Answer:
Step-by-step explanation:
1. Height of the equilateral triangle = a√3/2
8√3/2=4√3=6.9
2. 60 (equilateral triangle means all three sides and angles are equal)
First you need to use the distributive property: 27(x+4)=-6
27x+108=-6
then you need to subtract 108 from -6 to
get x alone. 27x= 102
Lastly divide 102 by 27 to finally get x alone: x=3.777
the answer would be: x= 3.77 or 3.8
Answer:
The amount received after 5 years is 1827.39
Step-by-step explanation:
The amount received by Bridget from his grandfather as the birthday gift = 1400
.
Since he wants to deposit it and save for college, he earns interest rate = 5.4%
He deposited this money for the years = 5 years.
Here, the Present value (PV) is = 1400
Interest rate ( r ) = 5.4% or 0.054
Since the interest rate is compounded semi annually, So, n = 10
Now if we calculate the future value of 1400 with interest rate 5.4 percent:
Therefore, 1827.39 will be the total money in his account after five years.
The value of 'x' is 24.2 and the value of 'y' is 46.5.
To solve this, we do the following steps.
<u>Step 1:</u> Divide 'y' into 2 parts, 'a' and 'b'. 'a' would be the lower leg of the 45°-45°-90° triangle, while 'b' is the lower leg of the 30°-60°-90° triangle.<em>
</em><u>Step 2:</u> Given the hypotenuse (34) of the 30°-60°-90° triangle, solve for 'b' using the cosine of 30°.
cos30° = b/34 [adjacent over hypotenuse]
b = 34cos30° [cross-multiply]
b = 29.4
<u>Step 3:</u> Solve for the 90° leg (the side opposite the 30° angle) using the Pythagorean Theorem. We will name this leg "h" (cuz height).
l² + l² = hyp²
29.4² + h² = 34²
h² = 1156 - 864.36
√h² = √291.64
h = 17.1
<u>Step 4:</u> Solve for 'x' by using the 45°-45°-90° triangle ratio (1:1:√2). √2 would be the hypotenuse of the 45°-45°-90° triangle, while 1 would be both congruent legs.
Side 'h' is one of the legs; side 'a' is the other. Since these legs are congruent, 'a' also measures 17.1. Now all we need to do is solve for 'x', which is our hypotenuse. To do this, we simply multiply the measure of side 'h' or 'a' by √2.
x = 17.1 × √2
x = 24.2
<u>Step 5:</u> Now that we got the value of 'x', solve for 'y' by adding the measures of sides 'a' and 'b' together.<em>
</em><u /> y = a + b
y = 17.1 + 29.4
y = 46.5
And there you have it! <em>Hope this helps.</em>
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Answer: the first one
Step-by-step explanation: just trust me ;)
