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Lynna [10]
3 years ago
6

Write an algebraic expression for 8 less than 4 times a number

Mathematics
1 answer:
Flura [38]3 years ago
4 0

Answer:

8<4*X

Step-by-step explanation:

8 less than is 8< the 4 times 4* a number so a variable, X

PLZ MARK ME AS BRAINIEST!

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Crystal bought new art supplies that were on sale for $25.45. If
Keith_Richards [23]

Answer:

The orginal price was $33.09.

Step-by-step explanation:

You take 30% and move the decimal two places to the left, which gives you .3

Then mutiply .3 to $25.45. This gives you $7.64.

Add $7.64 to discounted price ($25.45) and you get $33.09.

5 0
3 years ago
1. A retirement account is opened with an initial deposit of $8,500 and earns 8.12% interest compounded monthly. What will the a
Rudik [331]

Answer:

Part A) \$42,888.48  

Part B) A=\$22,304

Part C) The graph in the attached figure

Step-by-step explanation:

Part A) What will the account be worth in 20 years?

we know that    

The compound interest formula is equal to  

A=P(1+\frac{r}{n})^{nt}  

where  

A is the Final Investment Value  

P is the Principal amount of money to be invested  

r is the rate of interest  in decimal

t is Number of Time Periods  

n is the number of times interest is compounded per year

in this problem we have  

t=20\ years\\ P=\$8,500\\ r=0.0812\\n=12  

substitute in the formula above  

A=8,500(1+\frac{0.0812}{12})^{12*20}  

A=8,500(1.0068)^{240}  

A=\$42,888.48  

Part B) What if the deposit were compounded monthly with simple interest?  

we know that

The simple interest formula is equal to

A=P(1+rt)

where

A is the Final Investment Value

P is the Principal amount of money to be invested

r is the rate of interest  

t is Number of Time Periods

in this problem we have

t=20\ years\\ P=\$8,500\\r=0.0812

substitute in the formula above

A=8,500(1+0.0812*20)

A=\$22,304

Part C) Could you see the situation in a graph? From what point one is better than the other?

Convert the equations in function notation

A(t)=8,500(1.0068)^{12t} ------> equation A

A(t)=8,500(1+0.0812t)  -----> equation B

using a graphing tool  

see the attached figure  

Observing the graph, from the second year approximately the monthly compound interest is better than the simple interest.

5 0
3 years ago
Consider the equation below. (If an answer does not exist, enter DNE.) f(x) = x4 ln(x) (a) Find the interval on which f is incre
Ainat [17]

Answer: (a) Interval where f is increasing: (0.78,+∞);

Interval where f is decreasing: (0,0.78);

(b) Local minimum: (0.78, - 0.09)

(c) Inflection point: (0.56,-0.06)

Interval concave up: (0.56,+∞)

Interval concave down: (0,0.56)

Step-by-step explanation:

(a) To determine the interval where function f is increasing or decreasing, first derive the function:

f'(x) = \frac{d}{dx}[x^{4}ln(x)]

Using the product rule of derivative, which is: [u(x).v(x)]' = u'(x)v(x) + u(x).v'(x),

you have:

f'(x) = 4x^{3}ln(x) + x_{4}.\frac{1}{x}

f'(x) = 4x^{3}ln(x) + x^{3}

f'(x) = x^{3}[4ln(x) + 1]

Now, find the critical points: f'(x) = 0

x^{3}[4ln(x) + 1] = 0

x^{3} = 0

x = 0

and

4ln(x) + 1 = 0

ln(x) = \frac{-1}{4}

x = e^{\frac{-1}{4} }

x = 0.78

To determine the interval where f(x) is positive (increasing) or negative (decreasing), evaluate the function at each interval:

interval                 x-value                      f'(x)                       result

0<x<0.78                 0.5                 f'(0.5) = -0.22            decreasing

x>0.78                       1                         f'(1) = 1                  increasing

With the table, it can be concluded that in the interval (0,0.78) the function is decreasing while in the interval (0.78, +∞), f is increasing.

Note: As it is a natural logarithm function, there are no negative x-values.

(b) A extremum point (maximum or minimum) is found where f is defined and f' changes signs. In this case:

  • Between 0 and 0.78, the function decreases and at point and it is defined at point 0.78;
  • After 0.78, it increase (has a change of sign) and f is also defined;

Then, x=0.78 is a point of minimum and its y-value is:

f(x) = x^{4}ln(x)

f(0.78) = 0.78^{4}ln(0.78)

f(0.78) = - 0.092

The point of <u>minimum</u> is (0.78, - 0.092)

(c) To determine the inflection point (IP), calculate the second derivative of the function and solve for x:

f"(x) = \frac{d^{2}}{dx^{2}} [x^{3}[4ln(x) + 1]]

f"(x) = 3x^{2}[4ln(x) + 1] + 4x^{2}

f"(x) = x^{2}[12ln(x) + 7]

x^{2}[12ln(x) + 7] = 0

x^{2} = 0\\x = 0

and

12ln(x) + 7 = 0\\ln(x) = \frac{-7}{12} \\x = e^{\frac{-7}{12} }\\x = 0.56

Substituing x in the function:

f(x) = x^{4}ln(x)

f(0.56) = 0.56^{4} ln(0.56)

f(0.56) = - 0.06

The <u>inflection point</u> will be: (0.56, - 0.06)

In a function, the concave is down when f"(x) < 0 and up when f"(x) > 0, adn knowing that the critical points for that derivative are 0 and 0.56:

f"(x) =  x^{2}[12ln(x) + 7]

f"(0.1) = 0.1^{2}[12ln(0.1)+7]

f"(0.1) = - 0.21, i.e. <u>Concave</u> is <u>DOWN.</u>

f"(0.7) = 0.7^{2}[12ln(0.7)+7]

f"(0.7) = + 1.33, i.e. <u>Concave</u> is <u>UP.</u>

4 0
3 years ago
Rhonda is drawing a 3-inch square inside an isosceles triangle with two side lengths measuring 7 inches and 14 inches. Which of
Aleksandr-060686 [28]

Answer:

7

Step-by-step explanation:

I just need to type more or my answer gets auto delete but yeah it is 7

5 0
3 years ago
Suppose the function f(t) = 95 cosine (StartFraction pi Over 10 EndFraction t) + 120 models the height of a seat on a Ferris whe
drek231 [11]

Answer:

im not 100% bit i think its 95ft

Step-by-step explanation:

5 0
3 years ago
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