Name the intersection of plane ACG and plane BCG

2 answers:

3 0

Answer:
CG

Explanation:
A plane is defined using three points.
The intersection between two planes is a line

Now, we are given the planes:
ACG and BCG

By observing the names of the two planes, we can note that the two points C and G are common.
This means that line CG is present in both planes which means that the two planes intersect forming this line.

Hope this helps :)

Ede4ka [16]4 years ago

3 0

c. CG
In the given problem, the place ACG and plane BCG. These planes intersect at CG in which intersection is either a point, line or curve that an entity or entities both possess or is in contact with. In the plane we can understand that the common line for both plane ACG and plane BCG is CG. Further examples can include, plane KTGX and plane KUYT, in this case you can imagine a rectangular prism in which they both intersect at line KT.

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If the sum of the legs of a right triangle is 49 inches and the hypotenuse is 41 inches, find the length of the other two sides

german

The length of one leg is x inches.
The sum of the legs is 49 inches, so the length of the other leg is 49-x inches.
The length of the hypotenuse is 41 inches.

Use the Pythagorean theorem:
$(\hbox{one leg})^2 + (\hbox{the other leg})^2=(\hbox{hypotenuse})^2 \\ x^2+(49-x)^2=41^2 \\
x^2+2401-98x+x^2=1681 \\
2x^2-98x+2401=1681 \ \ \ |-1681 \\
2x^2-98x+720=0 \\ \\
a=2 \\ b=-98 \\ c=720 \\ b^2-4ac=(-98)^2-4 \times 2 \times 720=9604-5760=3844 \\ \\
x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}=\frac{-(-98) \pm \sqrt{3844}}{2 \times 2}=\frac{98 \pm 62}{4} \\
x=\frac{98-62}{4} \ \lor \ x=\frac{98+62}{4} \\
x=\frac{36}{4} \ \lor \ x=\frac{160}{4} \\
x=9 \ \lor \ x=40$

$
49-x=49-9 \ \lor \ 49-x=49-40 \\
49-x=40 \ \lor \ 49-x=9$

The lengths of the legs are 9 inches and 40 inches.

4 0

4 years ago

consider the function represented by the equation 16b = 4r - 12. write the equation in function notation, where b is the indepen

katovenus [111]

When you write a function in the form $y=f(x)$ , y is the dependent variable, and x is the independent variable.

So, if b is the independent variable, it means that we have to solve the expression for r.

To do so, we perform the following steps: start with

$16b = 4r - 12$

Add 12 to both sides

$16b+12 = 4r$

Divide both sides by 4:

$4b+3 = r$

So, we wrote the expression in the form $r = f(b) = 4b+3$ , which means that r is the dependent variable and b is the independent variable, as requested.