All categories

2 years ago

9. What is the coefficient of y^2? in the expansion of (x + y)^2??

Mathematics

1 answer:

klemol [59]2 years ago

3 0

Answer:

The coefficient of y² will be 1, which we can see when we expand the expression:

(x + y)²

= (x +y)(x + y)

= x² + xy + xy + y²

= x² + 2xy + y²

You might be interested in

Based only on the information given in the diagram, which congruence

romanna [79]

<h3>1 Answer: Choice D) SAS</h3>

=================================================

Explanation:

LA stands for Leg Angle. More specifically, the angle is an acute angle. This theorem only works for right triangles. We see that ED = LK which is one pair of congruent leg segments. So that takes care of the L part of LA. However, we don't know anything about the acute angles. We don't know if angle E = angle L, or if angle F = angle M, or something along those lines. We need angle markers to tell us or not.

In short, we only have half the info needed for LA, so we must cross choice A off the list.

----------------

HA stands for hypotenuse angle, or hypotenuse acute angle, and this rule only applies for right triangles. We don't know anything about the hypotenuse lengths if they are the same or not.

Similar to choice A, we don't know anything about the acute angles either.

Those two facts mean we must cross off choice B.

----------------

AAS stands for Angle Angle Side. The order is important because the side is not between the angles. The diagram only shows one pair of angles that are congruent to one another. That pair being the 90 degree angles indicated with the square marker. We don't have another pair of angles, so we cannot use AAS.

Cross choice C off the list.

-----------------

We can use SAS because we have two pairs of congruent sides and one pair of congruent angles.

The congruent sides are

ED = LK (double tickmarks)
DF = KM (single tickmarks)

That takes care of the two "S"s of "SAS". The "A" would be those two right angles which are congruent to one another. The angles are between the congruent sides which is important. Recall that SSA is not a valid congruence theorem.

So that's why choice D is the only answer.

-----------------

Side note: We could use the LL theorem, where L stands for leg, since we are given two pairs of congruent legs for each triangle. Like LA and HA, this only applies to right triangles. LL is a special case of SAS. However, LL isn't listed so we'll just be sticking with SAS as the only answer.

8 0

3 years ago

Help please help!! my grade is down

lisov135 [29]

plug in -2 for x

7*-2 -10 = -24

7 0

2 years ago

A poll asks shoppers at the mall how many cups of water they typically drink in a day. The results of the poll are listed below.

juin [17]

Answer:

D 9.5

Step-by-step explanation:

Write data in increasing order.

3, 5, 5, 6, 6, 6, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 10, 10, 10, 10, 11

Find the median

Median is 8

Lower half of the data is : 3, 5, 5, 6, 6, 6, 7, 7, 8, 8,

First quartile is the median of the lower half of the data=6+6 /2 =6

Upper half of the data is: 8, 8, 8, 9, 9, 10, 10, 10, 10, 11

The Third quartile is the median of the upper half=9+10 / 2 = 9.5

<u />

3 0

3 years ago

Read 2 more answers

Determine the dimensions of a rectangular solid (with square base) with a maximum volume if its surface are is 337.5 square cent

juin [17]

The question is asking to determine the dimension of a rectangular solid with a maximum volume if its surface area is 337.5 square centimeters and base on my further computation, I would say that the answer would be x= sqrt 56.25 and y = 7.5 and having a maximum volume of 421.875. I hope this would help

7 0

2 years ago

Does anyone understand this?. I also have to show my work.

snow_lady [41]

Answer:

Ans A). The graph is shown.

Ans B). 18.3333 C temperature when F is 65 temperature

Ans C). 32 F when the line crosses the horizontal axis

Ans D). Slope of line C= $\frac{5}{9}(F -32)$ is $\frac{5}{9}$

Step-by-step explanation:

Given equation is C= $\frac{5}{9}(F -32)$

Ans A).

For the table,

Take the four value of F as 32,41,50,59.

For F = 32.

The value of C is

C= $\frac{5}{9}(F -32)$

C= $\frac{5}{9}(32 -32)$

C=0.

For F = 41.

The value of C is

C= $\frac{5}{9}(F -32)$

C= $\frac{5}{9}(41 -32)$

C=05

For F = 50.

The value of C is

C= $\frac{5}{9}(F -32)$

C= $\frac{5}{9}(50 -32)$

C=10

For F = 59.

The value of C is

C= $\frac{5}{9}(F -32)$

C= $\frac{5}{9}(32 -32)$

C=15

<em>Note: The figure shows a graph of given equation with points.</em>

Ans B). Estimate temperature in C when the temperature in F is 65

For F = 65.

The value of C is

C= $\frac{5}{9}(F -32)$

C= $\frac{5}{9}(32 -32)$

Ans C). At what temperature, graph lien cross the horizontal axis

When the line crosses the horizontal axis, C=0

Therefore,

C= $\frac{5}{9}(F -32)$

0= $\frac{5}{9}(F -32)$

0= $(F -32)$

F=32 Temperature.

Ans D). Slope of the line C= $\frac{5}{9}(F -32)$

The slope of line is given by s= $\frac{Y1-Y2}{X1-X2}$

Take points from the table of answer A.

let (32,0) and (41,5) using for slope.

s= $\frac{Y1-Y2}{X1-X2}$

s= $\frac{0-5}{32-41}$

s= $\frac{5}{9}$

Slope of line C= $\frac{5}{9}(F -32)$ is $\frac{5}{9}$

7 0

3 years ago