Which ordered pair is a solution to the system of inequalities?
y > 3x
y <2 +5

Note: Consider we need to find the solution of given equation.

Given:

The equation is

[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]

To find:

The solution of the equation.

Solution:

We have,

[tex]\dfrac{1}{x}+\dfrac{x}{2}=\dfrac{11}{6}[/tex]

[tex]\dfrac{2+x^2}{2x}=\dfrac{11}{6}[/tex]

By cross multiplication, we get

[tex]6(2+x^2)=11(2x)[/tex]

[tex]12+6x^2=22x[/tex]

[tex]6x^2-22x+12=0[/tex]

[tex]2(3x^2-11x+6)=0[/tex]

Divide both sides by 2.

[tex]3x^2-11x+6=0[/tex]

Splitting the middle term, we get

[tex]3x^2-9x-2x+6=0[/tex]

[tex]3x(x-3)-2(x-3)=0[/tex]

[tex](x-3)(3x-2)=0[/tex]

Using zero product property, we get

[tex]x-3=0[/tex] and [tex]3x-2=0[/tex]

[tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex]

Therefore, the solutions of the given equation are [tex]x=3[/tex] and [tex]x=\dfrac{2}{3}[/tex].

Quadratic equations are algebraic equations that can be factored or broken down into simpler forms(factors).

Transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0

We are given the algebraic equation:  1/x+x/2=11/6

Transforming it into a quadratic equation, we find the Lowest common denominator of the fractions in the quadratic equations.

LCD(x,2,6) = 6x

Multiply all through the fractions by 6x

(1/x * 6x)+ (x/2 * 6x) = (11/6 * 6x)

6 + 3x² = 11x

Rewriting the equation:

3x² - 11x + 6 = 0

Therefore, transforming 1/x+x/2=11/6 to quadratic equations is 3x² - 11x + 6 = 0

To learn more, visit the link below:

https://brainly.com/question/18251794

The discriminant is greater than zero, the equation has 2 solutions

Given the quadratic expression as shown:

-x^4 + 4x + 1 + 3 = 0

x^4 - 4x - 4 = 0

The discriminant is given as b^2 - 4ac

where;

a = 1

b = -4

c = -4

Substitute

D =(-4)^2 - 4(1)(-4)

D = 16 + 16
D = 32

Since the discriminant is greater than zero, the equation has 2 solutions

Learn more on discriminant here; https://brainly.com/question/24730520

Answer: 2

Step-by-step explanation: got it right

Answer:

Slope= -1/2 ; y-inter = 0

Step-by-step explanation:

Answer:

you just see whats on the side and write it down so its 16-20

Step-by-step explanation:

Answer:

False

Step-by-step explanation:

Cause the graphs show false instead of being true

Answer:

1

Step-by-step explanation:

The discriminant of the quadratic equation 2x2+4x-7=0 is 1

Answer: 5

Step-by-step explanation:

Answer:

A. Elimination; a coefficient in Equation I is an integer multiple of a coefficient

in Equation II.

Step-by-step explanation:

4 is a multiple of 2. Therefore, the answer would be A.

Answer: I don't see the amount per football

Step-by-step explanation:

Answer:

X=-3

Step-by-step explanation:

2x+15=-3x

15=-5x

x=15/-5

x=-3

Answer:

x = -3

Step-by-step explanation:

2x + 15 = -3x

15 = -5x

x = -3

Answer:

2

Step-by-step explanation:

ez any thing else just hit me up of so

Answer:

1.9 degrees above the normal temperture

Step-by-step explanation:

Normal temperture: 98.6 degrees Fahrenheit

100.5 - 98.6 =  1.9  

Answer:

(-5,-5)

Step-by-step explanation:

Answer:

The answer is C because you have to multiply them both:)

Answer:

The answer is C

Step-by-step explanation:

What I'm about to write is overkill for this question, but it works for any common denominator. Factor the denominators.

10: 2 * 5

5 : 1 * 5

You need 1 five and 1 two. The answer is 10

The correct way to go about doing the question is to multiply the 5 by 2 and the 2 on top by 2

2*2/5*2 = 4/10

1/10        1 / 10

4/10 + 1/10

Step-by-step explanation:

4x^2+2x-5

4(-1)^2+2(-1)-5

4-2-5

2-5= -3

Answer:

123

Step-by-step explanation:

3 + (16 - 1)8

3 + (15)8

3 + 120

123

Answer:

Amelie drove 3/4 mile.She then drove another 8/9 mile. How many miles did she drive in all?

Step-by-step explanation:

Answer:

The correct option is C) 12.00%.

Step-by-step explanation:

This can be calculated using the formula for calculating the effective annual rate (EAR) as follows:

EAR = ((1 + (i / n))^n) - 1 .............................(1)

Where;

EAR = effective annual rate =  12.682%, or 0.12682

i = annual percentage rate (APR) = ?

n = Number of compounding periods or months = 12

Substituting the values into equation (1) and solve for i, we have:

0.12682 = ((1 + (i / 12))^12) - 1

0.12682 + 1 = (1 + (i / 12))^12

1.12682 = (1 + (i / 12))^12

(1.12682)^(1/12) = (1 + (i / 12))^(12/12)

1.12682^0.0833333333333333 = 1 + (i / 12)

1.00999962428035 - 1 = i / 12

0.00999962428035 = i / 12

i = 0.00999962428035 * 12

i = 0.119995491364199, or 11.9995491364199%

Approximating to 2 decimal places, we have:

i = 12.00%

Therefore, the correct option is C) 12.00%.

Answer:

150

Step-by-step explanation:

x/5=30

x=30*5

x=150

Hoped this helped!

Step-by-step explanation:

x/5 = 30

5 × x/5 = 5 × 30

x = 5 × 30

x = 150

Answer:

Following are the solution to the given point:

Step-by-step explanation:

Please find the comp[lete question in the attached file.

Given:

[tex]\bold{ \lim_{n \to \ \infty} (1+ \frac{r}{n})^{nt} =e^{rt}}[/tex]

In point 1:

[tex]\to y = (1+ \frac{r}{n})^{nt}[/tex]

In point 2:

[tex]\to \ln (y)= nt \ln(1+ \frac{r}{n})[/tex]

In point 3:

Its key thing to understand, which would be that you consider the limit n to[tex]\infty[/tex],  in which r and t were constants!  

[tex]=lim_{n \to \ \infty} \ln (y) = lim_{n \to \ \infty} nt \ln(1+\frac{r}{n})\\\\= lim_{n \to \ \infty} \frac{\ln(1+\frac{r}{n})}{\frac{1}{nt}}\\\\= lim_{n \to \ \infty} \frac{\frac{-r}{\frac{n^2}{(1+\frac{r}{n})}}}{- \frac{1}{n^2t}}\\\\= lim_{n \to \ \infty} \frac{\frac{rn^2t}{n^2}}{(1+\frac{r}{n})}\\\\= lim_{n \to \ \infty} \frac{rt}{(1+\frac{r}{n})}\\\\= \frac{rt}{(1+\frac{r}{0})}\\\\=rt[/tex]

In point 4:

[tex]\to \lim_{n \to \ \infty} = (1+\frac{r}{n})^{nt}[/tex] and

[tex]\to \lim_{n \to \ \infty} = A_0e^{rt}[/tex]

Answer:

sorry if im wrong but im pretty sure -5/3

Step-by-step explanation:

Answer:

2/1

Step-by-step explanation:

A calculator showed me that this was the answer. I would give you the link but I would probably get deleted. I already got warned so yeah.

Hope this helps!

Answer:

y = 3x + 10

Step-by-step explanation:

Answer:

im pretty sure it is (0,5) or (10,0)

Step-by-step explanation:

Answer:

0.8809

Step-by-step explanation:

Given that:

The population proportion p = 4% = 4/100 = 0.04

Sample mean x = 16

The sample size n = 300

The sample proportion [tex]\hat p =\dfrac{x}{n}[/tex]

= 16/300

= 0.0533

∴

[tex]P(\hat p \leq 0.0533) = P\bigg ( \dfrac{\hat p - p}{\sqrt{\dfrac{P(1-P)}{n}}}\leq\dfrac{0.0533 - 0.04}{\sqrt{\dfrac{0.04(1-0.04)}{300}}}\bigg )[/tex]

[tex]P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{\sqrt{\dfrac{0.04(0.96)}{300}}}\bigg )[/tex]

[tex]P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{\sqrt{\dfrac{0.0384}{300}}}\bigg )[/tex]

[tex]P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{\sqrt{1.28 \times 10^{-4}}}\bigg )[/tex]

[tex]P(\hat p \leq 0.0533) = P\bigg ( Z\leq\dfrac{0.0133}{0.0113}}\bigg )[/tex]

[tex]P(\hat p \leq 0.0533) = P\bigg ( Z\leq1.18}\bigg )[/tex]

From the z tables;

= 0.8809

OR

Let X be the random variation that follows a normal distribution;

Then;

population mean [tex]\mu[/tex] = n × p

population mean [tex]\mu[/tex] = 300 × 0.04

population mean [tex]\mu[/tex] = 12

The standard deviation [tex]\sigma = \sqrt{np(1-p)}[/tex]

The standard deviation  [tex]\sigma = \sqrt{300 \times 0.04(1-0.04)}[/tex]

The standard deviation [tex]\sigma = \sqrt{11.52}[/tex]

The standard deviation  [tex]\sigma = 3.39[/tex]

The z -score can be computed as:

[tex]z = \dfrac{x - \mu}{\sigma}[/tex]

[tex]z = \dfrac{16 -12}{3.39}[/tex]

[tex]z = \dfrac{4}{3.39}[/tex]

z = 1.18

The required probability is:

P(X ≤ 10) = Pr (z  ≤ 1.18)

= 0.8809

Answer:

11118 people voted

Step-by-step explanation:

Given

[tex]Eligible\ Voters = 21800[/tex]

[tex]Registered\ Voters = 85\%[/tex]

[tex]Voted\ Voters = 60\%[/tex]

Required

Determine the number of voters

First, we need to determine the number of registered voters.

[tex]Number = \%Registered\ Voters * Eligible\ Voters[/tex]

[tex]Number = 85\% * 21800[/tex]

[tex]Number = 18530[/tex]

Next, we determine the actual voters using

[tex]Voters = \%Voters * 18530[/tex]

[tex]Voters = 60\% * 18530[/tex]

[tex]Voters = 11118[/tex]

Hence, 11118 people voted

Answer:

up

Step-by-step explanation:

postive, up!

Answer:

..........UP..........

Answer:

x= 3d/k +8b/k i think

Step-by-step explanation:

Answer:

36

Step-by-step explanation:

Median is the Middle number in the sequence.

Hope this Helps!!

:D