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2 years ago

Three Step Linear Equations Solve for x 8x+5=-6x+3

Mathematics

2 answers:

tensa zangetsu [6.8K]2 years ago

8 0

Answer:

x = -1/7 or -0.14285 - in decimal form

Step-by-step explanation:

8x + 5 = -6x + 3

8x + 6x = 3 - 5 { change side }

14x = -2 { basic addition and subtraction }

x = -2/14 { changing sides }

x = -1/7 { simplified }

AysviL [449]2 years ago

8 0

Answer:

Subtract

from both sides of the equation

the answer is x=-1

7 a fraction

Step-by-step explanation:

sorry i know that its sloppy

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Is anyone able to figure this out, I can't do this

katrin [286]

Answer:

C. √2 - 1

Step-by-step explanation:

If we draw a square from the center of the large circle to the center of one of the small circles, we can see that the sides of the square are equal to the radius of the small circle (see attached diagram)

Let r = the radius of the small circle

Using Pythagoras' Theorem $a^2+b^2=c^2$

(where a and b are the legs, and c is the hypotenuse, of a right triangle)

to find the diagonal of the square:

$\implies r^2 + r^2 = c^2$

$\implies 2r^2 = c^2$

$\implies c=\sqrt{2r^2}$

So the diagonal of the square = $\sqrt{2r^2}$

We are told that the radius of the large circle is 1:

⇒ Diagonal of square + r = 1

$\implies \sqrt{2r^2}+r=1$

$\implies \sqrt{2r^2}=1-r$

$\implies 2r^2=(1-r)^2$

$\implies 2r^2=1-2r+r^2$

$\implies r^2+2r-1=0$

Using the quadratic formula to calculate r:

$\implies r=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

$\implies r=\dfrac{-2\pm\sqrt{2^2-4(1)(-1)}}{2(1)}$

$\implies r=\dfrac{-2\pm\sqrt{8}}{2}$

$\implies r=-1\pm\sqrt{2}$

As distance is positive, $r=-1+\sqrt{2}=\sqrt{2}-1$ only

5 0

3 years ago

Read 2 more answers

Kenji earned the test scores below in English class.

vitfil [10]

Answer:

Step-by-step explanation:

Mean is all the numbers divided by the amount of numbers listed and Median is what ever number is in the middle (when in order of value). when there's not a exact middle number u add the two numbers in the middle and divide it by two

8 0

3 years ago

Simplify the expression c^-6 * d^4/ c^-16 * d^14

Naily [24]

Answer:

$\dfrac{c^{10}}{d^{10}}$

Step-by-step explanation:

Although the way you wrote problem, this is not what it looks like, I think this is what you meant.

$\dfrac{c^{-6} \times d^{4}}{c^{-16} \times d^{14}} =$

$= \dfrac{c^{-6}}{c^{-16}} \times \dfrac{d^{4}}{d^{14}}$

$= c^{-6 - (-16)} \times d^{4 - 14}$

$= c^{-6 + 16} \times d^{-10}$

$= c^{10} \times d^{-10}$

$= \dfrac{c^{10}}{d^{10}}$

7 0

3 years ago

21. In 4 + In(4x - 15) = In(5x + 19)

Alexxx [7]

Answer:

$x=-30;\quad \:I\ne \:0$

Step-by-step explanation:

$In\cdot \:4+In\left(4x-15\right)=In\left(5x+19\right)$

$\:4+In\left(4x-15\right):\quad -11nI+4nxI\\In\cdot \:4+In\left(4x-15\right)\\=4nI+nI\left(4x-15\right)\\\\\:In\left(4x-15\right):\quad 4nxI-15nI\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b-c\right)=ab-ac\\a=In,\:b=4x,\:c=15\\=In\cdot \:4x-In\cdot \:15\\=4nxI-15nI\\=In\cdot \:4+4nxI-15nI\\\mathrm{Simplify}\:In\cdot \:4+4nxI-15nI:\quad -11nI+4nxI\\In\cdot \:4+4nxI-15nI\\\mathrm{Group\:like\:terms}\\=4nI-15nI+4nxI\\\mathrm{Add\:similar\:elements:}\:4nI-15nI=-11nI\\=-11nI+4nxI\\$

$\mathrm{Expand\:}In\left(5x+19\right):\quad 5nxI+19nI\\In\left(5x+19\right)\\=nI\left(5x+19\right)\\\mathrm{Apply\:the\:distributive\:law}:\quad \:a\left(b+c\right)=ab+ac\\a=In,\:b=5x,\:c=19\\=In\cdot \:5x+In\cdot \:19\\=5nxI+19nI\\\\-11nI+4nxI=5nxI+19nI\\\\\mathrm{Add\:}11nI\mathrm{\:to\:both\:sides}\\-11nI+4nxI+11nI=5nxI+19nI+11nI\\Simplify\\4nxI=5nxI+30nI\\\mathrm{Subtract\:}5nxI\mathrm{\:from\:both\:sides}\\4nxI-5nxI=5nxI+30nI-5nxI\\\mathrm{Simplify}\\-nxI=30nI\\$

$\mathrm{Divide\:both\:sides\:by\:}-nI;\quad \:I\ne \:0\\\frac{-nxI}{-nI}=\frac{30nI}{-nI};\quad \:I\ne \:0\\\mathrm{Simplify}\\\frac{-nxI}{-nI}=\frac{30nI}{-nI}\\\mathrm{Simplify\:}\frac{-nxI}{-nI}:\quad x\\\frac{-nxI}{-nI}\\\mathrm{Apply\:the\:fraction\:rule}:\quad \frac{-a}{-b}=\frac{a}{b}\\=\frac{nxI}{nI}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{xI}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=x\\\mathrm{Simplify\:}\frac{30nI}{-nI}:\quad -30\\\mathrm{Apply\:the\:fraction\:rule}:$

$\quad \frac{a}{-b}=-\frac{a}{b}\\\mathrm{Cancel\:the\:common\:factor:}\:n\\=\frac{30I}{I}\\\mathrm{Cancel\:the\:common\:factor:}\:I\\=-30\\x=-30;\quad \:I\ne \:0$

3 0

3 years ago

What is the volume of a sphere with a radius of 7 cm? Sphere V = 4 3 πr3 1. Substitute the radius into the formula: V = 4 3 π

netineya [11]

Answer:

1436.75504 or 1372/3π cm^3

Step-by-step explanation:

The volume of a sphere can be found using:

V = 4/3 πr^3

We know the radius is 7, so we can substitute 7 in for r

V = 4/3 π7^3

Evaluate the exponent

V = 4/3 π 343

If we want the answer in terms of pi, multiply the two other numbers, that are not pi: 4/3 and 343.

v= (4/3*343)π

v=1372/3π

If we want an exact answer, multiply 1372/3 and pi

v=1436.75504

So, the volume is 1436.75504 or 1372/3 π cm^3

4 0

3 years ago

Read 2 more answers