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3 years ago

Which expression represents the composition [g-f. h](x) for the functions below?

Mathematics

1 answer:

ss7ja [257]3 years ago

7 0

Answer:

the composition of the expression [g-f.h](x) is g(x)=5x2

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Find the first three terms in the expansion , in ascending power of x , of (2+x)^6 and obtain the coefficient of x^2 in the expa

Nataly_w [17]

Answer:

The first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

coefficient of $x^{2}$ in the expansion of $(2+x - x^{2})^{6}$ = (240 - 192) = 48

Step-by-step explanation:

$(2+x)^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times x^{k} \times 2^{6 - k})$

= $6_{C_{0}} \times x^{0} \times 2^{6} + 6_{C_{1}} \times x^{1} \times 2^{5} + 6_{C_{2}} \times x^{2} \times 2^{4}$ + terms involving higher powers of x

= $64 + 192 \times x^{1} + 240 \times x^{2}$ + terms involving higher powers of x

so, the first 3 terms in the expansion of $(2 + x)^{6}$ , in ascending power of x are,

$64 , 192 \times x^{1} {\textrm{ and }}240 \times x^{2}$

Again,

$(2+x - x^{2})^{6}$

= $\sum_{k=0}^{6}(6_{C_{k}} \times (2 + x)^{k} \times (-x^{2})^{6 - k})$

Now, by inspection,

the term $x^{2}$ comes from k =5 and k = 6

for k = 5, the coefficient of $x^{2}$ is , $(-32) \times 6$ = -192

for k = 6 , the coefficient of $x^{2}$ is, $6_{C_{2}} \times 2^{4}$ = 240

so, coefficient of $x^{2}$ in the final expression = (240 - 192) = 48

3 0

3 years ago

What is the answer to 4x+y=10

Alina [70]

Answer:

y = -4x + 10

Step-by-step explanation:

I am going to assume you are trying to write the equation of a line.

4x + y = 10

4x - 4x + y = 10 - 4x

y = -4x + 10

7 0

3 years ago

If nine times a certain number is subtracted from 7 the result is 52. Find the number.

mezya [45]

Answer:

Let the number to find be x

7 - 9x = 52

-9x = 52-7

- 9x = -45

Divide by - 9

x = 5

The number is 5

Hope this helps.

6 0

3 years ago

Read 2 more answers

What is the solution to y=-x+3 and y=4x-2

DIA [1.3K]

Answer: x=1

y=2

Step-by-step explanation:

y=-x+3

y=4x-2

-----------

y=y

-x+3=4x-2

3+2=4x+x

5=5x

x=1

y=-1+3

y=2

3 0

3 years ago

In the collection of beads, StartFraction 4 Over 20 EndFraction are blue. Which model shows the percent of beads that are blue?

jolli1 [7]

Option B model shows the percent of beads that are blue.

Solution:

Fraction of beads blue = $\frac{4}{20}$

To convert it into percent multiply the fraction by 100.

$$\text {Percent of} \ \frac{4}{20}=\frac{4}{20}\times 100\%$

$$=\frac{4\times 100}{20} \%$

Cancel the common factors, we get

= 20%

$$=\frac{20}{100}$

This means total number of boxes 100 and shaded in blue color 20.

Therefore option 2 represents $\frac{20}{100}$ .

Hence option B model shows the percent of beads that are blue.

8 0

3 years ago