Write down in terms of n, an expression for the nth term
of the following sequences:
a) 4 1 -2 -5 -8
b) -7 -12 -17 -22 -27​

Step-by-step explanation:

x^2-25=

[tex] {x}^{2} - 25 = (x - 5)(x + 5) [/tex]

Question:

(a) How many bacteria would be found in 24 hours

(b) How many bacteria would be found in 2 days

(c) How long for 1000 bacteria to be found

Answer:

(a) 282429536481 bacteria

(b) [tex]7.97*10^{22[/tex] bacteria

(c) 6 days

Step-by-step explanation:

The question illustrates an exponential function

[tex]y = ab^x[/tex]

Where

[tex]a = Initial\ Value = 1[/tex]

[tex]b=Rate = 3[/tex] --- i.e. triples

[tex]x = number\ of\ hours[/tex]

Solving (a): Bacteria in 24 hours

In this case:

[tex]x = 24[/tex]

Substitute [tex]x = 24[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]

So:

[tex]y = ab^x[/tex]

[tex]y = 1 * 3^{24[/tex]

[tex]y = 1 * 282429536481[/tex]

[tex]y = 282429536481[/tex] bacteria

Solving (b): Bacteria in 2 days

[tex]2\ days =48\ hours[/tex]

So:

[tex]x = 48[/tex]

Substitute [tex]x = 48[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]

So:

[tex]y = ab^x[/tex]

[tex]y = 1 * 3^{48[/tex]

[tex]y =7.97*10^{22[/tex] bacteria

Solving (c): How long for 1000 bacteria

In this case:

[tex]y = 1000[/tex]

Substitute [tex]y = 1000[/tex], [tex]b = 3[/tex] and [tex]a = 1[/tex]

So:

[tex]y = ab^x[/tex]

[tex]1000 = 1 *3^x[/tex]

[tex]1000 = 3^x[/tex]

Take Log of both sides

[tex]Log1000 = Log3^x[/tex]

This gives:

[tex]Log1000 = xLog3[/tex]

Make x the subject

[tex]x = \frac{Log1000}{Log3}[/tex]

[tex]x \approx 6[/tex]

Hence: It takes 6 days

Answer:

$8,014.30

Step-by-step explanation:

Answer:

85%

40% × ? = 34

? =

34 ÷ 40% =

34 ÷ (40 ÷ 100) =

(100 × 34) ÷ 40 =

3,400 ÷ 40 =

85

Answer:

y+4=-2(x+1)

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=-2(x-(-1))

y+4=-2(x+1)

Answer:

Step-by-step explanation:

tan23=h1/500

h1=500tan23

tan50=h2/500

h2=500tan50

The height of the building is h1+h2 so

H=500(tan23+tan50)ft (exact)

H=808.1 ft (rounded to nearest tenth of a foot)

Answer:

OMG THANK YOU-

Answer:

x = 14

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Equality Properties

Algebra I

Geometry

Step-by-step explanation:

Step 1: Define

We can see from the diagram that the 2 angles are supplementary

(6x - 10)° + (7x + 8)° = 180°

Step 2: Solve for x

Answer:

The Akkadian and Assyrian empires were two of the world’s first empires. Their conquests reshaped Mesopotamia. The many empires that would follow, worldwide,

Step-by-step explanation:

Answer:

Step-by-step explanation:

a-b=2

[tex]\frac{27^{\frac{1}{3} b} }{9^{\frac{1}{2}a } } \\=\frac{(3^{3}) ^{\frac{1}{3} b} }{(3^{2} )^{\frac{1}{2} a} } \\=\frac{3^b}{3^a} \\=3^{b-a} \\=3^{-(-b+a)} \\=3^{-2}\\=\frac{1}{3^2} \\=\frac{1}{9}[/tex]

Answer:

The answer is 125. If you were to pair 250 people in 2, that would be 250 divided by 2.  And 250 divided by 2 is 125.

Step-by-step explanation:

Answer:

9 months

Step-by-step explanation:

Answer:

it will be 9 months like the first person said

Answer:

A. A reflection over the x-axis and a vertical stretch.

Step-by-step explanation:

Let [tex]h(x) = x^{2}[/tex], to obtain [tex]k(x) = -4\cdot x^{2}[/tex], we need to use the following two operations:

(i) Vertical stretch

[tex]g(x) = k\cdot f(x)[/tex], [tex]k\in \mathbb{R}^{+}[/tex]

(ii) Reflection over the x-axis

[tex]g(x) = -f(x)[/tex]

Let prove both transformations in [tex]h(x)[/tex]:

Step 1 - Vertical stretch ([tex]k = 4[/tex])

[tex]h'(x) = 4\cdot x^{2}[/tex]

Step 2 - Reflection over the x-axis

[tex]k(x) = -4\cdot x^{2}[/tex]

Hence, correct answer is A.

Answer:

15.4 I did this on delta math

It would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.

The formula for calculating the future value (FV) of an investment with continuous compounding is:

[tex]FV = Pe^{rt}[/tex]

Where P is the initial principal, r is the annual interest rate (expressed as a decimal), t is the time period (in years), and e is the mathematical constant e (approximately 2.71828).

In this case, we have P = $350, r = 4.5% = 0.045, and we want to find the time t when the FV is $700. Substituting these values into the formula, we get:

[tex]700 = 350e^{0.045t}[/tex]

Dividing both sides by $350, we get:

[tex]2 = e^{0.045t}[/tex]

Taking the natural logarithm of both sides, we get:

[tex]ln(2) = ln\times e^{0.045t}[/tex]

Using the properties of logarithms, we can simplify this to:

ln(2) = 0.045t ln(e)

Since ln(e) = 1, we can simplify further to:

ln(2) = 0.045t

Finally, solving for t, we get:

t = ln(2) / 0.045 ≈ 15.4

Therefore, it would take approximately 15.4 years, to the nearest tenth of a year, for the value of the account to reach $700 with continuous compounding.

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4. Overall, there are 45 students.

13 students achieved a mark over 65

[tex]\frac{13}{45} *100[/tex] = 29%

Therefore the answer is b. 29%

5. b is incorrect.

This is because retrievers account for 10% of the dogs, not 15%.

100%-(35% + 45% + 10%) = 10%

Answer:

B

Step-by-step explanation:

Divide each coordinate by 2

3/2=1.5

2/2=1

Answer:

85 cards

Step-by-step explanation:

Answer:

(-3,1.5) (0,3) (3'3)

Step-by-step explanation:

multiply all the coordinates by 1/2

Answer:

1: 23.85

2: 83%

3: 44

Step-by-step explanation:

1 - do 53x0.45 (23.85)

2 - Divide 20 by 24, which you get 0.833333333 and move the decimal 2x to the right. You get 83.3333333, but round. So 83%

3 - do 80x0.55 (44)

Answer: Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.

Step-by-step explanation: The leg is the smallest number and the hypothenuse is the biggest nunber.

Answer:

Sofia used the length of one of the legs as c when she should have used the length of the longest side as c.

Step-by-step explanation:

Answer:

$872.70

Step-by-step explanation:

Add all numbers from Mon-Fri.

So 985.

Multiply it by 0.78

So $768.30

Add 0.78 and 0.38

So 1.16

Then multiply 90 by 1.16

So $104.40

Then add the two numbers.

768.30+104.40

So $872.70

Hope this helps

Answer:

4.5 x 14 = 63

Explanation:

The area of a parallelogram is the product of any base and the altitude to that base: A = bh.

Answer:

They are both 12

Change 16 1/4 into 4.

4 • 3

12

16 • 3 is 48

1/4 of 48 is 12

Hope this helps

Answer:

C = $2.40

n = 6

Step-by-step explanation:

For Noelle,

Equation that represents the monthly cost 'C',

C = 0.2n + 1.20

Here, n = number of checks written in a month

For Micah,

Monthly cost for writing checks 'C' = $1.20

Number of checks 'n' = 3

Since, Cost of writing checks ∝ Number of checks written

C' ∝ n

C' = kn

k = [tex]\frac{C'}{n}[/tex]

Here, k = proportionality constant

For C' = 1.2 and n = 3

k = [tex]\frac{1.2}{3}[/tex]

k = 0.4

Equation will be,

C' = 0.4n

For any month C = C'

Therefore, 0.2n + 1.20 = 0.4n

0.4n - 0.2n = 1.20

0.2n = 1.20

n = 6

Number of checks written by Noelle and Micah = 6

For n = 6,

C = 0.2(6) + 1.20

C = $2.40

Cost of writing checks = $2.40

Step-by-step explanation:

1. Use the Pythagorean theorem to solve for side KM:

2. Cosine is adjacent over hypotenuse, so cosine of M would be KM/34, or 30/34

3. Tangent is opposite over adjacent, so tangent of L will be KM/16, or 30/16

4. Sine is opposite over hypotenuse, so sine of M will be 16/34

5. KM=30, solved for in step 1.

hope this helps!!

Answer:

x = 33°

Step-by-step explanation:

From the figure attached,

FB and FC are two secants intersecting each other at point F outside the circle.

Measure of angles between the secants measures half of the difference between the intercepted arcs.

x° = [tex]\frac{1}{2}(\text{arc BC}-\text{arc DE})[/tex]

x° = [tex]\frac{1}{2}(108-42)[/tex]

x = 33°

Answer:

The bill was $36.95 without tax.

The price before tax was the amount of $37.25 which is before a 9% sales tax was added to their bill.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.

Their bill was charged a 9% sales tax.

Amy paid the bill with a $10 gift certificate plus $30.60

Use the equation P + rP =T,

where P is the price before tax, r is the sales tax rate, and T is the total price, including tax.

The price before tax (P) is unknown.

The total price(T) = 30.60 + 10 = 40.60

The sales tax rate (r) = 9% = 9/100 = 0.09

⇒ P + rP = T

Substitute the values in the above equation, and we get

⇒ P + (0.09)P = 40.60

⇒ P(1 + 0.09) = 40.60

⇒ P(1.09) = 40.60

⇒ P = 30.60/(1.09)

Apply the Division operation, and we get

⇒ P = 37.247706

Rounded to the nearest hundredth

⇒ P = 37.25

Therefore, the price before tax was the amount of $37.25.

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