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3 years ago

3x+4y=29 6x+5y=43 Solve through elimination

Mathematics

1 answer:

vagabundo [1.1K]3 years ago

6 0

Answer:

Let's solve your system by elimination.

3x+4y=29;6x+5y=43

Multiply the first equation by -2,and multiply the second equation by 1.

−2(3x+4y=29)

1(6x+5y=43)

Becomes:

−6x−8y=−58

6x+5y=43

Add these equations to eliminate x:

−3y=−15

Then solve−3y=−15for y:

−3y=−15

−3y −3 = −15

−3

(Divide both sides by -3)

y=5

Now that we've found y let's plug it back in to solve for x.

Write down an original equation:

3x+4y=29

Substitute5foryin3x+4y=29:

3x+(4)(5)=29

3x+20=29(Simplify both sides of the equation)

3x+20+−20=29+−20(Add -20 to both sides)

3x=9

3x 3 = 9

(Divide both sides by 3)

x=3

Answer:

x=3 and y=5

Step-by-step explanation:

I love this stuff 229 999 0523

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Finding Hypotenuse Lengths. Find the length of the hypotenuse.

ioda

Answer:

11) $\frac{3\sqrt{5}}{2}$

12) $4\sqrt{5}$

13) $22$

14) $18$

15) $2$

16) $24\sqrt{3}$

Step-by-step explanation:

For these problems I used the pythagorean theorem: $a^{2}+ b^{2}= c^{2}$ and SOHCAHTOA

Sin = $\frac{opposite}{hypotenuse}$

Cos = $\frac{adjacent}{hypotenuse}$

Tan = $\frac{opposite}{hypotenuse}$

11)

First find the length of the bottom side by using Cos

$cos(60)=\frac{x}{3}$

$3(cos(60))=x$

$1.5=x$

Then plug it into the formula for the pythagorean theorem to find the hypotenuse

$3^{2}+ 1.5^{2}= c^{2}$

$9+2.25=c^{2}$

$\sqrt{11.25}=\sqrt{c^{2}}$

$\frac{3\sqrt{5}}{2}$

12)

Find the length of the bottom side using Cos

$cos(60)=\frac{x}{8}$

$8(cos(60))=x$

$4=x$

Then plug it into the formula for the pythagorean theorem to find the hypotenuse

$8^{2}+ 4^{2}= c^{2}$

$64+16=c^{2}$

$\sqrt{80} =\sqrt{c^{2} }$

$4\sqrt{5}$

13)

Find the length of the other side by using Tan

$tan(30)=\frac{x}{11\sqrt{3} }$

$11\sqrt{3}* (tan(30)=x$

$11=x$

Then plug it into the formula for the pythagorean theorem to find the hypotenuse

$(11\sqrt{3}) ^{2}+ 11^{2}= c^{2}$

$363+121=c^{2}$

$\sqrt{484} =\sqrt{c^{2}}$

$22$

14)

(This is probably an easier way to do these problems)

Find the hypotenuse by using Cos ( $\frac{adjacent}{hypotenuse}$ )

$cos(60)=\frac{9}{x}$

$cos(60)x=9$

$x=\frac{9}{cos(60)}$

$x=18$

15)

Find the hypotenuse using Sin ( $\frac{opposite}{hypotenuse}$ )

$sin(30)=\frac{1}{x}$

$sin(30)x=1\\x=\frac{1}{sin(x)}$

$x=2$

16)

Find the hypotenuse using Cos ( $\frac{adjacent}{hypotenuse}$ )

$cos(60)=\frac{12\sqrt{3} }{x}$

$cos(60)x=12\sqrt{3}$

$x=\frac{12\sqrt{3} }{cos(60)}$

$x=24\sqrt{3}$

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4 years ago

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Sergio039 [100]

If this is for E2020 the answer is
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3 years ago

Read 2 more answers

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Lunna [17]

Answer:

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Step-by-step explanation:

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polet [3.4K]

Given:

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To find:

The slope of the line.

Solution:

Formula for slope:

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A system of equations is shown. 0.6d+0.05e=-4.5 -0.12d+0.3e=2.76 d= e=

Drupady [299]

I would multiply to get rid of the decimals and work with whole numbers.
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60d + 5e = -450
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60d + 5e = -450
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155e = 930
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Now plug 6 back in for e and solve for d.
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60d + 30 = -450
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