Answer:
2(2 +5)
Step-by-step explanation:
We presume you want to rewrite the expression making use of the distributive property. For that, it is helpful to find a factor common to the two terms. The GCD of 4 and 10 is 2, so we can factor that out:
4 + 10 = 2(2 +5)
_____
Of course, you can use any factor you like. It doesn't need to be an integer.
= (1/3)(12 +30)
= 0.4(10 +25)
= 4(1 +2.5)
Ratio of girls : boys = 5 : 4
<u>Find total parts:</u>
Total parts = 5 + 4 = 9
<u>Find 1 part:</u>
9 parts = 36
1 part = 36 ÷ 9 = 4
<u>Find 5 parts (Girls):</u>
Girls = 5 parts = 4 x 5 = 20
Answer: There are 20 girls.
Answer:
(a) (x+1)(x-1)
(b)(3x+1)(3x-1)
(c) (x+3)(x+5)
(d)(2x+5)(2x+3)
(e)(x+y)(x-y)
(f) 
Step-by-step explanation:
We have to factorize the following expressions:
(a) x²-1 =(x+1)(x-1) (Answer) {Since we know the formula (a²-b²) =(a+b)(a-b)}
(b) 9x²-1 =(3x+1)(3x-1) (Answer) {Since we know the formula (a²-b²) =(a+b)(a-b)}
(c) x²+8x+15 = x² +3x+5x+15 =(x+3)(x+5) (Answer)
(d) 4x²+16x+15 =4x²+10x+6x+15 = 2x(2x+5) +3(2x+5) =(2x+5)(2x+3) (Answer)
(e) x²-y² =(x+y)(x-y) (Answer)
(f) 
(Answer) {Since we know the formula (a²-b²) =(a+b)(a-b)}
Answer:
x=1/2
Step-by-step explanation:
Find, correct to the nearest degree, the three angles of the triangle with the vertices d(0,1,1), e( 2, 4,3) − , and f(1, 2, 1)
Ksju [112]
Well, here's one way to do it at least...
<span>For reference, let 'a' be the side opposite A (segment BC), 'b' be the side opposite B (segment AC) and 'c' be the side opposite C (segment AB). </span>
<span>Let P=(4,0) be the projection of B onto the x-axis. </span>
<span>Let Q=(-3,0) be the projection of C onto the x-axis. </span>
<span>Look at the angle QAC. It has tangent = 5/4 (do you see why?), so angle A is atan(5/4). </span>
<span>Likewise, angle PAB has tangent = 6/3 = 2, so angle PAB is atan(2). </span>
<span>Angle A, then, is 180 - atan(5/4) - atan(2) = 65.225. One down, two to go. </span>
<span>||b|| = sqrt(41) (use Pythagorian Theorum on triangle AQC) </span>
<span>||c|| = sqrt(45) (use Pythagorian Theorum on triangle APB) </span>
<span>Using the Law of Cosines... </span>
<span>||a||^2 = ||b||^2 + ||c||^2 - 2(||b||)(||c||)cos(A) </span>
<span>||a||^2 = 41 + 45 - 2(sqrt(41))(sqrt(45))(.4191) </span>
<span>||a||^2 = 86 - 36 </span>
<span>||a||^2 = 50 </span>
<span>||a|| = sqrt(50) </span>
<span>Now apply the Law of Sines to find the other two angles. </span>
<span>||b|| / sin(B) = ||a|| / sin(A) </span>
<span>sqrt(41) / sin(B) = sqrt(50) / .9080 </span>
<span>(.9080)sqrt(41) / sqrt(50) = sin(B) </span>
<span>.8222 = sin(B) </span>
<span>asin(.8222) = B </span>
<span>55.305 = B </span>
<span>Two down, one to go... </span>
<span>||c|| / sin(C) = ||a|| / sin(A) </span>
<span>sqrt(45) / sin(C) = sqrt(50) / .9080 </span>
<span>(.9080)sqrt(45) / sqrt(50) = sin(C) </span>
<span>.8614 = sin(C) </span>
<span>asin(.8614) = C </span>
<span>59.470 = C </span>
<span>So your three angles are: </span>
<span>A = 65.225 </span>
<span>B = 55.305 </span>
<span>C = 59.470 </span>
