 (1) = -3

<em>y = -3</em>

<em>ii)</em>

<em>put x = </em>\frac{1}{4}<em>     given b > 1 so we can choose b = 2</em>

<em></em>y = log_{2} (\frac{1}{4} )<em></em>

<em></em>y = log_{2} (2^{-2}  )<em></em>

we will apply logarithmic formula

log x ⁿ = n log (x)

y = log_{2} (2^{-2}  ) = -2 log_{2} (2) = -2 (1) = -2

<em>y = -2</em>

<em>iii) </em>

<em>put x = </em>\frac{1}{2}<em>     given b > 1 so we can choose b = 2</em>

<em></em>y = log_{2} (\frac{1}{2} )<em></em>

y = log_{2} (2^{-1}  )

<em>we will apply logarithmic formula </em>

<em>log x ⁿ = n log (x)</em>

y = log_{2} (2^{-1}  ) = -1 log_{2} (2) = - (1) = -1

<em>y = -1</em>

<em>iv) </em>

<em>put x = 1     given b > 1 so we can choose b = 2</em>

<em></em>y = log_{2} (1 )<em> = 0</em>

<em>y = 0</em>

<em>v) </em>

<em>put x = </em>2<em>     given b > 1 so we can choose b = 2</em>

y = log_{2} (2 )

<em>y = 1</em>

<em></em>

<u><em>Final answer:-</em></u>

<u><em>The satisfied table of the given function</em></u>

<em>x                    1/8            1/4             1/2              1             2</em>

<em>y                    -3                 -2            -1               0               1</em>

<em></em>

8 0
3 years ago
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Consider continuous functions f, g, h, and k. Then complete the statements.
Ghella [55]

It wouldn't let me post the answer. See images for the answer and explanation

7 0
2 years ago
Wilber can mow 500 ft2 yard in 10 minutes. If he does not slow down, how long will it take Wilber to mow his neighbors yard that
NeTakaya

Answer:

70 hours

Step-by-step explanation:

3500 by 50 is 70

4 0
3 years ago
I need help can tell me tell me on a playground what is something that is shorter than a meter
Novosadov [1.4K]
One meter is 3.28 feet, so anything shorter than that. A basketball, maybe a very young child?
8 0
3 years ago
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