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3 years ago

81p² + 5 = 41 how do I solve by square roots

Mathematics

1 answer:

ycow [4]3 years ago

3 0

Answer:

p = ± $\frac{2}{3}$

Step-by-step explanation:

Given

81p² + 5 = 41 ( subtract 5 from both sides )

81p² = 36 ( divide both sides by 81 )

p² = $\frac{36}{81}$ ( take the square root of both sides )

p = ± $\sqrt{\frac{36}{81} }$

= ± $\frac{\sqrt{36} }{\sqrt{81} }$ = ± $\frac{6}{9}$ = ± $\frac{2}{3}$

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Can anyone help me?

ArbitrLikvidat [17]

Answer:

The factored form of 4m³ – 28m² – 120m is 4m(m – 10)(m + 3). The zeroes of the function would be m = 0, m = –3, and m = 10.

Step-by-step explanation:

I'll give this a shot.

4m³ – 28m² – 120m = 0 — The original expression

4m³ – 28m² – 120m — Did that 0 have any purpose? I just deleted it.

4(m³ – 7m² – 30m) — There's a common factor in here, 4. Let's pull that aside.

4m(m² – 7m – 30) — Actually, there's two common factors. The second one is m! Let's pull that out too!

To factor an expression, you have to break apart the middle term, so to speak. That's only possible if you can find two numbers whose product equals that of the outside terms and whose sum equals the middle term. Here, I'm just dealing with numbers and putting that variable aside.

–30 = 10 × –3

–30 = –10 × 3

–30 = –2 × 15

–30 = 2 × –15 — To solve for any potential factors, let's find all the numbers integers that multiply to –30

Now let's see which one adds up to –7!

15 – 2 = 13 — it's not this one

2 – 15 = –13 — nor this one

10 – 3 = 7 — we're pretty close! Let's switch that negative

3 – 10 = –7 — here we go! Here's our numbers!

4m[(m² – 10m) + (3m – 30)] — now we break apart the middle term. This is all multiplied by 4m, so that still encases everything with brackets.

4m[m(m – 10) + 3(m – 10)] — Factoring the two expressions

4m(m + 3)(m – 10) — simplifying to find our answer! Ta-da!

8 0

3 years ago

Mike and Kim invest $12,000 in equipment to print yearbooks for schools. Each yearbook costs $5 to print and sells for $15. How

UkoKoshka [18]

They must sell 1200 yearbooks to break even hope this helped

5 0

3 years ago

Hazel knits 5 centimeters of scarf eachnight. After 5 nights of knitting, how manycentimeters of scarf will Hazel have knit into

natta225 [31]

Answer:

Hazel will have knitted 25 centimeters of the scarf

SOLUTION

Problem Statement

We are told Hazel knits 5 centimeters of scarf every night for 5 nights. We are required to find the length of the scarf Hazel will have knitted after 5 nights.

Solution

We are told Hazel makes 5 centimeters of scarf every night. Thus, for each night up till 5 nights, we just need to add the length of scarf Hazel has made.

Let us count for each night.

Night 1:

Hazel makes 5 centimeters of the scarf.

Night 2:

Hazel makes extra 5 centimeters, which means she has made:

$\begin{gathered} (5+5)\text{centimeters} \\ =10\text{ centimeters} \end{gathered}$

Night 3:

Hazel makes extra 5 centimeters, which means she has made:

$\begin{gathered} (10+5)\text{centimeters} \\ =15\text{ centimeters} \end{gathered}$

NIght 4:

Hazel makes extra 5 centimeters, which means she has made:

$\begin{gathered} (15+5)\text{centimeters} \\ =20\text{ centimeters} \end{gathered}$

NIght 5:

Hazel makes extra 5 centimeters, which means she has made:

$\begin{gathered} (20+5)\text{centimeters} \\ =25\text{ centimeters} \end{gathered}$

Final Answer

Thus, Hazel will have knitted 25 centimeters of the scarf

5 0

1 year ago

For an outdoor concert by the city orchestra, concert organizers estimate that 10,000 people will attend if it's not raining. If

Vlada [557]

Answer:

The number of expected people at the concert is 8,500 people

Step-by-step explanation:

In this question, we are asked to determine the expected number of people that will attend a concert if we are given the probabilities that it will rain and it will not rain.

We proceed as follows;

The probability that it will rain is 30% or 0:3

The probability that it will not rain would be 1 -0.3 = 0.7

Now, we proceed to calculate the number of people that will attend by multiplying the probabilities by the expected number of people when it rains and when it does not rain.

Mathematically this is;

Number of expected guests = (probability of not raining * number of expected guests when it does not rain) + (probability of raining * number of expected guests when it rains)

Let’s plug values;

Number of expected guests = (0.3 * 5,000) + (0.7 * 10,000) = 1,500 + 7,000 = 8,500 people

4 0

3 years ago

Which statement best describes the effect of replacing the function f(x) = 2x + 2 with the function g(x) = 2x - 3?

FrozenT [24]

The correct answer is: The graph shifts 5 units right

Explanation:
Below is the graph attached of both the equations:

Red line: Represents f(x) = 2x + 2.
Blue line: Represents g(x) = 2x - 3.

As you can see in the graph that g(x) is shifted 5 units right to f(x).

If you move towards right by 1 unit, you have to subtract 1 from f(x) until you reach g(x) like:
2x + 2 - 1 = 2x + 1 (1 unit)
2x + 1 - 1 = 2x (1 unit)
2x - 1 = 2x - 1 (1 unit)
2x - 1 -1 = 2x - 2 (1 unit)
2x -2 - 1 = 2x -3 (1 unit)

Total 5 units.

Hence the correct answer is the graph shifts 5 units right.

7 0

3 years ago

Read 2 more answers

81p² + 5 = 41 how do I solve by square roots​

81p² + 5 = 41 how do I solve by square roots