Which of the following is a radical equation???

The lines represented by the equations y = -X – 3 and

xz_007 [3.2K]

The equations y = -x -3 and 5y + 5x = -15 represents the same line option 'the same line' is correct.

<h3>What is linear equation?</h3>

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

We have two equation of the line:

y = -x -3 and

5y + 5x = -15

From the equation 5y + 5x = -15:

Divide by 5 on the above equation:

y + x = -3

or

y = -x -3

The two equations y = -x -3 represents the same line.

Thus, the equations y = -x -3 and 5y + 5x = -15 represents the same line option 'the same line' is correct.

Learn more about the linear equation here:

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3 0

2 years ago

Need help please!!!!

ArbitrLikvidat [17]

Given : A inequality is given to us . The inequality is 19 ≥ t + 18 ≥ 11 .

To Find : The correct option between the given ones . To write the compound inequality with integers .

Solution : The given inequality to us is 19 ≥ t + 18 ≥ 11 . Let's simplify them seperately .

$\red{\tt Case\:1}$

⇒ 19 ≥ t + 18 .

⇒ t + 18 ≤ 19 .

⇒ t ≤ 19 - 18 .

⇒ t ≤ 1 = 1 ≥ t . ..................(i)

$\red{\tt Case\:2}$

⇒ t + 18 ≥ 11 .

⇒ t ≥ 11 - 18.

⇒ t ≥ -7 . ....................(ii)

On combing (i) & (ii) .

$\Large\boxed{\green{\bf \red{\longmapsto} 1 \geqslant t \geqslant -7 }}$

This means that t is less than or equal to 1 but greater than or equal to (-7) .

4 0

3 years ago

Solving a trigonometric equation involving an angle multiplied by a constant

PIT_PIT [208]

In these questions, we need to follow the steps:

1 - solve for the trigonometric function

2 - Use the unit circle or a calculator to find which angles between 0 and 2π gives that results.

3 - Complete these angles with the complete round repetition, by adding

$2k\pi,k\in\Z$

4 - these solutions are equal to the part inside the trigonometric function, so equalize the part inside with the expression and solve for x to get the solutions.

1 - To solve, we just use algebraic operations:

$\begin{gathered} \sqrt[]{3}\tan (3x)+1=0 \\ \sqrt[]{3}\tan (3x)=-1 \\ \tan (3x)=-\frac{1}{\sqrt[]{3}} \\ \tan (3x)=-\frac{\sqrt[]{3}}{3} \end{gathered}$

2 - From the unit circle, we can see that we will have one solution from the 2nd quadrant and one from the 4th quadrant:

The value for the angle that give positive

$+\frac{\sqrt[]{3}}{3}$

is known to be 30°, which is the same as π/6, so by symmetry, we can see that the angles that have a tangent of

$-\frac{\sqrt[]{3}}{3}$

Are:

$\begin{gathered} \theta_1=\pi-\frac{\pi}{6}=\frac{5\pi}{6} \\ \theta_2=2\pi-\frac{\pi}{6}=\frac{11\pi}{6} \end{gathered}$

3 - to consider all the solutions, we need to consider the possibility of more turn around the unit circle, so:

$\begin{gathered} \theta=\frac{5\pi}{6}+2k\pi,k\in\Z \\ or \\ \theta=\frac{11\pi}{6}+2k\pi,k\in\Z \end{gathered}$

Since 5π/6 and 11π/6 are π radians apart, we can put them together into one expression:

$\theta=\frac{5\pi}{6}+k\pi,k\in\Z$

4 - Now, we need to solve for x, because these solutions are for all the interior of the tangent function, so:

$\begin{gathered} 3x=\theta \\ 3x=\frac{5\pi}{6}+k\pi,k\in\Z \\ x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z \end{gathered}$

So, the solutions are:

$x=\frac{5\pi}{18}+\frac{k\pi}{3},k\in\Z$

4 0

2 years ago

calvin and 4 of his friends want to share 4 pounds of nuts equally.write an expression to show the fraction of the nuts each fri

PilotLPTM [1.2K]

4/5

The 4 is how many pounds of nuts there are and dividing by 5 shows that you are sharing the nuts equally amongst the 5 friends.

5 0

3 years ago

Part A) Julio makes a scale drawing of the kitchen floor to determine how many square feet of flooring he needs to buy . The sca

serg [7]

Part A)
we know that
scale ----------> inch/4 feet=0.25 in/ft

[scale]=[scale drawing]/[actual]
[actual]=[scale drawing]/[scale]

for length --------> 4 1/2 in ---------> 4.5 in (scale drawing)
[actual]=[4.5]/[0.25]=18 ft

for width ---------> 3 3/8 in ---> (3*8+3)/8 ---> 27/8 in (scale drawing)
[actual]=[27/8]/[0.25]=13.5 ft

the answer part A is
length actual kitchen floor is 18 ft
width actual kitchen floor is 13.5 ft

Part B)
the area of one square in the actual=(1/2)*(1/2)=0.25 ft²
total area gray tiles=0.25*14=3.5 ft²
total area white tiles=0.25*10=2.5 ft²

find how many tiles 2 in by 2 in of each color will he need
1ft²-------------> 144 in²
gray tiles
3.5 ft²---------------> 3.5*144=504 in²
[tiles 2 in by 2 in gray]=504/(2*2)=126 gray tiles

white tiles
2.5 ft²---------------> 2.5*144=360 in²
[tiles 2 in by 2 in white]=360/(2*2)=90 white tiles

the answer Part B) is
126 gray tiles
90 white tiles

6 0

4 years ago

Read 2 more answers