The three side lengths of four triangles are given. Which triangle is a right triangle?
Triangle 1: 13.6.7
Triangle 2: 7.8.13
Triangle 3: 10, 11, 12
Triangle 4: 10.9.8

Answer:

144a^2

Step-by-step explanation:

8×9×2=144

144a^1×a

144a^1×a^1

144a^1+1

144a^2

After answering the given query, we can state that As a result, the slope function grows on the range -4 x  2.

The inclination of a line determines how sharp it is. A gradient gradient is gradient overflow is an algebraic formula for the gradient. The vertical change (run) between two spots is divided by the height change (rise) between the same two locations to determine the slope. The equation for a straight line, written as y = mx plus b, is represented using the curve form of a formula. The slope is m, b is b, and the line's y-intercept is located at these points. (0, b). As an example, consider the y-intercept and slope of the equation y = 3x - 7. (0, 7). The y-intercept is situated where the inclination of the path is m, b is b, and (0, b).

(y2 - y1)/(x2 - x1) = (5 - (-7))/(2 - (-4)) = 12/6 = 2 is the slope of the line section from (-4, -7) to (2, 5).

The function is growing on this period because the slope is positive.

(y2 - y1)/(x2 - x1) = (2 - 5)/(5 - 2) = (-3)/3 = -1 is the slope of the line section from (2, 5) to (5, 2).

The function is declining on this period because the slope is negative.

(y2 - y1)/(x2 - x1) = (2 - 2)/(7 - 5) = 0/2 = 0 is the slope of the line section from (5, 2) to (7, 2).

The function is neither growing nor declining on this interval because the slope is zero.

As a result, the function grows on the range -4 x  2.

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Answer:

answer D

Step-by-step explanation:

hello,

\(f(x)=-5^x-4 \ and \ g(x)=-3x-2\\(f-g)(x)=f(x)-g(x)=-5^x-4+3x+2=-5^x+3x-2\)

hope this helps

The value of function (f - g) (x) is,

⇒ 5ˣ + 3x - 2

A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).

Given that;

Functions are,

⇒ f (x) = - 5ˣ - 4

⇒ g (x) = - 3x - 2

Hence, We get;

The value of function (f - g) (x) is,

⇒ (f - g) (x)

⇒ f (x) - g(x)

⇒ (5ˣ - 4) - (- 3x - 2)

⇒ 5ˣ - 4 + 3x + 2

⇒ 5ˣ + 3x - 2

Thus, The value of function (f - g) (x) is,

⇒ 5ˣ + 3x - 2

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Answer:

\(\large \boxed{\mathrm{view \ explanation}}\)

Step-by-step explanation:

∠BED is measuring 90 degrees (right angle).

The opposite angle of angle ∠BED will also be 90 degrees because of vertical angles.

∠AEC is measuring 90 degrees (right angle).

The angles on a line add up to 180 degrees.

∠AEC and ∠AEB add up to 180 degrees.

90 + ∠AEB = 180

∠AEB = 90

∠AEB is measuring 90 degrees (right angle).

Angles in a circle around the center add up to 360 degrees.

∠BED + ∠AEC + ∠AEB + ∠CED = 360

90 + 90 + 90 + ∠CED = 360

∠CED = 90

∠CED is measuring 90 degrees (right angle).

Answer:

Therefore option 2 is correct.

given:

solve:

option 1:

(x + 4)(x + 1)

x² + 4x + x + 4

x² + 5x + 4

option 2:

(4x+1) (x+1)

4x² + 4x + x + 1

4x² + 5x + 1

option 3:

4x + 5

option 4:

( 4x² + x ) (x + 1)

4x³ + 4x² + x² + x

4x³ + 5x² + x

Answer:

(4x + 1)(x + 1)

Step-by-step explanation:

The blue squares mean \(x^2\)

The red rectangles mean \(x\)

The yellow square means \(+1\)

So adding the tiles together we get:  \(4x^2+5x+1\)

Reading along the bottom = 4x + 1

Reading down the right side = x + 1

If we multiply these:

\((4x + 1)(x + 1)=4x^2+4x+x+1=4x^2+5x+1\)

which is the same as above, so correct!

The value of BE is 42in

Similar triangles are triangles that have the same shape, but their sizes may vary. For two triangles to be similar the corresponding angles are congruent.

Also the ratio of the corresponding sides are equal.

This means that;

15/21 = 30/BE

represent BE by x

15/21 = 30/x

15x = 21×30

15x = 630

divide both sides by 15

x = 630/15

x = 42

Therefore the value of BE is 42 in

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Production: 168,500 units.

Direct materials: 337,000 pounds.

Direct labor: Calculated based on units produced.

Factory overhead: Calculated based on direct labor hours.

1. Production Budget for the Third Quarter:

BLACK DIAMOND COMPANY Production Budget (in units) Third Quarter

Budgeted sales units: 170,000

Add: Desired ending inventory units: 5,500

Total required units: 175,500

Less: Beginning inventory units: 7,000

Units to produce: 168,500

2. Direct Materials Budget for the Third Quarter:

BLACK DIAMOND COMPANY Direct Materials Budget Third Quarter

Units to produce: 168,500

Materials needed for production (pounds): 2 pounds per snowboard

Total materials required (pounds): 337,000 pounds

Materials to purchase (pounds): Total materials required - Beginning inventory pounds - Desired ending inventory pounds

3. Direct Labor Budget for the Third Quarter:

BLACK DIAMOND COMPANY Direct Labor Budget Third Quarter

Units to produce: 168,500

Direct labor hours needed: 0.5 hour per snowboard

Cost of direct labor: Direct labor hours needed * Direct labor rate

4. Factory Overhead Budget for the Third Quarter:

BLACK DIAMOND COMPANY Factory Overhead Budget Third Quarter

Direct labor hours needed: Calculated from the direct labor budget

Budgeted variable overhead: Direct labor hours needed * Variable overhead rate

Budgeted total factory overhead: Budgeted fixed overhead + Budgeted variable overhead

Note: The specific rates for direct materials, direct labor, and variable overhead were not provided in the given information and would need to be included in the calculations based on the company's specific cost structure.

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The first pair of electrons go axially. The second pair go equatorially. Hence, the correct answer is axial; equatorial

For the trigonal bipyramidal electron domain geometry, the first pair of electrons will go to the equatorial position because it has less electron-electron repulsion than the axial position. The second pair of electrons will go to the axial position because the axial position has more space and less repulsion from the equatorial pairs.

Six atoms make up the molecular geometry, with one in the middle and the other five forming a triangle pyramid. The atoms on either side of the center have different bond angles. The compounds phosphorus pentachloride and phosphorus pentafluoride are two examples of trigonally bipyramidal molecules.

To reduce electron-electron repulsion, the initial pair of electrons would prefer to occupy one of the axial locations. The axial locations are further apart from each other compared to the equatorial positions, which are closer together. Hence, axial positioning of the initial pair of electrons would provide a shape that is more stable. According to the VSEPR theory, the remaining electron domains (i.e., lone pairs and/or bonded pairs) would be dispersed among the other places once the initial pair of electrons occupy an axial position.

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Answer:

-9/8

Step-by-step explanation:

The two points given are

(1,6) and (9,-3)

The slope is given by

m = (y2-y1)/(x2-x1)

   = (-3-6)/(9-1)

   = -9/8

The graph of the equation y = \(2^{x}\) - 5 is obtained by shifting the graph of

y =\(2^{x}\)  downside by 5 units.

To find a graph of equation y = \(2^{x}\) - 5, we can start with the reference of the parent function y = \(2^{x}\) and also apply the necessary transformations.  Initiating with the graph of the parent function y =\(2^{x}\) - 5.

This is an exponential function that passes through the point( 0, 1) and has a positive pitch. Apply the transformation -5 units over. This means we shift the entire graph over by 5 units. The point( 0, 1) will now come( 0,-4).thus, the graph of the equation y =  \(2^{x}\)- 5 is attained by shifting the graph of y =  \(2^{x}\) downcast by 5 units. The factual shape of the graph will act as that of the parent exponential function, but it'll be shifted over by 5 units.

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The correct question is given below-

Graph the equation shown below by transforming the given graph of the parent function. y= \(2^{x}\) obtain  y=\(2^{x}\)-5.

Based on the diagram, the point of tangency is Point Z. Therefore, the answer is B.

A point of tangency is a point at which a straight line, called a tangent line, touches a curve or a circle at only one point.

At the point of tangency, the tangent line is perpendicular to the radius of the circle that intersects the point of tangency.

The point of tangency is the point where a tangent line to the circle touches the circle at only one point.

In the given diagram, the line segment XZ appears to be a tangent to the circle.

Therefore, the point of tangency is the point where the line segment XZ touches the circle.

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Answer:

First we write y and its derivatives as power series:

y=∑n=0∞anxn⟹y′=∑n=1∞nanxn−1⟹y′′=∑n=2∞n(n−1)anxn−2

Next, plug into differential equation:

(x+2)y′′+xy′−y=0

(x+2)∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0

x∑n=2∞n(n−1)anxn−2+2∑n=2∞n(n−1)anxn−2+x∑n=1∞nanxn−1−∑n=0∞anxn=0

Move constants inside of summations:

∑n=2∞x⋅n(n−1)anxn−2+∑n=2∞2⋅n(n−1)anxn−2+∑n=1∞x⋅nanxn−1−∑n=0∞anxn=0

∑n=2∞n(n−1)anxn−1+∑n=2∞2n(n−1)anxn−2+∑n=1∞nanxn−∑n=0∞anxn=0

Change limits so that the exponents for  x  are the same in each summation:

∑n=1∞(n+1)nan+1xn+∑n=0∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−∑n=0∞anxn=0

Pull out any terms from sums, so that each sum starts at same lower limit  (n=1)

∑n=1∞(n+1)nan+1xn+4a2+∑n=1∞2(n+2)(n+1)an+2xn+∑n=1∞nanxn−a0−∑n=1∞anxn=0

Combine all sums into a single sum:

4a2−a0+∑n=1∞(2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an)xn=0

Now we must set each coefficient, including constant term  =0 :

4a2−a0=0⟹4a2=a0

2(n+2)(n+1)an+2+(n+1)nan+1+(n−1)an=0

We would usually let  a0  and  a1  be arbitrary constants. Then all other constants can be expressed in terms of these two constants, giving us two linearly independent solutions. However, since  a0=4a2 , I’ll choose  a1  and  a2  as the two arbitrary constants. We can still express all other constants in terms of  a1  and/or  a2 .

an+2=−(n+1)nan+1+(n−1)an2(n+2)(n+1)

a3=−(2⋅1)a2+0a12(3⋅2)=−16a2=−13!a2

a4=−(3⋅2)a3+1a22(4⋅3)=0=04!a2

a5=−(4⋅3)a4+2a32(5⋅4)=15!a2

a6=−(5⋅4)a5+3a42(6⋅5)=−26!a2

We see a pattern emerging here:

an=(−1)(n+1)n−4n!a2

This can be proven by mathematical induction. In fact, this is true for all  n≥0 , except for  n=1 , since  a1  is an arbitrary constant independent of  a0  (and therefore independent of  a2 ).

Plugging back into original power series for  y , we get:

y=a0+a1x+a2x2+a3x3+a4x4+a5x5+⋯

y=4a2+a1x+a2x2−13!a2x3+04!a2x4+15!a2x5−⋯

y=a1x+a2(4+x2−13!x3+04!x4+15!x5−⋯)

Notice that the expression following constant  a2  is  =4+  a power series (starting at  n=2 ). However, if we had the appropriate  x -term, we would have a power series starting at  n=0 . Since the other independent solution is simply  y1=x,  then we can let  a1=c1−3c2,   a2=c2 , and we get:

y=(c1−3c2)x+c2(4+x2−13!x3+04!x4+15!x5−⋯)

y=c1x+c2(4−3x+x2−13!x3+04!x4+15!x5−⋯)

y=c1x+c2(−0−40!+0−31!x−2−42!x2+3−43!x3−4−44!x4+5−45!x5−⋯)

y=c1x+c2∑n=0∞(−1)n+1n−4n!xn

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Answer:

445 remainder 3

Step-by-step explanation:

9 × 4 = 36

40 - 36 = 4

Bring down the 0.

9 × 4 = 36

40 - 36 = 4

Bring down the 8.

9 × 5 = 45

48 - 45 = 3

Hope that helps.

Step-by-step explanation:

3×5×2 = 30 lorry trips to deliver 2,500 crates.

3 lorries, 5 trips per day, 2 days

that means that one lorry trip transports

2,500 / 30 = 250/3 = 83.33333... crates = 83 1/3 crates.

now we need x lorries each making 6 trips per day in 1 day (so, 6 trips, period) to transport 10,000 crates.

that looks like

x × 6 × 83.33333... = 10,000

x × 6 × 83 1/3 = 10,000

x × (6×83 + 6 × 1/3) = 10,000

x × (498 + 2) = 10,000

500x = 10,000

x = 20

so, we need 20 lorries each doing 6 trips in one day to transport 10,000 crates in one day.

these are altogether 20×6 = 120 lorry trips.

that is 4 times the number of the original scenario (30 trips).

and logically, when doing 4 times the work, we achieve 4 times the result (10,000 crates instead of 2,500).

"The gradient vector of the function - f(x, y) = ln(xy) — x³ at the point (-1, 1) is (-2, -1)" is True.

To find the gradient vector of the function -f(x, y) = ln(xy) - x³, we need to take the partial derivatives of the function with respect to x and y.

Let's find the partial derivatives:

∂/∂x (-f(x, y)) = ∂/∂x (-ln(xy) + x³)

= -∂/∂x (ln(xy)) - ∂/∂x (x³)

To find ∂/∂x (ln(xy)), we can apply the chain rule:

∂/∂x (ln(xy)) = ∂/∂x (ln(x) + ln(y))

= 1/x

And ∂/∂x (x³) = 3x²

Therefore, ∂/∂x (-f(x, y)) = -1/x - 3x²

Now, let's find ∂/∂y (-f(x, y)):

∂/∂y (-f(x, y)) = ∂/∂y (-ln(xy) + x³) = -∂/∂y (ln(xy)) - ∂/∂y (x³)

Using the chain rule again, ∂/∂y (ln(xy)) = ∂/∂y (ln(x) + ln(y)) = 1/y

And ∂/∂y (x³) = 0

Therefore, ∂/∂y (-f(x, y)) = -1/y

At the point (-1, 1), we evaluate the partial derivatives:

∂/∂x (-f(-1, 1)) = -1/(-1) - 3(-1)² = 1 - 3 = -2

∂/∂y (-f(-1, 1)) = -1/1 = -1

So, the gradient vector at the point (-1, 1) is (-2, -1).

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1)The slope of the line is C) 13. 2)It would be inefficient since it is not the most optimal use of resources.the correct option is C. 3)The equilibrium price and quantity are D) $25 and 10 dozens of roses per day, respectively.

1) Y = 13X + 38, where Y is a function of X.

The slope of the line is 13.

Therefore, the correct option is C.

2) Kolin catches 25 fish and gathers 70 fruits. If we consider the combination, then it would be inefficient since it is not the most optimal use of resources.

Therefore, the correct option is C.

3) Using the given figure, we can see that the point where the demand and supply curves intersect is the equilibrium point. At this point, the equilibrium price is $25 and the equilibrium quantity is 10 dozens of roses per day.

Therefore, the correct option is D. The equilibrium price and quantity are $25 and 10 dozens of roses per day, respectively.

Note that this is the point of intersection between the demand and supply curves, which represents the market equilibrium.

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Answer:

there's no picture

Step-by-step explanation:

sorry

The main answer to the question is: None of these alternatives is correct. If the mean of a normal distribution is negative, the variance must not be negative. The explanation to support the answer is given below:

Normal distribution is a statistical distribution that depicts how values are dispersed in a dataset. It is also known as Gaussian distribution or bell curve because of its bell-shaped pattern. It is described by two parameters, i.e., mean and standard deviation.The mean of a normal distribution specifies the location of the center of the distribution. The variance of a normal distribution indicates the amount of variation from the mean. Variance is always positive, no matter whether the mean is positive or negative.

Therefore, if the mean of a normal distribution is negative, the variance must not be negative.Hence, none of these alternatives is correct. If the mean of a normal distribution is negative, the variance must not be negative.

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The line tangent to f(x) = x + sin(x) is parallel to the secant line connecting the endpoints at x = π on the interval [-2π, 2π].

Let's begin by finding the slope of the secant line connecting the endpoints of the function. The endpoints of the function on the interval [-2π, 2π] are (-2π, -2π + sin(-2π)) and (2π, 2π + sin(2π)), which evaluate to (-2π, 0) and (2π, 0), respectively.

The slope of the secant line is

m = (0 - 0)/(2π - (-2π)) = 0

Since we want the tangent line to be parallel to the secant line, the slope of the tangent line should also be 0. We can find the equation of the tangent line using the point-slope form

y - (x + sin(x)) = 0

y = x + sin(x)

To find the points on the interval where the tangent line is parallel to the secant line, we need to find the values of x where the derivative of f(x) is equal to 0 (i.e., where the slope of the tangent line is 0). The derivative of f(x) is

f'(x) = 1 + cos(x)

Setting this equal to 0 and solving for x, we get

cos(x) = -1

x = π

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The given question is incomplete, the complete question is:

At how many points on the interval [-2pi, 2pi] is the line tangent to f(x)=x+sin x parallel to the secant line connecting the function endpoints?

Answer:

12.566

12.6 (simplified to the tenths)

12.57(simplified to the hundredths)

Step-by-step explanation:

The diameter of a circle is always double of the radius

π is always ≈ 3.14

π * 2^2 = π * 4  ≈ 12.566

The indicated limit of the expression (3x - 18)/(x - 9) as x approaches 3 is 1.

To find the limit, we first observe that both the numerator and denominator contain a common factor of (x - 9). By factoring out this common factor, we can rewrite the expression as (3(x - 6))/(x - 9). Now, applying the limit properties, we can evaluate the limit as x approaches 3. As x approaches 3, the term (x - 6) also approaches 3 - 6 = -3.

Therefore, the numerator becomes 3(-3) = -9, and the denominator becomes 3 - 9 = -6. Finally, taking the ratio of -9 and -6 gives us the limit of 1. Thus, the indicated limit is 1.

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Both Elena and Lin are right , in my opinion. According to Elena, length BC is 16.5 units. Lin estimates that BC is 17.1 units long.

The remainder of the query is included in the attachment. The figure shows that ED is parallel to A B and B C is parallel to A B. In light of the Pythagoras theorem,

\($\mathrm{AC}^ 2=\mathrm{AB}^ 2+\mathrm{BC}^ 2$\)

\($\mathrm{BC}^ 2=196-36=160$\)

\($\mathrm{BC}=12.649$\) or \($12.65$\)

Both Elena and Lin are right .A visual that conveys information rather than just representing it. particularly : a diagram demonstrating the relationships and arrangements (as between parts): a dotted line drawing used in science or math .

A diagram is a picture that shows how something works, how it's organised, or how it's related to something else. Even when they go by the names "map," "chart," or "graph," several diagram kinds are still considered to be diagrams. as flowcharts, organisational charts, and mind maps. An illustration that depicts an object's component elements and their relationships to one another is called a diagram.

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Since k and l are integers, k + l is also an integer, this proves that (a + b) ≡ (c + d) (mod n).

Since k and l are integers, k − l is also an integer, this proves that (a − b) ≡ (c − d) (mod n)

a. To prove that (a + b) ≡ (c + d) (mod n), we need to show that n divides (a + b) − (c + d), or equivalently, that (a + b) − (c + d) is an integer multiple of n. We have:

(a + b) − (c + d) = a − c + (b − d)

Since a ≡ c (mod n) and b ≡ d (mod n), we can write a = c + kn and b = d + ln for some integers k and l. Substituting these into the above equation, we get:

(a + b) − (c + d) = (c + kn) + (d + ln) − c − d = kn + ln = (k + l)n

Since k and l are integers, k + l is also an integer, and therefore, (a + b) − (c + d) is an integer multiple of n. This proves that (a + b) ≡ (c + d) (mod n).

b. To prove that (a − b) ≡ (c − d) (mod n), we need to show that n divides (a − b) − (c − d), or equivalently, that (a − b) − (c − d) is an integer multiple of n. We have:

(a − b) − (c − d) = a − c − (b − d)

Since a ≡ c (mod n) and b ≡ d (mod n), we can write a = c + kn and b = d + ln for some integers k and l. Substituting these into the above equation, we get:

(a − b) − (c − d) = (c + kn) − (d + ln) − c + d = kn − ln = (k − l)n

Since k and l are integers, k − l is also an integer, and therefore, (a − b) − (c − d) is an integer multiple of n. This proves that (a − b) ≡ (c − d) (mod n).

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Examples of numbers that are rational number but not natural

-4, -5, 4/5, 0.89, 0.

Rational Numbers:

A type of real number known as a rational number is represented by the formula p/q, where q is not equal to zero. A rational number is any fraction with a non-zero denominator. 1/2, 1/5, 3/4, and other such numbers are a few examples of rational numbers. The number "0" is also a rational number because there are many ways to represent it, including 0/1, 0/2, 0/3, etc. However, since they give us infinite values, 1/0, 2/0, 3/0, etc. are illogical. Check the irrational numbers here as well and contrast them with the rational ones.

Natural Number:

All positive integers from 1 to infinity are included in the number system, which also includes natural numbers, which are also used for counting. There is no zero included (0). In fact, counting numbers are 1, 2, 3, 5, 6, 7, 8, 9, etc.

Real numbers, which only include the positive integers 1, 2, 3, 4,5, and 6, are made up of natural numbers. Negative numbers, fractions, decimals, and zero are not included.

Notably, zero and negative numbers are not considered to be natural numbers.

Few examples of numbers that are rational number but not natural

-4, -5, 4/5, 0.89, 0.

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To test the null hypothesis that the mean of the population is 3 against the alternative hypothesis μ≠3, we can use a hypothesis test with a significance level α.

In hypothesis testing, we compare a sample statistic to a hypothesized population parameter. In this case, we want to determine if the mean of the population is significantly different from 3.

To conduct the test, we first collect a sample of data. Then, we calculate the sample mean and standard deviation.

We use these statistics to calculate the test statistic, which follows a t-distribution with (n-1) degrees of freedom, where n is the sample size.

Next, we determine the critical region based on the significance level α. For a two-tailed test, we divide α by 2 to get the critical values for both tails of the distribution.

Finally, we compare the test statistic to the critical values.

If the test statistic falls within the critical region, we reject the null hypothesis and conclude that the mean of the population is significantly different from 3.

Otherwise, if the test statistic falls outside the critical region, we fail to reject the null hypothesis.

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there are two values of x in the interval where the instantaneous rate of change of is equal to the average rate of change of over the interval.

To find the average rate of change of over the interval , we need to calculate the slope of the line passing through the two endpoints of the interval.

The slope of the line passing through the points and is given by:

( - )/( - ) = ( -3 - 3)/(1 - (-1)) = -6/2 = -3

Therefore, the average rate of change of over the interval is -3.

To find how many values of in the interval have instantaneous rate of change equal to the average rate of change, we need to find the derivative of :

f'(x) = 3x^2 - 3x - 3

Setting f'(x) equal to the average rate of change, we get:

3x^2 - 3x - 3 = -3

Simplifying the equation, we get:

3x^2 - 3x = 0

Factoring out 3x, we get:

3x(x - 1) = 0

Therefore, the solutions are x = 0 and x = 1.

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Answer:

12t - 1

Step-by-step explanation:

(9t+5) + (3t-6)

9t + 5 + 3t - 6

12t - 1

Answer: No solution.

Answer 2: (130/51, 157/51)

Answer:

where is the table

Step-by-step explanation:

please make the statement clear instead of copy and pasting the question so we can answer the question correctly