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3 years ago

Find r please 35r<-35r+40

Mathematics

1 answer:

MakcuM [25]3 years ago

5 0

Answer:

solve it like there is an equals sign instead of less than

Step-by-step explanation:

get r on the same side

35r+35r<40

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Definition for equations

MissTica

Here’s your definition

3 0

4 years ago

The equation 5x - 7(x-1) = ax+b has exactly one solution.

Dimas [21]

Answer:

a = -2 and b = 7

Step-by-step explanation:

We need to solve for the value of "a" and "b".

We need to distribute and make the left side of the equation same form as the right side of the equation and match the coefficients, simple.

We will use the distributive property shown below to expand the left side and simplify.

Distributive Property: a(b-c) = ab - ac

Now, simplifying left hand side:

5x - 7(x - 1)

= 5x -7(x) -7(-1)

= 5x -7x +7

= -2x + 7

The right hand side is "ax + b".

If we match left-hand side and right-hand side, we see that:

a = -2

and

b = 7

THese are the only solution.

8 0

3 years ago

Explain the difference between an equation, like x=5, and an inequality, like x_> 5.

andrew11 [14]

X=5 is a definite answer and one solution. While X greater than OR equal to 5 means that it could be 5 AND anything above 5, which gives multiple of choices for solutions. (I believe this write but it’s been awhile since I did algebra stuff)

7 0

4 years ago

Harold uses the binomial theorem to expand the binomial (3x^5 - 1/9y^3)^4

riadik2000 [5.3K]

<h3>The complete question:</h3>

Harold uses the binomial theorem to expand the binomial $(3x^5 -\dfrac{1}{9}y^3)^4$

(a) What is the sum in summation notation that he uses to express the expansion?

(b) Write the simplified terms of the expansion.

Answer:

(a). $(3x^5 -\dfrac{1}{9}y^3)^4=$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}( -\dfrac{1}{9}y^3)^k $$$

(b). $(3x^5 -\dfrac{1}{9}y^3)^4=81x^{20}-12x^{15}y^3+\dfrac{2x^{10}y^6}{3}-\dfrac{4x^5y^9}{243}+\frac{y^{12}}{6561}$

Step-by-step explanation:

(a).

The binomial theorem says

$(x+y)^n=$$\sum_{k=0}^{n} \binom{n}{k}x^{n-k}y^k $$$

For our binomial this gives

$\boxed{(3x^5 -\dfrac{1}{9}y^3)^4=$$\sum_{k=0}^{n} \binom{4}{k}x^{4-k}y^k $$}$

(b).

We simplify the terms of the expansion and get:

$$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}y^k $$= \binom{4}{0}(3x^5)^{4-0}(-\dfrac{1}{9}y^3 )^0+\binom{4}{1}(3x^5)^{4-1}(-\dfrac{1}{9}y^3 )^1+\\\\\binom{4}{2}(3x^5)^{4-2}(-\dfrac{1}{9}y^3 )^2+\binom{4}{3}(3x^5)^{4-3}(-\dfrac{1}{9}y^3 )^3+\binom{4}{4}(3x^5)^{4-4}(-\dfrac{1}{9}y^3 )^4$

$$$\sum_{k=0}^{n} \binom{4}{k}(3x^5)^{4-k}(-\frac{1}{9}y^3 )^k $$= (3x^5)^{4}+4(3x^5)^{3}(-\frac{1}{9}y^3 )+6(3x^5)^{2}(-\frac{1}{9}y^3 )^2+\\\\4(3x^5)(-\frac{1}{9}y^3 )^3+(-\frac{1}{9}y^3 )^4$

$\boxed{(3x^5 -\dfrac{1}{9}y^3)^4=81x^{20}-12x^{15}y^3+\dfrac{2x^{10}y^6}{3}-\dfrac{4x^5y^9}{243}+\frac{y^{12}}{6561} }$

3 0

3 years ago

Please help me. thank you so much

Sergio [31]

Answer:

7.5

Step-by-step explanation:

So the constant proportionality is easy, it is the depindent veriable (how much it cost) divided by the independent veriable (how much fabric you have).

Put simply you know how much it will cost if you know how many yards you have. so if i have 2 yards i know it cost 15 dolars.

We could make a simple algebraic expretion that describes the proportionality.

C⁒y=7.5

So 7.5 is our constant, so if you know the cost or how many yards we have we always know what the other is.

So if i had 6.7 yards how much would it cost.

It would cost $50.25, what i did was i multiplied 6.7*7.5(our constant) and we got out cost c. Just to dubble check we can plug it in;

50.25⁒6.7 does=7.5 so it works.

8 0

3 years ago