Solve each triangle for the missing values shown. Show all work necessary. Use exact values

Answers

Answer 1

[tex] Cos 60°= \frac{1}{2} = \frac{Adjacent} {Hypotenuse} = \frac{y} {10} \\\\ 2y=10 \\\\ y=5 [/tex]

Now, use Pythagoras theorem to find x

[tex] x^2+y^2=10^2 \\\\ \to x^2+5^2=10^2 \\\\ \to x^2+25=100 \\\\ \to x^2 = 100-25 \\\\ \to x^2= 75 \\\\ \to x= \sqrt{75} \\\\ \bf 5 \sqrt{3} [/tex]

Similarly,

[tex] Sin 45°= \frac{1}{\sqrt{2}} = \frac{Opposite} {Hypotenuse} =\frac{2 \sqrt{2}} {a} \\\\ a= 2 \sqrt{2} \times \sqrt{2} \\\\ a=4 [/tex]

Now, use Pythagoras theorem to find b

[tex] b^2+(2 \sqrt{2}) ^2=a^2 \\\\ \to b^2+8=4^2 \\\\ \to b^2=16-8 \\\\ \to b^2 = 8\\\\ \to b= \sqrt{8} \\\\ \bf b=2 \sqrt{2} [/tex]

You can solve all of them in a similar way.

: )

Related Questions

1. Determine the lateral and total surface
area of the pyramid.

(I need full explanation on how to solve

Answers

Answer:

Laterial surface area: 73 cm²Total surface area: 93 cm²

Step-by-step explanation:

The laterial surface area is the sum of the areas of the triangles. There are two triangles with dimensions: base = 4 cm, height = 8cm and two triangles with dimensions: base = 5cm, height = 8.2cm.

The laterial surface area LSA is:

LSA = 2 • ( 4.8/2) + 2 • ( 5 • 8.2/2)

LSA = 4 • 8 + 5 • 8.2

LSA = 73 cm²

The total surface area SA is the LSA plus the area of the base of the pyramid, which is a rectangle with dimensions: 4cm x 5cm:

SA = LSA + 4 • 5

SA = 73 cm + 20 cm²

SA = 93 cm²

A system of liner equation has been graphed in the diagram. Determine a responsible solution for the system of equation.

Answers

The answer is B. Even just looking at the negatives of the other solutions, you can see that it is B because the intersection has a negative x and a positive y.

3x+5y=27.50 & 6x+3y=27

I love you

Answers

Answer:

what do u want me to do withthis question

can u edit then I’ll edit

Step-by-step explanation:

help plzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz

Answers

Answer:

The second box is the answer

Step-by-step explanation:

Solution

V=whl=5·5·5=125

Solve the following quadratic equations using factoring.
a. x2 + 10x + 24 = 0

Answers

Answer:

x = - 6, x = - 4

Step-by-step explanation:

Given

x² + 10x + 24 = 0 ← in standard form

(x + 6)(x + 4) = 0 ← in factored form

Equate each factor to zero and solve for x

x + 6 = 0 ⇒ x = - 6

x + 4 = 0 ⇒ x = - 4

Rewrite the function in standard form.
f(x) = 4(x - 2)^2+ 3

Answers

Answer:

f(x) = 4x^2 - 13

Step-by-step explanation:

f(x)=4(x-2)^2 + 3 parentaties first

f(x) = 4 (x^2 - 4)+ 3 multiply by what's infront parentaties

f(x) = 4x^2 - 16 + 3 combine light terms

f(x) = 4x^2 - 13 Answer

Hope I helped :)

NO LINKS PLEASE HELP A bag containing 35 marbles has red and green marbles. If the ratio of green marbles to red marbles is 2 to 5, how many green marbles are in the bag
O 25
O 14
21
10

Answers

Let 2x = the number of green marbles
Let 5x = the number of red marbles
2x + 5x =35
7x = 35
x = 5
Green: 2x = 10
Red: 5x = 25

2/5 of 35 is 14.So 14 green marbles.

Match the description to the appropriate term.
internal energy
heat
thermal energy

Answers

You got it correct? Wdym

Answer:

so the two missing angles sum to 180 - 90 = 90

z + 5z = 90

6z = 90

z = 15

5z = 75

find the value of each variables

Answers

Answer:

X=11

y=22

Step-by-step explanation:

[tex]tan60\frac{11\sqrt{3} }{x} \\\\\sqrt{3} =\frac{11\sqrt{3} }{x} \\\\x=\frac{11\sqrt{3} }{\sqrt{3} }[/tex]

⇒x=11

[tex]Sib 60=\frac{11\sqrt{3} }{y} \\\\\frac{\sqrt{3} }{2} =\frac{11\sqrt{3} }{y} \\\\y=\frac{11\sqrt{3} }{\sqrt{\frac{3}{2} } }[/tex]

⇒ y=22

hope it helps....

.Distribute and combine like terms: −4(7r + 7)

Answers

Answer:

−28r−28

Step-by-step explanation:

−4(7r+7)

=(−4)(7r+7)

=(−4)(7r)+(−4)(7)

5th grade math. correct answer will be marked brainliest

Answers

Answer:

70/9

Step-by-step explanation:

You can rewrite 8 pounds as 72/9.

Take away 2/9 and you are left with 70/9.

Answer:

[tex]\frac{2}{9} x \frac{8}{1} = \frac{16}{9} = 1 \frac{7}{9}[/tex]

the question is find the product of -8 and the sum of -2(10x + 3y) and -5(6y -7x)

Answers

Answer:

Step-by-step explanation:

-2(10x + 3y)

-20x -6y [-2 multiplied by 10x = 20x, negative + positive = negative]

-5(6y -7x)

-30y + 35x

-20x -6y -30y +35x

35x - 20x -30y -6y

15x - 36y

Answer = 15x -36y

Answer:

- 120x + 288y

Step-by-step explanation:

Begin by summing the 2 expressions

- 2(10x + 3y) - 5(6y - 7x) ← distribute parenthesis

= - 20x - 6y - 30y + 35x ← collect like terms

= 15x - 36y

Now multiply the result by - 8

- 8(15x - 36y) ← distribute

= - 120x + 288y

please help me find the missing angles for each problem

Answers

Answer:

1) L1 = 123

L3 = 57

2) L1 = 49

L3 = 131

3) L2 = 116

L4 = 64

4) L1 = 108

L2 = 72

5) L3 = 69

L4 = 111

6) L3 = 124

L4 = 56

Van kept track of the number of hours that he spent at the
pool each week for several weeks. He spent 6, 2, 6, 3, and
3 hours.
What is the mean number of hours that Van spent at the pool each week?
A. 20 hours
B. 4 hours
C. 3 hours
D. 5 hours

Answers

Answer:

B. 4 hours

Step-by-step explanation:

add every number up

6+2+6+3+3= 20

then divide by the number of numbers you used to add with.

20÷5=4

4 hours

geometry ^
please help me

Answers

2.99

by process of a elimination it can’t be the bottom two since the object is getting larger. If you take 6.21/5.4 you end up with 1.15. So now if you take 2.99/2.6 it also equals to 1.15.

What is the volume of this rectangular prism?

Jasper built a dollhouse for his younger sister.

A rectangular prism has a length of 24 inches, width of 8 inches, and height of 10 inches. A triangular prism has a triangular base of 24 inches and height of 6 inches. The height of the prism is 8 inches.
Which equation shows how to determine the volume of the dollhouse?
V = 24 (10) (8) + one-half (6) (24) (8)
V = 24 (10) (8) + one-third (6) (24) (8)
V = 24 (10) (8) + one-half (6) (24) (10)
V = 24 (10) (8) + one-third (6) (24) (10)

Answers

Answer:

It's A :)

Also can i please have brainliest :)

Answer:

Step-by-step explanation:

For all values of x,
f(x) = 2x-3 and g(x) = x²+1

a) Find fg(x)
Simplify and give your answer in the form ax² + b

b) Find gf(x)
Simplify and give your answer in the form ax² + bx+c

Answers

Answer:

For f(x) = 2x + 3 and g(x) = -x 2 + 1, find the composite function defined by (f o g)(x)

(f o g)(x) = f(g(x))

= 2 (g(x)) + 3

= 2( -x 2 + 1 ) + 3

= - 2 x 2 + 5 Given f(2) = 3, g(3) = 2, f(3) = 4 and g(2) = 5, evaluate (f o g)(3)

Step-by-step explanation:

. Find the sum of the infinite series, if it exists.

-270+135-67.5+⋯

Answers

Answer:

-180

Step-by-step explanation:

135/-270 = -1/2

67.5/135 = -1/2

The series is an infinite geometric series with r = -1/2

Since -1 < |r| < 1, the series has a sum

and equals a/(1 - r) a = -270

S = a/(1 - r) = -270/(1 + 1/2) = -270/(3/2) = -180

Is 80, 150, 170 a pythagorean triple?

Answers

Answer:

Yes

Step-by-step explanation:

80² + 150² = 170²

6400 + 22500 = 28900

28900 = 28900

5) Write the 5 number summary and draw a box and whisker plot.
58, 67, 44, 72,51, 42, 60, 46, 69

Answers

Answer:

Mean: 56.55

Median: 58

Minimum: 42

Maximum: 72

Q1: 45

Q2: 58

Q3: 68

IQR: 23

Range: 30

Other Questions

Which choice shows three lengths that cannot be the lengths of the three sides of a triangle? 2 cm, 8 cm, 8 cm B. 2 cm, 3 cm, 6cm C. 4cm, 5 cm, 7 cm . D. S cm. 6 cm. 9 cm Which statement about the form of government established by the U.S. Constitution is true?Question 3 options:Congress could not impose taxes or declare war.The laws of individual states were superior to federal law.The president was appointed by the Supreme Court to a lifetime term.Power would be shared among three branches of government Sybil transfers property with a tax basis of $5,000 and a fair market value of $6,000 to a corporation in exchange for stock with a fair market value of $3,000 and $2,000 cash in a transaction that qualifies as a section 351 transfer. The corporation assumed a liability of $1,000 on the property transferred. What is Sybil's tax basis in the stock received in the exchange?A) $6,000.B) $5,000.C) $4,000.D) $3,000. Studies have shown that children are especially vulnerable to the effects of ultraviolet (UV) radiation. Tanning beds expose the skin to nearly ten times as much UV radiation as natural sunlight. With that knowledge, a law was passed in some states to prevent individuals under the age of 18 from using tanning beds. Which statement best explains why UV radiation is so harmful?a) It can increase harmful DNA mutations in cells.b) Diseases are all caused by exposure to environmental factors.c) Homeostasis in an organism is increased by the presence of UV radiation.d)UV Radiation decreases the likelihood that mutations will occur. 25 points.The story is Freak the Mighty.Question 1: Think about the novel or short story you read for Module Five. What is the theme? Cite quotations and page numbers from your novel or short story to support your ideas.Question 2: Write a short paragraph explaining how the theme developed in your story. Cite quotations and page numbers from your novel or short story to support your ideas.Question 3: Think about the novel or short story you read for Module Five. What does the resolution tell you about the future of the protagonist? Cite quotations and page numbers from your novel or short story that support your ideas. If a varies directly with x squared, and a = 8 when x = 4 find the constant variation of k What sparked the downfall of the U.S. oil industry in the 1980s?A. increased spendingB. new discoveries of oilC. the governmentD. OPEC actions black power movement essay How many grams is 2.393 x 10^24 atoms of O?70.45 g O140.9 g O63.58 mole O63.58 g O GUYS PLEASE HELP ME THIS IS DUE IN 10 MINUETS HELP PLEASEEEEE B.Daniel called his best friend Fredrich on Friday afternoon and invited him to come to his house after dinner to watch theirfavorite movie. It had been a long and tiring day and Fredrich looked forward to doing something since he already finishedanswering his modules. After dinner, he hopped on his bicycle and pedaled over to Daniel's house. The house was dark, andwhen he rang the bell, there was no answer. Fredrich turned to hop on his bike and rode home.1. What had Fredrich realized?2. List evidence to support your answer. Of the following elements ____ can form a rare +4 ion *a) Aluminumb) Leadc) Kryptond) Uranium How was the US affected by the Cuban Missile Crisis? Select three options.The US reopened trade with Cuba.The US had to remove missiles from bases in Europe.The US was no longer threatened by missiles in Cuba.The US no longer had to fear the USSR military power.The US had to accept a communist dictatorship in Cuba. You walk into homeroom and see a huge cake on your desk." What might be happening? Write your hypothesis below.my answer: If I see a huge cake on my desk, then there would be a party**What evidence supports your hypothesis?answer:help me A box of chocolates has 5 creme filled, 8 peanut butter filled, and 7 caramel filled chocolates. What is the probability, expressed as apercent of randomly selecting a creme filled chocolate?A) 5%B) 15%C) 20%D) 25% The transformation rule (x, y) (`x/3`, `y/3`) is applied to the figure shown. Which are the final coordinates?Select one:1. (18,9),(18,9),(18,9),(18,9)2. (9,9),(18,9),(18,9),(9,9)3. (1,1),(2,1),(2,1),(1,1)4. (2,1),(2,1),(2,1),(2,1) PLS PLS PLS HELP I WILL MARK BRAINLIEST use away in this sentence to make the meaning the same as the Sentence above If we have 0.072 g of FeCl3 then how many moles are there? 1. When did stromatolites appear on Earth?ArcheanHadeanMesozoicProterozoic