Answer:
f(x) + g(x) = 3x + 7
Step-by-step explanation:
f(x) = 2x + 2, g(x) = x + 5
f(x) + g(x) = 2x + 2 +x + 5
f(x) + g(x) = 2x +x + 5 +2
f(x) + g(x) = 3x + 7
The formula in getting the arithmetic sequence:
an = a1<span> + (n – 1)d.
</span>
We can substitute the values in order for us to know how many terms the sequence has.
an = 7373
a1 = 1313
d = 303
an = a1<span> + (n – 1)d
</span>7373 = 1313 + (n-1) 303
7373 = 1313 + 303n - 303
-303n = 1313 - 303 - 7373
303n = -1313 + 303 + 7373
303n = 6363
n = 21
So, there are 21 terms in the sequence given.
<span>
6 Find an exact value. sin 75°
</span>sin(A+B)=sin(A)cos(B)+cos(A)sin<span>(B)
</span>sin(45)=cos(45)=(2^0.5)/2 sin(30)=0.5 cos(30)=(3^0.5)/2
sin(45+30)=sin(45)cos(30)+cos(45)sin(30)=(6^0.5+2^0.5)/4
the answer is the letter d) quantity square root of six plus square root of two divided by four.
<span>
7. Find an exact value. sine of negative eleven pi divided by twelve.
</span>sin(-11pi/12) = -sin(11pi/12) = -sin(pi - pi/12) = -sin(pi/12) = -sin( (pi/6) / 2)
= - sqrt( (1-cos(pi/6) ) / 2) = -sqrt( (1-√3/2) / 2 ) = -(√3-1) / 2√2=(√2-√6)/4
the answer is the letter c) quantity square root of two minus square root of six divided by four.
<span>
8. Write the expression as the sine, cosine, or tangent of an angle. sin 9x cos x - cos 9x sin x
</span>
sin(A−B)=sinAcosB−cosAsinB
sin(9x−x)= sin9xcosx−cos9xsinx= sin(8x)
the answer is the letter c) sin 8x
<span>
9. Write the expression as the sine, cosine, or tangent of an angle. cos 112° cos 45° + sin 112° sin 45°</span>
cos(A−B)=cosAcosB<span>+sinA</span>sinB
cos(112−45)=cos112cos45<span>+sin112</span>sin45=cos(67)
the answer is the letter d) cos 67°
10. Rewrite with only sin x and cos x.
sin 2x - cos 2x
sin2x =
2sinxcosx<span>
cos2x = (cosx)^2 - (sinx)^2 = 2(cosx)^2 -1 = 1- 2(sinx)^2</span>
sin2x- cos2x=2sinxcosx-(1- 2(sinx)^2=2sinxcosx-1+2(sinx)^2
sin2x- cos2x=2sinxcosx-1+2(sinx)^2
<span>
the answer is the letter <span>
b) 2 sin x cos2x - 1
+ 2 sin2x</span></span>
Answer:
x=5
Step-by-step explanation:
2(x+4)+2x+3=3x+16
One solution was found :
x = 5
Answer: The TV is 48 inches wide.
Step-by-step explanation: To find the solution to this equation we must use the Pythagorean theorem. The Py. Theo. is basically the formula :
a^2 + b^2 = c^2 You say this as "A squared plus b squared equals c squared"
To use this formula you must plug in the given values of a and b, to find c. A and b represent the two bases of the triangle, while c is the hypotenuse. In this equation we already have the value of c and a. We need to find b, but in order to do that we use a different formula. We use : c^2 - a^2 = b^2
See :
52^2 - 20^2 = b^2 *The ^2 means "to the power of" aka an exponent*
2704 - 400 = b^2 *When dealing with ^2, all you do is multiply the number by itself*
2304 = b^2 *Next, we find the square root of our current number.*
48 = b
*Another way to solve this equation is to memorize all the Pythagorean Triples. With that knowledge, you wont even need to use the formula because you will already know all three values. I hope this helped you understand :)
