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3 years ago

What is the least common multiple (LCM) of 8 and 10?

Mathematics

1 answer:

Svet_ta [14]3 years ago

4 0

Answer:

LCM (8,10) = 2 × 2 × 2 × 5 = 40

Step-by-step explanation:

Least common multiple is the smallest number that is multiple of both the given numbers.

Example: LCM of 2 and 3 is 6 .

6 is a multiple of both 2 and 3 .

Given numbers are 8 and 10

First write both in factor form,

⇒ 8 = 2 × 2 × 2

⇒ 10 = 2 × 5

We find LCM by writing common terms one times and multiplying all terms together,

Here, 2 is common to both 8 and 10 so we write it once only.

Thus, LCM (8,10) = 2 × 2 × 2 × 5 = 40.

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A teacher weights the following grades as follows:

Semmy [17]

Answer:

Final exam, Homework, Projects, quizzes

Step-by-step explanation:

15% is the lowest, 1/5 is 20% so that's next, 25% is the next largest, and 0.4 is 40%

7 0

3 years ago

Write an equation for the perpendicular bisector of the line segment joining the two points.

Leona [35]

Points (1, 7) and (-3, 2)

Slope for a line between (x₁, y₁) and (x₂, y₂) , m = (y₂ -y₁) / (x₂- x₁)

The slope for the line joining the two points = (2 - 7) / (-3 - 1) = -5/-4

Slope = 5/4

Hence the perpendicular bisector would have a slope of -1/(5/4) = -4/5

By condition of perpendicularity

For points (1, 7) and (-3, 2),

Formula for midpoints for (x₁, y₁) and (x₂, y₂) is ((x₁ +x₂)/2 , (y₁+ y₂)/2)

Midpoint for (1, 7) and (-3, 2) = ((1+ -3)/2 , (7+2)/2) = (-2/2, 9/2)

= (-1, 9/2)

Since the slope of perpendicular bisector is -4/5 and passes through the midpoint (-1, 9/2)

Equation y - y₁ = m (x - x₁)

y - 9/2 = (-4/5) (x - -1)

y - 9/2 = (-4/5)(x + 1)

   5(y - 9/2) = -4(x + 1)

   5y - 45/2 = -4x - 4

   5y = -4x - 4 + 45/2

5y + 4x = 45/2 - 4

5y + 4x = 22 1/2 - 4 = 18 1/2

5y + 4x = 37/2

10y + 8x = 37

The equation of the line to perpendicular bisector is 10y + 8x = 37

7 0

4 years ago

The length of a shadow of a tree is 150 feet when the angle of elevation of the sun is 39°. Approximate the height of the tree.

fomenos

Answer:

The height of tree is approximately 121.5 feet.

Step-by-step explanation:

We are given following in question:

Length of shadow = 150 feet

Angle of elevation of the sun =

$\theta = 39^\circ$

The tree and the shadow forms a right angled triangle.

Thus, with the help of trigonometric relation, we can write:

$\tan \theta = \dfrac{\text{Height of tree}}{\text{Length of shadow}}$

Let x feet be the height of tree.

Putting all the values, we get,

$\tan 39^\circ = \dfrac{x}{150}\\\\0.80978 = \dfrac{x}{150}\\\\\Rightarrow x = 150\times 0.80978\\\Rightarrow x = 121.467 \approx 121.5$

Thus, the height of tree is approximately 121.5 feet.

6 0

4 years ago

Klye bought a DVD that cost $19.23, including tax. She gave the sales clerk a $20 Bill.how much change should kyle receive

igomit [66]

Klye would receive $0.77 back as change. You have to subtract $20.00 - $19.23

4 0

3 years ago

Read 2 more answers

What is the measure of arc AB when m angle APB=78 102 156 204 39

Elis [28]

In the given figure above, we can use the formula for tangent-tangent angle. This is under the type of angle whose vertex is outside the circle and its sides intersects the circle.

Applying the tangent-tangent angle formula:

m∠APB = $\frac{1}{2}$ (ALB - AB)

m∠APB = angle of the vertex
ALB = measure of arc ALB
AB = measure of arc AB

we all know that the total measure of arc is equal to 360, hence, ALB + AB = 360

let: x = measure of arc AB
360 - x = measure of arc ALB

substitute:

78 = $\frac{1}{2}$ {(360 - x) - x}
78 = $\frac{1}{2}$ (360 - 2x)
78 = 180 - x   ⇒ simplifying further by dividing both 360 and -2x by 2
x = 180 - 78   ⇒ combining like terms
x = 102
arc AB = 102 ⇒ Answer

5 0

3 years ago