X, Y and Z form the vertices of a triangle. XY = 12.4m, XZ = 10.4m and YZ = 8.7m. Find the angle ∠ YXZ rounded to 1 DP.

Answers

Answer 1

Answer:

43.8°

Step-by-step explanation:

Applying,

Cosine rule,

From the diagram attached,

x² = y²+z²-2yxcos∅.................... Equation 1

where ∅ = ∠YXZ

Given: x = 8.7 m, y = 10.4 m, z = 12.4 m

Substitute these values  into equation 1

8.7² = 10.4²+12.4²-[2×10.4×12.4cos∅]

75.69 = (108.16+153.76)-(257.92cos∅)

75.69 = 261.92-257.92cos∅

collect like terms

257.92cos∅ = 261.92-75.69

257.92cos∅ = 186.23

Divide both sides by the coefficient of cos∅

cos∅ = 186.23/257.92

cos∅ = 0.722

Find the cos⁻¹ of both side.

∅ = cos⁻¹(0.7220)

∅ = 43.78°

∅ = 43.8°


Related Questions

Write an equation of the line in slope intercept form given the information below slope=-4 point=(2,-4)

Answers

Answer:

y=-4x+4

Step-by-step explanation:

y-y1=m(x-x1)

y-(-4)=-4(x-2)

y+4=-4(x-2)

y=-4x+8-4

y=-4x+4

A slope of a line is the change in y coordinate with respect to the change in x coordinate. The equation of the line in slope intercept form which is passing through (2,-4) is  -4x +7.

What is the slope of a line?

A slope of a line is the change in y coordinate with respect to the change in x coordinate. The equation of a line in slope intercept form is given by

y = mx + c.

Given the slope of the line, m=-4. Also, the point through which the line is passing,

(x₁ ,y₁) =(2,-4)

Since the equation of the line in the slope-intercept form of the line is given by

y = mx +c

Since, the above line is passing through (2, -4) and the slope is -4.

Therefore,-4 = -4(2) + c⇒ -4 = -8 + c⇒ -1 +8 = c⇒ c = 7

Substitute the value of m and c in the equation

y = mx + c

⇒ y = mx + c

⇒ y = -4x +7

Therefore, the equation of line in slope intercept form which is passing through (2, -4) is y = -4x +7.

Learn more about the slope of the line here:

https://brainly.com/question/14511992

#SPJ2

Sahil got 28 questions right on the math test. Angelina got 7 more wrong answers than Sahil. There were 40 questions on the test. How many answers did Angelina get right on the math test? Which equation represents this situation?


A. a + 7 = 12
B. a + 7 = 28
C. 7 + 12 = a
D. 7 = 40 - a

Answers

Answer:

40-28=12 Sahil got 28 right and 12 wrong

12+7=19 Angelina got 19 wrong and 21 right

40-19= 21

B would be correct

a +7=28

a= 28-7

a=21

Q. Find missing angle
a.60
b.36
c.30
d.41
e.49

Answers

Answer:

b or c

Step-by-step explanation:

find the measure of side NO. Figures are not drawn to scale.​

Answers

Its being dilated by 3 therefore your answer is 9.9

The motives for developing calculus in the 1700s were: A. problems in physics. B. problems in biology. C. problems in psychology. D. problems in computer science. E. problems in economics.

Answers

Answer:

the answer is A

Step-by-step explanation:

The question is in the image. Please help me.

Answers

Answer:

Step-by-step explanation:

The standard form of a circle is

[tex](x-h)^2+(y-k)^2=r^2[/tex] where h and k are the center of the circle and r is the radius. Our center is located at (0, 1), so h = 0 and k = 1. Going from the center straight up of down we have to move 2 units to get to a point on the outside of the circle, so r = 2. Filling in our equation:

[tex](x-0)^2+(y-1)^2=2^2[/tex] which simplifies a bit to

[tex]x^2+(y-1)^2=4[/tex]

Check
What is the slope of the line on the graph?
X
-2
2.
4
-2
-4

Answers

[tex]slope = \frac{1}{2} [/tex]

Hope it helps you...

Find the value of x. Round to the nearest degree.
A) 27
B) 60
C) 30
D) 26

Answers

The value of x is B) 60°

Answer:

Step-by-step explanation:

take x degree as reference angle

using sin rule

sin x=opposite/hypotenuse

sin x=9/18

sinx=0.50

x=sin 30

x=30 degree

Sochi starts reading at 11 25 AM and ends at 12 09 PM How many minutes does Sochi read? Use the number pad to enter your answer in the box minutes​

Answers

Answer:

Step-by-step explanation:

11.25=11.25 hrs

12.09=12.09 hrs

time=12.09-11.25=44 minutes

Answer:

44 minutes

Step-by-step explanation:

35 minutes from 11:25 AM to 12 pm

9 minutes from 12:00 pm to 12:09 pm

35 + 9 = 44 minutes.

Gary was looking for a new cell phone plan. Company A is offering $50 for the phone and $.20 per minute for data usage. How much would Company A’s phone plan cost if Gary spends on average 200 minutes for data?

Answers

Answer:

$90

Step-by-step explanation:

c = 50 + .2m

c = 50 + .2(200)

c = 50 + 40

c = 90

Leia cuts congruent triangular patches with an area of 27 square centimeters from a rectangular piece of fabric that is 18 centimeters long and 6 centimeters wide.

How many of the patches can Leia cut from 30 pieces of the fabric?

Answers

Answer:

112 patches can be made.

Please help if your awake lol ugh it’s a question check the picture :)

Answers

I really hope that helps cause I went all out and best of wishes!!

The given information is the _____ of the if-then statement.

A then
B if
C none of the above

Answers

C is the answer




Because If we use A then it will not make sense same with b so it is c

You guys are legit tjamks

Answers

Answer:

The answer is option C. 13/15

Step-by-step explanation:

1-2/15= 13/15

I need help with this homework

Answers

Answer:

Step-by-step explanation:

P(even) fraction: 12/25 %: 48%

P(more than 20) fraction: 1/5... %: 20%

P(even and more than 20) fraction: 2/25 %: 8%

P(less than 5 or more than 20) fraction: 9/25 %: 36%

P(prime and less than 10) fraction: 4/25 %: 16%

P(multiple of 5) fraction: 1/5 %:20%

HELP PLEASE ILL GIVE YOU BRAINLIEST

Answers

Answer:

Equation: 80-25= m

Solution: 80-25= 55

Check: 25+55= 80

Step-by-step explanation:

BigBrain

Identify the explicit function for the sequence in the table x 1,2,3,4,5 y 9,14,19,24,29

Answers

Answer:

[tex]a_{n}[/tex] = 5n + 4

Step-by-step explanation:

There is a common difference between the consecutive terms of y

29 - 24 = 24 - 19 = 19 - 14 = 14 - 9 = 5

This indicates the sequence is arithmetic with explicit formula

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 9 and d = 5 , then

[tex]a_{n}[/tex] = 9 + 5(n - 1) = 9 + 5n - 5 = 5n + 4

answer options for anyone who can give correct answer

Manuel, a plumber, has several pieces of pipe on his truck. He has a piece 6 feet long. A piece 7 feet long, one 9 feet long, and a piece 13 feet long. Find the total length of pipe in feet. If he uses 5 feet of pipe on a job, how many feet of pipe are left?

Answers

I believe it is 30 bc it is 35ft of pipe minus 5 ft on a job?

Choose the correct simplification of the expression the quantity 4 times x all over y all to the second power

Answers

Answer:

[tex]( \frac{4x}{y})^{2}[/tex]

Step-by-step explanation:

a store has 9 blue hats and 7 red hats for sale write the ratio of blue hats to all the hats

Answers

Answer:

9 :  7, or 9/16 to 7/16

Step-by-step explanation:

We know that there are 9 blue hats.

We know there are 7 red hats.

This is a 9 : 7 ratio.

In fraction form, we must find the total ratio, use that as the denominator, then take the seperate amounts, such as bluei adn red hats, and use that as the numerator:

9+7=denominator

denominator = 16

Blue hats = 9

Ratio of red = 9/16

Red hats = 7

Ratio of red = 7/16

Hope this helps!

Which of the following theorems verifies that AHIJE AKLM? H K M ОА. НА O O O B. LA O C. HL O D. AA​

Answers

Answer: Choice A)  HA

===================================

Explanation:

HA = hypotenuse angle

The tickmarks tell us that the hypotenuse IJ is the same length as the hypotenuse LM. So that's the "hypotenuse" portion of "HA".

The "angle" portion refers to the acute angles HIJ and KLM being the same measure, as shown by the curved arc marking. We aren't referring to the right angles because the HA theorem can only be used for right triangles, so that means the right angle is already built into it (and we can ignore the right angles).

Notice how HA is a special case of AAS.

What is the volume of the cylinder shown? Use 3.14 for pi. 4cm is the radius and 9cm is the height.

Answers

Answer:

The formula is 4cm times 9cm which is 36cm. Then times that by pi which is 113.04. The answer is 113.04

Step-by-step explanation:

Answer:

Volume - 452.16 cm

Step-by-step explanation:

First we need to find the area of the circle.

Area of a circle - (3.14)r^2

Insert the radius in the formula -

(3.14) (4)^2

3.14 x 16

50.24 is the area of the circle

Now, we have to multiply this value by the height of the cylinder in order to find the volume.

50.24 x 9 = 452.16 cm

The area of a square piece of land in square units can be represented by the expression 9q^4r^8s^6What is the length
of one side of the piece of land?

Answers

Answer:

I'll setup the problem, you do the calculation

Step-by-step explanation:

given the area of a square, you take the square and that is the side of the square

[tex] \sqrt{9 {q}^{4} {r}^{8} {s}^{6} } [/tex]

the square root of a number that is raised to a power is found by dividing the power by 2

example

[tex] \sqrt{ {x}^{6} } = {x}^{3} [/tex]

do that for each term and you have you answer

comment if you have questions

CAN SOMEONE HELP ME PLEASEEEEEEE

Answers

Answer:

a) = 7x² + 4y²

b) = 3x + 7xy - 7

Step-by-step explanation:

a) = (9 - 2) x² + (-3 + 7) y²

= 7x² + 4y²

b) = (8 - 5) x + (3 + 4) xy - 7

= 3x + 7xy - 7

I really need help do can someone do it step by step so I can understand plzzzz​

Answers

V=12000 sq feet
Forgive me if I’m wrong I’ll redo it if so

Answer:

96×pi ft³

Step-by-step explanation:

by the way, it is totally easy to search for formulas on the internet.

the volume of a cone is

Vc = pi×r²×height/3

we have been given the slant height (10 ft) and the lateral "wall" area of the cone (60×pi ft²).

this wall area is

Aw = pi×r×slant height

60×pi = pi×r×10

60 = r×10

6 = r

so, now we know r fuer the volume formula, and we need the height of the cone (the inner one).

we use Pythagoras

10² = r² + height²

100 = 36 + height²

height² = 64

height = 8 ft

so, now we use the main formula for the volume

Vc = pi×r²×height/3 = pi×6²×8/3 = pi×36×8/3 = pi×12×8 =

= 96×pi ft³

cubic feet ! it is a volume !

How many terms dose the polynomial have 2x^9 + 3x^6 - x - 20?

Answers

Answer:

3

Step-by-step explanation:

2x^9 = 1

3x^6 = 2

- x - 20 = 3

Select all of the expressions that are equivalent to
2(2x + y + 3y)


4x + 8y

6x + 7y

4x + 2y + 6y

4x + 4y + 3y

Answers

Answer:

2(2x + y + 3y)

=

4x + 8y

4x + 2y + 6y

Which of the graphs below represents a system of equations that has no
solution?

Answers

Answer:

the second graph which shows parallel lines

Step-by-step explanation:

Find m∠1 and m∠2. Tell which theorem can be used.

Answers

Answer:

1 = 117 ( vertically opposite angles are equal )

2 = 117 ( corresponding angles are always equal )

Step-by-step explanation:

Answer:

angle one=122 because it is using the alternate interior angle theorem

angle 2=58 because it is using the consecutive interior angle theorem

hope this helps

have a good day :)

Step-by-step explanation:

remember consecutive=same sine 122 is on the same side of angle 2 just substract 180-122=58

since 122 is on the opposite side of angle 1 it's going to be alternate something so since it's on the inside its going to be alternate interior angle

can someone tell me if what i selected is right? and if it’s not which one it is? thank you!

Answers

I think you have the correct answer

Answer:

-7x^2 + 5x + 12 AC = -84 factors = 12, -7

-7x^2 - 7x + 12x + 12

-7x (x + 1) + 12 (x + 1)

(-7x + 12) (x + 1)

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