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4 years ago

Solve for x

1" title=" \frac{x}{a} = \frac{x}{b} " alt=" \frac{x}{a} = \frac{x}{b} " align="absmiddle" class="latex-formula">

Mathematics

1 answer:

lesya [120]4 years ago

6 0

$Domain:\ a\neq0\ \wedge\ b\neq0$

$\dfrac{x}{a}=\dfrac{x}{b}\qquad|\text{cross multiply}\\\\bx=ax\qquad|\text{subtract ax from both sides}\\\\bx-ax=0\\\\x(b-a)=0\qquad|\text{divide both sides by }\ b-a\neq0\\\\x=0$

$\dfrac{x}{a}=\dfrac{x}{b}\\\\if\ a\neq b\ then\ x=0\\\\if\ a=b\ then\ x\in\mathbb{R}$

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The cost of a circular table is directly proportional to the square of the radius. A circular table with a radius of 50cm costs

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Answer:

£135 is the correct answer.

Step-by-step explanation:

Let C be the cost of table.

And let R be the radius of table.

Cost of table is directly proportional to square of radius.

As per question statement:

$C\propto R^{2}$ or

$C=a\times R^2 ....... (1)$

where $a$ is the constant to remove the $\propto sign$ .

It is given that

$C_1 =$ £60 and $R_1 = 50\ cm$

$C_2 = ?$ when $R_2= 75\ cm$

Putting the values of $C_1$ and $R_1$ in equation (1):

$60=a \times 50^2 ....... (2)$

Putting the values of $C_2$ and $R_2$ in equation (1):

$C_2=a \times 75^2 ....... (3)$

Dividing equation (2) by (3):

$\dfrac{60}{C_2}= \dfrac{a \times 50^2}{a \times 75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{50^2}{75^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{2^2}{3^2}\\\Rightarrow \dfrac{60}{C_2}= \dfrac{4}{9}\\\Rightarrow C_2 = 15 \times 9 \\\Rightarrow C_2 = 135$

So, <em>£135 is the correct answer</em>.

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3 years ago

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Answer:

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3 years ago

What is 14% of 40 million?

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14% of 40,000,000 is 5,600,000

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3 years ago

Can someone please help me with 3,4,5,6 pleaseeee!

FromTheMoon [43]

Answer:

3) m∠E = 102°

4) m∠V = 41°

5) x = 9

6) m∠J = 77°

Step-by-step explanation:

3) Find m∠E:

∠DFE and ∠GFH are opposite angles, so they have equal measures.

Now you know have 3 expressions for the angle measures of ΔGFH

Write an equation and solve for x:

(10x + 3) + (13x - 5) + 90 = 180

combine like terms:

23x + 88 = 180

subtract 88:

23x = 92

divide by 23:

x = 4°

Now that you have the value of x, you can evaluate both expressions given for ΔDFE:

6(4) + 11 = 35°

10(4) + 3 = 43°

Solve for the missing angle:

35 + 43 + m∠E = 180

m∠E + 78 = 180

m∠E = 102°

4) Find m∠V

ΔRST is an equilateral triangle (all sides are equal)

An equilateral triangle has 3 equal angles:

180 ÷ 3 = 60°

∠STR and ∠UTV are supplementary (add up to 180°):

m∠STR + m∠UTV = 180

m∠UTV + 60 = 180

∠UTV = 120°

Now that you have this angle, you can calculate the value of x:

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9x + 117 = 180

9x = 63

x = 7

Now you can calculate the measure of ∠V

m∠V = 5(7) + 6 = 41°

5) Find the value of x

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In an isosceles triangle, the base angles are congruent.

Write an equation and solve for x:

29 + 29 + (8x - 14) = 180

8x + 44 = 180

8x = 136

x = 17

6) Find m∠J

Same as the last one, base angles are congruent.

Write an equation and solve for x:

(8x + 5) + (8x + 5) + (5x - 19) = 180

21x - 9 = 180

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x = 9

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m∠J = 8(9) + 5 = 77°

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