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3 years ago

Select all of the solutions to the system graphed below.

Mathematics

1 answer:

ra1l [238]3 years ago

3 0

0,-2

4,4

2,0

3,5

Step-by-step explanation:

that was my answer

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Just Monitor your credit report regularly

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3 years ago

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One satellite is scheduled to be launched from Cape Canaveral in Florida, and another launching is scheduled for Vandenberg Air

Lisa [10]

Answer:

$P(A) = 0.45$

$P(B) = 0.32$

Step-by-step explanation:

Given

$P(A) > P(B)$

$P(A\ u\ B) = 0.626$

$P(A\ n\ B) = 0.144$

Required

Find P(A) and P(B)

We have that:

$P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)$ --- (1)

and

$P(A\ n\ B) = P(A) * P(B)$ --- (2)

The equations become:

$P(A\ u\ B) = P(A) + P(B) - P(A\ n\ B)$ --- (1)

$0.626 = P(A) + P(B) - 0.144$

Collect like terms

$P(A) + P(B) = 0.626 + 0.144$

$P(A) + P(B) = 0.770$

Make P(A) the subject

$P(A) = 0.770 - P(B)$

$P(A\ n\ B) = P(A) * P(B)$ --- (2)

$0.144 = P(A) * P(B)$

$P(A) * P(B) = 0.144$

Substitute: $P(A) = 0.770 - P(B)$

$[0.770 - P(B)] * P(B) = 0.144$

Open bracket

$0.770P(B) - P(B)^2 = 0.144$

Represent P(B) with x

$0.770x - x^2 = 0.144$

Rewrite as:

$x^2 - 0.770x + 0.144 = 0$

Expand

$x^2 - 0.45x - 0.32x + 0.144 = 0$

Factorize:

$x[x - 0.45] - 0.32[x - 0.45]= 0$

Factor out x - 0.45

$[x - 0.32][x - 0.45]= 0$

Split

$x - 0.32= 0 \ or\ x - 0.45= 0$

Solve for x

$x = 0.32\ or\ x = 0.45$

Recall that:

$P(B) = x$

So, we have:

$P(B) = 0.32 \ or \ P(B) = 0.45$

Recall that:

$P(A) = 0.770 - P(B)$

So, we have:

$P(A) = 0.770 - 0.32 \ or\ P(A) =0.770 - 0.45$

$P(A) = 0.45 \ or\ P(A) =0.32$

Since:

$P(A) > P(B)$

Then:

$P(A) = 0.45$

$P(B) = 0.32$

6 0

3 years ago

This extreme value problem has a solution with both a maximum value and a minimum value. use lagrange multipliers to find the ex

harina [27]

$L(x,y,z,\lambda)=8x+8y+4z+\lambda(4x^2+4y^2+4z^2-36)$

$L_x=8+8\lambda x=0\implies 1+\lambda x=0$
$L_y=8+8\lambda y=0\implies 1+\lambda y=0$
$L_z=4+8\lambda z=0\implies 1+2\lambda z=0$
$L_\lambda=4x^2+4y^2+4z^2-36=0\implies x^2+y^2+z^2=9$

$yL_x=y+\lambda xy=0$
$xL_y=x+\lambda xy=0$
$\implies yL_x-xL_y=y-x=0\implies y=x$

$2zL_x=2z+2\lambda xz=0$
$xL_z=x+2\lambda xz=0$
$\implies 2zL_x-xL_z=2z-x=0\implies x=2z$

$2zL_y=2z+2\lambda yz=0$
$yL_z=y+2\lambda yz=0$
$\implies 2zL_y-yL_z=2z-y=0\implies y=2z$

$x=y=2z\implies x^2+y^2+z^2=9\iff 4z^2+4z^2+z^2=9z^2=9\implies z=\pm1$

$z=\pm1\implies y=x=\pm2$

So we have two critical points, (2, 2, 1) and (-2, -2, -1), which respectively give a max of 36 and a min of -36.

5 0

3 years ago

The length of a rectangular football field, including both end zones, is 120 yards. The area of the field is 57,600 square feet.

egoroff_w [7]

Answer:

3a.False,the width is 53.33 yards

3b.true, the Length is 120 yards=360 feet

3c.True, width of the field is 160 feet.

3d. True,rea of the field is 6,400 square yards.

Step-by-step explanation:

Hello , I think I can help you with this

to solve this you must know the equivalence between feet and yard, which is

3 feet = 1 yard

Also, the area of a rectangle is the product of its length by its width

Area=length *width

Step 1

convert 120 yards into feet using a rule of three

3 feet = 1 yard

x feet= 120 yards

3/1=x/120

x=(120*3)/1

x=360 feet

120 yards= 360 feet

Step 2

isolate the width from the area´s equation to find out it.

Area=57600 square feet

length=360 feet

Area=length *width

width=Area/length

Width=57600 square feet/360 feet

Width=160 feet

Step 3

convert 160 feet into yards

1 yard= 3 feet

x yard= 160 feet

1/3=x/160

x=(1*160)/3

x=53.33 yards

width=53.33 yards

the area is (square yards)

Area=120 yards*53.33 yards

Area=6400 square yards

Step 4

Answer the questions.

3a.False,the width is 53.33 yards

3b.true, the Length is 120 yards=360 feet

3c.True, width of the field is 160 feet.

3d. True,rea of the field is 6,400 square yards.

Have a nice day.

7 0

3 years ago

What is the radius and diameter of the following circle?

siniylev [52]

Answer:

Step-by-step explanation:

Where's the circle?

3 0

3 years ago

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Select all of the solutions to the system graphed below.​

Select all of the solutions to the system graphed below.