Elizabeth rose her bike 6 1/2 miles from her house to the library and then another 2 2/5 miles to her friend milos house.

Use the angle relationship in the figure below to solve for x. Assume that lines a and b are parallel and the given angles are g

Daniel [21]

9514 1404 393

Answer:

x = 5°

Step-by-step explanation:

The marked angles are "alternate exterior angles," hence congruent.

2x +90° = x +95°

x = 5° . . . . . . . . . . . . subtract (x+90°) from both sides

4 0

2 years ago

12<br> Using side lengths only, could the triangles be similar?<br> 0.5<br> m05 1 1.5

Murljashka [212]

Answer:

$\large\boxed{\text{No.}\ \dfrac{0.5}{1}\neq\dfrac{1}{1.5}\neq\dfrac{1.5}{2}}$

Step-by-step explanation:

$\text{Let}\\ a,\ b,\ c\ -\ \text{sides of a triangle ABC, where}\ a\leq b\leq c\\d,\ e,\ f\ -\ \text{sides of a triangle}\ DE F,\ \text{where}\ d\leq e\leq f.\\\\\triangle ABC\sim\triangle DE F\iff\dfrac{a}{d}=\dfrac{b}{e}=\dfrac{c}{f}\\\\/\text{corresponding sides are in proportion}/$

$\bold{WARNING !!!}\\\\\text{No triangle like QRS exists!}\\\\1 + 0.5 = 1.5 !!!\\\\\text{The sum of the lengths of the two shorter sides of the triangle}\\\text{must be greater than the length of the longest side.}$

$\text{Despite this, let's check the ratios}$

$\text{We have:}\\\\\triangle XYZ\to a=1,\ b=1.5,\ c=2\\\triangle QRS\to d=0.5,\ e=1,\ f=1.5$

$\text{Check:}\\\\\dfrac{d}{a}=\dfrac{0.5}{1}=0.5\\\\\dfrac{e}{b}=\dfrac{1}{1.5}=\dfrac{10}{15}=\dfrac{2}{3}\\\\\dfrac{f}{c}=\dfrac{1.5}{2}=\dfrac{15}{20}=\dfrac{3}{4}\\\\\dfrac{d}{a}\neq\dfrac{e}{b}\neq\dfrac{f}{c}\neq\dfrac{d}{a}$

8 0

3 years ago

Solve this equation 4log√x - log 3x =log x^2

ruslelena [56]

Answer:

$x = \frac{1}{3}$

Step-by-step explanation:

*Move terms to the left and set equal to zero:

4㏒(√x) - ㏒(3x) - ㏒(x²) = 0

*simplify each term:

㏒(x²) - ㏒(3x) - ㏒(x²)

㏒(x²÷x²) -㏒(3x)

㏒(x²÷x² / 3x)

*cancel common factor x²:

㏒( $\frac{1}{3x}$ )

*rewrite to solve for x :

10⁰ = $\frac{1}{3x}$

1 = $\frac{1}{3x}$

1 · x = $\frac{1}{3x}$ · x

1x = $\frac{1}{3}$

*that would be our answer, however, the convention is to exclude the "1" in front of variables so we are left with:

x = $\frac{1}{3}$

5 0

3 years ago

What is <br> 5(2x+8)-5x=5(5x+6?

yanalaym [24]

5(2x+8)-5x=5(5x+6)

Distribute

10x+40-5x=25x+30

combine like terms

5x+40=25x+30

-5x -5x

subtract 5x from both sides

40=20x+30

-30 -30

subtract 30 from both sides

10=20x

÷20 ÷20

divide both sides by 20

1/2=x is your final answer

4 0

3 years ago

Which expression is equivalent to (x'2-2)'5

Greeley [361]

Answer: D = x'10 − 10x'8 + 40x'6 − 80x'4 + 80x'2 − 32

Step-by-step explanation:

3 0

2 years ago