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3 years ago

What is the ordered pair for point b on the graph (-1,4) (4,-1) (5,1) (1,5)

Mathematics

1 answer:

IRINA_888 [86]3 years ago

5 0

Option C: (5,1) is the ordered pair for point B

Explanation:

The graph is plotted with unit scale 1 units for both x and y axis.

We need to determine the ordered pair for point B.

<u>Ordered pair:</u>

Since, the graph is plotted with unit scale 1, the point B is 5 units away from the point (0,0)

Thus, the x - coordinate for point B is 5.

Also, the point B is 1 unit away from the point (0,0)

Thus, the y - coordinate is 1

The coordinates of point B is (5,1)

Thus, the ordered pair for point B is (5,1)

Hence, Option C is the correct answer.

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Find the area of the right triangle.

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saveliy_v [14]

5. Answer: see explanation

<u>Step-by-step explanation:</u>

If the roots are m and 3m, then x = m and x = 3m

⇒ x - m = 0 and x - 3m = 0

⇒ (x - m)(x - 3m) = 0

⇒ x² - 4mx + 3m² = 0

Since x² + px + q = 0 then p = -4m and q = 3m²

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= 3(16m²) = 48m²

= 48m²

3p² = 48m² = 16q ⇒ 3p² = 16q

**********************************************************************************************

6. Answer: 8 or 18

<u>Step-by-step explanation:</u>

The Area of the entire rectangle (A = L × w) is 12 × 10 = 120

The Area of the shaded region is 72, so the Area of the non-shaded region is 120 - 72 = 48.

There are two non-shaded triangles.

Bigger non-shaded Δ: L = 12-x, w = 10 ⇒ $A = \dfrac{10(12-x)}{2}$
Smaller non-shaded Δ: L = x, w = x ⇒ $A=\dfrac{x(x)}{2}$

Combine the Areas of both triangles and set it equal to the Area of the non-shaded region:

$\dfrac{x(x)}{2}+\dfrac{10(12-x)}{2}=48\\\\\\\dfrac{x^2}{2}+\dfrac{120-10x}{2}=48\\\\\\\dfrac{x^2-10x+120}{2}=48\\\\\\x^2-10x+120=96\\\\x^2-10x+24=0\\\\(x-4)(x-6)=0\\\\x - 4 = 0\quad or\quad x-6=0\\x=4\qquad or\qquad x=6\\\\\text{Based on the image provided, it appears that the x-value will be the}\\\text{smallest of the two possible solutions (4), but both solutions are valid.}$

Area of ΔBEF:

$\text{when x = 4, A =}\ \dfrac{4(4)}{2}=\dfrac{16}{2}=8\\\\\\\text{when x = 6, A =}\ \dfrac{6(6)}{2}=\dfrac{36}{2}=18$

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3 years ago

The plane flew over a beacon which is 280 miles from bristol. write down the gmt times when the plane flew over the beacon.

eimsori [14]

According to graph, GMT time when the plane flew over the beacon was 9:24.

While looking closely at the graph on x axis , one will notice that each hour is divided into 5 parts and hence each part has 12 minutes. looking at y axis, one may find that each part on y axis resembles 20miles. Hence at 280 miles away from Bristol, The GMT time is 9:24.

<h3>What is a graph?</h3>

In mathematics, a graph is a visual representation or diagram that shows facts or values in an ordered way.

The relationships between two or more items are frequently represented by the points on a graph.
The study of graphs, which are mathematical constructions used to represent pairwise relationships between things, is known as graph theory in mathematics. Vertices (also known as nodes or points) make up a graph in this sense, which are connected by edges (also called links or lines).
Undirected graphs, in which edges connect two vertices symmetrically, are distinguished from directed graphs, in which edges connect two vertices asymmetrically. One of the main topics of study in discrete mathematics is graphs.

Know more about graph numerical

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