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3 years ago

Let x cm be the width of a rectangle whose length is 16 cm longer than its width.

Mathematics

1 answer:

nika2105 [10]3 years ago

6 0

We know that Length = x + 16 and Width = x.

Since the perimeter of the rectangle is 2 lengths + 2 widths,

Perimeter = 2(2x + 16) = 4x + 32.

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Two lines are perpendicular if and only if they intersect to form right angle

mart [117]

That is true, perpendicular lines must form right angles

5 0

3 years ago

find the gradient of the line joining (3,7) and (6,9). Hence, find the acute angle it makes with the positive x-y axis

stiv31 [10]

Answer:

33.7 degrees

Step-by-step explanation:

As we go from (3,7) to (6,9), x increases by 3 and y increases by 2. Thus, the gradient (slope) of the line connecting these two points is

m = rise / run = 2/3. Using the slope-intercept formula y = mx + b, we obtain

7 = (2/3)(3) + b, or 7 = 2 + b, so we see that b = 5 and y = (2/3)x + 5. The y-intercept is (0, 5).

Next we find the x-intercept. We set y = (2/3)x + 5 = to 0 and solve for x:

(2/3)x = -5, or (3/2)(2/3)x = -5(3/2), or x = -15/2, so that the x-intercept is

(-15/2, 0). This line intersects the x-axis at (-15/2, 0).

Now look at the segment of this line connecting (-15/2, 0) and (0, 5). Here x increases by 15/2 and y increases by 5, and so the tangent of the acute angle in question is

tan Ф = 5 / (15/2) = 10 / 15 = 2/3.

Using the inverse tangent function, we get Ф = arctan 2/3, or approx.

33.7 degrees.

I believe you meant "the acute angle it makes with the positive x-axis."

3 0

3 years ago

Simplify: StartRoot StartFraction 27 x Superscript 12 Baseline Over 300 x Superscript 8 Baseline EndFraction EndRoot StartFracti

ale4655 [162]

The solution of the expression is $\rm \dfrac{9\times x^4}{100}$ .

Given that

Equation; $\dfrac{27x^{12}}{300x^8}$

We have to simplify the equation.

According to the question

To simplify the equation follow all the steps given below.

Equation; $\sqrt{\dfrac{27x^{12}}{300x^8}}$

Then,

$= {\dfrac{27x^{12}}{300x^8}}\\\\ = \dfrac{3\times 3\times 3 \times x^{8} \times x^{4}}{3 \times 100\times x^8}}\\\\=\dfrac{9\times x^4}{100}$

Hence, the required expression is $\rm \dfrac{9\times x^4}{100}$ .

To know more about Expression click the link given below.

brainly.com/question/16179118

8 0

3 years ago

Is 13/16 a real number

tamaranim1 [39]

Yeah it is 13/16 is a real number

3 0

1 year ago

A highway engineer knows that his crew can lay 5 miles of highway on a clear day, 2 miles on a rainy day, and only 1 mile on a s

lesya692 [45]

Answer:

Mean = 3.7

Variance = 2.61

Step-by-step explanation:

From the data given; we can represent our table into table format for easier solution and better understanding.

Given that:

A highway engineer knows that his crew can lay 5 miles of highway on a clear day, 2 miles on a rainy day, and only 1 mile on a snowy day

Let X represent the crew;

P(X) represent their respective probabilities

clear day rainy day snowy day

X 5 2 1

P(X) 0.6 0.3 0.1

From Above; we can determine our X*P(X) and X²P(X)

Let have the two additional columns to table ; we have

X P(X) X*P(X) X²P(X)

5 0.6 3 15

2 0.3 0.6 1.2

1 0.1 0.1 0.1

Total 1.0 3.7 16.3

The mean $\mu$ can be calculated by using the formula:

$\sum \limits ^n _{i=1}X_i P(X_i)$

Therefore ; mean $\mu$ = 3.7

Variance $\sigma^2 = \sum \limits ^n _{i=1}X^2_i P(X_i)- \mu^2$

Variance = 16.3 -3.7²

Variance = 16.3 - 13.69

Variance = 2.61

4 0

4 years ago