Which statement best describes the function?

A. The function is negative when x<0

B.the function is negative when x<0 and when x>0

C. The function is never negative

D. The function is negative when x>0

If sinθ⋅cosθ = 1/2, then the value of sinθ + cosθ = √2

We know that the trigonometric sine function is nothinng but the ratio of the length of the opposite side of angle to that of the hypotenuse in a right triangle.

And cosine function (cos function) is the ratio of the length of the adjacent side of angle to that of the hypotenuse.

Given that  sinθ⋅cosθ = 1/2

2(sinθ⋅cosθ) = 1             .........(1)

We know that trigonometric identity,

sin(2θ) = 2 sinθ cosθ

so equation (1) becomes,

sin(2θ) = 1            

We know that sin(π/2) = 1

Comparing with equation sin(2θ) = 1 we get,

2θ = π/2

θ = π/4          

Using trigonometric table,

sin(π/4) = 1/√2

and cos(π/4) = 1/√2

The value of  sinθ+cosθ would be,

sin(π/4) + cos(π/4)

= (1/√2) + (1/√2)

= 2/√2

= √2

Learn more about equation here:

https://brainly.com/question/649785

#SPJ4

The complete question is:

If sinθ⋅cosθ=1/2 find the value of sinθ+cosθ

The ordered pairs that defines the solutions of the system of equations f(x) = x² - 2x + 3; f(x) = -2x + 7 are

(2, 3) and (-2, 11)

Ordered pairs refers to the arrangement of 2 numbers in the form (a, b)

As used in the cartesian coordinates

a refers to a point in the x direction b refers to a point in the y direction

Solutions of the system of equation is the points where the straight line intersect the curve or where the two graphs intersect.

the point of intersection

x² - 2x + 3 = -2x + 7

x² - 2x + 2x + 3 - 7 = 0

x² + 3 - 7 = 0

x² - 4 = 0

solving for x

x² = 4

x = √4

x = 2 OR -2

solving for y

For x = 2, y = -2 * 2 + 7 = 3

For x = -2, y = -2 * -2 + 7 = 11

hence we have the points to be (2, 3) and (-2, 11)

Learn more about ordered pairs here:

https://brainly.com/question/29232584

#SPJ1

The numbers are sort from least to greatest as 0, 1/13, 49/100, 8/9, 1/2, 1, 11/10

A fraction can be defined as the part of a whole number, variable or element.

There are several types of fractions, some of which includes;

From the information given, we have the fractions;

0, 1, 1/2, 8/9, 49/100, 11/10, 1/13

To arrange the values from least to greatest, we have to divide the fractions and find their decimal forms, we have;

1/2 = 0.5

8/9 = 0.89

49/100 = 0.49

11/10 = 1.1

1/13 = 0. 08

However, the arrangement is 0, 1/13, 49/100, 8/9, 1/2, 1, 11/10

Learn more about fractions here:

https://brainly.com/question/78672

#SPJ1

a) The ordered pair so that the set still remains the function is (-5, 17)

b) The ordered pair so that the set does not remain the function is (-26, 15).

In mathematics, a function is represented as a rule that produces a distinct result for each input x. In mathematics, a function is indicated by a mapping or transformation. The collection of all the values that the function may input while it is defined is known as the domain. The entire set of values that the function's output can produce is referred to as the range. The set of values that could be a function's outputs is known as the co-domain.

Given:

A Relation is said to be a function if the input value or the x- value is unique and have their corresponding output.

But if the input value repeats then it may no longer be a function.

First, Add a ordered pair so that the set still remains the function as

(-5, 17)

and, Add a ordered pair so that the set does not remain the function as

(-26, 15).

Learn more about Function here:

https://brainly.com/question/12431044

#SPJ1

A logarithm is the inverse operation of exponentiation, that is to say, log(a^b) = b, where log is logarithm, a is the base and b is the exponent.

A logarithmic function is called such because it relates the logarithm of a number to the number itself.

In other words, it is a function that expresses the value of the logarithm for a given number. This function is represented by the notation y = logb(x) where y is the logarithm, b is the base, and x is the number.

The logarithmic function is used to solve exponential equations, it is also useful in many fields such as mathematics, physics, engineering, and finance.

To know more about logarithms visit: brainly.com/question/28346542

#SPJ4

The rectangular prism's volume is equal to [tex]$V=9.375 \mathrm{~m}^3$[/tex]. Prism volume (V) is equal to B ×h, where h is the prism's height and B is the area of the base.

1.25 metres in length, 2.5 metres in width, 3 metres in height, and a diagonal length of 4.10030487 metres make up the total surface area. [tex]$\mathrm{S}_{\text {tot }}[/tex]=[tex]28.75 \mathrm{~m}^2$[/tex] , Latitudinally exposed area [tex]$S_{\text {lat }}=22.5 \mathrm{~m}^2$[/tex] , maximum surface area is [tex]$S_{\text {top }}=3.125 \mathrm{~m}^2$[/tex] , surface area of the ground is [tex]$S_{\text {bot }}=3.125 \mathrm{~m}^2$[/tex] so that the volume is [tex]$V=9.375 \mathrm{~m}^3$[/tex]

When determining the volume of a rectangular prism , we multiply its length, width, and height. The base's area multiplied by the height gives the rectangular prism its volume. Length, width, and height are the cubic units that make up a rectangular prism's volume. Any rectangular solid's volume, V, is equal to the sum of its dimensions, height, width, and depth. In terms of the area of the base, we might alternatively express the formula for a rectangular solid's volume. Size times width equals the base's area, B.

To learn more about rectangular prism refer to :

https://brainly.com/question/24284033

#SPJ1

Answer:

Mary bought the most flour

Step-by-step explanation:

Ana bought 12 3/6 kg of flour

12 3/6 = 75/6 = 12.5 kg of flour

Mary has brought 14 2/8 kg of flour

14 2/8 = 114/8 = 14.25 kg of flour

Kristina bought 11 8/12 kg of flour.

11 8/12 = 140/12 = 11.66 kg of flour

So, Mary bought the most flour.

The opposite of number 27 is -27

We know that the opposite of a number is nothing but the number which is at the same distance from 0 but in the opposite direction on a number line.

Here we have been givena number 27

Let a number 'p' be the opposite of number 27

If we plot 27 on the number line then we can observe that it is  located to the right of 0 on the number line.

So, from the definition of opposite of a number p would be at the same distance from 0  i.e., 27 units but in the opposite direction on a number line.

so, the number p would be -27

Therefore, -27 is opposite of 27

Learn more about the number here:

https://brainly.com/question/28210925

#SPJ4

The length of HG can be expressed as HG = b√2.

Triangle is a three-sided polygon with three straight sides that intersect at three vertices. It is one of the most basic shapes in geometry and is found in nature in the form of mountains, icebergs and even the human face. It has a variety of applications in mathematics, engineering, and other fields. Triangles are also used to define angles and even the area of a plane.

This is because the triangle is a right triangle, and the Pythagorean Theorem states that the sum of the squares of the two shorter sides is equal to the square of the hypotenuse. Therefore,
HG2 = b2 + b2 = 2b2,
which reduces to HG = b√2.

To know more about triangle click-
https://brainly.com/question/309896
#SPJ1

When 392,196 is divided by 87, the answer obtained using long division is 4,508.

The mathematical procedure for splitting big numbers into several smaller groups or sections is known as long division. The dividend is the number we divide into smaller groups, while the divisor is the number through which we divide. Difficulty difficulty can be solved by breaking it down into manageable parts.

Dividend : 392,196

Divisor: 87 (number that divides)

39 / 87 = 0

392 / 87 = 4 (87x 4 = 348) - 4 is the first digit of the result

392 - 348 = 44 (remainder)

441 (next digit is one) / 87 = 5 (87x 5= 435) - 5 is the second digit

441-435 = 6 (remainder)

69 / 87 = not possible so add a 0, which is the third digit

696 / 87 = 8 (87x 8 = 696)

696- 696 = 0 (not remainder)

When 392,196 is divided by 87, the answer obtained using long division is 4,508.

To know more about long division visit:

https://brainly.com/question/13625284

#SPJ1

I understand that the question you are looking for is:

392,196 divided by 87 (Using long division)

Answer:

37?

I am SO sorry if this is wrong

The distance between points L and K is 4 units.

The distance formula between two points (x₁, y₁) and (x₂, y₂) is gien by,

[tex]D = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2[/tex].

Given, Are two points L and K.

The coordinate points of L(- 2, 6) and K(- 2, 2).

Therefore, The distance between points L and K is,

[tex]|LK| = \sqrt{(- 2 + 2)^2 + (2 - 6)^2}[/tex].

[tex]|LK| = \sqrt{16}[/tex].

[tex]|LK| = 4[/tex].

learn more about the distance formula here :

https://brainly.com/question/12040665

#SPJ1

The F-ratio is a measure used in statistical tests, specifically in ANOVA (Analysis of Variance) to test for differences between means of multiple groups.

a) On average, what value is expected for the F-ratio if the null hypothesis is true?

The answer is a. 1. If the null hypothesis is true, it means that there is no significant difference between the means of the groups being compared. Under this assumption, the F-ratio is expected to have a value close to 1, as the variance between the groups is not significantly different from the variance within the groups.

b) On average, what value is expected for the F-ratio if the null hypothesis is false?

The answer is d. Much greater than 1.00. If the null hypothesis is false, it means that there is a significant difference between the means of the groups being compared. Under this assumption, the F-ratio is expected to have a value much greater than 1, as the variance between the groups is significantly larger than the variance within the groups.

To learn more about F-ratio,

https://brainly.com/question/27310923

#SPJ4

All expressions that are equivalent to 8.5x + 0.5 +3.5x - 2x are (12x - 2x + 0.5) and (10x + 0.5).

Expressions that are equivalent perform the same thing even when they have distinct appearances.

When we enter the same value for the variable, two algebraic expressions that are equivalent have the same value.

By combining like terms, we can create expressions that are equivalent to a given expression. Terms with the same variables raised to the same powers are said to be "like terms". 

Here we have

8.5x + 0.5 +3.5x - 2x

The above expression can be simplified as given below

=>  8.5x + 0.5 +3.5x - 2x  

Add and subtract like terms

=> 8.5x +3.5x - 2x + 0.5

=> 12x - 2x + 0.5

=> 10x + 0.5  

Therefore,

All expressions that are equivalent to 8.5x + 0.5 +3.5x - 2x are (12x - 2x + 0.5) and (10x + 0.5).

Learn more about Equivalent expressions at

https://brainly.com/question/24242989

#SPJ1

The domain of a logarithm function is (0, ∞). The range of the logarithm function is all real numbers.

What is a function?

A function in mathematics from a set X to a set Y allocates exactly one element of Y to each element of X. The sets X and Y are collectively referred to as the function's domain and codomain, respectively.

The given function is f(x) = log x.

When the value of x is less than or equal to 0, then the value of log x is undefined.

The possible value of x where f(x) exists is the domain of a function.

In the given function the value of x must be greater than zero.

The domain of the function is (0,∞).

log (0.1) = -1

log (0.023) = -1.638

The value of log x can be any real number.

The possible value of the logarithm function is any real number. Thus the range of the function is (-∞, ∞).

To learn more about domain and range, click on the below link:

https://brainly.com/question/16444481

#SPJ4

Answer:

I)3^4 x 3^7=3^4+7(b/c the base is similar)

3^4 x 3^7=3^11

Ii) first 3^4=3x3x3x3=81

3^7=2187

then 81 x 2187=177147

a) An equation to find the percent P of recorded music sold as full-length cassettes for any year x between 2001 and 2006 : y = -0.5x + 3.4

b) The percent of recorded music sold as full-length cassettes in 2004 = 1.9%

As, between 2001 and 2006, the percent of recorded music sold was decreased by about 0. 5% per year.

This means, the slope m = -0.5

In 2001, full-length cassettes represented 3. 4% of total music sales.

This means the y-intercept would be c = 3.4

So, an equation to find the percent P of recorded music sold as full-length cassettes for any year x between 2001 and 2006 would be,

y = mx + c

Substituting value of m and c,

y = -0.5x + 3.4

Now  to find the percent of recorded music sold as full-length cassettes in 2004

Here, the number of years x would be

x = 2004 - 2001

x = 3

So, the percent of recorded music sold would be,

y = (-0.5 × 3) + 3.4

y = 1.9%

Learn more about an equation here:

https://brainly.com/question/649785

#SPJ4

Therefore , the solution of the given problem of probability comes out to be  P =0.286(approx).

Probability is the likelihood or potential for something to event.  For instance, there is only one way to get a head and a total of two possible outcomes, hence the probability of flipping a coin and getting heads is 1 in 2. (a head or tail). P(heads) must equal 12. Classical: (equally likely results) (equally probable outcomes) S, the sample location (the collection of all distinct outcomes that could occur), Definition of Relative Frequency and Subjective Probability.

Here,

Given : S = {9,10,11,12,13,14,15}

If A is a subset of S, A could be {14,15}.

If a subset A represents the complement of spinning a number greater than 13, its sample space is A = {14,15}.

Thus,

To find the probability that it will land on number greater than 13

P = likelihood of event / total no of events

=> P = 2/7

=> P = 0.2857

=> P =0.286(approx)

Therefore , the solution of the given problem of probability comes out to be  P =0.286(approx).

To know more about probability , visit

https://brainly.com/question/30034780

#SPJ1

Answer: As for the inequality question you asked,

-2/3, -11/3, and 2.5 are decimal numbers.

-11/3 is smaller than -2/3 because -3.67 is smaller than -0.67

-2/3 is smaller than 2.5 because -0.67 is smaller than 2.5

So the inequality that correctly orders the numbers -2/3, -11/3, and 2.5 is -11/3 < -2/3 < 2.5

It's worth noting that this inequality uses the less than (<) symbol to show the order of the numbers from the smallest to the largest, and it's also worth to remember that this inequality is true only for these specific values, if any of the values were changed it would've resulted in a different inequality.

Step-by-step explanation:

By the concept of the proportional method we determine that the height of the tower would be 48 feet.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

The model given can be interpreted by the concept of proportional method

a : b : : c : d.

Therefore,

5 : 6 : : 40 : x.

5/6 = 40/x.

5x = 240.

x = 240/5.

x = 48 feet.

learn more about proportion here :

https://brainly.com/question/7096655

A function whose equation is of the form y = ax + b, where a and b are constants, a does not equal zero, and x is any real number, and whose graph is a straight line.

Given an equation y = 14x -4 there is an equation that is perpendicular to this given equation.

from the slope-intercept of a linear equation:

The linear function equation is the slope-intercept form. Thus, it is expressed as f(x) = mx + b where m is the slope and b is the y-intercept of the line.

thus the slope of the given equation is 14

The slope of the required equation = 1/14

Since both equations are perpendicular

From the slope intercept of the required line equation of a line:

y = 1/14x + c...(2)

Since, it passes through the point (28, 16)

Thus, 16 = 1/14 *28 + c

c = 16

from equation 2

y = 1/14 x + 14

from the table, two given coordinates of a linear function are (4, 36) and (6, 56)

thus slope of the line = (y₂ - y₁) / (x₂ - x₁)

Slope of the line = 20/2 = 10

Equation of a line:

y = 10x +c

Since, it passes through the point  (4, 36)

Thus, 36 = 40 + c

c = -4

Therefore, the required equation from the table is y = 10x - 4

Learn more about linear functions here:

https://brainly.com/question/11897796

#SPJ1

Answer:

The numbers are being divided by 2 each time.

240/2 = 120

120/2 = 60

So the next set of numbers would be:

30, 15 because

60/2 = 30

30/2 = 15

Step-by-step explanation:

Hope it helps!

Answer:     [tex]\frac{3}{8}[/tex]➗[tex]\frac{3}{4}[/tex]

Step-by-step explanation:  Are you looking to work out and calculate how to multiply 3/8 by 3/4? In this really simple guide, we'll teach you exactly what 3/8 times 3/4 is and walk you through the step-by-process of how to multiply two fractions together.

Answer: 1. The first graph has the x and y axis values as minutes and frequency, but the title is bicycling.

2. it's a dotted graph, which doesn't give enough information since that graph does not have to be linear, but when you have a graph like that you want a line graph.

Answer:

the other dude answered it better than i did

Step-by-step explanation:

Can be cracked within eight hours by the average hacker.

With spaces included in the character count, 8 characters equals between 1 and 2 words. If spaces are excluded from the character count, 8 characters equals between 1 and 3 words.

There are 8-character passwords with capital letters, lowercase letters, and numerals that begin and end with the same symbol.A password of eight characters with just lowercase and capital letters offers 200 billion potential permutations.“1uppercase” is an example of an 8-character password. This password has one uppercase, one lowercase, one number, and one special character.

To learn more about  8-character passwords to refer:

https://brainly.com/question/13543093

#SPJ4

Answer:

-4.3

Step-by-step explanation:

It is asking for the temperature at midnight so to find out what it is. We simply subtract the starting temperature of 11.4f from 15.7 degrees

( 11.4 - 15.7 ). That would leave us with -4.3f at night.

Answer:

25

Step-by-step explanation:

Given expression:

[tex]5^{1125} \times 0.2^{1123}[/tex]

Rewrite 0.2 as a fraction:

[tex]\implies 5^{1125} \times \left(\dfrac{1}{5}\right)^{1123}[/tex]

[tex]\textsf{Apply exponent rule} \quad \left(\dfrac{a}{b}\right)^c=\dfrac{a^c}{b^c}:[/tex]

[tex]\implies 5^{1125} \times \dfrac{1^{1123}}{5^{1123}}[/tex]

Simplify the numerator by applying the exponent rule a¹ = a:

[tex]\implies 5^{1125} \times \dfrac{1}{5^{1123}}[/tex]

[tex]\textsf{Apply the fraction rule} \quad a \times \dfrac{b}{c}=\dfrac{ab}{c}:[/tex]

[tex]\implies \dfrac{5^{1125} \times1}{5^{1123}}[/tex]

[tex]\implies \dfrac{5^{1125}}{5^{1123}}[/tex]

[tex]\textsf{Apply exponent rule} \quad \dfrac{a^b}{a^c}=a^{b-c}:[/tex]

[tex]\implies 5^{1125-1123}[/tex]

Simplify the exponent:

[tex]\implies 5^{2}[/tex]

Simplify:

[tex]\implies 5 \cdot 5[/tex]

[tex]\implies 25[/tex]

A right triangle with congruent legs and acute angles is an Isosceles Right Triangle.

A special right triangle is a right triangle that has a consistent characteristic that facilitates calculations on the triangle or for which straightforward formulas are available.

Angles in a right triangle, for instance, might create straightforward connections like 45°-45°-90°. An "angle-based" right triangle is what this is. When the side lengths of a right triangle form ratios of whole numbers, such as 3:4:5, or other unusual numbers, like the golden ratio, the triangle is said to be "side-based."

Without using more complex techniques, one can rapidly determine different lengths in geometric problems by understanding the relationships between the angles or side ratios of certain particular right triangles.

Learn more about the Triangles here;

brainly.com/question/30108144

#SPJ4

The numbers in the arrangement can be represented by x, y, z, a, b, c and d, where x is at the top and d is at the bottom. The relationship between the numbers is as follows:

x = y - z

y = a - b

z = c - d

We can use this information to find the values of z, c, and d in terms of x, y, and a:

z = y - x

c = z + d

d = z - c

Since we are looking for the four greatest distinct possible values for z, we can assume that x, y, and a are as small as possible (i.e. 0) and c and d are as large as possible.

Thus, the four greatest distinct possible values for z are:

z = y - x = 0 - 0 = 0

z = a - y = 0 - 0 = 0

z = c - d = c

z = c - d = d

The sum of these four values is 0 + 0 + c + d = c+d.

To know more about algebra visit :

https://brainly.com/question/24875240

#SPJ4