Acarpenter is making a brace for a chair. to do so she intersects two pieces of wood to make two sets of vertical angles. the obtuse angles formed are each 145°. what is the measurement of each acute angle formed? a. 25° b. 35° c. 180° d. 90°

The acute angles are 35 degrees each.

Step-by-step explanation:

A carpenter intersects two pieces of wood to make two sets of vertical angles.

The vertically opposite angles are equal.

Given is - the obtuse angles formed are each 145°.

Means there will be 2 obtuse angle (145 degrees each) and 2 acute angles.

And all these 4 angles form 360 degrees.

Lets say the acute angle is = x

Calculation is as follows: (imagine moving in a circle with 4 parts.)

=>

=>

=>

x = 35 degrees.

Hence, the acute angles are 35 degrees each.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

step-by-step explanation:

f(x)=2x^2 -1 

translation is a function transformation that transform the function in a way of translating. by translating the function its graph is moved  up an down. moving the function f(x) 2 units to the left will be the new function g(x) with the equation: g(x)=f(x+2)=2(x+2)^2 -1