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ArbitrLikvidat [17]
3 years ago
9

What is the most precise name for quadrilateral ABCD with vertices A(-4, -4), B(-4, -2), C(-1, -2), and D(-1, -4)?

Mathematics
2 answers:
baherus [9]3 years ago
5 0
D a rectangle because it has four sides easy for abcd
KATRIN_1 [288]3 years ago
3 0

Answer:

Option D.

Step-by-step explanation:

The given vertices of quadrilateral ABCD are A(-4, -4), B(-4, -2), C(-1, -2), and D(-1, -4).

Distance formula:

d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Using distance formula, we get

AB=\sqrt{\left(-4-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{0^2+(2)^2}=\sqrt{4}=2

Similarly,

BC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-2\right)\right)^2}=3

CD=\sqrt{\left(-1-\left(-1\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=2

AD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-4\right)\right)^2}=3

AB = CD

BC = AD

Measure of diagonals:

AC=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-2-\left(-4\right)\right)^2}=\sqrt{13}

BD=\sqrt{\left(-1-\left(-4\right)\right)^2+\left(-4-\left(-2\right)\right)^2}=\sqrt{13}

AC = BD

Since measure of opposite sides are equal and measure of diagonals are equal, therefore the given quadrilateral ABCD is a rectangle.

Hence, the correct option is D.

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The Length of a standard jewel case is 7cm more than its width. The area of the rectangular top of the case is 408cm. Find the l
salantis [7]

Answer:

The length of the case is 24 cm and its width is 17cm.

Step-by-step explanation:

The Length of a standard jewel case is 7cm more than its width.

Let the length be represented by L and the width be represented by W, this means that:

L = 7 + W

The area of the rectangular top of the case is 408cm². The area od a rectangle is given as:

A = L * W

Since L = 7 + W:

A = (7 + W) * W = 7W + W²

The area is 408 cm², hence:

408 = 7W + W²

Solving this as a quadratic equation:

=> W² + 7W - 408 = 0

W² + 24W - 17W - 408 = 0

W(W + 24) - 17(W + 24) = 0

(W - 17) (W + 24) = 0

=> W = 17cm or -24 cm

Since width cannot be negative, the width of the case is 17 cm.

Hence, the length, L, is:

L = 7 + 17 = 24cm.

The length of the case is 24 cm and its width is 17cm.

4 0
3 years ago
How do i plot 2 3/10 on a number line ?
klemol [59]

Answer:

First, find 2. Then find the 3/10 mark following 2 (if there is one). That is where you put your point. If there are no 10ths markings, it is up to you or your teacher how to plot it.

4 0
3 years ago
Aqa Q8 Write down all the whole numbers that are between 20 and 50 and have a difference of 4 between their digits.
adelina 88 [10]

Answer:

The first 100 whole numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25,26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, ...

Step-by-step explanation:

3 0
3 years ago
This is dealing with special triangles
hram777 [196]
All the sides of an equilateral triangle are the same, and all three angles are 60 degrees. If we want the height of the triangle, we can draw a vertical line straight down the center. This will bisect the top angle into two 30 degree angles and form a 90 degree corner at the base. The base will be split into two equal pieces. In this case 14 and 14 (half of 28).

To find the height, we can use a couple methods. First is Pythagorean Theorem which states that a^2 + b^2 = c^2. We know c = 28 and a = 14, so we can solve for the height. b = sqrt(28^2 - 14^2) = sqrt(588).. 588 can be factored into 196 and 3. So we can simplify the radical to 14sqrt(3).

The second way to find the height is to use trigonometry. We can use cos(30) = h/28 and solve for h to get h = 28cos30 or 14sqrt(3).

---

The next problem is asking the same thing. The altitude is the height. So use either of the methods above to get 2sqrt(3).
3 0
3 years ago
How does a digit in the ten thousand place compare to a digit in the thousands place
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It is ten times bigger than the other
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