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2 years ago

A student claims that 3x + 2y = 5xy. Use a visual representation to show whether this is true or false

Mathematics

1 answer:

Ket [755]2 years ago

7 0

Answer:

It is true, except when x = 2/5, since it is an asymptote.

Step-by-step explanation:

3x=5xy-2y

3x=y(5x-2)

3x/5x-2=y

5x-2=0 -------> 5x=2 --------> x=2/5

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The gas mileage for a certain vehicle can be approximated by m=−0.05x2+3.5x−49, where x is the speed of the vehicle in mph. Dete

Whitepunk [10]

Answer:

Step-by-step explanation:

Given the gas mileage for a certain vehicle modeled by the equation m=−0.05x²+3.5x−49 where x is the speed of the vehicle in mph. In order to determine the speed(s) at which the car gets 9 mpg, we will substitute the value of m = 9 into the modeled equation and calculate x as shown;

m = −0.05x²+3.5x−49

when m= 9

9 = −0.05x²+3.5x−49

−0.05x²+3.5x−49 = 9

0.05x²-3.5x+49 = -9

Multiplying through by 100

5x²+350x−4900 = 900

Dividing through by 5;

x²+70x−980 = 180

x²+70x−980 - 180 = 0

x²+70x−1160 = 0

Using the general formula to get x;

a = 1, b = 70, c = -1160

x = -70±√70²-4(1)(-1160)/2

x = -70±√4900+4640)/2

x = -70±(√4900+4640)/2

x = -70±√9540/2

x = -70±97.7/2

x = -70+97.7/2

x = 27.7/2

x = 13.85mph

x ≈ 14 mph

Hence, the speed(s) at which the car gets 9 mpg to the nearest mph is 14mph

4 0

2 years ago

Yesterday, two friends went into a bank to open savings accounts. Allie started by putting $783 in her account, and she will dep

posledela

<u>Answer:</u>

Both accounts of Nick and Allie will have same amount of $864 in time period of 4 weeks.

<u>Solution: </u>

Given, Yesterday two friends went into a bank to open savings accounts.

Allie started by putting $783 in her account, and she will deposit an additional $27 each week.

Nick made no initial deposit, but he will add $288 more each week.

In a few weeks, the friends will have the same account balance.

Here, account balance of Allie for every week forms an A.P as

783, 810, 837, ……. With common difference 27

And, account balance of nick for every week will be

0, 288, 576, …….. with common difference 288

Let, after n weeks the balance in both accounts be equal.

Then, nth term of both series will be equal, we know that, nth term tn of A.P is a + (n – 1)d

Where, a is first term, d is common difference and n is number of terms.

Now, nth term of allie series = nth term of nick series.

783 + (n – 1) x 27 = 0 + (n – 1) x 288

Here, we used same n for both sides because n represents number of weeks and it is common to both

783 + 27n – 27 = 288n – 288

756 + 288 = 288n – 27n

261n = 1044

n = 4.

So, it will take 4 weeks to have same balance and now, substitute n value in nth term of nick series.

$4 \text { th term }=0+(4-1) \times 288 \rightarrow 4^{\text {th }} \text { term }=3 \times 288=864$

Hence, both accounts will have same amount of $864 in time period of 4 weeks

4 0

2 years ago

Mariah is randomly choosing three books to read from the following: 5 mysteries, 7 biographies, and 8 science fiction novels. Wh

Gekata [30.6K]

Answer:

not choosing all mysteries

Step-by-step explanation:

The complement of an event is the remaining possibilities.

Our event is Mariah choosing 3 mysteries.

The other possibilities include that she chooses at least one book that is not a mystery; this means the complement is not choosing all mysteries.

7 0

2 years ago

Read 2 more answers

Lamont builds a triangular shape fence to hide his pool pump

Monica [59]

I don't understand what you are trying to say

5 0

2 years ago

A candy store sells caramels and milk chocolate by the pound the table below shows the total cost in dollars for a pound of each

MakcuM [25]

The cost of $1\frac{3}{4}$ pounds chocolate milk is $6.25 more than the cost of $1\frac{3}{4}$ pounds of Caramel.

Step-by-step explanation:

Given,

Cost of one pound of Caramels = $10.28

Cost of $1\frac{3}{4}$ pounds of Caramel = $10.28*1\frac{3}{4}$

Cost of $1\frac{3}{4}$ pounds = $10.28*\frac{7}{4}=\frac{71.96}{4}= \$17.99$

Cost of one pound of chocolate milk = $13.85

Cost of $1\frac{3}{4}$ pounds = $13.85*1\frac{3}{4}=13.85*\frac{7}{4}$

Cost of $1\frac{3}{4}$ pounds = $\frac{96.95}{4}=\$24.24$

Difference = 24.24 - 17.99 = $6.25

The cost of $1\frac{3}{4}$ pounds chocolate milk is $6.25 more than the cost of $1\frac{3}{4}$ pounds of Caramel.

Keywords: difference, multiplication

Learn more about multiplication at:

#LearnwithBrainly

5 0

2 years ago