3. Graph the function.<br> xy + 25 = 0

Is this a function yes or no? right answers only please!

jenyasd209 [6]

Yes it is a function

5 0

3 years ago

Read 2 more answers

Solve for y 16y^2-25=0

Pepsi [2]

Answer:

$\large\boxed{x=-\dfrac{5}{4}\ \vee\ x=\dfrac{5}{4}}$

Step-by-step explanation:

$16y^2-25=0\\\\METHOD\ 1:\\\text{use}\ a^2-b^2=(a-b)(a+b)\\\\16=4^2\ \text{and}\ 25=5^2\ \text{therefore we have}\\\\4^2y^2-5^2=0\\\\(4y)^2-5^2=0\\\\(4y-5)(4y+5)+0\iff4y-5=0\ \vee\ 4y+5=0\\\\4y-5=0\qquad\text{add 5 to both sides}\\4y=5\qquad\text{divide both sides by 4}\\\boxed{y=\dfrac{5}{4}}\\\\4y+5=0\qquad\text{subtract 5 from both sides}\\4y=-5\qquad\text{divide both sides by 4}\\\boxed{x=-\dfrac{5}{4}}$

$METHOD\ 2:\\\\16y^2-25=0\qquad\text{add 25 to both sides}\\\\16y^2=25\qquad\text{divide both sides by 16}\\\\y^2=\dfrac{25}{16}\to y=\pm\sqrt{\dfrac{25}{26}}\\\\y=-\dfrac{\sqrt{25}}{\sqrt{16}}\ \vee\ x=\dfrac{\sqrt{25}}{\sqrt{16}}\\\\\boxed{y=-\dfrac{5}{4}\ \vee\ x=\dfrac{5}{4}}$

7 0

3 years ago

Read 2 more answers

After breaking your penny bank, you notice that you have $4.87 in quarters ($0.25), dimes ($0.10), nickels ($0.05), and pennies

ira [324]

Answer: Option 'c' is correct.

Step-by-step explanation:

Let the number of dimes be 'x'.

Let the number of nickels be ' $\dfrac{3}{2}x$ '.

Let the number of pennies be $\dfrac{3}{2}\times 2x=3x$

Let the number of quarters be '3x-34'.

As we know that

1 quarter = $0.25

1 dime = $0.10

1 nickel = $0.05

1 penny = $0.01

According to question, we get that

$0.10x+0.05\times \dfrac{3x}{2}+0.01\times 3x+0.25(3x-34)=4.87\\\\0.10x+0.075x+0.03x+0.75x-8.5=4.87\\\\\\0.955x=4.87+8.5\\\\0.955x=13.37\\\\x=\dfrac{13.37}{0.955}\\\\x=14$

So, the number of pennies is given by

$3x=3\times 14=42$

Hence, Option 'c' is correct.

3 0

3 years ago

6x - 2y = 5

laiz [17]

Answer:

The given system has NO SOLUTION.

Step-by-step explanation:

Here, the given system of equation is:

6 x - 2 y = 5 .......... (1)

3 x - y = 10 .... (2)

Multiply equation 2 with (-2), we get:

3 x - y = 10 ( x -2)

⇒ - 6 x + 2 y = - 20

Now, ADD this to equation (1) , we get:

6 x - 2 y - 6 x + 2 y = 5 - 20

or, 0 = - 15

WHICH IS NOT POSSIBLE as 0 ≠ -15

Hence, the given system has NO SOLUTION.

7 0

3 years ago

The time needed to complete a final examination in a particular college course is normally distributed with a mean of 77 minutes

Komok [63]

Answer:

a. The probability of completing the exam in one hour or less is 0.0783

b. The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is 0.3555

c. The number of students will be unable to complete the exam in the allotted time is 8

Step-by-step explanation:

a. According to the given we have the following:

The time for completing the final exam in a particular college is distributed normally with mean (μ) is 77 minutes and standard deviation (σ) is 12 minutes

Hence, For X = 60, the Z- scores is obtained as follows:

Z= X−μ /σ

Z=60−77 /12

Z=−1.4167

Using the standard normal table, the probability P(Z≤−1.4167) is approximately 0.0783.

P(Z≤−1.4167)=0.0783

Therefore, The probability of completing the exam in one hour or less is 0.0783.

b. In this case For X = 75, the Z- scores is obtained as follows:

Z= X−μ /σ

Z=75−77 /12

Z=−0.1667

Using the standard normal table, the probability P(Z≤−0.1667) is approximately 0.4338.

Therefore, The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is obtained as follows:

P(60<X<75)=P(Z≤−0.1667)−P(Z≤−1.4167)

=0.4338−0.0783

=0.3555

Therefore, The probability that student will complete the exam in more than 60 minutes but less than 75 minutes is 0.3555

c. In order to compute how many students you expect will be unable to complete the exam in the allotted time we have to first compute the Z−score of the critical value (X=90) as follows:

Z= X−μ /σ

Z=90−77 /12

Z=1.0833

UsING the standard normal table, the probability P(Z≤1.0833) is approximately 0.8599.

Therefore P(Z>1.0833)=1−P(Z≤1.0833)

=1−0.8599

=0.1401

Therefore, The number of students will be unable to complete the exam in the allotted time is= 60×0.1401=8.406

The number of students will be unable to complete the exam in the allotted time is 8

6 0

3 years ago

3. Graph the function. xy + 25 = 0