Explain why every positive number has two square roots.

The trigonometric value equation is solved and sin θ = 24/25

Given data ,

Let the triangle be represented as ΔABC

Now , the measure of sides of the triangle are

From the trigonometric relations , we get

sin θ = opposite / hypotenuse

cos θ = adjacent / hypotenuse

tan θ = opposite / adjacent

tan θ = sin θ / cos θ

And , sin² θ + cos² θ = 1

where the measure of cos θ = 7/25

On simplifying the equation , we get

sin θ = √ ( 1 - cos² θ )

sin θ = √ ( 1 - 49/625 )

sin θ = √576/625

sin θ = 24/25

Hence , the trigonometric relation is sin θ = 24/25

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Answer:

(-1, 1.5).

Step-by-step explanation:

To find the midpoint of line segment AB with endpoints A(2, 5) and B(-4, -2), you can use the midpoint formula. The midpoint formula states that the midpoint (M) of a line segment with endpoints (x₁, y₁) and (x₂, y₂) is given by:

M = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)

Let's calculate the midpoint using this formula:

x-coordinate of midpoint:

x = (2 + (-4)) / 2 = -2 / 2 = -1

y-coordinate of midpoint:

y = (5 + (-2)) / 2 = 3 / 2 = 1.5

Therefore, the midpoint of line AB is M(-1, 1.5).

Answer:

11/66, or 11 times

Based on the above. (see image attached), The value of GF in the rhombus is option A: 26.4

A four-sided shape with equal side lengths is known as a rhombus. Equally sided four-sided figure is also referred to as an equilateral quadrilateral, because equilateral denotes that its sides have the same length.

Note that the properties of a rhombus are :

So, note that:

DH = HF = 16

GH = HE = 21

Therefore, by Using Pythagoras theorem we can look for GF by:

GF = √21² + 16²

= √441 + 256

= √697

= 26.4007575649

= 26.4

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The domain of the composite function (f - g)(-1) is derived to be 12 which makes c the correct option.

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

We shall evaluate the domains of the function (f - g)(-1) as follows:

Observing from the table of values, at the point x = -1 we have;

f(x) = 5 and g(x) = -7

So;

(f - g)(-1) = 5 - (-7)

(f - g)(-1) = 5 + 7

(f - g)(-1) = 12

Therefore, the value for domain of the composite function (f - g)(-1) is derived to be 12.

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Answer:

8 hours and 20 minutes

Step-by-step explanation:

Let's assume the distance between Lagos and Port Harcourt is approximately 500 kilometers. With an average speed of 60 km per hour, we can use the formula:

Time = Distance / Speed

Substituting the values, we get:

Time = 500 km / 60 km/h ≈ 8.33 hours

Therefore, it would take approximately 8 hours and 20 minutes for the car to travel from Lagos to Port Harcourt, assuming the distance is around 500 kilometers and the average speed is 60 km per hour. Please note that this is just an example calculation, and the actual time may vary depending on the distance and road conditions.

The value of x is 12.82, the value of z is 40.25.

Using Pythagorean theorem

50²= 39² + y²

y²= 2500- 1521

y= 32.28

Again Using Pythagorean theorem

z²= y²+ x²

z²- x²= 979

and, (39 + x)² = 50² + z²

(39 + x)² = 50² + (x² + 979)

1521 + 78x + x² = 2500 + x² + 979

78x = 1000

x ≈ 12.82

Substituting this value of x back into the first equation, we get:

z² - x² = 979

z² - (12.82)² = 979

z² ≈ 1620.12

Taking the square root of both sides, we get:

z ≈ 40.25

Therefore, the value of x is 12.82, the value of z is 40.25.

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26. The length FE in the circle is 6 units

27. The arc AE has a measure of 64 degrees

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

The circle

Given that the lengths from the center to either chords are equal

This means that

FE = 6 units

For the other circle, we have

BC = 58 degrees

AB = ED

The arc AE is calculated as

AE = 180 - BC - ED

Where

AB = ED = BC = 58 degrees

So, we have

AE = 180 - 58 - 58

Evaluate

AE = 64

Hence, the arc AE is 64 degrees

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[tex]6\left[\cos\left( \frac{11\pi }{6} \right) +i\sin\left( \frac{11\pi }{6} \right) \right] \\\\\\ 6\left[\cfrac{\sqrt{3}}{2}~~,~-\cfrac{1}{2}i \right]\implies (3\sqrt{3}~~,~-3i) ~~ \approx ~~ \stackrel{ \textit{\LARGE S} }{(5.2~~,~-3i)}[/tex]

Answer:

-------------------------

Use the formula for the sum of n terms of a GP:

And use the nth term formula:

We can rearrange the sum formula to solve for the first term:

Plugging in the given values, we get:

Therefore, the first term of the GP is 121.5.

The cosine of the angle's complement is 20/29

Let's start by using the fact that the sum of the measures of an angle and its complement is 90 degrees.

Let's call the angle A, and its complement B. Then we have:

cos A = 21/29

We want to find cos B. We know that cos B = sin A, because the sine of an angle is equal to the cosine of its complement.

So we need to find sin A.

We can use the Pythagorean identity:

sin²A + cos²A = 1

Substituting in cos A = 21/29, we get:

sin²A + (21/29)² = 1

Solving for sin A, we get:

sin A = ± 20/29

Therefore, we have:

cos B = sin A = 20/29

Hence, the cosine of the angle's complement is 20/29

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The three true statements about the function and its graph are The graph of the function is a parabola, The graph does not open down (it opens upwards). and None of the given points, (20, -8) or (0, 0), lie on the graph.

Based on the quadratic function f(x) = x^2 – 5x + 12:

The value of f(-10) = 82 is not true.

To find the value of f(-10), substitute x = -10 into the function: f(-10) = (-10)^2 - 5(-10) + 12 = 100 + 50 + 12 = 162.

The graph of the function is a parabola.

This statement is true. The quadratic function has a degree of 2, which means its graph will be a parabola.

The graph of the function opens down.

This statement is not true. The coefficient of the x^2 term in the quadratic function is positive (1), so the parabola opens upwards.

The graph contains the point (20, -8).

This statement is not true. To verify if the point (20, -8) is on the graph, substitute x = 20 into the function: f(20) = (20)^2 - 5(20) + 12 = 400 - 100 + 12 = 312. Therefore, the point (20, -8) does not lie on the graph.

The graph contains the point (0, 0).

This statement is not true. To verify if the point (0, 0) is on the graph, substitute x = 0 into the function: f(0) = (0)^2 - 5(0) + 12 = 0 - 0 + 12 = 12. Therefore, the point (0, 0) does not lie on the graph.

Therefore, the three true statements about the function and its graph are:

The graph of the function is a parabola.

The graph does not open down (it opens upwards).

None of the given points, (20, -8) or (0, 0), lie on the graph.

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The answers to all parts is shown below.

a. According to the graph, the concentration after 8 hours is approximately 22 mg/L.

b. The concentration increases from 0 to approximately 30 mg/L over the first 4 hours, and then decreases from approximately 30 mg/L to 16 mg/L between 4 and 20 hours.

c. The drug is at its maximum concentration after approximately 4 hours, with a maximum concentration of approximately 30 mg/L.

d. According to the graph, it takes approximately 12 hours for the concentration to decrease from the maximum concentration of approximately 30 mg/L to 16 mg/L.

e. After 1 week, the graph predicts that the concentration will be very close to 0 mg/L. After 1 month, the concentration is predicted to be essentially 0 mg/L.

f. During the first 4 hours, the concentration increases from 0 to approximately 30 mg/L.

Between 4 and 8 hours, the concentration decreases slightly from approximately 30 mg/L to 28 mg/L.

Between 8 and 12 hours, the concentration decreases more rapidly from 28 mg/L to approximately 22 mg/L.

Between 12 and 20 hours, the concentration decreases gradually from 22 mg/L to 16 mg/L.

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The probability of rolling a number other than 1 on a standard number cube is 5/6.

When rolling a standard number cube, there are six equally likely outcomes, one for each face of the cube. To find the probability of rolling a number other than 1, we need to determine the number of              favorable outcomes and divide it by the total number of possible outcomes.

In this case, the favorable outcomes are rolling any number from 2 to 6, which gives us five possibilities. Therefore, the probability of rolling a number other than 1 is 5 out of 6.

Expressing this as a fraction, the probability can be written as 5/6. This means that out of all the possible outcomes, there is a 5/6 chance of rolling a number that is not 1.

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Answer:

[tex]\sin\theta=\dfrac{\sqrt{5}}{5}[/tex]

[tex]\cos\theta=\dfrac{2\sqrt{5}}{5}[/tex]

[tex]\tan\theta=\dfrac{1}{2}[/tex]

[tex]\csc\theta=\sqrt{5}[/tex]

[tex]\sec\theta=\dfrac{\sqrt{5}}{2}[/tex]

Step-by-step explanation:

The cotangent ratio is the reciprocal of the tangent ratio.

[tex]\cot \theta = \dfrac{1}{\tan \theta}[/tex]

Therefore, if cot θ = 2 then:

[tex]\dfrac{1}{\tan \theta}=2[/tex]

[tex]\tan \theta=\dfrac{1}{2}[/tex]

The tangent of an angle is defined as the ratio of the length of the opposite side to the length of the adjacent side in a right triangle:

[tex]\tan\theta = \sf \dfrac{opposite}{adjacent}[/tex]

Therefore, the length of the side opposite angle θ is 1 and the length of the side adjacent angle θ is 2.

[tex]\boxed{\begin{minipage}{9 cm}\underline{Pythagoras Theorem} \\\\$a^2+b^2=c^2$\\\\where:\\ \phantom{ww}$\bullet$ $a$ and $b$ are the legs of the right triangle. \\ \phantom{ww}$\bullet$ $c$ is the hypotenuse (longest side) of the right triangle.\\\end{minipage}}[/tex]

We can use Pythagoras Theorem to calculate the length of the hypotenuse, H:

[tex]1^2+2^2=H^2[/tex]

[tex]1+4=H^2[/tex]

[tex]H^2=5[/tex]

[tex]H=\sqrt{5}[/tex]

Therefore, the length of the hypotenuse is √5.

Now we have the lengths of the three sides of the right triangle, we can find the other trigonometric function of angle θ.

[tex]\boxed{\begin{minipage}{8cm}\underline{Trigonometric functions}\\\\$\sf \sin\theta=\dfrac{O}{H}\quad\cos\theta=\dfrac{A}{H}\quad\tan\theta=\dfrac{O}{A}$\\\\\\$\sf\csc\theta=\dfrac{H}{O}\quad\sec\theta=\dfrac{H}{A}\quad\cot\theta=\dfrac{A}{O}$\\\\\\where:\\\phantom{ww}$\bullet$ $\theta$ is the angle.\\\phantom{ww}$\bullet$ $\sf O$ is the side opposite the angle.\\\phantom{ww}$\bullet$ $\sf A$ is the side adjacent the angle.\\\phantom{ww}$\bullet$ $\sf H$ is the hypotenuse.\\\end{minipage}}[/tex]

Given values:

Substitute these values into the six trigonometric functions:

[tex]\sin\theta=\dfrac{O}{H}=\dfrac{1}{\sqrt{5}}=\dfrac{\sqrt{5}}{5}[/tex]

[tex]\cos\theta=\dfrac{A}{H}=\dfrac{2}{\sqrt{5}}=\dfrac{2\sqrt{5}}{5}[/tex]

[tex]\tan\theta=\dfrac{O}{A}=\dfrac{1}{2}[/tex]

[tex]\csc\theta=\dfrac{H}{O}=\dfrac{\sqrt{5}}{1}=\sqrt{5}[/tex]

[tex]\sec\theta=\dfrac{H}{A}=\dfrac{\sqrt{5}}{2}[/tex]

[tex]\cot\theta=\dfrac{A}{O}=\dfrac{2}{1}=2[/tex]

Answer:

5

Hope this helps!

Step-by-step explanation:

Plug in m = 1 into the equation.

m = 1  :  [tex]\frac{4}{m} +1[/tex]  =>  [tex]\frac{4}{(1)} +1[/tex] = 4 + 1 = 5

Answer:

Step-by-step explanation:

This is a triangle with sides 15.2 cm, 6.6 cm, and 15.6 cm. To solve for the angles, we can use the Law of Cosines:

c^2 = a^2 + b^2 - 2ab cos(C)

where a = 6.6 cm, b = 15.6 cm, c = 15.2 cm, and C is the angle opposite side c.

Using this formula, we can solve for the cosine of angle C:

cos(C) = (a^2 + b^2 - c^2) / 2ab

cos(C) = (6.6^2 + 15.6^2 - 15.2^2) / (2 * 6.6 * 15.6)

cos(C) = 0.748

Taking the inverse cosine of 0.748, we get:

C = 41.5 degrees

To find the other angles, we can use the Law of Sines:

a/sin(A) = b/sin(B) = c/sin(C)

Using this formula, we can solve for angle B:

sin(B) = (b/sin(C)) * sin(A)

sin(B) = (15.6/sin(41.5)) * sin(A)

sin(B) = 0.614 * sin(A)

Using the fact that sin(A) + sin(B) + sin(C) = 1, we can solve for sin(A) and sin(B):

sin(A) = (sin(C) - sin(B)) / (1 + cos(C))

sin(A) = (sin(41.5) - 0.614 * sin(A)) / (1 + cos(41.5))

Solving for sin(A), we get:

sin(A) = 0.266

Using this value of sin(A), we can solve for sin(B):

sin(B) = 0.614 * sin(A)

sin(B) = 0.157

Taking the inverse sine of these values, we get:

A = 15.4 degrees

B = 123.1 degrees

Therefore, the triangle has angles of approximately 15.4 degrees, 123.1 degrees, and 41.5 degrees.

Answer:

F(- 3) = - 2 , F(0) = 0

Step-by-step explanation:

(a)

F(- 3) with x = - 3 is in the interval x < 0 , then

F(- 3) = 3x = x + 1 = - 3 + 1 = - 2

(b)

F(0) with x = 0 is in the interval x ≥ 0 , then

F(0) = 3x = 3 × 0 = 0

Answer: Most Data takes 10 seconds to download. (sorry if this answer is very vague its hard to explain)

the base of the triangle below is b. bc.

a. The z-score for a value of 25 is -0.57, to the nearest hundredth.

b. The percent of the data is greater than 34 is about 2%.

To find the z-score for a value of 25, we can use the following formula;

z = (x - μ) /σ

where;

z = (25 - 27) / 3.5

z = -0.57

Rounding to the nearest hundredth, we get the z-score of -0.57.

The z-score for x = 34 is calculated as follows;

z = (x - μ) / σ

z = (34 - 27) / 3.5

z = 2

Using a standard normal distribution table, we find that the percentage of data that is greater than 34 = 2.28%.

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There are more than one solution for the given system.

Hence the correct option is C.

The given system of equations is,

y=-x-3

2y + 2x = -6

Write the equation in the form of ax + by = c,

Therefore, the system be

x  +  y  = -3

2x + 2y = -6

We know that,

The system of equations  a₁x + b₁y = c₁ and a₂x + b₂y = c₂

If  [tex]\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}[/tex]

Then the system has more than one solution.

Therefore,

1/2 = 1/2 = -3/-6

              =  1/2

Hence, this has more than one solution or roots.

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12.50

Parallel lines are lines that will never intersect.

Parallel Lines

Parallel lines run opposite of each other without intersecting. For lines to be parallel, they must have the same slope. The equation given to us is written in slope-intercept form. The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. So, the slope from the equation is 12.50.

Finding Parallel Lines

In order to find other lines that are parallel to the line given, all we need to do is write another equation with the same slope. However, 2 lines that are the same are not considered to be parallel. This means that for 2 lines to be parallel they must have the same slope but different y-intercepts. For example, a parallel line could be y = 12.50x + 6.

Answer:

How could the intersection of the graphs of the two equations be located on a coordinate grid?

-From the origin, move three units right and nine units up

What does the solution to a system of two linear equations mean on a graph?

-The point of intersection of the two lines

Can you have more than one solution to a system of linear equations?

-Yes, if both lines are the same exact line

Can you have exactly two solutions to a system of linear equations?

-No, because lines are straight

Can you have no solutions to a system of linear equations?

-Yes, if the lines are parallel

Step-by-step explanation:

Please look at the images attached. Sorry for the bad handwriting, I'm on a computer.

Basically, a linear system of equations has one solution if the equations yield two lines that intersect exactly once.

A linear system of equations has no solutions if the lines are parallel, because they will never intersect.

A linear system of equations has infinite solutions if the system of equations yields two lines that are the same, because they will forever intersect.

If you have any questions about these answers, please tell me in the comments below my answer. I'll be happy to answer them :)

The expression that is equivalent to [tex]49^{\frac{3}{2}}[/tex] is given as follows:

D. 343.

The power of a power rule is used when a single base is elevated to multiple exponents.

Then the simplified expression is obtained keeping the base, while the exponents are multiplied.

The expression for this problem is given as follows:

[tex]49^{\frac{3}{2}}[/tex]

49 is the square of 7, hence:

49 = 7².

Then the expression can be simplified as follows:

[tex]7^2^{\frac{3}{2}}[/tex]

The multiplication of the exponents is of:

2 x 3/2 = 3.

(when we apply the power of power rule, we keep the base and multiply the exponents)

Hence:

7³ = 343.

The problem is given by the image presented at the end of the answer.

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Answer:

y ≤ - [tex]\frac{2}{7}[/tex] x

Step-by-step explanation:

the blue region indicates where the solutions lie

that is below the given line

the equation of the line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

calculate m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (- 7, 2) ← 2 points on the line

m = [tex]\frac{2-0}{-7-0}[/tex] = [tex]\frac{2}{-7}[/tex] = - [tex]\frac{2}{7}[/tex]

the line crosses the y- axis at (0, 0 ) ⇒ c = 0

y = - [tex]\frac{2}{7}[/tex] x ← equation of line

the line is solid thus the region below is denoted by y ≤ , that is

y ≤ - [tex]\frac{2}{7}[/tex] x

Answer:

18 ft.

Step-by-step explanation:

The table of at least 4 values of the function is

x 0   -6   6  3

y  36  0  0 27

The domain is All set of real values and the range: y ≤ 36

The x and y intercepts of the rainbow are x = (-6, 0) and (6, 0) y = (0, 36)

Given that we have

y = -x² + 36

From the graph, we have the following values

x      y

0    36

-6    0

6    0

Set x  = 3

So, we have

y = -3² + 36

Evaluate

y = 27

So, we have

x      y

0    36

-6    0

6    0

3    27

From the graph, we have

These values mean that;

For the x and y intercepts of the rainbow, we have

x = (-6, 0) and (6, 0)

y = (0, 36)

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The population of the patch land in 50 years is given as follows:

13,547.

An exponential function has the definition presented as follows:

[tex]y = ab^\frac{x}{n}[/tex]

In which the parameters are given as follows:

The parameter values in this problem are given as follows:

a = 42, b = 2, n = 6.

Hence the function for the population after x years is given as follows:

[tex]y = 42(2)^\frac{x}{6}[/tex]

The population in 50 years is given as follows:

[tex]y = 42(2)^\frac{50}{6}[/tex]

y = 13,547.

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