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3 years ago

0=(1x+1)(1x-3) if m(x) =10, find the value of x

Mathematics

1 answer:

Anna11 [10]3 years ago

6 0

Answer:

x=1+sqrt(14) & 1-sqrt(14).

Step-by-step explanation:

(1x+1)(1x-3)=0

(x+1)(x-3)=0

m(x)=(x+1)(x-3)=10

(x+1)(x-3)=10

x^2+x-3x-3=10

x^2-2x-3=10

x^2-2x-3-10=0

x^2-2x-13=0

Apply the quadratic formula with a=1, b=-2 and c=-13.

The answer is x=1+sqrt(14) & 1-sqrt(14).

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2 years ago

For the given term, find the binomial raised to the power, whose expansion it came from: 15(5)^2 (-1/2 x) ^4

Elina [12.6K]

Answer:

C. $(5-\frac{1}{2})^6$

Step-by-step explanation:

Given

$15(5)^2(-\frac{1}{2})^4$

Required

Determine which binomial expansion it came from

The first step is to add the powers of he expression in brackets;

$Sum = 2 + 4$

$Sum = 6$

Each term of a binomial expansion are always of the form:

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

Where n = the sum above

$n = 6$

Compare $15(5)^2(-\frac{1}{2})^4$ to the above general form of binomial expansion

$(a+b)^n = ......+15(5)^2(-\frac{1}{2})^4+.......$

Substitute 6 for n

$(a+b)^6 = ......+15(5)^2(-\frac{1}{2})^4+.......$

[Next is to solve for a and b]

From the above expression, the power of (5) is 2

Express 2 as 6 - 4

$(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......$

By direct comparison of

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

and

$(a+b)^6 = ......+15(5)^{6-4}(-\frac{1}{2})^4+.......$

We have;

$^nC_ra^{n-r}b^r= 15(5)^{6-4}(-\frac{1}{2})^4$

Further comparison gives

$^nC_r = 15$

$a^{n-r} =(5)^{6-4}$

$b^r= (-\frac{1}{2})^4$

[Solving for a]

By direct comparison of $a^{n-r} =(5)^{6-4}$

$a = 5$

$n = 6$

$r = 4$

[Solving for b]

By direct comparison of $b^r= (-\frac{1}{2})^4$

$r = 4$

$b = \frac{-1}{2}$

Substitute values for a, b, n and r in

$(a+b)^n = ......+ ^nC_ra^{n-r}b^r+.......$

$(5+\frac{-1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ ^6C_4(5)^{6-4}(\frac{-1}{2})^4+.......$

Solve for $^6C_4$

$(5-\frac{1}{2})^6 = ......+ \frac{6!}{(6-4)!4!)}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6!}{2!!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6*5*4!}{2*1*!4!}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{6*5}{2*1}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+ \frac{30}{2}*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15*(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15(5)^{6-4}(\frac{-1}{2})^4+.......$

$(5-\frac{1}{2})^6 = ......+15(5)^2(\frac{-1}{2})^4+.......$

Check the list of options for the expression on the left hand side

The correct answer is $(5-\frac{1}{2})^6$

3 0

2 years ago

Write an equation of the line that has a slope of 5 and goes through the point (3,3)

professor190 [17]

Answer:

y=5x-12

Step-by-step explanation:

The general equation of a line is y=mx+b.

The equation you currently have is y=5x+b.

Plug in the point (3,3) which will get you 3=5(3)+b.

Solve the equation by solving what the y-intercept (b) is to create the new final equation.

3=5(3)+b

3=15+b

b=3-15

b=-12

y=5x-12

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2 years ago

Wade wants to buy sweaters. he has $175 and each sweater coast $12.00. write and solve an inequality to find how many sweaters h

Wittaler [7]

X = number of sweaters
175 - 55 > 12X
120 > 12X
10 > X
the most amount of sweaters he can buy is 10

5 0

2 years ago

.............................

nikdorinn [45]

Answer:

Step-by-step explanation:

3/r=1/y-2/x

3/r=x-2y /xy

7 0

2 years ago