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Vitek1552 [10]
3 years ago
12

Determine the type of boundary line and shading for the graph of the inequality 5x+y grader than or equal to -10

Mathematics
1 answer:
iVinArrow [24]3 years ago
6 0
5x + y > = -10
y > = -5x - 10

It will be a solid line because ur problem contains an equal sign.
It will be shaded on the side that includes the origin...because when u sub in (0,0), which is the origin, ur inequality is true
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What is the value of r? 1.2r−1 1.3r=40
Alexus [3.1K]
  the value is 
1.2r-11.3r=40

-10.Ir=40
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3 years ago
30 POINTS PLEASE HELP!!! 4. The following equations represent the same quadratic function written in standard, vertex, and inter
sergij07 [2.7K]

Answer:

A

Step-by-step explanation:

So we have the quadratic equation and it's written in three equivalent forms:

f(x)=0.5x^2+x-1.5\\f(x)=0.5(x+1)^2-2\\f(x)=(0.5x+1.5)(x-1)

Let's determine the characteristics of the quadratic equation with the given equations.

From the first equation, since the leading coefficient (0.5) is positive, we can be certain that the graph opens upwards.

Also, the constant term is -1.5, so the y-intercept is (0,-1.5).

The second equation is the vertex form. Vertex form has the format:

f(x)=a(x-h)^2-k

Where (h,k) is the vertex. From the second equation we know that h is -1 (because (x+1) is the same as (x-(-1))) and k is -2. Therefore, the vertex is (-1,-2).

And since the graph points upwards, this means that (-1,-2) is the minimum point of the function. In other words, the range of the function is greater than or equal to -2. In interval notation, this is:

[-2,\infty)

This also means that the end behavior of the graph as a x approaches negative and positive infinity is positive infinity because the graph will always go straight up.

Also, the third form is the factored form. With that, we can solve for the zeros of the quadratic. The zeros are:

0.5x+1.5=0\text{ and } x-1=0\\0.5x=-1.5 \text{ and }x=1\\x=-3\text{ and }x=1

Therefore, the graph crosses the x-axis at x=-3 and x=1.

So, from the three equations, we gathered the following information:

1) The graph curves upwards.

2) The roots of zeros of the function is (-3,0) and (1,0).

3) The y-intercept is (0,-1.5).

4) The vertex is (-1,-2). This is also the minimum point.

5) Therefore, the range of the graph is all values greater than or equal to -2.

6) The end behavior of the graph on both directions go towards positive infinity.

Therefore, our correct answer is A.

B is not correct because the line of symmetry (or the x-coordinate of the vertex) here is -1 and not 1/2.

C is not correct because the graph goes towards <em>positive </em>infinity since it shoots straight up.

And D is not correct because the y-intercept is (0,-1.5).

3 0
2 years ago
Read 2 more answers
Express the fractions 2/3, 3//4 and 5/6 as equivalent fractions with a denominator of<br>12​
lina2011 [118]

Answer:

like 2/3 or 15/16; Mixed number - like 1 1/2 or 4 5/6; Integer - like 5 or 28

Step-by-step explanation:

6 0
3 years ago
Question 1
wariber [46]

Answer:

Step-by-step explanation:

n 1

<

>

f( – 2)

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How do we work this? I cannot figure out the path to solve. Th 4x2 + 3x + 1, evaluate f( - 2)

f( – 2)

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How do we work this? I cannot figure out the path to solve. Th

5 0
3 years ago
The fox population in a certain region has a continuous growth rate of 7 percent per year. It is estimated that the population i
rjkz [21]

Answer:

P(t) = 14300e^0.07t

Step-by-step explanation:

Let :

Population as a function of years, t = P(t) ;

Growth rate, r = 7%

Estimated population on year 2000 = Initial population = 14300

The given scenario can be modeled using an exponential function as the change in population is based in a certain percentage increase per period.

P(t) = Initial population*e^rt

P(t) = 14300*e^(0.07t)

P(t) = 14300e^0.07t

Where, t = number of years after year 2000.

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2 years ago
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