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3 years ago

Graph y greater than or equal to (x+2)^2

Mathematics

1 answer:

katovenus [111]3 years ago

3 0

Answer:

See attached image

Step-by-step explanation:

The graph of $y\geq (x+2)^2$ is not the one shown on the picture. Although the highlighted are (above the curve) is correct, since that corresponds to the y-values larger than those of the parabola, the problem is that in the picture given, the actual trace of the parabola (which corresponds to the equality $y=(x+2)^2$ , is shown with dotted trace - which by convention indicates that the trace is NOT included.

Since the inequality symbol in our inequality DOES contain the equal sign (larger than OR EQUAL to), the parabola's trace should be represented with a solid line. (see attached image)

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Find the area of quadrilateral ABCD whose vertices are A(1,1) B(7,-3) C(12,2) D(7,21)

sasho [114]

Answer:

The area of quadrilateral ABCD is 139 unit^2.

Step-by-step explanation:

Given:

Quadrilateral ABCD whose vertices are A(1,1) B(7,-3) C(12,2) D(7,21).

Now, to find the area.

The coordinates of the quadrilateral are A(1,1), B(7,-3), C(12,2), D(7,21).

So, to find the area we need to bisect the quadrilateral ABCD and get the triangles ABC and ADC and then calculate their areas:

In Δ ABC:

$A(x_1,y_1)=(1,1)\:,\:B(x_2,y_2)=(7,-3)\:and\:C(x_3,y_3)=(12,2)$

Now, to get the area of triangle ABC:

$Area\,of\,triangle\,=\,\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|$

$Area\,of\,triangle\,=\,\frac{1}{2}\left|1(-3-2)+(7)(2-1)+12(1--3)\right|$

$Area\,of\,triangle\,=\,\frac{1}{2}\left|1(-5)+(7)(1)+12(4)\right|$

On solving we get:

$Area\,of\,triangle\,=25.$

In Δ ADC:

$A(x_1,y_1)=(1,1)\:,\:D(x_2,y_2)=(7,21)\:and\:C(x_3,y_3)=(12,2)$

Now, to get the area of triangle ADC:

$Area\,of\,triangle\,=\,\frac{1}{2}\left|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)\right|$

$Area\,of\,triangle\,=\,\frac{1}{2}\left|1(21-2)+(7)(2-1)+12(1-21)\right|$

On solving it by same process as above we get:

$Area\,of\,triangle\,=114$

Now, to get the area of the quadrilateral we add the areas of the triangles ABC and ADC:

$25+114\\=25+114\\=139\ unit^2$

Therefore, area of quadrilateral ABCD is 139 unit^2.

4 0

3 years ago

WILL GIVE 75 POINTS & SEND $10 ON CASHAPP!

Anna11 [10]

Answer:

What is the question tell me clearly.

Step-by-step explanation:

6 0

3 years ago

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Daniel's grandmother sent him $74.70 for his birthday. If Daniel spends $72.17 on a new video game, how much birthday money will

tamaranim1 [39]

Answer:

$2.53 left

Explanation:

Since the question is asking us how much money Daniel has left, we must subtract the amount he spent on the video game by the original amount (the amount of money his grandmother sent him).

$74.70-72.17= ?\\74.70-72.17= 2.53$

So, based on our calculations, Daniel should have $2.53 left.

7 0

4 years ago

The length of each side of a square is

shepuryov [24]

Answer:

x=3

Step-by-step explanation:

P= 4

since we know that the length of each side of a square increased by 6 inches,

x+6

36=4(x+6)

x=3

Sorry, I didn’t do the steps to show how I got my answer as 3. Hope this helps!

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4 years ago

A circle has a radius of 6 in. Find the area of its inscribed equilateral triangles.

Lina20 [59]

The area of the inscribed triangle = 3(6^2 x sin 120°) = 3(36sin 120°) = 3(31.18) = 93.53 square in.

8 0

3 years ago