Simplify the following expression: [tex]\sqrt{x} 48a^{8}[/tex]

Step-by-step explanation:

It is given that, an air conditioning system can circulate 320 cubic feet of air per minute. We need to find how many cubic yards of air can it circulate per minute?

1 yard = 3 foot

1 feet = (1/3) yard

320 feet = 106.66 yard

[tex]320\ \text{feet}^3=320\times( \dfrac{1}{3})^3\ \text{yard}^3\\\\=11.85\ \text{yard}^3[/tex]

So, it will circulate 11.85 cubic yard of air per minute.

Answer:

x=−4

Step-by-step explanation:

Answer:

-4

Step-by-step explanation:

Given:

Solving for x:

Answer:

I can only answer the first one for now but the answer is x^2 - 6x + 9.

Step-by-step explanation:

f(x) = x^2 and g(x) = x - 3.

To find f(g(x))  we replace the x in f(x) by g(x).

f(g(x)) = (x - 3)^2

= x^2 - 6x + 9.

Answer:

An algebraic expression (in mathematics) can be defined as an expression which is made up of variables and constants along with algebraic operations( i.e. addition, subtraction etc)

Answer:

It is an expression built up from integer constants and algebric expressions.

Answer:

Step-by-step explanation:

Given the f(x) = 12x as  the number of inches in x feet and g(x) = 3.28x gives the approximate number of feet in x meters, to find the composite function that can be used to convert metres to inches will give;

f[g(x)] (This means we are substituting the function that is measured in metres into the functions measured in inches).

Given g(x) = 3.28x,

f[g(x)] = f(3.28x)

f(3.28x) means that we are to replace the variable of x in f(x) with 3.28x as shown;

f(3.28x) = 12(3.28x)

f(3.28x) = 39.36x

f[g(x)] = 39.36x

Hence the composite function that could be used to convert meters to inches is expressed as 39.36x.

Answer:

the measure of x is 18° and the measure of y is 29°

Step-by-step explanation:

Step 1

Find the measure of angle x

we know that

If ray NP bisects <MNQ

then

m<MNQ=m<PNM+m<PNQ ------> equation A

and

m<PNM=m<PNQ -------> equation B

we have that

m<MNQ=(8x+12)°

m<PNQ=78°

so

substitute in equation A

(8x+12)=78+78-------> 8x+12=156------> 8x=156-12

8x=144------> x=18°

Step 2

Find the measure of angle y

we have

m<PNM=(3y-9)°

m<PNM=78°

so

3y-9=78------> 3y=87------> y=29°

therefore

the answer is

the measure of x is 18° and the measure of y is 29°

Answer:

-0.22222222222222222222222

Step-by-step explanation:

Answer:

.6

...................

Answer: 6 : 10  or 3:5

Step-by-step explanation:

If they are 6 cats and 10 dogs then the ratio of cats to dogs it 6 to 10  or 6/10

Answer:

5 units

Step-by-step explanation:

Notice that the x-coordinate is the same for both points, but that the y-coordinates differ by five units.  The distance between these two points is therefore 5 units.

Step-by-step explanation:

17 miles = 1 day to work

14 miles =1 day to home

Therefore total miles driven in 5 days =

( 17×5) +(14×5) = 105+60

ANSWER =165 miles per week

Answer:

155 miles each week

Step-by-step explanation:

One day is 17 miles to and 14 miles home = 17+14 = 31

He does this 5 days a week

5 * 31 = 155 miles

Answer:

angle 3 is 33 degrees.

Step-by-step explanation:

complementary angle-adds up to 90 degrees

supplementary angle- adds up to 180 degrees.

if angle 1 is 123, then angle two is 180-123 degrees(57)

if angle two is 57 degrees, angle 3 is 90-57 degrees (33)

Answer:

Step-by-step explanation:

Since ∠1 and ∠2 are supplementary the sum of their angles is 180°

So to find ∠2 add ∠1 and ∠2 and equate them to 180° to solve for ∠2

So we have

∠1 + ∠2 = 180

∠2 = 180 - ∠1

From the question

m∠1 = 123°

So we have

∠2 = 180 - 123

∠2 = 57°

From the question , ∠2 is a complement of ∠3 the sum of their angles is 90°

That's

∠2 + ∠3 = 90

∠3 = 90 - ∠2

∠3 = 90 - 57

We have the final answer as

Hope this helps you

Answer:

k=21

Step-by-step explanation:

Find the slope of MN which is 1/5 (use the slope formula)

Use the slope formula for AB using k as y_2

Substitute and you get k=21

21-2.25/-2.25-1.5=-5

The lines are perpendicular because the slopes are the negative reciprocal of one another.

Answer:

The midpoint is ( 1, -1.5)

Step-by-step explanation:

To find the midpoint

Add the x coordinates of the endpoints and divide by 2 to get the x coordinate of the midpoint

(5+-3)/2 = 2/2 = 1

Add the y coordinates of the endpoints and divide by 2 to get the y coordinate of the midpoint

(3+-6)/2 = -3/2 = -1.5

The midpoint is ( 1, -1.5)

Answer:

mid point = 1,  -1.5

Step-by-step explanation:

mid point between two points C(5, 3) and D(-3, -6)

M = (x1 + x2)/2  , (y1 + y2)/2

mid point = (5 + (-3)) / 2 ,  (3 + -6)/2

mid point = 2/2 , -3/2

mid point = 1,  -1.5

Answer:

she can only get 1 servings

Answer:

1 cause 4/8 is a half  of the jug at it's full  brethall

so one 1/2

the common denominator is 10 (between 5 and 2)

for each numerator:

we divide the common denominator with the denominator of each fraction and then multiply with the numerator of the fraction

first fraction's numerator:

10 (c.d.) : 5 (denominator) = 2

2 * 2 (numerator) = 4

second one:

10 (c.d.) : 2 (denominator) = 5

5 * 1 (numerator) = 5

The fractions are 4/10 and 5/10

Answer:

x = -10

Step-by-step explanation:

62 = 12 - 5x

-12 .   -12

62 - 12 = -5x

50 = -5x

__ .  __

-5 .    -5

-10 = x    

Answer:

AB and CD

Step-by-step explanation:

Given

Shape: Parallelogram

Parallel Side: AB and CD

Required

Determine the opposite sides

From the given parameters, we understand that:

AB is parallel to CD

Since they are parallel, then AB is opposite to CD

Hence, the opposite sides are AB and CD

Answer:

p = 6

Step-by-step explanation:

-3p+6=-12

Subtract 6 from each side

-3p+6-6=-12-6

-3p = -18

Divide each side by -3

-3p/-3 = -18/-3

p = 6

Answer:

x + 4  < 12

Step-by-step explanation:

Given

sum of a number x and 4

It can be written mathematically as

x + 4

Then

x + 4 is less than 12

less than is represented as <

Thus,

x + 4  < 12

Thus, inequality is x + 4  < 12

Answer:

The equation for the parabola that passes through the points (−1,8), (2,−4), and (−6,−12) is [tex]y = -x^{2}-3\cdot x +6[/tex].

Step-by-step explanation:

Let be (−1,8), (2,−4), and (−6,−12) points contained in a parabola, which is represented by a second-order polynomial. To determine the constant of the second-order polynomial, the following system of equations must be solved:

[tex]a - b+c = 8[/tex]

[tex]4\cdot a +2\cdot b +c = -4[/tex]

[tex]36\cdot a -6\cdot b +c = -12[/tex]

There are several methods for solving this: Equalization, Elimination, Substitution, Determinant and Matrix. The solution of this system is: [tex]a = -1[/tex], [tex]b = -3[/tex] and [tex]c = 6[/tex]. Hence, the equation for the parabola that passes through the points (−1,8), (2,−4), and (−6,−12) is [tex]y = -x^{2}-3\cdot x +6[/tex].

Answer:

3x-12 =7

Step-by-step explanation:

you distribute the 3 to the x and the -4

Answer:

yes

Step-by-step explanation:

yes because if you do the math you and you use your brain it's obvious

Step-by-step explanation:

cause I know it

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data:

38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450, 1750, 3000

The range :

(maximum - minimum) = (3000 - 38) = 2962

Variance :

Σ(x - mean)² / (n-1)

Where n = number of observations

Mean = (38+50+50+55+55+95+95+130+180+213+250+350+450+1750+3000) = 6761 / 15 = $450.73

Σ(x - mean)² = 9527804.9333334

N - 1 = 15 - 1 = 14

Hence,

Variance = Σ(x - mean)² / (n-1)

Variance = 9527804.9333334 / 14

Variance = $680557.50

Standard deviation = √variance

Standard deviation = √680557.50

Standard deviation = $824.96

CHECK IF OUTLIERS EXIST:

Using the outlier formula:

Lower outlier = Q1 - (1.5 × IQR)

Upper outlier = Q3 + (1.5 × IQR)

Q1 = 55 ; Q3 = 350 ; IQR = 295

Lower outlier = 55 - (1.5 × 295) = - 387.5

Upper outlier = 350 + (1.5 × 295) = 792.5

Remove values below the lower outlier value and values above the upper outlier value.

Hence outliers in the data are : 1750 and 3000

To save computation time :

We can recalculate our statistical measure by leaving out the outliers using online, excel or calculator functions :

Data without outlier :

38, 50, 50, 55, 55, 95, 95, 130, 180, 213, 250, 350, 450

Range = (450 - 38) = 412

Variance = Σ(x - mean)² / (n-1)

Variance = 201626.77 / 12

Variance = $16,802.23

Standard deviation:

√variance

√16,802.23

= $129.62341

According to the results obtained the presence of outliers has a great effect on the outcome the result.

Answer:

14322 * 10¹²

1.4322 * 10¹⁶

Step-by-step explanation:

14322000000000000

14322 * 10¹²

1.4322 * 10¹⁶

Answer:

C

Step-by-step explanation:

The river discharges 4 x 10^6 cubic feet of water into the Pacific Ocean each second.

There are 86,400 seconds in one day.

Amount of water discharges each day-

=4x10^6x86400

=345600000000

=3.456 x 10 ^11

Answer: C

Step-by-step explanation:

1) First multiply 4 * 10^6 = 4,000,000

Then multiply 4,000,000 by 86,400 = 3.456 * 10^11

Answer:

Distance = [tex]\sqrt{113}[/tex]

Step-by-step explanation:

[tex](1, 5) = (x_1,y_1)\\ (-7, -2)=(x_2,y_2)\\\\d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\ \\d = \sqrt{(-7-1)^2+(-2-5)^2}\\ \\d = \sqrt{(-8)^2+(-7)^2}\\ \\d = \sqrt{64+49}\\ \\d = \sqrt{113} \\\\[/tex]

Answer:[tex]\sqrt{113}[/tex]

Step-by-step explanation:

Distance formula: [tex]\sqrt{(x2-x1)^2+(y2-y1)^2}[/tex]

x1=1     x2=-7     y1=5     y2=-2

----------------------------------------------------------------

 [tex]\sqrt{(-7-1)^2+(-2-5)^2}[/tex]

=[tex]\sqrt{(-8)^2+(-7)^2}[/tex]

=[tex]\sqrt{64+49}[/tex]

=[tex]\sqrt{113}[/tex]

Hope this helps!! :)

Please let me know if you have any question or need further explanation

Answer:

O3(-8 + 1) = 3(-8) + 3(1)

Step-by-step explanation:

GOOD LUCK WITH BRAINLY I HOPE I HELPED :)

The expressions demonstrates the distributive property is

3(-8 + 1) = 3(-8)+ 3(1).

This property states that multiplying the total of two or more addends by a number will produce the same outcome as multiplying each addend by the number separately and then adding the results together.

We know the standard forms for distributive property as

For addition: a x (b+ c) = a x b + a x c

For Subtraction: ax (b- c)= a x b - a x c

1. 3+ 4+ 5 = 4 + 3 + 5 is Associative Property.

2. -2(5 + 7) = -2(7 +5) is Associative Property

3. 3(-8 + 1) = 3(-8)+ 3(1) is Distributive Property

Learn more about Distributive Property here:

https://brainly.com/question/5637942

#SPJ7

Answer:

The distance from the ground to the top of the ladder = 18.7 feet

Step-by-step explanation:

The distance from the ground to the top of the ladder is 9 feet more than the distance from the building to the base of the ladder.

distance from the building to the base of the ladder.= X

The distance from the ground to the top of the ladder = 9+x

Solving the triangle using Pythagorean theorem

X² +(x+9)²= 21²

X² + x² + 18x +81= 441

2x² +18x -360 = 0

X² +9x -180 = 0

X= (-9-28.3)/2 or (-9+28.3)/2

Definitely x is going to be a positive number

So

X= (-9+28.3)/2

X=9.65 feet

The distance from the ground to the top of the ladder = 9+x

The distance from the ground to the top of the ladder = 9+9.65

The distance from the ground to the top of the ladder = 18.65

The distance from the ground to the top of the ladder = 18.7 feet

Building is 9.65 foot far from ladder.

Length of ladder = 21 foot. This diagonal ladder is Hypotenuse to the right angled triangle formed between building & ladder.

Let the distance from building to base of ladder = x. This is the base of right angled triangle.

So, distance from ground to top of ladder = x + 9. This is the height of right angled triangle.

As per Pythagorus Theorem,

[tex]Hypotenuse^2 = Base^2 + Height^2[/tex]

[tex]21^2 = x^2 + (x+9)^2[/tex]

441 = [tex]x^2 + x^2 + 81 + 18x[/tex]  

360 = [tex]2x^2 + 18x[/tex]

[tex]2x^2 + 18x[/tex] - 360 = 0

x = -b + [tex]\sqrt{b^2 - 4ac[/tex] / 2a  

x = 9.65 { Building distance to ladder base }

To learn more, refer https://brainly.com/question/17275943

Answer:

Step-by-step explanation:

We are presented with three items

two dices and a coin

The sample space for a dice is S=(1,2,3,4,5,6)

and the sample space for a coin is S=(head and tail)

In the options provided all are possible outcomes for the two dices and the coin except for options "C" ,and this is because "8" is not a sample space in a dice

Answer:

2,8 Heads

Step-by-step explanation:

A standard coin has two values, {Heads or Tails}, while a standard die has six values {1, 2, 3, 4, 5, or 6}.  So, obtaining a 2 is possible, however the 8 is not.