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vampirchik [111]
3 years ago
10

You have the choice of logging on at one of two Internet cafés. Their posted rates are as follows: Log-On Café: $5.50 plus $0.15

for every minute online eCafé: $4.00 plus $0.20 for every minute online Which café is the best option if you plan on using the Internet for 45 minutes? What is the equation that relates the number of minutes used and the total cost, and how much money will you save?
Mathematics
1 answer:
erastovalidia [21]3 years ago
4 0
1. 5.50 + 0.15 * 45 = 12.25

2. 4 + 0.20 * 45 = 13

So the first option is slightly better, you can save 13-12.25= $0.75.
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Find the value of x in each case: Given: Iso. ΔABC, HM ∥DG Find: x, m∠CAB, m∠CBA
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1. Start with ΔCIJ.

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  • ∠CJI and ∠KJA are congruent as vertical angles, then m∠KJA =m∠CJI=7x-25°.

2. Lines HM and DG are parallel, then ∠KJA and ∠JAB are consecutive interior angles, then m∠KJA+m∠JAB=180°. So

m∠JAB=180°-m∠KJA=180°-(7x-25°)=205°-7x.

3. Consider ΔCKL.

  • ∠LFG and ∠CLM are corresponding angles, then m∠LFG=m∠CLM=8x;
  • ∠CLM and ∠CLK are supplementary, then m∠CLM+m∠CLK=180°, m∠CLK=180°-8x;
  • the sum of the measures of all interior angles in ΔCLK is 180°, then m∠CKL=180°-m∠CLK-m∠LCK=180°-(180°-8x)-42°=8x-42°;
  • ∠CKL and ∠JKB are congruent as vertical angles, then m∠JKB =m∠CKL=8x-42°.

4. Lines HM and DG are parallel, then ∠JKB and ∠KBA are consecutive interior angles, then m∠JKB+m∠KBA=180°. So

m∠KBA=180°-m∠JKB=180°-(8x-42°)=222°-8x.

5. ΔABC is isosceles, then angles adjacent to the base are congruent:

m∠KBA=m∠JAB → 222°-8x=205°-7x,

7x-8x=205°-222°,

-x=-17°,

x=17°.

Then m∠CAB=m∠CBA=205°-7x=86°.

Answer: 86°.

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Step-by-step explanation:

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