expressions that are equal to 4 times the square root of 5

Answer:

x = 12 and x = -6

Step-by-step explanation:

First subtract 6x on both sides to get a 2nd degree polynomial equal to zero:

[tex]x^2-6x-72=0[/tex]

To complete the square, the formula is to divide 'b' by 2 and square the result. The general form for a 2nd degree polynomial of the variable 'x' is as follows:

[tex]ax^2+bx+c=0[/tex]

For your case, b = 6. Therefore, the term that must be added and subtracted to our equation is:

[tex](6/2)^2=3^2=9[/tex]

Add and subtract 9 to our equation to get:

[tex]x^2-6x+9-9-72=0[/tex]

The first three terms form a perfect square, we have:

[tex](x^2-6x+9)-9-72=0[/tex]

[tex](x^2-6x+9)-81=0[/tex]

What multiplies to equal 9 but adds to equal -6? That would be -3 and -3. Therefore:

[tex](x-3)^2-81=0[/tex]

Add 81 to both sides to get:

[tex](x-3)^2=81[/tex]

We want to take the square root, but recall a square root has a positive and negative branch. Therefore we have two solutions:

[tex]x-3=9[/tex]

[tex]x-3=-9[/tex]

[tex]x=12[/tex]

[tex]x=-6[/tex]

The height of the tree that forms an angle of 64 degrees and point from the tree is 49 feet is 100.46 ft

The situation forms a right angle triangle.

using trigonometric ratios,

tan 64 = opposite / adjacent

Where

Therefore,

tan 64 = h / 49

cross multiply

h = 49 × tan 64

h = 49 × 2.05030384158

h = 100.464888237

h = 100.46 ft

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[tex]~~~~~5\sin 2x +4 =10 \sin^2 x\\\\\implies 5\cdot 2\sin x \cos x+4 =10 \sin^2 x\\\\\implies 10 \sin x \cos x +4 = 10\sin^2 x\\\\\implies 10\tan x + 4\sec^2 x = 10\tan^2 x~~~~~;[\text{Divide both sides by}~ \cos^2 x]\\\\\implies 10\tan^2 x -10 \tan x -4(1+ \tan^2 x)=0\\\\\implies 10\tan^2 x -10 \tan x -4 -4\tan^2 x =0\\\\\implies 6 \tan^2 x -10 \tan x -4 =0\\\\\implies 3 \tan^2 x -5 \tan x -2 =0~~~~~;[\text{Divide both sides by 2}]\\\\\implies 3\tan^2 x - 6\tan x +\tan x -2 =0\\\\[/tex]

Answer:

8

Step-by-step explanation:

From 5 to get to 20 it would be (X4), so we would do the same for the 2, and 2 times 4 would be 8. The answer is 8.

Answer:

24

Step-by-step explanation:

The way you calculate the volume of a shape is length x width x height. 4 x 3 x 2 = 24.

Answer:

2776 is the surface area.

Step-by-step explanation:

19 x 48 = 912 x 2 = 1824. 7 x 19 = 133 x 2 = 266. 49 x 7 = 343 x 2 = 686.

Answer:

2762

Step-by-step explanation:

The formula is:
2*(width*length+height*lenght+height*width)
2*(19*48+7*48+7*19)

this equals 2762

Answer:

- sign indicates the fact that it's Below sea level

Answer:

7 with a remainder of 2

Step-by-step explanation:

i just did the math rn

Answer:

x = -1

Step-by-step explanation:

First we expand both sides :

Let's start with the right side:

6(x-1) = 6x-6

Now we do the left side:

4(x-2) = 4x-8

Now we add 6 to both sides:

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

Simplify:

6x = 4x -2

Subtract 4x from both sides:

6x - 4x = (4x-2) - 4x

Simplify:

2x = -2

Divide both sides by 2:

2x÷2 = -2÷2

Simplify:

x = -1

I dont see a box so can't do the second part.

Hope this helps and brainliest please

Answer:

24

Step-by-step explanation:

when x = 5,

4(5-2)(5-3) + 7(5-2)(5-5) - 6(5-3)(5-5)

= 4(3)(2) + 7(3)(0) - 6(2)(0)
= 24

Answer:

NOT a right triangle

Step-by-step explanation:

IF it is a right triangle, then the Pythagorean theorem would apply

13^2 + 82^2  = 83^2   ?????

169  + 6724  = 6889

6893  = 6889 ?     No...it is NOT a right triangle

Answer:

they are three I will explain

Step-by-step explanation:

x+4/3÷6/x

this 3 expressions are equivalent to the equation above

1. x+4/3{x/6}

2. {x/6}x+4/3

3. x^2 + 4x /18

Factor out the numerator first

The hole is at x-3=0 i.e x=3

And

The hole is at (3,6)

Answer:

-60 = x

Step-by-step explanation:

(-1/4)x - 12 = x + 3

(-1/4)x = x + 15

-0.25x = x + 15

-60 = x

Answer:

-1/2 x + 3

Step-by-step explanation:

Arithmetic sqaure: a + (n-1) * d

              where "a" is the first term, "d" is the common difference

Here given:

a = 10 gallons

d = 5.5 gallons

Solve for first 5 terms:

10 + (1-1) * 5.5 = 10

10 + (2-1) * 5.5 = 15.5

10 + (3-1) * 5.5 = 21

10 + (4-1) * 5.5 = 26.5

10 + (5-1) * 5.5 = 32

first five terms: 10, 15.5, 21, 26.5, 32

General formula

So

Answer:

10

Step-by-step explanation:

My guy just plug in the number for x it's not that hard

Answer: Alex 28

Frank 22

Step-by-step explanation: Age difference is 6. Addition is 50

Answer:

slope = 1/2

Step-by-step explanation:

Pick two convenient integer coordinates

 I'll use  (0,-1) and (2,0)

slope =   (y1-y2)/(x1-x2) =   (-1-0) / ( 0-2) = 1/2

Answer:

Step-by-step explanation:

The cross sectional area of a basketball would indeed be a circle. The units for surface area would be meters squared. The units meters cubed would be volume. Area is inherently a 2-dimensional problem. Therefore, having 3-dimensional units makes no sense. In your case, the correct answer would be yards squared

Answer:

14

Step-by-step explanation:

2(9)-4=14

the slope is m= -1/5.

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

y_2 - y₁ = m(x₂ - x₁).

here, we have,

the slope of the line that passes through the points (-1, 6) and (14, 3)

Slope: m=  y_2 - y₁/(x₂ - x₁).

              = 3-6/14+1

              = -1/5.

hence, the slope is m= -1/5.

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The geometric series will be D. 2 + 14 + 98 + 686 because it is having a common ratio 7.

In mathematics, a geometric series is the sum of an infinite number of terms that have a constant or common ratio between successive terms

A. 6 + 13 + 20 + 27 .

the difference between two terms are 13-6 = 7 , 20-13= 7

The terms are increasing by 7. So it is not geometric

B. 7 + 21 + 35 + 45

the difference between two terms are 21-6 = 14 , 35-21= 14

The terms are increasing by 14. So it is not geometric

C. 14 + 21 + 28 + 35

the difference between two terms are 21-14 = 7 , 28-21= 7

The terms are increasing by 7. So it is not geometric

D. 2 + 14 + 98 + 686

Here the difference is not same, so we find the ratio

14/2= 7

98/14= 7

686/98= 7

So common ratio is 7

When the common ratio is same then it is Geometric series

Hence the geometric series will be D. 2 + 14 + 98 + 686 because it is having a common ratio 7.

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Answer:

D

Step-by-step explanation:

multiplied by 7 each time

Answer:

i cant see the photo, but i would love to help

Step-by-step explanation:

Answer:

9.411

Step-by-step explanation:

Answer:9.144

Step-by-step explanation:

Answer:

a = 39.2650873379cm

b = 11.5529459767cm

Step-by-step explanation:

a - Use the area of a triangle equation -  1/2 * a * b * Sin(C)

1/2 * 8 * 10 * Sin(79) = 39.2650873379cm

b - Use the cosine rule - c^2 = a^2 + b^2 - (2 * a * b * Sin(C)

64 + 100 - (2 * 8 * 10 * Cos(79)) = 133.4705607398

c = square root of 6.9396506484 = 11.5529459767cm

Put to however many significant figures / decimal places required.

:)

Answer:

they played 20 games together

Step-by-step explanation:

use percentages

Let x be the number of total games.

If 60% is won games then 40% is lost games.

(8/x)*100 = 40

8/x = 4/10

80 = 4x

X = 80/4

Therefore the number of games is 20

Answer:

minus 48 to 90 then divide the answer by 2

Answer:

42°

Step-by-step explanation:

The 2 acute angles in a right triangle add up to 90°

90° - 48° = 42°

Hope this helps