Choose the correct simplification of 9x^2(4x + 2x^2 − 1)

Answer:

5

Step-by-step explanation:

This shape is formed by two right triangles.

Let's start by the little one.

Let y be the third side.

Using the Pythagorian theorem we get:

y^2 = 6^2 + 3^2

y^2 = 36 + 9

y^2 = 45

y = 3√(5)

●●●●●●●●●●●●●●●●●●●●●●●●

Now let's focus on the second triangle. Let z be the third side.

The Pythagorian theorem:

6^2 + x^2 = z^2

Using the Pythagorian theorem on the big triangle :

[3√(5)]^2 + z^2 = (3+x)^2

45 + z^2 = 3x^2 + 6x + 9

36 +z^2 = 3x^2 +6x

So we have a system of equations.

36+ x^2 = z^2

36 +z^2 = 3x^2 +6x

We want to khow the value of x so we will eliminate z .

Add (36+x^2 -z^2 =0) to the second one.

36 + x^2-z^2+36+z^2 = 3x^2+6x

72 + x^2 = 3x^2 +6x

72 - 2x^2 -6x = 0

Multipy it by -1 to reduce the number of - signs

2x^2 + 6x -72 = 0

This is a quadratic equation

Let A be the discriminant

● a = 2

● b = 6

● c = -72

A = b^2-4ac

A = 36 -4*2*(-72) = 36 + 8*72 =612

So this equation has two solutions

The root square of 612 is approximatively 25.

● (-6-25)/4 = -31/4 = -7.75

● (-6+25)/4 = 19/4 = 4.75 wich is approximatively 5

A distance cannot be negative so x = 5

Complete Question

The complete question is shown on the first uploaded image

Answer:

Yes  the test  suggest that the true average percentage of organic matter in such soil is something other than 3%

Step-by-step explanation:

From the question we are told that

  The  sample mean is  [tex]\= x = 2.482\%[/tex]

  The  standard deviation is [tex]\sigma = 1.614[/tex]

   The  standard error is [tex]SE = 0.295[/tex]

     The  sample size is [tex]n = 30[/tex]

   The  level of significance is  [tex]\alpha = 0.05[/tex]

  The  null hypothesis is [tex]H_o : \mu = 3\%[/tex]

   The  alternative hypothesis is  [tex]H_a : \mu \ne 3\%[/tex]

Now  the degree of freedom is evaluated as

       [tex]df = n - 1[/tex]

       [tex]df = 30 - 1[/tex]

       [tex]df = 29[/tex]

The test statistics is mathematically evaluated as

         [tex]t = \frac{ 2.482 - 3}{ 0.295}[/tex]

         [tex]t = -1.756[/tex]

The p-value is obtained from the the student t -distribution table , the value is  

        [tex]p-value = P( T \le t)= 2 * t_{ t, df } = t_{ -1.756 , 29 } = 2 *0.0448= 0.0896[/tex]

The reason for the 2 in the equation is because the test is a two -tailed test i.e  -1.756 and  1.756

Given that the [tex]p-value > \alpha[/tex] then we fail to reject the null hypothesis

Hence the test the suggest that the true average percentage of organic matter in such soil is something other than 3%

Answer:

There are no values of  x  that make the equation true.

No solution

Step-by-step

hope it help

Hi

2-9x = -6x+5-3x

-9x+6x+3x = 5-2

  0x = 3

as  0 ≠ 3 , there is no answer possible to your equation.

Answer:

14 °F

Step-by-step explanation:

To answer this problem, we will use the known celsius to fahrenheit conversion formula.

[Celsius * (9/5)] + 32 = Fahrenheit

Now we just plug in the value of celsius:

[-10 * (9/5)] + 32 = Fahrenheit

[ -2 * 9 ] + 32 = Fahrenheit

[ -18 ] + 32 = Fahrenheit

14 = Fahrenheit

So you should right 14(°F) on the label.

Cheers.

Answer:  5.22 seconds

Step-by-step explanation:

t represents time and y represents the height.

Since we want to know when the ball hits the ground, find t when y = 0

Ball 1 starts at a height of 109 --> h = 109

0 = -16t² + 109

16t² = 109

   [tex]t^2=\dfrac{109}{16}\\[/tex]

   [tex]t=\sqrt{\dfrac{109}{16}}[/tex]

   [tex]t=\dfrac{\sqrt{109}}{2}[/tex]

   t = 5.22

=> H = 109

=> 0 = -16t² + 109

=> 16t² = 109

=> t² = 109/16

=> t = 109/2

=> t = 5.22 sec

Therefore, 5.22 second is the answer.

The shape is missing, so i have attached it.

Answer:

2.6

Step-by-step explanation:

From the image attached, the diameter of the inner semi - circle is 0.5 yards while the length of each side of the pillow is 0.2 yards.

Thus, for us to find the length of the seam which is along the edges of the pillow, we will calculate the perimeter of the outer semicircle, then add the perimeter of the inner semicircle and also add the sides too.

Now, due to the fact that the length of the sides of the pillow are 0.2 yards each, the diameter of the outer circle would be;

0.5 + 0.2 + 0.2 = 0.9 yards. So, the perimeter of the outer semicircle is,

P0 = πd/2 = π × 0.9/2 =0.45π yds

The perimeter of the inner semicircle would be given as;

PI = πd/2 = π × 0.5/2 =0.25π yds.

Thus, we can calculate the total perimeter of the pillow as;

PT = P0 + PI + 0.2 + 0.2

PT = 0.45π + 0.25π + 0.2 + 0.2

PT ≈ 2.6 yards

Alex will need 2.6 yds

Answer:

0.5

Step-by-step explanation:

Answer:

Perimeter= 29.12 unit

Step-by-step explanation:

Perimeter of the triangle is the length of the three sides if the triangle summef up together

Let's calculate the length of each side.

For (-4,-6),(3,3)

Length= √((3+4)²+(3+6)²)

Length= √((7)²+(9)²)

Length= √(49+81)

Length= √130

Length= 11.40

For (-4,-6),(7,2)

Length= √((7+4)²+(2+6)²)

Length= √((11)²+(8)²)

Length= √(121+64)

Length= √185

Length= 13.60

For (3,3),(7,2)

Length=√( (7-3)²+(2-3)²)

Length= √((4)²+(-1)²)

Length= √(16+1)

Length= √17

Length= 4.12

Perimeter= 4.12+13.60+11.40

Perimeter= 29.12 unit

Answer:

$20

Step-by-step explanation:

Company A:

Buy 300 shares at $1.45 per share.

Sell 300 shares at $1.65 per share.

Profit: ($1.65 - $1.45) * 300 = $60

Company B:

Buy 200 shares at $1.20 per share.

Sell 200 shares at $1.10 per share.

Loss: ($1.20 - $1.10) * 200 = $20

Net profit:

$40 - $20 = $20

Answer:

Step-by-step explanation:

Profit on Company A =$(1.65−1.45)×300=$60.

Loss on Company B =$(1.20−1.10)×200=$20.

Therefore the total profit Jamal achieved was $60−$20=$40.

Answer:

Hey there!

The area of a rectangle is the length times width.

Thus, we can write the equation, 600=30w.

Solving for the width, we get that the width is equal to 20 ft.

Let me know if this helps :)

Answer:

20 feet across.

Step-by-step explanation:

You will have to do a simple equation solve.

x is how many feet across the court is.

* could be our multiplying sign

600 = 30*x

Now divide 30 on both sides. 30 will cross out (since 30/30 is 1 and anything times 1 is the same number as it was before) on the right side and 600/30 is 20 so we change the 600 to 20.

That leaves 20 = x.

So it is 20 feet across.

Answer:

(A) 37.5 miles

Step-by-step explanation:

The trains x and y are travelling on tracks starting simultaneously from a from opposite ends of 100 miles roads.

Translate these information into a simple represention to visualize the problem. (Picture below)

■■■■■■■■■■■■■■■■■■■■■■■■■■

First let's calculate the velocity of both trains.

The velocity formula is:

● V = d/t

d is the distance travelled and t is the tile needed to do it.

● V(x) = 100/5 = 20 miles per hour

● V(y) = 100/3 = 33.33.. wich is approximatively 33 after rounding to the nearest unit.

■■■■■■■■■■■■■■■■■■■■■■■■■■

After calculateingboth velocities, Let's find when the trains meet.

First understand what does it mean matematically when both trains meet.

Go back to the representation and notice what happens when the trains meet.

Let t be that moment.

When x and y reches the meeting point at t, the sum of the distances they have travelled is equal to the total distance wich is 100 miles .

We khow that V = d/t so d = V×t

Let's find the expression of the distances both trains travelled when they have met each other.

● d = V(x) × t

● d' = V(y) × t

■■■■■■■■■■■■■■■■■■■■■■■■■■

So the equation will be:

● V(x) × t + V(y) × t = 100

Factor using t

● t (V(x) + V(y) ) = 100

Replace V(x) and V(y) by their values

● t (20+33) = 100

● 53 t = 100

Divide both sides by 53

● 53t /53 = 100/53

● t = 1.88

■■■■■■■■■■■■■■■■■■■■■■■■■

Replace t in the expression of the distance that train x has travelled when meeting y.

● d = V(x) × t

● d = 20 × 1.88

● d = 37.6 wich is approximatively 37.5 miles

Answer:

A typical example would be when a statistician wishes to estimate the ... by the standard deviation ó) is known, then the standard error of the sample mean is given by the formula: ... The central limit theorem is a significant result which depends on sample size. ... So, the sample mean X/n has maximum variance 0.25/ n.

Step-by-step explanation:

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Hope this can help you.

1: 8 faces and 9 with the base 9 vertices and 16 edges

2: 3 faces and 5 with the bases 6 vertices and 9 edges

3: 3 faces and 4 with the base 4 vertices and 6 edges

Answer:

-7/1, -2.1, square root of 5, square root of 9, and last 3.5

Step-by-step explanation:

Square root of 9 is 3.

Square root of 5 is 2.24

-7/2 as a decimal is -3.5

So, from least to greatest order is:

-7/2 > -2.1 > Square root of 5 > Square root of 9 > 3.5

Step-by-step explanation:

a.

[tex]y = k {r}^{2} [/tex]

[tex]7 = k {3}^{2} [/tex]

[tex]7 = 9k[/tex]

[tex]k \: = \frac{7}{9} [/tex]

[tex]y \: = \frac{7}{9} {r}^{2} [/tex]

b.

[tex]y \: = \frac{7}{9} \times {15}^{2} [/tex]

[tex]y = \frac{7}{9} \times 225[/tex]

y = 175

Answer:

the point is (4,0)

Step-by-step explanation:

The x-intercept is the point on the x-axis where y=0.

Set y=0

0=4x-16

16=4x

x=4, y=0

So the notation for the point is (4,0).

Good luck!

Answer:

(4, 0)

Step-by-step explanation:

4x - 16 = 0

4x = 16

x = 4

Answer:

1

Step-by-step explanation:

Answer:

Hello There!!

Step-by-step explanation:

The answer is 1 as that means its certain that the event will happen.

hope thus helps,have a great day!!

~Pinky~

Answer:

D). (-4,-8)​

Step-by-step explanation:

An image at (8,-4) if rotated at an angle of 90° wipl have another location.

First of all, an image at (8,-4) is in the fourth quadrant, and if it's to rotate clockwise at 90° iths supposed to be in the third quadrant.

And in the third quadrant both x and y is negative.

So the new position is at (-4,-8)​

Answer:

x = -1 or x = -5

Step-by-step explanation:

−3 * |2x + 6| = −12 / -3

|2x + 6| = 4

because this is an absolute value equation there are 2 solutions:

2x + 6 = 4 or 2x + 6 = -4

2x = -2 or 2x = -10

x = -1 or x = -5

Answer:

x = -1 or x = -5

Step-by-step explanation:

cuz it is

Hey  There!

Answer:

Step-by-step explanation:

HCF

If HCF is  ''9'' that means that ''9'' is the divisible of two numbers.

So 18 and 19 can be divided by 9 and that's the highest divisible for both factors.

And always remeber the answer is a ''Prime factor.''

LCM

If LCM is ''3'' that means ''3'' is the lowest common multiple out of  two numbers.

Hope this helps!

Have a nice Day!:)

Answer:  4 seconds

Step-by-step explanation:

x refers to time. Since we want to know how long it is in the air, we need to find the time (x) when the ball lands on the ground (y = 0)

0 = -12x² + 48x

0 = -12x(x - 4)

0 = -12x     0 = x - 4

0 = x          4 = x

x = 0 seconds is when the ball was kicked

x = 4 seconds is when the ball landed on the ground

Answer:

y = 2(x - 3)² + 5

Step-by-step explanation:

The equation of a parabola in vertex form is

y = a(x - h)² + k

where (h, k) are the coordinates of the vertex and a is a multiplier

Here (h, k) = (3, 5), thus

y = a(x - 3)² + 5

To find a substitute (1, 13) into the equation

13 = a(1 - 3)² + 5 ( subtract 5 from both sides )

8 = 4a ( divide both sides by 4 )

a = 2, then

y = 2(x - 3)² + 5 ← equation of parabola in vertex form

Answer:

Perimeter of ABCD = 36 ft

Step-by-step explanation:

Given:

A (1,7)

B (7,7)

C (7,1)

D (1,1)

Find:

Perimeter of ABCD

Computation:

Distance between two point = √(x1-x2)² + (y1-y2)²

So,

AB = √(1-7)²+(7-7)²

AB = 6 ft

BC = √(7-7)²+(7-1)²

BC = 6 ft

CD = √(7-1)²+(1-1)²

CD = 6 ft

DA = √(1-1)²+(1-7)²

DA = 6 ft

Perimeter of ABCD = AB + BC + CD + DA

Perimeter of ABCD = 6 + 6 + 6 +6

Perimeter of ABCD = 36 ft

The perimeter of the plot is the sum of side length of the plot of land.

The perimeter of the plot is 24 feet.

Represent the vertices as follows:

[tex]W = (1,7)[/tex]

[tex]X = (7,7)[/tex]

[tex]Y = (7,1)[/tex]

[tex]Z = (1,1)[/tex]

First, we calculate the side length using the following distance formula:

[tex]d = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}[/tex]

So, we have:

[tex]WX = \sqrt{(1- 7)^2 + (7- 7)^2} = \sqrt{36} = 6[/tex]

[tex]XY = \sqrt{(7- 7)^2 + (7- 1)^2} = \sqrt{36} = 6[/tex]

[tex]YZ = \sqrt{(7- 1)^2 + (1- 1)^2} = \sqrt{36} = 6[/tex]

[tex]ZW = \sqrt{(1- 1)^2 + (1- 7)^2} = \sqrt{36} = 6[/tex]

The perimeter (P) is then calculated as follows:

[tex]P = WX + XY + YZ + ZW[/tex]

So, we have:

[tex]P = 6 + 6 + 6 + 6[/tex]

[tex]P = 24[/tex]

Hence, the perimeter of the plot of land is 24 feet.

Read more about perimeters at:

https://brainly.com/question/394193

Answer:

1.

d. (-14) + (-8)

2.

a. (-14) + 8

Step-by-step explanation:

(-14) - 8 is equal to (-14) + (-8) because we still add two negative values so the result wouldn't change.

(-14) - (-8) is equal to (-14) + 8 because there's two negative sign in front of 8 and two negative values multiplied makes a positive result.

Answer:

1. D  

2. A

Step-by-step explanation:

1.  It asks you what expression has the same value as (-14)-8.  All you need to do is find other equations that have the same value as that.  So the equation is -14-8.  IF a negative is outside a parenthesis with a positive number inside like -(+5), it is going to be -5.  If it's both negative: -(-5), it will be +5.  If it is both positive: +(+5), it is going to be +5.  

IMPORTANT!

- and + = -

- and - = +

+ and + = +

What we are looking for: -14-8

So choice A is (-14)+8 which is simplified to -14+8.  So, this one isn't right.

Choice B: 14-(-8)= 14+8.  So, it's incorrect.

Choice C: 14+(-8)= 14-8.  Again, it's not -14-8 so it's not right.

Choice D: (-14)+(-8)= -14-8.  This equation matches the one we are looking for!  So it's correct!

2. Same thing as number 1.  Let's simplify the equation it wants us to find first.  

(-14)-(-8)= -14+8

So -14+8 is what we are looking for.

Choice A: (-14)+8= -14+8.  It matches!  So it is correct.  Let's look at the other options anyway.

Choice B: 14-(-8)= 14+8.  Nope.  Not right.

Choice C: 14+(-8)= 14-8 because - always beats +.  So, this one is also incorrect.

Choice D: (-14)+(-8)= -14-8.  Oops, this is also wrong.  So choice A is the right answer.

Keep in mind, when you start getting questions like this with numbers inside the parenthesis as well, you want to remember the same rules for positive and negative, but also multiply the numbers together:

(When there is a number outside and inside a parentheses, multiply them.)

2(5)=10, CORRECT!    2+(5) is not 2 times 5.  It's whatever is closest to the parentheses, in this case being the positive sign.  So + and 5 is just 5!

IMPORTANT!

-2(-5)= - and - is positive, so positive (2 times 5).  Positive 10.

-2(+5)= - and + is negative, so negative (2 times 5). Negative 10.

+2(+5)= + and + is positive, so positive (2 times 5).  Positive 10.

Answer:

Each guest must bring 5 cans.

Step-by-step explanation:

1000-565=435

435/87=5

Answer:

I hope you are searching for this......

Answer:

x = 8

Step-by-step explanation:

Hello!

What we do to one side of the equation we have to do to the other side.

3x - 6 = 18

Add 6 to both sides

3x = 24

Divide both sides by 3

x = 8

The answer is 8

Hope this helps!

Answer:

x=8

Step-by-step explanation:

(3x-6)=18

Add 6 to each side

(3x-6+6)=18+6

3x= 24

Divide by 3

3x/3 = 24/3

x = 8

Answer:

Sphere Volume = 4/3 * PI * radius^3

Sphere Volume = 4/3 * PI * 8^3

Sphere Volume = 4/3 * PI * 512

Sphere Volume = 2,144.7 cubic inches

Step-by-step explanation:

Answer:

Step-by-step explanation:

If there are 30 students in a class with natasha in the class and natasha is to select four leaders in the class of which she is already part of the selection, this means there are 3 more leaders needed to be selected among the remaining 29 students (natasha being an exception).

Using the combination formula since we are selecting and combination has to do with selection, If r object are to selected from n pool of objects, this can be done in nCr number of ways.

nCr = n!/(n-r)!r!

Sinca natasha is to select 3 more leaders from the remaining 29students, this can be done in 29C3 number of ways.

29C3 = 29!/(29-3)!3!

29C3 = 29!/(26!)!3!

29C3 = 29*28*27*26!/26!3*2

29C3 = 29*28*27/6

29C3 = 3,654 different ways.

This means that there are 3,654 different ways to select the 4 leaders so that natasha is one of the leaders

Answer:

130 degree

Step-by-step explanation:

Interior angles of the triangle:

81, 49, (180-x)

and by sum of all angles of triangle is 180 degree,

therefore,

81 + 49 + 180 - x = 180

x = 130 degree