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3 years ago

Please help and simplify these expressions and show how u found them! i will mark brainliest !

Mathematics

2 answers:

dem82 [27]3 years ago

7 0

Answer:

3) 3k+20

4) 4+2d

Step-by-step explanation:

You first have to distribute by multiplying the number next to the expression in the parenthesis. Then you combine like terms.

3) 5(k+4)-2k

Step 1: (5×k= 5k) (5×4=20) equation is now 5k+20-2k

Step 2: 5k-2k=3k since they both have the same variable you combine like terms. Equation is now 3k+20 (Final answer)

4) 2(3+d-1)

Step 1: (2×3=6) (2×d=2d) (2×[-1]=2) Equation is now 6+2d-1.

Step 2: (6-2=4) Since both 6 and 1 don't have any variable their like terms and you combine them. Equation is now 4+2d (Final answer)

Diano4ka-milaya [45]3 years ago

6 0

5(k+4)-2k
Multiply the k and the 4 by 5
Now you have 5k+20-2k
Minus 2k from 5k
Now you have 3k+ 20 that’s the answer

2(3+d-1)
Multiply 3, d, and 1 by 2
Now you have 6+2d-2
Minus 2 from 6
Now you have 4+2d that’s the answe

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What are the characteristics of the function f(x)=2(x-4)^5? Check all that apply

GaryK [48]

Answer:

Option B , C , E are characteristics of the function .

Step-by-step explanation:

Given : function f(x)=2(x-4)^5.

To find : What are the characteristics of the function .

Solution : We have given that f(x)=2 $(x-4)^{5}$ .

By the End Point behavior : if the degree is even and leading coefficient is odd of polynomial of function then left end of graph goes down and right goes up.

Since , Option E is correct.

It has degree 5 therefore, function has 5 zeros and atmost 4 maximua or minimum.

Option C is also correct.

By transformation rule it is vertical stretch and shift to right (B )

Therefore, Option B , C , E are characteristics of the function .

3 0

3 years ago

A lidless box is to be made using 2m^2 of cardboard find the dimensions of the box that requires the least amount of cardboard

Jlenok [28]

1.8, Problem 37: A lidless cardboard box is to be made with a volume of 4 m3 . Find the dimensions of the box that requires the least amount of cardboard. Solution: If the dimensions of our box are x, y, and z, then we’re seeking to minimize A(x, y, z) = xy + 2xz + 2yz subject to the constraint that xyz = 4. Our first step is to make the first function a function of just 2 variables. From xyz = 4, we see z = 4/xy, and if we substitute this into A(x, y, z), we obtain a new function A(x, y) = xy + 8/y + 8/x. Since we’re optimizing something, we want to calculate the critical points, which occur when Ax = Ay = 0 or either Ax or Ay is undefined. If Ax or Ay is undefined, then x = 0 or y = 0, which means xyz = 4 can’t hold. So, we calculate when Ax = 0 = Ay. Ax = y − 8/x2 = 0 and Ay = x − 8/y2 = 0. From these, we obtain x 2y = 8 = xy2 . This forces x = y = 2, which forces z = 1. Calculating second derivatives and applying the second derivative test, we see that (x, y) = (2, 2) is a local minimum for A(x, y). To show it’s an absolute minimum, first notice that A(x, y) is defined for all choices of x and y that are positive (if x and y are arbitrarily large, you can still make z REALLY small so that xyz = 4 still). Therefore, the domain is NOT a closed and bounded region (it’s neither closed nor bounded), so you can’t apply the Extreme Value Theorem. However, you can salvage something: observe what happens to A(x, y) as x → 0, as y → 0, as x → ∞, and y → ∞. In each of these cases, at least one of the variables must go to ∞, meaning that A(x, y) goes to ∞. Thus, moving away from (2, 2) forces A(x, y) to increase, and so (2, 2) is an absolute minimum for A(x, y).

5 0

3 years ago

What is the value of the sum of all the terms of the geometric series 300, 60, 12, …?

ruslelena [56]

<h3>Answer: 375</h3>

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

Work Shown:

a = 300 = first term

r = 60/300 = 0.2 = common ratio

We multiply each term by 0.2, aka 1/5, to get the next term.

Since -1 < r < 1 is true, we can use the infinite geometric sum formula below

S = a/(1-r)

S = 300/(1-0.2)

S = 300/0.8

S = 375

----------

As a sort of "check", we can add up partial sums like so

300+60 = 360
300+60+12 = 360+12 = 372
300+60+12+2.4 = 372+2.4 = 374.4
300+60+12+2.4+0.48 = 374.4+0.48 = 374.88

and so on. The idea is that each time we add on a new term, we should be getting closer and closer to 375. I put "check" in quotation marks because it's probably not the rigorous of checks possible. But it may give a good idea of what's going on.

----------

Side note: If the common ratio r was either r < -1 or r > 1, then the terms we add on would get larger and larger. This would mean we don't approach a single finite value with the infinite sum.

3 0

3 years ago

Ratio between 80% and 20%

musickatia [10]

4:1 is the answer............

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3 years ago

A lawyer has found 60 investors for a limited partnership to purchase an inner-city apartment building, with each contributing e

Mars2501 [29]

Answer:

1. The lawyer has 34 investors that contribute with $3,000 and has 26 investors that contribute with $6,000.

2. The jar has 26 nickels and 44 dimes that worth $5.70.

3. The concession stand has sold 1600 sodas and 1400 hotdogs

Step-by-step explanation:

For all the problems we are going to follow the same process that will consist on 1. Define the variables. 2. Formulate the system of two linear equations 3. Solve by the elimination method 4. Give the answer.

First problem.

- Variables:

x = number of investors that contribute with $3,000

y = number of investors that contribute with $6,000

- System of equations.

First equation will be the result of adding the number of investors that will give us a total of 60 investors then:

x + y = 60

Second equation is the result of multypling the number of investors by its invest and adding between them to get the $258,000 they have raised:

3,000x + 6,000y = 258,000

The system will be:

x + y = 60

3,000x + 6,000y = 258,000

- Solve by the elimination method.

To cancel x we are going to multiply by -3000 in both sides of the first equation and we will leave the second equation the same but in the first row to make easier the calculations then:

3,000x + 6,000y = 258,000

(x + y ) (-3,000) = 60 (-3,000) solve the multiplications

3,000x + 6,000y = 258,000

-3,000x - 3,000y = -180,000 solve the operations

0 + 3,000y = 78,000 clear y

$y = \frac{78,000}{3,000}$ solve the division

y = 26

For calculate x, replace the y value in the first equation and solve it

x + 26 = 60

x = 60 - 26

x = 34

- Answer

The lawyer has 34 investors that contribute with $3,000 and has 26 investors that contribute with $6,000.

Second problem

- Variables:

x = number of nickels

y = number of dimes

- System of equations.

First equation will be the result of adding the number of nickels and dimes that will give us a total of 70 coins in the jar then:

x + y = 70

Second equation is the result of multypling the number of coins by its value and adding between them to get the $5.70 that the jar worth:

0.05x + 0.1 y = 5.70

The system will be:

x + y = 70

0.05x + 0.1 y = 5.70

- Solve by the elimination method.

To cancel x we are going to multiply by -0.05 in both sides of the first equation and we will leave the second equation the same but in the first row to make easier the calculations then:

0.05x + 0.1 y = 5.70

(x + y ) (-0.05) = 70 (-0.05) solve the multiplications

0.05x + 0.1 y = 5.70

-0.05x - 0.05y = -3.50 solve the operations

0 + 0.05y = 2.20 clear y

$y = \frac{2.20}{0.05}$ solve the division

y = 44

For calculate x, replace the y value in the first equation and solve it

x + 44 = 70

x = 70 - 44

x = 26

- Answer

The jar has 26 nickels and 44 dimes that worth $5.70.

Third problem.

- Variables:

x = number of sodas sold by $2

y = number of hotdogs sold by $3

- System of equations.

First equation will be the result of adding the number of sodas and hotdogs that is of 3000 then:

x + y = 3000

Second equation is the result of multypling the number of sodas and hotdogs by its price and adding between them to get the $7400 of the receipts:

2x + 3y = 7400

The system will be:

x + y = 3000

2x + 3y = 7400

- Solve by the elimination method.

To cancel x we are going to multiply by -2 in both sides of the first equation and we will leave the second equation the same but in the first row to make easier the calculations then:

2x + 3y = 7400

(x + y ) (-2) = 3000 (-2) solve the multiplications

2x + 3y = 7400

-2x - 2y = -6000 solve the operations

0 + 1y = 1400 clear y

$y = \frac{1400}{1}$ solve the division

y = 1400

For calculate x, replace the y value in the first equation and solve it

x + 1400 = 3000

x = 3000 - 1400

x = 1600

- Answer

The concession stand has sold 1600 sodas and 1400 hotdogs

6 0

3 years ago