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Which equation represents an inequality in the system of inequalities shown in the graph? Which point is a solution to the system?Which equation represents an inequality in the system of inequalities shown in the graph? Which point is a solution to the system?

Answers

Answer 1

Answer:

The equation that represents an inequality in the system of inequalities shown in the graph is;

y < 2x + 2

The point that is a solution to the system is; (-1, -2)

Graph Inequalities

The image of the graph is missing and so i have attached it.

From the graph, we see one broken line passing through the points x = -1 and y = 2.

We also see an unbroken line passing through the points x = ½ and y = -1

Now, when we use a broken line it means greaterthan or less than but when we use a thick line which is unbroken it means y ≤ or y ≥.

Now, if we shade below the line, it is (y< or y≤) but if we shade above the line, it is (y> or y≥).

Now, we see that the solution will be in between the broken line and the thick line.

Thus, the equation is;

y < 2x + 2 with the solution as coordinates as (-1, -2)

Read more about graph inequalities at;brainly.com/question/11234618

Answer 2

Answer:

Answer:

y<2x+2

(-1,-2)

explanation:

person above gets credit, hope it helps!

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Over the past several months, the water level of a lake has been decreasing by 3% each week. If the highest water level before the decrease started was 520 ft, what was the level at the end of 8 weeks?

Can someone plz help me solved this problem! I’m giving you 10 points! I need help plz help me! Will mark you as brainiest!

Answers

Answer: (a) 8(x + a) --> 8x + 8a

(b) 8(2x + h) --> 16x + 8h

Step-by-step explanation:

f(x) = 8x²

f(a) = 8a²

$(f(x)-f(a))/(x-a)\quad = \quad (8x^2-8a^2)/(x-a)\quad = \quad (8(x-a)(x+a))/(x-a)=\large\boxed{8(x+a)}$

f(x + h) = 8(x + h)²

= 8(x² + 2xh + h²)

= 8x² + 16xh + 8h²

f(x) = 8x²

$(f(x+h)-f(x))/(h) = ((8x^2+16xh+8h^2)-8x^2)/(h)\n\n\n.\qquad \qquad \qquad \quad =(16xh + 8h^2)/(h)\n\n\n.\qquad \qquad \qquad \quad =(8h(2x + h))/(h)\n\n\n.\qquad \qquad \qquad \quad =\large\boxed{8(2x+h)}$

Answer:

$a. \quad 8\left(x+a\right)\n\nb. \quad 8\left(2x+h\right)$

Step-by-step explanation:

Best Regards!

Test the following numbers for divisibility by 3, 5, 6 and 11. (Do not divide or factorise.) a) 68 979

Answers

Final answer:

The number 68,979 is divisible by 3 but not by 5, 6, or 11.

Explanation:

To test a number for divisibility by 3, we sum up its individual digits. If the sum is divisible by 3, then the number itself is divisible by 3. For the number 68,979, the sum of its digits is 6 + 8 + 9 + 7 + 9 = 39. Since 39 is divisible by 3, 68,979 is also divisible by 3.

To test a number for divisibility by 5, we simply check if the last digit is either 0 or 5. In the number 68,979, the last digit is 9, which is neither 0 nor 5. Therefore, 68,979 is not divisible by 5.

To test a number for divisibility by 6, we need to check if it is divisible by both 2 and 3. From the previous tests, we already know that 68,979 is divisible by 3, so we now need to check if it is divisible by 2. Since the last digit is 9, which is an odd number, 68,979 is not divisible by 2, and therefore not divisible by 6.

To test a number for divisibility by 11, we take the alternating sum of its digits. In this case, we have 6 - 8 + 9 - 7 + 9 = 9. Since 9 is not divisible by 11, 68,979 is not divisible by 11.

Learn more about divisibility here:

brainly.com/question/34253396

Find the average value of f(x) = 7x^2(x^3+1)6 over the interval [0, 2].

Answers

The average value is

$\displaystyle\frac1{2-0}\int_0^27x^2(x^3+1)^6\,\mathrm dx$

Let $u=x^3+1$ , so that $\mathrm du=3x^2\,\mathrm dx$ :

$\displaystyle\frac12\int_1^9\frac73u^6\,\mathrm du=\frac16u^7\bigg|_1^9=\frac{9^7-1}6=\frac{2,391,484}3$

A study is given in which scientists examined data on mean sea surface temperatures (in degrees Celsius) and mean coral growth (in millimeters per year) over a several-year period at different locations. Here are the data: Sea Surface Temperature 29.69 29.87 30.16 30.22 30.48 30.65 30.80
Growth 2.63 2.57 2.67 2.50 2.47 2.38 2.25

Required:
a. Find the mean and standard deviation of both sea surface temperature x and growth y and the correlation r between x and y.
b. Find the least-squares line. The result should agree with your work in part (a) up to roundoff error. (Round your answers to three decimal places.)
c. Say in words what the numerical value of the slope tells you.

Answers

Answer:

Kindly check explanation

Step-by-step explanation:

Given the following :

Sea Surface Temperature (x) : 29.69 29.87 30.16 30.22 30.48 30.65 30.80

Growth : (y) 2.63 2.57 2.67 2.50 2.47 2.38 2.25

Mean (x) :

Σ(X) / n

n = number of observations

Mean (m1) = Σ(X) / n = 211.87 / 7 = 30.27

Standard deviation(sx) = 0.3742 (using calculator)

Mean (m2) :

Σ(y) / n = 17.47 / 7 = 2.50

Standard deviation(sy) = 0.1354 ( using calculator)

Correlation (r) :

(1/n)Σ[(x - m1) / sx] × [(y - m2) /sy]

Using calculator to save computing time :

r = - 0.8642

b. Find the least-squares line. The result should agree with your work in part (a) up to roundoff error. (Round your answers to three decimal places.)

The least square line using the regression calculator :

y = -0.31 + 11.96x

Comparing to the regression equation format :

y = mx + c

Where ;

-0.31 = intercept ; 11.96 = slope ; x = independent variable ; y = dependent variable

c. Say in words what the numerical value of the slope tells you.

For every 1° degree rise in surface temperature, growth increases by 11.96

Find the value of each missing variable.

Answers

Answer:

The value of x is 17 and that of y is 8.

Answer:

x=17 y=8

Step-by-step explanation:

A recipe for 2 dozen corn muffins calls for 3 cups of flour. The number of muffins varies directly with the amount of flour you use. Write a direct variation equation to represent this.