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3 years ago

Describe how the names of the negative integer powers of 10 correspond to the names of the positive integer powers of 10.

Mathematics

1 answer:

vredina [299]3 years ago

4 0

"th" is added to the name of the negative power. Here are a few of them ...

10¹ = ten; 10⁻¹ = tenth

10² = hundred; 10⁻² = hundredth

10³ = thousand; 10⁻³ = thousandth

10⁶ = million; 10⁻⁶ = millionth

10⁹ = billion; 10⁻⁹ = billionth

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Write an equation in standard form for the line that passes through (5, -2) and is perpendicular to 3x-4y=12

Tasya [4]

The equation in standard form for the line that passes through (5, -2) and is perpendicular to 3x - 4y = 12 is 4x + 3y = 14

<h3>Solution:</h3>

Given that line that passes through (5, -2) and is perpendicular to 3x - 4y = 12

We have to find the equation of line

The slope intercept form is given as:

y = mx + c ------ eqn 1

Where "m" is the slope of line and "c" is the y-intercept

Let us first find the slope of line

Given equation of line is 3x - 4y = 12

On rearranging the above equation to slope intercept form,

3x - 4y = 12

4y = 3x - 12

$y = \frac{3}{4}x - 3$

On comparing the above equation with slope intercept form,

$m = \frac{3}{4}$

Thus the slope of line is $m = \frac{3}{4}$

We know that product of slope of given line and slope of line perpendicular to given line is always -1

slope of given line x slope of line perpendicular to given line = -1

$\begin{array}{l}{\frac{3}{4} \times \text { slope of line perpendicular to given line }=-1} \\\\ {\text {slope of line perpendicular to given line }=\frac{-4}{3}}\end{array}$

Now we have to find the equation of line with slope $m = \frac{-4}{3}$ and passes through (5, -2)

Substitute $m = \frac{-4}{3}$ and (x, y) = (5, -2) in eqn 1

$-2 = \frac{-4}{3}(5) + c\\\\-2 = \frac{-20}{3} + c\\\\-6 = -20 + 3c\\\\3c = 14\\\\c = \frac{14}{3}$

The required equation of line is:

Now substitute $m = \frac{-4}{3}$ and $c = \frac{14}{3}$

$y = \frac{-4}{3}x + \frac{14}{3}$

The standard form of an equation is Ax + By = C

x and y are variables and A, B, and C are integers

Rewriting the above equation,

$y = \frac{-4}{3}x + \frac{14}{3}$

3y = -4x + 14

4x + 3y = 14

Thus the equation of line in standard form is found out

6 0

3 years ago

Help? Show work! (TV ) ⃗ bisects ∠STU,m∠STV=(1/4 x+8)°, and m∠UTV=(x+2)°.Find m∠STU.

Doss [256]

Answer:

m∠STU = 20 °

Step-by-step explanation:

Since the line bisects the angle, we have that the two bisected angles are equal

Thus, mathematically;

x + 2 = x/4 + 8

Multiply through by 4

4x + 8 = x + 32

4x-x = 32-8

3x = 24

x = 24/3

x = 8

So to find the value of the original angle, we input 8 into each of the bisected angles and add together

mathematically, that will be ;

10 + 10 = 20

7 0

3 years ago