All categories

2 years ago

Find the solution to the system of equations. x + y + z = 25 y+z= 18 Z= 7

Mathematics

1 answer:

Umnica [9.8K]2 years ago

6 0

Answer:

x=7

y=11

z=7

Step-by-step explanation:

x + y + z = 25

y+z= 18

Z= 7

Substitute the third equation into the second

y+z=18

y+7 = 18

y = 18-7

y = 11

Now substitute y=11 and z=7 into the first

x +y+z = 25

x+11+7 = 25

x+18 = 25

x = 25-18

x=7

You might be interested in

The first, third and thirteenth terms of an arithmetic sequence are the first 3 terms of a geometric sequence. If the first term

Salsk061 [2.6K]

Answer:

The first three terms of the geometry sequence would be $1$ , $5$ , and $25$ .

The sum of the first seven terms of the geometric sequence would be $127$ .

Step-by-step explanation:

Let $d$ denote the common difference of the arithmetic sequence.

Let $a_1$ denote the first term of the arithmetic sequence. The expression for the $n$ th term of this sequence (where $n\!$ is a positive whole number) would be $(a_1 + (n - 1)\, d)$ .

The question states that the first term of this arithmetic sequence is $a_1 = 1$ . Hence:

The third term of this arithmetic sequence would be $a_1 + (3 - 1)\, d = 1 + 2\, d$ .
The thirteenth term of would be $a_1 + (13 - 1)\, d = 1 + 12\, d$ .

The common ratio of a geometric sequence is ratio between consecutive terms of that sequence. Let $r$ denote the ratio of the geometric sequence in this question.

Ratio between the second term and the first term of the geometric sequence:

$\displaystyle r = \frac{1 + 2\, d}{1} = 1 + 2\, d$ .

Ratio between the third term and the second term of the geometric sequence:

$\displaystyle r = \frac{1 + 12\, d}{1 + 2\, d}$ .

Both $(1 + 2\, d)$ and $\left(\displaystyle \frac{1 + 12\, d}{1 + 2\, d}\right)$ are expressions for $r$ , the common ratio of this geometric sequence. Hence, equate these two expressions and solve for $d$ , the common difference of this arithmetic sequence.

$\displaystyle 1 + 2\, d = \frac{1 + 12\, d}{1 + 2\, d}$ .

$(1 + 2\, d)^{2} = 1 + 12\, d$ .

$d = 2$ .

Hence, the first term, the third term, and the thirteenth term of the arithmetic sequence would be $1$ , $(1 + (3 - 1) \times 2) = 5$ , and $(1 + (13 - 1) \times 2) = 25$ , respectively.

These three terms ( $1$ , $5$ , and $25$ , respectively) would correspond to the first three terms of the geometric sequence. Hence, the common ratio of this geometric sequence would be $r = 25 /5 = 5$ .

Let $a_1$ and $r$ denote the first term and the common ratio of a geometric sequence. The sum of the first $n$ terms would be:

$\displaystyle \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}$ .

For the geometric sequence in this question, $a_1 = 1$ and $r = 25 / 5 = 5$ .

Hence, the sum of the first $n = 7$ terms of this geometric sequence would be:

$\begin{aligned} & \frac{a_1 \, \left(1 - r^{n}\right)}{1 - r}\\ &= \frac{1 \times \left(1 - 2^{7}\right)}{1 - 2} \\ &= \frac{(1 - 128)}{(-1)} = 127 \end{aligned}$ .

7 0

2 years ago

Beth is putting liquid fertilizer on the plants in 4 flowerpots. her measuring spoon holds 1/8 teaspoon the directions say to pu

VARVARA [1.3K]

20 times 1/8+1/8+1/8+1/8+1/8=5/8 times 4 because of the four pots = 20

5 0

3 years ago

Read 2 more answers

2•2 divided by 2+2-2=

dsp73

The answer would be 2.

7 0

3 years ago

Read 2 more answers

Lucy deposits $7000 into an account that pays simple interest at a rate of 3% per year. How much interest will she be paid in th

Fofino [41]

7000*.03*6=?? Step 1. multiply 7000*.03=210 Step 2. multiply 210*6=1260. the answer is $1,260.00

5 0

2 years ago

Simplify x^2-9x-22/x-11

OleMash [197]

Answer:

x^2-11/-8x

Step-by-step explanation:

We can solve this equation easily by using PEMDAS, or order of operations.

<u>Parenthesis</u>

<u>Exponents</u>

<u>Multiplication>Division (Depends on which comes first left to right)</u>

<u>Addition>Subtraction (See multiplication>division)</u>

Now that we know the order of the operations, we can solve.

First, we cant solve for x^2 because we dont know the value of x, so well leave that alone. Same with 22/x. All we can do is use the commutative property.

So our equation is now x^2-11/-8x

Hope this helps!

6 0

3 years ago