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pantera1 [17]
3 years ago
7

-3 \cdot f(-8) + 7 \cdot g(2) =−3⋅f(−8)+7⋅g(2)=minus, 3, dot, f, left parenthesis, minus, 8, right parenthesis, plus, 7, dot, g,

left parenthesis, 2, right parenthesis, equals

Mathematics
1 answer:
dsp733 years ago
3 0

Answer:

-22

Step-by-step explanation:

The graph from which the information is to be read is attached below.

We want to find the value of −3⋅f(−8)+7⋅g(2).

From the graph:

  • f(-8)=-2
  • g(2)=-4

Therefore:

−3⋅f(−8)+7⋅g(2)=−3(-2)+7(-4)

=6-28

=-22

−3⋅f(−8)+7⋅g(2)=-22

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On a coordinate plane, a dashed straight line with negative slope goes through (0, 1) and (2, negative 2). Everything to the lef
charle [14.2K]

Answer:

y

Step-by-step explanation:

The straight line passes through (0,1) and (2,-2).

Equation of a straight line passing through two points (x1,y1) and (x2,y2)

is given by:

y-y_{1}=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}(x-x_{1})

y-1=\frac{-2-1}{2-0}(x-0)

y=-\frac{3}{2}x+1

Everything to the left of the line is shaded.

We have to visualize the graph:the straight line has a positive y-intercept and a negative slope.The graph is given in the attachment below.

From the figure we can see origin lies on the shaded region.Hence (0,0) should satisfy the inequality.

LHS=y=0

RHS=-\frac{3x}{2}+1=1\ (x=0)

LHS<RHS as 0<1

Hence , the inequality is:

y

8 0
3 years ago
Read 2 more answers
Find the next two terms in the pattern 100,98,94,88,80…
olga_2 [115]

Answer:

its 70 and 58

Step-by-step explanation:

The pattern: -2, -4, -6, -8, -10, -12...

5 0
2 years ago
Your goal is to have an emergency fund equal to 3 months living expenses. Your living expenses are $700 a month. Your take-home
anyanavicka [17]
6.4 months Because 10% of $1,100 is $110 

multiply 110 by 6.4 and you get 704 

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6 0
3 years ago
Which two rational numbers does √14 lie between?
Fiesta28 [93]

First, let's find what √14 equals.

√14 ≈ 3.74

Now, we can solve for all the answer choices.

Option A:

19/6 = 3.1666...

22/7 = 3.1428...

Option B:

Doesn't need to be solved.

3.17

3.71

Option C:

√4 = 2

√9 = 3

Option D:

Doesn't need to be solved.

3.70

3.75

The only option that contains √14 between it, is Option D.

Hope This Helped! Good Luck!

7 0
2 years ago
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Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat
zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term x^2, which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form f(x)=ax^2+bx+c is given by the expression: x_v=\frac{-b}{2a}

Since in our case a=1 and b=5, we get that the x-position of the vertex is: x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the x_v=-\frac{5}{2}. Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0
3 years ago
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