Drag the blue movable points to produce a graph that correctly represents the inequality

Triple a number, x, increased by 1 is between -20 and 10. What are the solutions for x?

Bumek [7]

Hello,
$-20 \leq 3x+1 \leq 10\\
\Rightarrow\ -21 \leq 3x \leq 9\\
\Rightarrow\ -7 \leq x \leq 3\\

Sol=[-7\ 3]\ if\ x\ is\ a\ real.
$

3 0

3 years ago

HELP!!!!!! I believe its B but I am not sure! :(

n200080 [17]

Answer:

A

Step-by-step explanation:

When solving for x as an exponent, we need to use logarithms in order to undo the operation and rearrange the terms. We use log rules to bring down the exponent and solve. Logarithms are the inverse operations to exponents and vice versa. We have one special kind of logarithm called the natural logarithm whose base is e. We write it as ln. Since our base is e here, we will use the natural logarithm to rearrange and isolate x.

$e^{4x-1} =3$

We begin by applying the natural logarithm to each side.

$ln(e^{4x-1}) =ln(3)$

Log rules allow use to rearrange the exponent as multiplication in front of the log.

$(4x-1)ln(e) =ln(3)$

ln e as an inverse simplifies to 1.

$(4x-1)(1)=ln(3)$

We now apply the inverse operations for subtraction and multiplication.

$4x-1+1=1+ln(3)\\4x=1+ln(3)\\\frac{4x}{4} =\frac{1+ln3}{4} \\x =\frac{1+ln3}{4}$

Option A is correct.

5 0

3 years ago

Mary got a sales job at her father's company. She was paid $9 per hour plus a 5%commission on her sales. Last week sheworked 40

horsena [70]

Answer:

Mary was paid $638

Step-by-step explanation:

Mary was paid 360 $ for working alone because

$40 * 9 = $360

Mary was paid $278

5 % * $5560 = $278

360 + 278 = 638 $

5 0

3 years ago

The liquid base of an ice cream has an initial temperature of 86°C before it is placed in a freezer with a constant temperature

Karolina [17]

The temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

From Newton's law of cooling, we have that

$T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$

Where

$(t) = \ time$

$T_{(t)} = \ the \ temperature \ of \ the \ body \ at \ time \ (t)$

$T_{s} = Surrounding \ temperature$

$T_{0} = Initial \ temperature \ of \ the \ body$

$k = constant$

From the question,

$T_{0} = 86 ^{o}C$

$T_{s} = -20 ^{o}C$

∴ $T_{0} - T_{s} = 86^{o}C - -20^{o}C = 86^{o}C +20^{o}C$

$T_{0} - T_{s} = 106^{o} C$

Therefore, the equation $T_{(t)}= T_{s}+(T_{0} - T_{s})e^{kt}$ becomes

$T_{(t)}=-20+106 e^{kt}$

Also, from the question

After 1 hour, the temperature of the ice-cream base has decreased to 58°C.

That is,

At time $t = 1 \ hour$ , $T_{(t)} = 58^{o}C$

Then, we can write that

$T_{(1)}=58 = -20+106 e^{k(1)}$

Then, we get

$58 = -20+106 e^{k(1)}$

Now, solve for $k$

First collect like terms

$58 +20 = 106 e^{k}$

$78 =106 e^{k}$

Then,

$e^{k} = \frac{78}{106}$

$e^{k} = 0.735849$

Now, take the natural log of both sides

$ln(e^{k}) =ln( 0.735849)$

$k = -0.30673$

This is the value of the constant $k$

Now, for the temperature of the ice cream 2 hours after it was placed in the freezer, that is, at $t = 2 \ hours$

From

$T_{(t)}=-20+106 e^{kt}$

Then

$T_{(2)}=-20+106 e^{(-0.30673 \times 2)}$

$T_{(2)}=-20+106 e^{-0.61346}$

$T_{(2)}=-20+106\times 0.5414741237$

$T_{(2)}=-20+57.396257$

$T_{(2)}=37.396257 \ ^{o}C$

$T_{(2)} \approxeq 37.40 \ ^{o}C$

Hence, the temperature of the ice cream 2 hours after it was placed in the freezer is 37.40 °C

Learn more here: brainly.com/question/11689670

6 0

2 years ago

Read 2 more answers

Find the area of the shape shown below.

maw [93]

Answer:

The area is 28.

Step-by-step explanation:

Visualize the rectangle as 2 split squares.

The top square is easily 4x4, so the area of that part is 16.

Now visualize the bottom square as two rectangles.

To find the area of the dented side, you would use the equation of finding the area of a triangle, a=(w x h) $\frac{1}{2}$ because the dented side is actually just one half of the rectangle on the other side.

Since it is the same height as the top square, but is 2 in width, it would be written as a=(2 x 4) $\frac{1}{2}$ . So the area of that part is 4, and the area of the other rectangle would be just 2 x 4 so it is 8.

Totaling these numbers, you get the area of the full rectangle.

8 0

4 years ago

Read 2 more answers