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3 years ago

2x + 3y = 533x - y = 19

Mathematics

1 answer:

Keith_Richards [23]3 years ago

5 0

Answer:

x = 10

y = 11

Step-by-step explanation:

Solve for x:

2x + 3y = 53

3x(3) - y(3) = 19(3)

2x + 3y = 53

9x - 3y = 57

Add:

2x = 53

9x = 57

11x = 110

Solve algebraically:

x = 110 ÷ 11

x = 10

Now solve for y:

2(10) + 3y = 53

20 + 3y = 53

3y = 53 - 20

3y = 33

y = 33 ÷ 3

y = 11

Verify for the second equation:

3x - y = 19

3(10) - (11) = 19

30 - 11 = 19

30 = 19 + 11

30 = 30 (Correct)

Cheers!

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4 years ago

Which of the following is true about the right triangle?

katrin2010 [14]

Option 1. $cos (a) = \frac{3}{5}$ , option 3. $sin (a) = \frac{4}{5}$ , and option 5. $tan (a) = \frac{4}{3}$ are true about the right triangle.

Step-by-step explanation:

Step 1:

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Here the hypotenuse measures 15 units. Assume the other side measures x.

$15^{2} = x^{2} +9^{2} , x^{2} = 15^{2} -9^{2} .$

$x^{2} = 144, x= 12.$

Step 2:

$sin \theta = \frac{oppositeside}{hypotenuse} ,cos \theta = \frac{adjacentside}{hypotenuse} , tan \theta = \frac{oppositeside}{adjacentside}.$

For angle A, the opposite side is 12 units long, the adjacent side is 9 units long and the hypotenuse is 15 units long.

$sin (a) = \frac{12}{15} ,cos(a) = \frac{9}{15} , tan(a) = \frac{12}{9}.$

$sin (a) = \frac{4}{5} ,cos (a) = \frac{3}{5} , tan (a) = \frac{4}{3}.$

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3 years ago

Pleaseee helpp im giving a lot of points if corrected

Dafna11 [192]

Answer:

x = 38°

Step-by-step explanation:

Complementary angles = 90°

90° = x + x+14

90° = 2x + 14

104 = 2x

x = 52°

the next angle should be 52 - 14 = 38°

So x = 38°

If my answer is incorrect, pls correct me!

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3 years ago

Please give me the correct answer

vladimir1956 [14]

Answer:

10 centimeters

Step-by-step explanation:

formula for volume of a cylinder = πr² · h

1. Set up the equation

(3.14)(r²)(14) = 4,396

2. Simplify

(43.96)(r²) = 4,396

3. Solve

r² = 100

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6 0

3 years ago

The leaning tower of Pisa currently "leans" at a 4 degree angle and has a vertical height of 55.86 meters. How tall was the lean

Marizza181 [45]

Answer:

56 meters.

Step-by-step explanation:

Please find the attachment.

Let the leaning tower's be h meters tall, when it was originally built.

We can see from our attachment that the side with length 55.86 meters is hypotenuse and h is adjacent side for 4 degree angle.

Since we know that cosine relates the adjacent and hypotenuse of a right triangle.

$\text{Cos}=\frac{\text{Adjacent}}{\text{Hypotenuse}}$

Upon substituting our given values we will get,

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$h=55.996\approx 56$

Therefore, the leaning tower was approximately 56 meters, when it was originally built.

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3 years ago

2x + 3y = 533x - y = 19​

2x + 3y = 533x - y = 19