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1 year ago

24 inches = blank centimeters

Mathematics

1 answer:

Alona [7]1 year ago

6 0

We want to express 24 inches as centimeters. Through a quick research, we can find that 1 inch = 2.54 centimeters.

So, to find the total number we take the amount of inches and multiply it by 2.54. That would be

$24\text{ inches }\cdot\frac{2.54\text{ centimeters}}{1\text{ inches}}=\text{ 60.96 centimeters}$

so 24 inches = 60.96 centimeters

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Which of the following is an extraneous solution of (45 minus 3 x) Superscript one-half Baseline = x minus 9?

STALIN [3.7K]

The extraneous solution of the given radical equation is x = 3

<h3>Finding the extraneous solution:</h3>

Here we have the radical equation:

$\sqrt{45 - 3x} = x - 9$

We want to get the extraneous solution, to get it, we first need to square both sides of the equation, so we get:

$(\sqrt{45 - 3x} )^2 = (x - 9)^2\\\\45 - 3x = x^2 - 18x + 81$

Now we got a quadratic equation, we can rewrite it as:

$x^2 - 18x + 81 + 3x - 45 = 0\\\\x^2 - 15x + 36 = 0$

To solve this we use Bhaskara's formula, we will get:

$x = \frac{15 \pm \sqrt{(-15)^2 - 4*1*36} }{2*1} \\\\x = \frac{15 \pm 9}{2}$

Then the two solutions are:

x = (15 + 9)/2 = 12

x = (15 - 9)/2 = 3

<h3>Which one is the extraneous solution?</h3>

Let's evaluate both solutions in our original equation and let's see which is the one that does not work:

for x = 12 we have:

$\sqrt{45 - 3*12} = 12 - 9\\3 = 3$

This is true.

For x = 3 we have:

$\sqrt{45 - 3*3} = 3 - 9\\\\6 = -6$

This is false, so the extraneous solution is x = 3.

If you want to learn more about extraneous solutions, you can read:

brainly.com/question/2959656

4 0

2 years ago

find the values of the six trigonometric functions for angle theta in standard position if a point with the coordinates (1, -8)

frutty [35]

Answer:

cosФ = $\frac{1}{\sqrt{65}}$ , sinФ = $-\frac{8}{\sqrt{65}}$ , tanФ = -8, secФ = $\sqrt{65}$ , cscФ = $-\frac{\sqrt{65}}{8}$ , cotФ = $-\frac{1}{8}$

Step-by-step explanation:

If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:

cosФ = $\frac{x}{r}$
sinФ = $\frac{y}{r}$
tanФ = $\frac{y}{x}$
secФ = $\frac{r}{x}$
cscФ = $\frac{r}{y}$
cotФ = $\frac{x}{y}$

Where r = $\sqrt{x^{2}+y^{2} }$ (the length of the terminal side from the origin to point (x, y)

You should find the quadrant of (x, y) to adjust the sign of each function

∵ Point (1, -8) lies on the terminal side of angle Ф in standard position

∵ x is positive and y is negative

→ That means the point lies on the 4th quadrant

∴ Angle Ф is on the 4th quadrant

∵ In the 4th quadrant cosФ and secФ only have positive values

∴ sinФ, secФ, tanФ, and cotФ have negative values

→ let us find r

∵ r = $\sqrt{x^{2}+y^{2} }$

∵ x = 1 and y = -8

∴ r = $\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}$

→ Use the rules above to find the six trigonometric functions of Ф

∵ cosФ = $\frac{x}{r}$

∴ cosФ = $\frac{1}{\sqrt{65}}$

∵ sinФ = $\frac{y}{r}$

∴ sinФ = $-\frac{8}{\sqrt{65}}$

∵ tanФ = $\frac{y}{x}$

∴ tanФ = $-\frac{8}{1}$ = -8

∵ secФ = $\frac{r}{x}$

∴ secФ = $\frac{\sqrt{65}}{1}$ = $\sqrt{65}$

∵ cscФ = $\frac{r}{y}$

∴ cscФ = $-\frac{\sqrt{65}}{8}$

∵ cotФ = $\frac{x}{y}$

∴ cotФ = $-\frac{1}{8}$

8 0

3 years ago

Marlin davies buys a truck for $28,000. In three years, the truck depreciates 48% in value. How muck is the truck worth in three

Finger [1]

28,000*48%=13440

The truck is worth $13,440 in three years.

8 0

3 years ago

Read 2 more answers

Answers in geometry questions that I need to print

Nuetrik [128]

Answer:

2) m∠CBD = 25°

The measure of arc CDB = 230°

4) m arc XY = 10°

The measure of arc WZX = 330°

6) The answer is (c) ⇒ 10 millimeters

Step-by-step explanation:

2) ∵ the measure of arc BC = 130°

∵ Arc BCD is the semi-circle its measure 180°

∴ The measure of arc cd = 180 - 130 = 50°

∵ ∠CBD is inscribed angle subtended by arc CD

∴ m∠CBD = 1/2 measure arc CD

∴ m∠CBD = 50 ÷ 2 = 25°

∵ The measure of the circle is 360°

∵ The measure of arc BC = 130°

∴ The measure of arc CDB = 360 - 130 = 230°

4) ∵ The measure of arc WY = 40°

∵ The measure of arc XZ = 30°

∵ The measure of arc WZ = 60°

∵ m arc WY + m arc XZ - m arc XY = m arc WZ

∴ m arc XY = 40 + 30 - 60

∴ m arc XY = 10°

∵ The measure of the circle is 360°

∴ The measure of arc WZX = 360 - m arc WX

∵ The measure of arc WX = WY - XY = 40 - 10 = 30°

∴ The measure of arc WZX = 360 - 30 = 330°

6) In the circle O

∵ OC ⊥ AB and OX ⊥ ZY

∵ OC = OX

∴ AB = ZY ⇒ Theorem

∵ AB = 10 millimeters

∴ ZY = 10 millimeters ⇒ answer (C)

3 0

4 years ago

What does x equal in the equation x-12+5x=24

Bess [88]

Answer:

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers