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3 years ago

Please help with the question in the photo below.

Mathematics

2 answers:

kkurt [141]3 years ago

7 0

Answer:

53.8°

Step-by-step explanation:

Use cosine law

67² = 72² + 76² - 2(72)(76)cosX

cosX = 719/1216

X = 53.75190075

maw [93]3 years ago

7 0

Answer:

Step-by-step explanation:

Since we know the three sides and no angle is known, we would apply the law of Cosines which is expressed as

a² = b² + c² - 2abCosA

Where a,b and c are the length of each side of the triangle and A is the angle corresponding to a. Likening the expression to the given triangle, it becomes

SR² = SQ² + QR² - 2(SQ × QR)CosQ

67² = 76² + 72² - 2(76 × 72)CosQ

4489 = 5776 + 5184 - 2(5472)CosQ

4489 = 10960 - 10944CosQ

10944CosQ = 10960 - 4489

10944CosQ = 6471

CosQ = 6471/10944

CosQ = 0.59

Q = Cos^(- 1)0.59

Q = 53.8° to the nearest tenth

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In the figure, AB∥CD. Find x and y.

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Answer:

y=131°

x=53°

Step-by-step explanation:

∠ ABD and ∠ BDC are supplementary.

The sum of the supplementary angles =180 °

thus y-4+x=180...........i

x and 37° are complementary, that is, they add up to 90°

Thus, x=90-37=53°

Using this value in equation 1 we obtain:

y-4°+53° =180°

y= 180°-53°+4°

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What is 30% off of $200.00 ?

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There are some nickels, dimes, and quarters in a large piggy bank. For every 2 nickels there are 3 dimes. For every 2 dimes ther

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Answer: a) Number of nickels, dimes, and quarters are 80, 120, 300 respectively.

b) The coins are worth of 91 dollars i.e. $91 in the piggy bank.

Explanation:

Since we have given that

For every 2 nickels there are 3 dimes ,

So, their ratio will be 2:3

and for every 2 dimes there are 5 quarters.\,

So, their ratio will be 2:5

Now, we'll first find the ratio of nickles to dimes to quarters i.e.

Nickle Dimes Quarters

2 3

2 5

So, it becomes ,

Nickle : Dimes : Quarters

2×2 : 3×2 : 3×5

4 : 6 : 15

Now, let the number of nickle be 4x

Let the number of dimes be 6x

Let the number of quarters be 15x

According to question,

$4x+6x+15x=500\\\\25x=500\\\\x=\frac{500}{25}=20$

So, number of nickels is given by

$4x=4\times 20=80$

Number of dimes is given by

$6x=4\times 20=120$

Number of quarters is given by

$15x=4\times 20=300$

As we know that

$1\ nickel=5\ cents\\\\1\ dime=10\ cents\\\\1\ quarter=25\ cents$

So, According to our question, we get

$80\times 5+120\times 10+300\times 25=400+1200+7500=9100\ cents\\\\1\ cent=0.01\ dollar\\\\9100\ cents=9100\times 0.01\ dollars=91\ dollars.$

Hence,

a) Number of nickels, dimes, and quarters are 80, 120, 300 respectively.

b) the coins are worth of 91 dollars i.e. $91 in the piggy bank.

7 0

3 years ago