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2 years ago

Find the slope of the line that passes through each pair of points. Express as a

Mathematics

1 answer:

Fiesta28 [93]2 years ago

8 0

Use the formula m = y2 - y1 / x2 - x1
-2 - 3 / 7 - 4
-5 / 3
the slope of the line in simplest form is -5/3

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A cuboid with a volume of 924cm^3 has dimensions 4cm, (x+1)cm and (x+11). Show clearly that x^2+12x-220=0 solve the equation by

garik1379 [7]

Answer:

$x^2+12x-220=0$ -- Proved

$x = 10\ \ \ x = -22$

Step-by-step explanation:

Given

$Volume = 924cm^3$

$Dimension: 4cm; (x+1)cm; (x+11)cm$

Required

Show that $x^2+12x-220=0$

The volume is calculated as:

$4 * (x + 1) * (x + 11) = 924$

Open the brackets

$(4x + 4) * (x + 11) = 924$

$4x^2 + 44x + 4x + 44 = 924$

$4x^2 + 48x+ 44 = 924$

Collect Like Terms

$4x^2 + 48x+ 44 - 924=0$

$4x^2 + 48x -880=0$

Divide through by 4

$\frac{4x^2}{4} + \frac{48x}{4} -\frac{880}{4}=0$

$x^2+12x-220=0$

Solving further:

Expand the expression

$x^2 + 22x - 10x - 220 = 0$

Factorize:

$x(x + 22) - 10(x + 22) = 0$

$(x - 10)(x + 22) = 0$

Split:

$x - 10 = 0;\ \ \ x + 22 = 0$

$x = 10\ \ \ x = -22$

5 0

2 years ago

Solve for X: -2(x+3)=-2(x+1)-4

vodomira [7]

Answer:

All real numbers are solutions.

Step-by-step explanation:

3 0

3 years ago

Each edge of a cube is 9 centimeters long. Find the total length of all the edges of the cube.

posledela

Answer:

108 centimeters

Step-by-step explanation:

There are 12 edges total.

9 x 12 = 108

4 0

2 years ago

14. Peter needs to buy a package of pencils to write his final exam. The store offers two packages.

miskamm [114]

Answer:

Step-by-step explanation:

peter can buy pack of nine pencils

6 divided by 1.68 =3.5

9 divided by 2.34=3.8

package 2 is just 0.3 more

it give 3 more pencils for 0.3

6 0

3 years ago

Rewrite in logarithmic form 19^2 = 361

Aneli [31]

Answer:

$\log_{19}{361}=2$

Step-by-step explanation:

We know that taking logarithms performs the transformation ...

$b^e=x\\\\e\cdot\log{b}=\log{x}\quad\text{take logs}\\\\e=\dfrac{\log{x}}{\log{b}}\quad\text{divide by $\log{b}$}\\\\\log_b{x}=e\quad\text{use the change of base formula}$

Then for b=19, e=2, x=361, we have

$\boxed{\log_{19}{361}=2}$

8 0

3 years ago