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2 years ago

Number of solutions to a system of equations algebraic. How many solutions does the system have? Can someone help me please....

Mathematics

2 answers:

Svet_ta [14]2 years ago

8 0

Answer:

A Exactly 1 solution

Step-by-step explanation:

if we express both equations as y = mx+b

we will see that both equations have different slopes (i.e "m" values are different).

By definition, 2 straight lines of different slopes will intersect at only one location (i.e there is only one solution)

Anna007 [38]2 years ago

5 0

Answer:

A Exactly one solution

Step-by-step explanation:

Each equation represents a line.

Solve each equation for y.

3x + y = 8

y = -3x + 8 First equation solved for y.

2x + 2y = 8

x + y = 4

y = -x + 4 Second equation solved for y.

The slope of the first equation is -3.

The slope of the second equation is -1.

Since the two equations are of lines and have different slopes, the two lines must intersect at one single point. That point is the solution of the system of equations.

Answer: A Exactly one solution

You might be interested in

If m=3 = what is the value of 3m?

Bond [772]

Answer: 9

Step-by-step explanation:

M=3 and the equation is 3m so your going to multiply. So the equation would be 3*3 and 3*3=9 so that's your answer

6 0

3 years ago

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

Help a sister out :))

soldi70 [24.7K]

Answer:

125

Step-by-step explanation:

-125 x -1

5 0

3 years ago

Fill in the blank‘s to complete the equation that describes the diagram

Harman [31]

-4 + -10 = -14
Negative 4 plus negative 10 = negative 14 (thats what I think the answers gonna be, but im not that sure though)

5 0

3 years ago

Find the height of a parallelogram with base<br> 9.44 meters and area 70.8 square meters.

Snowcat [4.5K]

Answer:

7.5 metres

Step-by-step explanation:

The formula for the area of a parallelogram is Area = base x height.

In the problem, you are given the base, which is 9.44 metres, and the area, which is 70.8 square metres.

When you plug everything into our area formula, you should get:

70.8 = 9.44 x height

To solve for height, you would divide both sides by 9.44.

70.8 ÷ 9.44 = height

7.5 = height

Don't forget your units, which is <u>metres</u>!

height = 7.5 metres

7 0

2 years ago

Number of solutions to a system of equations algebraic. How many solutions does the system have? Can someone help me please....​

Number of solutions to a system of equations algebraic. How many solutions does the system have? Can someone help me please....