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.