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3 years ago

What is the missing term in this arithmetic sequence? 9, 14, 19, __, 29, 34, …

1 answer:

5 0

The common difference is a₂-a₁=14-9=5.
The fourth term is the third term plus the common difference -> 19+5=24.
The answer is B.

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Marcos bought 3 bags of chips that cost $0.79.

viktelen [127]

Answer:

$2.63

Step-by-step explanation:

3 x $0.79 = 2.37

5.00 - 2.37 = $2.63

8 0

3 years ago

Read 2 more answers

Solve the equation!3 tan^3θ = tan θ

andreev551 [17]

3 tan³ t(theta) = tan t(theta)
3 tan³ t - tan t = 0
tan t ( 3 tan² t - 1 ) = 0
tan t = 0
t 1 = k π , k ∈ Z
3 tan ² t - 1 = 0
3 tan ² t = 1
tan ² t = 1/3
tan t = +/- √3/3
t 2 = π / 6 + k π
t 3 = - π / 6 + k π , k ∈ Z

8 0

3 years ago

Moonshine Problem: How many gallons of 20% moonshine and how many gallons of 30% moonshine have to be mixed together to make 100

Sindrei [870]

Answer:

50 gallons 20%

50 gallons 30%

Step-by-step explanation:

If x is gallons of 20% moonshine, and y is gallons of 30% moonshine, then:

x + y = 100

0.20x + 0.30y = 0.25(100)

Solve the system of equations using substitution or elimination. Using substitution:

0.20x + 0.30(100 − x) = 0.25(100)

0.20x + 30 − 0.30x = 25

5 = 0.10x

x = 50

y = 50

3 0

3 years ago

For the figures below, assume they are made of semicircles, quarter circles and squares. For each shape, find the area and perim

ICE Princess25 [194]

Answer:

Part a) The area of the figure is $\frac{9}{2}(4+\pi )\ cm^{2}$

Part b) The perimeter of the figure is $3(2+2\sqrt{2}+ \pi)\ cm$

Step-by-step explanation:

Step 1

Find the area of the figure

In this problem we have that

The figure ABC is the half of a square and the other figure is a semicircle

<u>Find the area of the figure ABC</u>

we have

$AB=6\ cm, BC=6\ cm$

The area of the half square ABC is equal to find the area of triangle ABC

$A1=\frac{1}{2}*6*6=18\ cm^{2}$

<u>Find the area of the semicircle</u>

The area of the semicircle is equal to

$A2=\pi r^{2}/2$

we have that

$r=6/2=3\ cm$

substitute

$A2=\pi (3)^{2}/2$

$A2=(9/2) \pi\ cm^{2}$

The area of the figure is equal to

$18\ cm^{2}+(9/2) \pi\ cm^{2}= \frac{9}{2}(4+\pi )\ cm^{2}$

Step 2

Find the perimeter of the figure

The perimeter of the figure is equal to

$P=AB+AC+length\ CB$

we have

$AB=6\ cm$

Applying Pythagoras theorem

$AC=\sqrt{6^{2}+6^{2}}\\AC=6\sqrt{2}\ cm$

Remember that

the circumference of a semicircle is equal to

$C=\frac{1}{2}2\pi r=\pi r$

$r=6/2=3\ cm$

$C=\pi(3)$

$C=3 \pi\ cm$

The perimeter of the figure is equal to

$P=6\ cm+6\sqrt{2}\ cm+3 \pi\ cm$

Simplify

$P=3(2+2\sqrt{2}+ \pi)\ cm$

5 0

3 years ago

Please help! How on earth do I do this? In the year 2015, Anna bought a new car for $36,000. In 2017, she was told that the valu

Klio2033 [76]

Part A

Purchase Value of Anna's Car in 2015 = $36,000

Depreciated Value of Anna's Car in 2017 = $25,000

We know that the value of the car is depreciating linearly.

From the above data, we can see that the value of the car has reduced by $36,000-$25,000 = $11,000 over 2 years.

⇒ Per year the value has been depreciated by $\frac{11000}{2}$

⇒ Per year the value has been depreciated by $5,500

So if the value of a car in 2015 is V₀ then value of the car after t years can be determined by the below function:

V (t) = V₀ - (t*5,500), where t indicates the years passed since 2015

OR V (t) = 36,000 - (t*5,500), where t indicates the years passed since 2015

Part B

Suggested value of Anna's car for trade in option in 2018 = $15,000

In 2018, 3 years would have been passed since 2015. Using the value of t = 3 in the function determined in Part A:

V(3) = V₀ - (3*5,500)

⇒ V(3) = 36,000 - (16,500)

⇒ V(3) = $19,000

From the above calculations, we can see that the value of the car in 2018 should be $19,000, however the suggested value for trade in is indicated as $15,000 which is lower than what the value of the car should be. Hence, basis linear depreciation, the $15,000 value is not fair for the car in 2018.

3 0

3 years ago