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katovenus [111]
2 years ago
8

Which ordered pair is a solution to the system of linear equations? 2x + 3y= 6 –3x + 5y = 10

Mathematics
1 answer:
n200080 [17]2 years ago
7 0

Answer:

(0,2)

Step-by-step explanation:

solve by addition/elimination

2x + 3y= 6

–3x + 5y = 10  

multiply first equation by 3  and second one by 2 to eliminate x)

6x+9y=18

-6x+10y=20 (add the two equations)

6x+9y-6x+10y=38

19y=38

y=38/19=2

2x+3y=6

2x=6-6

x=0

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Over which interval is the graph of f(x) = one-halfx2 + 5x + 6 increasing?
kaheart [24]

Answer:

\large\boxed{x\in[-5,\ \infty)}

Step-by-step explanation:

f(x)=\dfrac{1}{2}x^2+5x+6\\\\\text{The coeficient of}\ x^2\ \text{is the positive number. Therefore the parabola is op}\text{en up}.\\\\\text{If a parabola op}\text{en up, then the graph increasing in interval}\ (h,\ \infty),\\\text{and decreasing in interval}\ (-\infty,\ h).\ \text{Where}\ h\ \text{is a first coordinate of a vertex.}\\\\\text{For}\ y=ax^2+bx+c,\ h=\dfrac{-b}{2a}.\\\\\text{We have}\ a=\dfrac{1}{2}\ \text{and}\ b=5.\ \text{Substitute:}\\\\h=\dfrac{-5}{2\left(\frac{1}{2}\right)}=-\cdot\dfrac{5}{1}=-5.

8 0
3 years ago
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The function f(x) is shown in the graph.
anzhelika [568]

The function that describes the graph is an exponential function

<h3>How to determine the function type?</h3>

From the graph, we have the following highlights:

  • Initially, when x increases; y seem not to increase
  • Then, x and y increase at the same time
  • Finally, y increase and x seem not to increase

The above is the description of an exponential function

Hence, the function that describes the graph is an exponential function

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3 0
2 years ago
Write the fractions as fractions with a common denominator 3/4 and 1/3
JulijaS [17]

3/4 and 1/3

4x3 = 12 that will be the common denominator.

For 3/4 we first divide 12/4 = 3 and then multiply 3 x3 = 9 that's the numerator

For 1/3 we first divide 12/3 = 4 and then multiply 1x4 = 4 that's the numerator

The fractions will be rewrited as: 9/12 and 4/12

3 0
1 year ago
A math class is having a discussion on how to determine if the expressions 4x-x+5 and 8-3x-3 are equivalent using substitution.
bixtya [17]

Answer:

option (b) is correct.

Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.

Step-by-step explanation:

Given : A math class is having a discussion on how to determine if the expressions 4x - x + 5 and 8 - 3x - 3 are equivalent using substitution.

We have to choose the correct method from the given options that the class has suggested.

Since we have to show the given expressions 4x - x + 5 and 8 - 3x - 3 are equivalent using substitution.

We will choose a single value of x  and then evaluate both the  given expression at that single value and if the output of both expression comes out to be same then the two expressions must be equivalent.

For example lets take x = 2,

Then  expression 4x - x + 5 becomes 4(2) - 2 +5 = 8 - 2 + 5 = 6 + 5 = 11

also, expression 8 - 3x - 3  becomes 8 - 3(2) - 3 = 8- 6 - 3 = 8  - 9  = -1

thus, the value is not equal hence, the two expression are not equivalent.

Thus, option (b) is correct.

Both expressions should be evaluated with one value. If the final values of the expressions are the same, then the two expressions must be equivalent.

6 0
3 years ago
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Answer: 25%

Step-by-step explanation:

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