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3 years ago

Marissa is painting her rectangular patio, with the exception of a bench that does not need to be painted:

Mathematics

1 answer:

mars1129 [50]3 years ago

5 0

Answer:

A = (x + 15)(x + 10) − 5

Step-by-step explanation:

(x+15)(x+10)-5=A would be a solution

To make this easier, let's assign x a value. Let's say 3.

(3+15)(3+10)-5=A

(18)(13)-5=A

234-5=A

A=229

Now with this, we put x in the answer choice and the answer that gives an area of 229 is correct.

A. A=(3+20)(3+10)+12=(23)(13)+12=299+12=311 Answer A is wrong.

B. A=(3+20)(3+10)-12=(23)(13)-12=299-12=287 Answer B is wrong.

C. A=(3+26)(3+15)=(29)(18)=522 Answer C is wrong.

D. A=(3+14)(3+8)=(17)(11)=187 Answer D is wrong.

It's either I'm wrong or the answer choices are wrong.

New answer choices!

A. A=(3+20)(3+11)

=(23)(14)=322 Answer A is wrong.

B. A=(3+15)(3+10)+5

=(18)(13)+5=234+5=239 Answer B is wrong.

C. A=(3+15)(3+10)−5

=(18)(13)-5=234-5=229 Answer C is correct.

D. A=(3+9)(3+10)=(12)(13)=156 Answer D is wrong.

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Factor the greatest common factor from the polynomial 3x^2 + 6x -9

ryzh [129]

Answer:

$3(x+3)(x -1)$

Step-by-step explanation:

$3x^2 + 6x -9$

All the terms in this polynomial are divisible by 3. Factor 3 out of this polynomial:

$= 3(x^2 + 2x -3)$

Now, factor inside the parentheses by grouping:

$= 3(x^2 -1x+3x -3)$

We knew to split the +2x up into -1x and 3x because -1 and 3 multiply to get -3, which is the last value in the polynomial.

$= 3(x(x -1)+3(x -1))\\= 3(x+3)(x -1)$

Therefore, the final factored polynomial is $3(x+3)(x -1)$ .

4 0

2 years ago

Consider the given function and the given interval. f$x$ = 2 sin$x$ - sin$2 x$ text(, ) [0 text(, ) pi] (a) Find the avera

Finger [1]

a. The average value of $f$ on the given interval is

$\displaystyle f_{\rm ave}=\frac1{\pi-0}\int_0^\pi(2\sin x-\sin2x)\,\mathrm dx=\boxed{\frac4\pi}$

b. Solve for $c$ :

$\dfrac4\pi=2\sin c-\sin2c\implies\boxed{c\approx1.238\text{ or }c\approx2.808}$

4 0

3 years ago

If the principal is $300 rate 3% time 4 years then what is the interest earned and the new balance

Tomtit [17]

Answer:

a) Interest earned = $36

New Balance = $336

b) Interest rate = 0.05 or 5%

New Balance = $517.5

c) time t = 5

New Balance = $612.5

d) Principal Amount = $675

New Balance = $783

Step-by-step explanation:

We are given:

a) Principal (P) = $300

Rate (r) = 3% or 0.03

Time (t)= 4 years

Interest earned = ?

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding interest

$Simple \ Interest (I)= P\times r\times t\\Simple \ Interest (I)= 300\times 0.03\times 4\\Simple \ Interest (I)= 36$

So, Interest earned = $36

New Balance = Principal + Interest = 300+36 = $336

b) a) Principal (P) = $300

Rate (r) = ?

Time (t)= 3 years

Interest earned = 67.50

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding rate

$Simple \ Interest (I)= P\times r\times t\\67.50= 450\times r\times 3\\67.50=1350\times r\\r=\frac{67.50}{1350}\\r=0.05 \ or \ 5\%$

So, Interest rate = 0.05 or 5%

New Balance = Principal + Interest = 450+67.50 = $517.5

c) Principal (P) = $500

Rate (r) = 4.5% or 0.045

Time (t)= ?

Interest earned = $112.50

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding time

$Simple \ Interest (I)= P\times r\times t\\112.50= 500\times 0.045\times t\\112.50=22.5 \times t\\t=\frac{112.50}{22.5}\\t=5$

So, time t = 5

New Balance = Principal + Interest = 500+112.50 = $612.5

d) Principal (P) = ?

Rate (r) = 8% or 0.08

Time (t)= 2 years

Interest earned = 108.00

The formula used is: $Simple \ Interest (I)= P\times r\times t$

Putting values and finding Principal

$Simple \ Interest (I)= P\times r\times t\\108=P\times 0.08 \times 2\\108=P\times 0.16\\P=\frac{108}{0.16}\\P=675$

So, Principal Amount = $675

New Balance = Principal + Interest = 675+108 = $783

8 0

3 years ago

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system. She knows that 2,

kherson [118]

Answer:

The correct option is (C) convenience sample.

Step-by-step explanation:

Convenience sampling is a kind of non-probability sampling, i.e. all items does not have an equivalent chance or probability of being selected. This type of sampling method does not comprises of random collection of items.

Convenience sampling is where we take in items which are easy to reach or collect.

For example, sampling the the students of your own class or collecting sample from your own neighborhood.

In this case the Chief Financial Officer of Harrison Haulers, Inc. asks her staff to inspect the last 200 vouchers of the 2500 payroll vouchers that have been issued since January 1, 2000.

She did so because her staff did not have that much time in hand and it is quite convenient to check the last 200 vouchers.

This is because it is quite easy to review the last 200 payroll vouchers since they would be the most recent ones and quite easily accessible.

So, the sampling method used by the Chief Financial Officer of Harrison Haulers, Inc. is Convenience sampling.

Thus, the correct option is (C).

5 0

3 years ago

What is a rational number

siniylev [52]

It's a number that can be expressed as a fraction, the numerator and the denominator of which, are integers.

7 0

3 years ago