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2 years ago

What is the solution to the equation 5x=6?

2 answers:

4 0

Answer: To find equation solutions, solve x+2=0 and x+3=0. To find equation solutions, solve x + 2 = 0 and x + 3 = 0. x2+5x+6=0 Two solutions were found : x = -2 x = -3 Step by step solution : Step 1 :Trying to factor by splitting the middle term 1.1 Factoring x2+5x+6 The first term is, x2 its ...

Step-by-step explanation:

Leni [432]2 years ago

3 0

Answer:

6 / 5 ( or ) 1.2

Step-by-step explanation:

5x = 6

x = 6 / 5

( or )

x = 1.2

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To put a narrow border around a square photo, Alicia has 32 inches of trim. The area of the photo is 60 square inches. Will she

olga nikolaevna [1]

Answer: Yes, she will have enough trim for all four sides of the square, because the perimeter of the square photo (30.98 inches) is less than 32 inches of trim she has.

Step-by-step explanation:

The formula for calculate the area of a square is:

$A=s^2$

Where "s" is the lenght of any side of the square.

The formula for calculate the perimeter of a square is:

$P=4s$

Where "s" is the lenght of any side of the square.

We know that that the area of the photo is 60 square inches, therefore, we can solve for "s" from the formula $A=s^2$ and find its value:

$A=s^2\\\\s=\sqrt{A}[\\\\s=\sqrt{60in^2}\\\\s=2\sqrt{15}in$

Substituting the value of "s" into the formula $P=4s$ , we get that the perimeter of the photo is:

$P=4(2\sqrt{15}in)=30.98in$

Therefore, since Alicia has 32 inches of trim and $30.98in$ , we can conclude that she will have enough trim for all four sides of the square.

8 0

3 years ago

Find an equation for the line that passes through the points (5.-5) and (-4,-2)

ANEK [815]

Answer:

$\large\boxed{y=-\dfrac{1}{3}x-\dfrac{10}{3}\to x+3y=-10}$

Step-by-step explanation:

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (5, -5) and (-4, -2).

Substiute:

$m=\dfrac{-2-(-5)}{-4-5}=\dfrac{-2+5}{-9}=\dfrac{3}{-9}=-\dfrac{1}{3}$

Put the value of the slope and the coordinates of the point (5, -5) to the equation of a line:

$-5=-\dfrac{1}{3}(5)+b$

$-5=-\dfrac{5}{3}+b$ add 5/3 to both sides

$-\dfrac{15}{3}+\dfrac{5}{3}=b\\\\-\dfrac{10}{3}=b\to b=-\dfrac{10}{3}$

Finally we have the equation of a line in the slope-intercept form:

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$

Convert to the standard form (Ax + By = C):

$y=-\dfrac{1}{3}x-\dfrac{10}{3}$ multiply both sides by 3

$3y=-x-10$ add x to both sides

$x+3y=-10$

4 0

3 years ago

A triangular prism and two nets are shown:

lilavasa [31]

Answer:

Net for the prism will have 3 rectangles with dimensions 5 by 15, 12 by 15 , and 13 by 15, and 2 triangles with legs 5 inches and 12 inches.

The correct net is net a.

Surface area = sum of areas of the three rectangles and sum of the two triangles.

SA = (5 x 15) + (12 x 15) + (13 x 15) + (5 x 12) = 75 + 180 + 195 + 60 = 510 square inches.

Step-by-step explanation:

Hope this helped

4 0

2 years ago

Find the roots of:

Elena-2011 [213]

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{1) \ 2x^3-7x^2+8x-3=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of -3 are 1, -1, 3, +3. So:

| 2 -7 8 -3

1 | 2 -5 3

| 2 -5 3 0

1 | 2 -3

2 -3 0

So the factorization is (x-1)² (2x-3)=0. So:

$\bf{ x_1=x_2=1 \qquad x_2=\dfrac{3}{2} }$

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{2) \ x^3-x^2-4=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of -4 are 1, -1, 2, -2, 4, -4. So:

| 1 -1 0 -4

2 | 2 2

1 2 2 0

So the factorization is (x-2)(x²+x+2)=0 . When calculating the discriminant of the trinomial, it is concluded that it has no roots since the result is negative. So you only have one solution.

$\bf{ 1^2-4(2)(2)=1-16=-15 < 0 \quad \Longrightarrow \quad x=2 }$

$\large\displaystyle\text{$\begin{gathered}\sf \pmb{3) \ 6x^3+7x^2-9x+2=0 } \end{gathered}$}$

Synthetic division is used since the equation is of the third degree. The divisors of 2 are 1, -1, 2, -2. So:

| 6 7 9 2

-2 | -12 10 -2

6 -5 1 0

So the factorization is (x+2)(6x²-5x+1)=0 . The quadratic equation is solved by the general formula:

$\bf{ x_{2, 3}&=\dfrac{5\pm \sqrt{(5)^2-4(6)(1)}}{2(6)}=\dfrac{5\pm \sqrt{25-24}}{12}=\dfrac{5\pm 1}{12} }}$

$\large\displaystyle\text{$\begin{gathered}\sf \begin{matrix} x_1=-2&\ \ \ \ \ \ x_{2}=\dfrac{6}{12} \qquad &\ \ \ x_3=\dfrac{4}{12}\\ &\ \ \ x_2=\dfrac{1}{2} \qquad &x_3=\dfrac{1}{3} \end{matrix} \end{gathered}$}$

6 0

2 years ago

Which is the graph of f(x) =

Mrac [35]

It is impossible to know because you haven’t completed your question , the formula isn’t complete

5 0

2 years ago