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2 years ago

Write the definition of the vertex of an angle as a biconditional statement

Mathematics

2 answers:

geniusboy [140]2 years ago

5 0

Answer:

The vertex of an angle is formed, if and only if the sides of the angles intersect or meet.

Step-by-step explanation:

The definition of the vertex of an angle is - The vertex of the angle is the point, where the sides of the angle intersect.

A bi conditional statement is in the form of - p if and only if q.

Hence, the definition of the vertex of an angle as a bi conditional statement can be written as :

The vertex of an angle is formed, if and only if the sides of the angles intersect or meet.

daser333 [38]2 years ago

4 0

The highest point,the top, or apex it is just like a mountain,its vertex is called an peak

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Step-by-step explanation:

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2 years ago

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Lisa [10]

Answer:

A. x + y > 30 8x + 10y ≥ 450

Step-by-step explanation:

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2 years ago

What is the following product? RootIndex 3 StartRoot 16 x Superscript 7 Baseline EndRoot times RootIndex 3 StartRoot 12 x Supers

KengaRu [80]

Answer:

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}\sqrt[3]{3x} }$

Step-by-step explanation:

Given

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9}$

Required

Find the products

From laws of indices;

$\sqrt[m]{a} * \sqrt[m]{b} = \sqrt[m]{a*b}$

So;

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{16x^7 * 12x^9}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{16* x^7 * 12 * x^9}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{16*12* x^7 * x^9}$

From laws of indices

$a^m * a^n = a^(m+n); So,$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{16*12* x^{7+9}}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{16*12* x^{16}}$

Expand 16 * 12

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{4*4*4*3* x^{16}}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = \sqrt[3]{4^3 *3* x^{16}}$

From laws of imdices

$a^{\frac{1}{m}} = \sqrt[m]{a}$

So;

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4^3 *3* x^{16}})^{\frac{1}{3}}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4^{3*{\frac{1}{3}}} *3^{{\frac{1}{3}}}* x^{16*{\frac{1}{3}}}})$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{\frac{1}{3}}}* x^{\frac{16}{3}}}$

Divide 16 by 3 (Write as ,mixed number)

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{\frac{1}{3}}}* x^{5\frac{1}{3}}}$

Split mixed numbers

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{\frac{1}{3}}}* x^{5+\frac{1}{3}}}$

Apply law of indices

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 *3^{{\frac{1}{3}}}* x^{5}*{x ^\frac{1}{3}}}$

Reorder

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 * x^{5}*3^{{\frac{1}{3}}}*{x ^\frac{1}{3}}}$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}*3^{{\frac{1}{3}}}*{x ^\frac{1}{3}}}$

Apply law of indices

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}*\sqrt[3]{3} *\sqrt[3]{x} }$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}*\sqrt[3]{3*x} }$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}*\sqrt[3]{3x} }$

$\sqrt[3]{16x^7} * \sqrt[3]{12x^9} = {4 x^{5}\sqrt[3]{3x} }$

6 0

2 years ago

Express 30p as a fraction of £3.00

neonofarm [45]

Answer:

$\frac{1}{10} \£$

Step-by-step explanation:

We know that £1 equals 100p.

Knowing this relation, we can use the rule of three

$30p \times \frac{ \£1}{100p} =0.3 \£$

Then, we form the fraction

$\frac{0.3 \£}{\£ 3.00} =\frac{3}{30} =\frac{1}{10} \£$

Therefore, the fraction of of £3.00 is

$\frac{1}{10} \£$

4 0

2 years ago

Michael is walking from home to work. The function graphed represents the remaining distance to his work, in kilometers, x hours

Karolina [17]

x intercept- the number of remaining hours it takes to walk to work.

y intercept- the remaining distance from home to work.

Just took the quiz. Hope this helps you guys baiii <33

3 0

2 years ago

Read 2 more answers