Answer:
Step-by-step explanation:
Question 1:
First, write the equation out:
4(x+3)=7x-3
solve for x:
4x+12=7x-3
15=3x
x=5
Question 2:
Do the same on the second question:
30-x=3x-6
36=4x
x=9
Answer:
D) 3.8 cm
Step-by-step explanation:
There are several ways this problem can be solved. Maybe the easiest is to use the Law of Cosines to find angle BAC. Then trig functions can be used to find the length of the chord.
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In triangle BAC, the Law of Cosines tells us ...
a² = b² +c² -2bc·cos(A)
A = arccos((b² +c² -a²)/(2bc)) = arccos((8² +6² -3²)/(2·8·6)) = arccos(91/96)
A ≈ 18.573°
The measure of half the chord is AB times the sine of this angle:
BD = 2(AB·sin(A)) ≈ 3.82222
The length of the common chord is about 3.8 cm.
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<em>Additional comment</em>
Another solution can be found using Heron's formula to find the area of triangle ABC. From that, its altitude can be found.
Area ABC = √(s(s-a)(s-b)(s-c)) . . . . where s=(a+b+c)/2
s=(3+8+6)/2 = 8.5
A = √(8.5(8.5 -3)(8.5 -8)(8.5 -6)) = √54.4375 ≈ 7.64444
The altitude of triangle ABC to segment AC is given by ...
A = 1/2bh
h = 2A/b = 2(7.64444)/8 = 1.911111
BD = 2h = 3.822222
Sorry :/ hope u get the rank back soon!
Answer:
t = 5/2
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
<u>Algebra I</u>
Step-by-step explanation:
<u>Step 1: Define</u>
3t + 7 = 2 + 5t
<u>Step 2: Solve for </u><u><em>t</em></u>
- [Subtraction Property of Equality] Isolate <em>t</em> terms: 7 = 2 + 2t
- [Subtraction Property of Equality] Isolate <em>t</em> term: 5 = 2t
- [Division Property of Equality] Isolate <em>t</em>: 5/2 = t
- Rewrite: t = 5/2
Answer:
1600
Step-by-step explanation:
b : g : total
9 : 7 : 16
difference-> 9-7=2
2u->100
1u-> 50
16u-> 1600