[tex]Expand $(a + 2)(3a^2 + 12)(a - 2).$[/tex]

Answer: 5.24 units, 10.48 units , 15.72  units

Step-by-step explanation:

Volume of a rectangular solid is given by :-

V = lwh, where l = length , w= width and h = height

Given: A rectangular solid has edges whose lengths are in the ratio 1:2:3.

Let lengths of the rectangular solid x , 2 x, 3x.

volume of the solid is 864 cubic units

Then, Volume of rectangle = [tex]x (2x)(3x) =864\ \text{cubic units}[/tex]

[tex]\Rightarrow\ 6x^3 = 864\\\\\Rightarrow\ x^3 =144\\\\\Rightarrow\ x=(144)^{\frac{-1}{3}}\approx5.24[/tex]

Lengths of rectangular solid 5.24 units, 2 (5.24) units , 3(5.24) units

= 5.24 units, 10.48 units , 15.72  units

Answer:

x-1

Step-by-step explanation:

| x-1|  x> 1

Since x is greater than x, the absolute value will be positive so we can remove it

x-1

Lets use a number to check

Let x = 4

| 4-1|    4>1

3  which is positive

Answer:

x - 1

Step-by-step explanation:

| x - 1 |

x > 1

x is greater than 1. The absolute value is not needed, since the value inside will only be for positive integers.

x - 1

We can check by plugging x as 2.

2 - 1 = 1 (positive)

2 > 1

Answer:

864.36 boxes

Step-by-step explanation:

In the question above, we are given the following values,

Confidence interval 95%

Since we know the confidence interval, we can find the score.

Z score = 1.96

σ , Standards deviation = 15mm

Margin of error = 1 mm

The formula to use to solve the above question is given as:

No of boxes =[ (z score × standard deviation)/ margin of error]²

No of boxes = [(1.96 × 15)/1]²

= 864.36 boxes

Based on the options above, we can round it up to 97 boxes.

Answer:

-5,-8,-11,-14,-17

Step-by-step explanation:

-3n -2

n=1   -3(1) -2 = -3-2 = -5

n=2   -3(2) -2 = -6-2 = -8

n=3   -3(3) -2 = -9-2 = -11

n=4   -3(4) -2 = -12-2 = -14

n=5   -3(5) -2 = -15-2 = -17

We can substitute n with each term in order.

First Term:

-3(1) - 2

-3 - 2

-5

Second Term:

-3(2) - 2

-6 - 2

-8

Third Term:

-3(3) - 2

-9 - 2

-11

Fourth Term:

-3(4) - 2

-12 - 2

-14

Fifth Term:

-3(5) - 2

-15 - 2

-17

Therefore, the sequence is -5, -8, -11, - 14, -17

Best of Luck!

Answer:

first option

Step-by-step explanation:

Given

[tex]\frac{15}{x}[/tex] + 6 = [tex]\frac{9}{x^2}[/tex]

Multiply through by x² to clear the fractions

15x + 6x² = 9 ( subtract 9 from both sides )

6x² + 15x - 9 = 0 ( divide through by 3 )

2x² + 5x - 3 = 0 ← in standard form

Consider the factors of the product of the coefficient of x² and the constant term which sum to give the coefficient of the x- term.

product = 2 × - 3 = - 6 and sum = + 5

The factors are + 6 and - 1

Use these factors to slit the x- term

2x² + 6x - x - 3 = 0 ( factor the first/second and third/fourth terms )

2x(x + 3) - 1(x + 3) = 0 ← factor out (x + 3) from each term

(x + 3)(2x - 1) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 3 = 0 ⇒ x = - 3

2x - 1 = 0 ⇒ 2x = 1 ⇒ x = 0.5

Solution set is { - 3, 0.5 }

Answer:

x = 30

(30, 0)

Step-by-step explanation:

The x-intercept is when the graph crosses the x-axis when y = 0. In that case, simply plug in 0 for y:

x + 6(0) = 30

x + 0 = 30

x = 30

Answer: (30,0)

Step-by-step explanation:

x-intercept can be found in the form x = my + b, where b is the x-intercept. Thus, simply turn x+6y=30 into x-6y+30, to find that the x-intercept is (30,0)

Hope it helps <3

Answer:

NL=10.82

Step-by-step explanation:

Start by finding the area of the triangle.  We do this by using c as the base.

1/2bh=1/2(12)(25)=150

Now that we know the area is 150, we turn the triangle so b is the base and use the formula again.  This time we’re looking for the height, which is NL.

1/2bh=

1/2(27.73)h=150

13.865h=150

h=10.8186

Rounded to the nearest hundredth, it’s NL=10.82

Complete question :

Sharon is making a large batch of soup. The soup reaches a height of 25 in a cylindrical pot whose diameter is 30cm. To store the soup for later, she'll pour it into ice cube molds where each cube has edges that are 7cm long. How many whole cubes can Sharon make?

Answer:

About 51 ice cubes

Step-by-step explanation:

Given the following :

Height (h) of cylindrical pot = 25

Diameter = 30cm

Edge of ice cube = 7cm long

Volume of cylinder (v) = πr^2h

V = π * (30/2)^2 * 25

V = π * 15^2 * 25

V = 17671.458cm^3

Therefore, the soup occupies 17673.75cm^3

Volume of cubes to store the soup for later:

The volume of a cube is given by the formula:

V = a^3

Where a is the length of it's edge

V = 7^3

V = 343cm^3

Number of cubes required to store soup:

(Volume of cylinder / Volume of ice cube)

17671.458cm^3 / 343cm^3

= 51.520287

This is about 51 whole cubes

Answer:

2

Step-by-step explanation:

We can use 2 points to find the slope

m = (y2 -y1)/(x2-x1)

Using ( 0,1) and (1,3)

    = (3-1)/(1-0)

   = 2/1

  = 2

Answer:

2

Step-by-step explanation:

Take any two points -- I'm using (0, 1) and (1, 3). You can think of slope as (change in y)/(change in x), or simply rise/run. (3-1)/(1-0) is equal to 2.

*Note: (-1/2,1/2) is not in the same line as the other four points.

Answer:

The number of possible outfits Dustin can wear is 73 outfits

Step-by-step explanation:

The information given are;

The number of hats Dustin has = 5

The number of shirts Dustin has = 5

The number of pants Dustin has = 5

The number of shoes Dustin has = 5

The colors of Dustin's clothing are blue, green, gray, silver, and gold

Given that the shoes go with at least two other clothing of the same color, we have;

The number of ways the color of the shoes can be selected = 5 ways

The number of ways of selecting the same color for 2 of the remaining 3 clothing = 3 ways

The number of ways of selecting the color of the fourth clothing = 5 ways

The total number of ways = 5 × 3 × 5 = 75 ways

The number of ways in which all silver can be selected = 1 way

The number of ways in which all gold can be selected = 1 way

Since Dustin refuses to wear all silver and all gold, the total number  of ways the outfits can be selected = 75 - 1 - 1 = 73 ways = 73 is the number of possible outfits

Therefore, the number of possible outfits Dustin can wear = 73 outfits.

Answer:

L = 18 = hours worked by Lisa

a = 12 = hours worked by Abigail

Step-by-step explanation:

Given the following :

Abigail's earning = $20

Lisa's earning = $25

Last week :

Let number of hours worked by Abigail = a

Number of hours worked by Lisa = L

Total earning = $690

Total hours worked :

a + L = 30 - - - - (1)

To obtain their total earning:

(Lisa's earning per hour * hours worked) + (Abigail's earning per hour * hours worked)). $690

($25 * L) + ($20 * a) = $690

25L + 20a = 690 - - - - (2)

a + L = 30 - - - - (1)

25L + 20a = 690 - - - - (2)

L = 30 - a

25(30 - a) + 20a = 690

750 - 25a + 20a = 690

-5a = 690 - 750

-5a = - 60

a = 12

From (1)

a + L = 30 - - - - (1)

12 + L = 30

L = 30 - 12

L = 18

L = 18 = hours worked by Lisa

a = 12 = hours worked by Abigail

SOH CAH TOA

Sin = opp/hyp

Cos = adj/hyp

Tan = opp/adj

7) 21/35 or 3/5

8) 21/20

9) 30/50 or 3/5

10) 40/50 or 4/5

Answer:

[tex]{\mathrm{view \: explanation}}[/tex]

Step-by-step explanation:

[tex]sin \theta = \frac{opposite}{hypotenuse}[/tex]

[tex]cos \theta = \frac{adjacent}{hypotenuse}[/tex]

[tex]tan \theta = \frac{opposite }{adjacent }[/tex]

[tex]sinX=\frac{21}{35}[/tex]

[tex]tanX=\frac{21}{20}[/tex]

[tex]sinC=\frac{30}{50}[/tex]

[tex]cosC=\frac{40}{50}[/tex]

Answer:

0.16

Step-by-step explanation:

See the picture attached for reference.

As you see the best points are the green areas which covers 2 out of 5 zones.

Since it is same for both broken points, the probability of  this is:

Answer is 0.16

__♥__♥_____♥__♥___ Put This

_♥_____♥_♥_____♥__ Heart

_♥______♥______♥__ On Your

__♥_____/______♥__ Page If

___♥____\_____♥___ You Had

____♥___/___♥_____ Your Heart

______♥_\_♥_______ Broken

________♥_________…………….

Answer :Answer: Did you get helped on this one?          

Step-by-step explanation: okay yup yup have a good day OKAY

Step-by-step explanation: HAVE A GOOD ONE OKAY

Answer:

[tex]\large\boxed{\sf \ \ 49 \ \ }[/tex]

Step-by-step explanation:

Hello,

we need to get the discriminant = 0 meaning

[tex]\Delta = b^2-4ac = 0\\\\<=>14^2-4c=0\\\\<=>c=\dfrac{196}{4}=49[/tex]

And then the square is

[tex]x^2-2\cdot 7\cdot x+7^2=(x-7)^2[/tex]

Hope this helps

Answer: 17.75

Step-by-step explanation:

The interquartile range(IQR) is the 3rd quartile - the 1st quartile.

How to get quartiles:

First get the median:

3.5, 10.4, 16, 21.7, 27.7

10.4, 16, 21.7

16

Then find the median of the first half of data(3.5, 10.4)

(3.5+10.4)/2 = 6.95

Then find the median of the last half of data(21.7, 27.7)

(21.7+27.7)/2 = 24.7

Then to get the IQR subtract 6.95 from 24.7 to get 17.75

Hope it helps <3

Answer11.3

Step-by-step explanation:

Since there is an odd amount of values

find you lower median by taking the 3 lower numbers and using the middle number 10.4 (Q1)

then find your higher median with the 3 higher numbers and using the middle number 21.7 (Q3)

Then subtract Q3 - Q1

21.7-10.4 giving you the answer 11.3

Answer:

A ( -4, -7)

Step-by-step explanation:

if you translate -1, three units to the left u get -4 and then when u go nine units down u get -7 do it on a grid and u will see wut im talkin about : )

Answer:

A.

Step-by-step explanation:

Answer:

what are you going to do with that?

Answer:

t > 212

Step-by-step explanation:

Given

Boiling point = 212°F

Required

Inequality that shows temperature greater than the boiling point

From the question, temperature is represented with t.

The inequality "greater than" is represented with >

So, temperature greater than the boiling point implies that t > 212

Answer: t > 212

Step-by-step explanation:

The question says "Write an inequality that is true only for temperatures that are higher than the boiling point of water."

This means t has to be higher than 212 since it says only for temperatures that are higher than the boiling point.

But since we have to write an inequality the answer would be: t > 212.

I know I did this very late and you probably don't need it but i was bored

Answer:

x = 6

Step-by-step explanation:

Since KN is the perpendicular bisector, that means ∠KNM = ∠KNQ = 90° and MN = NQ so therefore, since they are right triangles, ΔKNM ≅ ΔKNQ because of HL. Therefore, KM = KQ by CPCTC so:

5x - 3 = 3x + 9

2x = 12

x = 6

p=paul's height

s=steve's height

t=theresa's height

p=s

1 and 1/2=3/2

1 and 1/3=4/3

p=-16+(3/2)t

s=-6+(4/3)t

p=s so

-16+(3/2)t=-6+(4/3)t

add 6 to both sides

-10+(3/2)t=(4/3)t

times both sides by 6 to clear fractions

-60+9t=8t

minus 9t both sides

-60=-t

times -1

60=t

t=60

theresa is 60 inches or 5ft

steve and paul are 84 inches or 7ft (wow!)

Answer:

Step-by-step explanation:

you have the hypotenuse side and adjacent side, so you would use cosine (adj/hyp). since you are trying to find the angle, you use the inverse operation.

put it in the calculator and you should get 0.98176535657.

Answer:

x^5

Step-by-step explanation:

x^2 . x^3

x^(2+3)

x^5

Answer:

C. Fertility= Nutrients * Moisture / Pollutant

Step-by-step explanation:

F=NM/P

F= Fertility of the soil

N= Amount of nutrients in the soil

M= Amount of moisture in the soil

P= Amount of pollutant in the soil

F=NM/P

Fertility of the soil

= Amount of nutrients in the soil * Amount of moisture in the soil / Amount of pollutant in the soil

Fertility= Nutrients * Moisture / Pollutant

Option C is the correct answer

Answer:

12 feet

Step-by-step explanation:

Use the Pythagorean Theorem to find how high up the tree the top of the ladder reaches.

13 feet - hypotenuse

5 feet - can be a or b

a² + b² = c²

5² + b² = 13²

25 + b² = 169

b² = 144

b = √144

b = 12

The top of the ladder reaches 12 feet up the tree.

Hope that helps.

Answer:

12 ft

Step-by-step explanation:

These circumstances describe a triangle with hypotenuse 13 ft and bottom side 5 ft.  The vertical side (height above ground to top of ladder) is to be found.  According to the Pythagorean Theorem,

5^2 + (vertical side)^2 = 13 ft = 169, and so

(vertical side) = sqrt( 169 - 25 ) = 144 (ft)

The top of the ladder is s 12 ft above the ground.

Answer:

[tex]\boxed{F(x)>0}[/tex]

Step-by-step explanation:

The range is the set of possible values of y (the output).

The input value x is all real numbers, because there are no restrictions on x.

When the input x is all real numbers, the output is always greater than 0.

[tex]2^{-15}= 0.00003051757[/tex]

[tex]2^{8}= 256[/tex]

[tex]2^{-4}= 0.0625[/tex]

Answer:

The temperature at 5376 ft is approximately 63°F

The assumption made was that the temperature varies linearly with elevation

Step-by-step explanation:

The parameters given are;

Temperature at 6288 feet = 56°F = 286.5

Temperature at 2041 feet = 87°F = 303.71

We are to find the temperature at 5376 feet

Let the temperature be the y-coordinate value and the elevation be the x-coordinate value, to find the temperature, we have the temperature gradient given by the relation;

[tex]m = \dfrac{y_2-y_1}{x_2 - x_1} = \dfrac{303.71-286.5}{2041 - 6288}= -4.05 \times 10^{-3} \ K/ft[/tex]

The temperature at 5376 ft will be the temperature at 2041 added to the decrease in temperature from climbing to 5376 ft

The increase in elevation is 5376 - 2041 = 3335 ft

The decrease in temperature = 3335 ft × (-4.05 × 10⁻³) K/ft = -13 .5 K

The temperature at 5376 ft will then be 303.71 - 13.5 = 290.196 K = 62.68°F ≈ 63°F

The assumption made was that the decrease in temperature with elevation is linear.

Answer:

10 cm overlap required to make a 30 cm long strip.

Step-by-step explanation:

Given:

Four paper strips of the same length.

Two of them glued together with a 4 cm overlap to make a new strip which is 36 cm long.

To find:

Overlap required to make a strip which is 30 cm long = ?

Solution:

First of all, let us understand the concept of overlap.

Please refer to the attached image.

Let length of each strip be [tex]x[/tex] cm.

Given that there is 4 cm overlap resulting in new strip of length 36 cm.

The overlapping length is counted only once as clear from the figure attached.

So, Let us try to find the equation:

[tex]x +(x-4) = 36\\\Rightarrow 2x=40\\\Rightarrow x = 20\ cm[/tex]

i.e. each strip length is 20 cm.

Now, let us assume, an overlap of 'y' cm is to be made to make a new strip of 30 cm.

The equation will be:

[tex](20-y)+20 =30\\\Rightarrow y = 40-30\\\Rightarrow y = 10\ cm[/tex]

Answer: The missing side is 5 units.

Step-by-step explanation:

Pythagorean Theorem states that a^2+b^2=c^2.  Let the hypotenuse be x.

[tex]4^2+3^2=x^2\\16+9=x^2\\25=x^2\\\sqrt{25}=\sqrt{x^2}\\\left[\begin{array}{c}x=5\end{array}\right][/tex]

Hope it helps <3

Answer:

BC = 8

Step-by-step explanation:

16 ( sin 30 degrees ) = BC

16 (0.5)

16/2

BC = 8

Give the other person brainliest they deserve it.