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3 years ago

Can someone help right away!! please!!

Mathematics

1 answer:

larisa [96]3 years ago

4 0

Answer:

y = - 2x + 1

Step-by-step explanation:

Substitute an x value from the table into the equation

x = 1 : y = - 2(1) = - 2 ← require to add 1 to obtain y = - 1

x = 4 : y = - 2(4) = - 8 ← require to add 1 yo obtain y = - 7

Then equation describing the relationship is

y = - 2x + 1

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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

Sophia's school has 23 classrooms. Each classroom has 10 tables. How many tables are there in the school?

amid [387]

If there is 23 classrooms and each has 10 then you would have to times 23 by 10 - 23x10=230

4 0

3 years ago

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A cylinder with a radius of 4 yd and a volume of 80yd (find the height)

Afina-wow [57]

Answer:

Height of the cylinder = 1.60yd

Step-by-step explanation:

Volume of a cylinder =

V = πr^2h

V - volume of cylinder

π - 3.142

r - radius of cylinder

h - height of cylinder

We are provided with

V - 80

r - 4

π - 3.142

h - ?

80 = 3.142 * 4^2 * h

80 = 50.272 * h

To find h, divide both sides by 50.272

80/50.272 = 50.272h/ 50.272

1.599 = h

h = 1.60yd

7 0

3 years ago

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Simplify 4^2 * 4^8= A.)4^16 B.)4^10 C.)16^16 D.)16^10 please help me i need this asap.

SVEN [57.7K]

Answer:

4^{10}

Step-by-step explanation:

Complete the exponents first.

4*4=16

4*4*4*4*4*4*4*4=65536

65536 *16= 1048576

The answer is $4^{10}$

You can also find this if you add the exponents.

6 0

3 years ago

Solve the system by substitution.<br> y = x<br> y = 2x – 8

m_a_m_a [10]

Answer:

y=8

x=8

Step-by-step explanation:

y=2y-8

-y=-8

y=8

x=8

6 0

3 years ago

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