MATHEMATICS HIGH SCHOOL

Can you guys please help me solve these

Answers

Answer 1

Answer:

Answer:

See explanation below

Step-by-step explanation:

In all cases you need to isolate x on one side of the inequality symbol using inverse operations.

1.-

$15+x\leq -45\n15-15+x\leq -45-15\nx\leq -60$

where we subtracted from both side 15 in order to leave x by itself on the left.

2.-

$x-14>12\nx-14+14>12+14\nx>26$

where we added 14 in order to isolate x on the left

3.-

In this case we need to divide both sides by -5 in order to isolate the x which is being multiplied by the factor -5, but he have to recall that multiplying or dividing by a negative number changes the direction of the inequality symbol (in our case from < into > )

$-5x<35\n(-5\,x)/(-5) >(35)/(-5) \nx>-7$

4.-

$2x>-42\n(2\,x)/(2) >(-42)/(2) \nx>-21$

In this case we simply divide both sides by two, and there is no change in the direction of the inequality because the number we are using to divide is a positive number (2)

Related Questions

Find the -intercept and -intercept of the line.3x-7y=-21x-intercept y-intercept
Solve the equation 3(x+2)=5x-2
Write the equation y= 5x-11 in standard form
The point P(1,1/2) lies on the curve y=x/(1+x). (a) If Q is the point (x,x/(1+x)), find the slope of the secant line PQ correct to four decimal places for the following values of x: (1) .5 (2) .9 (3) .99 (4) .999 (5) 1.5 (6) 1.1 (7) 1.01 (8) 1.001
Jim has three times as many comic books as Charles. Charles has 2/3 as many books as Bob. Bob has 27 books. How many comic books does Jim have?

Prove that 2x^2+x+8>0 for all real values of x.

Answers

$y = 2x^2 + x + 8$ is a polynomial of even degree, with a positive $x^2$ coefficient, meaning that
- it will have exactly one turning point
- that turning point will be a minimum

So, if the y-coordinate of the turning point is positive, then this polynomial will be positive for all real values of x.

At a turning point, the gradient of y will be equal to 0. The gradient of y is given by
$\frac{\mathrm{d}y}{\mathrm{d}x} = 4x + 1$ .

To find the turning point, set this equal to 0 and solve for x:
$4x + 1 = 0 \implies x = -(1)/(4)$ .

Substituting this value into the equation gives
$y = 2(-(1)/(4))^2 + (-(1)/(4)) + 8 = (1)/(4) - (1)/(4) + 8 = 8 \ \textgreater \ 0$ .

Since the minimum point of the equation is greater than 0, the equation will be greater than 0 for all real values of x.

Please help me... I will crown you Brainlyest

Answers

Answer:

Step-by-step explanation:

it's a positive line so it's not A or B. C would be under 1 and the line is above 1 making it D

Answer:

b or c not sure which

Step-by-step explanation:

good luck rise/run so 2/3

Which expressions are equivalent to 16x4 − 64? Check all that apply. 16x4 + 16x – 16x – 64 16x4 – 8x – 8x – 64 (4x2 + 8)(4x2 – 8) 16(x2 + 2)(x2 – 2) 4(4x4 – 8)