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3 years ago

The Measure Of A Angle Is 18 Less Than Twice Its Complement. Find The Measure Of The Angle.

Mathematics

1 answer:

SpyIntel [72]3 years ago

7 0

Answer: 54

Step-by-step explanation: 2x -18 = 90

2x = 108

x = 54

*Complement means complementary angle. Complementary angles always add up to 90 degrees!

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Name 3 of the 4 features listed below for the function g (x) = log2 (x + 4) - 1 and include a description of how you found those

givi [52]

(1) Vertical asymptote: $x=-4$

(2) Domain: $x>-4$

(3) X intercept: $(-2,0)$ and Y intercept : $(0,1)$

(4) The function g(x) is shifted 4 units to the left and shifted 1 unit down.

Explanation:

The parent function is $f(x)=\log _{2} x$

The transformed function is $g(x)=\log _{2}(x+4)-1$

(1) Vertical asymptote:

The vertical asymptote of a function can be determined by equating

$x+4=0$

Thus, $x=-4$

The vertical asymptote is $x=-4$

(2) Domain:

The domain of a function is the set of all independent x-values.

$x+4>0$

Thus, $x>-4$

The domain of a function is $x>-4$

(3) X and Y intercepts:

To determine the x intercept, let us substitute y=0 in $g(x)=\log _{2}(x+4)-1$

$\begin{equation}\begin{aligned}\log _{2}(x+4)-1 &=0 \\\log _{2}(x+4) &=1 \\x+4 &=2^{1} \\x &=-2\end{aligned}$

Thus, the x intercept is $(-2,0)$

To determine the y intercept, let us substitute x=0 in $g(x)=\log _{2}(x+4)-1$

$\begin{equation}\begin{aligned}y &=\log _{2}(0+4)-1 \\&=\log _{2} 4-1 \\&=2-1 \\&=1\end{aligned}$

Thus, the y intercept is $(0,1)$

(4) To determine the transformation:

The transformed function $g(x)=\log _{2}(x+4)-1$ is shifted 4 units to the left and shifted 1 unit downwards.

4 0

3 years ago

If jobs arrive every 15 seconds on average, what is the probability of waiting more than 30 seconds?

Aleksandr [31]

Answer: 0.14

Step-by-step explanation:

Given: Mean : $\lambda=15\text{ per seconds}$

In minutes , Mean : $\lambda=4\text{ per minute}$

The exponential distribution function with parameter $\lambda$ is given by :-

$f(t)=\lambda e^{-\lambda t}, \text{ for }x\geq0$

The probability of waiting more than 30 seconds i.e. 0.5 minutes is given by the exponential function :-

$P(X\geq0.5)=1-P(X\leq0.5)\\\\=1-\int^{0.5}_{0}4e^{-4t}dt\\\\=1-[-e^{-4t}]^{0.5}_{0}\\\\=1-(1-e^{-2})=1-0.86=0.14$

Hence, the probability of waiting more than 30 seconds = 0.14

5 0

3 years ago

Evaluate expression 15/x for x=3

irga5000 [103]

Answer:

x=5

Step-by-step explanation:

15÷5=3

that is the right answer

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2 years ago

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Is y=-2x+b linear or non linear

Anuta_ua [19.1K]

Hint: if you were to graph this, and it curves, then its a linear, if not its straight, then its non linear

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3 years ago

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Translate the sentence into an inequality. Ten times the sum of a number and 21 is at most 16. Use the variable y for the unknow

irga5000 [103]

Answer:

10y+ 21 ≥ 16

Step-by-step explanation:

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3 years ago