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4 years ago

At the bake sale the students earned $48.76. If there were 3 students how much did each student earn?

Mathematics

1 answer:

jeka944 years ago

7 0

Its $16.25 hope yhu get it right

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Find cotθ, cosθ, and secθ, where θ is the angle shown in the figure.

Darina [25.2K]

Answer:

$\cos( \theta) = \frac{5}{8} \\ {8}^{2} = {5}^{2} + {opp}^{2} \\ {opp}^{2} = 64 - 25 = 39 \\ opp = \sqrt{39} \\ \sin(\theta) = \frac{\sqrt{39}}{8} \\ \tan(\theta) = \frac{ \sqrt{39} }{5} \\ \cot(\theta) = \frac{1}{\tan(\theta)} = \frac{1}{\frac{ \sqrt{39} }{5}} \\ \cot(\theta) = \frac{5}{ \sqrt{39} } \\ \csc( \theta) = \frac{1}{\sin(\theta)} = \frac{1}{\frac{\sqrt{39}}{8}} \\ \csc( \theta) = \frac{8}{ \sqrt{39} } \\ \sec( \theta) = \frac{1}{\cos( \theta) } = \frac{1}{ \frac{5}{8} } \\ \sec( \theta) = \frac{8}{5}$

5 0

2 years ago

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

What is the correct definition for tan 0

Reptile [31]

$tan\theta=\frac{sin\theta}{cos\theta}\\\\\\Look\ at\ the\ picture.\\\\In\ a\ right\ triangle:\\\\sin\theta=\frac{a}{c};\ cos\theta=\frac{b}{c};\ tan\theta=\frac{a}{b}\\\\\frac{sin\theta}{cos\theta}=\frac{\frac{a}{c}}{\frac{b}{c}}=\frac{a}{c}\times\frac{c}{b}=\frac{a}{b}=tan\theta$

3 0

3 years ago

Two increased by three equals the quotient of ten and two

RideAnS [48]

5 because increased by means to add 2+3
and quotient means the answer to a division problem 10/2 so ur answer is 5

4 0

4 years ago

A 90° angle is divided into 2 angles.

Lemur [1.5K]

Answer:

this angle's sum is 90°

(3x+40)°+(4x-6)=90°

7x+34=90°

7x=90-34

7x=56

x=56/7

x=8

3x+40 = 3×8+40 = 64°

4x-6 = 4×8-6 = 26°

8 0

3 years ago