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3 years ago

Solve by elimination method 5x-2y=11, 3x+4y=4.

Mathematics

1 answer:

anastassius [24]3 years ago

8 0

Answer:

x = 2 y= -1/2

Step-by-step explanation:

5x-2y=11 {1} . 2

3x+4y=4 {2} . 1

-> 10x-4y=22

+ 3x+4y = 4

-> 13x = 26

-> x= 26/13 x= 2/1 x= 2

-> 3(2)+4y=4

->6+4y=4 -> 4y= 4-6

-> 4y= -2 -> y= -2/4 -> y=-1/2

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The ratio of pink roses bushes to white rose bushes in the city Garden is about 12 to 15. If there were 92 pink rose bushes, abo

andreyandreev [35.5K]

Answer:

$115\ white\ rose\ bushes$

Step-by-step explanation:

Let

x------> the number of pink roses bushes

y----> the number of white rose bushes

we know that

$\frac{x}{y} =\frac{12}{15}$

$y=\frac{15}{12}x$ -----> equation A

$x=92$

substitute the value of x in the equation A

$y=\frac{15}{12}(92)=115\ white\ rose\ bushes$

8 0

3 years ago

Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = 9t + 9 cot(t/2), [π/4, 7π/4]

agasfer [191]

Answer:

the absolute maximum value is 89.96 and

the absolute minimum value is 23.173

Step-by-step explanation:

Here we have cotangent given by the following relation;

$cot \theta =\frac{1 }{tan \theta}$ so that the expression becomes

f(t) = 9t +9/tan(t/2)

Therefore, to look for the point of local extremum, we differentiate, the expression as follows;

f'(t) = $\frac{\mathrm{d} \left (9t +9/tan(t/2) \right )}{\mathrm{d} t}$ = $\frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9 \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2}$

Equating to 0 and solving gives

$\frac{9\cdot sin^{2}(t)-\left (9\cdot cos^{2}(t)-18\cdot cos(t)+9 \right )}{2\cdot cos^{2}(t)-4\cdot cos(t)+2} = 0$

$t=\frac{4\pi n_1 +\pi }{2} ; t = \frac{4\pi n_2 -\pi }{2}$

Where n $_i$ is an integer hence when n₁ = 0 and n₂ = 1 we have t = π/4 and t = 3π/2 respectively

Or we have by chain rule

f'(t) = 9 -(9/2)csc²(t/2)

Equating to zero gives

9 -(9/2)csc²(t/2) = 0

csc²(t/2) = 2

csc(t/2) = ±√2

The solutions are, in quadrant 1, t/2 = π/4 such that t = π/2 or

in quadrant 2 we have t/2 = π - π/4 so that t = 3π/2

We then evaluate between the given closed interval to find the absolute maximum and absolute minimum as follows;

f(x) for x = π/4, π/2, 3π/2, 7π/2

f(π/4) = 9·π/4 +9/tan(π/8) = 28.7965

f(π/2) = 9·π/2 +9/tan(π/4) = 23.137

f(3π/2) = 9·3π/2 +9/tan(3·π/4) = 33.412

f(7π/2) = 9·7π/2 +9/tan(7π/4) = 89.96

Therefore the absolute maximum value = 89.96 and

the absolute minimum value = 23.173.

7 0

3 years ago

A retailer buys pants at $28.00 and sells them for $42.00. The percent of markup on cost is

Elena L [17]

30% is the answer to the question.

4 0

2 years ago

Read 2 more answers

Help Help!!!!!!!!!!!!!!!

BabaBlast [244]

Answer:

$\frac{7}{10} y$

Step-by-step explanation:

To add fractions <em>with the same denominator</em>, simply add the numerators:

$\frac{a}{b} + \frac{c}{b} = \frac{a+c}{b}$

So:

$\frac{3}{10} y+\frac{4}{10} y=\frac{7}{10} y$

6 0

3 years ago

Find the equation of the line in slope-intercept form (-1,-1) and (1,0)

ArbitrLikvidat [17]

Answer:

An equation in slope-intercept form of the line will be

$y\:=\frac{1}{2}x-\frac{1}{2}$

Step-by-step explanation:

The slope-intercept form of the line equation

y = mx+b

where m is the slope and b is the y-intercept

Given the points

(-1, -1)

(1, 0)

Finding the slope between (-1,-1) and (1,0)

$\mathrm{Slope}=\frac{y_2-y_1}{x_2-x_1}$

$\left(x_1,\:y_1\right)=\left(-1,\:-1\right),\:\left(x_2,\:y_2\right)=\left(1,\:0\right)$

$m=\frac{0-\left(-1\right)}{1-\left(-1\right)}$

$m=\frac{1}{2}$

substituting m = 1/2 and (-1, -1) in the slope-intercept form of the line equation to determine the y-intercept

$y = mx+b$

$-1=\frac{1}{2}\left(-1\right)+b$

$-\frac{1}{2}+b=-1$

Add 1/2 to both sides

$-\frac{1}{2}+b+\frac{1}{2}=-1+\frac{1}{2}$

$b=-\frac{1}{2}$

substituting m = 1/2 and b = -1/2 in the slope-intercept form of the line equation

$y = mx+b$

$y\:=\frac{1}{2}x+\left(-\frac{1}{2}\right)$

$y\:=\frac{1}{2}x-\frac{1}{2}$

Therefore, an equation in slope-intercept form of the line will be

$y\:=\frac{1}{2}x-\frac{1}{2}$

3 0

2 years ago

Solve by elimination method 5x-2y=11, 3x+4y=4.​

Solve by elimination method 5x-2y=11, 3x+4y=4.