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3 years ago

What is the solution to the system of equations? {x+2y=10y=12x+3

Mathematics

1 answer:

Marianna [84]3 years ago

5 0

The solution to given system of equations are $(x,y) = (\frac{4}{25} , \frac{123}{25})$

Solution:

Given that we have to find solution to the system of equations

Given equations are:

x + 2y = 10 ------ eqn 1

y = 12x + 3 ------ eqn 2

We can solve the above equations by substitution method

Substitute eqn 2 in eqn 1

x + 2(12x + 3) = 10

x + 24x + 6 = 10

25x = 10 - 6

25x = 4

$x = \frac{4}{25}$

Substitute the above value of x in eqn 2

$y = 12(\frac{4}{25}) + 3\\\\y = \frac{48}{25} + 3\\\\y = \frac{48+75}{25}\\\\y = \frac{123}{25}$

Thus the solution to given system of equations are $(x,y) = (\frac{4}{25} , \frac{123}{25})$

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Heidi grew her hair out for many years. Her hair was 12/10 of a meter long. She donated her hair by cutting off 5/6 of a meter.

coldgirl [10]

Answer:

0.37 meters.

Step-by-step explanation:

12/10 of 1 meter = 1.2meters

5/6 of 1 meter = 0.8333333333 meters.

1.2 meters - 0.833333333 meters = 0.366666667 meters.

~0.37 meters

Please give brainliest if I am correct, if I am not; sorry about that.

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3 years ago

GEOMETRY HELP!

tigry1 [53]

Answer:

1. Length of BC = 35

2. SU = 3.5

3. AC = 50 inches

Part 1: AB = 10 cm

Part 2: AD = 2 cm

5. Width of River AB = 145.45 ft

Step-by-step explanation:

The length of BC is (x+4)+(2x+1) = 3x+5

Now, if we figure out x, we can plug that in and find length of BC.

Using similarity with the two triangles shown, we can set-up the ratio as:

$\frac{8}{12}=\frac{x+4}{2x+1}$

Now, cross multiplying and solving for x:

$\frac{8}{12}=\frac{x+4}{2x+1}\\8(2x+1)=12(x+4)\\16x+8=12x+48\\4x=40\\x=\frac{40}{4}=10$

Now plugging in x=10 into 3x+5, we have 3(10)+5 = 35

Length of BC = 35

Using pythagorean theorem in triangle PQT, we can solve for QT.

$(\sqrt{2})^2+(\sqrt{2})^2=QT^2\\2+2=QT^2\\4=QT^2\\QT=\sqrt{4}=2$

QT = RS = 2

Now using pythagorean theorem on Triangle RSU, we can solve for SU. So:

$RS^2+SU^2=RU^2\\2^2+SU^2=4^2\\SU^2=4^2-2^2\\SU^2=12\\SU=\sqrt{12}=3.5$

SU = 3.5

If we draw a straight line as Segment AC, we have a right triangle with both legs measuring 30 and 40 inches, respectively. AC is the hypotenuse. Using pythagorean theorem, we can find out AC:

$AB^2+BC^2=AC^2\\30^2+40^2=AC^2\\2500=AC^2\\AC=\sqrt{2500}=50$

Thus AC = 50 inches

AB:

We can set-up a similarity ratio to solve for AB. We can write:

$\frac{12}{20}=\frac{6}{AB}$

Now, cross multiplying, we can solve for AB:

$\frac{12}{20}=\frac{6}{AB}\\12AB=6*20\\12AB=120\\AB=\frac{120}{12}=10$

Thus, AB = 10 cm

AD:

We know, AB = BF + FD + DA

We also know, FD = 6, AB = 10 and BF & DA are same. So we can write DA in place of BF and solve. Thus:

$AB = BF + FD + DA\\10=AD+6+AD\\10-6=2AD\\4=2AD\\AD=2$

Thus, AD = 2 cm

A single piece of information is missing from this problem. They have given DE = 32 ft.

Now, we see that triangle EDC is similar to triangle ABC, so their corresponding sides are proportional. Thus we can set-up a ratio as:

$\frac{DC}{BC}=\frac{DE}{BA}$

Now we can put the information we know and solve for AB, the width of the river.

$\frac{DC}{BC}=\frac{DE}{BA}\\\frac{22}{100}=\frac{32}{AB}\\22AB=32*100\\22AB=3200\\AB=\frac{3200}{22}=145.45$

Width of River AB = 145.45 ft

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3 years ago

Which measure of central tendency should be used when there is an outlier?

katrin2010 [14]

Answer:

Median.

Step-by-step explanation:

The median is a better measure than the mean when there is an outlier.

3 0

3 years ago

What can i do to be brainiest

grigory [225]

You can answer some questions that say (PLEASE ANSWER I WILL GIVE YOU BRAINIEST!!!!!!!) it usually happens if you answer it first ;D

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3 years ago

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Pelomyxa palustris is an amoeba with a length of 4.9 mm.Amoeba proteus has a length of 0.7 mm.How many amoeba proteus would you

prohojiy [21]

Answer:

Step-by-step explanation:

Let n represent the number we're looking for. Then ...

n × (proteus length) = 3 × (palustris length)

n × 0.7 mm = 3 × 4.9 mm

n = (3 × 4.9 mm)/(0.7 mm) = 3 × 49/7 = 3 × 7

n = 21

You would have to line up 21 amoeba proteus to equal the length of three pelomyxa palustris.

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3 years ago