Given sin⁡θ=1/2 determine the value of sec θ. 0°<θ<90°

Given Choices

2/√3
√3/2
2
1

The domain restrictions for (f/g)(x) are (c) x = 0, 6

From the question, we have the following parameters that can be used in our computation:

f(x) = x² - 5x - 6

g(x) = x² - 6x

The composite function (f/g)(x) is calculated as

(f/g)(x) = f(x)/g(x)

substitute the known values in the above equation, so, we have the following representation

(f/g)(x) = (x² - 5x - 6 )/(x² - 6x)

For the domain restriction, we have

x² - 6x = 0

When solved, we have

x =  6 or x = 0

Hence, the domain restrictions for (f/g)(x) are (c) x = 0, 6

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Question

Given f(x) = x² - 5x - 6 and g(x) = x² - 6x, what are the domain restrictions

for (f/g)(x)?

A) x = +6

B) x = 0

C) x = 0,6

D) x = -2,6

to get the slope of any straight line, we only need two points off of it, let's use the ones in the picture below.

\((\stackrel{x_1}{8}~,~\stackrel{y_1}{25})\qquad (\stackrel{x_2}{24}~,~\stackrel{y_2}{35}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{35}-\stackrel{y1}{25}}}{\underset{run} {\underset{x_2}{24}-\underset{x_1}{8}}}\implies \cfrac{10}{16}\implies \cfrac{5}{8}\)

Answer:

Step-by-step explanation:

Answer:

c = 8

Step-by-step explanation:

Using the Intersecting Chords Theorem, we can form the following equation and solve for c:

\(ab=cd\\(10)(8.8)=11c\\88=11c\\c=8\)

The expression that describe the end behavior of the expression f(x)= (3.25)^x + 6 is The curve begins infinitely close to the line y equals 6 in the second quadrant.

The behavior of the graph of a function at its "ends" on the x-axis is referred to as the end behavior of a function, f.

For example, if we look at the right end of the x-axis (as x approaches + ∞) and the left end of the x-axis (as x approaches - ∞), the end behavior of a function explains the trend of the graph.

The graph of the function is attached and from the graph it shows that the graph continued to tend towards towards line y = 6

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Answer:

\(2\, \log_{10}(x) + \log_{10}(5) = \log_{10}(5\, x^{2})\).

Step-by-step explanation:

For any given base \(b > 0\), \(x > 0\), and \(y > 0\):

\(\log_{b}(x) + \log_{b}(y) = \log_{b}(x\, y)\).

For all real \(y\) (including both \(y > 0\) and \(y \le 0\),) as long as \(b > 0\), \(x > 0\):

\(y\, \log_{b}(x) = \log_{b}(x^{y})\).

Apply the second rule to rewrite \(2\, \log_{10}(x)\):

\(\begin{aligned}2\, \log_{10}(x) &= \log_{10}(x^{2})\end{aligned}\).

Apply the first rule:

\(\begin{aligned}\log_{10}(x^{2}) + \log_{10}(5) = \log_{10}(5\, x^{2})\end{aligned}\).

Overall:

\(\begin{aligned}& 2\, \log_{10}(x) + \log_{10}(5)\\ =\; & \log_{10}(x^{2}) + \log_{10}(5) \\ =\; & \log_{10}(5\, x^{2})\end{aligned}\).

Answer:

Step-by-step explanation:

Answer:V=whl

Step-by-step explanation:

L=Length

W= Width

H= Height

Answer: ∠16 and ∠11

Step-by-step explanation:

      All of these answer options include ∠16, so we know we're looking for an angle that is corresponding to ∠16. A corresponding angle is an angle that is in the same relative position. We will look at ∠9, ∠11, ∠2, and ∠12 since those are the given answer options, and see which is corresponding.

The correct corresponding angles are ∠16 and ∠11.

Answer:

Both of these curves are equal to each other.

Step-by-step explanation:

We have

\(x(t) = 4 + t\)

and

\(y(t) = 2 \sqrt{t} \)

Solve for t in the x function

\(x = 4 + t \)

Subsitue this in for t.

\(y = 2 \sqrt{x - 4} \)

We get

a square root function shifted to right 4 units and stretched vertically by a factor of 2.

We can also prove this by graphing.

Answer:

\((\frac{f}{g})(x) = \sqrt{x + 1}\)

Step-by-step explanation:

Given

\(f(x) = \sqrt{x^2 - 1\)

\(g(x) =\sqrt{x - 1\)

Required

Find \((\frac{f}{g})(x)\)

\((\frac{f}{g})(x)\) is calculated as:

\((\frac{f}{g})(x) = \frac{f(x)}{g(x)}\)

This gives:

\((\frac{f}{g})(x) = \frac{\sqrt{x^2 - 1}}{\sqrt{x - 1}}\)

Apply difference of two squares on the numerator

\((\frac{f}{g})(x) = \frac{\sqrt{x - 1}*\sqrt{x + 1}}{\sqrt{x - 1}}\)

\((\frac{f}{g})(x) = \sqrt{x + 1}\)

Answer:

Bill earns $220.00 in 22 weeks.

Step-by-step explanation:

If he is paid 20 dollars every 2 weeks for a car wash, we need to find out how many he gets for 22 weeks.

20 dollars = 2 weeks, to find 22, multiply both of the values by 11 to get to 22.

11(2 weeks = 20 dollars)

22 weeks = 220.

The amount of money earned in 22 weeks is $220.

Option D is the correct answer.

An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.

Example: 2 + 3x + 4y = 7 is an expression.

We have,

The amount for each car wash = $20

Number of car wash in two weeks = 1

Now,

Number of car washes in 22 weeks.

= 22 / 2

= 11

Now,

The amount earned in 11 car washes.

= 11 x 20

= $220

Thus,

Amount earned in 22 weeks is $220.

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8+z/3=12

8+4=12

12/3=4

z=12

Answer: x = 10

see in the picture, ΔACE has:

+) BF//AE

+) B and F are  midpoints.

=> BF is the median line of the triangle ACE

=> BF = 1/2. AE

=> AE = 2BF

⇔ 5x - 4 = 2.23 = 46

⇔ 5x = 46 + 4 = 50

⇔ x = 50/5 = 10

Step-by-step explanation:

Answer:

The naswer is 6

Step-by-step explanation:

Answer:

the mean is 10

Step-by-step explanation:

4+6+8+20+12=50

50÷5=10

so the mean is 10

Answer:

A

Step-by-step explanation:

40×10=40

2×1=2

5×1/10=0.5

2×1/100=0.09

3×1/1000=0.003

40+2+0.5+0.09+0.003=42.593

The expression (a) (4 * 10) + (2 * 1) + (5 * 1/10) + (9 * 1/100) + (3 * 1/1000) has a greater value

To determine the expression greater than 42.537, we simply solve the given options till we arrive at a solution.

For option A, we have:

(4 * 10) + (2 * 1) + (5 * 1/10) + (9 * 1/100) + (3 * 1/1000)

Evaluate the products

40 + 2 + 0.5 + 0.09 + 0.003

Evaluate the sum

42.593

By comparison,

42.593 is greater than 42.537

Hence, the expression (a) has a greater value

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The scientific notation of the given number is 6.11×10⁻⁴. Therefore, option E is the correct answer.

Scientific notation is a method for expressing a given quantity as a number having significant digits necessary for a specified degree of accuracy, multiplied by 10 to the appropriate power such as 1.56×10⁷.

The given decimal number is 0.000611.

0.000611 in scientific notation, we get

6.11×10⁻⁴

Therefore, option E is the correct answer.

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Answer: 2.214285714, probably B maybe? I'm not sure what D is.

Step-by-step explanation: (14)x + 1 = 32.

Your goal here is to get the x by itself so that you will know how much it is worth.

First step I would take is to subtract 1 from both sides to get rid of the one on the side with the x. What you do on one side is what you must do on the other side.

Now you have (14)x = 31

Next step I would take is divide both sides by 14 so that you can finally get the x by itself.

Now you have 2.214285714, so I would choose whatever answer that is closest to.

Answer:

The y value of a point where a vertical line intersects a graph represents an output for that input x value. If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output.

The equation of line H in fully simplified slope-intercept form is y = 15x + 10.

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical expression:

y - y₁ = m(x - x₁)

Where:

First of all, we would find the slope of this line;

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m) = (40 - 10)/(2 - 0)

Slope (m) = 30/2

Slope (m) = 15.

At data point (0, 10) and a slope of 15, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 10 = 15(x - 0)

y = 15x + 10

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Missing information:

The question is incomplete and the complete question is shown in the attached picture.

The required probability of drawing a red marble from the bag and any specific card from the deck is 1/156.

There are 12 marbles in the bag, and 4 of them are red, so the probability of drawing a red marble is 4/12, or 1/3.

There are 52 cards in the deck, and the probability of drawing any specific card is 1/52.

This probability assumes that the events are independent, meaning that the outcome of one event does not affect the outcome of the other event.

In this case, drawing a marble from the bag and drawing a card from the deck are independent events, so their probabilities can be multiplied.

Therefore, the probability of drawing a red marble from the bag and any specific card from the deck is (1/3) x (1/52) = 1/156.

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Answer:

54 = 6x

Step-by-step explanation:

Answer:

A = $2122.17

Step-by-step explanation:

Before we start plugging everything in, we must convert the rate 7% to a decimal.  Thus r = 0.07 as 7/100 = 0.07.  Now we can plug in 1500 for P, 0.07 for r, 4 for k, and 5 for t in compound interest formula, then round to the nearest hundredth to find the amount, A:

A = 1500(1 + 0.07/4)^(4 * 5)

A = 1500(1.0175)^(20)

A = 2122.167294

A = 2122.17

Thus, the amount accumulated after investing $1500 for 5 years at an interest rate of 7% compounded 4 times per year is about $2122.17.

The domain of the composite functions:

a). (f + g)(-2) = 23

b). (f - g) (-2) = 1

c). f(x) - g(x) = x² - 5x - 13

A function is composite when the co- domain of the first mapping is the domain of the second mapping

Given the functions f(x) = x² - 4x and g(x) = x + 13, we shall evaluate the domains of the functions as follows:

a). (f + g)(-2) = (-2)² - 4(-2) + (-2) + 13

(f + g)(-2) = 4 + 8 - 2 + 13

(f + g)(-2) = 23

b). (f - g) (-2) = (-2)² - 4(-2) - (-2) - 13

(f - g)(-2) = 4 + 8 + 2 - 13

(f - g) (-2) = 1

c). f(x) - g(x) = x² - 4x - x - 13

f(x) - g(x) = x² - 5x - 13

Therefore, the domain of the composite functions:

a). (f + g)(-2) = 23

b). (f - g) (-2) = 1

c). f(x) - g(x) = x² - 5x - 13

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Answer:

(59-6) × \(\sf{(\frac{1}{3})}^{3}\) + 27 ÷ 3

=53 × \(\sf\frac{{1}^{3}}{{3}^{3}}\) + 3³ ÷ 3

=53 × \(\sf\frac{1}{27}\) + \(\sf{3}^{3-1}\)

=\(\sf\frac{53\times1}{27}\) + \(\sf{3}^{2}\)

=\(\sf\frac{53}{27}\) + 9

=9 + \(\sf\frac{53}{27}\) + 9

=\(\sf\frac{9\times27+53}{27}\)

=\(\sf\frac{243+53}{27}\)

=\(\sf\frac{296}{27}\)

=\(\sf\frac{270}{27}+\frac{26}{27}\)

=\(\sf10+\frac{26}{27}\)

=\(\sf10\frac{26}{27}\)

\(\sf\:\)

8² ÷ 4 × (2 + 3) - 9

=(8×8) ÷ 4 × 5 - 9

=64 ÷ 4 × 5 - 9

=4³ ÷ 4 × 5 - 9

=\(\sf{4}^{3-1}\) × 5 - 9

=4² × 5 - 9

=(4×4) × 5 - 9

=16 × 5 - 9

=80 - 9

=71

Answer:

D

Step-by-step explanation:

hhgxhsbjxkxjebdibfhejx

Answer:

Always

Step-by-step explanation:

We know that,

As every natural number n be represented in a rational form: n/1, any natural number can be represented in the form p/q, where q≠0. Hence, all natural numbers are rational numbers.