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2 years ago

How many odd integers are there between 101 and 199?

Mathematics

2 answers:

Rudiy272 years ago

5 0

Answer:

Step-by-step explanation:

im guessing for points

Nonamiya [84]2 years ago

3 0

Answer:

49 odd integers

Step-by-step explanation:

since 199-101 is 98 so there is 98 integers between 101 and 199

then we have to divide 98 by 2 to find out how much odd(or even) integers are between 101 and 199

since 98 divided by 2 is 49 there are 49 odd integers between 101 and 199

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Is the binomial a factor of the polynomial function?

olchik [2.2K]

Answer:

YES

Step-by-step explanation:

The given polynomial is: $f(x) = x^3 + 4x^2 - 25x - 100$

(x - a) is a factor of a polynomial iff x = a is a solution to the polynomial.

To check if (x - 5) is a factor of the polynomial f(x), we substitute x = 5 and check if it satisfies the equation.

∴ f(5) = 5³ + 4(5)² - 25(5) - 100

= 125 + 100 - 125 - 100

= 225 - 225

= 0

We see, x = 5 satisfies f(x). So, (x - 5) is a factor to the polynomial.

Now, to check (x + 2) is a factor.

i.e., to check x = - 2 satisfies f(x) or not.

f(-2) = (-2)³ + 4(-2)² - 25(-2) - 100

= -8 + 16 + 50 - 100

= -108 + 66

≠ 0

Therefore, (x + 2) is not a factor of f(x).

To check (x - 4) is a factor.

∴ f(4) = 4³ + 4(4)² - 25(4) - 100

= 64 + 64 - 100 - 100

= 128 - 200

≠ 0

Therefore, (x - 4) is not a factor of f(x).

7 0

2 years ago

weeeeeb [17]

Answer:

2x + y = -4

Step-by-step explanation:

standard form of equation of straight line is

ax+by = c

that is terms containing x and y should be on LHS and constant term should be on RHS

______________________________________________

Given equation

y + 1 = - 2x - 3

lets bring -2x on LHS ,

add 2x on lHS and RHS

y + 1 + 2x = - 2x - 3 + 2x

=> y + 1 + 2x = -3

on lHS, 1 is there which constant term lets bring it on RHS

subtract 1 from both sides

y + 1 + 2x - 1= -3 -1

y + 2x = -4

rearranging it

2x + y = -4 (Answer)

8 0

3 years ago

(ANSWER FOR FREE BRAINPOINTS!) (FIRST TO ANSWER GETS BAINLIEST) The local park has a rectangular swimming pool that measures 40

iren [92.7K]

Answer:

9 yards

Step-by-step explanation:

Since both pools are similar, therefore the ratio of their length and width would be equal. That is:

Length of the current swimming pool : length of the new swimming pool = width of the current swimming pool : width of the new swimming pool

Thus, we can set up a proportion as shown below:

Let the width of the new swimming pool be x.

40 : 24 = 15 : x

$\frac{40}{24} = \frac{15}{x}$

Cross multiply

$40*x = 15*24$

$40x = 360$

Divide both sides by 40

$x = \frac{360}{40}$

$x = 9$

The width of the new swimming that is smaller would be 9 yards.

4 0

2 years ago

A) How many ways can 2 integers from 1,2,...,100 be selected

Anna007 [38]

Answer with explanation:

→Number of Integers from 1 to 100

=100(50 Odd +50 Even)

→50 Even =2,4,6,8,10,12,14,16,...............................100

→50 Odd=1,3,,5,7,9,..................................99.

→Sum of Two even integers is even.

→Sum of two odd Integers is odd.

→Sum of an Odd and even Integer is Odd.

(a)

Number of ways of Selecting 2 integers from 50 Integers ,so that their sum is even,

=Selecting 2 Even integers from 50 Even Integers , and Selecting 2 Odd integers from 50 Odd integers ,as Order of arrangement is not Important, ,

$=_{2}^{50}\textrm{C}+_{2}^{50}\textrm{C}\\\\=\frac{50!}{(50-2)!(2!)}+\frac{50!}{(50-2)!(2!)}\\\\=\frac{50!}{48!\times 2!}+\frac{50!}{48!\times 2!}\\\\=\frac{50 \times 49}{2}+\frac{50 \times 49}{2}\\\\=1225+1225\\\\=2450$

=4900 ways

(b)

Number of ways of Selecting 2 integers from 100 Integers ,so that their sum is Odd,

=Selecting 1 even integer from 50 Integers, and 1 Odd integer from 50 Odd integers, as Order of arrangement is not Important,

$=_{1}^{50}\textrm{C}\times _{1}^{50}\textrm{C}\\\\=\frac{50!}{(50-1)!(1!)} \times \frac{50!}{(50-1)!(1!)}\\\\=\frac{50!}{49!\times 1!}\times \frac{50!}{49!\times 1!}\\\\=50\times 50\\\\=2500$

=2500 ways

7 0

2 years ago

Type the correct answers out, thank you - 20 POINTS

nadezda [96]

AB and BC form a right angle at their point of intersection. This means AB is perpendicular to BC.

We are given the coordinates of points A and B, using which we can find the equation of the line for AB.

Slope of AB will be:

$m= \frac{-1-1}{14-2}=-1/6$

Using this slope and the point (2,1) we can write the equation for AB as:

$y-1= \frac{-1}{6}(x-2) \\ \\ 
y= -\frac{1}{6}x+ \frac{1}{3}+1 \\ \\ 
y=-\frac{1}{6}x+ \frac{4}{3} 
$

The above equation is in slope intercept form. Thus the y-intercept of AB is 4/3.

Slope of AB is -1/6, so slope of BC would be 6. Using the slope 6 and coordinates of the point B, we can write the equation of BC as:

y - 1 = 6(x - 2)
y = 6x - 12 + 1
y = 6x - 11

Point C lies on the line y = 6x - 11. So if the y-coordinate of C is 13, we can write:

13 = 6x - 11
24 = 6x
x = 4

The x-coordinate of point C will be 4.

Therefore, the answers in correct order are:

4/3 , 6, -11, 4

8 0

2 years ago

How many odd integers are there between 101 and 199?​

How many odd integers are there between 101 and 199?