Where do planes PRS and QRST intersect?

By the binomial theorem,

[tex]\displaystyle \left(x^2-\frac1x\right)^6 = \sum_{k=0}^6 \binom 6k (x^2)^{6-k} \left(-\frac1x\right)^k = \sum_{k=0}^6 \binom 6k (-1)^k x^{12-3k}[/tex]

I assume you meant to say "independent", not "indecent", meaning we're looking for the constant term in the expansion. This happens for k such that

12 - 3k = 0   ===>   3k = 12   ===>   k = 4

which corresponds to the constant coefficient

[tex]\dbinom 64 (-1)^4 = \dfrac{6!}{4!(6-4)!} = \boxed{15}[/tex]

Answer:

AB = 21

Step-by-step explanation:

Tales' theorem

[tex]\frac{12}{14} =\frac{18}{AB}[/tex]

[tex]AB=\frac{(14)(18)}{12}[/tex]

[tex]AB=21[/tex]

Hope this helps

(i)Given that:

AE || BD

AB = ? [Let AB be x]

BC = 3

ED = 12

DC = 4

We know that

By Basic Proportionality Theorem,

AB/BC = ED/DC

On substituting these values in the above formula

⇛ AB / 3 = 12 / 4

On applying cross multiplication then

⇛ x(4) = (12)3

⇛ 4x = 36

Shift the number 4 from LHS to RHS.

⇛ x = 36÷4

⇛ x = 36/4

Therefore, AB = 9

Answer: The value of AB for the given problem is 9.

Similarly,

(ii) Given that:

EB || DC

AE = 14

ED = 12

AB = ? [Let AB be X]

BC = 18

We know that

By Basic Proportionality Theorem,

AE / ED = AB / BC

On substituting these values in the above formula

⇛ 14 / 12 = x / 18

On applying cross multiplication then

⇛ 14(18) = (12)x

⇛ 252 = 12x

Shift the number 252 from LHS to RHS.

⇛ X = 256÷12

⇛ X = 21

Therefore, AB = 21

Answer: The value of AB for the given problem is 21

Additional comment:

Basic Proportionality Theorem

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The measure of angle BAC is 20 degrees

The angle on a straight line is 180 degrees.

There are 9 equal sections on the straight line.

This means that the measure of each section is:

Each section = 180/9

Evaluate

Each section = 20

So, we have:

BAC = 20 degrees

Hence, the measure of angle BAC is 20 degrees

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#SPJ2

Answer: It is called a "variable" or sometimes an "unknown". In x + 2 = 7, x is a variable

Answer:

it it went down 16%

Step-by-step explanation:

if you calculate it, 16 out of 19 points is 84%. this means that it went down 16%.

Explanation:

The decrease is 3 since 19-16 = 3. Divide this decrease value by the original count: 3/19 = 0.1579 = 15.79% = 16% approximately

Answer:

Step-by-step explanation:

−4q-(-8p)+10

= -4q + 8p + 10.

(There are no like terms).

Answer:

360 is the answer

Step-by-step explanation:

hi

have a good day

hope it helps you

thank me later

carryonlearing

Answer:

Step-by-step explanation: 2\frac{u^2}{8}u^4=10\frac{u^3}{9}u

Answer:

i am just here for points

Step-by-step explanation:

Answer:

Step-by-step explanation:

When James is twice as old as John, the difference in their ages will be John's age: 10. That is 5 years from now, so John's age now is 10 -5 = 5.

John is 5 years old.

__

3 years ago, John was 2 and James was 12. Their total age at that time was 14.

Answer:

y = 6x+8

Step-by-step explanation:

y = mx+b

y = 6x + b

2 = 6(-1)+b

2 = -6+b

8 = b

y = 6x+8

Answer:

so there are 100 pennies in one dollar so

100*1000000=100000000

or 100 million

Hope This Helps!!!

Answer:

q=4v/x

Step-by-step explanation:

Answer:

3rd option

Step-by-step explanation:

The equation of a vertical line parallel to the y- axis is

x = c

where c is the value of the x- coordinates the line passes through

The only equation in this form is option 3

3x - 2 = 0 , as

3x = 2 and

x = [tex]\frac{2}{3}[/tex] ← equation of vertical line

Answer:

Step-by-step explanation:

For x=2, the dimensions are ...

  height = x = 2 inches

  width = 2x² +15 = 2(2²) +15 = 8 +15 = 23 inches

  length = 4x² +5x +3 = (4x +5)x +3 = (4·2 +5)2 +3 = 29 inches

The equation that matches the given points is g(x) = -1.4x + 7.6

The standard form of a linear  equation is expressed as [tex]g(x)=mx + b[/tex]

Using the coordinate points (3, 3.4), (4,2)

[tex]m=\frac{2-3.4}{4-3}\\m=\frac{-1.4}{1}\\m=-1.4[/tex]

Substitute m = -1.4 and the coordinate (4, 2) into the formula:

[tex]2=4(-1.4)+b\\2=-5.6+b\\b=2+5.6\\b=7.6[/tex]

Get the required equation:

[tex]g(x)=mx+b\\g(x)=-1.4x+7.6[/tex]

Hence the equation that matches the given points is g(x) = -1.4x + 7.6

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Answer:

Step-by-step explanation:

The answer is 38 miles

Answer:

they took off 35$

Step-by-step explanation:

hope this helps

Answer:

$35

Step-by-step explanation:

10 divided by 350 = $35

Answer:

Step-by-step explanation:

x + 4y = 8

-x           -x

4y = -x + 8

divide by 4

y= -1/4x + 2

then graph

Answer:

The answer is 15

Step-by-step explanation:

15*3=45-5=40

Answer:

[tex]x=4[/tex]

Step-by-step explanation:

We can solve this question by understanding what is first says. The expression tells us 4 square which is 16 plus to to the power of x and all that divided by two: [tex]16+2^{x} / 2 = 16[/tex]

Now we can solve for x:

1.  [tex]16 + 2^{x} = 32[/tex]

2. [tex]2^{x}=16[/tex]

3. [tex]x=4[/tex]

Lin should aim the ball at 7.8 feet away from point  B

From the question (see attachment), we have the following equivalent ratios:

[tex]AB : BE = DC :CE[/tex]

This is so because triangles ABE and DCE are similar triangles.

Such that:

[tex]BE + CE = 20[/tex]

[tex]AB = 16[/tex]

[tex]DC = 16 + 9 = 25[/tex]

So, we have:

[tex]AB : BE = DC :CE[/tex]

[tex]16 : BE = 25: CE[/tex]

Make CE the subject in [tex]BE + CE = 20[/tex]

[tex]CE=20 - BE[/tex]

Substitute 20 - BE for CE in [tex]16 : BE = 25: CE[/tex]

[tex]16 : BE = 25: 20 - BE[/tex]

Express as ratio

[tex]\frac{16 }{ BE} = \frac{25}{ 20 - BE}[/tex]

Cross multiply

[tex]16(20 - BE) = 25BE[/tex]

Open bracket

[tex]320 - 16BE = 25BE[/tex]

Collect like terms

[tex]25BE + 16BE = 320[/tex]

[tex]41BE = 320[/tex]

Divide both sides by 41

[tex]BE = 7.8[/tex]

Hence, she should aim at 7.8 feet away from point  B

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Answer:You want to make a bank shot. Sketch the path of the cue ball so it will bounce off of the bottom side and knock the yellow stripe 9 ball into the top middle pocket.

Step-by-step explanation:

Answer:

272×620=168,640

Step-by-step explanation:

If koala airlines carries 272 in average then the answer is 168,640

Answer:

Step-by-step explanation:

The answer would be -19

Hope you could get an idea from here.

Doubt clarification - use comment section.

Answer:

−5<n≤2 I think, I don't really understand the question either I'm sorry!!!!

Answer:

number of adult shirts sold (a) = 20

number of youth shirts sold (b) = 10

Step-by-step explanation:

a = number of adult shirts sold

y = number of youth shirts sold

30 = a + y

$324.50 = 11.50a + 9.45y

This is the resulting system of equations from the given information in the problem.

Solve for y in the first equation and then substitute the equation for y into the second equation :

a+y=30 --> y=30-a

324.50 = 11.50a + 9.45(30-a)

Solve for a.

324.50 = 11.50a + 283.5 - 9.45a

41 = 2.05a

a = 20

Now that we have solved for a, we can back substitute into our equation for y and solve.

y=30-(20)

y = 10

CHECK:

(20)+(10) = 30 True

(11.50)(20) + (9.45)(10) = 324.5  True

Answer: 8 or -6

Step-by-step explanation:

x^2 - 2x = 48

x^2 - 2x - 48 = 0

(x-8)(x+6) = 0

x = 8 or -6

Answer:

he can shoot 12 shots in 1minute

Step-by-step explanation:

3minutes = 36 shots

1 minute= 36 divided by 3 which is equal to 12

Answer:

189.52

Step-by-step explanation:

184 x 0.03

5.52

184 + 5.52

189.52

Answer:

184*1.03 = £189.52

Step-by-step explanation: