MATHEMATICS HIGH SCHOOL

If h(x) = x − 1 and j(x) = −4x, solve h[j(5)] and select the correct answer below.−21
−20
−19
−16

Answers

Answer 1

Answer:

Answer:

Option A is correct

$h[j(5)] = -21$

Step-by-step explanation:

Given the functions:

$h(x) = x-1$ and

$j(x) = -4x$

Find the value of $h[j(5)]$

$h[j(x)]$

⇒ $h[-4x]$

Replace x with -4x in h(x) we have;

$h[j(x)] = -4x-1$

Substitute x = 5 we have;

$h[j(5)] = -4(5)-1$

⇒ $h[j(5)] = -20-1=-21$

Therefore, the value of $h[j(5)]$ is, -21

Answer 2

Answer: -21. J(x)= -4(5)= -20 ; H[J(5)]= -20-1 = -21

Answer:

The correct representation of the expression are:

$(x+4)/(3)((x)/(6))$

$((x)/(6))(x+4)/(3)$

$(x^2+4x)/(18)$

Step-by-step explanation:

We are given an algebraic expression as:

$(x+4)/(3)$ ÷ $(6)/(x)$

This expression could also be written as:

$=((x+4)/(3))/((6)/(x))$

We know that any expression of the form:

$((a)/(b))/((c)/(d))$ is given by:

$((a)/(b))/((c)/(d))=(a* d)/(b* c)}$

Hence, we get the given expression as:

$=((x+4)/(3))/((6)/(x))=((x+4)* x)/(3* 6)\n\n=(x+4)/(3)* (x)/(6)$

Also, on solving we get:

$=((x+4)/(3))/((6)/(x))=(x^2+4x)/(18)$

A spin balancer rotates the wheel of a car at 500 revolutions per minute. If the diameter of the wheel is 26 inches, what road speed is being tested?a. 26 rad/s
b. 3.2 rad/s
c. 52 rad/s
d. 81 rad/s

Answers

Answer:

c. 52 rad/s

Step-by-step explanation:

Final question does not correspond with available option. The real question is: What is the angular speed in radians per second?

At first we assume that spin balance rotates at constant rate and convert given angular speed, measured in revolutions per minute, into radians per second:

$\omega = \left(500\,(rev)/(min) \right)\cdot \left(2\pi\,(rad)/(rev) \right)\cdot \left((1)/(60)\,(min)/(sec) \right)$

$\omega \approx 52.360\,(rad)/(s)$

Which corresponds to option C.

The wheel rotates at an angular speed of 52 rad/s and the equivalent road speed is about 39 mph.

To solve this, we need to consider the given spin speed which is 500 revolutions per minute and convert this to rev per second by dividing by 60.

This is because a minute has 60 seconds.

Hence, the wheel rotates at 500/60 = 8.33 rev/s.

Furthermore, we need to know that in physics, one full revolution equals 2π radians (this is the equivalent of going around a circle once).

So, to convert from revolution to radian, we multiply by 2π, so the wheels is spinning at 8.33 * 2π ≈ 52.36 rad/s, which most closely matches option c. 52 rad/s.

Lastly, the linear (or road) speed can be calculated by multiplying the Angular momentum by the radius of the wheel (which is half the diameter), so v = (52.36 rad/s) * (13 in) = 680.68 in/s.

To convert it to mph, note that 1 inch/s = 0.057 mph, hence the wheel is spinning at about 39 mph.

Learn more about Angular momentum here:

brainly.com/question/37906446

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Johnny heads to the store with $20. He spends $7 on a t-shirt, then buys some candy bars for $1.50 each. How many candy bars could he buy if he spent all of his money?