Answer: The answer is x = 6 units.
Step-by-step explanation: Please refer to the attached diagram
The diagram in the question shows two triangles placed on each other and for convenience sake has been labelled ABDCE. Triangle ABC is a right angled triangle, and so is triangle ADE. From the marks on the lines, we can infer that line AD is equal in measurement to line DB. Also line AE is equal in measurement to line EC.
Therefore we can see the similarity in both triangles, if AD and AE equals DB and EC, then it follows that DE equals BC.
Hence if AD = DB and
AE = EC, and
DE = BC
Then, x - 3 = ½x
(½x can also be expressed as x/2)
x - 3 = x/2
By cross multiplication we now have
2(x - 3) = x
2x - 6 = x
By collecting like terms we now have
2x - x = 6
x = 6
Answer: 232 pages
Step-by-step explanation:
Total digits = 588
1 digit page number:
1 to 9 = 1 × 9 = 9
Number of pages = 9/1 = 9
2 - digit page number :
10 - 99 = 2 × 90 = 180
Number of pages = 180/2 = 90
3 - digit page number :
588 - (9 + 180) = 588 - 189 = 399
Number of pages with 3 - digits = 399/3 = 133
Therefore, the total number of pages the book has is :
(9 + 90 + 133) = 232 pages
Answer:
(D) -k2 + k - 13
Step-by-step explanation:
Pulling out like terms :
2.1 Pull out like factors :
-k2 + k - 13 = -1 • (k2 - k + 13)
Trying to factor by splitting the middle term
2.2 Factoring k2 - k + 13
The first term is, k2 its coefficient is 1 .
The middle term is, -k its coefficient is -1 .
The last term, "the constant", is +13
Step-1 : Multiply the coefficient of the first term by the constant 1 • 13 = 13
Step-2 : Find two factors of 13 whose sum equals the coefficient of the middle term, which is -1 .
-13 + -1 = -14
-1 + -13 = -14
1 + 13 = 14
13 + 1 = 14
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
-k2 + k - 13
Processing ends successfully
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So point slope form is y=mx+b where m=slope and b=y intercept so
in (x,y) form
one solution is x=1 and y=3, also slope is 2 so
m=2
subsitute
3=2(1)+b
3=2+b
subtract 2
1=b
equation is
y=2x+1
tricky answers so simplify them
A: y-1=2(x-3)
distribute
y-1=2x-6
add 1
y=2x-5
not the answer
B: y-3=2(x-1)
distribute
y-3=2x-2
add 3
y=2x+1
correct
the answer is B
