Expression a 4 x (1.5 + 100.25 x 3.65) expression b x (1.5 + 100.25) x 3.65

It is now 3:15 pm. Is it possible to drive 135 miles and arrive before 5:00 pm if ypu drove 55 mph? Explain your answer

Troyanec [42]

Well, how long will it take you to drive 135 miles at 55mph?

at 55 mph, you're doing 55 miles every hour, so we can simply get the quotient of 135/55 and that's how many hours it'll take you to drive 135 miles at that speed.

$\bf \cfrac{135}{55}\implies \cfrac{27}{11}\implies 2\frac{5}{11}~hours\implies \textit{about 2hrs, 27 minutes}$

so, it takes you that long, however, from 3:15 to 5:00pm there are only 45mins + 60mins or 1hr and 45 minutes, namely 1¾ hr.

so 2hrs and 27 minutes is much later than 1¾ hr, so, no dice, you can't arrive at 5pm, actually you'll arrive around 5:42pm.

6 0

3 years ago

Read 2 more answers

F(x)= x+4; D: {-5, -3, 0, 4}

Vika [28.1K]

Step-by-step explanation:

-5+4=-1

-3+4=1

0+4=4

4+4=8

6 0

3 years ago

What is 7(-h -3) = -3(-h+4) what does it equal

prohojiy [21]

Answer: 4

Step-by-step explanation:

4 0

3 years ago

Solve the equation by graphing. If exact roots cannot be found, state the consecutive integers between which the roots are locat

zavuch27 [327]

Answer:

The equation contains exact roots at x = -4 and x = -1.

See attached image for the graph.

Step-by-step explanation:

We start by noticing that the expression on the left of the equal sign is a quadratic with leading term $x^2$ , which means that its graph shows branches going up. Therefore:

1) if its vertex is ON the x axis, there would be one solution (root) to the equation.

2) if its vertex is below the x-axis, it is forced to cross it at two locations, giving then two real solutions (roots) to the equation.

3) if its vertex is above the x-axis, it will not have real solutions (roots) but only non-real ones.

So we proceed to examine the vertex's location, which is also a great way to decide on which set of points to use in order to plot its graph efficiently:

We recall that the x-position of the vertex for a quadratic function of the form $f(x)=ax^2+bx+c$ is given by the expression: $x_v=\frac{-b}{2a}$

Since in our case $a=1$ and $b=5$ , we get that the x-position of the vertex is: $x_v=\frac{-b}{2a} \\x_v=\frac{-5}{2(1)}\\x_v=-\frac{5}{2}$

Now we can find the y-value of the vertex by evaluating this quadratic expression for x = -5/2:

$y_v=f(-\frac{5}{2})\\y_v=(-\frac{5}{2} )^2+5(-\frac{5}{2} )+4\\y_v=\frac{25}{4} -\frac{25}{2} +4\\\\y_v=\frac{25}{4} -\frac{50}{4}+\frac{16}{4} \\y_v=-\frac{9}{4}$

This is a negative value, which points us to the case in which there must be two real solutions to the equation (two x-axis crossings of the parabola's branches).

We can now continue plotting different parabola's points, by selecting x-values to the right and to the left of the $x_v=-\frac{5}{2}$ . Like for example x = -2 and x = -1 (moving towards the right) , and x = -3 and x = -4 (moving towards the left.

When evaluating the function at these points, we notice that two of them render zero (which indicates they are the actual roots of the equation):

$f(-1) = (-1)^2+5(-1)+4= 1-5+4 = 0\\f(-4)=(-4)^2+5(-4)_4=16-20+4=0$

The actual graph we can complete with this info is shown in the image attached, where the actual roots (x-axis crossings) are pictured in red.

Then, the two roots are: x = -1 and x = -4.

5 0

3 years ago

My cupcake recipe makes 12 cupcakes and requires 3/2 sticks of butter. I can only buy whole sticks of butter. How many whole sti

Alex

We find out the ratio 100: 12= 25/3
We need the number of <span>sticks of butter: 25/3 x 3/2= 25/2=12.5
That means you must buy 13 </span><span>sticks of butter
Have fun</span>

3 0

3 years ago