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Alekssandra [29.7K]

3 years ago

11

Please help with question 2

1 answer:

Rufina [12.5K]3 years ago

6 0

I would distribute first.

$-5-3x\geq 2(10+2x)+3$

$-5-3x\geq 20+4x+3$

$-5-3x\geq 4x+23$

$7x \leq -28$

$x\leq -4$

Hope this helps.

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Please help 10 points !!

enyata [817]

The will intersect at a point with a positive x coordinate.

We can tell this because they actually already have a shared space on the graph. If you plot the 3 points of g(x) given, you'll see that f(x) and g(x) both share the coordinate (1, 3). As a result, we know that they do intersect and it is where x (1) is a positive number.

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3 years ago

Factor: d2 + 16dm + 64m2

lutik1710 [3]

Answer:

$(d + 8m)^2$

Step-by-step explanation:

$d^2 + 16dm + 64 m^2 = (d + 8m)^2$

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3 years ago

Read 2 more answers

You are creating an open top box with a piece of cardboard that is 16 x 30“. What size of square should be cut out of each corne

Arada [10]

Answer:

$\frac{10}{3} \ inches$ of square should be cut out of each corner to create a box with the largest volume.

Step-by-step explanation:

Given: Dimension of cardboard= 16 x 30“.

As per the dimension given, we know Lenght is 30 inches and width is 16 inches. Also the cardboard has 4 corners which should be cut out.

Lets assume the cut out size of each corner be "x".

∴ Size of cardboard after 4 corner will be cut out is:

Length (l)= $30-2x$

Width (w)= $16-2x$

Height (h)= $x$

Now, finding the volume of box after 4 corner been cut out.

Formula; Volume (v)= $l\times w\times h$

Volume(v)= $(30-2x)\times (16-2x)\times x$

Using distributive property of multiplication

⇒ Volume(v)= $4x^{3} -92x^{2} +480x$

Next using differentiative method to find box largest volume, we will have $\frac{dv}{dx}= 0$

$\frac{d (4x^{3} -92x^{2} +480x)}{dx} = \frac{dv}{dx}$

Differentiating the value

⇒ $\frac{dv}{dx} = 12x^{2} -184x+480$

taking out 12 as common in the equation and subtituting the value.

⇒ $0= 12(x^{2} -\frac{46x}{3} +40)$

solving quadratic equation inside the parenthesis.

⇒ $12(x^{2} -12x-\frac{10x}{x} +40)$ =0

Dividing 12 on both side

⇒ $[x(x-12)-\frac{10}{3} (x-12)]$ = 0

We can again take common as (x-12).

⇒ $x(x-12)[x-\frac{10}{3} ]$ =0

∴ $(x-\frac{10}{3} ) (x-12)= 0$

We have two value for x, which is $12 and \frac{10}{3}$

12 is invalid as, w= $(16-2x)= 16-2\times 12$

∴ 24 inches can not be cut out of 16 inches width.

Hence, the cut out size from cardboard is $\frac{10}{3}\ inches$

Now, subtituting the value of x to find volume of the box.

Volume(v)= $(30-2x)\times (16-2x)\times x$

⇒ Volume(v)= $(30-2\times \frac{10}{3} )\times (16-2\times \frac{10}{3})\times \frac{10}{3}$

⇒ Volume(v)= $(30-\frac{20}{3} ) (16-\frac{20}{3}) (\frac{10}{3} )$

∴ Volume(v)= 725.93 inches³

6 0

3 years ago

A and B are two events. Let P(A)=0.5 , P(B)=0.9 and P(A and B)=0.15 .

Nana76 [90]

Answer:

option-C

Step-by-step explanation:

we are given

Let P(A)=0.5

P(B)=0.9

P(A and B)=0.15

we know that

$P(A|B)=\frac{P(Aand B)}{P(B)}$

now, we can plug values

$P(A|B)=\frac{0.15}{0.9}$

$P(A|B)=0.16666$

but we have

P(A)=0.5

we can see that both are not equal

$P(A|B)\neq P(A)$

so, A and B are not independent

so, option-C........Answer

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3 years ago

Find the vertex focus and directrix of (x-2)^2=-8(y+3)

tatuchka [14]

Answer:

Step-by-step explanation:

the directrix is y=-1

I don't know what the vertex focus is.

6 0

3 years ago