Q.13 is no solution since the y intercept of the 2 equation differ but gradient is the same therefore if you were to draw a graph there wont be any intersection between the equations
the next question's answer is no solution
Answer:
Answers: 46, 23, and 111
Step-by-step explanation:
To answer, we need to know the angles. Therefore, give each angle a name. Angle 1 will be x, 2 will be y, 3 will be z. So, using this system of equations:
x=2y
z=y+88
x+y+z=180
Substituting, z = 1/2(x)+88, now plug z into the third equation:
x+1/2(x)+1/2(x)+88=180
this simplifies to 2x+88=180
subtracting 88 from both sides leaves 2x=92
x=46
plug this in to the first equation: 46 = 2y, so y = 23
plug this into the third one leaves z = 111
Hope this helps!
Answer:
225
Step-by-step explanation:
The sum of this series is given by the formula:
![S_n=\frac{n}{2}[2a+(n-1)d]](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D)
Where
S_n is the sum
a is the first term (we get this by plugging in n = 1 into "2n-1", we have 2(1) - 1 = 1)
n is the number of terms (the sum is defined for n = 1 to n = 15, so 15 terms)
d is the common different (the difference is successive terms. Here, 2nd term would be 2(2) - 1 = 3, and first term was 1, so d = 3 -1 = 2)
<em>plugging in the info, we will get the sum:</em>
<em>![S_n=\frac{n}{2}[2a+(n-1)d]\\S_{15}=\frac{15}{2}[2(1)+(15-1)(2)]\\=225](https://tex.z-dn.net/?f=S_n%3D%5Cfrac%7Bn%7D%7B2%7D%5B2a%2B%28n-1%29d%5D%5C%5CS_%7B15%7D%3D%5Cfrac%7B15%7D%7B2%7D%5B2%281%29%2B%2815-1%29%282%29%5D%5C%5C%3D225)
</em>
<em>The sum is 225</em>
<span>y= 2x ^2 - 8x +9
</span>y = a(x - h)2 + k, where (h, k) is the vertex<span> of the parabola
</span>so
y= 2x ^2 - 8x + 9
y= 2x ^2 - 8x + 8 + 1
y = 2(x^2 - 4x - 4) + 1
y = 2(x - 2)^2 + 1 ....<---------<span>vertex form</span>
Answer:
12
Step-by-step explanation:
First, you will have to use trigonometry. Since the side of the triangleis the opposite of the angle 53 and the hypotenuse, you will use sin.
Sin 53 degrees = opposite side / hypotenuse side.
The opposite side is x and the hypotenuse side equals 15.
sin53= x/15
15 ( sin 53 ) =x
x= 11.97953
Round
x=12
