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Lynna [10]
3 years ago
14

Solve the following simultaneous equation using either the substitution method or the elimination method, showing all the necess

ary steps.
Will award brainliest!!

Mathematics
1 answer:
slavikrds [6]3 years ago
4 0

Answer:

x=1\frac{83}{91}\\y=-2\frac{73}{91}

Step-by-step explanation:

#Using the method of substitution and replacement of unknown values.

Given that

\frac{3}{2}x+\frac{2}{3}y=1...(i)\\and\\\frac{1}{6}x-\frac{3}{5}y=2...(ii)\\

Express eqtn (ii) in terms of x

\frac{1}{6}x=2+\frac{3}{5}y\\x=12+\frac{18}{5}y

Replacing for x in eqtn (i)

\frac{3}{2}(12+\frac{18}{5}y)+\frac{2}{3}y=1\\18+\frac{27}{5}y+\frac{2}{3}y=1\\18-1=-\frac{91}{15}y\\y=-2\frac{73}{91}

Substitute y value in eqtn(ii) to obtain x

Y=-2\frac{73}{91}\\\frac{1}{6}x-\frac{3}{5}y=2\\x=2+\frac{3}{5}(-2\frac{73}{91})\\x=1\frac{83}{91}

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A bag contains purple marbles and red marbles, 55 in total. The number of purple marbles is 7 more than 5 times the number of re
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Answer:

There would be 8 red marbles and 47 purple marbles.

Step-by-step explanation:

In order to find this, we can first set the amount of red marbles as x. Once we do this, it is possible to model the number of purple marbles as 5x + 7. Knowing this, we can add the two together and set equal to 55.

x + 5x + 7 = 55

6x + 7 = 55

6x = 48

x = 8

With 8 red marbles, we know the rest must be purple (47)

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What is the simplified expression for –3cd – d(2c – 4) – 4d?
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-5cd

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What are the x-intercepts of the parabola? y=-3(x+5)(x-9)
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That parabola hits (-5,0) and (9,0) so the x-intercepts are -5 and 9

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Jim saw that other bank offered the same rates but compounded the interest more often. Consider if he still put $15,000 into a s
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Compound interest is the addition of interest on the interest of the principal amount.

<h3>What is compound interest?</h3>

Compound interest is the addition of interest on the interest of the principal amount. It is given by the formula,

A = P(1+ \dfrac{r}{n})^{nt}

As it is given that the principal amount is $15,000; while the rate of interest is 2.8%, and the amount is invested for a period of 5 years.

A.) When the interest is charged weekly,

As we know that there are 52 weeks in a year, therefore, n = 52, substitute the values,

A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{52})^{52 \times 5}\\\\A = \$17,253.46

B.) When the interest is charged daily,

As we know that there are 365 days in a year, therefore, n = 365, substitute the values,

A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{365})^{365 \times 5}\\\\A = \$19,554.55

C.) When the interest is charged Continuously,

As we know that the formula for continuous compounding is given as,

A = Pe^{rt}

Substitute the values, we will get,

A = 15000 \times (e^{0.024 \times 5})\\\\A= \$16,912.45

D.) When the interest is charged Monthly,

As we know that there are 12 months in a year, therefore, n = 12, substitute the values,

A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{12})^{12\times 5}\\\\A = \$15211.23

E.) When the interest is charged Semi-annually,

As we know that the interest is charged Semi-annually, therefore, n = 2, substitute the values,

A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{2})^{2\times 5}\\\\A = \$17,237.36

F.) When the interest is charged Quarterly,

As we know that the interest is charged Quarterly, therefore, n = 4, substitute the values,

A = P(1+ \dfrac{r}{n})^{nt}\\\\A = 15000(1+ \dfrac{0.028}{4})^{4\times 5}\\\\A = \$17,245.7

Learn more about Compound Interest:

brainly.com/question/25857212

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Answer:

7.9km

Step-by-step explanation:

(a)See attached for the diagram representing this situation.

(b)

In Triangle ABC

\text{Using Law of Sines}\\\dfrac{\sin A}{a}=\dfrac{\sin C}{c} \\\dfrac{\sin A}{5.2}=\dfrac{\sin 58^\circ}{6.8} \\\sin A=5.2 \times \dfrac{\sin 58^\circ}{6.8}\\A=\arcsin (5.2 \times \dfrac{\sin 58^\circ}{6.8})\\A=40.43^\circ

Next, we determine the value of Angle B.

\angle A+\angle B+\angle C=180^\circ\\40.43+58+\angle B=180^\circ\\\angle B=180^\circ-(40.43+58)\\\angle B=81.57^\circ

Finally, we find b.

\text{Using Law of SInes}\\\dfrac{b}{\sin B}=\dfrac{c}{\sin C} \\\dfrac{b}{\sin 81.57^\circ}=\dfrac{6.8}{\sin 58^\circ} \\b=\dfrac{6.8}{\sin 58^\circ} \times \sin 81.57^\circ\\b=7.9km $ (to the nearest tenth of a kilometer)

The distance between the small plane and the observation tower is 7.9km.

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