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2 years ago

I need help i dont know what to do

Mathematics

1 answer:

vladimir1956 [14]2 years ago

8 0

9514 1404 393

Answer:

∠CAB = 28°

∠DAC = 64°

Step-by-step explanation:

What you do in each case is make use of the relationships you know about angles in a triangle and around parallel lines. You can also use the relationships you know about diagonals in a rectangle, and the triangles they create.

Left

Take advantage of the fact that ∆AEB is isosceles, so the angles at A and B in that triangle are the same. If we call that angle measure x, then we have the sum of angles in that triangle is ...

x + x + ∠AEB = 180°

2x = 180° -124° = 56°

x = 28°

The measure of angle CAB is 28°.

Right

Sides AD and BC are parallel, so diagonal AC can be considered a transversal. The two angles we're concerned with are alternate interior angles, so are congruent.

∠BCA = ∠DAC = 64°

The measure of angle DAC is 64°.

(Another way to look at this is that triangles BCE and DAE are congruent isosceles triangles, so corresponding angles are congruent.)

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How big is the home field advantage in the National Football League (NFL)? To investigate, we select a sample of 80 games from t

ElenaW [278]

Answer:

0.74 to 6.06

Step-by-step explanation:

The groups are independnet,

SE(xh bar-xa bar)=sqrt [sh^2/nh+sa^2/na]=sqrt [10.1^2/80+10.3^2/80]=1.61

At df=157, the t critical is 1.65

90%c.i=(xh bar-xa bar)+-tcritical SE(xh bar-xa bar)

=(25.2-21.8)+-1.65*1.61

=0.74 to 6.06

5 0

2 years ago

A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of

belka [17]

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==> t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348

5 0

2 years ago

GO.o has 3 orange picks for every 2 green. If there are 25 picks in all, how many picks are orange?

Reika [66]

Given

GO.o has 3 orange picks for every 2 green

there are 25 picks in all

Find out how many picks are orange.

To proof

As given in question

GO.o has 3 orange picks for every 2 green

i.e the ratio of orange to every green becomes

$\frac{Orange}{Green}:\frac{3}{2}$

total number of picks = 25

let the GO.o pick of 3 orange picks for every 2 green =x

than the equation becomes

3x + 2x = 25

5x = 25

x = 5

Than

the number of oranges = 3x

putting the value of x

= 15

the number of green = 2x

= 10

thus the 15 picks are orange.

Hence proved

4 0

2 years ago

Read 2 more answers

I need help fast...........

Gennadij [26K]

15x - 5(3x-7) = 14
15x - 15x+ 35 = 14
35 = 14 ...NOT TRUE

answer
NO solution

you got it correct

5 0

2 years ago

What is the volume of a hemisphere with a diameter of 3.8 in, rounded to the nearest tenth of a cubic inch?

Natali5045456 [20]

Answer:14.4In^3

Step-by-step explanation:

Diameter=3.8In

radius(r)=3.8 ➗ 2=1.9In

volume of hemisphere=2/3 x π x r^3

Volume=2/3 x 3.14 x(1.9)^3

Volume=2/3x3.14x1.9x1.9x1.9

Volume=(2x3.14x1.9x1.9x1.9) ➗ 3

Volume=43.07452 ➗ 3

Volume=14.4In^3

6 0

2 years ago