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2 years ago

Which number line represents the solution set for the inequality 3(8 – 4x) < 6(x – 5)?

Mathematics

1 answer:

poizon [28]2 years ago

5 0

3(8-4x)<6(x-5)

24 - 12x < 6x - 30

18x > 54

x > 3

answer is B. x > 3

<em>Sure hope this helps you! :D</em>

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Find all real solutions of the equation. (Enter your answers as a comma-separated list.)

34kurt

Answer:

0,1

Step-by-step explanation:

x^2 − x = 0

Factor out an x

x(x-1) =0

Using the zero product property

x=0 x-1=0

Solving each equation

x=0 x-1+1 =0+1

x=0 x=1

The solutions are

x=0,1

7 0

3 years ago

What is the equation of the line that represents the horizontal asymptote of the function f(x)=25,000(1+0.025)^(x)?

posledela

Answer:

The answer is below

Step-by-step explanation:

The horizontal asymptote of a function f(x) is gotten by finding the limit as x ⇒ ∞ or x ⇒ -∞. If the limit gives you a finite value, then your asymptote is at that point.

$\lim_{x \to \infty} f(x)=A\\\\or\\\\ \lim_{x \to -\infty} f(x)=A\\\\where\ A\ is\ a\ finite\ value.\\\\Given\ that \ f(x) =25000(1+0.025)^x\\\\ \lim_{x \to \infty} f(x)= \lim_{x \to \infty} [25000(1+0.025)^x]= \lim_{x \to \infty} [25000(1.025)^x]\\=25000 \lim_{x \to \infty} [(1.025)^x]=25000(\infty)=\infty\\\\ \lim_{x \to -\infty} f(x)= \lim_{x \to -\infty} [25000(1+0.025)^x]= \lim_{x \to -\infty} [25000(1.025)^x]\\=25000 \lim_{x \to -\infty} [(1.025)^x]=25000(0)=0\\\\$

$Since\ \lim_{x \to -\infty} f(x)=0\ is\ a\ finite\ value,hence:\\\\Hence\ the\ horizontal\ asymtotes\ is\ at\ y=0$

5 0

3 years ago

Use a matrix to solve the system:

Romashka-Z-Leto [24]

Answer:

(2.83 , 1 , 4)

Step-by-step explanation:

$2x+2y-z=4\\4x-2y-2z=2\\3x+3y-4z=-4\\$

Rewrite these equations in matrix form

$\left[\begin{array}{ccc}2&2&-1\\4&-2&-2\\3&3&-4\end{array}\right] \left[\begin{array}{ccc}x\\y\\z\end{array}\right]=\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\$

we can write it like this,

$AX=B\\X=A^{-1}B$

so to solve it we need to take the inverse of the 3 x 3 matrix A then multiply it by B.

We get the inverse of matrix A,

$A^{-1}=\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right] \\$

now multiply the matrix with B

$X=A^{-1}B\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}7/15&1/6&-1/5\\1/3&-1/6&0\\3/5&0&-2/5\end{array}\right]\left[\begin{array}{ccc}4\\2\\-4\end{array}\right] \\\\\\\left[\begin{array}{ccc}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}2.83\\1\\4\end{array}\right] \\$

4 0

2 years ago

How many digits are written when 1000 to the power of 2015 is expressed as a numeral?

PtichkaEL [24]

Answer: There are 6046 digits will be written on expansion upto 2015th power.

Step-by-step explanation:

Since we have given that

$1000^{2015}$

We have to find the number of digits ,

So,

$1000^{2015}\\\\=(10^3)^{2015}\\\\=10^{6045}$

Since we know that

$10^n\text{ has n+1 number of digits }$

so,

$10^{6045}\text{ has 6046 number of digits }$

Hence, there are 6046 digits will be written on expansion upto 2015th power.

6 0

3 years ago

WILL GIVE BRAINLIEST! SUPER CONFUSED!!!

kondor19780726 [428]

Answer:

For 1948 Men's :Interquartile range is 1.5, Median is 58.3

For 2012 Men's: Interquartile range is 0.315, Median is 47.86

You can infer that in 2012 the swimmers were better and it was more competitive as the interquartile range was lower and the median was also lower as well

Step-by-step explanation:

1948 Men's 100m

57.3, 57.8, 58.1, 58.3, 58.3, 59.3, 59.6,1:00.5

⬆ ⬆ ⬆

Low IQR Median High IQR

Low IQR is average of 57.8 and 58.1 = 57.95

High IQR is average of 59.3 and 59.6 = 59.45

Median is average of 58.3 and 58.3 = 58.3

Interquartile range is High IQR- Low IQR

59.45 - 57.95=1.5

2012 Men's 100m

47.52, 47.53, 47.8, 47.84, 47.88, 47.92, 48.04, 48.44

⬆ ⬆ ⬆

Low IQR Median High IQR

Low IQR is average of 47.53 and 47.8 = 47.665

High IQR is average of 48.04 and 47.92 = 47.98

Median is average of 47.88 and 47.84 = 47.86

Interquartile range is High IQR-Low IQR

47.98-47.665=0.315

5 0

3 years ago