A construction crane has a boom which extends 50 ft from the base. If the crane is stationed 30 ft from a building, how high up the building wall can the crane reach?

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The crane will go 40 ft up the building wall.

Step-by-step explanation:

To solve this, we need to use the Pythagorean Theorem, a²+b²=c².

First, we know that the crane is stationed 30 ft away from the building. As such, we know this is one of the legs of our right triangle. We also know that the hypotenuse is the boom of a construction crane, so we know that 50 will be c. Now, we simply plug in the equation. Remember that the building height will be the other missing leg we need to find.

30²+b²=50²

900+b²=2500

900-900+b²=2500-900

b²=1600

√b²=√1600

b=40

The crane will reach up to 40 ft up the building.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).