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Derrick has 3 times as many CDs as Joshua. Which equation compares the number of CDs that the two boys have? (Let d = number of Derrick's CDs and j = number of Joshua's CDs.) O A. 3d = j E ов O B. 3j = d c C. 3 + d = j OD. 3 + j = d​

Solution :

For the bigger rectangle

Width of bigger rectangle = W

Length of bigger rectangle, L = 2W

For the smaller rectangle

Width , w = W+4

Length, l = L = 2W

Area, a =120 [tex]m^2[/tex]

Now we know,

Area = length x width

[tex]$a=l \times w$[/tex]

[tex]$120=(2W) \times (W+4)$[/tex]

[tex]$120=2W^2 + 8W$[/tex]

[tex]$2W^2+8W-120=0$[/tex]

[tex]$W^2+4W-60=0$[/tex]

[tex]$(W+10)(W-6) = 0$[/tex]

We get, either [tex]W=-10[/tex]   (rejecting)

                or     [tex]W=6[/tex]

∴ length of the bigger rectangle, [tex]$L=2W $[/tex]

                                                          = 2(6)

                                                           = 12 m

 Length of the smaller rectangle, [tex]$L=2W$[/tex]

                                                            = 2(6)

                                                           = 12 m

Hence, the length of the two gardens is 12 m.                                                            

Answer:

where is the rest of the question??

Step-by-step explanation:

The cost for one batch of fried rice will be $4.62.

Since the rice is bought at $0.71 a pound and one batch of fried rice requires 6.5 pounds of rice, then the cost of one batch of rice will be:

= $0.71 × 6.5

= $4.615

= $4.62 approximately.

In conclusion, the cost for one batch of fried rice will be $4.62.

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Answer:

V= 562.5 pi cm^3 or approximately 1766.25 cm^3

Step-by-step explanation:

If the diameter is 15, the radius is d/2 = 15/2 = 7.5

The volume of a sphere is

V = 4/3 pi r^3

V = 4/3 ( pi ) (7.5) ^3

V= 562.5 pi

If we use the approximation of 3.14 for pi

V = 1766.25 cm^3

Answer:

The best option would be the second one.

Step-by-step explanation:

This is the only option that shows that x can only be greater than -8. The circled dot means x cannot be the number the dot is sitting on, in this case, -8.

Answer:

b option is the weight answer I think.

Answer:

k = 4

Step-by-step explanation:

In the equation: x² - 2x - 24

Replace the x with x + 3

(x+3)² - 2(x+3) - 24

x² + 6x + 9 - 2x - 6 -24

Let's rearrange it

x² + 6x -2x - 24 + 9 - 6

x² - 4x - 21

f(x+3) = x² - 4x - 21

The equivalent value of k from the function is k = -4

The function rule is the relationship between the input or domain and the output or range. A relation is a function if and only if there exists one value in the range for every domain value.

A function is a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.

Given data ,

Let the function be represented as A

Now , the value of A is

f ( x ) = x² - 2x - 24

Let the second function be represented as B

Now , the value of B is

f ( x + 3 ) = x² - kx - 21

On simplifying , we get

f ( x + 3 ) = ( x + 3 )² - 2 ( x + 3 ) - 24

f ( x + 3 ) = x² + 6x + 9 - 2x - 6 - 24

f ( x + 3 ) = x² + 4x - 21

So , from the equations , we get

-kx = 4x

Divide by -x on both sides , we get

k = -4

Hence , the equation is k = -4

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Answer:

Step-by-step explanation:

Let's do this out as best as we can here. Here's the problem:

2 |  3   1   2   -7

___________

The rule is to bring down the first term, whatever it is (ours is a 3), and multiply it by the number "outside" which is a 2. Put that product up under the number next to the 3:

2 |  3   1   2   -7

          6          

    3

Then add straight down, and multiply that sum by the 2 outside and put that product under the next number (the 2 "inside" the box):

2 |  3   1   2   =7

          6  14      

     3   7

And do the same thing. Add straight down, multiply the sum by 2 and put the product up under the next number, -7, and add again. The final is shown below:

2 |  3     1     2     -7

            6   14     32

    3      7    16    25

The last number in the very bottom row, the depressed polynomial row, is the remainder. Ours is a 25. This is the super easy way to divide polynomials, as long as our divisor is a linear (first degree) term.

Answer:

000

Step-by-step explanation:

000

The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees

4a) Given the following

Opposite side = 38cm (side facing the given angle)

Required

Adjacent and hypotenuse side

According to SOH CAH TOA

[tex]tan \theta = \frac{opp}{hyp}\\tan 32=\frac{38}{hyp}\\hyp=\frac{38}{tan 32}\\hyp=\frac{38}{0.6249}\\hyp= 60.81cm[/tex]

Next is to get the adjacent

[tex]Cos 32=\frac{adj}{60.81}\\adj=60.81cos32\\adj=60.81(0.8480)\\adj= 51.57cm[/tex]

Next is to get the missing angle

Since sum of angle in the triangle is 180degrees

32 + 90 + x = 180

122 + x = 180

x = 180 - 122

x = 58degrees

The unknown sides are 60.81cm and 51.57cm while the unknown angle is 58degrees.

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Answer: a

Step-by-step explanation:

Answer:

422.39

Step-by-step explanation:

[tex]A = \pi r^2\\A = 144\pi \\\\144\pi -30 = 422.39[/tex]

use a calculator for the above and round

Answer:

the cost of the tire=341.4$

Answer:

Graph A

Step-by-step explanation:

A directly proportional relationship must create a straight line that goes through the origin (0,0) ( note that the slope can be negative or positive in a proportional relationship. )

All graphs show a straight line going through the origin except Graph A.

Graph A shows a straight line however that line does not go through the origin therefore it is not a proportional relationship

Answer:

C.

Step-by-step explanation:

212/4 = 53, so 53/1, or 53 miles are driven every hour.

Answer:

PT = 16.3 units

Step-by-step explanation:

From the picture attached,

From ΔPQR and ΔPST,

QR ║ST [Given]

PQ is a transversal line.

Therefore, ∠PST ≅ ∠PQR [Corresponding angles]

∠P ≅ ∠P [Common angle]

ΔPQR ~ ΔPST [By AA property of similarity of two triangles]

Therefore, by the property of similarity, corresponding sides of the similar triangles will be proportional.

[tex]\frac{PQ}{PS}=\frac{PR}{PT}[/tex]

[tex]\frac{12+28}{28}= \frac{PT+7}{PT}[/tex]

[tex]\frac{40}{28}=1+\frac{7}{PT}[/tex]

[tex]\frac{10}{7}-1=\frac{7}{PT}[/tex]

[tex]\frac{10-7}{7}=\frac{7}{PT}[/tex]

PT = [tex]\frac{49}{3}[/tex]

PT = 16.3 units

Answer:

10/100*$x

Step-by-step explanation:

You will multiply the $x by 10%

a) The sinusoidal function is y = 7·sin(π/15(t - 2.5)) + 9

b) The height of the shorts at t =  10 minute is approximately 6 meters

The above answers were arrived at as follows

a) The general form of a sinusoidal equation is presented as follows;

y = A·sin(B(t - h)) + k

Where;

A = The amplitude of the graph of the function

The period, T = 2·π/B

h = The horizontal shift

k = The vertical shift

The maximum height of the blade = 16 meters

The minimum height of the blade  = 2 meters

The time the blade moves from maximum height to minimum height = 25 s - 10 s = 15 s

Therefore, the time it takes the blade to move from maximum height to minimum height, the period, T= 2 × 15 s = 30 s

Therefore;

B = 2·π/30 = π/15

B = π/15

When B·(t - h) = π/2, t = 10

Therefore;

(π/15)·(10 - h) = π/2

10 - h = 15/2

h = 10 - 15/2 = 2.5

The horizontal shift, h = 2.5

The amplitude, A = (Max - Min)/2

∴ A = (16 - 2)/2 = 7

A = 7

The vertical shift, k = Min - (-Amplitude)

∴ k = 2 - (-7) = 9

The vertical shift, k = 9 Up

Therefore, the equation of the sinusoidal equation that describes the height of shorts in terms of time is given by plugging in the values of the variables, A, B, h, and k to  get the following equation;

y = 7·sin(π/15·(t - 2.5)) + 9

b) The height of the shorts at exactly, t = 10 minutes = 600 seconds, is given as follows;

y = 7·sin(π/15·(t - 2.5)) + 9

10 minutes =  600 seconds

When t = 10 minutes = 600 seconds

∴ y = 7·sin(π/15(600 - 2.5)) + 9 = 5.5 ≈ 6

The height of the shorts at exactly t = 10 minutes ≈ 6 meters.

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Answer:

At most, Liam can only buy lunch for 6 people.

Step-by-step explanation:

It isn't going to be a decimal answer because there can't be half of a person

All you have to do is divide 50 by 8 and round down because you don't want to spend more than 50 dollars.

Writing it mathematically, it would be:

p [tex]\leq[/tex] 6

Answer:

Objective Function z

z =  5*x  +  4*y .       to maximize

Step-by-step explanation:

                           eggs             flour

P. Bread    (x)        2                   3

Z. Bread .   (y)       3                  4

Availability .        15                 16

Constraints.

Eggs availability .  15

2*x + 3*y ≤ 15

Flour availability 16 cups

3*x + 4*y ≤16

Objective Function z

z =  5*x  +  4*y .       to maximize

The model:

z =  5*x  +  4*y .       to maximize

Subject to:

2*x + 3*y ≤ 15

3*x + 4*y ≤16

x ≥ 0  y  ≥ 0 .  integers

Answer: C

Step-by-step explanation:

Correct on edg 2020

Answer:

8

Step-by-step explanation:

7 - 2 + 3 = 8

Answer:

9

Step-by-step explanation:

9 / 7 - 2 = 5 + 3 = 8 plus the Dog the man left behind, it would be 9

Their LCM is

70

hope it helps you.

Answer:

Their L.C.M IS

70....

IT IS YOUR ANSWER

A standard die has numbers = 1,2,3,4,5 and 6

Total outcomes = 6

P = Number of outcomes/Total Outcomes

Even and less than 4 = 1,2,3,4 and 6

P = 5/6

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Answer:

30*sqrt(2)

Step-by-step explanation:

5*sqrt(72)=5*sqrt(36*2)=5*6*sqrt(2)=30*sqrt(2)

Answer:

Step-by-step explanation:

Let largest value of data be L

and smallest value of data be S.

We are given that the range and coefficient of range of the data are 17 and 0.2 respectively.

Range formula is given by = Largest value - Smallest value

                   17  =   L - S

                  L = 17 + S ---------- [Equation 1]

Coefficient of range formula = (Largest - Smallest) ÷ (Largest + Smallest)

                                       0.2   =    l-s/l+s

                                      0.2 = 17/l+s

                 L + S = 17/0.2 = 85

So,    L + S = 85

       17 + S + S = 85   {using equation 1}

           2*S = 80

             S = 80/2 = 40

Putting value of S in equation 1, we get L = 20 + 40 = 60

Therefore,  Largest value, L = 60

               smallest value, S = 40

vhhg

Step-by-step explanation:

rrgggggggjjhjjhgghghhh

Answer:

Step-by-step explanation:

Given,

l || m

Therefore,

142° + (3x+8)° = 180° [Since Co-exterior angles]

=> 3x + 8 = 180 - 142

=> 3x + 8 = 38

=> 3x = 38 - 8

=> 3x = 30

[tex] = > x = \frac{30}{3} [/tex]

=> x = 10 (Ans)