How do the average rates of change for the pair of functions compare over the given​ interval?
f(x)=2x^2
g(x)=6x^2
-5≤x≤-2
ANSWER ASAP PLEASEEEEEE OMG I NEED HELP RIGHT NOW OR I WILLL DIE AND U GET A TON OF POINTS HELPPPPPPPPPP!!!!!!!!!!!! OMG HELPPPPPP MEEE

Step-by-step explanation:

speed = distance/time

hence expressions like miles or kilometers per hour, feet or meters per second, ...

so in our case that means

121/11 miles per hour = 11 mph

Answer:  6x² + 12x - 24

Step-by-step explanation:

The area of the rectangle is 6x² + 12x - 24. To find the area, we need to multiply the length and width of the rectangle. Therefore, we can multiply 2x² + 4x - 8 and 3x to get 6x² + 12x - 24.

Answer:

6x³ + 12x² - 24x

Explanation:

Area = Length x Width

Area = (2x² + 4x - 8) x 3x

Simplifying the expression, we get:

Area = 6x³ + 12x² - 24x

The probability of getting exactly 3 successes in 8 trials, with a success probability of 0.39, is 0.019 or 1.9%.

The chance of X successes in n separate trials, where each trial has a probability of success of p, is calculated using the binomial formula. The likelihood of 3 successes in 8 tries, with a success probability of 0.39, may be calculated using this method. This is the binomial formula:

P(X = k) is equal to (n pick k) * p * k * (1-p) (n-k)

Where (n pick k) denotes the variety of ways to select k successes from n trials, n is the number of trials, k is the number of successes, p is the probability of success, and so on.

We can enter the values provided in the formula using the following:

P(X = 3) = (8 pick 3) (8 choose 3) * (0.39)^3 * (1-0.39)^(8-3) (8-3)

P(X = 3) = (8! / (3! * (8-3)!)) * (0.39)^3 * (0.61)^5

P(X = 3) = (56) * (0.039304) * (0.088848) (0.088848)

P(X = 3) = 0.019

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The number of sweets Mandy had 43 and number of sweets Zack had is 77.

Let the number of sweets Zack have is 'x'.

Let the  number of sweets  Mandy have is 'y'.

Then, linear equation is-

x + y = 120  ..eq 1

After Mandy get 10 more sweets.

x + 10  = 2y

x - 2y = -10 ...eq 2

Solving eq 1 and eq 2 by elimination method:

3y = 130

y = 130/ 3

y = 43 sweets. (approx) number of sweets Mandy had.

x = 120 - 43

x = 77 sweets (approx) number of sweets Zack had.

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The sample mean of 33 is significantly different from 35 at the 5% level of significance.

We must perform a hypothesis test to see if we can claim that the population mean differs from 35. The null and alternative hypotheses can be set up as follows:

H0: μ = 35 (the population mean is equal to 35) (the population mean is equal to 35)

Ha: μ ≠ 35 (the population mean is not equal to 35) (the population mean is not equal to 35)

Given that this addition, and the as, and the as, and the as, and the as, and the as, and the as, and the as, and the as, and the as, The test statistic comes from:

z = (x- μ) / (σ / √n)

When n is the sample size, x is the sample mean, is the population mean, and is the population standard deviation.

Inputting the values provided yields:

z = (33 - 35) / (4.5 / √36) = -4 / 1.5 = -2.67

A two-tailed test with a test statistic of -2.67 has a p-value of roughly 0.008. Given that the population mean is actually 35, the likelihood of having a sample mean that is as extreme or more extreme than 33 is 0.008.

We reject the null hypothesis since the p-value is less than the significance level of 0.05 and come to the conclusion that there is enough data to show that the population mean is different from 35. In other words, at the 5% level of significance, the sample mean of 33 differs considerably from 35.

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Let's use the concept of proportion to find the number of minutes spent in 3 classes. We can set up a proportion using the fact that the ratio of time spent in two classes is equal to the ratio of time spent in three classes. Therefore, we can write:

[tex]$\frac{\text{time spent in class 1}}{\text{time spent in class 2}} = \frac{\text{total time spent in 2 classes}}{\text{time spent in class 3}}$[/tex]

Let's substitute the given values:

[tex]$\frac{\text{time spent in class 1}}{\text{time spent in class 2}} = \frac{100 \text{ minutes}}{m \text{ minutes}}$[/tex]

where m is the number of minutes spent in 3 classes.

Now we can cross-multiply to solve for m:

[tex]$\text{time spent in class 1} \times \text{time spent in class 3} = \text{time spent in class 2} \times \text{total time spent in 2 classes}$[/tex]

Plugging in the given values:

[tex]$\text{time spent in class 1} \times m = \text{time spent in class 2} \times 100 \text{ minutes}$[/tex]

We know that we spent 100 minutes in 2 classes, so we can substitute this value into the equation:

[tex]$\text{time spent in class 1} \times m = \text{time spent in class 2} \times 100 \text{ minutes} =[/tex][tex]\text{time spent in class 1} \times (100 \text{ minutes} - \text{time spent in class 1})$[/tex]

Simplifying and rearranging the terms:

[tex]$m \text{ minutes} = \frac{\text{time spent in class 1} \times (100 \text{ minutes} - \text{time spent in class 1})}{\text{time spent in class 1}}$[/tex]

[tex]$m \text{ minutes} = 100 \text{ minutes} - \text{time spent in class 1}$[/tex]

Therefore, the proportion that gives the number of minutes spent in 3 classes is:

[tex]$\frac{\text{time spent in class 1}}{\text{time spent in class 2}} = \frac{100 \text{ minutes}}{m \text{ minutes}} =\large\boxed{ \frac{100 \text{ minutes} - m \text{ minutes}}{m \text{ minutes}}}$[/tex]

Answer: D: StartFraction 1 over 12 EndFraction.

Step-by-step explanation:To find the probability that both socks drawn are white, we can use the multiplication rule of probability.

The probability of drawing a white sock on the first draw is 3/9 (since there are 3 white socks out of 9 total socks in the drawer).

After the first sock is drawn and kept, there are 8 socks remaining in the drawer, including 2 white socks. So the probability of drawing a white sock on the second draw, given that a white sock was not replaced after the first draw, is 2/8.

Using the multiplication rule, we can find the probability of both events happening (drawing a white sock on the first try and drawing a white sock on the second try):

P(white, then white) = P(white on first draw) × P(white on second draw | white on first draw)

P(white, then white) = (3/9) × (2/8)

P(white, then white) = 1/12

Therefore, the probability that both socks drawn are white is option D: StartFraction 1 over 12 EndFraction.

The value of the trigonometric expression sin⁻¹ (sin (-33π /47)) will be negative 2.20.

Trigonometric functions examine the interaction between the dimensions and angles of a triangular form.

Simply put, inverse trigonometric operations are the opposites of the fundamental trigonometric parameters sine, cosine, secant, cosecant, tangent, and cotangent.

The expression is given below.

⇒ sin⁻¹ (sin (-33π /47))

The value of the expression is given as,

⇒ sin⁻¹ (sin (-33π /47))

⇒ - 33π /47

⇒ - 2.20

The value of the trigonometric expression sin⁻¹ (sin (-33π /47)) will be negative 2.20.

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Answer: 6 pounds

Step-by-step explanation: 80-30.44= 49.56

49.56/8.26=6

0.538461153857567856854

Answer:

Step-by-step explanation:

We can use a standard normal distribution table or calculator to determine the probabilities. Here are the answers:

(b) P(z > 2.37) = 0.0083

(c) P(z < -1.23) = 0.1093

(d) P(1.14 < z < 3.35) = 0.0473

(e) P(-0.77 < z < -0.56) = 0.0749

(f) P(z > 2) = 0.0228

(g) P(z < -3.28) = 0.0005

(h) P(z = 1.98) = 0 (since the normal distribution is continuous, the probability of a single point is zero).

Answer:

its a true statement if that what your asking

Step-by-step explanation:

[tex](-5)2-(-2)4 = -10 -(-8) = -10+8 = \bf-2[/tex]

The solution of x is 2.1 units

From the question, we have the following parameters that can be used in our computation:

The triangle

From the triangle, we have the following equation

sin(38) = 1.3/x

Make x the subject of the above equation

So, we have the following representation

x = 1.3/sin(38)

Evaluate

x = 2.1

Hence, the value of x is 2.1

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Therefore, we have shown that if five points are picked in the interior of a square with a side length of 2, then at least two of these points are no farther than √2 apart.

What is a square?

A quadrilateral with four equal edges is called a square. There are numerous items in our environment that have a square form. Equal sides and interior angles that are both 90 degrees distinguish each square form.

Let us divide the square into four congruent squares, each with side length 1, by drawing two lines perpendicular to each other that pass through the center of the square.

Since there are five points in the interior of the original square, there must be at least two points in one of these smaller squares by the Pigeonhole Principle.

The diagonal of this smaller square has length √2, which means that any two points in this square are no farther than √2 apart.

Therefore, the two points we selected from the interior of the original square must be no farther than √2 apart.

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The population proportion's best point estimate, p, is 0.53 (553/1043).

Proportion is a mathematical concept involving the comparison of two or more values, quantities, or amounts. It is usually expressed as a ratio or a fraction. Proportion can be used to compare different sizes, amounts, or values, to determine if they are equivalent, or to determine if one is a multiple of the other. Proportion can also be used to compare the same amounts or values at different times or in different contexts. For example, one can use the concept of proportion to compare prices, wages, or populations in different cities or countries.

The margin of error E for a 99% confidence interval can be found using the formula E = z*sqrt(p*(1-p)/n).
For this problem, E = 2.58*sqrt(0.53*(1-0.53)/1043) = 0.032.
The confidence interval is (0.498, 0.562).
We are 99% confident that the population proportion of people who feel vulnerable to identity theft is between 0.498 and 0.562.

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The pοpulatiοn prοpοrtiοn's best pοint estimate, p, is 0.53 (553/1043).

Prοpοrtiοn is a mathematical cοncept invοlving the cοmparisοn οf twο οr mοre values, quantities, οr amοunts. It is usually expressed as a ratiο οr a fractiοn. Prοpοrtiοn can be used tο cοmpare different sizes, amοunts, οr values, tο determine if they are equivalent, οr tο determine if οne is a multiple οf the οther.

Prοpοrtiοn can alsο be used tο cοmpare the same amοunts οr values at different times οr in different cοntexts. Fοr example, οne can use the cοncept οf prοpοrtiοn tο cοmpare prices, wages, οr pοpulatiοns in different cities οr cοuntries.

The margin οf errοr E fοr a 99% cοnfidence interval can be fοund using the fοrmula E = z × √ (p × (1-p)/n).

Fοr this prοblem, E = 2.58 × × (0.53*(1-0.53)/1043) = 0.032.

The cοnfidence interval is (0.498, 0.562).

We are 99% cοnfident that the pοpulatiοn prοpοrtiοn οf peοple whο feel vulnerable tο identity theft is between 0.498 and 0.562.

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The amount of tax is $20.3232 and the selling price is $105.00.

The given data:

Original Price: $84.68

Sales tax rate: 24%

Tax amount  = 24% of Original Price

                     = 24*84.68 / 100

                     = $20.3232

Selling price  = Original Price + Tax amount

Selling price  = $84.68 + $20.3232

Selling price  = $105.00

Thus, the amount of tax is $20.3232 and the selling price is $105.00.

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1. The variable a in the polynomials can have a value of either -5 or -1.

2. The variable x in the polynomials can have a value of either -5 or 1.

From the question, we are to determine the value of the variable when the polynomials are equal.

To find the value of the variable when two polynomials have the same value, we can set them equal to each other and solve for the variable.

For the trinomial a^2+7a+6 and the binomial a+1 to have the same value, we set them equal to each other:

a^2 + 7a + 6 = a + 1

We can rearrange this equation to get it in standard form:

a^2 + 6a + 5 = 0

Now we can factor the left side of the equation:

(a+5)(a+1) = 0

This gives us two possible solutions:

a = -5 or a = -1

Hence, the value is -5 or -1.

For the trinomial 3x^2-x+1 and the trinomial 2x^2+5x-4 to have the same value, we set them equal to each other:

3x^2-x+1 = 2x^2+5x-4

We can rearrange this equation to get it in standard form:

x^2+6x-5 = 0

Now we can factor the left side of the equation:

(x+5)(x-1) = 0

This gives us two possible solutions:

x = -5 or x = 1

Hence, the value is -5 or 1.

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There is only one solution, this means that the equation has a unique solution

From the question, we have the following parameters that can be used in our computation:

6x + 2 = 5x + 17

To solve the equation 6x + 2 = 5x + 17, we need to isolate the variable x on one side of the equation.

We can do this by subtracting 5x from both sides:

6x + 2 - 5x = 5x + 17 - 5x

Simplifying both sides:

x + 2 = 17

Subtracting 2 from both sides:

x = 15

So the solution to the equation 6x + 2 = 5x + 17 is x = 15.

The solution represents the value of x that makes the equation true, and in this case, that value is 15.

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Maximum profit of $2500 and the same optimal production policy of making 3 batches of grade A paper and 5 batches of grade B paper.

To determine the amounts of each grade of paper to produce, we need to maximize the profit by finding the optimal production policy. We can set up an optimization problem to find the maximum profit. Let xA = batches of grade A paper and xB = batches of grade B paper. Then the objective function is to maximize P = 500xA + 250xB.

The constraints are as follows: 25xA + 10xB ≤ 100 (Scrap cloth)

10xA + 20xB ≤ 120 (Scrap paper)

xA ≥ 0, xB ≥ 0 (Nonnegativity)

The maximum profit occurs when xA = 3 and xB = 5, which yields a maximum profit of $2500. Therefore, the optimal production policy is to make 3 batches of grade A paper and 5 batches of grade B paper.

If the company is required to produce at least one batch of each type, the maximum profit and optimal production policy will not change. The new constraints would be xA ≥ 1, xB ≥ 1. Solving this optimization problem yields the same maximum profit of $2500 and the same optimal production policy of making 3 batches of grade A paper and 5 batches of grade B paper.

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Answer:

Step-by-step explanation:

The volume of dirt removed can be calculated by multiplying the length, width, and depth of the trench. First, we need to convert the depth from feet and inches to feet.

3-1/2 ft = 3.5 ft

The volume of dirt removed is:

V = length x width x depth

V = 81 ft x 4 ft x 3.5 ft

V = 1134 cubic feet

Therefore, 1134 cubic feet of dirt was removed from the trench.

To find the critical points of the function y = -4x(x^4 - 2)^3, we need to find the values of x where the derivative of the function is equal to zero or undefined.

First, we can find the derivative of y with respect to x using the chain rule and the power rule:

y' = -4(x^4 - 2)^3 * (4x^3) - 4x * 3(x^4 - 2)^2 * 4x^3

Simplifying:

y' = -4x^3(x^4 - 2)^2 * (4(x^4 - 2) + 12x^2)

y' = -4x^3(x^4 - 2)^2 * (16x^4 + 44x^2 - 8)

Now, we need to find the values of x where y' = 0 or y' is undefined. We can factor out -4x^3(x^4 - 2)^2 from the expression for y':

y' = -4x^3(x^4 - 2)^2 * (16x^4 + 44x^2 - 8)

y' = -4x^3(x^4 - 2)^2 * 4(4x^4 + 11x^2 - 2)

Therefore, y' = 0 when:

4x^4 + 11x^2 - 2 = 0

We can use the quadratic formula to solve for x^2:

x^2 = (-11 ± sqrt(11^2 - 44(-2))) / (2*4)

x^2 = (-11 ± sqrt(141)) / 8

x^2 ≈ -1.082 or x^2 ≈ 0.823

Since x^2 cannot be negative, the only critical point occurs when:

x^2 ≈ 0.823

Taking the square root of both sides, we get:

x ≈ ±0.907

Therefore, the critical points for y = -4x(x^4 - 2)^3 are approximately x = -0.907 and x = 0.907.

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y = -2(x - 4.5)²+ 1.5 is quadratic equation of the parabola passing through the points (3, -3) and (6, 6)

A quadratic equation is a second-order polynomial equation in a single variable x , ax2+bx+c=0. with a ≠ 0 .

To find the equation of a parabola, we need to know its basic form, which is given as:

y = a(x - h)² + k

where (h, k) is the vertex of the parabola and a is a constant that determines the shape of the parabola.

To find the value of a, we need to use the given points (3, -3) and (6, 6).

The x-coordinate of the vertex can be found as the average of the x-coordinates of the given points:

h = (3 + 6)/2 = 4.5

The y-coordinate of the vertex can be found as the average of the y-coordinates of the given points:

k = (-3 + 6)/2 = 1.5

Therefore, the vertex of the parabola is (4.5, 1.5).

Finding the value of a

We can use one of the given points to find the value of a. Let's use the point (3, -3)

-3 = a(3 - 4.5)² + 1.5

-3 = a(1.5)² + 1.5

-4.5 = a(1.5)²

a = -4.5/(1.5)²

a = -2

Now that we know the values of h, k, and a, we can write the equation of the parabola as:

y = -2(x - 4.5)² + 1.5

Therefore, the equation of the parabola passing through the points (3, -3) and (6, 6) is y = -2(x - 4.5)²+ 1.5

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The height will be 6 feet, so the correct option is C.

Here we know that the diameter of the flagpoler is the linear equation:

D(h) = 12 - 0.5*h

Where the variable h is the number of feet above the base.

If the diameter is 9 inches, then we need to solve

9 = 12 - 0.5*h

For the variable h, so let's do that:

9 = 12 - 0.5*h

9 - 12 = -0.5*h

-3/-0.5 = h

6  =h

The correct option is C, the number of feet above the base is 6 feet.

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The perimeter and the area of the rectangle is as follows:

perimeter=182 cm

area=2028cm².

A rectangle is a closed, four-sided figure in two dimensions. The opposite sides of a rectangle are equal and parallel to one another, and all of its angles are 90 degrees.

The area of a rectangle is equal to the product of the rectangle's length and breadth, or "l" and "w," and is written as follows:

Rectangular Area = (l x w)

The formula for the perimeter, 'P' of a rectangle whose length and width are 'l' and 'w' respectively is 2(l + w).

Formula for the Perimeter of a Rectangle: 2 (Length + Width)

Now in the question given,

Length of the rectangle = 8cm.

Width of the rectangle = 6cm.

So, original perimeter=2 × (8+6) +28 cm and

original area=8 × 6= 48 cm²

Now the scale factor = 6.5

New length = 8 × 6.5 = 52cm

width = 6 × 6.5 = 39cm.

New perimeter = 2(52+39) =182 cm.

New area = 52 × 39 = 2028cm².

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The complete question is:

What will be the perimeter and the area of the rectangle below if it is enlarged using a scale factor of 6.5?

Answer:

D = 16h

where
D = distance in miles
h = time in hours

Step-by-step explanation:

Cyclist travels 4 miles in 1/4 hour
So her speed in mph = 4 ÷ 1/4

When you divide by a fraction, flip and fraction and multiply

4 ÷ 1/4 = 4 x 4/1 = 16 mph

So in 1 hour cyclist travels 16 miles

Equation is
D = 16h

where
D = distance in miles
h = time in hours

Answer:

Below

Step-by-step explanation:

Domain is the 'x' values a function can have = {-1,0,1,2,3,4}

Range is the possible 'y' values = {-2,3,6,7}

Answer:

5.5

Step-by-step explanation:

Since BD is parallel to AE

=> AB/AC = ED/EC

AB/22 = 11/44

AB = 1/4(22)

AB = 5.5

Answer:

The length of segment AB is 5.5 mm.

Step-by-step explanation:

As segment BD is parallel to segment AE (as indicated by the arrows on the line segments), use the the Side Splitter Theorem for similar triangles to determine the length of segment AB.

If a line parallel to one side of a triangle intersects the other two sides, then this line divides those two sides proportionally.

Therefore, according to the Side Splitter Theorem:

[tex]\implies \sf AB : AC = ED : EC[/tex]

[tex]\implies \sf AB : 22 = 11 : 44[/tex]

[tex]\implies \sf \dfrac{AB}{22} = \dfrac{11}{44}[/tex]

[tex]\implies \sf \dfrac{AB}{22} \cdot 22= \dfrac{11}{44} \cdot 22[/tex]

[tex]\implies \sf AB= \dfrac{242}{44}[/tex]

[tex]\implies \sf AB= 5.5[/tex]

Therefore, the length of segment AB is 5.5 mm.

We can use the standard form of a quadratic function, which is y = ax^2 + bx + c, to solve this problem. Since we have two points, we can create two equations and solve for the coefficients a, b, and c.

First, we have:

-5 = a(5)^2 + b(5) + c

-14 = a(8)^2 + b(8) + c

Simplifying these equations, we get:

25a + 5b + c = -5

64a + 8b + c = -14

Next, we can use the third point to eliminate one of the coefficients. Since the x-value of the third point is not given, we can use the fact that the quadratic function is a parabola and the axis of symmetry passes through the midpoint of the two given points. The midpoint of (5, -5) and (8, -14) is ((5+8)/2, (-5-14)/2) = (6.5, -9.5). This means that the x-value of the vertex of the parabola is x = 6.5.

We can use the vertex form of a quadratic function to find the y-value of the vertex, which is -b/(2a). Plugging in x = 6.5 and y = -9.5, we get:

-9.5 = a(6.5)^2 + b(6.5) + c

Simplifying this equation, we get:

42.25a + 6.5b + c = -9.5

Now we have three equations with three unknowns:

25a + 5b + c = -5

64a + 8b + c = -14

42.25a + 6.5b + c = -9.5

We can solve for a, b, and c by using determinants:

| 25 5 1 | |-5 5 1 | |25 -5 1 |

| 64 8 1 | -> |-14 8 1 | -> |64 -14 1 |

| 42.25 6.5 1| |-9.5 6.5 1 | |42.25 -9.5 1 |

Using a calculator, we get:

|25 -5 1 |

|64 -14 1 |

|42.25 -9.5 1| -> -178.75

| 25 -5 1 |

|-14 8 1 |

|-9.5 6.5 1| -> -175.5

| 64 -14 1 |

|-5 5 1 |

|42.25 -9.5 1| -> 0

Since the determinant of the coefficient matrix is not zero, the system of equations has a unique solution. Therefore, we can solve for a, b, and c by using Cramer's rule:

a = |-5 -5 1 |

|-14 8 1 |

{-9.5 6.5 1| / -178.75

= 1.25

b = |25 -5 -5 |

|64 -14 8 |

{42.25 -9.5 6.5| / -178.75

= -10.25

c = |25 5 1 |

|64 8 1 |

{42.

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The graph represents a system of two inequalities, y ≤ −3x + 1, and y ≤ 1 over 2x + 3.

Graph is a data structure consisting of nodes, or vertices, connected by edges. It can be used to represent a variety of real-world relationships and network topologies, such as social networks, communication networks, and even transportation systems. Graphs are useful for representing data efficiently and providing a visual representation of the data. They can be used to model problems, find solutions, and even identify patterns in the data.

The area shaded and labeled A is the region where y ≤ −3x + 1 is satisfied.
The area shaded and labeled B is the region where y ≤ 1 over 2x + 3 is satisfied. The area shaded and labeled AB is the region where both of the inequalities are satisfied.

The graph shows that the two functions intersect, creating a region of overlap in the shaded area labeled AB. This is happening because the two inequalities have a common region of overlap between them, which is shown by the shaded area labeled AB. This common region of overlap indicates that there are values of x and y which satisfy both of the inequalities, meaning that the two functions have a common region of overlap.

This system of inequalities can be used to identify the region of values which satisfy both of the inequalities. Any point located within the shaded area labeled AB will be a valid point which satisfies both of the inequalities. This can be used to identify the range of values which satisfy both of the inequalities, and can be used to determine the best solution for a given problem.

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Answer:

Step-by-step explanation:

60≥7t-3

add 3 to both sides

63≥ 7t

divide by 7

9≥t