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4 years ago

{ y = - 4x-23-4x-3y=13

Mathematics

1 answer:

sleet_krkn [62]4 years ago

7 0

For this case we have the following system of equations:

$y = -4x-23\\-4x-3y = 13$

We solve by the substitution method:

We substitute the first equation in the second equation:

$-4x-3 (-4x-23) = 13$

We apply distributive property considering that $- * - = +:$

$-4x + 12x + 69 = 13\\8x + 69 = 13$

We subtract 69 from both sides of the equation:

$8x = 13-69\\8x = -56$

We divide by 8 on both sides of the equation:

$x = \frac {-56} {8}\\x = -7$

We look for the value of the variable y:

$y = -4 (-7) -23\\y = 28-23\\y = 5$

Thus, the solution of the system is $(x, y): (-7,5)$

Answer:

$(x, y): (-7,5)$

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Answer:

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3 years ago

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A gift box is 10 inches long and 6 inches wide. It is 3 inches tall. What is the volume of the box? PLEASE SHOW YOUR WORK!

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Answer:

180 in

Step-by-step explanation:

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3 years ago

Aysha has 40 cubes in a bag.

marissa [1.9K]

Given:

Total number of cubes = 40

Red cubes = 18

Blue cubes = 13

Yellow cubes = 9

Aysha adds some more red cubes into the bag.

The probability now that she will take a red cube is 0.5.

To find:

The probability that she will take a yellow cube.

Solution:

Let Aysha adds x red cubes into the bag. Then,

Number of total cubes = 40+x

Number of red cubes = 18+x

Probability of getting a red cube is:

$P(Red)=\dfrac{18+x}{40+x}$

The probability now that she will take a red cube is 0.5. So,

$\dfrac{18+x}{40+x}=0.5$

$18+x=0.5(40+x)$

$18+x=20+0.5x$

$x-0.5x=20-18$

$0.5x=2$

Divide both sides by 0.5.

$x=\dfrac{2}{0.5}$

$x=4$

It means Aysha adds 4 more red cubes into the bag.

Now, the total number of cubes int he bag is:

$40+4=44$

Probability of getting a yellow cube is:

$P(Yellow)=\dfrac{\text{Number of yellow cubes}}{\text{Total number of cubes}}$

$P(Yellow)=\dfrac{9}{44}$

Therefore, the required probability is $P(Yellow)=\dfrac{9}{44}$ .

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3 years ago

Evaluate the expression when x=-2 and y=3 3x-4y

Illusion [34]

The expression re-written: 3(2) - 4(3)

First, we multiply (PEMDAS)

3 * 2 = 6

4 * 3 = 12

6 - 12 = -6

Answer: - 6

7 0

3 years ago

The half-life of caffeine in a healthy adult is 4.8 hours. Jeremiah drinks 18 ounces of caffeinated

statuscvo [17]

We want to see how long will take a healthy adult to reduce the caffeine in his body to a 60%. We will find that the answer is 3.55 hours.

We know that the half-life of caffeine is 4.8 hours, this means that for a given initial quantity of coffee A, after 4.8 hours that quantity reduces to A/2.

So we can define the proportion of coffee that Jeremiah has in his body as:

P(t) = 1*e^{k*t}

Such that:

P(4.8 h) = 0.5 = 1*e^{k*4.8}

Then, if we apply the natural logarithm we get:

Ln(0.5) = Ln(e^{k*4.8})

Ln(0.5) = k*4.8

Ln(0.5)/4.8 = k = -0.144

Then the equation is:

P(t) = 1*e^{-0.144*t}

Now we want to find the time such that the caffeine in his body is the 60% of what he drank that morning, then we must solve:

P(t) = 0.6 = 1*e^{-0.144*t}

Again, we use the natural logarithm:

Ln(0.6) = Ln(e^{-0.144*t})

Ln(0.6) = -0.144*t

Ln(0.6)/-0.144 = t = 3.55

So after 3.55 hours only the 60% of the coffee that he drank that morning will still be in his body.

If you want to learn more, you can read:

brainly.com/question/19599469

7 0

3 years ago