The line y = 2x +k is a tangent to the curve x² + 2xy + 20 = 0.
a Find the possible values of k.
b For each of these values of k, find the coordinates of the point of contact
of the tangent with the curve.​

Answer:

y=3

Step-by-step explanation:

good luck

Answer:

[tex]\huge\boxed{\tt{3}}[/tex]

Step-by-step explanation:

Given the expression:

[tex]\displaystyle \frac{3y+6}{2x}[/tex]

Given that: y = 4 , x = 3

[tex]\displaystyle = \frac{3(4)+6}{2(3)} \\\\= \frac{12+6}{6} \\\\= \frac{18}{6} \\\\= 3\\\\\rule[225]{225}{2}[/tex]

Hope this helped!

Answer:

Length = 22m

Breadth = 20m

Step-by-step explanation:

Given:

Area = 440 m²

Let the breadth be x m

According to the question:

Length = (x+ 2) m

Area of a rectangle = length × breadth

Substitution the values of area, length and breadth

440 = (x+2) × x

440 = x² + 2x

x² + 2x - 440 = 0

x² + 22x - 20x - 440 = 0

x (x + 22) - 20 (x + 22) = 0

(x + 22)  (x - 20) = 0

x = -22 and 20

Since the value of breadth cannot be in negative, therefore the value of breadth will be 20 m.

Length = (x + 2)

⇒ 20 + 2

⇒ 22 m

Answer:

1) 5x = 25

x = 5

2) y/4 = 7

y = 28

3) n/2 = 19

n = 38

4) 6g = 54

g = 9

5) 8b = 64

b = 8

6) h/6 = 11

h = 66

7) f/4 = 9

f = 36

8) 7s = 49

s = 7

Given:

A figure of a right angle triangle.

To find:

The value of x to the nearest hundredth.

Solution:

In a right angle triangle,

[tex]\tan \theta=\dfrac{Opposite}{Adjacent}[/tex]

In the given triangle,

[tex]\tan 62^\circ=\dfrac{x}{35}[/tex]

[tex]1.8807=\dfrac{x}{35}[/tex]

[tex]1.88073\times 35=x[/tex]

[tex]65.82555=x[/tex]

Approx the value to the nearest hundredth (two decimal place).

[tex]x\approx 65.83[/tex]

Therefore, the value of x is 65.83 units.

Answer:  B, 10.11km

Step-by-step explanation:

If All 6 members swam 1685 meters... you would have 10110 meters in total...

since 1000 meters is one kilometer.., it would be b... 10.11km

Answer:

A logical sentence is written as:

If P, then Q.

Where:

P = hypothesis

Q = conclusion.

For this particular case, we know that a number is even only if the number is divisible by 2.

Then we can write:

if a number is divisible by 2, then it is an even number.

Here we have:

hypothesis = a number is divisible by 2.

conclusion = the number even.

Answer:

V=lbh=2.4×3×6=43.2cm^3

We are given a candy batband we are given its dimensions

We need to find it's volume

Volume of a cuboid is given by l×b×h

Volume = length × breadth × height

Volume = 2.4 × 3 ×6

Answer:

10 Newtons to the left

Step-by-step explanation:

The overpowering force is the pull that is 30 Newton's left. We subtract this from the smaller force of 20!

[tex]30N-20N=10N[/tex]

Have a Happy April Fool's XD

Answer:

caca

Step-by-step explanation:

caca

The question has missing details. However, general questions that could be asked is as follows:

(1) The number of miles traveled after using (say) 5 gallons

(2) The number of gallons used after traveling for (say) 36 miles

Answer:

See Explanation

Step-by-step explanation:

Given

[tex]s = 120 - 12r[/tex]

A linear equation is represented as:

[tex]y = c + mx[/tex]

Where

[tex]c =y\ intercept[/tex] and

[tex]m = slope.[/tex]

c, in this question represents the initial capacity of the tank.

So, the initial capacity is 120 liters

Solving (a): r = 5

[tex]s = 120 - 12r[/tex]

[tex]s = 120 - 12 * 5[/tex]

[tex]s = 120 - 60[/tex]

[tex]s = 60[/tex]

60 miles traveled

Solving (b): s = 36

[tex]s = 120 - 12r[/tex]

[tex]36 = 120 - 2r[/tex]

Collect like terms

[tex]2r =120 -36[/tex]

[tex]2r =84[/tex]

Solve for r

[tex]r = 42[/tex]

42 gallons used

Answer:

18

Step-by-step explanation:

Answer:

Use substitution to receive: 18

Step-by-step explanation:

6a - 4b when a = 5 and b =  3

6(5) - 4(3)

30 - 12 = 18

Answer:

Here we don't have the options, so i will answer in a general way.

Every sentence that has the general structure like:

"something is greater than something"

"something is smaller than something"

"Something is no greater than something"

"something is no smaller than something"

There are a lot of other sentences, for example the ones like:

"N is at least equal to M" written as: N ≥ M

"N is at most equal to M" written as: N ≤ M

And there may be other ways to represent inequalities in sentences, but this is the most general way

Then the given sentence:

"One-half + k greater than 18"

This is written as:

1/2 + k > 18

Which is an inequality.

Answer:

ABD

Step-by-step explanation:

took one for the team

Answer:

no

Step-by-step explanation:

The given ratios 3/11 and 17/6 are not proportional.

A ratio is the relation between two numbers as a / b. A proportion is the equality of two ratios as a / b = c / d.

Ratio and proportion can be applied to solve Mathematical problems dealing with unit values of the quantities.

The given ratios are 3/11 and 17/6.

In order to check the proportionality cross multiplication is done as follows,

3/11 and 17/6

Cross multiply the numerators and denominators as follows,

3 × 6 and 17 × 11

=> 18 and 187

Since the cross multiplication of the numerators and denominators are not equal, the given ratios are not proportional.

Hence, the given ratios are not proportional.

To know more about ratio and proportion click on,

brainly.com/question/14279414

#SPJ5

Answer:

49

Step-by-step explanation:

x=180-131=49

Answer:

The population size is relatively small In total population sampling, researchers choose to study the entire population because the size of the population that has the particular set of characteristics that we are interest in is typically very small. Therefore, if you failed to include a small number of units (e.g., people) in your research, a significant piece of the puzzle that you are trying to understand may be missing.

Answer:

Step-by-step explanation:

A line can be expressed as

y=mx+b, where m=slope and b=y intercept

We are given m=6 and b=-5 so we can just use them in the equation.

y=6x-5

So C is the correct answer.

Answer:

sorry if u need help, hope u feel better! :)

Answer:

20% of students picked the vanilla cake.

Step-by-step explanation:

Total number of students: 16 + 64 = 80

Proportion that chose vanilla cake: 16/80 (simplify by dividing by 16) = 1/5 = 0.2 * 100 = 20%

x = cos (47) = Pi/3, cos 47 = X/3

Step-by-step explanation:

x = 2.05, 2.05 (2.05)²

Answer:

The answer is 48pi

Step-by-step explanation:

Circumference: C=2*pi*radius

The radius of Circle B is 2*12=24

Thus, the circumference of Circle B is: 2*pi*24=48pi

Answer:

our mama

Step-by-step explanation:

Given:

[tex]a_1=-4[/tex] and [tex]a_n=a_{n-1}+9[/tex] where [tex]n\geq 2[/tex].

To find:

The explicit formula for the given recursive formula.

Solution:

We know that recursive formula of an AP is:

[tex]a_n=a_{n-1}+d[/tex]

Where, d is the common difference.

We have,

[tex]a_n=a_{n-1}+9[/tex]

Here, d=9.

The first term of the AP is [tex]a_1=-4[/tex].

The explicit formula for an AP is:

[tex]a_n=a_1+(n-1)d[/tex]

Substituting [tex]a_1=-4[/tex] and [tex]d=9[/tex], we get

[tex]a_n=-4+(n-1)9[/tex]

[tex]a_n=-4+9n-9[/tex]

[tex]a_n=-13+9n[/tex]

Therefore, the required explicit formula for the given sequence is [tex]a_n=-13+9n[/tex].

Answer:

Hope this helps out ! :D

The possible positive and negative measures are 155° and -205° respectively.

It is given that an angle has a reference angle of 25° and its terminal side lies in Quadrant II.

It is required to find the possible positive measure and negative measure for the angle.

the angle between the terminal side of the angle and the x-axis.

The terminal side lies in Quadrant II.

The positive measure is:

=180-25

=155°.

And the negative measure is:

= 155-360

= -205°.

Thus, the possible positive measure and negative measures are 155° and -205° respectively.

Learn more about the reference angle here:

https://brainly.com/question/16210309

Answer:

replace x with number then multiply or divide

Step-by-step explanation:

Answer:

Hi how are you doing today Jasmine

Answer:  son is 12 years old

Step-by-step explanation:

Let m be the age of mother, f be the age of father, and s be the age of son.

m + f + s = 28 x 3 = 84

m + son = 23 x 2 = 46

f + s = 25 x 2 = 50

m = 46 - s

f = 50 - s

we plug in m and f to the functions.

we get 46 - s + 50 - s + s = 84  

96 - s = 84  

-s = -12  

s = 12 years old

Answer:

(4.5, -0.5)

Step-by-step explanation:

dude just use desmos its so much easier :)

Answer:

Not Perpendicular

Step-by-step explanation:

Answer:Answer:  

1,482 square feet    

Step-by-step explanation: Find total area - 37 x 46 = 1,702

Find area of patio and garden - 16 x 10 = 160 for the patio, 12 x 5 = 60 for the garden

Subtract from total area - 1702 - 160 = 1542, 1542 - 60 = 1,482 sq ft