The measures of the angles of a triangle are shown in the figure below. Solve for X

Answer:

The longest side length b is approximately 13.172 cm

Step-by-step explanation:

The given parameters are;

The area of the triangle = 22.4 cm²

The given angles of the triangle = ∠97°

The given side of the triangle = 3.7 cm

The formula for the area of a triangle, A = 1/2 × a × b × sin(C)

Where;

a, and b are the side legs forming the angle C

Therefore,  we have;

A = 22.4 = 1/2 × 3.7 × a × sin(97°)

a =  22.4/(1/2 × 3.7 × sin(97°)) ≈ 12.199

a ≈ 12.199 cm

Therefore, by cosine rule, we have;

b² = a² + c² - 2 × a × c × Cos(B)

Substituting the values, gives;

b² = 12.199² + 3.7² - 2 × 12.199 × 3.7 × Cos(97°)

b² ≈ 173.507

∴ b ≈ √173.507 ≈ 13.172

b ≈ 13.172 cm

Answer:

Andy is designing a dice tray in the shape of a rectangular prism to use during a role-playing game. The tray needs to be three centimeters high and have a volume of 252 cubic centimeters in order for the dice to roll properly. The length of the tray should be five centimeters longer than its width.

The volume of a rectangular prism is found using the formula V = l · w · h, where l is the length, w is the width, and h is the height.

Complete the equation that models the volume of the tray in terms of its width, x, in centimeters.

3x2 + 15x = 252

Is it possible for the width of the tray to be 7.5 centimeters?

no it is too large

Step-by-step explanation:

An equation is formed when two equal expressions. The equation that models the volume of the tray in terms of its width, x, in centimeters is 3x² + 15x - 252 = 0.

An equation is formed when two equal expressions are equated together with the help of an equal sign '='.

Let the width of the rectangular prism die be represented by x.

Given that the length of the tray should be five centimeters longer than its width. Therefore, the length and the width of the prism can be written as,

Width = x

Length = x + 5

Further, it is given that the volume of die is 252 cubic centimeters in order for the dice to roll properly. Also, the height of the prism is 3 centimeters. Therefore, the Volume can be written as,

Volume = Length × Width × Height

252 = (x + 5) × x × 3

252 = 3x(x+5)

252 = 3x² + 15x

3x² + 15x - 252 = 0

Hence, the equation that models the volume of the tray in terms of its width, x, in centimeters is 3x² + 15x - 252 = 0.

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Answer:

good handwritting the first is 87

Step-by-step explanation:

Answer:

x = 8, y = 2

Step-by-step explanation:

Multiply the second equation by -2:

x + 6y = 20

-2x - 6y = -28

Add the equations and simplify:

-x = -8

x = 8

Plug x = 8 back into the first equation and solve for y:

8 + 6y = 20

6y = 12

y = 2

Answer:

x=8

Y=2

or

(x,y)=(8,2)

Step-by-step explanation:

x+6y=20

x+3y=14

solve the equation for x

x+6y=20

x=14-3y

substitute the given value of x into the equation

x+6y=20

14-3y+6y=20

14+3y=20

3y=20-14

3y=6

3y/3=6/3

y=2.

substitute the given value of y into the equation

x=14-3y

x=14-3×2

x=14-6

x=8.

the possible solution of the system is the ordered pair (x,y)

(x,y)=(8,2)

or

x=8

Y=2

Proof:

Check if the given ordered pair is the solution of the system of equations

8+6×2=20

8+3×2=14

simply the equalities

20=20

14=14

since all of the equalities are true, the ordered pair is the solution of the system

(x,y)=(8,2)

Answer:

7.1 yard per min

Step-by-step explanation:

Answer:

3

Step-by-step explanation:

Find the prime factors of each term in order to find the greatest common factor (GCF).

So the greatest number of both is 3

Hope this helps

Answer:

uhm chile anyways

Step-by-step explanation:

i just want points lol

Answer:

34

Step-by-step explanation:

So -9x is 36,36-2=34

Answer:

34

Step-by-step explanation:

-9(-4)-2

36-2

34

Answer:

No because it does no pass the vertical line test

Step-by-step explanation:

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[tex]slope = \frac{9 - 7}{5 - 12} \\ [/tex]

[tex]slope = \frac{2}{ - 7} \\ [/tex]

[tex]slope = - \frac{2}{7} \\ [/tex]

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Answer:

[tex]\boxed {\boxed {\sf m= -\frac{2}{7}}}[/tex]

Step-by-step explanation:

The slope of a line can be found using the following formula:

[tex]m=\frac{y_2-y_2}{x_2-x_1}[/tex]

Where (x₁,y₁) and (x₂,y₂) are the points on the line.

We are given the points (12,7) and (5,9). Therefore:

[tex]x_1=12\\y_1=7\\\\x_2=5 \\y_2=9[/tex]

Substitute the values into the formula.

[tex]m=\frac{9-7}{5-12}[/tex]

Solve the numerator.

[tex]m=\frac{2}{5-12}[/tex]

Solve the denominator.

[tex]m=\frac{2}{-7}[/tex]

This fraction cannot be reduced further, so it is the answer.

The slope of the line is -2/7

Answer:

5 calories per minute

Step-by-step explanation:

225÷45=5

Answer:

The company manufactures 5 delta cars, 8 beta cars and 12 sigma cars.

Step-by-step explanation:

let in the motor company x number of delta cars, y number of beta cars and z number of sigma cars are manufactured.

from the condition given in the question we can write

9x + 13y + 9z = 257 ........ (1)

4x + 6y + 4z = 116 ........... (2) and    

3x + 4y + z = 59 ......... (3)

From equation (2) we get

9x + 13.5y + 9z = 261 ....... (4) {Multiplying with  both sides}

solving equations (1) and (4) we get

0.5y = 4

and ⇒ y = 8.

from equation (2) putting the value of y we get,  

4x + 4z = 116 - 48 = 68

⇒x + z = 17 .....(5)

Now, from equation (3) putting y = 8 we get,  

3x + z = 59 - 32 = 27 ....... (6)  

hence, solving equations (5) and (6) we get, 17 - x = 27 - 3x

⇒ 2x = 10

⇒ x = 5  

So, z = 17 - x = 12

therefore, the company manufactures 5 delta cars, 8 beta cars and 12 sigma cars.

Answer:

Step-by-step explanation:

Triangle A - Equilateral triangle because all the angles are equal which means all the sides will be equal.

Triangle B - Isosceles Triangle because 2 sides are equal (we know this because 2 of the angles are equal)

Triangle C - Equilateral triangle because all the sides are equal.

Triangle D - Scalene triangle because all the sides have different lengths.

Step-by-step explanation:

subtraction if that wut u askim

Answer:39 i dont im 12 ps out

Step-by-step explanation:

The no. of apples on the tree today

= The no. of apples on the tree yesterday - 5

Let us take 'the no. of apples on the tree today' as 'x'

and 'the no. of apples on the tree today' as 'y'

Therefore, x = y - 5

Hope this is the thing u are looking for

Answer:

undefined

Step-by-step explanation:

Horizontal lines have no slope. The line on the graph is vertical, so we can't really tell what slope it is. But there isn't any run and only rise, therefore the slope is "undefined."

Answer:

84

Step-by-step explanation:

p^2-r^2= 10^2-(-4)^2

100-16=84

Answer:

The answer is A. Sorry, i dont have enough time to support my answer. I am rushing sdjeuesjcvjs

Answer:

-72

Step-by-step explanation:

first replace x with -12 so 5(-12)-12

then simplify which makes it -60-12

finally solve that which gives you -72

hope this helps :)

Answer:

Yes, you have enought money

Step-by-step explanation:

45 times 107% (100 for the total cost and and 7 for the tax) is equal to 48.15. You have 50 dollars, therefore you can buy your shoes.

F. Square root of 39

Step-by-step explanation:

Value of [tex]\boldsymbol{x}[/tex] is [tex]\boldsymbol{\sqrt{39}}[/tex] units.

Option F. is correct.

Two triangles are said to be similar if their sides are proportional and their corresponding angles are equal.

[tex]\bigtriangleup ABD \sim \bigtriangleup CAD[/tex]

[tex]\boldsymbol{\frac{AD}{CD}=\frac{BD}{AD} }[/tex]

  [tex]\frac{x}{13}=\frac{3}{x}[/tex]

  [tex]x^2=39[/tex]

   [tex]x=\sqrt{39}[/tex] units.

Value of [tex]\boldsymbol{x}[/tex] is [tex]\boldsymbol{\sqrt{39}}[/tex] units.

Option F. is correct.

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Answer:

7 seconds i think let me know if its wrong

Step-by-step explanation:

Answer:

it would be 5:2

Step-by-step explanation:

none of these are equivalent to the ratio and 2:5 would be 2 to 5

Answer:

5:2

Step-by-step explanation:

Answer:

n(AUB) = 33

Step-by-step explanation:

U is the 21'st letter of the alphabet so

9 + 1 + 2 + 21 =33

n(AUB) = 33

The correct format of the question is

After an​ accident, police can use the formula [tex]v=2\sqrt{5L }[/tex] to estimate the​ speed, v, in miles per​ hour, that a car was traveling by measuring the length of the skid​ marks, L, in feet. Estimate the speed of a car that left skid marks 118 ft long. If the posted speed limit is 45 ​mi/h, was the car​ speeding? The speed of a car that left skid marks 118 ft long was about nothing ​mi/h.

Answer:

48.6mi/h, Yes the car was speeding.

Step-by-step explanation:

The speed of the car is given by  [tex]v=2\sqrt{5L }[/tex]

Skid length (L) = 118ft

V= [tex]2\sqrt{5*118}[/tex]

  = 2 [tex]\sqrt{590}[/tex]  

  =  2*24.3

V = 48.6mi/h

Since the speed limit is 45mi/h and the velocity of this driver is 48.6mi/h it is clear that was speeding by 3.6mi/h over speed limit.

Answer:

1296

Step-by-step explanation:

6x6x6x6

6^4

Answer:

6×6×6×6

Step-by-step explanation:

I hope this helps

Answer:

37.2 = 38

Step-by-step explanation:

After divideing 1265 by 34, you will get 37.2. As you cannot have books not in bookshelves, you will have to round up and have 38 bookshelves.

Answer:

here you go. hope this helps!