Geometry - HSPT Math

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, , we can solve for the area of both of our rectangles

To find our final answer, we need to add the areas together.

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, , we can solve for the area of both of our rectangles

To find our final answer, we need to add the areas together.

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, , we can solve for the area of both of our rectangles

To find our final answer, we need to add the areas together.

To find the area of the figure above, we need to slip the figure into two rectangles.

Using our area formula, , we can solve for the area of both of our rectangles

To find our final answer, we need to add the areas together.

Determine the volume of both cubes and then subtract the smaller from the larger. The large cube volume is 9” * 9” * 9” = 729 in3 and the small cube is 3” * 3” * 3” = 27 in3. The difference is 702 in3.

A cube that has three times as long sides is 3x3x3=27 times bigger than the original. Therefore, the answer is 5x27= 135.

Volume of a cylinder? V = πr2h. Rewritten as a diameter equation, this is:

V = π(d/2)2h = πd2h/4

Sub in h and V: 36p = πd2(4)/4 so 36p = πd2

Thus d = 6

The area of a triangle is found with the equation

.

Since we do not have the height, we cannot answer the question.

If broken down into parts, this is an easy problem. It is first necessary to isolate the dimensions of the walls. If the room is 9 ft high, we know 18 x 15 designates the area of the floor and ceiling. Based on this, we know that the room has the following dimensions for the walls: 18 x 9 and 15 x 9. Since there are two of each, we can calculate the total area of walls - ignoring doors and windows - by doubling the sum of these two areas:

2 * (18 * 9 + 15 * 9) = 2 * (162 + 135) = 2 * 297 = 594 ft2

Now, we merely need to calculate the area "taken out" of the walls:

For the door: 3 * 7 = 21 ft2

For the windows: 2 * (2 * 5) = 20 ft2

The total wall space is therefore: 594 – 21 – 20 = 553 ft2

The coordinate length between you and your school is equivalent to the hypotenuse of a right triangle with sides of 3 and 4 units:

The distance is 5 coordinate lengths, and each coordinate length corresponds to 1.3 miles of distance, so

A point is located on the -axis if and only if it has -coordinate (first coordinate) 0. Of the five choices, only fits that description.

The coordinates of a point are determined by the distance from the origin. The first point in the ordered pair is the number of units to the left or right of the origin. Negative numbers indicate the number of units to the left while positive numbers indicate the number of units to the right. The second number indicates the number of units above or below the origin. Positive numbers indicate the number of units above while negative numbrs indicate the number of units below the origin. The vertices of the square are:

A point is located on the -axis if and only if it has a -coordinate equal to zero. So the answer is .

The value of the slope (m) is rise over run, and can be calculated with the formula below:

The coordinates of the first end of the plank would be (0,3), given that this is the starting point of the plank (so x would be 0), and y would be 3 since the brick is 3 inches tall.

The coordinates of the second end of the plank would be (18,9) since the plank is 18 inches long (so x would be 18) and y would be 9 since the box was 9 inches tall at the other end.

From this information we know that we can assign the following coordinates for the equation:

and

Below is the solution we would get from plugging this information into the equation for slope:

This reduces to

To find the speed of the deer, you must have the distance traveled and the time.

The distance is found using the Pythagorean Theorem:

The answer must be in miles per hour so the total miles are divided by the hours to get the final answer:

The horizontal distance from point to the vertical line is two units. Since this point is reflected across , the new point will also be 2 units to the right of line .

Therefore, the correct answer is:

Write the slope formula and substitute the two points.

The smallest block from which a circle could be made would be a square that perfectly matches the diameter of the given circle. (This is presuming we have perfectly calibrated equipment.) Such a square would have dimensions equal to the diameter of the circle, meaning it would have sides of 50 inches for our problem. Its total area would be 50 * 50 or 2500 in2.

Now, the waste amount would be the "corners" remaining after the circle was cut. The area of the circle is πr2 or π * 252 = 625π in2. Therefore, the area remaining would be 2500 - 625π. The cost of the waste would be 0.2 * (2500 – 625π). This is not an option for our answers, so let us simplify a bit. We can factor out a common 5 from our subtraction. This would give us: 0.2 * 5 * (500 – 125π). Since 0.2 is equal to 1/5, 0.2 * 625 = 125. Therefore, our final answer is: 500 – 125π dollars.

Since you have moved left seven units, you have moved seven units in a negative horizontal direction, making the -coordinate of your current location .

Since you have moved up three units and down nine units, you have moved six units down - this is six units in a negative vertical direction, making the -coordinate of your current location .

Therefore, the ordered pair for your current location is .