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3 years ago

Which is the best description of the equivalency of the two expressions?

Mathematics

1 answer:

Reil [10]3 years ago

8 0

Answer:

They are equivalent expression because when x = 2, the expressions have the same value.

Step-by-step explanation:

Equivalent expressions are identified when the value of the variable can be substituted in each equation and the same result is found. So, even though the expression may look different, when you put the same number in for the variable, you will get the same value. You can also 'simplify' your expressions by combining like terms:

Expression 1: 5x² - 2x + 6x - 4 + 3 = 5x² + 4x - 1

Expression 2: 6x² - x² - 6x + 10x + 6 - 7 = 5x² + 4x -1

Since both expressions are the same after simplifying, they will produce the same value when x = 2, so they are equivalent.

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Use the system of equations. Please show your steps and how you solved it!

Alinara [238K]

1. 3x+3y=15
-3y = -3y (subtract 3y from both sides)
3x = 15-3y
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3 = 3 3 (divide each number by 3)
x = 5- y

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3 years ago

Travis drew this graph to plan his rectangular garden. The points on the graph mark the four corners of the fence around the gar

s2008m [1.1K]

The length of the rectangular garden which Travis drew on graph is equal to the large side of the rectangle made by four points and width is equal to short side.

<h3>What is the perimeter of a rectangle?</h3>

The measure of the boundary of the sides of a rectangles called its perimeter. The perimeter of a rectangle is twice the sum its length and width.

P=2(l+w)

Here, (l) is the length of the rectangle and (w) is the width of the rectangle.

Travis drew a graph to plan the rectangular garden he has. The points over the graph marked are the four corners of the fence around the garden.

Now let suppose the two corner marked are with total distance of x while other two with total distance of y. Then the length will be x and width will be y.

Thus, the length of the rectangular garden which Travis drew on graph is equal to the large side of the rectangle made by four points and width is equal to short side.

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1 year ago

Please look at the picture, I need help ASAP.

forsale [732]

See below for the proof that the areas of the lune and the isosceles triangle are equal

<h3>How to prove the areas?</h3>

The area of the isosceles triangle is:

$A_1 = \frac 12r^2\sin(\theta)$

Where r represents the radius.

From the figure, we have:

$\theta = 90$

So, the equation becomes

$A_1 = \frac 12r^2\sin(90)$

Evaluate

$A_1 = \frac 12r^2$

Next, we calculate the length (L) of the chord as follows:

$\sin(45) = \frac{\frac 12L}{r}$

Multiply both sides by r

$r\sin(45) = \frac 12L$

Multiply by 2

$L = 2r\sin(45)$

This gives

$L = 2r\times \frac{\sqrt 2}{2}$

$L = r\sqrt 2$

The area of the semicircle is then calculated as:

$A_2 = \frac 12 \pi (\frac{L}{2})^2$

This gives

$A_2 = \frac 12 \pi (\frac{r\sqrt 2}{2})^2$

Evaluate the square

$A_2 = \frac 12 \pi (\frac{2r^2}{4})$

Divide

$A_2 = \frac{\pi r^2}{4}$

Next, calculate the area of the chord using

$A_3 = \frac 12r^2(\theta - \sin(\theta))$

Recall that:

$\theta = 90$

Convert to radians

$\theta = \frac{\pi}{2}$

So, we have:

$A_3 = \frac 12r^2(\frac{\pi}{2} - \sin(\frac{\pi}{2}))$

This gives

$A_3 = \frac 12r^2(\frac{\pi}{2} - 1)$

The area of the lune is then calculated as:

$A = A_2 - A_3$

This gives

$A = \frac{\pi r^2}{4} - \frac 12r^2(\frac{\pi}{2} - 1)$

Expand

$A = \frac{\pi r^2}{4} - \frac{\pi r^2}{4} + \frac 12r^2$

Evaluate the difference

$A = \frac 12r^2$

Recall that the area of the isosceles triangle is

$A_1 = \frac 12r^2$

By comparison, we have:

$A = A_1 = \frac 12r^2$

This means that the areas of the lune and the isosceles triangle are equal

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1 year ago

Write the equation for the parabola that has x− intercepts (1.2,0) and (4,0) and y− intercept (0,12).

zzz [600]

Equation of a parabola is written in the form of f(x)=ax²+bx+c.
The equation passes through points (4,0), (1.2,0) and (0,12), therefore;
replacing the points in the equation y = ax² +bx+c
we get 0 = a(4)²+b(4) +c for (4,0)
0 = a (1.2)²+ b(1.2) +c for (1.2,0)
12 = a(0)² +b(0) +c for (0,12)
simplifying the equations we get
16a + 4b + c = 0
1.44a +1.2b + c = 0
+c = 12
thus the first two equations will be
16a + 4b = -12
1.44 a + 1.2b = -12 solving simultaneously
the value of a = 5/2 and b =-13
Thus, the equation of the parabola will be given by;
y= 5/2x² - 13x + 12 or y = 2.5x² - 13x + 12

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3 years ago

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Answer:

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2 years ago

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