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3 years ago

The sum of two numbers is 27. The larger number is 3 more than the smaller number. What are the two numbers?

Mathematics

1 answer:

pantera1 [17]3 years ago

7 0

The two numbers are 12 and 15

Solution:

Let the smaller number be "x"

Let the larger number be "y"

Given that,

The sum of two numbers is 27

Therefore, we frame a equation as:

Smaller number + Larger number = 27

x + y = 27 ------ eqn 1

The larger number is 3 more than the smaller number

Larger number = 3 + smaller number

y = 3 + x ------- eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 2 in eqn 1

x + 3 + x = 27

2x + 3 = 27

2x = 27 - 3

2x = 24

Substitute x = 12 in eqn 2

y = 3 + 12

Thus the two numbers are 12 and 15

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There is a triangular parking lot at the local mall. The second angle of the triangular parking lot is six more than twice as la

Travka [436]

Answer:

The measure of the three angles are;

The first angle is 62°

The second angle is 28°

The third angle is 90°

Step-by-step explanation:

The given information are;

The shape of the parking lot = Triangular

Let the angles of the triangle be given as follows

First angle = A

Second angle = B

Third angle = C

The given triangle interior angle dimensions are;

A = 6 + 2× B

C = A + B

However, we have;

A + B + C = 180° (Angle sum property for a triangle)

Therefore;

A + B + C = 180° gives;

C + C = 180° (Transitive property)

2·C = 180°

C = 180°/2 = 90°

C = 90°

However, C = A + B therefore;

90° = A + B and, A = 6 + 2 × B, we get;

A + B = 90° (Symmetric property)

6 + 2× B + B = 90° (Substitution property)

6 + 3·B = 90°

3·B = 90° - 6° = 84°

B = 84°/3 = 28°

B = 28°

From, A = 6 + 2 × B, we have;

A = 6 + 2 × 28° = 62°

A = 62°

First angle = A = 62°

Second angle = B = 28°

Third angle = C = 90°

The measure of the three angles are;

First angle is 62°

Second angle is 28°

Third angle is 90°.

8 0

3 years ago

Find S15 for the geometric series 72 + 12 + 2 + 1/3 +…

Gemiola [76]

S1 = 72
S2 = 12 = 72*(1/6)
S3 = 2 = 72*(1/6)^2
.
.
.
S15 = 72*(1/6)^14 = 9.18*10^(-10)

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3 years ago

Graph the line with the equation y = -1/3x + 4.

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Answer:

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Step-by-step explanation:

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2 years ago

If a construction work digs down to 30 feet below the surface of the ground. What is her elevation?

tresset_1 [31]

Answer:

-30 feet

Step-by-step explanation:

You are going down so it would be negative, if you were going up it would be posotive.

4 0

3 years ago

How much longer is the hypotenuse of the triangle than its shorter leg?

RUDIKE [14]

This is an incomplete question, here is a complete question and image is also attached below.

How much longer is the hypotenuse of the triangle than its shorter leg?

a. 2 ft

b. 4 ft

c. 8 ft

d. 10 ft

Answer : The correct option is, (b) 4 ft

Step-by-step explanation:

Using Pythagoras theorem in ΔACB :

$(Hypotenuse)^2=(Perpendicular)^2+(Base)^2$

$(AB)^2=(AC)^2+(BC)^2$

Given:

Side AC = 6 ft

Side BC = 8 ft

Now put all the values in the above expression, we get the value of side AB.

$(AB)^2=(6)^2+(8)^2$

$AB=\sqrt{(6)^2+(8)^2}$

$AB=10ft$

Now we have to calculate the how much longer is the hypotenuse of the triangle than its shorter leg.

Difference = Side AB - Side AC

Difference = 10 ft - 6 ft

Difference = 4 ft

Therefore, the 4 ft longer is the hypotenuse of the triangle than its shorter leg.

5 0

3 years ago

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