How to expand (x+3)( x-2), using the F.O.I.L method?

Let's manipulate the expression a little bit and see what we come up with: we have

[tex]\dfrac{x+z}{y+z}>\dfrac{x}{y} \iff \dfrac{x+z}{y+z}-\dfrac{x}{y}>0 \iff \dfrac{y(x+z)-x(y+z)}{y(y+z)}>0[/tex]

We can simplify the fraction as

[tex]\dfrac{xy+yz-xy-xz}{y(y+z)}=\dfrac{yz-xz}{y(y+z)}=\dfrac{z(y-x)}{y(y+z)}[/tex]

Since both [tex]y[/tex] and [tex]z[/tex] are positive, their sum will be positive as well. In other words, we can rewrite the fraction as

[tex]\underbrace{z}_{>0}\cdot\underbrace{\dfrac{1}{y}}_{>0}\cdot\underbrace{\dfrac{1}{y+z}}_{>0}\cdot (y-x)[/tex]

So, the sign of this fraction depends on the sign of [tex]y-x[/tex]. If its positive, then the whole fraction is positive (product of 4 positive factors). If it's negative, then the whole fraction is negative (product of 3 positive factors and a negative one).

In other words, we arrived to the desired conclusion:

[tex]\dfrac{x+z}{y+z}>\dfrac{x}{y}\iff y-x>0 \iff y>x[/tex]

Answer:

show the a pic

Step-by-step explanation:

Answer: The parabola is wider than the parent function

Step-by-step explanation:

If "a" is a fraction less than one, then the parabola becomes wider.

See graph (attached)

Answer:

12

Step-by-step explanation:

Each song should be 12 minute long.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value.

The band will play for 60 minutes.

If they want to play 5 songs in a duration of 60 minutes, we have to divide the total amount of minutes by how many songs they have to play.

Using the formula,

Total Duration / Total Songs = Duration Per Song

60 / 5 = 12

Therefore, Each song should be 12 minute long.

Learn more about the unitary method;

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Answer:

i cant answer that i'm only in 8th

Answer:  A

D: Divide each length of the scale drawing by the scale factor to find the lengths of the walls.

Answer:

Step-by-step explanation:

Answer:

2x+2(x+5)) = 24

Step-by-step explanation:

2x+ 2(x+5) = 24

x is represented by the shorter side. Multiply by 2 because of the 2 sides. For the longer side, since it is 5m longer than the shorter side, you have to write (x+5). Multiply by 2 because of the 2 sides. Finally, add them both together since it is the area and set it equal to 24.

We can write this as:

3 books / 1 week

This tells us that Sanjit reads 3 books per week.

Let's say he read for 3 weeks, we would multiply to find the number of books he read.

3 * 3 = 9 books

So, Sanjit can read 3 books in 1 week.

Best of Luck!

Answer:

3 books/1 week

Step-by-step explanation:

3 books

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

1 week

Answer:

44t + 11

Step-by-step explanation:

11(4t + 1)

Distribute 11 amongst the values inside the parenthesis

11(4t) + 11(1)

Multiply

44t + 11

Hope this helps :)

Answer:

[tex]44t + 11[/tex]

Step-by-step explanation:

[tex]11(4t + 1) \\ = 44t + 11[/tex]

Answer: [tex]1590cm^3[/tex]

Step-by-step explanation:

[tex]V=\frac{3\sqrt{3} }{2}a^2h[/tex]

a = base

h = height

[tex]V=\frac{3\sqrt{3} }{2}(6cm)^2(17cm)[/tex]

Solve the parentheses squared first.

[tex]V=\frac{3\sqrt{3} }{2}(36cm^2)(17cm)[/tex]

2 and 36 can be simplied

2/2=1

36/2=18

[tex]V=3\sqrt{3}(18cm^2)(17cm)[/tex]

[tex]V=3\sqrt{3}(306cm^3)\\ V=1590.02cm^3[/tex]

Rounded to the nearest whole number... [tex]1590cm^3[/tex]

Answer: 8

Step-by-step explanation:

Ella tiene que bajar los 6 pisos, mas 2.

6+2=8

Answer:

(7 x 5) + (7 X 3) = 7 X 8 or (7 x 4) + (7 X 4) = 7 X 8

Step-by-step explanation:

I think your question is missed of key information, allow me to add in and hope it will fit the original one.  

Please have a look at the attached photo.  

My answer:

=> the total cost = the total number of people * the ticket cost each

= 7 X 8

Hence, he can use this way to break apart the array to find the product:

(7 x 5) + (7 X 3) = 7 X 8 or (7 x 4) + (7 X 4) = 7 X 8

Hope it will find you well.

Answer:

32 units.

Step-by-step explanation:

look up a picture of a 306090 triangle, it will make sense :)

Answer:

32

Step-by-step explanation:

cos 30 = [tex]\frac{\sqrt{3} }{2}[/tex]

[tex]\frac{\sqrt{3} }{2}[/tex] = 16[tex]\sqrt{3}[/tex] / n

n = 16[tex]\sqrt{3}[/tex] * [tex]\frac{2}\sqrt{3} }[/tex]

n = 32 units

Answer:

square root of 30 is 30

because it comes in a point =5.477225575

Answer:

8N-2=33+N

Step-by-step explanation:

Answer:

The volume is 3150ft³

Step-by-step explanation:

This problem bothers on the mensuration of solid shapes, cuboid

Given data

Area =450 ft²

Height h =7ft

We know that the volume of a cuboid

Volume = length x width x height

Volume =lbh

Volume = area x height

Volume = 450*7= 3150ft³

Answer:

36 times larger.

Step-by-step explanation:

V= [tex]\pi *r^{2}*\frac{h}{3}[/tex] is the original volume of a cone formula.

If the radius is multiplied by 6 the new formula is:

V= [tex]\pi *(6x)^{2} * \frac{4}{3}[/tex]

Which is simplified to:

V= [tex]\pi *36r^2*\frac{h}{3}[/tex]

The only difference between the simplified formula and the original is the *36 so the new volume is 36 times larger when the radius is multiplied by 6.

Answer: Infinite solutions

Step-by-step explanation:

[tex]8-(2x-9)=17-2x[/tex]

Begin by distributing the negative into the parenthesis.

[tex]8-2x+9=17-2x[/tex]

Combine like terms;

[tex]17-2x=17-2x[/tex]

Subtract 17

[tex]-2x=17-17-2x[/tex]

[tex]-2x=-2x[/tex]

Add 2x

[tex]-2x+2x=0\\0=0[/tex]

Equation: 8 - (2x - 9) = 17 - 2x

First, we distribute the - sign.

8 -2x + 9 = 17 - 2x

Then, we combine like terms if there any on both sides.

17 - 2x = 17 - 2x

Now, we can see the equations are equal to each other.

However, we can go a step further and solve for x.

17 - 2x = 17 - 2x

Subtract 17 from both sides.

-2x = -2x

Divide both sides by -2.

x = x

Therefore, x has no value or is 0.

Answer:Perimeter, 50ft

Step-by-step explanation:since it is around the answer is 50 ft

The measure of arc HD, which represents the arc between points H and D, is also 102 degrees.

We have,

In the given figure, we have a circle with points P, K, L, H, and D on it. Secant RL and secant KH intersect inside the circle, forming an angle with a measure of 92 degrees.

Secant DR and secant LR intersect outside the circle at point R, forming an angle DRL with a measure of 38 degrees.

The intercepted arc closest to angle DRL has a measure of 18 degrees.

Since secant RL intersects the circle at some point, we can consider the arc between that point and point K.

The measure of this arc is given as 102 degrees.

Therefore,

The measure of arc HD, which represents the arc between points H and D, is also 102 degrees.

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Answer:

3x+2

Step-by-step explanation:

i had a test with the same question, i promise its right :)

Answer:

( w-7) (w+5)

Step-by-step explanation:

w^2 -2w - 35

What 2 numbers multiply to -35 and add to -2

-7*5 = -35

-7+5 = -2

( w-7) (w+5)

Answer:

(w + 5) • (w - 7)  = A

Step-by-step explanation:

factoring  w2-2w-35  

The first term is,  w2  its coefficient is  1 .

The middle term is,  -2w  its coefficient is  -2 .

The last term, "the constant", is  -35  

Step-1 : Multiply the coefficient of the first term by the constant   1 • -35 = -35  

Step-2 : Find two factors of  -35  whose sum equals the coefficient of the middle term, which is   -2 .

     -35    +    1    =    -34  

     -7    +    5    =    -2    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  5  

                    w2 - 7w + 5w - 35

Step-4 : Add up the first 2 terms, pulling out like factors :

                   w • (w-7)

             Add up the last 2 terms, pulling out common factors :

                   5 • (w-7)

Step-5 : Add up the four terms of step 4 :

                   (w+5)  •  (w-7)

          (w + 5) • (w - 7)  = 0

Answer:

(1, eᵗ)

Step-by-step explanation:

r(t) = (t, eᵗ)

v(t) = dr/dt

v(t) = (1, eᵗ)

Answer:

[tex]\frac{7}{16}[/tex]

Since there are 16 pastries in total, and 7 of them are chocolate, this will become your probability.

So, since the total is 16, this will be the denominator, and the 7 will be the numerator.

So, it will be [tex]\frac{7}{16}[/tex]

Answer:

The least number of package of cap required is 15, while that of shirt is 9

Step-by-step explanation:

Total number of members = 45

The cap comes in package of 3

The shirt comes in package of 5

The least number of the package of caps they need to order is =?

Since they're 45 in numbers, we can divide 45 by 3 to know the total number of package required to go round.

Number of package of caps = 45 / 3

Number of package of caps = 15

We can also go ahead and find the number of package for shirt required by using the same method, only this time we'll divide it by 5 instead of 3

Number of package for shirt = 45 / 5

Number of package for shirt = 9

Therefore, the least number of package of caps required is 15 while that of shirt is 9

Step-by-step explanation:

The three numbers are 23 25 and 27

23 + 25 + 27 = 75

The smallest number is 23

Answer:

6

Step-by-step explanation:

Sounds like a Bayes Theorem problem.

Events:

F: Roger makes his first serve.  We'll write ~F for "not F".

P(F) = .63

P(~F) = 1 - .63 = .37

W: Roger wins the point.  We don't know P(W) but we are given

P(W | F) = .78

P(W | ~F) = .57

We're asked for

P(~F | W)

The basic conditional probability theorem is

P(~F and W) = P(~F | W) P(W) = P(W | ~F) P(~F)

P(~F | W) = ( P(W | ~F) P(~F) ) / P(W)

We write

P(W) =  P(W | F) P(F) +  P(W | ~F) P(~F)

Substituting gives Bayes' Theorem:

P(~F | W) = ( P(W | ~F) P(~F) ) / ( P(W | F) P(F) +  P(W | ~F) P(~F) )

We know all the parts so we substitute,

P(~F|W) = ( .57(.37) ) / (.78(.63) + .57(.37) ) = 0.30029901751388294

Let's call that 30%

Answer: 30%

Answer:

0.3

Step-by-step explanation:

We need to reverse this because we only know the outcome. P(A|B) = P(B|A) * P(A) / P(B), so P(B|A) is B given that A happens, P(A) in this case is the probability that he missed the first serve. P(B) is the probability of winning the point. P(B) = P(B|A') * P(A') + P(B|A) * P(A), which means P(B) is the probability  of the point scored given that the serve was made multiplied by the probability of the serve being made plus the probability of B given that serve is missed multiplied by the probability that the serve is missed. This is 57% * 37% + 78% * 63%=0.21+0.49=0.7. So P(B)=0.7. P(B|A)*P(A)/P(B) would be 57% * 37% / 70% = 0.3. The probability that Federer missed his first serve given that he scored the point is 0.3.

Answer:

D.) 0.7+0.4−0.2=0.9