How many triangles can be constructed with angles measuring 35º, 62º, and 83º?A. 0

B. 1

C. 2

D. an infinite number

Answers

Answer 1

Answer: B)OPTION B only 1 is your answer.

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what is the first step in solving the quadratic equation x2 = ? take the square root of both sides of the equation. add to both sides of the equation. square both sides of the equation. subtract from both sides of the equation.

In triangle DEF m D=43 , m E=62, m EF=22. What is DE to the nearest tenth

Answers

The measure of DE of the triangle is given by law of sines and DE = 31.3

What is the law of sines?

The relationship between a triangle's sides and angles is provided by the Law of Sines. Trigonometry's law of sines can be expressed as a/sinA = b/sinB = c/sinC, where a, b, and c are the lengths of the triangle's sides, and A, B, and C are the triangle's respective opposite angles.

Law of Sines :

a / sin A = b / sin B = c / sin C

Given data ,

Let the triangle be represented as ΔDEF

Now , the measure of sides of the triangle are

The measure of EF = 22

The measure of angle ∠D = 43°

The measure of ∠E = 62°

And , the measure of ∠F = 180° - 43° - 62° = 75°

From the laws of sines , we get

a / sin A = b / sin B

On simplifying , we get

EF / sin 43° = ED / sin 62°

So , the measure of DE = ( 22 / 0.7 ) ( sin 75° )

And , the measure of DE = 31.3 units

Hence , the measure of DE of triangle is 31.3 units

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DE = 31.3
Detailed solution is attached

In the figure below, the two triangular faces of the prism are fight triangles with sides of length 3, 4, and 5. The other three faces are rectangles. What is the surface area of the prism. 72 sq. units 96 sq. units 84 sq. units 108 sq. units

Answers

The surface area of the prism will be given by:
SA=(surface area of triangles)+(surface area of rectangles)
surface area of triangles=2(1/2*3*4)=12 sq. units

area rectangles
the length of the hypotenuse will be:
c²=a²+b²
c=√(3²+4²)
c=√25
c=5
area=(3*5)+(4*5)+(5*5)=60

Total area=60+12=72 sq. units

Answer: 72 sq. units

Billy stacked six pieces of wood on top of one another. If each piecewas three-quarters of a foot tall, how tall was his pile?

Answers

$6*0.75=6* (3)/(4) = (6*3)/(4) = (18)/(4) = (16+2)/(4) = (16)/(4) + (2)/(4) =4.5$

Given: 9-4x = -19
Prove: x = 7

Answers

Answer:

Easy

Step-by-step explanation:

-19-9=-28

-28/-4=7

thus x=7

Final answer:

In solving the equation 9 - 4x = -19, we find that x = 7 is indeed the correct solution.

Explanation:

The given equation is 9 - 4x = -19. We are to solve this equation for x, and see if it equals 7, as stated in the question. Start by subtracting 9 from both sides, resulting in: -4x = -28. Next, divide both sides by -4 to solve for x, resulting in x = 7. So, indeed, for the given equation, x = 7 is the correct solution.

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Let P(x) = F(x)G(x) and Q(x) = F(x)/G(x), where F and G are the functions whose graphs are shown.(a) Find P '(2). (b) Find Q'(7).

Answers

Hello,

Very nice like question!

a)
F(2)=3 ; G(2)=2
F'(2)=0; G'(2)=1/2
P'(x)=F'(x)*G(x)+F(x)*G'(x)

P'(2)=0*2+3*1/2=3/2

b)
F(7)=5; G(7)=1
F'(7)=1/4; G'(7)=-2/3

Q'(x)=(F'(x)*G(x)-F(x)*G'(x)) / G²(x)

Q'(7)=(1/4*1-5*(-2/3))/1²=1/4+5/3=23/12

There are 480 jellybeans in an 8-ounce jar. How many jellybeans are there per ounce in the jar?0.017
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