All categories

3 years ago

Find the value of k for x^2 - 2kx+7k -12=0 so that they have two equal roots

Mathematics

1 answer:

Alisiya [41]3 years ago

5 0

Step-by-step explanation:

x^2 -2kx +7k -12 = 0

two equal roots -->Δ = b^2 -4ac = 4k^2 - 4(7k-12)=0 = 4(k^2 - 7k +12)=4(k-4)(k-3)=0

so k =3 and k =4

You might be interested in

David wants to pack 574 cereal bars into bags of 10 and bags of 8 the number of bags of 8 is 2 more than the bags of 10. How man

BabaBlast [244]

Answer: Number of bags of 8. = 33

Number of bags of 10. = 31

Step-by-step explanation:

Let x = Number of bags of 8.

y = Number of bags of 10.

As per given.

$8x+10y= 574$ (i)

$x=y+2$ (ii)

Put value of x from (ii) in (i)

$8(y+2)+10y= 574\\\\\Rightarrow\ 8y+16+10y=574\\\\\Rightarrow\ 18y=574-16\\\\\Rightarrow\ 18y=558\\\\\Rightarrow\ y=\dfrac{558}{18}\\\\\Rightarrow\ y=18$

Put this in (i), x= 31+2=33

Hence,

Number of bags of 8. = 33

Number of bags of 10. = 31

6 0

3 years ago

A new van is bought for $30,000 and depreciates in value by 8. 4% per year

Kobotan [32]

Answer:

2520 decrease per year

Step-by-step explanation:

8.4% is also .084 so you multiply .084 by 30,000 and get 2520.

5 0

2 years ago

Find the length of side a<br>will mark brainly

Mekhanik [1.2K]

Answer:

Step-by-step explanation:use the cube to count(cube is in the corner.)

5 0

3 years ago

Pls help me for brainliest answer

Ket [755]

Answer with Step-by-step explanation:

$a)3n + 4 \\ \\n = 1 \\ 3 \times 1 + 4 \\ 3 + 4 \\ =7 \\ \\ n = 2 \\ 3 \times 2 + 4 \\ 6 + 4 \\ = 10 \\ \\ n = 3 \\ 3 \times 3 + 4 \\ 9 + 4 \\ = 13 \\ \\ n = 4 \\ 3 \times 4 + 4 \\ 12 + 4 \\ = 16 \\ \\ n = 10 \\ 3 \times 10 + 4 \\ 30 + 4 \\ = 34 \\$

So in this sequence,

1st term = 7

2nd term = 10

3rd term = 13

4th term = 16

10th term = 34

$b)4n - 5 \\ \\ n = 1 \\ 4 \times 1 - 5 \\ 4 - 5 \\ = - 1 \\ \\ n = 2 \\ 4 \times 2 - 5 \\ 8 - 5 \\ = 3 \\ \\ n = 3 \\ 4 \times 3 - 5 \\ 12 - 5 \\ = 7 \\ \\ n = 4 \\ 4 \times 4 - 5 \\ 16- 5 \\ = 11 \\ \\ n = 10 \\ 4 \times 10 - 5 \\ 40 - 5 \\ = 35$

In this sequence,

1st term = -1

2nd term = 3

3rd term = 7

4th term = 11

10th term =35

5 0

3 years ago

A snail can move 1/30 miles in 1/3 hour. How fast does a snail move in miles /hours

bekas [8.4K]

Answer: 1/10 miles/hour

To find how fast a snail moves in miles per hour, we can find the unit rate using a proportion.

The unit rate is the amount per one unit. In this problem, the unit is for one hour. One way to find the unit rate is by using a proportion.

<h2>Proportions</h2>

Proportions look like two fractions set equal to each other with a missing variable to solve.

<h3>State our variables</h3>

let <em>x</em> be the number of miles per hour

<h3>Write a proportion</h3>

The first fraction has a number for the numerator (top) and denominator (bottom), because the question gives us the information. The second fraction has a missing value, <em>x</em>, that we are solving for. We can write <em>x</em> in the numerator.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}$

<h2>Solve</h2>

We can solve by finding the scale factor. The scale factor is the number we can multiply the numerator by to find <em>x</em>.

<h3>Find the scale factor</h3>

Start with the proportion.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{x\ mi}{1\ hr}}$

To find the scale factor,

Take the denominator from the fraction with a variable: $1\ hr$
Take the denominator from the fraction that has no variable: $\frac{1}{3}\ hr$
Divide step 1 by step 2 and solve: $1\ hr\ \div\ \frac{1}{3}\ hr = 3$

Our scale factor is <u>3</u>.

<h3>Solve for x</h3>

We can find <em>x</em> by multiplying the numerator in the first fraction by the scale factor. This is because <em>x</em> is also in the numerator.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{(\frac{1}{30}\ mi)*3}{1\ hr}}$

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{3}{30}\ mi}{1\ hr}}$

Simplify 3/30 by dividing the fraction by 3.

$\displaystyle{\frac{\frac{1}{30}\ mi}{\frac{1}{3}\ hr} = \frac{\frac{1}{10}\ mi}{1\ hr}}$

x = 1/10

∴ a snail moves 1/10 miles per hour.

Learn another way to solve proportions here: brainly.com/question/18437927

7 0

2 years ago