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3 years ago

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How many solutions does this linear system have? y = y equals StartFraction 2 over 3 EndFraction x plus 2. X 2 6x – 4y = –10 one

solution: (–0. 6, –1. 6) one solution: (–0. 6, 1. 6) no solution infinite number of solutions.

1 answer:

nordsb [41]3 years ago

3 0

The system of equations provides a unique solution(one solution) at (-0.6, 1.6).

<h2>Given to us,</h2>

$y=\dfrac{2}{3}x+2$
$6x-4y=-10$

<h3>Equation 2</h3>

As we already have the value of y from equation 1, substitute its value in equation 2,

$6x-4y=-10$

$6x-4(\dfrac{2}{3}x+2)=-10$

$6x-\dfrac{8}{3}x-8=-10$

$\dfrac{6x}{1}-\dfrac{8}{3}x=-10+8$

$\dfrac{6x\times 3}{1\times 3}-\dfrac{8}{3}x=-2$

$\dfrac{18x-8x}{3}=-2$

$10x=-6\\$

$x=\dfrac{-6}{10} \\\\x=-0.6$

<h3>Equation 1,</h3>

$y=\dfrac{2}{3}x+2$

substitute the value of x in equation 1,

$y=\dfrac{2}{3}(\dfrac{-6}{10})+2\\\\y = \dfrac{-2}{5}+2\\\\y= \dfrac{-2+10}{5}\\\\y = \dfrac{8}{5}\\\\y=1.6$

As we can see the system of equations provides a unique solution(one solution) at (-0.6, 1.6).

Learn more about the system of equations:

brainly.com/question/12895249

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Rectangle A is a scale drawing of Rectangle B and has 25% of its area. If rectangle A has side lengths of 4 cm and 5 cm , what a

SpyIntel [72]

Answer:

8 cm and 10 cm

Step-by-step explanation:

Hello, <em> </em>I can help you with this.

Step 1

According to the question there are two rectangles A and B,

Rectangle A is a scale drawing of Rectangle B and has 25% of its area

in other words

$Area_{A}=0.25*Area_{B} (Equation\ 1)\\$

Step 2

Let

Rectangle A

length (1)= 4 cm

length (2)= 5 cm

$Area_{A}=4\ cm * 5\ cm\\Area_{A}=20\ cm^{2}$

put this value into equation 1

$Area_{A}=0.25*Area_{B} (Equation\ 1)\\\\20\ cm^{2} =0.25*Area_{B} \\divide\ each\ side\ by\ 0.25\\\frac{20\ cm^{2} }{0.25}=\frac{0.25}{0.25}*Area_{B}\\ Area_{B}=80\ cm^{2}$

Now, we know the area of rectangle B, to know its length we need to formule other equation

Step 3

$Area_{B}=80\ cm^{2}\\length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\$

the ratio between the lengths must be constant, so the ratio of A must be equal to ratio in B, then

$\frac{length(1A)}{length(2A)}=\frac{length(1B)}{length(2B)} \\\\\\frac{4}{5}= \frac{length(1B)}{length(2B)}\\0.8=\frac{length(1B)}{length(2B)}\\length(1B)=0.8*length(2B) (Equation 3)$

Step three

using Eq 1 and Eq 2 find the lengths

put the value of length(1B) into equation (2)

$length (1B)*length (2B)=80\ cm^{2} (equation\ 2)\\\(0.8*length(2B)) (*length (2B)=80\ cm^{2} \\\\0.8*(length (2B))^{2} =80\ cm^{2}\\(length (2B))^{2} =\frac{80\ cm^{2}}{0.8} \\(length (2B))^{2}=100\\\sqrt{(length (2B))^{2}}=\sqrt{100\ cm^{2}} \\ length (2B)=10\ cm$

Now, put the value of length(2B) into equation 3 to know length (1B)

$length(1B)=0.8*length(2B)\\length(1B)=0.8*10\ cm\\length(1B)=8 cm$

I really hope this helps you, have a great day.

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3 years ago

The sum of a number, x, and 12 is -6. What is the value of x?

Anettt [7]

Step-by-step explanation:

12-(-6)=18

-18+12=-6

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2 years ago

An object is heated to 100°. It is left to cool in a room that

stepladder [879]

Answer:

Step-by-step explanation:

Use Newton's Law of Cooling for this one. It involves natural logs and being able to solve equations that require natural logs. The formula is as follows:

$T(t)=T_{1}+(T_{0}-T_{1})e^{kt}$ where

T(t) is the temp at time t

T₁ is the enviornmental temp

T₀ is the initial temp

k is the cooling constant which is different for everything, and

t is the time (here, it's in minutes)

If we are looking first for the temp after 20 minutes, we have to solve for the k value. That's what we will do first, given the info that we have:

T(t) = 80

T₁ = 30

T₀ = 100

t = 5

k = ?

Filling in to solve for k:

$80=30+(100-30)e^{5k}$ which simplifies to

$50=70e^{5k}$ Divide both sides by 70 to get

$\frac{50}{70}=e^{5k}$ and take the natural log of both sides:

$ln(\frac{5}{7})=ln(e^{5k})$

Since you're learning logs, I'm assuming that you know that a natural log and Euler's number, e, "undo" each other (just like taking the square root of something squared). That gives us:

$-.3364722366=5k$

Divide both sides by 5 to get that

k = -.0672944473

Now that we have a value for k, we can sub that in to solve for T(20):

$T(20)=30+(100-30)e^{-.0672944473(20)}$ which simplifies to

$T(20)=30+70e^{-1.345888946}$

On your calculator, raise e to that power and multiply that number by 70:

T(20)= 30 + 70(.260308205) and

T(20) = 30 + 18.22157435 so

T(20) = 48.2°

Now we can use that k value to find out when (time) the temp of the object cools to 35°:

T(t) = 35

T₁ = 30

T₀ = 100

k = -.0672944473

t = ?

$35=30+100-30)e^{-.0672944473t}$ which simplifies to

$5=70e^{-.0672944473t}$

Now divide both sides by 70 and take the natural log of both sides:

$ln(\frac{5}{70})=ln(e^{-.0672944473t})$ which simplifies to

-2.63905733 = -.0672944473t

Divide to get

t = 39.2 minutes

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3 years ago

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Answer: 5 people

Step-by-step explanation:

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You can also find that 6/12 is equal to 1/2 by dividing each side by 6. Then multiply 10 by 1/2 (or divide 10 by 2) to get the final answer of 5 people.

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