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3 years ago

Rewrite 6(40-10) using distributive property of multiplication over subtract

Mathematics

1 answer:

Stells [14]3 years ago

4 0

Answer:

240-60

Step-by-step explanation:

Multiply both numbers inside the parenthesis by what's on the outside

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Please help me with these please.

Charra [1.4K]

6. Answer: y = 5x - 11

Step-by-step explanation:

Parallel means "same slope". y = 5x - 2 is in the form y = mx + b,

so the slope (m) = 5

Next, input the point (x₁, y₁ = 2, -1) and slope (m = 5) into the Point-Slope formula:

y - y₁ = m(x - x₁)

y - (-1) = 5(x - 2)

y + 1 = 5x - 10

y = 5x - 11

*******************************************************************

7. Answer: $\bold{y = \dfrac{1}{3}x + 4}$

Step-by-step explanation:

Perpendicular means "opposite reciprocal slope". y = -3x + 7 is in the form y = mx + b, so slope (m) = -3 ⇒ m⊥ = $\frac{1}{3}$

Next, input the point (x₁, y₁ = 3, 5) and slope (m = $\frac{1}{3}$ ) into the Point-Slope formula:

y - y₁ = m(x - x₁)

$y - 5=\dfrac{1}{3}(x - 3)$

$y - 5 =\dfrac{1}{3}x - 1$

$y=\dfrac{1}{3}x + 4$

8 0

3 years ago

Determine the solution of the system. Show your work. Y = 5x – 9 Y = 2x + 6

snow_tiger [21]

Both define y, so they are equivalent.

5x-9=2x+6
3x-9=6
3x=15
x=5

Then plug in x into any of the equations
y=2(5)+6
y=10+6
y=16

Final answer: (5,16)

5 0

3 years ago

Read 2 more answers

In the following distribution, P(X<2) = 0.35, and expected value is 1.9

Flauer [41]

Solution :

We have :

X 0 1 2 3 4

P(X) 0.10 A 0.35 B C

a). P(X < 2) = 0.35

P(X < 2) = P(X = 0) + P(X = 1) = 0.35

⇒ 0.10 + A = 0.35

⇒ A = 0.25

So the value of A is 0.25

b). The total probability = 1

So ,

0.10 + A + 0.35 + B + C = 1

0.10 + 0.25 + 0.35 + B + C = 1

B + C = 1 - 0.70

B + C = 0.30 ......(i)

We have the expected value = 1.9

So, $\sum X P(X) = 19$ for x = 0, 1, 2, 3, 4

⇒ (0 x 0.10) + (1 x 0.25) + (2 x 0.35) + (3 x B) + (4 x C) = 1.9

⇒ 0 + 0.25 + 0.70 + 3B + 4C = 1.9

⇒ 3B + 4C = 1.9 - 0.95

⇒ 3B + 4C = 0.95 ...................(ii)

From (i), we take the value of B = 0.30 - C and substitute it in the equation (i), we get,

⇒ 3( 0.30 - C) + 4C = 0.95

⇒ 0.90 - 3C + 4C = 0.95

⇒ C = 0.95 - 0.90

= 0.05

Now substituting the value of C = 0.05 in (ii), we get,

⇒ B = 0.05 = 0.30

⇒ B = 0.25

c). The value of C is 0.05

4 0

3 years ago

Use complete sentences to describe why for any set B, that the empty set would be a subset of it.

ella [17]

Because empty set has no element which automatically make it a subset of every set.

Thank you for posting your question here at brainly. I hope the answer will help you. Feel free to ask more questions here.

6 0

4 years ago

Read 2 more answers

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