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3 years ago

Work out angle x 55°

Mathematics

1 answer:

just olya [345]3 years ago

5 0

Answer:

70°

Step-by-step explanation:

We know that the triangle is an iscoceles based on the 2 small lines drawn horizontally on 2 sides of the triangle.

We know that the base angles in an iscoceles triangle are the same, so the angle that has not been drawn is 55°.

55° + 55° = 110°

180° - 110° = 70° (180 comes from the entire triangle adding up to 180°)

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without building the graph, find the coordinates of the point of intersection of the lines given by the equation y=3x-1 and 3x+y

DaniilM [7]

<h2><u>1. Determining the value of x and y:</u></h2>

Given equation(s):

$y = 3x - 1$
$3x + y = -7$

To determine the point of intersection given by the two equations, it is required to know the x-value and the y-value of both equations. We can solve for the x and y variables through two methods.

<h3 /><h3><u>Method-1: Substitution method</u></h3>

Given value of the y-variable: 3x - 1

Substitute the given value of the y-variable into the second equation to determine the value of the x-variable.

$\implies 3x + y = -7$

$\implies3x + (3x - 1) = -7$

$\implies3x + 3x - 1 = -7$

Combine like terms as needed;

$\implies 3x + 3x - 1 = -7$

$\implies 6x - 1 = -7$

Add 1 to both sides of the equation;

$\implies 6x - 1 + 1 = -7 + 1$

$\implies 6x = -6$

Divide 6 to both sides of the equation;

$\implies \dfrac{6x}{6} = \dfrac{-6}{6}$

$\implies x = -1$

Now, substitute the value of the x-variable into the expression that is equivalent to the y-variable.

$\implies y = 3(-1) - 1$

$\implies$ $\ \ = -3 - 1$

$\implies$ $= -4$

Therefore, the value(s) of the x-variable and the y-variable are;

$\boxed{x = -1}$ $\boxed{y = -4}$

<h3 /><h3><u>Method 2: System of equations</u></h3>

Convert the equations into slope intercept form;

$\implies\left \{ {{y = 3x - 1} \atop {3x + y = -7}} \right.$

$\implies \left \{ {{y = 3x - 1} \atop {y = -3x - 7}} \right.$

Clearly, we can see that "y" is isolated in both equations. Therefore, we can subtract the second equation from the first equation.

$\implies \left \{ {{y = 3x - 1 } \atop {- (y = -3x - 7)}} \right.$

$\implies \left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.$

Now, we can cancel the "y-variable" as y - y is 0 and combine the equations into one equation by adding 3x to 3x and 7 to -1.

$\implies\left \{ {{y = 3x - 1} \atop {-y = 3x + 7}} \right.$

$\implies 0 = (6x) + (6)$

$\implies0 = 6x + 6$

This problem is now an algebraic problem. Isolate "x" to determine its value.

$\implies 0 - 6 = 6x + 6 - 6$

$\implies -6 = 6x$

$\implies -1 = x$

Like done in method 1, substitute the value of x into the first equation to determine the value of y.

$\implies y = 3(-1) - 1$

$\implies y = -3 - 1$

$\implies y = -4$

Therefore, the value(s) of the x-variable and the y-variable are;

$\boxed{x = -1}$ $\boxed{y = -4}$

<h2><u>2. Determining the intersection point;</u></h2>

The point on a coordinate plane is expressed as (x, y). Simply substitute the values of x and y to determine the intersection point given by the equations.

⇒ (x, y) ⇒ (-1, -4)

Therefore, the point of intersection is (-1, -4).

<h3>Graph:</h3>

5 0

2 years ago

Solve the Inequality and express each solution in set interval notation.

solniwko [45]

The correct answer is x=5

3 0

3 years ago

0=-20.5x+16.35x-0.1245

Pachacha [2.7K]

The value of x in the given equation $-20.5x+16.35x -0.1245 = 0\\$ is 0.03

<u>Step-by-step explanation:</u>

The given equation is that $-20.5x+16.35x -0.1245 = 0\\$

<u>The steps to be followed to solve the equation are :</u>

Add the like terms together to reduce the equation in a simplified form.

Here, there are two x terms and they must be reduced to a single term.

For this, add the both terms together so that the equation is simplified into one x term and a constant term.

⇒ $(-20.5x+16.35x) - 0.1245 = 0$

⇒ $4.15x-0.1245 = 0$

To eliminate the constant term on the left side of the equation, add 0.1245 on both sides.

⇒ $4.15x -0.1245+0.1245 = 0.1245$

⇒ $4.15x = 0.1245$

Now, the equation is further simplified by dividing 4.15 on both sides,

⇒ $4.15x / 4.15 = 0.1245/4.15$

⇒ $x = 0.03$

Therefore, the value of x is 0.03

7 0

4 years ago

The quotient of a number and 3 decreased by 121 is -164. Select the solution to the sentence shown.

docker41 [41]

Its algebra. The original equation is $\frac{x}{3} -121 = -164$

To solve for a variable, we reverse the order of operations, beginning with addition/subtraction, and then multiplication/division. To remove a number from one side, we must do the opposite to the other side. In this case, to get rid of the -121 we must add 121 to the -164. This gives us -43. Then, to get the x by itself, we must multiply the other side by 3. -43*3=129

When we are doing the opposite of an operation to the other side, we are really reversing the operation and, to keep both sides equal, we must do whatever we have done to one side to the other side. So when we have -121, we add 121 as it equals 0, therefore it is gone. Since a equation must be balanced, we have to do what we did to the other side (adding 121).

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3 years ago

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3 years ago