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State the nth term of the following sequence: 3, 7, 11, 15, 19

First we look at the jump between each term:7-3=4, 11-7=4, 15-11=4, 19-15=4So we know that the difference in each step is 4. So our expression with look like 4n+d for some number d.Comparing what we have wit...
HD
Answered by Huw D. • Maths tutor
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The equation (k+3)x^2 + 6x + k =5 has two distinct real solutions for x. Prove that k^2-2k-24<0

We argue using the discriminant of a quadratic polynomial. For a quadratic ax^2 + bx + c=0, the discriminant D is D = b^2 - 4ac. When this quadratic has two distinct real roots, we have that D &gt; 0. So we ...
HD
Answered by Huw D. • Maths tutor
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I don't understand why the function "f(x)=x^2 for all real values of x" has no inverse. Isn't sqrt(x) the inverse?

I don't understand why the function &quot;f(x)=x^2 for all real values of x&quot; has no inverse. Isn't sqrt(x) the inverse? I like to think of a function a bit like a machine. It takes in a number, and turn...
BM
Answered by Benjamin M. • Maths tutor
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x^2-9x+20=0

x 2 -9x+20=0x 2 -5x-4x+20=0x(x-5)-4(x-5)=0(x-4)(x-5)=0x-4=0x=4x-5=0x=5
GL
Answered by Georgia L. • Maths tutor
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Solve these simultaneously to find values for a and b: 6a + b = 16 and 5a - 2b = 19

In order to tackle questions like this with two letters of unknown value, first what we try to do is eliminate one of the variables completely from an equation. If we call 6a + b = 16 eqn 1 and 5a - 2b = 19 ...
MP
Answered by Malvika P. • Maths tutor
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