Answer:
(-19, 55)
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Algebra I</u>
- Solving systems of equations using substitution/elimination
Step-by-step explanation:
<u>Step 1: Define Systems</u>
y = -3x - 2
5x + 2y = 15
<u>Step 2: Solve for </u><em><u>x</u></em>
<em>Substitution</em>
- Substitute in <em>y</em>: 5x + 2(-3x - 2) = 15
- Distribute 2: 5x - 6x - 4 = 15
- Combine like terms: -x - 4 = 15
- Isolate <em>x</em> term: -x = 19
- Isolate <em>x</em>: x = -19
<u>Step 3: Solve for </u><em><u>y</u></em>
- Define original equation: y = -3x - 2
- Substitute in <em>x</em>: y = -3(-19) - 2
- Multiply: y = 57 - 2
- Subtract: y = 55
Answer: x=15
Explanation: you can set 2x+100 = 5x+55 because they are corresponding interior angles.
Work:
2x+100 = 5x+55
2x+100-5x = 55
2x-5x = 55-100
-3x = -45
divide by -3 to cancel the negative and get x by itself
x = 15
Hope this helped! :)
Answer:
angle Z=20°
side xy≈15.36
hypotenuse≈19.49
Step-by-step explanation:
Find angle z adding the other two angles and subtracting that by 180 to get 20.
(12)tan(20) gets you side xy which is 15.36
12^2+15.36^2=xz^2
Answer:
Step-by-step explanation:
Starting with ΔABC, draw the dilation image of the triangle with a center at the origin and a scale factor of two. Notice that every coordinate of the original triangle has been multiplied by the scale factor (x2). Dilations involve multiplication! Dilation with scale factor 2, multiply by 2
Reminder: the formula for a geom. seq. is
a(n) = a(1)*r^(n-1), where a(1) is the first term, n is the counter and r is the common ratio.
I first noted that 243 is a power of 3; specifically, 243=3^5, or 243=3(3)^4, or 243=(3^2)(3)^(4-1). Notice that I'm trying here to rewrite 243=3^5 in the form a(n) = a(1)*r^(n-1): a(4) = a(1)(3)^(4-1), or a(4) = a(1)(3)^3 = 243. Then by division we find that a(1) = 243/27 = 9. Is it possible that a(1)=9?
Let's try out our formula a(n)=9(3)^(n-1). Steal n=9 and see whether this formula gives u s 59049:
n(9) = 59049 = 9(3)^(9-1), or 9(3)^8. True or false? 3^8= 6561, and 9(3)^8 = 59049.
YES! That's correct.
Therefore, the desired formula is
a(n) = 9(3)^(n-1). The first term, a(1) is 9(3)^(1-1) = 9(3)^0 = 9*1 = 9.
