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Over [174]
3 years ago
9

State whether the decay is linear or​ exponential, and answer the associated question. The value of a car is decreasing by 9​% p

er year. If the car is worth ​$11 comma 000 ​today, what will it be worth in two​ years? g
Mathematics
1 answer:
Sunny_sXe [5.5K]3 years ago
7 0

Answer:

  • Exponential
  • A(2)=$9109.10

Step-by-step explanation:

Since the value of the car decreases by a common factor each year, the decay is exponential.

An exponential decay function is of the form

A(t)=A_0(1-r)^t$ where:\\Initial Value, A_0=\$11,000\\$Decay Factor, r=9%=0.09

Therefore, the function modeling the car's decay is:

A(t)=11000(1-0.09)^t

We want to determine the car's value in two years.

When t=2

A(2)=11000(1-0.09)^2\\A(2)=\$9109.10

The value of the car in 2 years will be A(t)=$9109.10

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If x = -6, which inequality is true?
Sveta_85 [38]

Answer:

A

Step-by-step explanation:

-5 - 3(-6) > 10

-5 - -18 > 10

-5 + 18 > 10

13 > 10

3 0
2 years ago
PLEASE!!!!!!!The adjoining figure shows two circles with the same center. The
Nookie1986 [14]
<h3><u>Answer:</u></h3>

\boxed{\boxed{\pink{\sf \leadsto Hence \ the \ area \ of \ shaded \ region \ is 264 cm^2}}}

<h3><u>Step-by-step explanation:</u></h3>

Here , two circles are given which are concentric. The radius of larger circle is 10cm and that of smaller circle is 4cm . And we need to find thelarea of shaded region.

From the figure it's clear that the area of shaded region will be the difference of areas of two circles.

Let the,

  • Radius of smaller circle be r .
  • Radius of smaller circle be r .
  • Area of shaded region be \bf Area_{shaded}

\bf \implies Area_{Shaded}= Area_{bigger}-Area_{smaller} \\\\\bf\implies Area_{Shaded} = \pi R^2 - \pi r^2  \\\\\bf\implies Area_{shaded} = \pi ( R^2-r^2)  \\\\\bf\implies Area_{shaded} = \pi [ (10cm)^2 - (4cm)^2]  \\\\\bf\implies Area_{shaded}  = \pi [ 100cm^2-16cm^2]  \\\\\bf\implies Area_{shaded}  = \pi \times 84cm^2  \\\\\bf\implies Area_{shaded}  = \dfrac{22}{7}\times 84cm^2  \\\\\bf\implies \boxed{\red{\bf Area_{shaded} = 264 cm^2 }}

<h3><u>Hence </u><u>the</u><u> </u><u>area</u><u> </u><u>of</u><u> the</u><u> </u><u>shaded </u><u>region</u><u> is</u><u> </u><u>2</u><u>6</u><u>4</u><u> </u><u>cm²</u><u>.</u></h3>

5 0
2 years ago
Karen earns $54.60 for working 6 hours. If the amount she earns varies directly with the
Andrei [34K]

Given:

Karen earns $54.60 for working 6 hours.

Amount she earns varies directly with the  number of hours she works.

She need to work to earn an  additional $260.

To find:

Number of hours she need to work to earn an  additional $260.

Solution:

Let the amount of earnings be A and number of hours be t.

According to question,

A\propto t

A=kt     ...(i)

where, k is constant of proportionality.

Karen earns $54.60 for working 6 hours.

54.60=k(6)

Divide both sides by 6.

\dfrac{54.60}{6}=k

9.1=k

Put k=9.1 in (i).

A=9.1t

Substitute A=260 in the above equation.

260=9.1t

Divide both sides by 9.1.

\dfrac{260}{9.1}=t

28.5714=t

t\approx 29

Therefore, she need to work extra about 29 hours to earn an  additional $260.

3 0
2 years ago
Solve using the quadratic formula. Show all work. Write each solution in simplest form. No decimals.
vagabundo [1.1K]

Answer:

A) -2 - i√3 , -2 + i√3

Step-by-step explanation:

Solve using quadratic formula

x² + 4x + 7 = 0

The Almighty Formula

= -b ± √b² - 4ac/2a

Where ax + bx² + c = 0

From the above question

a = 1, b = 4, c= 7

Hence,

-4 ± √4² - 4 × 1 × 7/2 × 1

-4 ± √16 - 28/2

=( -4 ± √-12)/2

Since

b² - 4ac < 0

We have two complex roots

Simplifying

( -4 ± √-12)/2

= -4/2 ± √-12/2

= -2 ± 2√3i/2

= -2 ± √3i

Therefore,

-2 - √3i , -2 + √3i

or

-2 - i√3 , -2 + i√3

Option A , is the correct answer

3 0
2 years ago
Juang has completed 80% of his homework. He has finished 12 problems. How many questions are on his homework?
Pani-rosa [81]

Answer:

15 or 20

Step-by-step explanation:

3 0
3 years ago
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