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k0ka [10]
3 years ago
5

Mr. Quark drove his car 314 miles in 6.5

Mathematics
1 answer:
Likurg_2 [28]3 years ago
8 0

Answer:

  a) 48.3 mph

  b) 24.7 mpg

  c) 0.04 gpm

Step-by-step explanation:

a) "per" means "divided by", so "miles per hour" means "miles divided by hours":

  (314 mi)/(6.5 h) = 48.3 mi/h

__

b) (314 mi)/(12.7 gal) = 24.7 mi/gal

__

c) (12.7 gal)/(314 mi) = 0.04 gal/mi

_____

Hopefully, you recognize that gallons per mile is the inverse of miles per gallon:

  1/(24.7 mi/gal) = (1/24.7) gal/mi = 0.04 gal/mi

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A pound of chocolate costs 6 dollars. Diane buys P pounds. Write an equation to represent the total cost c that Diane pays.
postnew [5]

Answer:

C=6P

Step-by-step explanation:

Because the cost (c) depends on the pounds (p), we have to multiple the weight by 6, because it is $6 per pound.

7 0
3 years ago
Please show the working and answer. you can take a picture for the working.
baherus [9]

Answer:

(a) The area of the triangle is approximately 39.0223 cm²

(b) ∠SQR is approximately 55.582°

Step-by-step explanation:

(a) By sin rule, we have;

SQ/(sin(∠SPQ)) = PQ/(sin(∠PSQ)), which gives;

5.4/(sin(52°)) = 6.8/(sin(∠PSQ))

∴ (sin(∠PSQ)) = (6.8/5.4) × (sin(52°)) ≈ 0.9923

∠PSQ = sin⁻¹(0.9923) ≈ 82.88976°

Similarly, we have;

5.4/(sin(52°)) = SP/(sin(180 - 52 - 82.88976))

Where, 180 - 52 - 82.88976 = ∠PQS = 45.11024

SP = 5.4/(sin(52°))×(sin(180 - 52 - 82.88976)) ≈ 4.8549

Given that RS : SP = 2 : 1, we have;

RS = 2 × SP = 2 × 4.8549 ≈ 9.7098

We have by cosine rule, \overline {RQ}² =  \overline {SQ}² +  \overline {SR}² - 2 × \overline {SQ} × \overline {SR} × cos(∠QSR)

∠QSR and ∠PSQ are supplementary angles, therefore;

∠QSR = 180° - ∠PSQ = 180° - 82.88976° = 97.11024°

∠QSR = 97.11024°

Therefore;

\overline {RQ}² =  5.4² +  9.7098² - 2 ×  5.4×9.7098× cos(97.11024)

\overline {RQ}² ≈ 136.42

\overline {RQ} = √(136.42) ≈ 11.6799

The area of the triangle = 1/2 ×\overline {PQ} × \overline {PR} × sin(∠SPQ)

By substituting the values, we have;

1/2 ×\overline {PQ} × \overline {PR} × sin(∠SPQ)

1/2 × 6.8 × (4.8549 + 9.7098) × sin(52°) ≈ 39.0223 cm²

The area of the triangle ≈ 39.0223 cm²

(b) By sin rule, we have;

\overline {RS}/(sin(∠SQR)) = \overline {RQ}/(sin(∠QSR))

By substituting, we have;

9.7098/(sin(∠SQR)) = 11.6799/(sin(97.11024))

sin(∠SQR) = 9.7098/(11.6799/(sin(97.11024))) ≈ 0.82493

∠SQR = sin⁻¹(0.82493) ≈ 55.582°.

8 0
3 years ago
Karina bought 4 packages of the type of gum shown.
Radda [10]

Answer:

Step-by-step explanation:4n+3=60

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5692 in standard form
Mamont248 [21]

Answer:

5.692 × 103.

Step-by-step explanation:

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Answer:

The answer is C or 10, -5!

Step-by-step explanation:

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