Find the sum x^2-2x-15 and 2x^2+5x-2

For which values of k does the system of linear equations have zero, one, or an infinite number of solutions? [Note: not all thr

viktelen [127]

Answer:

The system has an infinite solution at k = 6, otherwise for any value of k, it has zero solution.

Step-by-step explanation:

Consider the system of linear equations:

$3x_{1} -x_{2}=2\;\;\;\;\;\;(1)\\ 9x_{1} -3x_{2}=k\;\;\;\;\;(2)$

The system of linear equations can have zero, one, or an infinite number of solutions:

simplify equation (1):

$x_{2}=3x_{1} -2$

substitute in equation (2), we get

$9x_{1} -3(3x_{1}-2)=k\\9x_{1} -9x_{1}+6=k\\0+6=k$

we cannot find the value of $x_{1}$ and $x_{2}$ .

so, there is no solution.

Multiply the equation (1) with 3 and put k is 6,

$3(3x_{1} -x_{2})=3\times2\\9x_{1} -3x_{2})=6$

it means both equations are overlapped. Then, the solution has infinite solutions.

Hence, the system has an infinite solutions at k is 6 otherwise for any value of k it has no solution.

4 0

3 years ago

Why is the percent increase of 45 to 75 not equal to the percentage crease of 75 to 45 check all that apply.

nevsk [136]

Answer: B and F

Step-by-step explanation:

Since, In the first case original amount = 45

So, the increasing percentage when the original amount increases to 75,

= $\frac{75-45}{45} \times 100 = \frac{30}{45} \times 100= \frac{200}{3}$ %

In second case original amount = 75

So the decreasing percentage when the original amount decreases to 45,

= $\frac{75-45}{75} \times 100 = \frac{30}{75} \times 100= \frac{40}{1}$ %

Thus, We found that the ratio of the percent increase is not the same as the percent decrease ( because, $\frac{200}{3}\neq \frac{40}{1}$

Also, The original amount of the present increase is different from the original amount for the persons decrease. ( Because, $75\neq 45$

Therefore, Option B and F is correct only.

5 0

3 years ago

Read 2 more answers

savannah has $5 in her wallet. she owes her brother 20 and owes her sister 18 . she earned 25 babysitting. write an algebraic ex

sladkih [1.3K]

An equation that represents this is

(5-20-18)+25

The steps to solve it are as follows

(-15-18)+25
-33+25= (-8)

she is still 8 dollars in debt

7 0

3 years ago

Two times antonio's age plus three times Sarah's age equals 34. Sarah age is also five times antonio's age . How old is Sarah?

Sergio039 [100]

Let Sarah's age be s and Antonio's age be a.

According to your question,

2a + 3s = 34
s = 5a

substituting the value of s in eq. 1,

2a + 3(5a) = 34

= 2a + 15 a = 34

17a = 34

thus, a = 34/17 = 2

substituting the value of a is s,

s = 5(2)
= 10

Thus, Sarah's age is 10 years and Antonio's age is 2 years.

6 0

3 years ago

If the area of a circle is 16π, the circumference of the circle is:

tamaranim1 [39]

The answer is option A
Here’s the process
Hope you understand it!

3 0

3 years ago