Equation 1: 4y+2x= 4
equation 2: 4y+6x=8
4y+2x=4
-
4y+6x=8
—————
-4x=-4
x=1
plug back in 4y+2=4
4y=2
y=1/2
solution at (1, 1/2 )
Answer:
118
Step-by-step explanation:
AB and CD are parallel lines
∠ ABC + ∠DCB = 180 {Co- interior angles are supplementary}
3n - 47 + n + 7 = 180
3n + n - 47 + 7 = 180 {Combine like terms}
4n - 40 = 180
Add 40 to both sides
4n = 180 + 40
4n = 220
Divide both sides by 4
n = 220/4
n = 55
∠ABC = 3n - 47 = 3*55 - 47
= 165 - 47
∠ABC = 118
The set X is convex.
In geometry, a subset of an affine space over the real numbers, or more broadly a subset of a Euclidean space, is said to be convex if it contains the entire line segment connecting any two points in the subset. A solid cube is an example of a convex set, whereas anything hollow or with an indent, such as a crescent shape, is not. Alternatively, a convex region is a subset that crosses every line into a single line segment.
b)The set X is convex as any two points on the set X is included in the whole set as x>0. So a line joining any two points on the set X is completely inside the set x.
c)set X is not a closed set as the compliment of the set is not an open set.
d)Set X is not bounded. If a set S contains both upper and lower bounds, it is said to be bounded. A set of real numbers is therefore said to be bounded if it fits inside a defined range. hence set x is not bounded.
To learn more about convex sets:
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Answer:
![=\frac{x^2}{16} +\frac{y^2}{49}=1](https://tex.z-dn.net/?f=%3D%5Cfrac%7Bx%5E2%7D%7B16%7D%20%2B%5Cfrac%7By%5E2%7D%7B49%7D%3D1)
Step-by-step explanation:
The equation of this ellipse is
![\frac{(x-h)^2}{b^2} +\frac{y-k)^2}{a^2} =1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-h%29%5E2%7D%7Bb%5E2%7D%20%2B%5Cfrac%7By-k%29%5E2%7D%7Ba%5E2%7D%20%3D1)
for a vertical oriented ellipse where;
(h,k) is the center
c=distance from center to the foci
a=distance from center to the vertices
b=distance from center to the co-vertices
You know center of an ellipse is half way between the vertices , hence the center (h,k) of this ellipse is (0,0) and its is vertical oriented ellipse
Given that
a= distance between the center and the vertices, a=7
c=distance between the center and the foci, c=√33
Then find b
![a^2-b^2=c^2\\\\b^2=a^2-c^2\\\\\\b^2=7^2-(\sqrt{33} )^2\\\\\\b^2=49-33=16\\\\\\b^2=16](https://tex.z-dn.net/?f=a%5E2-b%5E2%3Dc%5E2%5C%5C%5C%5Cb%5E2%3Da%5E2-c%5E2%5C%5C%5C%5C%5C%5Cb%5E2%3D7%5E2-%28%5Csqrt%7B33%7D%20%29%5E2%5C%5C%5C%5C%5C%5Cb%5E2%3D49-33%3D16%5C%5C%5C%5C%5C%5Cb%5E2%3D16)
The equation for the ellipse will be
![\frac{(x-0)^2}{16} +\frac{(y-0)^2}{49} =1\\\\\\=\frac{x^2}{16} +\frac{y^2}{49} =1](https://tex.z-dn.net/?f=%5Cfrac%7B%28x-0%29%5E2%7D%7B16%7D%20%2B%5Cfrac%7B%28y-0%29%5E2%7D%7B49%7D%20%3D1%5C%5C%5C%5C%5C%5C%3D%5Cfrac%7Bx%5E2%7D%7B16%7D%20%2B%5Cfrac%7By%5E2%7D%7B49%7D%20%3D1)
Hello!
Point F is between points E and G
This means that the whole line is segment EG
We can make the equation
EF + FG = EG
Put in the values you know
19x - 13 + 11x = 18x + 20
Combine like terms
30x - 13 = 18x + 20
Subtract 18x from both sides
12x - 13 = 20
Add 13 to both sides
12x = 33
Divide both sides by 12
x = 2.75
Put x into the equation for EG
18(2.75) + 20 = EG
Multiply
49.5 + 20 = EG
Add
69.5 = EG
It says to write it as a mixed number
![69.5 = 69 \frac{1}{2}](https://tex.z-dn.net/?f=69.5%20%3D%2069%20%20%5Cfrac%7B1%7D%7B2%7D%20)
The answer is
![69 \frac{1}{2}](https://tex.z-dn.net/?f=69%20%20%5Cfrac%7B1%7D%7B2%7D%20)
Hope this helps!