Answer:
a. x = 24
b. x = 40
Step-by-step explanation:
a.
You are given a right triangle, so use the Pythagorean theorem
a^2 + b^2 = c^2
x^2 + 18^2 = 30^2
x^2 + 324 = 900
x^2 = 576
x = 24
b.
The sum of the measures of all angles is 360 degrees.
x + 2x + 2x + 20 + 3x + 20 = 360
8x + 40 = 360
8x = 320
x = 40
ANSWER
EXPLANATIONSolve for x, noting that scalar multiplication on matrices is distributive:
Note that
and
Therefore, since we add corresponding entries with matrix addition:
Answer:
5.57 feet
Step-by-step explanation:
In this problem, the light string, the height of the mast and the distance between the base of the mast and the end of the string form a right triangle, in which:
- The hypothenuse is the string
- The height is the mast
- The base is the distance between the base of the mast and the end of the light string
Here in this problem, we have:
(length of the string, hypothenuse)
(height of the mast, height)
So we can find the distance between the base of the mast and the end of the string just by applying Pythagorean's theorem:
the answer is (1+0.14/12)^(12))-1)*100=14.9% hope this helps u out
We have that
Part 1.] Match the following items.
1. 2, 4, 8, 16, . . ., 64---------- > <span>B. finite sequence
</span>2. 3, 6, 9, 12, . . . ------------- > <span>C. infinite sequence
</span>3. 3 + 9 + 27 + 81 + . . .------> <span>D. geometric series
</span>4. 3 + 5 + 7 + 9 + . . .----------> A. arithmetic series
5. 3, -3, 3, -3, 3,-3, . . .-------- ><span>E. alternating sequence
</span><span>
</span><span>Part 2.]-3, 6, -9, 12, -15, . . .
Which of the following represents the general term for the sequence given?
</span>A. (-1^n)*(3^n)
for n=1-----------> (-1^1)*(3^1)=-3
for n=2-----------> (-1^2)*(3^2)=9 -------------- a2=6 no represents
B. (-1^n)*(3n)
for n=1-----------> (-1^1)*(3*1)=-3
for n=2-----------> (-1^2)*(3*2)=6
for n=3-----------> (-1^3)*(3*3)=-9
for n=4-----------> (-1^4)*(3*4)=12
for n=5-----------> (-1^5)*(3*5)=-15
C. (-1^(n+1))*(3)
for n=1-----------> (-1^(1+1))*(3)=3---------- > a1=-3 no represents
the answer part B is option B. (-1^n)*(3n)
Part 3.] The first attached picture
Σ (2n+1) for n=1 to 5
n1---------> (2*1+1)=3
n2---------> (2*2+1)=5
n3---------> (2*3+1)=7
n4---------> (2*4+1)=9
n5---------> (2*5+1)=11
Σ (2n+1) for n=1 to 5=[3+5+7+9+11]=35
the answer part C is 35
Part 4.] The second attached picture
Σ (3n) for n=1 to 3
n1---------> (3*1)=3
n2---------> (3*2)=6
n3---------> (3*3)=9
Σ (3n) for n=1 to 3=[3+6+9]=18
the answer part 4 is 18
Part 5.] The third attached picture
Σ (2n+2) for n=1 to 4
n1---------> (2*1+2)=4
n2---------> (2*2+2)=6
n3---------> (2*3+2)=8
n4---------> (2*4+2)=10
Σ (2n+2) for n=1 to 4=[4+6+8+10]=28
the answer part 5 is 28
<span>Part 6.] Which of the following best describes the following set of numbers?
6+8+10+12+...+(4+2n)+...
8-6=2
10-8=2
12-10=2
</span><span>the next number is obtained by adding 2 to the previous number
</span>this is an Arithmetic Series
the answer is the option D. Arithmetic Series