Simplify the expression
3x^2y^5•(4xy^2)^3

Answer:

15 inches

Step-by-step explanation:

The longest side of the right triangular window frame is 39 inches

The height is 36 inches

Let the base of the window frame be x inches

So according to Pythagoras theorem,

x² + 36² = 39²

x² = 39² - 36² = 225

x = [tex]\sqrt{225}[/tex] = 15 inches

The third side of the window frame is therefore equal to 15 inches.

The length of the third side of the window frame will be 15 inches. Then the correct option is A.

The Pythagoras theorem states that the sum of two squares equals the squared of the longest side.

The Pythagoras theorem formula is given as

H² = P² + B²

The longest side has a length labeled as 39 inches. The height of the frame is labeled as 36 inches.

Let x be the length of the third side of the window frame. Then we have

39² = x² + 36²

 x² = 39² - 36²

 x² = 1521 - 1296

 x² = 225

  x = 15 inches

Then the correct option is A.

More about the Pythagoras theorem link is given below.

https://brainly.com/question/343682

#SPJ2

Answer:

y=1/2x+5 or d

Step-by-step explanation:

Answer is D

Step-by-step explanation:

Answer:

$ 555

Step-by-step explanation:

Salary for a 40-hour work week = $380

Total income for the week will be = Salary of regular 40 hours + Salary of 14 hours overtime

Salary per hour for the overtime work = $ 12.50

So,

The salary for 14 hours of overtime will be = $ 12.50 x 14 = $ 175

Therefore,

Total income for the week will be = $ 380 + $175 = $ 555

Thus, for a 40 hour work week and 14 hours of overtime the total income of the week will be $ 555

Answer:

c. 1,000,000 plate numbers

Step-by-step explanation:

Each of the 6 digits of a Delaware plate can take on any of 10 values, so there are ...

10×10×10×10×10×10 = 1,000,000

possible plate numbers.

Delaware can assign 1,000,000 license plate numbers under its six-digit numbering system, as each of the six places can have any digit from 0 to 9 giving 10^6 or one million possible combinations.

The question asks how many license plate numbers Delaware can assign under their six-digit numbering system. To find the number of possible combinations for a six-digit number where each digit can be any number from 0 to 9, we need to calculate 10 possibilities for each position (including the leading zero) multiplied together.

Therefore, the calculation follows this pattern: 10  imes 10  imes 10  imes 10  imes 10  imes 10, which equals 1,000,000 possible combinations. This is because each of the six places in the license plate number can have any of the ten digits from 0 to 9. So the answer to how many license plate numbers Delaware can assign under their system is 1,000,000 plate numbers.

Answer:

1.8 represents the initial number of the club members in hundreds.

Step-by-step explanation:

* Lets revise the exponential grows

- If a quantity grows by a fixed percent at regular intervals,

 the pattern can be depicted by this function.

- The function of the exponential growth is:

  y = a(1 + r)^x

# a = initial value (the amount before measuring growth)

# r = growth rate (most often represented as a percentage and

  expressed as a decimal)

# x = number of time intervals that have passed

* Now Lets study the problem to solve it

- The club's total number of members will grow exponentially

  each month

- The expression to model the number of club members, in

  hundreds, after advertising for t months is

  1.8(1.02)^12t

* Lets compare between this model and the function above

# a = 1.8 ⇒ initial number of members in hundreds

# r = 1.02 - 1 = 0.02 ⇒ growth rate

# x = 12t ⇒ number of time intervals

* 1.8 represents the initial number of the club members in hundreds.

Answer:

The length is 21 meters

Step-by-step explanation:

* Lets use variable to represent the dimensions of the rectangle

- The length of the rectangle is 6 meters longer than its width

# Let the width of the rectangle = x meters

∴ The length of the rectangle = x + 6 meters

- The area of the rectangle = Length × width

∵ The area of the rectangle = 315 meters²

∵ The length of the rectangle = x + 6

∵ The width of the rectangle = x

∴ x(x + 6) = 315 ⇒ open the brackets to solve the equation

∴ x² + 6x = 315 ⇒ subtract 315 from both sides

∴ x² + 6x - 315 = 0

- Lets factorize the quadratic equation to find the value of x

∵ The last term of the quadratic is negative

∴ The brackets have different sign

# x² = x × x ⇒ 1st terms in the two brackets

# -315 = -15 × 21 ⇒ 2nd terms in the two brackets

# x × -15 = -15x ⇒ 1st term in the first bracket and 2nd term in

  the second bracket

# x × 21 = 21x ⇒ 1st term in the second bracket and 2nd term

  in the first bracket

# 21x - 15 x = 6x ⇒ the middle term of the quadratic equation

∴ The factoriz of x² + 6x - 315 = 0 is

  (x + 21)(x - 15) = 0

∴ x + 21 = 0 OR x - 15 = 0

# x + 21 = 0 ⇒ subtract 21 from both sides

∴ x = -21 ⇒ neglect this answer because there is no negative

  value for the dimensions

# x - 15 = 0 ⇒ add 15 to both sides

∴ x = 15

- The value of the width is x

∴ The width = 15 meters

- The value of the length is x + 6

∴ The length = 15 + 6 = 21 meters

Answer:

㏒3(14) = 2.402 ⇒ 3rd answer

Step-by-step explanation:

* Lets revise some rules of the logarithmic functions

- log(a^n) = n log(a)

-  log(a) + log(b) = log(ab) ⇒ vice versa

- log(a) - log(b) = log(a/b)  ⇒ vice versa

* Lets solve the problem

- We have the value of ㏒3(2) and ㏒3(7)

- We must change the problem to these logarithm to solve

∵ 14 = 2 × 7

∴ We can write ㏒3(14) as ㏒3(2 × 7)

∴ ㏒3(14) = ㏒3(2 × 7)

* Now lets use the rules above

∵  log(ab) = log(a) + log(b)

∴ ㏒3(2 × 7) = ㏒3(2) + ㏒3(7)

∵ ㏒3(2) = 0.631 and ㏒3(7) = 1.771

∴ ㏒3(2 × 7) = 0.631 + 1.771 = 2.402

* ㏒3(14) = 2.402

g(4)=2×4_1

8-1

=9

hence the answer is 9

hope it helps you!!!!!!!!!

Answer:

g(4) = 7

Step-by-step explanation:

To evaluate g(4) substitute x = 4 into g(x), that is

g(4) = (2 × 4) - 1 = 8 - 1 = 7

1. a Early Pay: y = 45

 b. Deposit Plus: y = 12.00 + 4.00x

 c. Daily Pay: y = 6.00x

2.  Early pay = $25

   Deposit Plus = 12.00 + 4.00(4) =  12.00 + 16.00 = $28.00

 Daily Pay = 6.00(4) = $24.00

Daily Pay is the cheapest one.

3. Early Pay = $45

 Deposit Plus = 12.00 + 4.00(8) = 12.00 + 32.00 = $44.00

 Daily Pay = 6.00(8) = $48.00

Deposit Plus is the cheapest one.

4. Early Pay = $45

Deposit Plus = 12.00 + 4.00(12) = 12.00 + 48.00 = $60.00

Daily Pay = 6.00(12) = $72.00

Early Pay is the cheapest one.

5.  Since Jane likes to swim most days, it would be cheaper for her to do the Early pay option, because the price is a one time fee and she can swim every day.

Since Suzy doesn't really like to go swimming and might only go a couple times, it would be best for her to do the daily pay, that way she didn't spend any money up front if she doesn't swim at all.

Answer:

  (x, f(x)) ≈ (5.5, 4)

Step-by-step explanation:

You can go to the trouble to find the point where the second derivative is zero (the derivative has a maximum), or you can realize the function is symmetrical about y=4, which is where the point of inflection is. The x-value there is ...

  4 = 8/(1 +3e^(-0.2x))

  1 +3e^(-0.2x) = 8/4 = 2

  e^(-0.2x) = 1/3

  x = ln(1/3)/-0.2 = 5ln(3) ≈ 5.493 ≈ 5.5

We already know the value of f(x) is 4 there.

The point of maximum growth is about (5.5, 4).

Answer:

  (x^2 -2x +1) -16/(5x+10)

Step-by-step explanation:

The quotient and remainder can be found by polynomial long division or by synthetic division.

___

For synthetic division, it is recommended to divide the dividend and divisor by the leading coefficient of the divisor (5), so the divisor coefficient is 1. This results in a divisor of (x+2) and a remainder of -16/5. The simplified remainder becomes ...

  (-16/5)/(x+2) = -16/(5x +10)

See the attachments for the various methods of computing the quotient.

ANSWER

The correct choice is A

EXPLANATION

The given inequality is

y < -|x|

We substitute each point into the inequality to determine which one is a solution.

Option A

-2 < -|1|

-2 < -1.

This statement is true.

Hence (1,-2) is a solution.

Option B.

-1 < -|1|

-1 < -1.

This statement is false.

Option C

0 < -|1|

0 < -1.

This statement is also false.

Answer:

40 (cm)

Step-by-step explanation:

0. make up a new picture with additional elements (radius of the inscribed circle, it's 'x'; and some elements as shown in the attached picture);

1. the formula of the required perimeter is P=a+b+c, where c- hypotenuse.

2. apply the Pythagorean theorem: a²+b²=c², where c - hypotenuse, then calculate value of 'x' (attention! x>0, the length is positive value !)

3. substitute 'x' into the formula of the required perimeter. The result is 40.

PS. All the details are in the attached picture, answer is marked with red colour.

Answer:

x intercept= 3

y=-2

Step-by-step explanation:

the intercept is the point when the line crosses the axis

Answer:

  none of the above

Step-by-step explanation:

The transformation ...

  g(x) = k·f(x -a) +b

vertically stretches the function f(x) by a factor of "k", translates it to the right by "a" units and up by "b" units. There won't be any reflection across the x-axis unless the stretch factor (k) is negative.

You have k=2, a=2, b=-2, so the function is stretched by a factor of 2, then translated to the right and down by 2 units each.

_____

The stretch is done first. If it is done last, then the translation factor(s) are also stretched. All the answer choices given in your problem statement list the stretch last, so none is correct. (You are probably expected to choose d.)

Answer:

x^3 -6x^2 +18x-10

Step-by-step explanation:

f-g (x) = f(x) -g(x)

f(x) = x^3 -2x^2 +12x-6

g(x)  =4x^2 -6x +4

f(x) -g(x) =x^3 -2x^2 +12x-6 - (4x^2 -6x +4)

Distribute the minus sign

            x^3 -2x^2 +12x-6 - 4x^2 +6x -4

Combine like terms

           x^3 -2x^2- 4x^2 +12x+6x-6  -4

            x^3 -6x^2 +18x-10

Answer:

Option B

Step-by-step explanation:

Given

f(x)=  (x^2+x-2)/(x^3-1)

For vertical asymptotes we have to put the denominator of the function equal to zero:

x^3-1=0

x^3=1

So,

x=1

As the degree of denominator is greater than the degree of numerator, there will be only horizontal asymptote which will be y=0 because all the y values will be dragged down to the x-axis.  

So the horizontal asymptote: y=0

And Vertical asymptote: x =1

Answer:

b

Step-by-step explanation:

Answer:

Step-by-step explanation:

You can compute the slope from two of the points, then write the point-slope form of the equation of the line.

  slope = (change in y)/(change in x)

  = (15 -20)/(3 -1) = -5/2

Then the equation of the line, using the first point) is ...

  y = m(x -h) +k . . . . . . for slope m through point (h, k)

  y = -5/2(x -1) +20

The x-intercept is the value of x where y=0:

  0 = -5/2(x -1) +20 . . .put 0 where y is in the equation, then solve for x

  0 = (x -1) -8 . . . . . . . . multiply by -2/5 (the inverse of the x-coefficient)

  9 = x . . . . . . . . . . . . . simplify, add 9

The x-intercept is (9, 0).

__

The y-intercept is the value of y where x=0:

  y = -5/2(0 -1) +20 . . . . . . put 0 where x is in the equation, then solve for y.

  y = -2.5 +20 = 17.5

The y-intercept is (0, 17.5).

_____

Comment on the problem

Your question page seems to offer both lesson and video help. Either or both may be better than the written solution here.

Answer:

$ 38,824

Step-by-step explanation:

Total Area of land that was bought = [tex]4\frac{2}{8}[/tex] acres

Total Cost of this area = $ 165,000

We have to find the cost of 1 acre of land.

Cost of [tex]4\frac{2}{8}[/tex] acres of land = $ 165,000

Dividing both sides by [tex]4\frac{2}{8}[/tex], we get:

Cost of 1 acre of land = $ 165,000 ÷ [tex]4\frac{2}{8}[/tex]

= $ 38,824

Thus the cost of each acre of land  is $ 38,824 (rounded to nearest dollar)

Answer: $38,824

Step-by-step explanation:

Convert the mixed number [tex]4\ \frac{2}{8}[/tex] as a decimal number.

Divide the numerator by the denominator and add it to the whole number 4. Then:

[tex]4+0.25=4.25acres[/tex]

Then, knowing that 4.25 acres cost $165,000 , divide this amount by 4.25 acres to find the cost of each acre.

Therefore, you get that the cost of each acre rounded to nearest dollar is:

[tex]cost=\frac{\$165,000}{4.25}\\cost=\$38,824[/tex]

Step 1: Find the area of the living room on the blueprint with the formula Area = length x height

A = 4 x 8

A = 32

Step 2: We now know that the area of the living room on the blueprint is 32 inches, but we have to convert it into the actual answer. To do this multiply 32 by 40 (you have to do this because 1 inch is 40 inch in reality meaning that each inch in  the 32 inches is times 40 <<< Does that make sense?), so...

40 x 32 = 1,280

Hope this helped!

Answer:

The measurements for the actual room are, in inches, 160 x 320

Step-by-step explanation:

If you want the computed area, then multiply those numbers together since A=bh.  I assumed you were just looking for the measurements of the actual room.  Set up a ratio for the scale first, the model info in the numerator and the actual room info in the denominator:

[tex]\frac{m}{a}: \frac{1}{40}[/tex]

Here, the m is the model on paper and the a is the actual room.  So if the length of the room on paper is 4 inches, that will go on top with the model stuff and we will solve for the missing equivalent length of the actual room:

[tex]\frac{m}{a} :\frac{1}{40} =\frac{4}{x}[/tex]

Cross multiply to get that the length of the actual room is 160 inches long. Divide by 12 if you need that number in feet.

Doing the same with the width:

[tex]\frac{m}{a} :\frac{1}{40}=\frac{8}{y}[/tex]

Cross multiply to get that the width of the actual room is 320 inches.  Again, if you need that in feet, divide by 12.

Answer:

   c.  {(–4, 8.5)}

Step-by-step explanation:

A plot of the equation and the offered points is attached.

__

It might be helpful to put the equation into slope-intercept form.

  2y = -5x -3

  y = -5/2x -3/2

This shows you that y will be an odd multiple of 1/2 only for even values of x. So, we only need to check the points (-2, 9.5) and (-4, 8.5).

At x=-2, y = -5/2(-2) -3/2 = 5 -3/2 < 9.5 . . . . . (-2, 9.5) is not a solution

At x=-4, y = -5/2(-4) -3/2 = 10 -3/2 = 8.5 . . . . (-4, 8.5) is a solution

Of the offered choices, the only one in the solution set is (-4, 8.5).

Answer:

E. 44 meters

Step-by-step explanation:

The function that models the distance covered by the object is

[tex]s(t)=t^2+5t[/tex]

where s(t) is in meters and t is in seconds.

The distance covered by the object after 1 second is

[tex]s(1)=1^2+5(1)=6m[/tex]

The distance covered by the object after 1 second is

[tex]s(1)=5^2+5(5)=50m[/tex]

The distance covered between 1 second and 5 seconds is

50-6=44m

Answer:

person above is right

Step-by-step explanation:

right on plato

Answer:

23) option c

    JL ≈ 9.3

25) option c

      y ≈ 9.6

Step-by-step explanation:

Given in the question that,

cos(21°) = 9 / y

y = 9/cos(21°)

y = 9.64

y ≈ 9.6(nearest tenth)

Given in the question that the hypotenuse of right angle triangle = 12

To find,

height of the right angle triangle

angle k = 39°

so by using trigonometry identity

cos(39) = opp/hypo

cos(39) = JL / KL

JL = cos(39)(12)

JL = 9.32

JL ≈ 9.3

Answer:

Q 23.  Last option 7.6

Q 25 Third option

Step-by-step explanation:

To solve Q 23

From the figure we can write,

Sin 39 = Opposite side/Adjacent side

 = JL/KL

 = JL/12

JL= 12 * Sin 39

 = 12 * 0.629  = 7.55

 = 7.6

To solve Q 25

Cos 21 = 9/y

y = 9/Cos 21 = 9/0.9335

= 9.64

 = 9.6

Answer:

According to the given question if one of the angle of the triangle is 75 degree and the other two sides are of length 2 and 3 units respectively then option C is correct. Only One triangle can be formed where Angle B will be 40 degree. You can figure it out from the steps mentioned below first of all draw an Arc with the length either 3cm or 2 cm that will be the base of a triangle and then from the ending point again cut an arc then after from the starting point that is the point draw  an angle of 75 degree with the help of protactor and extend it to meet the Arc finally you can get the 40 degree.

Hope this helps. Name me brainliest please

you cannot show too much "work"

basically, you remove what is common to all of the factors, and then put brackets, as it will be multiplied back in, remember that when you multiply exponents with the same base, its same as adding them, so subtract to remove...

you can seperate two of the variables , then factor, then subtract the last one from those two, because it cannot be factored out , as in part2 #2

Answer:

The discriminant D=0

Step-by-step explanation:

For the duadratic polynomial [tex]ax^2+bx+c[/tex] the discriminant is

[tex]D=b^2-4ac.[/tex]

In your case, for the polynomial [tex]4x^2-20x+25,[/tex]

Answer:

The answer is 0 D

Answer:

[tex]4800+183x\geq 8000[/tex]

She must sell at least 18 policies to make an annual income of at least $8,000

Step-by-step explanation:

Let [tex]x[/tex] be the number of policies Mrs. Robinson must sell

We know that Mrs. Robins makes 3% on commission for each policy sold. We also know that the average price of a policy is $6,100, so she makes 3% of $6,100 per policy sold. To find the 3% of $6,100 we just need to multiply 3% and $6,100; then dive the result by 100%:

[tex]\frac{3*6,100}{100} =183[/tex]

Now we know that she makes $183 per policy sold. Since [tex]x[/tex] is the number of policies sold, [tex]183x[/tex] is her total commission for selling [tex]x[/tex] policies.

We also know that She makes $4,800 per year, so her total annual income is her salary plus her commissions, in other words:

[tex]4800+183x[/tex]

Finally, we know that she wants to make at least $8,000, so her salary plus her commissions must be greater or equal than $8,000:

[tex]4800+183x\geq 8000[/tex]

Let's solve the inequality:

1. Subtract 4800 from both sides

[tex]4800-4800+183x\geq 8000-4800[/tex]

[tex]183x\geq 3200[/tex]

2. Divide both sides by 183

[tex]\frac{183x}{183} \geq \frac{3200}{183}[/tex]

[tex]x\geq 17.48[/tex]

Since she can't sell a fraction of a policy, we must round the result to the next integer:

[tex]x\geq 18[/tex]

We can conclude that she must sell 18 policies to make an annual income of at least $8,000.

Answer:

Option C is correct.

Step-by-step explanation:

The equation used to represent the slop-intercept form is

y= mx + b

where m is the slope

and b is the y-intercept.

So, in the given question y-intercept = (0,8)

b= 8 and

slope =m= 1/2

the equation will be:

y = mx + b

y= (1/2)x + 8

So, Option C is correct.

35 cubic in.

7/2=3.5

10*4=20/2=10

10*3.5=35

Answer:

C

Step-by-step explanation:

g(x) = f(x - π/3), so g(x) is f(x) shifted to the right π/3 units.

Answer C.