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2 years ago

Which pair of expressions has the same value?

Mathematics

1 answer:

Alex787 [66]2 years ago

6 0

<h3>Option A) </h3>

Assuming that (-2)(-7) and 4 + (-18) are equal.

⇒ (-2)(-7) = 4 + (-18)

<u>Using the property [-x × -y = x × y = xy]:</u>

⇒ (-2)(-7) = 4 + (-18)
⇒ (2)(7) = 4 + (-18)

<u>Using the property [x + (-a) = x - a]:</u>

⇒ (2)(7) = 4 + (-18)
⇒ (2)(7) = 4 - 18
⇒ 14 = -14 (False)

<h3 /><h3>Option B) </h3>

Assuming that (2)(7) and 4 + 18 are equal.

⇒ (2)(7) = 4 + 18
⇒ 14 = 22 (False)

<h3>Option C) </h3>

Assuming that (–2)(7) and 18 + (–4) are equal.

⇒ (-2)(7) = 18 + (-4)

<u>Using the property [-x × y = -xy]:</u>

⇒ (-2)(7) = 18 + (-4)
⇒ (-)(2)(7) = 18 + (-4)
⇒ -14 = 18 + (-4)

<u>Using the property [x + (-a) = x - a]:</u>

⇒ -14 = 18 + (-4)
⇒ -14 = 18 - 4
⇒ -14 = 14 (False)

<h3>Option D)</h3>

Assuming that (2)(-7) and 4 - 18 are equal.

⇒ (2)(-7) = 4 - 18

<u>Using the property [-x × y = -xy]:</u>

⇒ (-)(2)(7) = 4 - 18
⇒ -14 = 4 - 18
⇒ -14 = -14 (True)

Therefore, Option D is correct.

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Chris has 7/8 yards of purple ribbon and one whole one over 6 yards of ribbon Chris has a total of three holes to over 3 yards o

MaRussiya [10]

Complete question :

Chris has 7/8 yards of purple ribbon and 1 1/6 yards of green ribbon. Chris has a total of 3 2/3 yards of ribbon. How many yards of Chris's ribbon are neither purple nor green.

Answer:

1.625 yards

Step-by-step explanation:

Purple ribbon = 7/8 yards

Green ribbon = 1 1/6 yards = 7/6 yards

Total ribbon = 3 2/3 yards = 11/3 yards

Ribbon that is neither purple nor green :

Total ribbon - (green + purple ribbon)

7/8 - (7/6 + 7/8)

11/3 - (28 + 21) / 24

11/3 - 49/24

= 1.625 yards

8 0

3 years ago

Suppose you need to know an equation of the tangent plane to a surface S at the point P(4, 1, 3). You don't have an equation for

Harlamova29_29 [7]

Answer:

-30(x-4) + 29 (y-1) -12(z-3) = 0

Step-by-step explanation:

You can find the perpendicular vector to both curves using the cross product between them, and that will give you all the information you need to find the equation of the tangent plane to the surface S.

Let's find the parameter of each curve for the specific point.

For the first curve notice that

$r( 0 ) = (4,1,3)$

And for the second curve notice that

$r2(1) = (4,1,3)$

Thus for the first curve we reach our point at $t=0,$ and for the second curve we reach our point at $u = 1 .$

Then we compute the tangent vector to our curves, and it would be given by the derivative so

$r1'(t) = (2,-2t,-5+2t)$ and at $t = 0$ we have that

$r1'(0) = (2,0,-5)$

Similarly

$r2'(1)=(3+2(1) , 6(1)^2 ,2) = (5,6,2)$

The the cross product between the two vectors would be

$(5,6,2) \times (2,0,-5) = (-30,29,-12)$

Since (-30,29,-12) would be the perpendicular vector to the tangent plane and (4,1,3) would be a point of the tangent then we would have that the equation of the tangent plane is given by

-30(x-4) + 29 (y-1) -12(z-3) = 0

4 0

3 years ago

What is the simplified form of the following expression? 4/7^3

timofeeve [1]

If your question is :
$\frac{4}{7^3}$

Then the answer is:
$\frac{4}{7*7*7} = \frac{4}{343}$

If your question is:
$(\frac{4}{7}) ^{3}$

Then the answer is:
$\frac{4*4*4}{7*7*7} = \frac{64}{343}$

6 0

3 years ago

Read 2 more answers

A quiz-show contestant is presented with two questions, question 1 and question 2, and she can choose which question to answer f

Mrrafil [7]

Answer:

The contestant should try and answer question 2 first to maximize the expected reward.

Step-by-step explanation:

Let the probability of getting question 1 right = P(A) = 0.60

Probability of not getting question 1 = P(A') = 1 - P(A) = 1 - 0.60 = 0.40

Let the probability of getting question 2 right be = P(B) = 0.80

Probability of not getting question 2 = P(B') = 1 - P(B) = 1 - 0.80 = 0.20

To obtain the better option using the expected value method.

E(X) = Σ xᵢpᵢ

where pᵢ = each probability.

xᵢ = cash reward for each probability.

There are two ways to go about this.

Approach 1

If the contestant attempts question 1 first.

The possible probabilities include

1) The contestant misses the question 1 and cannot answer question 2 = P(A') = 0.40; cash reward associated = $0

2) The contestant gets the question 1 and misses question 2 = P(A n B') = P(A) × P(B') = 0.6 × 0.2 = 0.12; cash reward associated with this probability = $200

3) The contestant gets the question 1 and gets the question 2 too = P(A n B) = P(A) × P(B) = 0.6 × 0.8 = 0.48; cash reward associated with this probability = $300

Expected reward for this approach

E(X) = (0.4×0) + (0.12×200) + (0.48×300) = $168

Approach 2

If the contestant attempts question 2 first.

The possible probabilities include

1) The contestant misses the question 2 and cannot answer question 1 = P(B') = 0.20; cash reward associated = $0

2) The contestant gets the question 2 and misses question 1 = P(A' n B) = P(A') × P(B) = 0.4 × 0.8 = 0.32; cash reward associated with this probability = $100

3) The contestant gets the question 2 and gets the question 1 too = P(A n B) = P(A) × P(B) = 0.6 × 0.8 = 0.48; cash reward associated with this probability = $300

Expected reward for this approach

E(X) = (0.2×0) + (0.32×100) + (0.48×300) = $176

Approach 2 is the better approach to follow as it has a higher expected reward.

The contestant should try and answer question 2 first to maximize the expected reward.

Hope this helps!!!

3 0

3 years ago

What is the value of x?<br><br> Enter your answer in the box.<br><br> x =

andreev551 [17]

The two angles form a straight line which equals 180 degrees:

10x-20 + 6x + 8 = 180

Combine like terms:

16x -12 = 180

Add 12 to both sides:

16x = 192

Divide both sides by 16:

X = 192/16

X = 12

7 0

3 years ago