1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
finlep [7]
3 years ago
5

Answer both with STEPS

Mathematics
1 answer:
Amanda [17]3 years ago
8 0

Answer:

7 )

x =  \frac{3\sqrt{2} }{2}

y= 3

8 )

x=6\sqrt{6}

y= 9\sqrt{2}

Step-by-step explanation:

7  )                                 8)

In Δ ABC                                      In Δ XYZ            

∠ C = 45°                                          ∠ X = 60°

∠ A = 90°                                           ∠ Y = 90°

AC= \frac{3\sqrt{2} }{2}             XY= 3\sqrt{6}

To Find :

x = ?

y = ?

Solution:

We Know

In Δ ABC

∠ C = 45°

∠ A = 90°

∴ ∠ B = 45°  ......Angle sum property of a triangle i.e 180°

∴  Δ ABC is an Isosceles Triangle

∴ AC = AB = x =  \frac{3\sqrt{2} }{2}

Now appplying Trignometry identity we get

\sin C = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\sin 45 = \frac{AC}{BC}\\\\\frac{1}{\sqrt{2} } =\frac{\frac{3\sqrt{2} }{2}}{y}\\\\y=\frac{3\times \sqrt{2}\times \sqrt{2}  }{2}\\\\y= 3

Now In Δ XYZ

∠ X = 60°

∠ Y = 90°

∴∠ Z = 30°  . .....Angle sum property of a triangle i.e 180°

Now appplying Trignometry identity we get

\tan X = \frac{\textrm{side opposite to angle X}}{\textrm{side adjacent to angle X}}

\tan 60 = \frac{YZ}{XY}\\\\\sqrt{3} =\frac{y}{3\sqrt{6} }\\  y= 3\sqrt{3} \sqrt{6} \\y= 9\sqrt{2}

Now,

\sin X = \frac{\textrm{side opposite to angle C}}{Hypotenuse}\\\\\\\sin 60 = \frac{YZ}{XZ}\\ \\\frac{\sqrt{3} }{2} =\frac{9\sqrt{2} }{x} \\\\x=\frac{18\sqrt{2} }{\sqrt{3} } \\\textrm{after fationalizing the denominator root 3 we get}\\\\x=6\sqrt{6}

You might be interested in
If two angles of measure (x + 3)º and (2x – 9)º
nydimaria [60]

Step-by-step explanation:

(X+3)(2x_9)

3x+12_12=90_12

3x=90_12

3x=78

X=26°

8 0
3 years ago
What is the answer to 7=-3c-2
Komok [63]

Answer:

c= -3

Step-by-step explanation:

3 0
3 years ago
-5x - 2y = 13<br> -4x + y = 0<br> Solve by substation
kotegsom [21]

Answer:

(x,y)=(-1,-4)

Step-by-step explanation:

-4x + y = 0

+4x         +4x

y=4x

-5x - 2y = 13

+5x          +5x

-2y = 5x+13

-2(4x) = 5x+13

-8x=5x+13

-5x -5x

-13x/-13=13/-13

x=-1

Thus:

y=4x

y=4(-1)

y=-4

5 0
3 years ago
steve has these score on the exams for this semester 89 92 and 87. How much will have to make on the fourth exam to have a final
Zinaida [17]
THIS IS THE CORRECT ANSWER I GOT WHEN SOLVING ON MY IPHONE

6 0
3 years ago
Elizabeth has $10, $5, and $1 bills worth $101. she has five more five dollar bills than ten dollar bills and 4 times more 1 dol
vesna_86 [32]

Let x be number of $10 dollar bills

Let y be number of $5 dollar bills

Let z be number of $1 dollar bills

From the question, we can come up with three equations (so we can find the values of x, y & z) :

  • 10x + 5y + z = 101
  • y - x = 5
  • z = 4x

The first equation comes from finding the total money Elizabeth has, which is $101.

The second equation comes from value of y (number of $5 bills) is more than value of x (number of $10 bills) by 5 dollars.

The third equation comes from the value of z (number of $1 bills) being 4 times more than the value of x (number of $10 bills).

Now, we will begin to find the value of x, y & z.

From the first equation,

10x + 5y + z = 101

Substitute the third equation (z = 4x) into z:

10x + 5y + 4x = 101

Simplify this and you get,

14x + 5y = 101

Now, we use the second equation. The second equation is y - x = 5. If we try to make y as the subject, it becomes y = 5 + x.

Now, substitute this into the value of y of the last working we did:

14x + 5(5+x) = 101

Simplify that and it becomes:

x = 4

Then, substitute this value of x into the second and third equations to find y and z.

y - x = 5

y - 4 = 5

y = 9

z = 4x

z = 4(4)

z = 16

Finally, let's check these answers by substituting them into the first equation to try and see if the total value is <em>really</em> $101.

10x + 5y + z = 10(4) + 5(9) + 16

10x + 5y + z = 40 + 45 + 16

10x + 5y + z = 101

Thus, our answers are correct. Elizabeth has FOUR $10 bills, NINE $5 bills and SIXTEEN $1 bills.

6 0
3 years ago
Read 2 more answers
Other questions:
  • What is the value of the underlined digit? 12,532.628 with the 3 underlined
    13·2 answers
  • Plz help one number 9 plz, merci
    7·1 answer
  • In the United States in 1986, 48.7% of persons age 25-pluswere males. Of these males 23.8% were college graduates. In addition,
    15·1 answer
  • a farmer has planted 0.3 of his orchard with cherry trees. the orchard is 8.59 acres in size. how many acres are planted with ch
    12·1 answer
  • Two parallel lines are crossed by a transversal.
    11·2 answers
  • in a pepper airplane contest, amanda's plane flew 19ft farther than Darren's plane.Darren's plane flew twice as far as Rachel's
    7·1 answer
  • Solve, for 0 ≤ θ &lt; 360 , the equation<br> sin2 θ = 1 + cos θ
    5·1 answer
  • Please Answer This, the question is on the picture. it needs to be a fraction
    6·1 answer
  • The difference of two numbers is 7. Three times the greater number is 72. Find the numbers​
    15·2 answers
  • Shane walked 3 meters west then turned the corner to walk 4 meters north to get to the library . He is going to walk home on the
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!