X ≤ 4 and X>-2<br> Interval Notation

Factor the expression. k2 + 5kf – 50f2

g100num [7]

Answer:

We have

k^2 - 25f^2 + 5kf - 25f^2 =

k^2 - (5f)^2 + 5f( k - 5f) =

( k - 5f )( k + 5f ) + 5f( k - 5f ) =

( k - 5f )( k + 5f + 5f ) =

( k - 5f )( k + 10f );

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Find the number of 3-digit numbers formed using the digits 1 to 9, without repetition, such the numbers either have all digits l

Tasya [4]

Answer: 120

Step-by-step explanation:

The total number of digits from 1 to 9 = 10

The number of digits from less than 5 (0,1,2,3,4)=5

Since repetition is not allowed so we use Permutations , then the number of 3-digit different codes will be formed :-

$^5P_3=\dfrac{5!}{(5-3)!}=\dfrac{5\times4\times3\times2!}{2!}=5\times4\times3=60$

The number of digits from greater than 4 (5,6,7,8,9)=5

Similarly, Number of 3-digit different codes will be formed :-

$^5P_3=60$

Hence, the required number of 3-digit different codes = 60+60=120

3 0

3 years ago

Will the following two equations have a solution? Explain. y = 3x + 5 y = 3x - 7

r-ruslan [8.4K]

Answer:

There is no solution because the slopes of the two lines are the same.

Step-by-step explanation:

3x + 5 = 3x - 7

-3x - 3x Subtract 3x from both sides

5 ≠ - 7 No solution

If this answer is correct, please make me Brainliest!

7 0

3 years ago

The product of three consecutive integers is 3360. What is the sum of the three integers?

Tom [10]

Step-by-step explanation:

let the integer be x .

three consecutive integers : x, x+1, x+2.

according to the problem,.

Let the first of the 3 consecutive numbers be X.

Therefore the second number is (X + 1)

The third number is therefore (X + 2)

The product of the 3 consecutive numbers is:

( X )( X + 1 )( X + 2 ) = 3360 Equation( 1 )

Expanding Equation ( 1 ) gives

X³ + 3X² + 2X - 3360 = 0 Equation (2)

Solve Equation (2 ) which gives the following values for X

X1 = 14

X2 = - 8.5 + i (12.951834)

X3 = - 8.5 - i (12.951834).

the numbers are 14,15,16.

sum is 14+15+16 = 45.

hope this helps you.

5 0

2 years ago

(20 points) A statistics practitioner calculated the mean and the standard deviation from a sample of 400. They are x = 98 and s

Nimfa-mama [501]

Answer:

The P-value is 0.0234.

Step-by-step explanation:

We are given that a statistics practitioner calculated the mean and the standard deviation from a sample of 400. They are x = 98 and s = 20.

Let = population mean.

So, Null Hypothesis, : = 100 {means that the population mean is equal to 100}

Alternate Hypothesis, : > 100 {means that the population mean is more than 100}

The test statistics that will be used here is One-sample t-test statistics because we're yet to know about the population standard deviation;

T.S. = ~

where, = sample mean = 98

s = sample standard deviation = 20

n = sample size = 400

So, the test statistics = ~

= -2

The value of t-test statistics is -2.

Now, the P-value of the test statistics is given by;

P( < -2) = 0.0234 {using the t-table}

8 0

3 years ago

X ≤ 4 and X>-2 Interval Notation