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sveticcg [70]
3 years ago
5

In ΔSTU, m∠S = (10x-5)^{\circ}(10x−5)

Mathematics
1 answer:
Triss [41]3 years ago
4 0

Answer:

Step-by-step explanation:

Ths sum of angle S,T,U is 180°. So,

10x-5 + 2x+4 + x-14 = 180

SOlve for x, and then you can find angle S.

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What type of exponential function is f(x)=0.6(2.4)^x ?
Vsevolod [243]

Answer:

<em>The function is of an exponential growth type</em>

<em>Rate of change is 240%</em>

Step-by-step explanation:

<u>Exponential Function</u>

The expression of an exponential function is

f(x)=c.a^{bx}

For a,b,c constants.

1.

The function will be of an exponential growth type if, when x increases, f increases. That behavior comes from the combination of the three constants a,b,c. The best approach to find that out is by taking the first derivative

f'(x)=b.c.lna.a^{bx}

Since a^{bx} is always positive, the product of b.c.lna must be positive to make f increasing. For example, if a>1 and both b and c are of the same sign, f increases for all x. If 0<a<1, then, since lna<0, the product b.c must be negative, i.e. both should have different signs

The function is expressed as

f(x)=0.6\ 2.4^x

we can see a>1, b and c are positive, so the function is of an exponential growth type.

2.

Talking about rates change of real functions takes us to the derivative function. We have already seen the derivative is dependent on all three constants and also of the value of x, so it cannot be predicted as a fixed percentage.

Now, if we picture the function as the general term of a sequence, where x can only take natural values, we can say

\displaystyle \frac{0.6(2.4)^{x+1}}{0.6(2.4)^{x}}=2.4

Each term is obtained as the previous term by 2.4. It's accurate to say the rate of change is 240%

3 0
3 years ago
Read 2 more answers
In what place is the 2 394.5012,
Naddik [55]

Answer:

Ten thousandths

Step-by-step explanation:

The 4 is in the ones place, so the 5 is in the tenths, the 0 in the hundredths, the 1 in the thousandths, so the 2 is in the ten thousandths.

8 0
3 years ago
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Admission to the circus costs $4 plus $0.50 per ride ella spent $17.50 at the circus
harina [27]
Ella spent $13.5 dollars on rides. So she got in 27 rides.
{Solution: subtract 17.50 - 4= 13.5...... and then divide 13.5/.50=27}
6 0
3 years ago
Describe the nature of the roots for this equation.<br> 3x^2+x-5= 0
m_a_m_a [10]

Answer:

<h2>This equation has no natural roots.</h2>

Step-by-step explanation:

3x^2+x-5=0\\\\\text{Use the quadratic formula for}\ ax^2+bx+c=0\\\\x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\text{For the given equation:}\\\\a=3,\ b=1,\ c=-5\\\\b^2-4ac=1^2-4(3)(-5)=1+60=61\\\\x=\dfrac{-1\pm\sqrt{61}}{(2)(3)}=\dfrac{-1\pm\sqrt{61}}{6}\notin\mathbb{N}

4 0
2 years ago
Read 2 more answers
Solve 4x + 2 &lt; 2x - 2
Gennadij [26K]
4x+2 \ \textless \  2x-2\ \ \ |subtract\ 2\ from\ both\ sides\\\\4x \ \textless \  2x -4\ \ \ |subtract\ 2x\ from\ both\ sides\\\\2x \ \textless \  -2\ \ \ \ |divide\ both\ sides\ by\ 2\\\\\boxed{x \ \textless \  -2}\to\boxed{x\in(-\infty;-2)}
7 0
3 years ago
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