All categories

3 years ago

Use factoring to solve the equation for x: (x−2)(2x−3)=(x−2)(x+1).

Mathematics

1 answer:

telo118 [61]3 years ago

5 0

Answer:

x = 4, 2

Step-by-step explanation:

$(x-2)(2x-3)=(x-2)(x+1)$

$\\\Rightarrow 2x^2-7x+6=x^2+x-2x-2\\\Rightarrow 2x^2-7x+6-x^2+x-2x-2=0\\\Rightarrow x^2-6x+8=0$

While splitting the middle term the sum of the term should give us the middle term and their product should give the last term

$\\\Rightarrow x^2-4x-2x+8=0$

-4-2 = -6

$-4\times -2=8$

$\\\Rightarrow (x-4)(x-2)=0\\\Rightarrow x=4, 2$

Hence, x = 4, 2

You might be interested in

A grocery store estimates that customers arrive at the rate of 15 per hour. The cashier can serve customers at a rate 20 per hou

IrinaK [193]

Answer:

3 customers

Step-by-step explanation:

Rate of arrival (λ) = 15 per hour

Service rate (μ) = 20 per hour

The number of customers in a system given the arrival rate and the mean service rate is given by:

$N = \frac{\lambda}{\mu-\lambda}\\$

Applying the given data:

$N = \frac{15}{20-5}\\N=3\ customers$

The average number of customers in the system is 3 customers.

6 0

3 years ago

Alexandra was out at a restaurant for dinner when the bill came. She wanted to leave a tip of 13%. What number should she multip

Karo-lina-s [1.5K]

Answer:

x = Total meal cost

y = Total cost-plus tip

113% * x = y

8 0

3 years ago

fritz wrote a set of related facts for the array below.which equation is not intended in the set of related facts for this array

oksian1 [2.3K]

Do you have the equation choices?

7 0

3 years ago

You are riding the bus to school and you realize it is taking longer because of all the stops you are making. The time it takes

Ksju [112]

Answer:

-1

Step-by-step explanation:

g(2) = (2) - 3(2) + 4(2) - 5

g(2) = 2 - 6 + 8 - 5

g(2) = 2 - 6 + 3

g(2) = 2 - 3

g(2) = -1

4 0

2 years ago

help me with the Quadratic equation.... x2+ (p - 5) x + 2q = 0 has the roots −3 and 6. Find the value of P and the value of q.

nirvana33 [79]

Step-by-step explanation:

The quadratic equation is x² + (p - 5)x + 2q = 0.

By Vieta's Formula,

we have SOR = -b/a and POR = c/a.

=> (-3) + (6) = -(p - 5) and (-3)(6) = 2q.

=> 3 = 5 - p and -18 = 2q

Hence, p = 2 and q = -9.

Alternate Method:

We have (x + 3) and (x - 6) as factors of the quadratic equation x² + (p - 5)x + 2q = 0.

=> (x + 3)(x - 6) = x² - 3x - 18.

By Comparing Coefficients,

(p - 5) = -3 and 2q = 18.

Hence p = 2 and q = -9.

8 0

3 years ago