2. Two lines are represented by equations: 2x + 4y = 21 and y = kx - 12. What value of k will
make lines parallel?

Answer:

Your is answer would be choice C which is : 32 cm

Step-by-step explanation:

Given:

The function is:

[tex]f(x)=\dfrac{2x}{x+4}[/tex]

To find:

The vertical and horizontal asymptotes of the given function.

Solution:

We have,

[tex]f(x)=\dfrac{2x}{x+4}[/tex]

For vertical asymptotes, equate the denominator and 0.

[tex]x+4=0[/tex]

[tex]x+4-4=0-4[/tex]

[tex]x=-4[/tex]

So, the vertical asymptote of the given function is [tex]x=-4[/tex].

The degree of the numerator is 1 and the degree of the denominator is also 1.

Since the degrees of numerator and denominator are equal, therefore the horizontal asymptote is:

[tex]y=\dfrac{a}{b}[/tex]

Where, a is the leading coefficient of numerator and b is the leading coefficient of denominator.

Leading coefficient of numerator is 2 and the leading coefficient of denominator is 1, so the horizontal asymptote is:

[tex]y=\dfrac{2}{1}[/tex]

[tex]y=2[/tex]

Therefore, the correct option is C.

Answer:

She has 5 candles left.

Step-by-step explanation:

Total of candy Sarah has = 25candies

If Sarah gave 2/5 of the candies to her sister, the total amount she gave her sister will be 2/5 of 25

2/5 of 25 = 10

The remaining candy left will be 25-10 which is 15.

If she gave 2/3 of the amount left to her friend, the amount she gave her friend will be 2/3×15 = 10candies.

Answer:

60cm²

Step-by-step explanation:

Area of a rectangle = length x breath

Let,

length (L) = (a-1) cm

breadth (B) = (a+3) cm

Putting the value of a = 7;

we get,

length= 7-1 = 6 cm

breadth= 7+3 = 10 cm

Therefore, area of the rectangle = L x B

= 6 x 10

= 60 cm²

Answer:

Step-by-step explanation:

Hello!

a= 7

L = 7+3 = 10

l= 7-1 = 6

area:

10*6 => 60cm²

Answer:

Denise = 16

Sister = 10

Step-by-step explanation:

D=denise

S=sister

Eq 1)   D=S+6

Eq 2)  D-8 =4S-8

replace D with S+6 in Eq 2

(S+6)-8 = 4S -8

S-2 = 4S -8

add 8 to both sides

S+6 =4S

subtract S from both sides

6 = 3S

divide both sides by 3

2 = S   ( this is the sister age 8 years ago )

2+8 = 10  current age

plug that into Eq 1)

D = 10 +6

D=16    (Denise's current age)

so

Denise = 16

Sister = 10

if you subtract 8 from each , then there ages 8 years ago would be

Denise =8

Sister = 2

and 2*4 = 8  

this checks

Complete question is;

In mountaineering, in general, the higher you go, the colder it gets. This formula shows how the heights and temperatures are related.

Temperature drop (°C) = height increase(m)/200

A) If the temperature at a height of 500 m is 23°C, what will it be when you climb to 1300 m

B) How far would you need to climb to experience a temperature drop of 5°C

Answer:

A) 19°C

B) 1500 m

Step-by-step explanation:

A) We are told that the temperature is at a height of 500 m is 23°C, now we want to find the temperature when height increases to 1300 m.

Thus, it means;

Height increase = 1300 - 500 = 800 m

Thus, from the formula;

Temperature drop (°C) = height increase(m)/200, we have;

Temperature drop (°C) = 800/200 = 4°C

Now,since Initial temperature was 23°C, thus temperature at this increased height ; 23°C - 4°C = 19°C

B) for a temperature drop of 5°C, we have;

5°C = height increase(m)/200

Height increase = 200 × 5

Height increase = 1000 m

Thus, you will need to climb; 500 + 1000 = 1500 m

Answer:

connect to

Step-by-step explanation:

dont know why people whole summery just put the answer

Relating a difficult text to a personal experience can certainly help readers understand and engage with the text.

Difficult text can refer to any type of written material that presents a challenge for the reader in terms of comprehension, vocabulary, or structure.

We have,

Relating a difficult text to a personal experience can certainly help readers understand and engage with the text.

When we connect new information to our existing knowledge and experiences, we are more likely to remember and comprehend the new information.

Additionally, making personal connections to the text can help readers to relate to the topic on a deeper, more emotional level, which can increase their interest and motivation to learn more.

For example,

If a reader is struggling to understand a complex scientific concept, they might try to relate it to an experience they had in their own life that involved similar principles.

This could involve recalling a time when they observed or experienced the concept in action or thinking about how the concept might be relevant to their own interests or goals. By making these connections, the reader may be able to better understand and remember the concept, as well as feel more invested in learning about it.

Overall, connecting difficult texts to personal experiences can be a useful strategy for improving reading comprehension and engagement, as well as making learning more enjoyable and meaningful.

Thus,

Relating a difficult text to a personal experience can certainly help readers understand and engage with the text.

Learn more about difficult texts here:

https://brainly.com/question/27403920

#SPJ5

Answer:

-4/5

Step-by-step explanation:

2/5 ÷ -1/2

Copy dot flip

2/5 * -2/1

-4/5

Answer:

x = 6

Step-by-step explanation:

we can multiply the entire equation by 3 to simplify the numbers

-2x + 27 = 4x - 9

27 = 6x - 9

36 = 6x

x = 6

Answer:

1. 496 ft, 2. 126 mm, 3. 880 in, 4 168 cm, 5. 960m, 6. 42

Step-by-step explanation:

SA= Surface area, and surface area is A=2(w×l+h×l+h×w) and volume is V=w×h×l

W=width

H=height

L=length

Answer:

1. SA=58

2. SA=48

3. SA=78

4. V=168

5. V=960

6 V=420

Step-by-step explanation:

on 1-3 you are looking for the surface area and in order to look for the surface area of a rectangle prism it is 2(height)x2(lenght)x2(width). so you just plug in the number height is how tall the shape is, length is how long the shape is and width is hpw far the shape goes back. then you multiply the H, L, W by 2 and the you add all of the numbers and boom you get your answer.

Now for the Volume you just multiply the heigh x length x width and boom you answer

Answer:

336π square millimeters

Answer:

A

Step-by-step explanation:

Answer:

pi/6, 5pi/6, 7pi/6, 11pi/6

Step-by-step explanation:

3(sec x)^2 -4=0

Add 4 on both sides:

3(sec x)^2=4

Divide 3 on both sides:

(sec x)^2=4/3

Take square root of both sides:

sec x=plus/minus sqrt(4/3)

Reciprocal identity:

cos x=plus/minus sqrt(3/4)

Simplify the radical:

cos x=plus/minus sqrt(3)/2

So we are looking on the unit circle where the first coordinate of the order pair is either sqrt(3)/2 or -sqrt(3)/2.

This happens at pi/6, 5pi/6, 7pi/6, 11pi/6

Answer:

[tex]\sf \boxed{\sf x = \dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{7\pi}{6},\dfrac{11\pi}{6}}[/tex]

Step-by-step explanation:

A trigonometric equation is given to us , and we need to find the solutions of the equation within the interval [ 0,2π ]

The given equation is ,

[tex]\sf\longrightarrow 3(sec x)^2-4=0 [/tex]

This can be written as ,

[tex]\sf\longrightarrow 3sec^2x - 4 = 0 [/tex]

Add 4 to both sides of the equation ,

[tex]\sf\longrightarrow 3sec^2x = 4 [/tex]

Divide both sides by 3 ,

[tex]\sf\longrightarrow sec^2x =\dfrac{4}{3} [/tex]

Put squareroot on both sides ,

[tex]\sf\longrightarrow sec \ x =\sqrt{\dfrac{4}{3} }[/tex]

Simplify ,

[tex]\sf\longrightarrow sec\ x =\pm \dfrac{2}{\sqrt3} [/tex]

Multiply numerator and denominator by √3 ,

[tex]\sf\longrightarrow \bf sec(x) = \dfrac{ 2\sqrt3}{3},-\dfrac{2\sqrt3}{3} [/tex]

Solve for x ,

[tex]\sf\longrightarrow x = \dfrac{\pi}{6} +2\pi n , \dfrac{11\pi}{6}+2\pi n , \textsf{ for any integer n } . [/tex]

Therefore all the possible solutions are ,

[tex]\sf\longrightarrow \boxed{\blue{\sf x = \dfrac{\pi}{6},\dfrac{5\pi}{6},\dfrac{7\pi}{6},\dfrac{11\pi}{6}}} [/tex]

Nature tends to repeat itself, and that means periodic phenomenon is found in many places. One example would be a heart beating. It repeats itself over and over to pump blood throughout the body. The period of the heartbeat varies, so it's not going to be one specific number.

One online source I found states "It beats or contracts about 70 times per minute". So that would make the period 60/70 = 0.86 seconds approximately. Every 0.86 seconds or so, the heart completes a full cycle. This is when the person is at rest and not doing any strenuous physical activity (in which case, the period would be much shorter).

Another biological example would be the act of breathing. This is also dependent on if the person is at rest or if they're doing some physical activity such as jogging.

As for an example that's outside the personal element, you could go for something like the motion of the tides. These periodic events are due to the position of the moon, which is also a periodic phenomenon. More broadly, the motion of the planets overall is periodic. However, there may be slight changes here and there as time goes on due to imperfections.

Periodic phenomena has to do with an event that repeats itself.

The term periodic phenomena has to do with an event that repeats itself. This repetition must follow a well defined pattern and the time in between the occurrence of the phenomena is called the period.

Two common examples of periodic periodic phenomenon are;

1) Day and light

2) The dropping of water from a closing tap.

The former is quite popular and the period of the phenomenon is 24 hours. In the later case, the period may range a little above five seconds or below.

Learn more about periodic phenomenon:https://brainly.com/question/6258118?

#SPJ6

Answer:

TC = 5x -10

Step-by-step explanation:

Answer:

5d-10=C

Step-by-step explanation:

Because 5 friends are out to dinner so the cost of one meal is multiplied by five. Then you subtract 10 off the total for your answer, which is represented by the variable c

Answer:

115

Step-by-step explanation:

When x = -11, x^2 = 121. y = 121 - 6 = 115.

Hope this helped,

~cloud

Answer:

115

Step-by-step explanation:

y = x^2 - 6

Let x = -11

y = (-11)^2 - 6

y = (121) -6

   = 115

The area of the triangle is (A) [tex]73.6ft^{2}[/tex].

Area = [tex]\frac{1}{2}[/tex] × [tex]a[/tex] × [tex]b[/tex] × [tex]sin[/tex] (θ)

Now, out the values in the formula for the solution.

[tex]A=\frac{1}{2} (16)(10)sin(67^{o} )\\A= 80sin(67^{o} )\\[/tex]

[tex]A=73.6ft^{2}[/tex]

Therefore, the area of the given triangle is (A) [tex]73.6ft^{2}[/tex].

Know more about the area of triangles here:

https://brainly.com/question/17335144

#SPJ2

Answer:

210 Km

Step-by-step explanation:

Distance travelled is calculated as

distance = speed × time ( time is in hours )

              = 90 × 2 [tex]\frac{1}{3}[/tex]

             = 90 × [tex]\frac{7}{3}[/tex]

            = 30 × 7

            = 210 Km

Answer:

please mark me as brainlist

Hello,

Your answer would be right side of the graph

Please mark as brainiest

The peak in the data would likely be the right side of the graph.

The distribution of a data set when displayed on a dot plot is said to be skewed left (left skewed) when most of the data appear on the right side of the graph. This means, the highest scores are on the right while the lowest values of the variable are on the left side of the graph (in order words, tapers towards the left of the graph). See the image labelled A in the attachment below.

Also, for a data set distribution that is skewed right (right skewed), most of the data appear on the left side of the graph. It will have a tail tapering to the right. See the image labelled A in the attachment below.

Therefore, for data set that ranges between 50 and 90, and the distribution is skewed left, the peak in the data would be to the right of the graph.

Learn more about skewness of a data set here:

https://brainly.com/question/3252860

Answer:

The answer is x = 1800

Step-by-step explanation:

Hope this helps :)

Have a nice day.

Given:

The expressions are:

[tex]\dfrac{7}{5}y[/tex]

[tex]0.68y[/tex]

[tex]\dfrac{3}{5}y[/tex]

[tex]1.32y[/tex]

To find:

The equivalent expression to the given expressions.

Solution:

There can be more than one equivalent expressions to the given expression.

[tex]\dfrac{7}{5}y=1.4y[/tex]

Therefore, [tex]1.4y[/tex] is equivalent to [tex]\dfrac{7}{5}y[/tex].

[tex]0.68y=\dfrac{68}{100}y[/tex]

[tex]0.68y=\dfrac{17}{25}y[/tex]

Therefore, [tex]\dfrac{17}{25}y[/tex] is equivalent to [tex]0.68y[/tex].

[tex]\dfrac{3}{5}y=0.6y[/tex]

Therefore, [tex]0.6y[/tex] is equivalent to [tex]\dfrac{3}{5}y[/tex].

[tex]1.32y=\dfrac{132}{100}y[/tex]

[tex]1.32y=\dfrac{33}{25}y[/tex]

Therefore, [tex]\dfrac{33}{25}y[/tex] is equivalent to [tex]1.32y[/tex].

Answer:

theta = [tex]\frac{\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{3\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{5\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{7\pi }{4}[/tex] + 2[tex]\pi[/tex]n

Step-by-step explanation:

sin^2 theta - cos^3 theta = 1

cos^3 theta = 1 - sin^2 theta

sin^2 theta - cos^3 theta = 0

Substitute

sin^2 theta - ( 1 - sin^2 theta ) = 0

Distribute negative

sin^2 theta - 1 + sin^2 theta = 0

Combine same values

2sin^2 theta - 1 = 0

2sin^2 theta = 1

sin^2 theta = [tex]\frac{1}{2}[/tex]

sin theta = +- [tex]\frac{1}{\sqrt{2}}[/tex]

Right Triangle:  1 - 1 - [tex]\sqrt{2}[/tex]

theta = [tex]\frac{\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{3\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{5\pi }{4}[/tex] + 2[tex]\pi[/tex]n, [tex]\frac{7\pi }{4}[/tex] + 2[tex]\pi[/tex]n

period of Sin function is 2[tex]\pi[/tex]

Answer:

24 + 8i

Step-by-step explanation:

t = 4

u = 6 + 2i

t x u

= 4 ( 6 + 2i )

= 24 + 8i

Answer:

24+8i

Step-by-step explanation:

i took the test

Step-by-step explanation:

Let ABCD be the parallelogram with ∠A = ∠B.  

We know: Sum of adjacent angles = 180°  

∠A + ∠B = 180º  

2∠A = 180º (∠A = ∠B)  

∠A = 90º  

∠B = ∠A = 90º  

∠C = ∠A = 90º (Opposite angles)  

∠D = ∠B = 90º (Opposite angles)  

Thus, each angle of the parallelogram measures 90º

Answer:

All 4 angles are 90 degrees.

Step-by-step explanation:

The measure of 2 adjacent angles in a parallelogram add up to 180 degrees.

If they have equal measure then they are both 90 degrees.

As it is a parallelogram:-

the measure of each angle is 90 degrees.

From the diagram shown, the sum of the angle on the straight line is 180degrees.

This means that:

m<a + m<z + m<b = 180 ............. 1

Given the following

m<a = m<x ...... 2

m<b = m<y ...... 3

Substitute equations 2 and 3 into equation1 to have:

m<x + m<y + m<y = 180

Rearrange

m<x + m<y + m<z = 180

This shows the required proof.

Learn more here: https://brainly.com/question/18481614

I think there's an error with this question. Mind to check it back and tell me the detail?

Answer:

x=2

Step-by-step explanation:

x+5=7

Subtract 5 from each side

x+5-5=7-5

x =2

Answer:

2

Step-by-step explanation:

x + 5 = 7

=> x = 7 - 5

=> x = 2