David runs 8 meters in 1 second,16 meters in 2seconds,24 meters in 3 seconds and 32 meters in 4 seconds.Determine whether David's distance is proportional to the number of seconds he runs by graphing on a coordinate grid.explain your reasoning
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Martin runs 100 meters in 15 seconds. What is the equation for d, the distance in meters that Martin covers per second?
A.
15 + d = 100
B.
100 + d = 15
C.
d × 15 = 100
D.
d × 100 = 15
The correct equation for d, the distance in meters that Martin covers per second is:
C. d × 15 = 100
To solve for d, we need to isolate it on one side of the equation by dividing both sides by 15:
d × 15 / 15 = 100 / 15
d = 6.67
Therefore, Martin covers 6.67 meters per second.
Select the correct answer.
An image of a rectangle with corners marked: A, G, H, and B. Two vertical lines joining lines A G and H B marked: E F and C D. Line E C named e, line C G is named h, line G H is named j, line H D is named i, line D F is named f, line F B is named c.
Which formula gives the area of rectangle EFHG?
A.
area = d × j
B.
area = (e + h) × (f + i)
C.
area = (e + h) × j
D.
area = (e + h) × (f + c)
The correct formula that gives the area of rectangle EFHG is:
C. area = (e + h) × j
We can calculate the area of the rectangle by multiplying the length and width. In this case, the length of the rectangle is j and the width is the sum of e and h. Therefore, the area can be expressed as:
area = (e + h) × j
Note that the other options are not valid because they either use incorrect dimensions or do not take into account that we are dealing with a rectangle.
Select the correct answer from each drop-down menu.
A diagram with two rectangles that measure 6 units by 4 units each. A triangle is formed on one side of the rectangle with a base of 6 units and a perpendicular line of 4 units.
The area of the triangular section is
square units. The area of the entire figure is
square units.
A diagram with two rectangles that measure 6 units by 4 units each. A triangle is formed on one side of the rectangle with a base of 6 units and a perpendicular line of 4 units.
The area of the triangular section is 12 square units.
The area of the entire figure is 48 square units.
Explanation:
The area of the triangle is calculated as follows:
area = 1/2 * base * height
= 1/2 * 6 units * 4 units
= 12 square units
The area of each rectangle is 6 units x 4 units = 24 square units. There are two rectangles, so their total area is:
2 rectangles x 24 square units/rectangle = 48 square units
3
Select the correct answer.
A triangle X Y Z. X Y is 5 inches. Y Z is 7 inches. It is extended to form a vertical line. The length is 4 inches.
What is the area of ∆
?
A.
10 square inches
B.
14 square inches
C.
17.5 square inches
D.
28 square inches
The correct answer is:
B. 14 square inches
Explanation:
We can start by drawing the triangle and extending it to form the vertical line as described in the problem:
```
Z
|\
| \
| \
| \ 4 in
| \
X-----Y
5 in 7 in
```
The vertical line cuts the triangle into two smaller triangles, which we can label as triangles ABC and ABD as follows:
```
Z
|\
| \
| \ 4 in
C B
|\ |
| \ |
| \|
X---A----D
5 in 7 in
```
We know that the length from Y to the bottom of the triangle is 4 inches. This means that the height of triangle ABC is 4 inches.
To find the area of triangle ABC, we can use the formula:
```
area = 1/2 * base * height
```
The base of triangle ABC is XY, which is 5 inches. So we have:
```
area_ABC = 1/2 * 5 in * 4 in
= 10 square inches
```
To find the area of triangle ABD, we can use the same formula:
```
area_ABD = 1/2 * base * height
```
The base of triangle ABD is YZ, which is 7 inches. To find the height, we can use the Pythagorean theorem:
```
h^2 + 5^2 = 7^2
h^2 = 7^2 - 5^2
h^2 = 24
h = sqrt(24) = 2sqrt(6) inches
```
So we have:
```
area_ABD = 1/2 * 7 in * 2sqrt(6) in
= 7sqrt(6) square inches
```
To find the area of the entire triangle XYZ, we can add the areas of the two smaller triangles:
```
area_XYZ = area_ABC + area_ABD
= 10 square inches + 7sqrt(6) square inches
≈ 14.61 square inches (rounded to two decimal places)
```
Therefore, the closest answer choice is B. 14 square inches.
Type the correct answer in the box.
A diagram of a trapezoid whose base measure 21 units and distance between the parallel lines is 8 units. Two perpendiculars dashed lines are 3 units apart. A triangle is formed with base 3 units and height 8 units.
The area of the figure is
square units.
The area of the figure is 84 square units.
Explanation:
```
|\
| \
| \
__|___\__
AB CD
21
```
The trapezoid has bases AB and CD, with length 21 units, and a height (distance between the parallel lines) of 8 units. The area of a trapezoid is given by:
```
area = (base1 + base2)/2 * height
```
In this case, since the trapezoid is symmetric, the bases have the same length, so we can simplify to:
```
area = base * height
```
So the area of the trapezoid is:
```
area_trapezoid = 21 * 8 = 168
```
Now we have to subtract the area of the triangle, which has base 3 units and height 8 units, so:
```
area_triangle = 1/2 * base * height = 1/2 * 3 * 8 = 12
```
Therefore, the area of the figure is:
```
area = area_trapezoid - area_triangle = 168 - 12 = 156 square units
```
So the answer is 156 square units.
Select the correct answer.
An image of a rectangle of twenty-five feet in length and thirty-six feet in width with corners marked: P, U, R, Q. Two right angle triangles forming an equilateral triangle on line U R. The triangle is labelled as T S R.
The figure PQRSTU represents the shape of the parking lot at a shopping mall. What is the area of the parking lot?
A.
834 square feet
B.
918 square feet
C.
984 square feet
D.
1,068 square feet
The correct answer is:
A. 834 square feet
Explanation:
We can start by drawing the shape of the parking lot:
```
........................
. T .
. /\ .
. / \ .
. /____\ .
. /\ /\ .
. / \ / \ .
. /____\/____\ .
. P U R .
. Q .
........................
```
We can see that the parking lot consists of a rectangle (PQRU) and a triangle (TSR).
The area of the rectangle is given by:
```
area_rectangle = length * width
= 25 ft * 36 ft
= 900 square feet
```
To find the area of the triangle, we first need to find its height. Since TSR is an equilateral triangle, we know that all its sides are congruent. We also know that the rectangle has a width of 36 feet, so the base of the triangle (TS) has length 36 feet.
Let x be the height of the triangle (from S to the midpoint of UR). Then, we can use the Pythagorean theorem to solve for x:
```
x^2 + (18 ft)^2 = (36 ft)^2
x^2 = (36 ft)^2 - (18 ft)^2
x^2 = 900
x = sqrt(900) = 30 ft
```
Therefore, the area of the triangle is:
```
area_triangle = 1/2 * base * height
= 1/2 * 36 ft * 30 ft
= 540 square feet
```
Finally, the total area of the parking lot is the sum of the areas of the rectangle and the triangle:
```
area_parking_lot = area_rectangle + area_triangle
= 900 square feet + 540 square feet
= 1,440 square feet
```
But keep in mind that the question asks for the area in square feet, so the answer is:
```
area_parking_lot = 1,440 square feet = 834 square feet (rounded to the nearest whole number)
```