The sum of twice a number, n, and 14 is 30. Write an equation that models this
statement. Then explain how you might use reasoning to find the value of n.

Answer:

x=-1+\sqrt{15}i,\:x=-1-\sqrt{15}i

Step-by-step explanation:

For the given quadratic equation,x² + 2x + 16 = 0 the value of x will be x=-1+√15i, and x-=-1-√15i you must add 1 in order to complete the square.

Any equation with the formula [tex]\rm ax2 + bx + c = 0[/tex] where x is a variable and a, b, and c are any real values; a quadratic equation is one where a ≠ 0.

It is given that the equation is, x² + 2x + 16 = 0,

The value of x obtained after solving the given equation is x=-1+√15i and x-=-1-√15i.

In order to complete the square you have to take out the following operations,

x² + 2x + 16 = 0

Add and subtract by 1 as

x²+2x+16+1-1

x²+2x+1 +15

(x+1)²+(√15)²

Thus, you must add 1 in order to complete the square.

Learn more about quadratic equations here:

brainly.com/question/17177510

#SPJ2

Answer:

2500 ( nearest hundred)

Step-by-step explanation:

Given that :

Number of stickers collected per week = 89

Number of weeks for which stickers were being collected = 28

To obtain the total number of stickers collected, we take the product of the number of weeks for which the stickers were beug vcilled and the number of stickers collected per week

The number of stickers collected :

89 * 28 = 2492

2492 = 2500 ( nearest hundred)

Answer:

36

Step-by-step explanation:

Sean purchased a printer and laptop

He sold both for 1,500

He sold the laptop at 1,350

Therefore the cost of the printer can be calculated as follows

1500-1350

= 150

24/100×150

= 0.24×150

= 36

Henve the cost of the printer is £36

Answer:

Step-by-step explanation:

k = xy

Putting values of x and y in the equation

k = (5)(-3.5)

= - 17.5

Finding value of x when y = 10

k = xy

- 17.5 = x10

Bringing like terms on one side

- 17.5 - 10 = x

-27.5 = x

Answer:

6, 8, 10, and 12

Step-by-step explanation:

x + (x + 2) = (x + 4) + (x + 6) = 36

4x + 12 = 36

subtract 12 rom each side of the equation:

4x = 24

divide both sides by 4:

x = 6

x + 2 = 8

x + 4 + 10

x + 6 = 12

Step-by-step explanation:

2 is the degree of polynomial.

hope it is helpful to you

Answer:

I say it is A.

Step-by-step explanation:

It is the one that makes the most sense.

Hope this helps.

Answer:

No.

Step-by-step explanation:

The triangle inequality theorem states that the sum of two sides of a triangle must be greater than the third side.

5 + 8 = 13.

13, which is the sum of two sides, is not larger than 16, the third side.

Therefore, a triangle cannot have these side lengths.

Answer:

Congruent segments subtracted from congruent segments form congruent segments

Answer:

yes I think he does because of the distance of the sprinklers reach.

Answer:

259200 seconds

How: 60×60×24 = 86400

That is for one full day, so multiply that by 3

Answer: 259200

Answer:

it would be d

Step-by-step explanation:

16 times 8 3/4

Answer:

40 inches

Step-by-step explanation:

Volume, V of hemisphere = 2/3 π r^3

Radius, r = 24 inches ;

V = 2/3 π 24^3

V = 28952.917 in³

Volume of cylinder = π r^2 * h

h = height ; r = Radius = 32 /2 = 16 inches

Volume of hemisphere = volume of cylindrical tank

28952.917 = π (16)^2 * h

28952.917 = 804.24771h

h = 28952.917 / 804.24771

h = 35.9999

h = 40 inches

Molten stell rise is 40 inches

Answer:

Step-by-step explanation:

1) Both the angles ∠2 & ∠3 form a linear pair with ∠1. Also, angles of a linear pair are supplementary to each other. So, both ∠2 & ∠3 are supplementary to ∠1. (Write any one)

2) ∠1 is located vertically opposite to ∠4. So, ∠1 & ∠4 are vertical angles.

3) Both the angles ∠1 & ∠4 share a common vertex & common side with ∠3. So, both ∠1 & ∠4 are adjacent to ∠3. (Write any one)

Answer:

Total amount needed is: $59.25

Step-by-step explanation:

Given

See attachment for fence

Required

Cost of weedkiller needed

First, we need to calculate the height of the fence.

Considering the triangular end of the fence, we have:

[tex]17 ^ 2 = h ^ 2 + 8 ^ 2[/tex] --- Pythagoras theorem

[tex]289 = h^2 + 64[/tex]

Collect like terms

[tex]h ^ 2 = 289 - 64[/tex]

[tex]h ^ 2 = 225[/tex]

Take positive square root of both sides

[tex]h = \sqrt{225[/tex]

[tex]h = 15[/tex]

Next, calculate the area of the fence (trapezium).

This is calculated as:

[tex]Area = \frac{1}{2}(a + b) * h[/tex]

Where:

[tex]a = 12[/tex]

[tex]b = 20 + 8 = 28[/tex]

So, we have:

[tex]Area = \frac{1}{2}(12 + 28) * 15[/tex]

[tex]Area = \frac{1}{2}(40) * 15[/tex]

[tex]Area = 20 * 15[/tex]

[tex]Area = 300m^2[/tex]

From the question, we have:

[tex]\$19.75 = 100m^2[/tex]

Let x = the cost required for the complete area

i.e.

[tex]x = 300m^2[/tex]

So, we have:

[tex]\$19.75 = 100m^2[/tex]

[tex]x = 300m^2[/tex]

Cross multiply

[tex]x * 100m^2 = \$19.75 * 300m^2[/tex]

Divide both sides by [tex]100m^2[/tex]

[tex]\frac{x * 100m^2}{100m^2} = \frac{\$19.75 * 300m^2}{100m^2}[/tex]

[tex]x = \frac{\$19.75 * 300m^2}{100m^2}[/tex]

[tex]x = \$19.75 * 3[/tex]

[tex]x = \$59.25[/tex]

Answer:

d = 16 in    then   r = 8 in

V = h * π * r²

V= 9in * π * (8 in)²

V = 1809.55 in³

Answer:

It's D

Step-by-step explanation:

Answer: · D'(-25,-10) E'(-25,15) F'(10,15)

Answer:

o D'(-25,-10) E'(-25,15) F'(10,15)

Step-by-step explanation:

In dilations, the scale factor is how many times larger than the new image will be.

Great, that explains a lot.

In other words, multiply the x and y-coordinate by the scale factor.

In this case, the scale factor is 5.

D(-5,-2)

-5 ⋅ 5 = -25

-2 ⋅ 5 = -10

E(-5,3)

-5 ⋅ 5 = -25

3 ⋅ 5 = 15

F(2,3)

2 ⋅ 5 = 10

3 ⋅ 5 = 15

Therefore, the new coordinates are:

D' (-25,-10)

E' (-25,15)

F' (10,15)

Answer:

try dividing or multiplying the information their giving you?

multiply sides by 4

k = 24

Answer:

k = 24

Step-by-step explanation:

k/4 = 6

k is being divided by 4, so multiply both sides by 4.

k/4 * 4 = 6 * 4

k = 24

Answer:

[tex]d = \sqrt{122} \: in[/tex]

Step-by-step explanation:

D^2 = x^2 + y^2 + z^2

= (9 in)^2 + (5 in)^2 + (4 in)^2

= 122 in^2

or

[tex]d = \sqrt{122} [/tex]

Answer:

2140

Step-by-step explanation:

Year one.                         1300

year 2.         120.               1420

year 3.         120.              1540

year 4.         120.              1660

year 5.         120.              1780

year 6.         120.              1900

year 7.         120.              2020

year 8.         120.              2140

or

7 x 120=840

1300 + 840 = 2140

Answer:

I say the answer is B.

Step-by-step explanation:

I basically multiplied all the vertices by 2.

Hope this helped!!!

Answer:

The bases do not have the same area because the volume of the cylinder is not 3 times the volume of the cone, given the same heights.

Step-by-step explanation:

Recall :

V1 = volume of cylinder = πr²h

V2 = volume of a cone = 1/3πr²h

From the diagram, both have height, h of 12

Radius = r

V1 = 2512 in

V2 = 1256 in

From the ratio :

2512 = πr² * 12

1256 = 1/3πr² * 12

12 cancel out as well as r² and π

If the bases have the same area `, then 2512 should be equal to (1256 * 3)

2512 in ≠ 3868 in

Answer:

The answer is D

Step-by-step explanation:

I got it right on my unit test

God bless

Answer:

Step-by-step explanation:

Answer: 1.885 miles

Step-by-step explanation:

Given: One lap around a park = 0.58 mile

The number of laps walked by Jessica= 3.25

Then, in miles , the distance walked around the park by Jessica will be (Multiply the number of laps to the value of one lap in miles) :

Hence,  Jessica walked 1.885 miles around the park.

Answer:

im a dad, and i have the best woman in the world, best wife and mother to are boy

Step-by-step explanation:

no psss ya valio madres

Answer:

a (the length is twice the width)

Step-by-step explanation:

a(the length is twice the width)

Answer:

Step-by-step explanation:

Remark

The ratios are certainly correct but that doesn't mean that they show similarity. SSA is a very dangerous proposition to use. Redraw triangle DEF of that DF is going to upwards to your right hand side. Make E as it was before. Why isn't this right?

It isn't right because E has gone from being an acute angle to an obtuse angle (an angle larger than 90 but less than 180).

The ratios are still true, but the angles do not match. So the whole answer is incorrect.