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3 years ago

B is between A and C. AB=2x+1, BC=3x-4, and AC=62. Find the value of 'x', and determine if B is a bisector.

1 answer:

6 0

∠AB = (2x + 1)°
∠BC = (3x - 4)°
∠AC = 62°

      ∠AB + ∠BC = ∠AC
(2x + 1)° + (3x - 4)° = 62°
   (2x + 1) + (3x - 4) = 62
      2x + 3x + 1 - 4 = 62
      5x - 3 = 62
      + 3   + 3
   5x = 65
      5     5
       x = 13°

Line B is a bisector between ∠AC.

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At the market, Ms. Winn bought 3/4 lb of grapes and 5/8 lb of cherries.

wolverine [178]

Answer:

Part a) Ms. Winn bought 12 oz of grapes

Part b) Ms. Winn bought 10 oz of cherries

Part c) Ms. Winn bought 2 oz more of grapes than cherries

Part d) Mr. Phillips bought 6 more ounces of fruit than Ms. Winn

Step-by-step explanation:

Part a) How many ounces of grapes did Ms. Winn buy?

Remember that

$1\ lb=16\ oz$

To convert lb to oz multiply by 16

we know that

Ms. Winn bought 3/4 lb of grapes

Convert lb to oz

Multiply by 16

$\frac{3}{4}\ lb= \frac{3}{4}(16)=12\ oz$

therefore

Ms. Winn bought 12 oz of grapes

Part b) How many ounces of cherries did Ms. Winn buy?

Remember that

$1\ lb=16\ oz$

To convert lb to oz multiply by 16

we know that

Ms. Winn bought 5/8 lb of cherries

Convert lb to oz

Multiply by 16

$\frac{5}{8}\ lb= \frac{5}{8}(16)=10\ oz$

therefore

Ms. Winn bought 10 oz of cherries

Part c) How many more ounces of grapes than cherries did Ms. Winn buy?

Subtract the ounces of cherries from the ounces of grapes

$12\ oz-10\ oz=2\ oz$

therefore

Ms. Winn bought 2 oz more of grapes than cherries

Part d) If Mr. Phillips bought 1 3/4 pounds of raspberries, who bought more fruit, Ms. Winn or Mr. Phillips? How many ounces more?

Remember that

$1\ lb=16\ oz$

To convert lb to oz multiply by 16

we know that

Mr. Phillips bought 1 3/4 pounds of raspberries

Convert mixed number to an improper fraction

$1\frac{3}{4}\ lb=\frac{1*4+3}{4}=\frac{7}{4}\ lb$

Convert lb to oz

Multiply by 16

$\frac{7}{4}\ lb= \frac{7}{4}(16)=28\ oz$

Remember that

Ms. Winn bought 12 oz of grapes and 10 oz of cherries

In total Ms. Winn bought

12 oz+10 oz=22 oz -----> total ounces of fruit

Mr. Phillips bought 28 oz of fruit

Ms. Winn bought 22 oz of fruit

$28\ oz > 22\ oz$

Find the difference

$(28\ oz-22\ oz)=6\ oz$

therefore

Mr. Phillips bought 6 more ounces of fruit than Ms. Winn

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