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2 years ago

If $x$, $y$, and $z$ are positive integers such that $6xyz+30xy+21xz+2yz+105x+10y+7z=812$, find $x+y+z$.

Mathematics

1 answer:

harina [27]2 years ago

8 0

Answer:

Step-by-step explanation:

When we simplify we get $z(6xy+21x+2y+7)+30xy+105x+10y=812.$

Then we continue to factor to get: $(z+5)(6xy+21x+2y+7)&=847.$

We then see that we can factor $(6xy+21x+2y+7)$ into $(z+5)(3x+1)(2y+7)&=847.$

we then do the prime factorization of 847, which i think is, $7*11*11$ . we have to find the numbers that multiply to 847 and then plug them into z+5, 3x=1,2y+7.

It has to be a positive, non-negative integer, right?

We also see that 3x+1=11 so we see that x=10/3 (which wont work).

So 3x+1=7, so x=2.

So 11 has to be in another term. It has to be in 2y+7=11 so y=2

for the last term we get z+5=11 so z=6

2+2+6=10

Hope this helps and if you want please consider giving me brainliest. :)

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You have $25 to buy 6 fishing lures. Write and solve an inequality that represents the prices you can pay per fishing lure.

Rus_ich [418]

We are given that we have $25 to pay for 6 fishing lures.

We can make an equality for this as follows:

Suppose price of one fishing lure is x dollars.

So we will use unitary method to find price of 6 fishing lures.

Price of 6 fishing lures = 6 * ( price of one fishing lure) = 6* x = 6x

Now we only have 25 dollars with us, so the price of 6 fishing lures has to be less than or equal to 25 dollars.

So creating an inequality,

$6x\leq25$

Now in order to find price for one fishing lure, we have to solve this for x.

Dividing both sides by 6 we have,

$x\leq\frac{25}{6}$

Converting to decimal,

$x\leq4.167$

Answer : The price of one fishing lure must be less than or equal to $4.167

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2 years ago

Helena uses a mixture of compost and topsoil in her garden. She purchased a total of 10 cubic yards of compost and topsoil for $

Annette [7]

Let C be the amount of compost

T be the amount of topsoil

Each compost cost = $25

Cost of C compost = 25C

Each topsoil cost = $15

Cost of T topsoil = 15T

Amount of compost + amount of topsoil = 10

C + T = 10 -------> Equation 1

cost of C compost + cost of T topsoil = 180

25C + 15T = 180 --------> equation 2

Solve the first equation for C

C + T = 10

C = 10 - T

Now plug it in second equation

25C + 15T = 180

25 ( 10 - T) +15T = 180

250 - 25T + 15T = 180 (combine like terms)

250 - 10 T = 180 (Subtract 250 on both sides)

-10T = 180 - 250

-10T = -70 ( divide by -10 on both sides)

T = 7

She purchased 7 cubic yards of topsoil .

4 0

2 years ago

Read 2 more answers

What is the value of x in the equation 4 x plus 8 y equals 40, when y equals 0.8? 4.6 8.4 10 12What is the value of a in the equ

Mama L [17]

Answer:

1. 8.4 2. 15

Step-by-step explanation:

1. 4x+8y= 40

wen y= 0.8

4x+8×0.8=40

4x=40-8×0.8

4x= 40- 6.4= 33.6

....x= 33.6/4 = 8.4

2. 3a+b= 54

wen b= 9

3a+ 9= 54

3a= 54- 9

3a=45

.....a = 45/3 = 15

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8 0

2 years ago

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Today the price of a Jeep is $25,000. In 1970, the price was $5,000. What's the price relative?

asambeis [7]

Solution:

we are given with

Today the price of a Jeep is $25,000. In 1970, the price was $5,000.

So we can write

The price of a Jeep, today = $25,000

The price of a Jeep,in 1970 = $ 5,000

Relative Price means price of a good relative to other. Its a ratio of the two goods times 100.

$Price \ \ relative =\frac{25000}{5000}*100\\ \\ \ Price \ \ relative =5*100=500\\ \\$

Hence the price relative is $500/-

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2 years ago

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What is the product of a+3 and −2a2+15a+6b2?

rewona [7]

For this case we must find the product of the following expression:

$(a + 3) (- 2a ^ 2 + 15a + 6b ^ 2)$

We apply distributive property term to term:

$(a + 3) (- 2a ^ 2 + 15a + 6b ^ 2) =\\-2a ^ 2 * a + 15a * a + 6b ^ 2 * a-6a ^ 2 + 45a + 18b ^ 2 =\\-2a ^ 3 + 15a ^ 2 + 6ab ^ 2-6a ^ 2 + 45a + 18b ^ 2=$

We add similar terms:

$-2a ^ 3 + (15-6) a ^ 2 + 6ab ^ 2 + 45a + 18b ^ 2 =\\-2a ^ 3 + 9a ^ 2 + 6ab ^ 2 + 45a + 18b ^ 2 =$

Finally, the expression is as:

$-2a ^ 3 + 9a ^ 2 + 6ab ^ 2 + 45a + 18b ^ 2$

Answeer:

$-2a ^ 3 + 9a ^ 2 + 6ab ^ 2 + 45a + 18b ^ 2$

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2 years ago