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3 years ago

Give a geometric interpretation of the triangle inequality

1 answer:

6 0

The sides must be long enough to make a triangle. (If the sides are not long enough, they won't meet, so cannot form a triangle.)

_____

If your version of the triangle inequality includes the "or equal to" case, then the segments must be long enough to meet, even though the result may look like a line segment.

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A polynomial P(x) and a divisor d(x) are given. Use long division to find a quotient Q(x) and the remainder R(x). Express P(x) i

Vilka [71]

It's a bit hard to explain but I hope this helps

5 0

3 years ago

The table shows information about some children.

Sindrei [870]

Answer:

$P(Age\ 12) = \frac{2}{3}$

Step-by-step explanation:

Given

Age 11 Age 12 Total

Girls 3 5 8

Boys 1 3 4

Required

$P(Age\ 12)$

The number of aged 12 children is:

$Age\ 12 = 5 + 3$

$Age\ 12 = 8$

The total number of children is:

$Total=8+4$

$Total = 12$

So, we have:

$P(Age\ 12) = \frac{Age\ 12}{Total}$

$P(Age\ 12) = \frac{8}{12}$

Simplify

$P(Age\ 12) = \frac{2}{3}$

3 0

3 years ago

9. Peter is trying to buy fencing for the perimeter of his garden. His garden is in the shape of a rectangle with a length of 2(

fomenos

Length: 2(x + 6); Width: 3.5x

A rectangle has 4 sides. 2 sides are lengths and 2 sides are widths.

The perimeter is the sum of the measures of all 4 sides.

perimeter = length + length + width + width

perimeter = 2(x + 6) + 2(x + 6) + 3.5x + 3.5x

Use the distributive property on 2(x + 6).

perimeter = 2x + 12 + 2x + 12 + 3.5x + 3.5x

Now let's group all terms with x first, then all the numbers.

perimeter = 2x + 2x + 3.5x + 3.5x + 12 + 12

Now we add like terms. Like terms have exactly the same variables and the same exponents. All terms with x are like terms and can be added together. All terms with no variable are like terms and can be added together.

perimeter = 11x + 24

11x and 24 are not like terms since 11x contains the variable x and 24 has no variable. Since 11x and 24 are not like terms, they cannot be added together. No more simplification can be done, and 11x + 24 is the answer.

Answer: 11x + 24

8 0

3 years ago

The table shows the distance y (in miles) that you travel on a road in x minutes. What type of function best models the data?

evablogger [386]

Answer:

Linear Function

Step-by-step explanation:

Given

The table showing values of x and y

Required

Determine the type of function

To determine the type of function, the table represents;

One will need to determine the table equation.

Start by solving for the slope;

$m = \frac{y_1 - y_2}{x_1 - x_2}$

When x - 0; y = 0 and When x = 80; y = 60.

This gives

$m = \frac{0 - 60}{0 - 80}$

$m = \frac{- 60}{- 80}$

$m = \frac{3}{4}$

The formula is determine as follows;

$y - y_1 = m(x - x_1)$

When x - 0; y = 0; m = 3/4; This gives

$y - 0 = \frac{3}{4}(x - 0)$

$y = \frac{3}{4}(x - 0)$

Open Bracket

$y = \frac{3}{4}x - 0$

$y = \frac{3}{4}x$

The above is an example of a linear equation.

<em>Hence; option B answers the question</em>

8 0

3 years ago

PART 1:

Tju [1.3M]

See the attached figure

A(4,8) B(0,7) C(4,3)
<span>the line of reflection is x=5
</span>
the reflection is (x,y)-------------------> (10-x,y)
therefore
A(4,8)-----------------> A1(10-4,8)------> A1(6,8)
B(0,7)-----------------> B1(10-0,7)------> B1(10,7)
C(4,3)-----------------> C1(10-4,3)------> C1(6,3)

4 0

3 years ago