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Phantasy [73]
3 years ago
14

Find the distance between the pair of points and then round your answer to the nearest tenth.

Mathematics
1 answer:
Travka [436]3 years ago
3 0

Answer:

d = 9.4 units (nearest tenth)

Step-by-step explanation:

Given the distance formula, d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}, distance between (-4, 5) and (4, 0) is calculated as follows:

Let (-4, 5) = (x_1, y_1)

(4, 0) = (x_2, y_2)

d = \sqrt{(4 - (-4))^2 + (0 - 5)^2}

d = \sqrt{(8)^2 + (- 5)^2}

d = \sqrt{64 + 25}

d = \sqrt{89}

d = 9.4 units (nearest tenth)

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Alex is creating an outdoor structure out of two 12 foot boards. The boards must have an angle of elevation
Whitepunk [10]

Answer:

5.0 ft - 5.6 ft

Step-by-step explanation:

Given that the structure is to be made using two 12 foot boards, then we expect the total perimeter to be equal to (2*12)= 24 ft.

Using the angle of elevation, 40° and the width of 8 ft then you can apply the formula for tangent of a triangle where ;

Tan α = opposite side length/adjacent length

Tan 40°= h/8

h= 8 tan 40° = 6.71 ft

Applying the cosine of an angle formula to find the length of the sliding side

Cosine β = adjacent length /hypotenuse

Cosine 40°= 8/ sliding side length

sliding side length = 8/cosine 40° =10.44 ft

Checking  the perimeter = 10.44 +8+6.71= 25.15 ft

This is more than the total lengths of the boards, so you need to adjust the height as;

24 - 18.44 = 5.56 ft ,thus the height should be less or equal to 5.56 ft

h≤ 5.6 ft

6 0
3 years ago
Which of the following fractions is equal to the repeating decimal 0.555
nataly862011 [7]

Answer:

5/9

Step-by-step explanation:

5/9 is 0.5 recurring

5 0
3 years ago
Read 2 more answers
In the interval 0 x 360 find the values of x for which cos x =0.7252
Sergeeva-Olga [200]

Answer:

x_1 = 43.5145\°

x_2 = 316.4855\°

Step-by-step explanation:

We have a positive value for the cosine of x, so we know that the value of x should be in the first quadrant (0 ≤ x ≤ 90) or in the fourth quadrant (270 ≤ x ≤ 360).

Now, let's find the value of x that gives cos(x) = 0.7252 using the inverse function of the cosine, that is, the arc cosine function.

The value of x can be calculated using:

x = arccos(0.7252)

Using this function in a calculator (you may find it as: cos^{-1}(x)), we have that:

x_1 = 43.5145\°

So this is the value of x in the first quadrant. To find the other value of x, in the fourth quadrant, that gives the same result, we just need to calculate 360° minus the value we found:

x_2 = 360\° - 43.5145\° = 316.4855\°

So the values of x are:

x_1 = 43.5145\°

x_2 = 316.4855\°

7 0
3 years ago
Properties of exponents<br> Rewrite the expression in the form b^n—— (b^2)^3/7
exis [7]

Answer:

b^{\frac{6}{7}}  is the required expression.

Step-by-step explanation:

(b^2)^{\frac{3}{7}}\\\\\mathrm{Apply\:exponent\:rule:\:}\left(a^b\right)^c=a^{bc},\:\quad \mathrm{\:assuming\:}a\ge 0\\\\=b^{2\cdot \frac{3}{7}}\\\\=b^{\frac{6}{7}}

Best Regards!

3 0
3 years ago
What is the coefficient of the term 13a in the expression 13a+6b
il63 [147K]

Answer:

The coefficient of the term 13a is, 13

Step-by-step explanation:

Coefficient term are the numbers that multiply the variables or letters

In the given expression: 13a+6b

13a means 13 times a , and a is the variable,

so 13 is the coefficient .

6b means 6 times b , and b is the variable ,

so 6 is the coefficient .

therefore, the coefficient of the term 13a in the given expression is, 13.

5 0
3 years ago
Read 2 more answers
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