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3 years ago

How to expand and simplify 5(3p+2)-2(5p-3)

2 answers:

7 0

$5(3p+2) -2(5p-3) \\ \\ 15p + 10 - 10p + 6 \\ \\ (15p - 10p) + 10 + 6 \\ \\ 5p + 10 + 6 \\ \\ 5p + 16 \\ \\ Answer: \fbox {5p + 16}$

Luda [366]3 years ago

5 0

5(3p+2) - 2(5p-3) Distribute the 5 and the 2
(5*3p) + (5*10) + (-2*5p) + (-2*-3)
15p + 50 - 10p + 6 Combine like terms
5p + 56

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In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 3.0 m/s up a 22.0° inclined track

Aloiza [94]

Answer:

Approximately $0.31\; \rm m$ , assuming that $g = 9.81\; \rm N \cdot kg^{-1}$ .

Step-by-step explanation:

Initial kinetic energy of the sled and its passenger:

$\begin{aligned}\text{KE} &= \frac{1}{2}\, m \cdot v^{2} \\ &= \frac{1}{2} \times 14\; \rm kg \times (3.0\; \rm m\cdot s^{-1})^{2} \\ &= 63\; \rm J\end{aligned}$ .

Weight of the slide:

$\begin{aligned}W &= m \cdot g \\ &= 14\; \rm kg \times 9.81\; \rm N \cdot kg^{-1} \\ &\approx 137\; \rm N\end{aligned}$ .

Normal force between the sled and the slope:

$\begin{aligned}F_{\rm N} &= W\cdot \cos(22^{\circ}) \\ &\approx 137\; \rm N \times \cos(22^{\circ}) \\ &\approx 127\; \rm N\end{aligned}$ .

Calculate the kinetic friction between the sled and the slope:

$\begin{aligned} f &= \mu_{k} \cdot F_{\rm N} \\ &\approx 0.20\times 127\; \rm N \\ &\approx 25.5\; \rm N\end{aligned}$ .

Assume that the sled and its passenger has reached a height of $h$ meters relative to the base of the slope.

Gain in gravitational potential energy:

$\begin{aligned}\text{GPE} &= m \cdot g \cdot (h\; {\rm m}) \\ &\approx 14\; {\rm kg} \times 9.81\; {\rm N \cdot kg^{-1}} \times h\; {\rm m} \\ & \approx (137\, h)\; {\rm J} \end{aligned}$ .

Distance travelled along the slope:

$\begin{aligned}x &= \frac{h}{\sin(22^{\circ})} \\ &\approx \frac{h\; \rm m}{0.375}\end{aligned}$ .

The energy lost to friction (same as the opposite of the amount of work that friction did on this sled) would be:

$\begin{aligned} & - (-x)\, f \\ = \; & x \cdot f \\ \approx \; & \frac{h\; {\rm m}}{0.375}\times 25.5\; {\rm N} \\ \approx\; & (68.1\, h)\; {\rm J}\end{aligned}$ .

In other words, the sled and its passenger would have lost (approximately) $((137 + 68.1)\, h)\; {\rm J}$ of energy when it is at a height of $h\; {\rm m}$ .

The initial amount of energy that the sled and its passenger possessed was $\text{KE} = 63\; {\rm J}$ . All that much energy would have been converted when the sled is at its maximum height. Therefore, when $h\; {\rm m}$ is the maximum height of the sled, the following equation would hold.

$((137 + 68.1)\, h)\; {\rm J} = 63\; {\rm J}$ .

Solve for $h$ :

$(137 + 68.1)\, h = 63$ .

$\begin{aligned} h &= \frac{63}{137 + 68.1} \approx 0.31\; \rm m\end{aligned}$ .

Therefore, the maximum height that this sled would reach would be approximately $0.31\; \rm m$ .

7 0

3 years ago

Connor wants to attend the town carnival. The price of admission to the

Vesna [10]

Answer:

14 rides

Step-by-step explanation:

16 = 0.79x + 4.5

11.5 = 0.79x

x = 14.55 or 14

rounding down because it can't go over $16.

0.79(14) + 4.5 = $15.56

7 0

3 years ago

Distributive property to expand -1/6(5x-12)

castortr0y [4]

Answer:

-5/6x+2

Step-by-step explanation:

hope that helps

3 0

3 years ago

Please help!!!!!!!!!!!! Will mark brainliest

Sauron [17]

Answer:

○ $\displaystyle 25$

Step-by-step explanation:

$\displaystyle 4 = 2\sqrt{25} - 6 \\ 4 = 2[5] - 6 \\ \\ 4 = 10 - 6$

I am joyous to assist you at any time.

3 0

2 years ago

Reduce to simplest form. -3/5 + (-8/2) =

Dominik [7]

Answer:

The answer is -4 3/5

Step-by-step explanation:

Let's reduce to its simplest form:

-3/5 + (-8/2) =

Step 1: Lowest Common Denominator (10):

- 6/10 + (-40/10) =

Step 2: Solve the parentheses:

- 6/10 - 40/10 =

Step 3: Subtract the fractions:

-46/10

Step 4: Simplify (Dividing by 2):

-23/5

Step 5: Converting the fraction to mixed number:

-4 3/5

The answer is -4 3/5

3 0

3 years ago