A line passes through the points (1,4) and (3,-4). Which is the equation of the line

The key characteristics of graph of f(x) = cosecx are, The range of the function is (−∞, −1]∪[1, ∞) and Asymptotes occurs every π, beginning at x = 0. So statements 1 & 3 are correct

Trigonometry is a branch of mathematics, which deals with the study of right angle triangles. Trigonometry is concerned with specified functions of angles and their applications to calculations.

There are 6 commonly used functions in trigonometry with their name and abbreviations-

sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), cosecant (cosec)

Given that,

A trigonometric function,

f(x) = cosecx

The range of cosecx is (−∞, −1]∪[1, ∞)

At x = 0, it is approaching to infinity from both the sides

So, y intercept is not 1

At every π interval, it has Asymptotes

It never intersects the x axis, So x-intercept is not exist here

Hence, statements 1 & 3 are correct

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The graph of f(x)=cscx has a range of (−∞, −1]∪[1, ∞) , no y-intercept, and asymptotes at every multiple of \pi, but no x-intercepts.

The key characteristics of the graph of the function f(x)=cscx include the following:

This is because the cosecant function is the reciprocal of the sine function, which ranges from -1 to 1.

So, the cosecant function will take on all values that are less than -1 or greater than 1.

The sine function, which is the reciprocal of the cosecant, equals 0 at this point, and division by zero is undefined.

since cosecant is the reciprocal of sine, the function is undefined at these points;

so statement c is incorrect.

Option a., c., d.

Answer:

[tex]-3.5[/tex]

Step-by-step explanation:

[tex] \frac{ - 5 - 2}{3 - 1} = \frac{ - 7}{2} = -3.5[/tex]

hope this helps you

Slope: [tex]-2/7[/tex]

Find the slope between your two points

[tex](x_{1} ,y_{1} )=(-5,3)\\(x_{2} ,y_{2} )=(2,1)[/tex]

Use the slope formula

[tex]y_{2} -y_{1} /x_{2} -x_{1}[/tex]

[tex]1-3/2--5[/tex]

[tex]-2/7[/tex]

Slope

[tex]-2/7[/tex]

Answer:

Step-by-step explanation:

mean=12.7413

median=6.75

mode=6

range=77

Answer:

mean=12.7413

median=6.75

mode=6

range=77

Step-by-step explanation:

Answer: 6x^2 + 17x + 12

Step-by-step explanation:

You multiply the two outside terms and the two inside terms then add

Answer:

20000

Step-by-step explanation:

1 km = 1000 m. 20 km = 20000, basically # of km times 100

Answer: 20,000 meters or 12.4 miles (Didn't know which one you meant)

Step-by-step explanation:

To get miles all you have to do is divide it by 1.6.

To get the meters all you have to do is to multiple it by 1000.

(Hope this helps)

Answer:

x=-26

Step-by-step explanation:

Distributive property first (both sides)

you would get

4x+2 = 3x-24

next you will subtract 3x from both sides

1x+2=-24

add 24 to both sides

1x+26=0

move 26 to the other side but since you flipped it you have to make it negative

x=-26

Answer:

Take the coefficient of ''n'', divide it by 2, and raise it to the second power;

[tex]n^2+n+(\frac{1}{2})^2[/tex]

[tex]n^2+n+\frac{1}{4}=0[/tex]

[tex]=(n+\frac{1}{2} )^2[/tex]

Answer:

The discriminant is positive

Step-by-step explanation:

You can find that because on the graph, the top of the curve is on Y and its positive. Its at positive 4 so its positive......sorry im not good at explaning hope this helped.....also you can check google images or videos and it explanes.

Answer:

Positive

Step-by-step explanation:

In order to answer this question, we need to figure out the equation of the quadratic.

We see that the vertex is at (0, 4) and that the points (1, 3) and (2, 0) are on the graph. The generic quadratic is: ax^2 + bx + c, so we can just plug in these three points to find a, b, and c:

4 = 0 + 0 + c  ⇒  c = 4

3 = a + b + c = a + b + 4  ⇒  a + b = -1

0 = 4a + 2b + c = 4a + 2b + 4  ⇒  4a + 2b = -4

We now have two linear equations (a + b = -1 and 4a + 2b = -4) so multiply the first one by 2 and subtract it from the second:

  4a + 2b = -4            ⇒             4a + 2b = -4

- 2(a + b) = (-1) * 2       ⇒         -   2a + 2b = -2

______________     ⇒       ______________

Our difference is 2a = -2, so a = -1. Plug this back in to find b: a + b = -1.

-1 + b = -1

b = 0

So our equation is -x^2 + 4 = 0.

The discriminant is just b^2 - 4ac. Here, it is: 0^2 - 4 * (-1) * (4) = 16.

So the discriminant is positive.

Hope this helps!

Answer:

D or 4 square root 3

Step-by-step explanation:

using distance formula -12 square rooted - 2 square root 3 = -4squareroot3. So, after that you would square giving 48 then square root giving 4 square root 3. (-4 square root 2 and -32 square rooted cancel out giving 0)

The equation that has the solution x = 4 is [tex]log_ 4 (3x+4) = 2[/tex].

Option A is the correct answer.

Solutions are the values of an equation where the values are substituted in the variables of the equation and make the equality in the equation true.

We also find the solution in a system of equations using the substitution or elimination method.

Example:

2x + 4 = 8

The solution is x = 2.

We have,

To find which equation has x = 4 as the solution,

We can substitute x = 4 into each equation and see which one gives a true statement.

Now,

[tex]log_4 (3x+4) = 2\\log_3 (2x-5) = 2\\log_x 64 = 4\\log_x 16 = 4[/tex]

We can write it as,

4² = 3x + 4

16 = 3x + 4

16 - 4 = 3x

3x = 12

x = 4

3² = 2x - 5

9 = 2x - 5

9 + 5 = 2x

14 = 2x

x = 7

[tex]x^4[/tex] = 64

x = [tex]64^{1/4}[/tex]

[tex]x^4[/tex] = 16

x = 16[tex]16^{1/4}[/tex]

x = 2

Thus,

[tex]log_ 4 (3x+4) = 2[/tex] has the solution x = 4.

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The complete question:

Which equation has x = 4 as the solution?

[tex]log_4 (3x+4) = 2\\log_3 (2x-5) = 2\\log_x 64 = 4\\log_x 16 = 4[/tex]

Answer:

the answer is the expression, 5n-3

Step-by-step explanation:

Answer:

The value of n is -3/2.

Step-by-step explanation:

In order to solve x, you have to use the Cross-Multiplication :

[tex] \frac{ - 3}{5n} = \frac{2}{5} [/tex]

[tex] - 3(5) = 2(5n)[/tex]

[tex] - 15 = 10n[/tex]

[tex]10n \div 10 = - 15 \div 10[/tex]

[tex]n = \frac{ - 15}{10} [/tex]

[tex]n = \frac{ - 3}{2} [/tex]

Answer: Either 2:3 or 3:2

The longest line that can be drawn in a right rectangular prism (a box) is the diagonal from one corner to the opposite corner. This is called the space diagonal. It can be calculated using the Pythagorean theorem in three dimensions. In this case, the longest line is 16.8 cm.

The longest line that can be drawn in a right rectangular prism, also known as a box, is the diagonal drawn from one corner of the box to the opposite corner. This longest line is also known as the space diagonal of the box. To find the length of the space diagonal, we use the Pythagorean theorem in three dimensions, which is given by the formula d = √(l² + w² + h²), where l, w, and h are the length, width, and height of the box respectively.

In this case, the length l is 13 cm, the width w is 8 cm, and the height h is 7 cm. Thus, the length of the space diagonal is d = √((13 cm)² + (8 cm)² + (7 cm)²) = √(169 cm² + 64 cm² + 49 cm²) = √282 cm² = 16.8 cm. Therefore, the longest line segment that can be drawn in the box is 16.8 cm long.

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The longest line segment that can be drawn in the prism is approximately 16.79 cm long.

 First, we calculate the diagonal of the base of the prism, which is the rectangle with dimensions 13 cm by 8 cm.

The diagonal of this rectangle can be found using the Pythagorean theorem in two dimensions:

[tex]\[ d_{\text{base}} = \sqrt{l^2 + w^2} \][/tex]

[tex]\[ d_{\text{base}} = \sqrt{13^2 + 8^2} \][/tex]

[tex]\[ d_{\text{base}} = \sqrt{233} \][/tex]

 Next, we find the diagonal of the entire prism by considering the diagonal of the base and the height of the prism:

[tex]\[ d_{\text{prism}} = \sqrt{d_{\text{base}}^2 + h^2} \][/tex]

[tex]\[ d_{\text{prism}} = \sqrt{(\sqrt{233})^2 + 7^2} \][/tex]

[tex]\[ d_{\text{prism}} = \sqrt{282} \][/tex]

 Therefore, the longest line segment that can be drawn in the prism is the space diagonal, which is approximately:

[tex]\[ d_{\text{prism}} \approx \sqrt{282} \][/tex]

[tex]\[ d_{\text{prism}} \approx 16.79 \text{ cm} \][/tex]

 So, the longest line segment that can be drawn in the prism is approximately 16.79 cm long.

Maria subtracted 10x instead of adding it on step 4

Answer:

[tex]x=2[/tex]

Step-by-step explanation:

Line 4 has the problem:

[tex]12x-10x=44-10x+10x[/tex]

The correct way to put it is:

[tex]12x+10x=44-10x+10x[/tex]

which comes out to:

[tex]12x+10x=44-10x+10x\\22x=44\\x=2[/tex]

Answer:

b=19

Step-by-step explanation:

2x(3x+5)+3(3x+5)= (3x+5)(2x+3)= 6x²+ 9x+10x+15=6x²+19x +15

6x² + 19x +15 = ax²+bx+c

a=6, b=19, c=15

Answer:

Two hundred years = 2 century

4 decates= 40 years

36 months =3 years

96hours=4 days

6 months =26.071 weeks

Answer:

9. 21 days = 3 weeks (7 days in a week)

10. 200 years = 2 centuries (100 years in a century)

11. 4 decades = 40 years (10 years in a decade)

12. 36 months = 3 years (12 months in a year)

13. 96 hours = 4 days (24 hours in a day)

14. 6 months = 26 weeks (52 weeks in a year divided by 2)

15. 2 weeks

16. 50 years

17. 65 days

18. 110 weeks

19. hours

20. months

21. centuries

22. years  

We can simplify the exponent by multiplying 10 to itself 7 times.

= 10 * 10 * 10 * 10 * 10 * 10 * 10

= 100 * 10 * 10 * 10 * 10 * 10

= 1000 * 10 * 10 * 10 * 10

= 10000 * 10 * 10 * 10

= 100000 * 10 * 10

= 1000000 * 10

= 10000000

10^7 = 10,000,000

~Good luck

Answer:

the length of angle R Q is 4

Answer:

31000 cm2

Step-by-step explanation:

Answer:

7g^2 (2 - 3g^2

Step-by-step explanation:

First, you have to factor out the GCF

in this case, factor out 7g^5 to get

7g^2 (2 - 3g^2)

At this point you can't factor anymore, so you get

7g^2 (2 - 3g^2)

Zachary ran faster with 4 minutes per lap compared to Khloe's 3 minutes per lap.

To compare the speeds of Khloe and Zachary, we need to find their respective speeds in terms of minutes per lap.

Khloe ran around the track 7 times in 21 minutes, so her speed is [tex]\( \frac{21}{7} = 3 \)[/tex] minutes per lap.

Zachary took 4 minutes to run around the track once, so his speed is [tex]\( 4 \)[/tex] minutes per lap.

Comparing their speeds, Zachary's speed is faster at 4 minutes per lap, whereas Khloe's speed is 3 minutes per lap.

In summary, Zachary ran faster than Khloe because he completed each lap in 4 minutes compared to Khloe's 3 minutes per lap.

Answer:

1400 miles

Step-by-step explanation:

Speed is the time rate of change of distance. It is the ratio of distance to time and is given by the equation:

[tex]Speed(S) = \frac{distance(d)}{time(t)}\\ S=\frac{d}{t}[/tex]

plane averaged 400 mph on a trip going east, but only 280 mph on the return trip.

The time spent (t₁) in going east is given by:

[tex]S=\frac{d}{t_1}\\ t_1=\frac{d}{S} =\frac{d}{400mph}[/tex]

The time spent (t₂) in going east is given by:

[tex]S=\frac{d}{t_2}\\ t_2=\frac{d}{S} =\frac{d}{280mph}[/tex]

The total time (t) = t₁ + t₂

t = t₁ + t₂ = 8.5 hours

[tex]\frac{d}{400}+\frac{d}{280} =8.5\\280d+400d=952000\\680d=952000\\d=1400miles\\[/tex]

Therefore the one way distance is 1400 miles

Answer:

771.4 units^3

Step-by-step explanation:

Formula for volume of a cylinder = V=πr^2h

Plug in the numbers to solve for the height (note: the height of an oblique or slanted cylinder is the same as a regular right cylinder)

2314.25 = π(8.9)^2 h

h=9.3

Then plug the height into the formula for a pyramid

V = 1/3πr^2

V = 1/3 π (8.9)^2 (9.3)

V = 771.4 units ^3

Answer:

225

Step-by-step explanation:

Using the basic components of summation ∑

∑n = [tex]\frac{1}{2}[/tex] n(n + 1) and ∑1 = n

Thus

∑ (2n - 1) ← for n = 1 to 15

= ∑2n - ∑1

= 2∑n - ∑1

= 2 ([tex]\frac{1}{2}[/tex] n(n + 1)) - n

= n(n + 1) - n ← Evaluate for n = 15 ( the upper value )

= 15 × 16 - 15

= 240 - 15

= 225

Answer:

255

Step-by-step explanation:

(5/7, 12/7) <- I think you meant to type that. Its the first one

Step 1: Substitute y=x+1 in for y in 5x + 2y = 7

5x + 2(x+1) = 7

Step 2: Solve it

5x + 2x + 2 = 7

       7x + 2 = 7

             - 2  - 2

              7x = 5

              ---    ---

               7     7

                x = 5/7

Step 3; Plug x into y=x+1

y = 5/7 + 1

y = 12/7

Answer:

{(5/7 , 12/7)}

Step-by-step explanation:

First plug y into one of the x's

5x + 2(x + 1)  = 7

Now solve for X

5x + 2x + 2 = 7

Combine like terms

7x + 2 = 7

Subtract 2 from each side

7x = 5

Divide to get x by itself

x = 5/7

Now plug that into the second equation for x

y = 5/7 + 1

now just solve it

y = 12/7 if they want it simplified then it's 1 5/7

Hope this helped!

Answer:

2, 4, 5

Step-by-step explanation:

Answer:

5x+3x AND 8x

(10b-10b) And 0

y-9(3) AND -27

Step-by-step explanation:

please give me brainliest

Answer:

No

Step-by-step explanation:

The absolute value of -8 is 8,and 6<8.

Mark me brainliest if I helped:D

Answer:

280

Step-by-step explanation:

360-80