Step-by-step explanation:
1.) Firstly, you need to count out how many things there are. 4 app, 5 entrees, 2 desserts. This makes 11 different things
2.) for 11 numbers there can be 9 ways for each number for 1st nine places since 0 can't be the fist figure and next two are reciprocated from 10 numbers. Therefore 10!/2!
3.)So 99 combinations have 10!/2! Permutations hence total ways are 99*10!/2!
3(x-5)=21
x-5=21/3
x-5=7
x=7+5
x=12
here is the answer.
Given that the AC and BC are perpendicular, their slopes are the negative inverse of each other which gives that the product of the slopes of AC and BC is -1
<h3>How can the prove that the product of the slopes is -1 be found?</h3>
The completed proof is presented as follows;
The slope of AC or GC is GF/FC by definition of slope. The slope of BC or CE is DE/CD by definition of slope.
<FCD = <FCG + <GCE + <ECD <u>by angle addition property </u> <FCD = 180° by the definition of a straight angle, and <GCE = 90° by definition of perpendicular lines. So by substitution property of equality 180° = <FCG + 90° + <ECD. Therefore 90° - <FCG = <ECD, by the <u>subtraction property of equality </u> . We also know that 180° = <FCG + 90° + <CGF by the triangle sum theorem and by the subtraction property of equality 90° - <FCG = <CGF, therefore <ECD = <CGF by the substitution property of equality. Then <ECD ≈ <CGF by the definition of congruent angles. <GFC ≈ <CDE because all right angles are congruent. So by AA ∆GFC ~ ∆CDE. Since <u>the ratio of corresponding sides of similar triangles are equal</u> then GF/CD = FC/DE or GF•DE = CD•FC by cross product. Finally, by the division property of equality GF/FC = CD/DE. We can multiply both sides using the slope of using the <u>multiplication property of equality </u> to get GF/FC × -DE/CD = CD/DE × -DE/CD. Simplify so that GF/FC × -DE/CD = -1. This shows that the product of the slopes of AC and BC is -1.
Learn more about perpendicular lines here:
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Answer:
Step-by-step explanation:
You will have to interpret the question with the aid of a diagram and make out the relevant angles and either make use of cosine rule,sine rule etc....Your knowledge on angles should be sound
