4x⁴+3x²y²+9y⁴
solve by step by step​

Answer:

3

Step-by-step explanation:

a tangent to a circle makes right angle with the radius at that point ( here the point is B)

thus,

ABC is a right angled triangle

By Pythagoras theorem :-

By Pythagoras theorem :-AC² = AB² + BC²

(r + 2)² = 4² + r²

r² + 4 + 4r = 16 + r²

subtracting r² from both sides and taking 4 common

4(1 + r) = 16

diving both sides by 4

1 + r = 4

r = 3 units

The value of r is,

⇒ r = 3 units

The Pythagoras theorem states that in a right triangle, the square of the hypotenuse is equal to the sum of the square of the other two sides.

Given that;

AB is tangent to circle C.

Now,

By Pythagoras theorem, we get:-

AC² = AB² + BC²

(r + 2)² = 4² + r²

r² + 4 + 4r = 16 + r²

subtracting r² from both sides and taking 4 common

4(1 + r) = 16

diving both sides by 4

1 + r = 4

r = 3 units

Thus, The value of r is,

⇒ r = 3 units

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Answer:

36 inches = 0.000568182 miles

9514 1404 393

Answer:

  (a)  P = 44 cm + 18 cm + 18 cm = 80 cm

  (b)  396 cm²

  (c)  (i) see attached: radius = 7 cm; height ≈ 16.58 cm; slant height = 18 cm

  (c)  (ii) 7 cm

Step-by-step explanation:

(a) The length of arc PQR is given by the formula ...

  s = rθ . . . . . where r is the radius and θ is the angle in radians

The angle θ in radians is (140°)(π/180°) = (140)(22/7)/(180) = 22/9

So, the arc length is ...

  PQR = (18 cm)(22/9) = 44 cm

Then the perimeter of the figure is ...

  P = PQR +RO +OP = 44 cm + 18 cm + 18 cm

  P = 80 cm

__

(b) The area of a sector is given by ...

  A = 1/2r²θ = 1/2(rs)

  A = (1/2)(18 cm)(44 cm) = 396 cm² . . . area of the sector

__

(c) (i) A drawing of the cone is attached. The "slant height" is 18 cm. The radius is found in part (ii) as 7 cm. The height is given by the Pythagorean theorem:

  height = √((slant height)² - radius²) = √(18² -7²) = √275

  height ≈ 16.58 . . . cm

(ii) The length of arc PQR is the circumference of the base of the cone, given by ...

  C = 2πr . . . . where r is the radius of the base of the cone

Filling in the known values, we find ...

  44 cm = 2(22/7)r

  (44 cm)(7/44) = r = 7 cm . . . . . multiply by 7/44 to find r

The radius of the base of the cone is 7 cm.

Answer:

Step-by-step explanation:

[tex]Cos \ 39 = \frac{adjacent \ side}{hypotenuse}\\\\0.7771 = \frac{7}{x}[/tex]

x * 0.7771 = 7

[tex]x =\frac{7}{0.7771}=9.007[/tex]

x = 9

130 is your answer!  Look at line A. 130 degrees. now if A and B are parallel then 5 on line B will also be 130 degrees.

I hope this helps!

Answer:

13

Step-by-step explanation:

Median of a trapezoid = sum of 2 bases divided by 2

Bases = 10 and 16

Median = (10 + 16)/2

10 + 16 = 26

26/2 = 13

Median = 13

Answer:

5.86

Step-by-step explanation:

Answer:

x = 5.86

Step-by-step explanation:

x / 15 = cos67°

x = 15cos67°

x = 5.86

Answer:

[tex]{ \tt{27 = {3}^{3} }} \\ { \tt{}} \sqrt[4]{27} = {27}^{ \frac{1}{4} } \\ { \tt{ = {3}^{3( \frac{1}{4}) } }} \\ = { \tt{ {3}^{ \frac{3}{4} } }} \\ { \boxed{ \bf{a = 3 \: \: and \: \: k = \frac{3}{4} }}}[/tex]

Answer:

Rocío respondió 43 preguntas correctas y 17 incorrectas.

Step-by-step explanation:

Dado que en las olimpiadas de Matemática, Rocío representó a su colegio, y la prueba consistía en 60 problemas, de los cuales cada respuesta correcta valía 4 puntos y por cada respuesta incorrecta había un punto en contra, y luego del examen, Rocío obtuvo un puntaje de 155, y ella respondió todas las preguntas y desea saber cuantas fueron correctas y cuantas incorrectas, para determinar dicha duda se debe realizar el siguiente calculo:

60 x 4 = 240

40 x 4 - 20 = 140

45 x 4 - 15 = 165

42 x 4 - 18 = 150

43 x 4 - 17 = 155

Por lo tanto, Rocío respondió 43 preguntas correctas y 17 incorrectas.

Answer:

12 liters per min

Step-by-step explanation:

Math

27/4 = x

9/16      1

27/4=(9/16)x

Divide both sides by 9/16

12=x

Answer:

Step-by-step explanation:

Step 3:

Let LM = x

OK = KP = 12 units [Radii of circle K]

LN = LP = 8 units [Radii of circle L]

Therefore, KL = KP + PL

KL = 12 + 8

     = 20 units

Step 4:

Since, ΔKOM and ΔLNM are the similar triangles,

By the property of two similar triangles, corresponding sides of these similar triangles will be proportional.

[tex]\frac{OK}{NL}=\frac{KM}{LM}[/tex]

[tex]\frac{12}{8}=\frac{x+20}{x}[/tex]

12x = 8(x + 20) [By cross multiplication]

12x = 8x + 160

12x - 8x = 160

4x = 160

x = 40

Answer:

8 cm and 9 cm

Step-by-step explanation:

Hi there!

The sum of the lengths of two sides of a triangle must always be greater than the length of the third side.

5 cm and 8 cm ⇒ 5+8=13; not greater than 13

6 cm and 7 cm ⇒ 6+7=13; not greater than 13

7 cm and 2 cm ⇒ 7+2=9; not greater than 13

8 cm and 9 cm ⇒ 8+9=17; greater than 13

Therefore, the last set of two sides is possible for the lengths of the the other two sides of this triangle.

I hope this helps!

Answer:

A radical is basically a fractional exponent and is denoted by the radical sign (√). The expression x2 means to multiply x by itself (x × x), but when you see the expression √x, you're looking for a number that, when multiplied by itself, equals x. Similarly, 3√x means a number that, when multiplied by itself twice, equals x, and so on. Just as you can multiply numbers with the same exponent, you can do the same with radicals, as long as the superscripts in front of the radical signs are the same. For example, you can multiply (√x × √x) to get √(x2), which just equals x, and (3√x × 3√x) to get 3√(x2). However, the expression (√x × 3√x) can't be simplified any further.

Answer:

slope is undefined

Step-by-step explanation:

Calculate the slope m using the slope formula

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

with (x₁, y₁ ) = (6, 2) and (x₂, y₂ ) = (6, - 3)

m = [tex]\frac{-3-2}{6-6}[/tex] = [tex]\frac{-5}{0}[/tex]

Division by zero is undefined , then slope is undefined

Answer:

1500

Step-by-step explanation:

The area of the regtangular floor is 360m². The floor is going to be retired with tiles having area of 240cm² . We need to find the number of times . Therefore ,

[tex]\implies 360m^2 = 360 \times 10^4 \ cm^2 [/tex]

And , the number of tiles required will be ,

[tex]\implies n =\dfrac{Area \ of \ floor}{Area \ of \ a \ tile }\\\\\implies n =\dfrac{ 360 \times 10^4 \ cm^2}{240 cm^2} \\\\\implies \underline{\underline{ n = 1,500 }}[/tex]

Hence the required answer is 1500 .

Answer:

Given : A=(1,2)≡(x  

1 ,y  

1

​

) and B=(3,−2)≡(x  

2

​

,y  

2

​

)

Let M=(x,y) be the midpoint of AB

x=(  

2

x  

1

​

+x  

2

​

​

) and  y=(  

2

y  

1

​

+y  

2

​

​

)

Then, x=  

2

1+3

​

and y=  

2

2−2

​

⟹x=2 and y=0

∴M=(2,0)

∴ Coordinates of the midpoint of AB is (2,0)

Step-by-step explanation:

Answer:

10

Step-by-step explanation:

20÷2=10 the half of 20 is 10 simple as that

Answer:

ok so together they picked 20 apples so

20=y+1/2y

y=40/3 or 13 1/3

thats how many nate picked and we divide by 2

6 2/3

Hope This Helps!!!

Hello,

Let's x² the square number

and 3*y the multiple of 3.

[tex]x^2+3y=90\\\\\boxed{y=-\dfrac{1}{3} x^2+30}\\\\[/tex]

2 solutions : for (x,y) as integers : (-6,18) and (6,18)

but one solution for (x²,3y) as integers : (36,54)

Answer:

[tex]2c+2b+17[/tex]

Step-by-step explanation:

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

Given:

[tex]2c-3b+6+7b-2b+11[/tex]

---------->>>>

Collect like terms.

[tex]2c+(-3b+7b-2b)+(6+11)[/tex]

---------->>>>

Simplify

[tex]2c+2b+17[/tex]

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

Hope this is helpful.

Answer:

2c-2b+17 if using algebra

Step-by-step explanation:

firstly group like terms 2c+(-3b)+7b-2b+6+11

2c-2b+17

Answer:

-1

Step-by-step explanation:

The formula to find the slope of a line is:

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

where (x1, y1) and (x2, y2) are points on the line. We can substitute the points (-10, 0) and (-13, 3) into the formula and simplify:

[tex]\frac{3-0}{-13-(-10)} =\frac{3}{-13+10} =\frac{3}{-3} =-1[/tex]

This means the slope of the line is -1.

Answer:

1.2 books per month

12/10

Step-by-step explanation:

Answer:

Step-by-step explanation:

[tex](5^3)^5=5^{15}[/tex] which is absolutely huge. In scientific notation it is

3.051757813 × 10¹⁰

Answer:

(5×5×5)=125

125^5=30,517,578,125

final answer=30,517,578,125

Answer:

the correct answer is C....I hope

Answer:

(in image attached)

Step-by-step explanation:

A.

Left: 6×-3

Right: -3×-2

Bottom: 6×-2

B.

48÷6 = 8

-42÷6 = -7

-56÷8 = -7

-56÷-7= 8

Answer:

Step-by-step explanation:

Its clear from the dot plot that:

So, the correct choice is C

The given information in the dot plot is,

i) An outlier is present at 10.

ii) The data's majority are concentrated at 0 to 4 interval.

iii) 10 is the only one, which is far away.

iv) We confirm that the data are skewed.

v) Because the most data is concentrated in one median's side.

Then the final answer will be,

C) The data are skewed and there is an outlier.

Therefore, option (C) is the answer.

Answer:  

11.0.0035

12.39×10^-4

13.)0.00031

14.59800

15.3.6×10^9

Step-by-step explanation:

Answer:

205 meters

Step-by-step explanation:

25 * 8.2 = 205

The first one because there is only one y value for every x value. The correct option is first.

To determine if a relation is a function, use the vertical line test: If any vertical line intersects the graph of the relation at more than one point, then the relation is not a function. On the other hand, if every vertical line intersects the graph of the relation at most once, then the relation is a function.

In first relation is considered a function, because each input x-value is associated with exactly one output y-value. In other words, for every x-value in the domain of the relation, there can be only one corresponding y-value in the range. Each x-value should not have more than one y-value associated with it.

Therefore, each x-value should not have more than one y-value associated with it. The correct option is first.

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