6. A line passes through the points (-2,5) and (6,9). Calculate the gradient of this line.

Answer:

[tex]\begin{aligned}{&\cos \theta=\frac{10}{26} \\\bf{&\tan \theta=\frac{24}{10}}\end{aligned}[/tex]

Step-by-step explanation:

Since the angle is in the first quadrant, the values of all trigonometric functions are positive. Also. the formulas for the trigonometric functions we need to find from the problem are shown below:
[tex]\begin{aligned}\cos \theta &=\frac{x}{r} \\\tan \theta &=\frac{y}{x}\end{aligned}[/tex]

Based on the formulas listed, the value of y and r are y = 24 and r = 26 respectively. This means that in order to determine the value of the other functions, we need In compute for the value of x using the Pythagorean Theorem:

[tex]\begin{aligned}r^{2} &=x^{2}+y^{2} \\r^{2}-y^{2} &=x^{2}+y^{2}-y^{2} \quad\left[\text { \text{Subtracting \ both \ sides \ of \ the \ equation\ by} } y^{2}\right] \\r^{2}-y^{2} &=x^{2} \\\sqrt{r^{2}-y^{2}} &=\sqrt{x^{2}} \\\sqrt{r^{2}-y^{2}} &=x \\\sqrt{26^{2}-24^{2}} &=x \\10 &=x\end{aligned}[/tex]Then, substituting this to the formula to determine the answers yields:

[tex]\begin{aligned}\cos \theta &=\frac{x}{r} \\&=\frac{10}{26} \\\tan \theta &=\frac{y}{x} \\&=\frac{24}{10}\end{aligned}[/tex]

Therefore, the answers are:

[tex]\begin{aligned}&\cos \theta=\frac{10}{26} \\&\tan \theta=\frac{24}{10}\end{aligned}[/tex]

Answer:

See below

Step-by-step explanation:

We are here given that ,

[tex]\longrightarrow \sin\theta =\dfrac{24}{26}[/tex]

And we would like to find out other trigonometric ratios ( since it is not mentioned about which two I will find out all 6 ) . As we know that ,

[tex]\longrightarrow \sin\theta =\dfrac{perpendicular}{hypotenuse} =\dfrac{p}{h}[/tex]

So that ,

[tex]\longrightarrow \dfrac{p}{h} =\dfrac{24}{26}[/tex]

Let us assume the given ratio to be 24x : 26x .

So we can say that ,

Now let's find out the value of base , so that we can find out the other ratios .

By Pythagoras Theorem ,

[tex]\longrightarrow (perpendicular) ^2+(base)^2=(hypotenuse) ^2[/tex]

Substitute the respective values ,

[tex]\longrightarrow (26x)^2=(24x)^2+b^2\\[/tex]

[tex]\longrightarrow 676x^2 = 576x^2+b^2\\ [/tex]

[tex]\longrightarrow b^2=100x^2\\[/tex]

[tex]\longrightarrow b =\sqrt{100x^2}\\[/tex]

[tex]\longrightarrow \boldsymbol{ b = 10x } [/tex]

Now we may find the other ratios as ,

[tex]\longrightarrow \cos\theta = \dfrac{base}{hypotenuse}=\dfrac{10x}{26x}=\boxed{\boldsymbol{\dfrac{5}{13}}}\\[/tex]

[tex]\longrightarrow \tan\theta =\dfrac{perpendicular}{base}=\dfrac{24x}{10x}=\boxed{\boldsymbol{\dfrac{12}{5}}}\\[/tex]

[tex]\longrightarrow \cosec\theta =\dfrac{hypotenuse}{perpendicular}=\dfrac{26x}{24x}=\boxed{\boldsymbol{\dfrac{13}{12}}}\\ [/tex]

[tex]\longrightarrow \sec\theta =\dfrac{hypotenuse}{base}=\dfrac{26x}{10x}=\boxed{\boldsymbol{\dfrac{13}{5}}} \\[/tex]

[tex]\longrightarrow \cot\theta =\dfrac{base}{perpendicular}=\dfrac{10x}{24x}=\boxed{\boldsymbol{\dfrac{5}{12}}} [/tex]

And we are done !

[tex]\huge\text{Hey there!}[/tex]

[tex]\mathsf{6\dfrac{1}{4} - 2\dfrac{3}{10}}\\\\\mathsf{\rightarrow \dfrac{6\times4+1}{4} - \dfrac{2\times10+3}{10}}\\\\\mathsf{\rightarrow \dfrac{24 + 1}{4} - \dfrac{20 + 3}{10}}\\\\\mathsf{\rightarrow \dfrac{25}{4} - \dfrac{23}{10}}\\\\\mathsf{\rightarrow \dfrac{79}{20}}\\\\\mathsf{\approx 3\dfrac{19}{20}}\\\\\\\huge\textbf{Therefore, your answer is: \boxed{\mathsf{Option\ C. \ 3 \dfrac{19}{20}}}}\huge\checkmark[/tex]

[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]

Answer: 89

Step-by-step explanation:

60 + 31 = 91

180 - 91 = 89

If this isn’t correct then sorry :/

Step-by-step explanation:

The period of f(x) is π.

To calculate the period using the formula derived from the basic sine and cosine equations. The period for function y = A sin (B a – c) and y = A cos ( B a – c ) is equal to 2πB radians. The reciprocal of the period of a function is equal to its frequency.

Answer:

9 months

Step-by-step explanation:

$500 - $240 = $260

$260/$30 = 8.67(3s.f.) ≈ 9 months

Recheck:

Balance after 9 months = 240 + (30×9) = 240 + 270 = $510

                                      ∴ $510 > $500

Answer:

66 percent

Step-by-step explanation:

⅔ are shaded which is 0.6 recurring which as a percentage is 66 percent. may have to say 66.6

Answer:

5x-18=4x+7 ( vertical opposite angle)

5x-4x=7+18

x=25

Answer:

2929 1/3 [tex]\pi[/tex] in^3

Step-by-step explanation:

The equation for the volume of a sphere is [tex]\frac{4}{3} \pi r^3[/tex].

Insert 13 for r.  Then, simplify.

Answer:

42 meters squared

Step-by-step explanation:

Lets split the trapezoid into 2 parts (6*5 and 2*6)

6*5+2*6

= 30+12

= 42

Answer:

36

Step-by-step explanation

5+7 = 12

12/2 = 6

6 * 6 = 36

formula = ((a+b)/2) * h

Answer: 31/4 or 7.75

Step-by-step explanation:

Answer:

28

Step-by-step explanation:

Answer:

y= -1/2x

Step-by-step explanation:

Option B passes through the origin, by -1/2x

Answer: f(-3) = -10

Step-by-step explanation:

[tex]Substitute \ $x=-3$\\\\$$\begin{aligned}&f(3)=2(-3)-4 \\&f(3)=-6-4 \\&f(3)=-10\end{aligned}$$[/tex]

divide 9 by 5 u will get 1.8 as the answer

Explanation:

9 over 5 = 9/5 = 18/10 = 1.8

You can also use long division as shown below.

Or you can use your calculator to quickly get this value.

Answer:

The last answer.

Step-by-step explanation:

Regular means all the side lenghts are the same and all the interior angle measures are the same. Think a stop sign.

Irregular polygons have different side lengths and different interior angle measures.

Answer:

5/32

Step-by-step explanation:

Answer:

Sarpong is 11.

Quartey is 39.

Step-by-step explanation:

Let Sarpong's age now = s.

Let Quartey's age now = q.

Now:

q + s = 50

In five years, their ages will be

Sarpong: s + 5

Quartey: q + 5

q + 5 = 4s

We have a system of two equations in two variables.

q + s = 50

q + 5 = 4s

We will use the substitution method.

Solve the second equation for q.

q = 4s - 5

Substitute 4s - 5 for q in the first original equation and solve for s.

4s - 5 + s = 50

5s = 55

s = 11

q + s = 50

q + 11 = 50

q = 39

Answer:

Sarpong is 11.

Quartey is 39.

The area of the considered triangle RST is given by: Option A: 9 sq. units.

If we have:

Then we get:

Area of a triangle = [tex]\dfrac{b \times h}{2} \: \rm unit^2[/tex]

The missing image is attached below.

If we take the base of the triangle as RS, then as the line UT is perpendicular to RS (as RS is parallel to x axis and UT is parallel to y axis) and touching from the base line RS to T, thus, it can be taken as height.

Thus, we have:

Area of RST = half of length of RS (base) times length of UT (height)

As visible from image, we have:

Length of RS = 6 blocks of unit length = 6 units

Similarly, length of UT = 3 units

Thus, we get:

Area of RST = [tex]\dfrac{6 \times 3}{2} = 9 \: \rm unit^2[/tex]

Thus, the area of the considered triangle RST is given by: Option A: 9 sq. units.

Learn more about area of a triangle here:

https://brainly.com/question/14503701

Hello!

This is a one-step equation, meaning that we can solve it in just 1 step.

This is the step:

3x=9

x=3

That's the answer; we can easily check it:

3*3=9

Hope everything is clear.

Let me know if you have any questions!

Always Remember: Knowledge Is Power!

Answer:

P = 1/5 = 0.20 = (20%)

Step-by-step explanation:

there are 12 horses and 8 cows, in total there are 20 animals

of which 4 horses are brown

Then

[tex]P=\frac{4}{20} =\frac{1}{5}[/tex]

Hope this helps

Answer:

D

Step-by-step explanation:

the equation of a line in slope- intercept form is

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

y = [tex]\frac{6}{9}[/tex] x + 9 ← is in slope- intercept form

with y- intercept c = 9

then the line crosses the y- axis at (0, 9 )

Answer: 94 degrees

Step-by-step explanation:

Answer: 3

Step-by-step:

15/5=3

Each segment of a fifteen-foot beam divided into five equal parts is 3 feet long.

Since acronym PEMDAS stands for Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This approach is used to answer the problem correctly and completely.

To find out the length of each segment of a fifteen-foot beam divided into five equal parts, we have to divide the total length of the beam by the number of segments it is being divided into.

We can do this using the division operation as shown below:

15 ÷ 5 = 3

Therefore, we can conclude that each segment of a fifteen-foot beam divided into five equal parts is 3 feet long.

More about the Algebra link is given below.

brainly.com/question/953809

#SPJ2

Answer:

Answer given above

Step-by-step explanation:

a.) 6 m n^8

b.)2x^8 y^3

c. ) d^3 e

Answer: Jason's team.

Step-by-step explanation: When finding the MAD, you need to find the mean of the data, which they said is 10.  The next step is to subtract numbers from the data from the mean, which is 10 for all three dot plots. For example, for Jason's team, we need to subtract all the 7's, 8's, 11's, 12's, and 13's, because those are the only parts of the plot with data.  Let's try subtracting 7 - 10.  The answer is -3, but we need to make it positive, because that's how data works, so it's actually 3.  You keep doing this for all three plots, which is provided below:

Jason's Team: 3, 3, 2, 2, 2, 1, 2, 3, 3, 3.

Hannah's Team: 3, 2, 2, 1, 0, 0, 1, 1, 3, 3.

Dion's Team: 1, 1, 1, 1, 0, 0, 0, 0, 1, 3.

Now, the next step is adding all these values and dividing it by ten, since that's how many numbers there are for the data.

Jason's Team MAD: 2.4.

Hannah's Team MAD: 1.6.

Dion's Team MAD: 0.8

As you can see, Jason's Team has the greatest MAD, which is your answer.

Let me know if this is right! :)

Answer:

Step-by-step explanation:

Answer:

C: No, beacause the lines are in the same plane.  

Step-by-step explanation:

because skewed lines must lie in different planes.  

just trust moi <3

The lines are in the same plane option third "No, because the lines are in the same plane" is correct.

Lines that intersect at a right angle are named perpendicular lines. Lines that are always the same distance apart from each other are known as parallel lines.

The question is incomplete.

The complete question is in the picture, please refer to the attached picture.

We have two lines shown in the picture, line l, and line m.

As we know the skew lines are in different planes and do not intersect.

Thus, the lines are in the same plane option third "No, because the lines are in the same plane" is correct.

Learn more about the perpendicular line here:

brainly.com/question/18271653

#SPJ5

Answer: No

Step-by-step explanation: In order for a triangle to be right, the first number and second number has to be smaller than the middle number.

20+30= 50

50>40

therefore 20,40,30 can not be a right triangle

Call the 3 sides a,b,c respectively. (a=20; b=30; c=40)

To form a right triangle with 3 lengths, they must satisfied the equation : [tex]a^{2} +b^{2} =c^{2}[/tex] (aka pythagorean theorem)

Replace numbers : [tex]20^{2} +30^{2} =40^{2}\\ 400 + 900 = 1600 (false)[/tex]

-> These lengths do not form a right triangle.

Answer:

4.295cm

Step-by-step explanation:

Here,

Circumference = 27cm

We know,

C=2πr

or, 27 = 2×22×r

7

or, 44×r = 27

7

27

or, r = 44

7

or, r = 27×7

44

Therefore, r = 4.295cm