Given the equation 3x + 25 = 7x − 5, which order of operations completely solves for x

Learning Task 4. Solve the problem by applying the sum and product of roots

Delvig [45]

Answer:

<em>Thus, the dimensions of the metal plate are 10 dm and 8 dm.</em>

Step-by-step explanation:

For a quadratic equation:

$x^2+bx+c=0$

The sum of the roots is -b and the product is c. Note the leading coefficient is 1.

We know the perimeter of the rectangular metal plate is 36 dm and its area is 80 dm^2. Being L and W its dimensions, then:

P=2(L+W)=36

A=L.W=80

Note both formulas are closely related to the roots of the quadratic equation, we only need to adjust the data for the perimeter to be exactly the sum of L+W and not double of it.

Thus we use the semi perimeter instead as P/2=L+W=18

The quadratic equation is, then:

$x^2-18x+80=0$

Factoring by finding two numbers that add up to 18 and have a product of 80:

$(x-10)(x-8)=0$

The solutions to the equation are:

x=10, x=8

Thus, the dimensions of the metal plate are 10 dm and 8 dm.

6 0

3 years ago

What is the equation of the line that passes through the points (-1, 7) and (2, 10) in Standard Form?

Usimov [2.4K]

bearing in mind that standard form for a linear equation means

• all coefficients must be integers, no fractions

• only the constant on the right-hand-side

• all variables on the left-hand-side, sorted

• "x" must not have a negative coefficient

$\bf (\stackrel{x_1}{-1}~,~\stackrel{y_1}{7})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{10}) \\\\\\ slope = m\implies \cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{10-7}{2-(-1)}\implies \cfrac{3}{2+1}\implies \cfrac{3}{3}\implies 1$

$\bf \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-7=1[x-(-1)]\implies y-7=x+1 \\\\\\ y=x+8\implies \boxed{-x+y=8}\implies \stackrel{\textit{standard form}}{x-y=-8}$

just to point something out, is none of the options, however -x + y = 8, is one, though improper.

3 0

3 years ago

Find the distance UV between the points U (7,-4) and V(-3,-6). Round your answers to the nearest tenth,if necessary

rodikova [14]

Answer:

<h3>The answer is 10.2 units</h3>

Step-by-step explanation:

The distance between two points can be found by using the formula

$d = \sqrt{ ({x1 - x2})^{2} + ({y1 - y2})^{2} } \\$

where

(x1 , y1) and (x2 , y2) are the points

From the question the points are

U (7,-4) and V(-3,-6)

The distance between them is

$|UV| = \sqrt{( {7 + 3})^{2} + ( { - 4 + 6})^{2} } \\ = \sqrt{ {10}^{2} + {2}^{2} } \\ = \sqrt{100 + 4} \: \\ = \sqrt{104} \: \: \: \: \: \: \: \: \\ = 2 \sqrt{26} \: \: \: \: \: \: \: \: \\ = 10.1980...$