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3 years ago

Is (1,7) a solution to the inequality y < 3x + 3?

Mathematics

1 answer:

IgorC [24]3 years ago

7 0

Answer:

yes

Step-by-step explanation:

because 7 is equal to 3 so the answer is correct

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six times a number is greater than 20 mare than that number. what are the possible values of that number

algol13

Answer:

x > 4

Suppose that x is some number so 6 times a number is 6*x. 20 more than that number is 20 + x. If you put it together the inequality would be 6x > 20 + x. Subtracting x from both sides would result in 5x > 20. Dividing by 5 gives you x > 4 which is the final answer. So the possible values of that number is anything greater than 4.

4 0

3 years ago

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Write the standard form equation of the ellipse shown in the graph, and identify the foci.

vlada-n [284]

Answer option A

From the given graph is a Vertical ellipse

Center of ellipse = (-2,-3)

Vertices are (-2,3) and (-2,-9)

Co vertices are (-6,-3) and (2,-3)

The distance between center and vertices = 6, so a= 6

The distance between center and covertices = 4 , so b= 4

The general equation of vertical ellipse is

$\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2}=1$

(h,k) is the center

we know center is (-2,-3)

h= -2, k = -3 , a= 6 and b = 4

The standard equation becomes

$\frac{(x+2)^2}{4^2} + \frac{(y+3)^2}{6^2}=1$

$\frac{(x+2)^2}{16} + \frac{(y+3)^2}{36}=1$

Foci are (h,k+c) and (h,k-c)

$c=\sqrt{a^2-b^2}$

Plug in the a=6 and b=4

$c=\sqrt{6^2-4^2}$

$c=\sqrt{20}$

$c=2\sqrt{5}$ , we know h=-2 and k=-3

Foci are $(-2,-3+2\sqrt{5})$ and $(-2,-3-2\sqrt{5})$

Option A is correct

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3 years ago

Please Help Fast 20 points

Brut [27]

Answer:

Step-by-step explanation:

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3 years ago

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For each triangle, check all that apply.

Anvisha [2.4K]

1 is an isosceles
2 is scalene
3 is an equilateral

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3 years ago

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Find the area of the regular octagon.

user100 [1]

Answer:

236.59mm²

Step-by-step explanation:

The formula for the area of a regular polygon is 1/2ap, with a being the apothem and p being the perimeter.

To start, get the perimeter by multiplying 7 (one side of the polygon) by 8 to get 56.

Next, we have to find the apothem (the perpendicular segment from the center of the polygon to one of the sides).

First, create a right triangle on an of the polygon's sides, where the hypotenuse is equal to the radius of the polygon, one of the legs is the apothem, and the other leg is equivalent to half of the side.

Next, using the polygon angle formula (n-2(360)/n), we can get the base angle of the triangle, 1/2(135), or 67.5.

We can use this angle and some trigonometry to find the the apothem.

First, use SOHCAHTOA to figure out if you will use sine, cosine, or tangent (in this case, tangent).

Next, set up an equation using the tangent of 67.5 to find the apothem - tan67.5 = a/3.

And set the equation equal to a (a = 3.5tan67.5).

Now that you have the apothem, plug it into the area formula to get A = 1/2(56)(3.5tan67.5) and solve!

(28)(3.5tan67.5)

(28)(8.4497)

236.59mm²

4 0

2 years ago

Is (1,7) a solution to the inequality y < 3x + 3?​

Is (1,7) a solution to the inequality y < 3x + 3?