what is the length of each leg in the right triangle shown below

Answer:

T = 60 degrees

Step-by-step explanation:

The dotted line is the height so it is a right angle

We are able to use trig functions since this is a right triangle

cos T = adj side / hyp

cos T = a/b

cos T = 8 sqrt(2) / 16 sqrt(2)

cos T = 1/2

Taking the inverse of each side

cos^-1 ( cosT) = cos^-1 ( 1/2)

T = 60 degrees

Answer:

[tex]\angle T=60^{\circ}[/tex]

Step-by-step explanation:

In all 30-60-90 triangles, the sides are in ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle. We know that two right triangles are created on both sides of the rectangle in the center. Notice that [tex]8\sqrt{2}\cdot 2=16\sqrt{2}[/tex] and since [tex]16\sqrt{2}[/tex] is the hypotenuse of the right triangle on the left, [tex]8\sqrt{2}[/tex] must be facing the 30 degree angle. Therefore, angle T must be 60 degrees.

Alternatively, the cosine of any angle in a right triangle is equal to its adjacent side divided by the hypotenuse.

Therefore, we have:

[tex]\cos \angle T=\frac{8\sqrt{2}}{16\sqrt{2}},\\\cos \angle T=\frac{1}{2},\\\angle T=\arccos(\frac{1}{2}),\\\angle T=\boxed{60^{\circ}}[/tex]

[tex]\bf \large \rightarrow \: \:2x \: + \: 8 \: = \: 0[/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: \frac{8}{2} \\ [/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: \cancel\frac{ 8}{ 2} \: \: ^{4} \\ [/tex]

[tex]\bf \large \rightarrow \: \:x \: = \: 4[/tex]

Option ( A ) is the correct answer.

Answer:

70 days

Step-by-step explanation:

that is the procedure above

Answer:

4.6

Step-by-step explanation:

tan(75) = 17/x

x = 17/tan(75)

x = 34-17√3

x = 4.6

Answered by GAUTHMATH

Answer:

y-3

Problem:

What is the remainder when the dividend is xy-3, the divisor is y, and the quotient is x-1. ?

Step-by-step explanation:

Dividend=quotient×divisor+remainder

So we have

xy-3=(x-1)×(y)+remainder

xy-3=(xy-y)+remainder *distributive property

Now we just need to figure out what polynomial goes in for the remainder so this will be a true identity.

We need to get rid of minus y so we need plus y in the remainder.

We also need minus 3 in the remainder.

So the remainder is y-3.

Let's try it out:

xy-3=(xy-y)+remainder

xy-3=(xy-y)+(y-3)

xy-3=xy-3 is what we wanted so we are done here.

Answer:

you can put the number on one side of the equation then the "x" part on the other side.

with c) 4x = 6-10

           4x = -4

            x = -4/4

            x = -1

with d) 7x - 1 = 4x + 8

           7x - 4x = 8 + 1

           3x  = 9

           x = 9/3

           x = 3

Answer:

c) x = -1.  d) x = 3

Step-by-step explanation:

c) move like terms together. then get x by itself

10 + 4x = 6

-10

4x = -4

4x/4 = -4/4

x = -1

d) move like terms together.  then get x by itself

7x-1 = 4x+8

+1          -4x

3x = 9

3x/3 =9/3

x = 3

Answer:

Step-by-step explanation:

Given,

[tex] \frac{7}{3} = \frac{x}{49} [/tex]

[tex] = > x = \frac{7}{3} \times 49[/tex]

[tex] = > x = \frac{343}{3} (ans)[/tex]

Answer:

343/3 or 114 1/3

Step-by-step explanation:

7/3 = x/49

Using cross products

3x = 7*49

3x =343

Divide by 3

3x/3 = 343/3

x =343/3

x =114 1/3

[tex] \\ \tt \longmapsto2x + 15 + 7 - 8x + 3x - 41 = 30 \\ \\ \tt \longmapsto 2x - 8x + 3x + 15 + 7 - 41 = 30 \\ \\ \tt \longmapsto - 3x - 19 = 30 \\ \\ \tt \longmapsto 3x + 19 = - 30 \\ \\ \tt \longmapsto 3x = - 30 -19 \\ \\ \tt \longmapsto 3x = - 49 \\ \\ \tt \longmapsto x = - \frac{49}{3}[/tex]

Answer:

Step-by-step explanation:

2x + 15 + 7 - 8x + 3x - 41 = 30

2x  - 8x + 3x + 15 + 7 - 41 = 30

Combine like terms

-3x - 19 = 30

Add 19 to both sides

-3x = 30 + 19

-3x = 49

Divide both sides by (-3)

x = 49/-3

x = -[tex]16\frac{1}{3}[/tex]

Answer:

133

Step-by-step explanation:

Given that :

Degree of confidence, α = 0.90 ; The Zcritical vlaue at α = 90% is 1.645

The margin of error, MOE = ±2

Standard deviation, s = 14

Using the relation :

n = (Zcritical * standard deviation) / MOE

n = ((1.645 * 14) / 2)²

n = (23.03 /2)²

n = 11.515²

n = 132.595

n = 133 samples

So you pretty much have all you need. 1/3 represents slope, and slope is m. Initial value would be your y intercept which is b.

y=1/3x-3

Answer:

y = x/3 - 3

Step-by-step explanation:

x/3 is the equivalent of 1/3(x)

Multiply the numerator and denominator by the conjugate of the denominator:

[tex]\dfrac{6+9i}{-1+4i} \times \dfrac{-1-4i}{-1-4i} = \dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2}[/tex]

Simplify:

[tex]\dfrac{(6+9i)(-1-4i)}{(-1)^2-(4i)^2} = \dfrac{-6-9i-24i-36i^2}{1-16i^2} = \dfrac{-6-33i-36i^2}{1-16i^2} = \dfrac{-6-33i+36}{1+16} = \boxed{\dfrac{30-33i}{17}}[/tex]

Answer:

45 and 23

Step-by-step explanation:

Let x equal the first number and y equal the second number.

We can set the following equations up with our information:

[tex]x+y=68[/tex]

[tex]x-y=22[/tex]

Adding the two equations together, we get:

[tex]2x=90[/tex]

Dividing by two, we receive [tex]x=45[/tex]

We can plug this into our first equation to get [tex]45+y=68[/tex].

Subtracting 45 from both sides, we get [tex]y=23[/tex].

The two numbers are 45 and 23, solved using system of equations.

A system of equations is a set of equations, involving similar variables used to solve for the variables simultaneously.

In the question, we are asked to find the two numbers, whose sum is 68 and the difference is 22.

We assume the two numbers to be x and y.

The sum of the two numbers is given to be 68.

This can be shown as an equation, x + y = 68 ... (i).

The difference of the two numbers is given to be 22.

This can be shown as an equation, x - y = 22 ... (ii).

Equations (i) and (ii) together makes a system of equation in the variables x and y.

To solve for the system of equation, we add (i) and (ii), to get:

x + y = 68

x - y = 22

_________

2x  = 90,

or, x = 45.

Substituting x = 45 in (i), we get:

x + y = 68,

or, 45 + y = 68,

or, y = 23.

Thus, the two numbers are 45 and 23, solved using system of equations.

Learn more about system of equations at

https://brainly.com/question/13729904

#SPJ2

Answer:

210

Step-by-step explanation:

In a normal distribtuion mean=mode=median

so 210=median

Answer:

a) Hence the equation of the sinusoidal function that describes the height of the shorts in terms of time is [tex]y = 9 + 7* sin(\pi * t / 15 - \pi / 6)[/tex]

b) Hence the height of the shorts at exactly t = 10 minutes, to

the nearest tenth of a meter is 5.5 meters

Step-by-step explanation:

a) The wind turbine blade traverses a circular path as it rotates with time (t), whose time variation is given by the following trajectory equation :

[tex]x^2 + (y-yc)^2 = R^2[/tex] ,

where  

R = (16 m - 2 m)/2 (since diameter = maximum height - minimum height of the pink short)

= 14 m / 2

= 7 m (radius of the circle)

Also, center of the circle will be at (0, 2 + R) i.e (0,9)

So,  is the trajectory path equation to the circle

Let [tex]x = 7* cos(w*t + \phi ) & y = 9 + 7* sin(w* t + \phi)[/tex] be the parametric form of the above circle equation which represent the position of the pink shorts at the tip of the blade at time t  

At t= 10s, y = 16 m so we have,

[tex]9 + 7 * sin(10* w + \phi) = 16[/tex] ---------------(1)

Also, at t= 25s, y =2 m so we have,

[tex]9 + 7* sin(25 * w +\phi) = 2[/tex]--------------(2)

Solving we have, [tex]10* w + \phi = \pi/2 & 25*w + \phi = 3*pi/2[/tex]

[tex]15* w = \pi\\\\w = \pi/15 & \phi = \pi/2 - 10*\pi/15 = -\pi / 6[/tex]  

Therefore [tex]y = 9 + 7* sin(\pi * t / 15 - \pi / 6)[/tex] is the instantaneous height of the pink short at time t ( in seconds)

b) At t= 10minutes = 10 * 60 s = 600s, we have,

[tex]y = 9 + 7 * sin(\pi * 600/15 - \pi / 6)\\\\= 9 + 7 * sin(40* \pi - \pi / 6)[/tex]

= 5.5 meters (pink short will be at 5.5 meters above ground level at t= 10 minutes)

Answer:

5

Step-by-step explanation:

Answer:

[tex]x=-21y+5[/tex]

Step-by-step explanation:

Hi there!

[tex]7y=\frac{5-x}{3}[/tex]

We can isolate x by performing inverse operations on both sides of the equation and canceling values out.

First, multiply both sides by 3 to cancel 3 out on the right side and isolate 5-x:

[tex]7y*3=\frac{5-x}{3}*3\\21y=5-x[/tex]

Now, subtract 5 from both sides to isolate -x:

[tex]21y-5=5-x-5\\21y-5=-x[/tex]

Finally, multiply both sides by -1 to change -x to x:

[tex]-21y+5=x\\x=-21y+5[/tex]

I hope this helps!

Answer:

The answer is 18 feet...

Step-by-step explanation:

C. 18ft is the answer

Answer:

$962.00

Step-by-step explanation:

We can start from the first sentence of the word problem and work from there.

First, the employee is working for 40 hours at $18.50 per hour. This means that for each hour, the employee is gaining $18.50 . This can be represented as $18.50 * 40 = $740 for their base pay.

Next, the employee works 8 hours of overtime at 1.5 * base pay (18.50). For each hour of overtime they work, they earn 1.5 * 18.50 = $27.75 dollars. Their earnings from overtime work for the week can be represented as

8 * 27.75 = $222

Because all the employee's hours are encompassed in overtime and base pay, we can add the two together to get

740 + 222 = $962.00 for their total pay for the week

Step-by-step explanation:

c. The slope is positive.

hope this helps you

have a nice day

Answer:

D) 20°

Step-by-step explanation:

Using the triangle sum theorem, you know that every triangle's interior angles add up to 180°. Therefore the bottom triangle's missing angle can be found by giving it the variable x.

57° + 30° + x = 180°

Simplify: 87° + x =180°

x=93°

By the vertical angles theorem, the vertical angle directly across this angle is congruent to this one. Meaning that the top triangle's angle are 67°, 93°, and unknown, which we can assign y. We can use the same method from above here.

67° + 93° + y = 180°

Simplify: 160° + y = 180°

y=20°

Answer:

(C). 26°

Step-by-step explanation:

Answer:

or,

3/4×2/3=6/8

or, 3/4×3/3=9/12

Answer:

Step-by-step explanation:

1/3×2/8=2/24

1/2×5/12=5/42

5/6×3/4=15/24

Hope it is helpful to you

Answer:

x = 35

Step-by-step explanation:

Let x be the one of the other angles

X is also the third angle since we know they are equal

The sum of the angles of a triangle is 180

110+x+x = 180

110 +2x= 180

2x = 180-110

2x= 70

Divide by 2

2x/2 = 70/2

x = 35

Answer:

[tex]x = 35 \degree[/tex]

Step-by-step explanation:

Let the unknown angle be x

Unknown Angles are equal to each other so,

[tex]x + x + 110 = 180[/tex]

sum of the interior angles in a triangle is 180°

[tex]2x + 110 = 180 \\ 2x = 180 - 110 \\ 2x = 70 \\ \frac{2x}{2} = \frac{70}{2} \\ x = 35 \degree[/tex]

Answer:

this is a 60 60 60 triangle, so one exterior angle is 120 degrees.

Step-by-step explanation:

hope it helps!

Answer:

-5, - 2, 3

Step-by-step explanation:

y=2x+3, y=-7, x=-5; y=-1, x=-2, y=9, x=3

Answer:

A is the answer to your question because it's the only answer in exponential form.

B and C are in slope forms.

D is in quadratic form.

Answer:

-w²+49x²-8wx

Step-by-step explanation:

if you want how I did this it's quite lengthy so let me know if you want the process

Answer:

-w^2 + 21xw - 64x ^2

Step-by-step explanation:

Answer:

65.3%

Step-by-step explanation:

what we want: p(2)+p(3)+p(4)

[tex]P(2)={5\choose2}*.4^2*.6^3\\P(3)={5\choose3}*.4^3*.6^2\\P(4)={5\choose4}*.4^4*.6\\P(2)+P(3)+P(4)= .6528[/tex]

which equal 65.28%

which rounds to

65.3%