Is point F interior to both circles

denpristay [2]

2 times a number minus 9 is less than or equal to 21. and in inequality form that’s: 2x - 9 >_ 21 and u make a number line and a closed circle on 15 and an arrow going right. i hope i understood your question right

7 0

3 years ago

Read 2 more answers

Using the binomial theorem , obtain the expansion of :

andrezito [222]

Answer:

see explanation

Step-by-step explanation:

Expand both factors and collect like term

Using Pascal' triangle with n = 6 to obtain the coefficients

1 6 15 20 15 6 1

Decreasing powers of 1 from $1^{6}$ to $1^{0}$

Increasing powers of 3x from $(3x)^{0}$ to $(3x)^{6}$

$1+3x)^{6}$

= 1. $1^{6}$ $(3x)^{0}$ + 6. $1^{5}$ $(3x)^{1}$ + 15. $1^{4}$ $(3x)^{2}$ + 20. $1^{3}$ $(3x)^{3}$ + 15.1² $(3x)^{4}$ + 6. $1^{1}$ $(3x)^{5}$ + 1. $1^{0}$ $(3x)^{6}$

= 1 + 18x + 135x² + 540x³ + 1215 $x^{4}$ + 1458 $x^{5}$ + 729 $x^{6}$

--------------------------------------------------------------------------------------

$(1-3x)^{6}$

= 1. $1^{6}$ $(-3x)^{0}$ + 6. $1^{5}$ $(-3x)^{1}$ + 15. $1^{4}$ $(-3x)^{2}$ + 20. $1^{3}$ $(-3x)^{3}$ + 15.1² $(-3x)^{4}$ + 6. $1^{1}$ $(-3x)^{5}$ + 1. $1^{0}$ $(-3x)^{6}$

= 1 - 18x + 135x² - 540x³ + 1215 $x^{4}$ - 1458 $x^{5}$ + 729 $x^{6}$

----------------------------------------------------------------------------------

Collecting like terms from both expressions

$(1+3x)^{6}$ + $(1-3x)^{6}$

= 2 + 270x² + 2430 $x^{4}$ + 1458 $x^{6}$

----------------------------------------------------

(2)

Using Pascal's triangle with n = 5

1 5 10 10 5 1

Decreasing powers of 1 from $1^{5}$ to $1^{0}$

Increasing powers of 2x from $(2x)^{0}$ to $(2x)^{5}$

$(1+2x)^{5}$

= 1. $1^{5}$ $(2x)^{0}$ + 5. $1^{4}$ $(2x)^{1}$ + 10. $1^{3}$ $(2x)^{2}$ + 10. $1^{2}$ $(2x)^{3}$ + 5. $1^{1}$ $(2x)^{4}$ + 1. $1^{0}$ $(2x)^{5}$

= 1 + 10x + 40x² + 80x³ + 80 $x^{4}$ + 32 $x^{5}$

8 0

3 years ago

HELPPP ASAPPP DUE SOONN

Andru [333]

The friction force exerted on the 2400kg car is 9408 Newtons

<h3>What force will be exerted on the 2400kg car?</h3>

First, we know that the friction force and mass are represented by a proportional relation, this means that we can write:

F = k*M

Where F is the force, M is the mass and k is the constant of proportionality.

We know that for a 1600kg car, a force of 6272N is exerted, replacing that we get:

6272N = k*1600kg

Solving for k we get:

k = (6272N)/(1600 kg) = 3.92 N/kg

Then the proportional relationship is:

F = (3.92 N/kg)*M

So if M = 2400kg, we have:

F = (3.92 N/kg)*2400kg = 9408 N

So the friction force exerted on the 2400kg car is 9408 Newtons

If you want to learn more about proportional realtions:

brainly.com/question/12242745

#SPJ1

8 0

2 years ago

Compare the ratios 4:5 and 16:20.

Katarina [22]

Answer:

They are equal

Step-by-step explanation:

When comparing ratios, we simply want to find out if the numbers are greater than, less than, or equal to each other. We have 4:5 and 16:20.

To find out the comparison;

Step 1: We find the LCM of the denominators ie 5 and 20, which is 20

Step 2: We divide the LCM by both sides, like this: 20÷5=4 and 20÷20=1.

Step 3: Now, multiply each ratio by the result of its individual denominator division ie

$\frac{4 \times 4}{5 \times 4} \: and \: \frac{16 \times 1}{20 \times 1} = \frac{16}{20} \: and \: \frac{16}{20}$

Step 4: Convert back to ratio form, we have: 16:20 and 16:20

From the above ratios, we have found out that 4:5 and 16:20 are equal when compared.

I hope this helps.

6 0

2 years ago

The list of numbers 41,35,30,25,20,15has a median of 25.The mode of the list of the numbers is 15 to the nearest whole, what is

salantis [7]

Answer:

1.2

Step-by-step explanation:

1.Arrange the numbers in order by size.

15,20,25,30,35,41

2.If there is an odd number of terms, the median is the center term.

with these numbers they are even (6 numbers total)

3.If there is an even number of terms, add the two middle terms and divide by 2.

30 ÷ 25=1.2

4 0

3 years ago