How to do number 15?

Solve the system by graphing

julia-pushkina [17]

The graph shows the solution to be (x, y) = (-1, 3).

8 0

3 years ago

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A family wants to remodel a house and spend at most $135,000 total for the entire project. a)If the builder wants to make a 15%

Troyanec [42]

Jjjbbjujbujbb. In un cmk bye j Sheeeeeeeesh

3 0

3 years ago

2) What is the inequality that this graph represents? -15 # 3 6 x

kvasek [131]

Answer: $y < -\frac{1}{2}x+3$

This is the same as writing y < (-1/2)x+3

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Explanation:

The dashed boundary line goes through (0,3) and (4,1)

Apply the slope formula for those two points

m = (y2-y1)/(x2-x1)

m = (1-3)/(4-0)

m = -2/4

m = -1/2

The slope of the dashed line is -1/2. The y intercept is 3. So we go from y = mx+b to y = (-1/2)x+3 to represent the equation of the dashed line. This is the same as writing $y = -\frac{1}{2}x+3$

We shade below the dashed line to represent the inequality $y < -\frac{1}{2}x+3$ . Points in the shaded region are solutions to the inequality. One example point is (0,0).

Note that we don't have "or equal to" as part of the inequality sign because we are not including points on the boundary. A solid line, rather than a dashed line, would include points on the boundary.

3 0

3 years ago

Let $f(x) = 2x^2 + 3x - 9,$ $g(x) = 5x + 11,$ and $h(x) = -3x^2 + 1.$ Find $f(x) - g(x) + h(x).$

Viefleur [7K]

QUESTION 1

Given that:

$f(x)=2x^2+3x-9$ ,

$g(x)=5x+11$ ,

and

$h(x)=-3x^2+1$

Then;

$f(x)-g(x)+h(x)=2x^2+3x-9-(5x+11)+(-3x^2+1)$

$f(x)-g(x)+h(x)=2x^2+3x-9-5x-11-3x^2+1$

Group similar terms;

$f(x)-g(x)+h(x)=2x^2-3x^2+3x-5x-11-9+1$

Simplify;

$f(x)-g(x)+h(x)=-x^2-2x-19$

QUESTION 2

Given that;

$f(x)=4x-7$ .

$g(x)=(x+1)^2$

and

$s(x)=f(x)+g(x)$

Substitute the functions;

$s(x)=4x-7+(x+1)^2$

Substitute x=3

$s(3)=4(3)-7+(3+1)^2$

$s(3)=12-7+(4)^2$

$s(3)=5+16$

$s(3)=21$

QUESTION 3

Given:

$f(x)=3x+2$

$g(x)=x^2-5x-1$

$f(g(x))=f(x^2-5x-1)$

This implies that;

$f(g(x))=3(x^2-5x-1)+2$

Expand the parenthesis;

$f(g(x))=3x^2-15x-3+2$

$f(g(x))=3x^2-15x-1$

QUESTION 4

The given function is;

$f(x)=3(x-6)^2+1$

Let

$y=3(x-6)^2+1$

$\Rightarrow y-1=3(x-6)^2$

$\Rightarrow \frac{y-1}{3}=(x-6)^2$

$\Rightarrow \sqrt{\frac{y-1}{3}}=x-6$

$\Rightarrow x=6+\sqrt{\frac{y-1}{3}}$

The range is:

$\frac{y-1}{3}\ge0$

$y-1\ge0$

$y\ge1$

The interval notation is;

$[1,+\infty)$

6 0

3 years ago

Your height and weight are examples of which level of measurement? A. Ordinal B. Nominal C. Ratio D. Interval

Ivahew [28]

Answer:

C. Ratio

True for this case we have a clear definition of the 0 since the 0 for the heigth and the weigth represent absence of mass. And the differences between numerical values for the two variables are meaingful.

Step-by-step explanation:

We want to know which type of variable represent the weigth and the height. Let's analyze one by one the options given:

A. Ordinal

False since by definition an ordinal variable is "is a categorical variable for which the possible values are ordered". And for this case the height and the weigth are not categorical since represent quantitative data.

B. Nominal

False by definition and ordinal variable is which one that can't be represented by numeric values, and for this case the weight and the height are not example of this definition.

C. Ratio

True for this case we have a clear definition of the 0 since the 0 for the heigth and the weigth represent absence of mass. And the differences between numerical values for the two variables are meaingful.

D. Interval

False on this scale we don't have a clear definition of the 0. And for this case the heigth and the weight have a known definition of the 0 corresponding to the absence of mass. And since the ratios are meaingful for the heigth and the weigth then can't be an interval variable.

8 0

3 years ago