11) Since the triangle has a pair of congruent base angles, it is an isosceles triangle which means that the two pairs of legs are congruent.
Make them equal to each other in an equation.
5x = x + 20
Subtract x from both sides.
4x = 20
Divide both sides by 4.
x = 5
12) The two legs are congruent so that means the base angles must be congruent. First find the measure of the base angles. Create an equation:
x + x + 50 = 180
Combine like terms.
2x + 50 = 180
Subtract 50 from both sides.
2x = 130
Divide both sides by 2.
x = 65
Now make the base angle plus x equal 180, because they form a straight line.
65 + x = 180
Subtract 65 from both sides.
x = 115
13) You know the vertex angle (top angle) is 90 degrees because it is supplementary to a right angle. The triangle is isosceles because the two legs are congruent, so make the base angles plus 90 add up to 180 in an equation.
x + x + 90 = 180
Combine like terms.
2x + 90 = 180
Subtract 90 from both sides.
2x = 90
Divide both sides by 2.
x = 45
Answer:
The numbers on the axis need to follow a repeating pattern
I think it's the last one coz in the graph, 50 jumps to 58 which breaks the repeating rule of 5
Well, a rational decimal is like a simple 3.1 or 4.5. It just cuts off easily. Another example would be a repeating decimal like 3.333333...
An irrational decimal is like 3.1415682983523576294875 with no pattern or cutoff point.
Sorry if I am wrong.
Answer:
pls help with what brainlics
Answer:
0.51 cm
Step-by-step explanation:
In right triangle MNP, MP = 4 cm, m∠N = 90°, m∠P = 21°
By the sine definition,
![\sin \angle P=\dfrac{\text{Opposite leg}}{\text{Hypotenuse}}=\dfrac{MN}{MP}\\ \\MN=MP\sin \angle P\\ \\MN=4\sin 21^{\circ}\approx 1.43\ cm](https://tex.z-dn.net/?f=%5Csin%20%5Cangle%20P%3D%5Cdfrac%7B%5Ctext%7BOpposite%20leg%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%3D%5Cdfrac%7BMN%7D%7BMP%7D%5C%5C%20%5C%5CMN%3DMP%5Csin%20%5Cangle%20P%5C%5C%20%5C%5CMN%3D4%5Csin%2021%5E%7B%5Ccirc%7D%5Capprox%201.43%5C%20cm)
Now, consider right triangle HMN (it is right because NH is an altitude). By the cosine definition,
![\cos \angle M=\dfrac{\text{Adjacent leg}}{\text{Hypotenuse}}=\dfrac{MH}{MN}\\ \\MH=MN\cos \angle M](https://tex.z-dn.net/?f=%5Ccos%20%5Cangle%20M%3D%5Cdfrac%7B%5Ctext%7BAdjacent%20leg%7D%7D%7B%5Ctext%7BHypotenuse%7D%7D%3D%5Cdfrac%7BMH%7D%7BMN%7D%5C%5C%20%5C%5CMH%3DMN%5Ccos%20%5Cangle%20M)
In the right triangle, two acute angles are always complementary, so
![m\angle M=90^{\circ}-m\angle P=90^{\circ}-21^{\circ}=69^{\circ}](https://tex.z-dn.net/?f=m%5Cangle%20M%3D90%5E%7B%5Ccirc%7D-m%5Cangle%20P%3D90%5E%7B%5Ccirc%7D-21%5E%7B%5Ccirc%7D%3D69%5E%7B%5Ccirc%7D)
Thus,
![MH=1.43\cos 69^{\circ}\approx 0.51\ cm](https://tex.z-dn.net/?f=MH%3D1.43%5Ccos%2069%5E%7B%5Ccirc%7D%5Capprox%200.51%5C%20cm)