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3 years ago

Fill in the blank. In the triangle below x = ______. Round your answer to two decimal places.

Mathematics

2 answers:

kirill [66]3 years ago

5 0

Tan42°=x/35

x=35tan42° units

x≈31.51 units (to nearest hundredth of a unit)

SSSSS [86.1K]3 years ago

5 0

Answer:

$x=31.51\ units$

Step-by-step explanation:

we know that

In the right triangle

$tan(42\°)=x/35$

isolate the variable x

$x=35tan(42\°)=31.51\ units$

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Give a geometric description of the following system of equations.a. 2x−4y=12 −3x+6y=−15.b. 2x−4y=12 −5x+3y=10.a. 2x−4y=12 −3x+6

Reptile [31]

Answer:

a. No solution, parallel lines.

b. One solution.

Step-by-step explanation:

Given the system of equations:

a. $2x-4y=12$

$-3x+6y=-15$

b. $2x-4y=12$

$-5x+3y=10$

To give a geometric description of the given system of equations.

The geometric description of a system of equations in 2 variables mean the system of equations will represent the number of lines equal to the number of equations in the system given.

i.e.

Number of planes = Number of variables

Number of lines = Number of equations in the system.

Here, we are given 2 variables and 2 equation in each system.

So, they can be represented in the xy-coordinates plane.

And the number of solutions to the system depends on the following condition.

Let the system of equations be:

$A_1x+B_1y+C_1=0\\A_2x+B_2y+C_2=0$

1. One solution:

There will be one solution to the system of equations, If we have:

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

2. Infinitely Many Solutions: (Identical lines in the system)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}= \dfrac{C_1}{C_2}$

3. No Solution:(Parallel lines)

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Now, let us discuss the system of equations one by one:

a. $2x-4y=12$ OR $2x-4y-12=0$

$-3x+6y=-15$ OR $-3x+6y+15=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -3, B_2 = 6, C_2= 15$

Here, the ratio:

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2} = -\dfrac{2}{3}\\\dfrac{C_1}{C_2} = -\dfrac{4}{5}$

$\dfrac{A_1}{A_2}=\dfrac{B_1}{B_2}\neq\dfrac{C_1}{C_2}$

Therefore, no solution i.e. parallel lines.

b. $2x-4y=12$ OR $2x-4y-12=0$

$-5x+3y=10$ OR $-5x+3y-10=0$

$A_1 = 2, B_1 = -4, C_1 = -12\\A_2 = -5, B_2 = 3, C_2 = -10$

$\dfrac{A_1}{A_2}= -\dfrac{2}{5}\\\dfrac{B_1}{B_2} = -\dfrac{4}{3}\\\dfrac{C_1}{C_2} = -\dfrac{6}{5}$

$\dfrac{A_1}{A_2}\neq\dfrac{B_1}{B_2}$

So, one solution.

Kindly refer to the images attached for the graphical representation of the given system of equations.

6 0

2 years ago

Order from least to greatest. 7/25, 6/25, 11/50.

fenix001 [56]

7/25, 6/25, and 11/50. Looks like they are already in order, or you meant to do that...

3 0

3 years ago

Suppose your local school district decides to randomly test high school students for attention deficit disorder (ADD). There are

REY [17]

Answer:

Option C is correct. Option f is the same as option C

Step-by-step explanation:

From the question, There are three high schools in the district, each with grades between nine to twelve. The school board decided to pool all of the students together and randomly samples 250 students in the whole district that has schools between the grade of nine to twelve.

In order to test for high school students in the district for Attention Deficit disorder(ADD), they could have chosen any 250 students from any school with grades betweem nine to twelve throughout the district.

4 0

3 years ago

1+1 pls help me nopwwwwww

lana66690 [7]

Your answer would be 2

7 0

3 years ago

36 divided by 2^2 - 4 * 2 = 36 divided by ___ -4 *2<br> = ___ -4 * 2 <br> = ___ -8 <br> = ___

cricket20 [7]

2^2=4 so divid 36/4 is 9 and 4*2=8 now subtract 9-8=1 next 36/1 = 36 same on top is 8 now 36-8=28. 28 - 8 is 20 then 20-8= 12 answer is 12

6 0

2 years ago

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