y = 6 - x; (-3,3)
is it a solution?

Hello!

[tex]\sf 3x^2-5x-7=0\\\\x = \dfrac{-b\±\sqrt{b^{2}-4ac } }{2a} \\\\\\x = \dfrac{-(-5)\±\sqrt{(-5)^{2}-4 ~\times~3~\times~ (-7) } }{2~\times~ (-5)} \\\\\\\boxed{\sf x = \dfrac{5\±\sqrt{109} }{-10}}[/tex]

The radius of Convergence  for the function [tex]\frac{\[(-1)^{n} \; x^{n} }{\sqrt[3]{n} }[/tex]  is 1.

The radius of the largest disk at the center of the series in which the series converges.

Perform the ratio test for absolute convergence, which says

if    [tex]\lim_{n \to \infty} \frac{a_{n}}{a_{n+1}}[/tex]   =L

Then,

1) if L<1, the series is absolutely convergent

2) If L>1, the series is divergent

3) If L= 1, apply a different test.

Now, Applying test

[tex]a_{n+1}[/tex] =[tex]\frac{(-1)^{{n+1} } \; x^{n+1}}{\sqrt[3]{n+1} }[/tex]

So,

[tex]\lim_{n \to \infty} \frac{a_{n+1}}{a_{n}}[/tex]  = [tex]\lim_{n \to \infty}|\frac{ (-1)^{{n+1} } \; x^{n+1}/\sqrt[3]{n+1} }{ (-1)^{n} \; x^{n} /\sqrt[3]{n} } |[/tex]

                     = [tex]\lim_{n \to \infty}|\frac{ (-1)^{{n+1} } \; x^{n+1}\sqrt[3]{n}}{ (-1)^{n} \; x^{n} \sqrt[3]{n+1} } |[/tex]

                     = [tex]\lim_{n \to \infty}|\frac{ (-1) \; x^{n}\sqrt[3]{n}}{ \sqrt[3]{n+1} } |[/tex]

                    = [tex]\lim_{n \to \infty}\sqrt[3]{\frac{1}{1+\frac{1}{n}} } } |x|[/tex]

Applying the limit n→∞,

= 1 x |x|

= |x|

By ratio test, the given series will be convergent if |x|< 1.

So, the radius of Convergence = 1

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The expression that represents the height of the prism is 2850/b where b is the base area

The given parameter is:

Volume = 2850

Let the height of the prism be h, and the base area be b.

The volume is calculated using:

V = bh

Make h the subject

h = V/b

Substitute V = 2850

h = 2850/b

Hence, the expression that represents the height of the prism is 2850/b

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x=-4

Step-by-step explanation:

see the picture for full solution

Answer:

20 + 6n > 75(the sign has an underline)

To determine how many miles Kayla needs to hike each week for the next 6 weeks to reach her goal of at least 75 miles, we can subtract the miles she has already hiked from her target goal and divide it by the number of weeks remaining.

Target goal - Miles already hiked = Miles remaining

75 miles - 20 miles = 55 miles remaining

Now, we divide the remaining miles by the number of weeks:

55 miles / 6 weeks = 9.17 miles per week (approximately)

Therefore, Kayla needs to hike approximately 9.17 miles each week for the next 6 weeks in order to reach her goal of at least 75 miles.

Answer:

See below ~

Step-by-step explanation:

Formula to find shaded area :

Kindly check and refer this working to find a satisfactory expression.

Area

Step-by-step explanation:

2 things to remember :

1. the sum of all angles in a triangle is always 180°.

2. the sum of all angles around a single point on one side of a line is also 180° (because the line can be seen as the diameter of a circle, the point as its center, and so every side of the line is a half-circle = 180°).

so, the third, unnamed angle in the triangle is the supplementary angle to 142° (that means they complete each other to full 180°).

it is therefore

180 - 142 = 38°

and then, inside the triangle

180 = 66 + x + 38 = 104 + x

x = 76°

Answer:

it would be around 9 or something, im estimating.

Step-by-step explanation:

Step-by-step explanation:

The volume of the Apple iPad Mini 2 is 12.561 in³.

The new volume of the  Pear-Apple is  24.53 in³.

The new volume of the  Pear-Apple is 5.3in³.

The scale factor to have a volume that is half that of the iPad Mini is 0.79.

The scale factor to have a volume that is double that of the iPad Mini is 1.26

Volume = length x width x height

7.9 x 5.30 x 0.30 = 12.561 in³

Dimensions after the 1.25 scale factor is applied: (1.25 x 7.9) x (1.25 x 5.30) x (1.25 x 0.3)

= 9.875 x 6.625 x0.375 = 24.53 in³

Dimensions after the 0.75 scale factor is applied: (0.75 x 7.9) x (0.75 x 5.30) x (0.75 x 0.3)

= 5.925 x 3.975 x 0.225 = 5.3in³

Scale factor to have a volume that is double that of the iPad Mini : [tex]2^{1/3}[/tex] = 1.26

Scale factor to have a volume that is half that of the iPad Mini : [tex]0.5^{1/3}[/tex] = 0.79

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Answer:

14 mm

Step-by-step explanation:

Just as the little side is 1/4 of the larger side , so is the perimeter

1/4 * 56 = 14 mm

Answer:

A=72CM^2

Step-by-step explanation:

The answer is 72cm^2 because the area of a triangle is h x b divided by two because the triangle is half of a square, since the square is side times side, the answer is 12x12 divided by two, wich is 144/2. The final answer is 72

Answer:

72

Step-by-step explanation:

area of a triangle = 1/2 × base length × height

base length = 12 and height = 12

so area = 1/2 × 12 × 12

==> multiply 12 by 12

area = 1/2 × 144

==> divide 144 by 2

area = 72

Answer:

Yes if Greg and his partner can both eat 18 inch pizza then together they can eat a 36 inch pizza

Step-by-step explanation:

18+18=36

x(36) is greater then or equal to 36 making this equation true

Answer:

6 pieces of rope

Step-by-step explanation:

if the total is 54 and each are 9 you can make an equation

54= 9 x a

solve for a

to do this you divide 54 by 9

54/9=6

Answer:

6 pieces of rope

Step-by-step explanation:

54/9

Answer:

  101°

Step-by-step explanation:

The angles BEA and BED are a linear pair. They total 180°. (They are supplementary.)

__

  ∠BEA +∠BED = 180° . . . angles of a linear pair are supplementary

  79° +∠BED = 180° . . . . use the given angle value

  ∠BED = 101° . . . . . . . . . subtract 79°

Answer:

x = 35.5

Step-by-step explanation:

assuming all sides are equal (a square),

4x = 142

4x / 4 = 142 / 4

x = 35.5

Answer:

1.7 meters

Step-by-step explanation:

because an equilateral triangle has 3 sides and they are all the same you can just divide 5.1 by 3

5.1 / 3 = 1.7

it is 1.7 m

Answer:

x are sides of the traingle

5.1 = 51upon10 51/10

51 upon 10 =3x

3x = 51 upon 10

x= 3/51 upon 10 =

x= 3*10upon 51

=10upon 17

side of the traingle is 10/17

Step-by-step explanation:

Answer:

Answer: C 2:3

Step-by-step explanation:

total students = 25

total girls = 15

total boys = 25-15 = 10

boys:girls = 10:15

divide by 5 to get 2:3

Answer:

Step-by-step explanation:

Step 1:

Step 2:

Pull out like factors:

Solution to this question:

Answer:

2x-3y

Step-by-step explanation:

-1/4×-8x= 8/4x = 2x

-1/4×12y= - 12y/4 = -3y

2x-3y

Answer:

very easy

Step-by-step explanation:

First of all

made a distance between

AB

BC

CD

AD

and diagnals

AC

BD

If the all are equal means it is a square

if diagnols are different means it is rectangle

if diagnals are not equal means it is parallelogram

thats it try your best

you can do it

best of luck

Answer:

-40%

Step-by-step explanation:

NV = new value

OV = old value

percent change = (NV - OV)/(OV) × 100%

percent change = (30 - 50)/(50) × 100%

percent change = -20/50 × 100%

percent change = -40%

Step-by-step explanation:

1. A

2. B

3. A

4. A

5. A

6. B

7. B

8.C

9. C

10. C

11. C

Answer:

x = √51

Step-by-step explanation:

The given figure is a right triangle.

Using the Pythagorean Theorem to find x

Answer:

2 3/4 miles more

Step-by-step explanation:

5 - 2 1/4 = 2 3/4

Answer:

4 units

Step-by-step explanation:

the area (A) of a triangle is calculated as

A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )

given A = 14 and h = 7 , then

[tex]\frac{1}{2}[/tex] × 7b = 14 ( multiply both sides by 2 to clear the fraction )

7b = 28 ( divide both sides by 7 )

b = 4 units

Answer:

Vol_prism = 48 (all answers should have the units cm^3)

Vol_pyramid = 25

Vol_cyl = 37.68

Vol_cone = 12.56

Vol_sphere = 113.04

Step-by-step explanation:

This was a very compact problem (5 problems!) You read the chart top to bottom and each column is a different problem.

Vol of a prism:

V = l×w×h = 4×4×3

= 48 cm^3

Vol of a pyramid:

V = 1/3Base•h

= 1/3 (5×5)•3

= 25 cm^3

Vol of a cylinder:

V = pi•r^2•h

= pi•2^2•3

= pi•4•3

= 12pi = 12(3.14)

= 37.68 cm^3

Vol of cone:

= 1/3pi•r^2•h

= 1/3pi•2^2•3

= 4pi = 4(3.14)

= 12.56 cm^3

Vol of a sphere:

V = 4/3pi•r^3

= 4/3 pi•3^3

= 4/3 pi•27

= 36pi = 36(3.14)

= 113.04 cm^3

Pheewwwww! That was a lot! Hopefully you are just reviewing all your volume formulas. Hope this helps!

Answer:

x = 1/20 y^2

Step-by-step explanation:

This is a rightward opening  (sideways ) parabola

Directrix = x = -5

Distance formula form point x,y  to directrix and focus are equal:  

(x - -5)^2 = (x-5)^2 + y^2

x^2 + 10x + 25 = x^2 - 10x  + 25 + y^2

20x = y^2

x = 1/20 y^2