Express 3a2b-1 with positive exponents.

Answer:

Step-by-step explanation:

Rectangle:

length = l = 12 cm

Width = w = 0.8 cm

Use Pythagorean theorem to find the diagonal

Diagonal² =  l² + w²

                = 12² + 0.8²

                = 144 + 0.64

                = 144.64

Diagonal = √144.64 = 12.03 cm

Diagonal of square  = diagonal of rectangle

                               = 12.03 cm

To find the side of square again use Pythagorean theorem,

side² + side² = 12.03²

2 sides² = 144.64

  side² = 144.64/2

  side² = 72.32

 side = √72.32

Side = 8.50 cm

Answer:

-36 = k

Step-by-step explanation:

-3 = k/12

Multiply each side by 12

-3*12 = k/12 *12

-36 = k

Answer: k= -36

Step-by-step explanation:

[tex]-3=\frac{k}{12}[/tex]

multiply both sides by 12

[tex]\frac{12k}{12}=12\left(-3\right)[/tex]

12*(-3)=-36

[tex]\frac{12k}{12}=12\left(-3\right)[/tex]

k=-36

Answer:

RM3,500

Step-by-step explanation:

Salary=RM375 per week

5% commission per week

If she target a minimum of RM 550.

Let x=minimum Sales

RM550=RM375 + 5% of x

RM550=RM375 + 0.05x

RM550 - RM375=0.05x

RM175=0.05x

Divide both sides by 0.05

RM175/0.05=0.05x/0.05

RM3,500=x

For Azila to earn a minimum of RM550 in a week, her salary will be RM375 plus 5% commission on the sales of RM3,500 value of product.

Check:

5% of RM3,500

=0.05*3,500

=RM175

Plus

Salary of RM375

RM175 + RM375=RM550

Answer:

160cm²

Step-by-step explanation:

To find the surface area of this prism, you just need to add up the areas of each side. To simplify the calculations a bit, we can take multiples of the sides which are the same. For example, here we have two equal trapezoids on each end, so we can multiply the area by two when adding.

The work is in the attachment.

Answer:

62

Step-by-step explanation:

4x + 6

4(14) + 6 (substituting x = 14)

56 + 6

62

Answer:

C. 19

Step-by-step explanation:

Given the function defined by F(x)=x²−2x+4, in order to get f(5), we will have to simply substitute x = 5 into the formula given as shown;

F(5) = 5²-2(5)+4

F(5) = 25 - 10 + 4

F(5) = 15 + 4

F(5) = 19

Hence, for the function F defined by F(x)=x²−2x+4, F(5) = 19

Answer:

Step-by-step explanation:

Given functions are

y = 5 cos ( 2π / 3 ) t

y = 5 cos ( 4π / 3 ) t

y= 10 cos ( 2π / 3 ) t

y = 10 cos ( 4π / 3 ) t

The pendulum half oscillation from left extreme to right extreme takes 1.5 s

So its time period of oscillation T = 1.5 x 2 = 3 s .

standard equation of oscillation is

y = A cos ω t where A is amplitude and ω is angular frequency .

Amplitude of oscillation A = 10 / 2 = 5 inch .

Among the given equation of motion only first two has amplitude equal to 5 . So both the last two are ruled out .

The angular frequency of first motion as per given equation

ω = 2π / 3

If time period is T

2π / T = 2π / 3

T = 3 s

So it matches with the time period of oscillation of pendulum .

Hence the first equation truly represents the oscillation of pendulum.

The function models the horizontal displacement as a function of time in seconds is  [tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex]  and this can be determined by using the given data.

Given :

It takes 1.5 seconds for a grandfather clock's pendulum to swing from left (initial position) to right, covering a horizontal distance of 10 inches.

For the oscillation the standard equation is given below:

[tex]\rm y = A\;cos \;\omega t[/tex]

where A is the amplitude, [tex]\omega[/tex] is the angular velocity, and t is the time.

Now, determine the time period that is:

T = 1.5 [tex]\times[/tex] 2

T = 3sec

Now, the angular frequency is given by:

[tex]\omega = \dfrac{2\pi}{3}[/tex]

So, the function models the horizontal displacement as a function of time in seconds is given below:

[tex]\rm y = 10 sin(\dfrac{2\pi}{3})t[/tex]

Therefore, the correct option is C).

For more information, refer to the link given below:

https://brainly.com/question/40973

Step-by-step explanation:

let f(x)=y

y=7x-13

y+13=7x

y+13/7=x

f-1(x)=x+13/7

Answer:

f(x) = 2x + 10

Step-by-step explanation:

Let's call this function f(x), where f(x) is time to get the order ready and x is the number of parts:

2x is the time to manufacture all parts of the order and 10 min is the time to pack them.

Answer:

2x + 10 is the correct answer :)

Answer:

Step-by-step explanation:

Hello, we know that the z complex solutions of

[tex]z^4=1[/tex]

are

1, i, -1, -i

so, the solutions of [tex]z^4=16=2^4[/tex] are

2, 2i, -2, -2i

Thank you

Answer:

0.000137

To 1 significant figure: 0.0001

To 2 significant figures: 0.00014

To 3 significant figures: 0.000137

To 4 significant figures: 0.0001375

To 5 significant figures: 0.00013745

Answer:

5xyz

Step-by-step explanation:

10x^2 y^2z and 15xyz^2

Rewriting

2*5*x*x*y*y*z   and 3*5 *x*y*z*z

What is common to both terms

5 x y z

The greatest common factor is 5xyz

Answer:

the GCF is 5(xyz)

Step-by-step explanation:

For the numbers, you want to find the largest number that both of the coefficients can be divided by. I'm not sure if your answer choices include variables, but if they do, its only xyz, nothing can be squared because both equations have different variables squared.

Answer:

[tex]\boxed{16 units}[/tex]

Step-by-step explanation:

Hey there!

Well since all the sides are congruent and there are 8 sides we can make the following expression,

P = 2*8

P = 16

Hope this helps :)

Answer:

16

Step-by-step explanation:

The sides of this figure are equal to each other .

the permiter is the sum of the sides

The figure has 8 sides.

● P = 8 × 2

● P = 16

Answer:

d=4

Step-by-step explanation:

Agency 1:

Total cost of renting a car=24.50d + 15.99

Agency 2:

Total cost of renting a car=27.50d + 3.99

Where, d=No. of days of renting the car

Which equation could be used to find the number of days, d, at which the rental fee is the same for both agencies?

The equation is by equating agency 1 and agency 2 equation

24.50d + 15.99 = 27.50d + 3.99

Collect like terms

24.50d - 27.50d = 3.99 - 15.99

-3d = -12

Divide both sides by -3

d= -12 / -3

=4

d=4

Check

Agency 1:

24.50d + 15.99

= 24.50(4) + 15.99

= 98 + 15.99

= 113.99

Agency 2:

27.50d + 3.99

= 27.50(4) + 3.99

= 110 + 3.99

= 133.99

Answer:

24.5d + 15.99 = 27.5d + 3.99

Step-by-step explanation:

The other person who answered this question was correct, they just explained it all the way through and since you guys skim through everything instead of reading, I'll put the answer. :)

Answer:

x=2

y=3

Step-by-step explanation:

x/2+y/3=2   so      

3x/6+2y/6=12/6

then multiply by 6

3x+2y=12    

equation number 2

x/3+y/2=13/6

2x/6+3y/6=13/6

multiply by 6

2x+3y=13

so the system is now

3x+2y=12  

2x+3y=13

from the first equation 2y=12-3x,  y=6 -  3x/2

then put  y in  the second equation

2x+3*(6-3x/2)=13

2x+18-9x/2=13

2x-9x/2=13-18

4x/2-9x/2=-5

-5x/2=-5

*(-1/5)    *(-1/5)

x/2=1

*2    *2

x=2

so y=6-3*2/2=6-3

y=3

Step-by-step explanation:

Given that:

(1/2x)+(1/3y) = 2 --------(1)

(1/3x)+(1/2y) = 13/6-----(2)

Put 1/x = a and 1/y = b then

(1) becomes

(a/2 )+( b/3) = 2

⇛ (3a+2b)/6 = 2

⇛ 3a+2b = 2×6

⇛ 3a+2b = 12 --------(3)

(2) becomes

(a/3)+(b/2)=13/6

⇛ (2a+3b)/6 = 13/6

⇛ 2a+3b=13----------(4)

On adding (3)&(4) then

3a+2b=12

2a+3b=13

(+)

_________

5a+5b = 25

_________

⇛ 5a+5b = 25

⇛ 5(a+b)=25

⇛ a+b=25/5

⇛ a+b=5 -------------(5)

On subtracting (3) from (4)

2a+3b=13

3a+2b=12

(-)

_________

-a+b = 1

_________

⇛ -a+b = 1

⇛ b = 1+a --------(6)

On Substituting the value of b in (5) then

a+1+a = 5

⇛2a+1 = 5

⇛ 2a = 5-1

⇛ 2a = 4

⇛ a = 4/2

⇛ a = 2

On Substituting the value of a in (6) then

b = 1+2

b = 3

Now,

a = 2

⇛ 1/x=2

⇛ “x” = 1/2

and

b= 3

⇛ 1/y = 3

⇛“y” = 1/3

Answer:- Hence, the value of x and y with be 1/2 and 1/3 respectively.

The solution for the given problem is (1/2,1/3)

Check:-

If x = 1/2 and y = 1/3 then

LHS = (1/2x)+(1/3y)

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

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

= (1/1)+(1/1)

= 1+1

=2

= RHS

LHS=RHS is true

and

LHS=(1/3x)+(1/2y)

⇛ 1/3(1/2)+ 1/2(1/3)

⇛ 1/(3/2)+1/(2/3)

⇛ (2/3)+(3/2)

⇛ (4+9)/6

⇛ 13/6

⇛ RHS

LHS = RHS is true

also read similar questions: Simultaneous equations: 1. 2x+2y=10 X+2y=6 2. 3x+y=18 2x+y=13 3. X+y=1 X-y=5 4. 3x+4y=29 X-4y=-17 5. 4c+3y=11 2x+y=7

https://brainly.com/question/12286263?referrer

Answer:

(2,−6)+(9,9)

(12,−5)⋅(5,6)

(4,4)⋅(4,4)

Step-by-step explanation:

Try one of these answers

Answer:

Let's simplify step-by-step.

2x(3−1)+3

=4x+3

Step-by-step explanation:

2x[3-1]=6x-2x=4x

4x+3

Answer as a fraction = 1/720

Answer in decimal form (approximate) = 0.001388

Answer in percent form (approximate) = 0.1388%

========================================================

Explanation:

Let A = 1 to indicate the number of ways to get the names to line up in alphabetical order.

There are B = 6*5*4*3*2*1 = 720 different ways to arrange the six people. Notice how I started at 6 and counted my way down to 1, multiplying all along the way. This can be shortened to factorial notation to say 6! = 720. Or you could use the nPr permutation formula to get the same result (use n = 6 and r = 6).

Once you have the values of A and B, we form the fraction A/B = 1/720 which is the probability of getting the names in alphabetical order.

If you need the answer in decimal form, then use your calculator to find

1/720 = 0.001388

which converts over to 0.1388%

Answer:

D. P(5+ 6's) = 0.4063

Step-by-step explanation:

Binomial distribution.

For the distribution to be applicable, the experiment must

1. Have a know and constant number of trials

2. Probability of success of each trial remains constant (and known if available)

3. Each trial is a Bernoulli trial, i.e. with only two outcomes, success or failure.

4. Independence between trials.

Let  

n = number of trials  = 25

p = probability of success of each trial  = 1 / 6

x = number of successes  (0 ≤ x ≤ n)  = 5

C(n,x) = number of combinations of picking x identical objects out of n

Applying binomial distribution

P(x,n) = probability of x successes in an experiment of n trials.

= C(n,x) * p^x * (1-p)^(n-x)

For n = 25 trials with probability of success (roll a 6) = 1/6

and x = 5,6,7,8,...25

It is easier to calculate the complement by

P(5+ 6's) = 1 - P(<5 6's)

= 1 - ( P(0,25) + P(1,25) + P(2,25) + P(3,25) + P(4,25) )

1- (

    P(0,25) = C(25,0) * (1/6)^0 * (5/6)^25 = 0.0104825960103961

    P(1,25) = C(25,1) * (1/6)^1 * (5/6)^24 = 0.05241298005198051

     P(2,25) = C(25,2) * (1/6)^2 * (5/6)^23 = 0.1257911521247532

    P(3,25) = C(25,3) * (1/6)^3 * (5/6)^22 = 0.1928797665912883

    P(4,25) = C(25,4) * (1/6)^4 * (5/6)^21 = 0.2121677432504171

)

= 1 - 0.59373

= 0.40626

= 0.4063 (to 4th decimal place)

Answer:

12.5 percent; 2/16; 1/8

Step-by-step explanation:

Peter and Mary make up 2 of the clubs members, so the probability that they are chosen is 2/16. This simplifies to 1/8, and in decimal form is .125. Therefore, the percentage form of the probability they are chosen is 12.5 percent.

Answer:

The area would be 128ft^2

2^4 i= 2x2x2x2

2^3 = 2x2x2

multiply them and you get 128ft6^2

Answer:

128ft^2

Step-by-step explanation:

took the quiz just now :D

Answer:

The third DJ had (3r)/2 songs. Multiply r by 3 because the second DJ had 3 times as many as the first. Then divide that number by 2 because the third DJ has half as many.

Step-by-step explanation:

Answer:

The third DJ had (3r)/2 songs. Multiply r by 3 because the second DJ had 3 times as many as the first. Then divide that number by 2 because the third DJ has half as many.

Step-by-step explanation:

just did

Answer:

Slope:[tex]\frac{2}{3}[/tex]

y-intercept:-2

Step-by-step explanation:

Answer:

C. 33.

Step-by-step explanation:

The sides of a 45-45-90 triangle are in the ratio 1:1:√2 so the side opposite to 45 degrees = 11√6 / √2.

Consider the larger triangle containing the 60 degree angle:

tan 60 = x / (11√6 / √2).

x = tan 60 * 11√6 / √2

x = 33.

The value of the variable x will be 33 units. Then the correct option is C.

It's a form of a triangle with one 90-degree angle that follows Pythagoras' theorem and can be solved using the trigonometry function.

The diagram is shown below.

Let h be the height of the triangle.

The value of h is given by the sine of angle 45°. Then the value of the height h will be

sin 45° = h / 11√6

h = 11√6 × 1/√2

h = 11√3 units

The value of h is given by the tangent of angle 60°. Then the value of the height h will be

tan 60° = x / h

x = 11√3 × √3

x = 11 × 3

x = 33 units

Thus, the value of the variable x will be 33 units.

Then the correct option is C.

More about the right-angle triangle link is given below.

https://brainly.com/question/3770177

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Question

In circle L, arc MNOP is 120° and the radius is 5 units. Which statement best describes the length of arc MNOP?

• one half the area of circle L

• one third the area of circle L

• one half the circumference of circle L • one third the circumference of circle L

Answer:

• one third the circumference of circle L

Step-by-step explanation:

In the question, we are told that:

In circle L, arc MNOP is 120° and the radius is 5 units.

We are asked to find the statement amongst the options that describes the arc length MNOP of Circle L

Step 1

Find the Area of circle

Area of a circle = πr²

r = 5 units

Area of a circle = π × 5²

Area of a circle = π × 25

Area of a circle = 78.53981634 square units

Step 2

Find the arc length of a circle

Arc length = 2πr × θ /360

r = 5 units

θ = 120°

Arc length = 2 × π × r × 120/360

Arc length = 2 × π × r × (1/3)

Arc length = 2 × π × 5 × (1/3)

Arc length = 10.47198 units

Step 3

Circumference of a circle = 2πr

= 2 × π × 5

= 31.415926536 units

Since the Circumference of a circle = 2πr

Arc length of the circle for the above calculation, = 2πr × 1/3

Therefore, the statement that best describes the arc length MNOP of Circle L is:

" the arc length MNOP is one third the circumference of circle L"

Answer:

the arc length MNOP is one third the circumference of circle L

Step-by-step explanation:

i fishie yupo

Answer: x=0.125 or 1/8

Step-by-step explanation:

[tex]7x-\frac{3}{4}=6x-\frac{5}{8}[/tex]

add 3/4 on both sides

[tex]7x-\frac{3}{4}+\frac{3}{4}=6x-\frac{5}{8}+\frac{3}{4}[/tex]

[tex]7x=6x+\frac{1}{8}[/tex]

subtract 6x on both sides

[tex]x=\frac{1}{8}[/tex]

Answer:

x = 1/8

Step-by-step explanation:

7x - 3/4 = 6x - 5/8

7x - 3/4 + 3/4 = 6x - 5/8 + 3/4

7x = 6x + 1/8

7x - 6x = 6x + 1/8 - 6x

x = (6x - 6x) + 1/8

x = 1/8

Answer:

w=10

Step-by-step explanation:

-2=-(w-8)

2=w-8

w=10

Question:

-2=-(w-8)

Answer:

-2=-w+8

w=8+2

w=10

Step-by-step explanation:

Answer:

62

Step-by-step explanation:

hope that helps! if it is an answer

The Phrase is: "The resulting number is 62."

We have the expression as

52 + 2x

Now, To evaluate the expression 52 + 2x when x = 5,

we substitute the value of x into the expression and simplify:

=52 + 2(5)

= 52 + 10

= 62.

Thus, The resulting number is 62.

Learn more about Expression here:

https://brainly.com/question/28170201

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Answer:

I think 1/2 is the ans

Step-by-step explanation:

quadratic function equation

would help