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3 years ago

Find two consecutive odd integers if twice the larger, increased by the smaller equals 37,

Mathematics

1 answer:

Alexxx [7]3 years ago

6 0

Answer:

11 and 13

Step-by-step explanation:

the first (smaller) odd integer can be called x

the second (larger) odd integer can be called x+2

2(x+2)+x = 37

[simplify . . .]

2x+4+x = 37

3x+4 = 37

[subtract 4 from each side]

3x = 33

[divide each side by 3; find smaller odd integer]

x = 11

[add 2 to find larger odd integer]

x+2 = 13

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soldier1979 [14.2K]

The product of a number and its reciprocal would be equal to one

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2 years ago

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3 years ago

Tara wants to fix the location of a mountain by taking measurements from two positions 3 miles apart. From the first position, t

Black_prince [1.1K]

Answer:

Shortest distance from the mountain is 3.17 miles.

Step-by-step explanation:

From the figure attached,

Let a mountain is located at point A.

Angle between the mountain and point B (∠B) = 53°

Angle between the mountain and point C (∠C) = 78°

Distance between these points = 3 miles

Since, m∠A + m∠B + m∠C = 180°

m∠A + 53° + 78° = 180°

m∠A = 180°- 131° = 49°

By applying sine rule in triangle ABC,

$\frac{\text{sin}(49)}{BC}=\frac{\text{sin}(53)}{AC}= \frac{\text{sin}(78)}{AB}$

$\frac{\text{sin}(49)}{3}=\frac{\text{sin}(53)}{AC}= \frac{\text{sin}(78)}{AB}$

$\frac{\text{sin}(49)}{3}=\frac{\text{sin}(53)}{AC}$

AC = $\frac{3\text{sin}(53)}{\text{sin}(49)}$

AC = 3.17 miles

$\frac{\text{sin}(49)}{3}=\frac{\text{sin}(78)}{AB}$

AB = $\frac{3\text{sin}(78)}{\text{sin}(49)}$

AB = 3.89 miles

Therefore, shortest distance from the mountain is 3.17 miles.

7 0

2 years ago

Fill in the table below by naming each prism and identifying the number of faces, vertices, and edges for each one of them.

Zarrin [17]

Answer:

Step-by-step explanation:

A prism is a solid figure and geometric in nature having the shape of its ends parallel to each other and its sides are parallelograms. Each prism are classifies based on the shape of its ends that are parallel to each other.

The name of the prism given in question according to their arrangement from left to right are triangular prism, trapezoidal prism, pentagonal prism and hexagonal prism.

Triangular prism is made up of 5 faces, 6 vertices and 9 edges

The trapezoidal prism is made up of 6 faces, 8 vertices and 12 edges

The pentagonal prism is made up of 7 faces, 10 vertices and 15 edges

The hexagonal prism is made up of 8 faces, 12 vertices and 18 edges

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3 years ago

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____ [38]

Answer:

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6 0

3 years ago