Re-write the quadratic function below in Standard Form<br> y = -7(x + 9) (x

To get from her home to a friend's house, Georgia must go past a school, then a post office.

Nataliya [291]

The time it takes for a certain object or person, in this case Georgia, to travel from one place to another is the quotient of the distance and speed. Such that the given above can be best represented by the equation below,
42 minutes = (7/8 + 5/6 + x) / 1/18
The value of x from the equation is approximately 0.625 miles.

3 0

3 years ago

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A construction worker needs to put a rectangular window in the side of a building. He knows from measuring that the top and bott

Sliva [168]

Answer: 5 feet

Step-by-step explanation: A rectangle is a quadrilateral with 4 sides. The opposite sides are parallel and have the same length.

Top and bottom of the window are opposite, so they have the same measure of 3 feet.

One length of the window is 5 feet. Since the last side is opposite to the length of the window, it has the same length, i.e., its value is 5 feet.

7 0

2 years ago

A vector with magnitude 9 points in a direction 190 degrees counterclockwise from the positive x axis. Write in component form

Over [174]

Answer:

$\vec{v}= \text{ or } \approx$

Step-by-step explanation:

Component form of a vector is given by $\vec{v}=$ , where $i$ represents change in x-value and $j$ represents change in y-value. The magnitude of a vector is correlated the Pythagorean Theorem. For vector $\vec{v}=$ , the magnitude is $||v||=\sqrt{i^2+j^2$ .

190 degrees counterclockwise from the positive x-axis is 10 degrees below the negative x-axis. We can then draw a right triangle 10 degrees below the horizontal with one leg being $i$ , one leg being $j$ , and the hypotenuse of the triangle being the magnitude of the vector, which is given as 9.

In any right triangle, the sine/sin of an angle is equal to its opposite side divided by the hypotenuse, or longest side, of the triangle.

Therefore, we have:

$\sin 10^{\circ}=\frac{j}{9},\\j=9\sin 10^{\circ}$

To find the other leg, $i$ , we can also use basic trigonometry for a right triangle. In right triangles only, the cosine/cos of an angle is equal to its adjacent side divided by the hypotenuse of the triangle. We get:

$\cos 10^{\circ}=\frac{i}{9},\\i=9\cos 10^{\circ}$