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SVEN [57.7K]
4 years ago
7

The Polleys want to put in a swimming pool next summer. They need to save $6,000 over 12 months in order to achieve this goal. T

hey set aside the same amount each month and after 7 months discovered they have saved $3,100. The Polleys know that they must adjust their plan in order to meet their goal, so they come up with the following options: Option A: Save the original amount each month but put the pool in one month later than originally planned. Option B: Increase savings each month by $100 from their original plan. Which of the following statements is true?
Mathematics
2 answers:
Crank4 years ago
7 0

Answer:

d.Neither option A nor option B will allow them to meet their goal.

Step-by-step explanation:

I got it right on edge

Sauron [17]4 years ago
6 0

Answer:

Therefore Neither option A nor option B will allow them to meet their goal....

Step-by-step explanation:

The Polleys need to save $6,000 over 12 months.

After 7 months they discovered that they have saved $ 3,100 but in actual they have to save $3,500. It means $400 are short. Therefore for the remaining months they must save $6000-$3100 = $2900. They have to save 2900/5 = $580 each month.

According to the Option A The original amount was $500, in 5 months they will save 500*5 =$2500. They need total of $2900, which means $400 are short.

According to the Option B  Increase savings each month by $100 from their original plan makes a total amount of $3000. This amount exceeds their goal.

Therefore Neither option A nor option B will allow them to meet their goal....

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(7 + 7i)(2 − 2i)
Ostrovityanka [42]

The complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

<h3>What is a complex number?</h3>

It is defined as the number which can be written as x+iy where x is the real number or real part of the complex number and y is the imaginary part of the complex number and i is the iota which is nothing but a square root of -1.

We have a complex number shown in the picture:

-7i(3 + 3i)

= -7i

In trigonometric form:

z = 7 (cos (90) + sin (90) i)

= 3 + 3i

z = 4.2426 (cos (45) + sin (45) i)

\rm 7\:\left(cos\:\left(90\right)\:+\:sin\:\left(90\right)\:i\right)4.2426\:\left(cos\:\left(45\right)\:+\:sin\:\left(45\right)\:i\right)

\rm =7\left(\cos \left(\dfrac{\pi }{2}\right)+\sin \left(\dfrac{\pi }{2}\right)i\right)\cdot \:4.2426\left(\cos \left(\dfrac{\pi }{4}\right)+\sin \left(\dfrac{\pi }{4}\right)i\right)

\rm 7\cdot \dfrac{21213}{5000}e^{i\dfrac{\pi }{2}}e^{i\dfrac{\pi }{4}}

\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}

=21-21i

After converting into the exponential form:

\rm =\dfrac{148491\left(-1\right)^{\dfrac{3}{4}}}{5000}

From part (b) and part (c) both results are the same.

Thus, the complex number  -7i into trigonometric form is 7 (cos (90) + sin (90) i) and  3 + 3i in trigonometric form is 4.2426 (cos (45) + sin (45) i)

Learn more about the complex number here:

brainly.com/question/10251853

#SPJ1

3 0
2 years ago
An equation in the form ax2+bx+c=0 is solved by the quadratic formula. The solution to the equation is shown below.x=−7±√ "572"
7nadin3 [17]

Answer:

B: a = 1, b= 7, c = -2

Explanation:

\sf Quadratic \ Equation : \dfrac{-b\pm \sqrt{b^2 - 4ac} }{2a}

Knowing This:

<u>solve for b</u>

  • -b = -7
  • b = 7

<u>solve for a</u>:

  • 2a = 2
  • a = 1

<u>solve c</u>:

  • b² - 4ac = 57
  • 7² - 4(1)(c) = 57
  • -4c = 57 - 49
  • -4c = 8
  • c = 8/-4 = -2
4 0
2 years ago
Read 2 more answers
In April, the Messa family gets 800 text messages included in their plan. Together, Tommy and Mary use half of the messages. Jac
laiz [17]

Answer: See explanation

Step-by-step explanation:

Total number of text messages = 800

Amount used by Tommy and Mary = 1/2 × 800 = 400

Number of messages uses by Jack and Stefanie = 240

The expression to find the number of messages Cathy uses will be:

= 800 - (1/2 × 800) - 240

Since the expression is 800 - (1/2 × 800) - 240, the number of messages that Cathy will use will be:

= 800 - (1/2 × 800) - 240

= 800 - 400 - 240

= 160 messages

3 0
3 years ago
The solutions to the equation 2x^2 + x - 1 = 2 are x = -3/2 or x = _______.
garik1379 [7]

Answer:

The remaining solution to the equation is x = 1

Step-by-step explanation:

2x^2 + x - 1 = 2

First set the equation to zero by subtracting 2 from each side:

2x^2 + x - 1 - 2 = 2 - 2

2x^2 + x - 3 = 0

Factor the left side of the equation:

2x^2 + x - 3 = 0

(2x + 3)(x - 1) = 0

Now set each factor to zero and solve:

2x+ 3 = 0

2x+ 3 - 3  = 0 - 3

2x= -3

2x/2= -3/2

x= -3/2 (The given expression)

x - 1 = 0

x - 1 + 1 = 0 + 1

x = 1

Since we already knew x = -3/2, the missing solution is x = 1.

4 0
3 years ago
A rectangle with an area of 8 ft² is dilated by a factor of 4. What is the area of the dilated rectangle?
prohojiy [21]

Answer:

Option 4) 128\ ft^{2}

Step-by-step explanation:

we know that

If two figures are similar then the ratio of its areas is equal to the scale factor squared

Let

z------> the scale factor

x-----> the area of the dilated rectangle

y----> the area of the original rectangle

so

z^{2}=\frac{x}{y}

we have

z=4

y=8\ ft^{2}

substitute and solve for x

4^{2}=\frac{x}{8}

x=16(8)=128\ ft^{2}

4 0
4 years ago
Read 2 more answers
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