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3 years ago

6

Aurora earns a salary of $25,000 per year. Her benefits are equal in value to 30 percent of her salary. What is the value of Aur

ora’s benefits?

2 answers:

GaryK [48]3 years ago

5 0

So her benefits is basically 25,000(0.30). The total benefits would be $7,500.

faust18 [17]3 years ago

4 0

$25,000 (.3) = 7500
Move the decimal over one to get 10% and then multiply by 3 (30%)

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DEFINE ALL OF THESE, ONE SENTENCE EACH, PLEASE

coldgirl [10]

<u>Answers:</u>

These are the three major and pure mathematical problems that are unsolved when it comes to large numbers.

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2 years ago

Fiona's Fashion Store is world renowned for its buttoned uniforms. A collection of 36 shirts and 42 jackets contains 842buttons.

Oduvanchick [21]

To solve the problem, what you must do is a system of two equations with two Ingonites that describe the problem.
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3 years ago

Read 2 more answers

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katen-ka-za [31]

It would be = -3.81 * 10^-3

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3 years ago

Graph y=-1/2x^2-1. Identify the vertex of the graph. tell whether it is a minimum or maximum. (To clarify, 1/2 is a fraction *x^

ahrayia [7]

$y= -\frac{1}{2} x^{2}-1$ is a quadratic function, so its graph is a parabola.

Notice that the coefficient of x is 0, this always means that the axis of symmetry is the y-axis.

That is, the vertex of the parabola is in the y-axis, so the x-coordinate of the vertex is 0.

for x=0, y=-1. So the vertex is (0, -1)

The coefficient of $x^{2}$ is negative. This means that the parabola opens downwards, so the vertex is a maximum.

Answer: (0, -1) , maximum (none of the choices)

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3 years ago

Find the length of each side of the triangle determined by the three points P1,P2, and P3. State whether the triangle is an isos

Tanya [424]

Answer:

The triangle is both an Isosceles triangle and a right triangle.

Step-by-step explanation:

Given the vertices of a triangle.

$P_{1} = (- 1, 4)$

$P_{2} = (6, 2)$ and

$P_{3} = (4, - 5)$

We find the distance between all the points to determine the length of each side of the triangle.

Distance between any two points, say, $(x_1, y_1)$ and $(x_2, y_2)$ is:

$\sqrt{\bigg ( \textbf{x}_{\textbf{2}} \hspace{1mm} \textbf{- x}_{\textbf{1}} \bigg )^{\textbf{2}} \textbf{+} \bigg( \textbf{y}_{\textbf{2}} \hspace{1mm} \textbf{- y}_{\textbf{1}} \bigg)^ {\textbf{2}}$

Length between $P_1$ and $P_{2}$ , (Side 1) :

$(x_1, y_1) = (- 1, 4)$ and

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{\bigg(6 - (-1) \bigg)^{2} \hspace{1mm} + \hspace{1mm} \bigg( 2 - 4 \bigg )^2$

$= \sqrt{7^2 + 2^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}}$

Length of Side 1 = $\sqrt{\textbf{53}}$ units.

Distance between $P_1$ and $P_2$ , (Side 2):

$(x_1, y_1) = (-1, 4)$

$(x_2, y_2) = (4, - 5)$

Distance = $\sqrt{ \bigg( 4 + 1 \bigg)^2 \hspace{1mm} + \bigg( - 5 - 4 \bigg ) ^2$

$= \sqrt{ 25 + 81 }$

$= \sqrt{\textbf{106}}$

Length of Side 2 = $\sqrt{\textbf{106}}$ units.

Distance between $P_2$ and $P_3$ , Side 3 :

$(x_1, y_1) = (4, 5)$

$(x_2, y_2) = (6, 2)$

Distance = $\sqrt{ 2^2 \hspace{1mm} + \hspace{1mm} 7^2}$

$= \sqrt{49 + 4}$

$= \sqrt{\textbf{53}$

Length of Side 3 = $\sqrt{\textbf{53}}$ units.

Note that the length of Side 1 = Length of Side 3.

That means the triangle is Isosceles.

Also, For a triangle to be right angle triangle, using Pythagoras theorem we have:

(Side 1)² + (Side 3)² = (Side 2)²

$\bigg( \sqrt{53} \bigg )^2 \hspace{1mm} + \hspace{1mm} \bigg( \sqrt{53} \bigg)^2 \hspace{1mm} = \hspace{1mm} \bigg ( \sqrt{106} \bigg ) ^2$

i.e, 53 + 53 = 106

Hence, the triangle is a right - angled triangle as well.

7 0

3 years ago