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3 years ago

The variable z is inversely proportional to x. When x is 3, z has the value 2.

Mathematics

1 answer:

kirill [66]3 years ago

3 0

Answer:

z = 6/13

Step-by-step explanation:

The new value of x is 13/3 times the old value. Since z is inversely proportional to x, it will be multiplied by the inverse of that, 3/13.

2 × 3/13 = 6/13 . . . . value of z when x=13

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3. List the angles of the triangle in order from smallest to largest.

Veseljchak [2.6K]

Answer:

The list of angles of the triangle in order from smallest to largest will be: A < C < B

Hence, option 'e' is true.

i.e (A,C,B)

Step-by-step explanation:

We know that in a triangle the greater angle has the longer side opposite to it.

From the given triangle,

Side AC = 7.2 is the longer side. Thus, B is the largest angle as it is opposite to the longer side AC = 7.2.

Then comes the second-longest side AB=4.9. Thus, C is the 2nd largest angle it is opposite to the second-longest side AB=4.9.

Finally comes the shortest side BC = 3.2. Thus, A is the shortest angle as it is opposite to the shortest side BC = 3.2.

Thus, the list of angles of the triangle in order from smallest to largest will be: A < C < B

Hence, option 'e' is true.

i.e (A,C,B)

6 0

3 years ago

Which is the equation of a hyperbola with directrices at y = ±2 and foci at (0, 4) and (0, −4)?

Advocard [28]

Answer:

Step-by-step explanation:

First off, I'm assuming that when you said "directrices" you mean the oblique asymptotes, since hyperbolas do not have directrices they have oblique asymptotes.

If we plot the asymptotes and the foci, we see that where the asymptotes cross is at the origin. This means that the center of the hyperbola is (0, 0), which is important to know.

After we plot the foci, we see that they are one the y-axis, which is a vertical axis, which means that the hyperbola opens up and down instead of sideways. Knowing those 2 characteristics, we can determine that the equation we are trying to fill in has the standard form

$\frac{(y-k)^2}{a^2}-\frac{(x-h)^2}{b^2}=1$

We know h and k from the center, now we need to find a and b. Those values can be found from the asymptotes. The asymptotes have the standard form

y = ± $\frac{a}{b}(x-h)+k$

Filling in our asymptotes as they were given to us:

y = ± $\frac{2}{1}(x-0)+0$ where a is 2 and b is 1. Now we can write the formula for the hyperbola!:

$\frac{(y-0)^2}{4}-\frac{(x-0)^2}{1}=1$ which of course simplifies to

$\frac{y^2}{4}-\frac{x^2}{1}=1$

4 0

4 years ago

it snowed 15% more in Big Bear than Arrow Head.If it snowed 50 inches in Arrow head, how many inches did it snow in Big Bear

Veronika [31]

It snowed 57.5 in Big Bear

Because 15% of 50 is 7.5 and 50+7.5=57.5

Hope this is helped

3 0

3 years ago

WHOEVER ANSWERS GETS A PRIZE!!!!

Karo-lina-s [1.5K]

Answer:

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5 0

3 years ago

Read 2 more answers

Write the quadratic function in the form g(x)=a (x-h)2 +kThen, give the vertex of its graph. G(x) =2x2 +20x+49Writing in the for

Snezhnost [94]

The quadratic function given to us is:

$g(x)=2x^2+20x+49$

We are asked to find the vertex form of the function.

The general formula for the vertex form of a quadratic equation is:

$\begin{gathered} g(x)=a(x-h)^2+k \\ \text{where,} \\ (h,k)\text{ is the coordinate of the vertex} \end{gathered}$

In order to write the function in its vertex form, we need to perform a couple of operations on the function.

1. Add and subtract the square of the half of the coefficient of x to the function.

2. Factor out the function with its repeated roots and re-write the equation.

Now, let us solve.

1. Add and subtract the square of the half of the coefficient of x to the function.

$\begin{gathered} g(x)=2x^2+20x+49=2(x^2+10x+\frac{49}{2}) \\ \text{half of coefficient of x:} \\ \frac{10}{2}=5 \\ \text{square of the half of the coefficient of x:} \\ 5^2=25 \\ \\ \therefore g(x)=2(x^2+10x+25-25+\frac{49}{2}) \end{gathered}$

2. Factor out the function with its repeated roots and re-write the equation.

$\begin{gathered} g(x)=2(x^2+10x+25)-2(25+\frac{49}{2}) \\ re-\text{write the above function} \\ g(x)=2(x^2+10x+25)-1 \\ \text{Let us factorize this:} \\ g(x)=2(x+5)^2-1 \end{gathered}$

Therefore, we can conclude that the Equation and vertex of the equation is:

$\begin{gathered} Equation\colon g(x)=2(x+5)^2-1 \\ \\ Vertex\colon(-5,-1) \end{gathered}$

5 0

1 year ago