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3 years ago

How many solutions does the following equation have? 14x + 12] = 0

Mathematics

1 answer:

Marysya12 [62]3 years ago

8 0

Answer:

$x=-\frac{6}{7}$

It has one solution

Step-by-step explanation:

$14x + 12] = 0\\\\14x+12=0\\\mathrm{Subtract\:}12\mathrm{\:from\:both\:sides}\\14x+12-12=0-12\\\\Simplify\\14x=-12\\\\\mathrm{Divide\:both\:sides\:by\:}14\\\frac{14x}{14}=\frac{-12}{14}\\\\Simplify\\x=-\frac{6}{7}$

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find the area of the trapezium whose parallel sides are 25 cm and 13 cm The Other sides of a Trapezium are 15 cm and 15 CM

Snezhnost [94]

$\huge\underline{\red{A}\blue{n}\pink{s}\purple{w}\orange{e}\green{r} -}$

Given - A trapezium ABCD with non parallel sides of measure 15 cm each ! along , the parallel sides are of measure 13 cm and 25 cm

To find - Area of trapezium

Refer the figure attached ~

In the given figure ,

AB = 25 cm

BC = AD = 15 cm

CD = 13 cm

Construction -

$draw \: CE \: \parallel \: AD \: \\ and \: CD \: \perp \: AE$

Now , we can clearly see that AECD is a parallelogram !

$\therefore$ AE = CD = 13 cm

Now ,

$AB = AE + BE \\\implies \: BE =AB - AE \\ \implies \: BE = 25 - 13 \\ \implies \: BE = 12 \: cm$

Now , In ∆ BCE ,

$semi \: perimeter \: (s) = \frac{15 + 15 + 12}{2} \\ \\ \implies \: s = \frac{42}{2} = 21 \: cm$

Now , by Heron's formula

$area \: of \: \triangle \: BCE = \sqrt{s(s - a)(s - b)(s - c)} \\ \implies \sqrt{21(21 - 15)(21 - 15)(21 - 12)} \\ \implies \: 21 \times 6 \times 6 \times 9 \\ \implies \: 12 \sqrt{21} \: cm {}^{2}$

Also ,

$area \: of \: \triangle \: = \frac{1}{2} \times base \times height \\ \\\implies 18 \sqrt{21} = \: \frac{1}{\cancel2} \times \cancel12 \times height \\ \\ \implies \: 18 \sqrt{21} = 6 \times height \\ \\ \implies \: height = \frac{\cancel{18} \sqrt{21} }{ \cancel 6} \\ \\ \implies \: height = 3 \sqrt{21} \: cm {}^{2}$

Since we've obtained the height now , we can easily find out the area of trapezium !

$Area \: of \: trapezium = \frac{1}{2} \times(sum \: of \:parallel \: sides) \times height \\ \\ \implies \: \frac{1}{2} \times (25 + 13) \times 3 \sqrt{21} \\ \\ \implies \: \frac{1}{\cancel2} \times \cancel{38 }\times 3 \sqrt{21} \\ \\ \implies \: 19 \times 3 \sqrt{21} \: cm {}^{2} \\ \\ \implies \: 57 \sqrt{21} \: cm {}^{2}$

hope helpful :D

6 0

2 years ago

Please help me I’m desperate

Dafna1 [17]

Answer:

<h2> The first</h2>

Step-by-step explanation:

$\frac29x+3>4\frac59\\{}\quad-3\quad-3\\\\\frac29x\ >\ 1\frac59\\\div\frac29\quad \, \div\frac29\\\\x>1\frac59\div\frac29\\\\x>\frac{14}9\times\frac92\\\\x>\frac{7}1\times\frac11\\\\x>7$

That means every x wich is greater than 7

4 0

3 years ago

Q4: Write the equation in slope-intercept form of the line that is perpendicular to

forsale [732]

Answer:

5y = x + 11

Step-by-step explanation:

Given parameters:

Equation of the line ;

y = -5x + 1

Coordinates = (2, -1)

Find the equation of a line perpendicular;

Solution:

A line perpendicular to y = -5x + 1 will have slope that is a negative inverse of the given one.

Equation of a straight line is expressed as;

y = mx + c

y and x are the coordinates

m is the slope

c is the y-intercept

So, the slope of the new line perpendicular is $\frac{1}{5}$ ;

Now let us find the y-intercept of the new line;

x = -1 and y = 2

2 = $\frac{1}{5}$ x (-1) + c

c = 2 + $\frac{1}{5}$ = $\frac{11}{5}$

The equation of the new line is;

y = $\frac{1}{5}$ x + $\frac{11}{5}$

or multiply through by 5;

5y = x + 11

5 0

3 years ago

Sin A 7 divided by 25

Brums [2.3K]

Answer:

Cos A = 24/25, Tan A = 7/25

Step-by-step explanation:

Given that Sin A = 7/25

Sin = Opp/hyp

Therefore using Pythagoras theorem, adjacent will be;

= √(25²-7²)

= √576

= 24

Thus;

Cos A = adjacent/hypotenuse

= 24/25

Cos A = 24/25

Tan A = opp/hypotenuse

= 7/25

Tan A = 7/25

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3 years ago

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One half liter of lemonade concentrate was added to 3 liters of water. How many 1/3 servings of lemonade can be made?

yuradex [85]

42 servings of lemonade can be made

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3 years ago