=
REAL NUMBERS
Simplifying a ratio of whole numbers: Problem type 1
Write the ratio as a fraction in simplest form, with whole numbers in the numerator and denominator.
35 to 30

The area of each parallelogram or triangle is 24 cm²,22.5 cm², 98 ft²,48 cm², 90 m², and  30 in² respectively.

In this skills practice problem, we are asked to find the perimeter and area of each parallelogram or triangle, based on their given dimensions. Let's start by defining the formulas for calculating the perimeter and area of each shape:

Perimeter of a parallelogram = 2 x (length + width)

Area of a parallelogram = base x height

Perimeter of a triangle = sum of the lengths of its sides

Area of a triangle = 1/2 x base x height

Now, let's apply these formulas to each shape:

Parallelogram with length 6 cm and width 4 cm:

Perimeter = 2 x (6 + 4) = 20 cm

Area = 6 x 4 = 24 cm²

Triangle with base 9 cm and height 5 cm:

Perimeter = 9 + 8 + 7 = 24 cm

Area = 1/2 x 9 x 5 = 22.5 cm²

Parallelogram with length 14 ft and width 7 ft:

Perimeter = 2 x (14 + 7) = 42 ft

Area = 14 x 7 = 98 ft²

Triangle with base 12 cm and height 8 cm:

Perimeter = 12 + 8 + 10 = 30 cm

Area = 1/2 x 12 x 8 = 48 cm²

Parallelogram with length 18 m and width 5 m:

Perimeter = 2 x (18 + 5) = 46 m

Area = 18 x 5 = 90 m²

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#SPJ11Triangle with base 6 in and height 10 in:

Perimeter = 6 + 8 + 10 = 24 in

Area = 1/2 x 6 x 10 = 30 in²

Therefore, we have calculated the perimeter and area of each given parallelogram or triangle.

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Answer:

y=-3/2x+7.5

Step-by-step explanation:

You need to find the slope by subtracting second point,(7,-3), from the first point, (5,0), you get the slope of -3/2.

you need to put it on a graph with that slope, place the original two points and you move the slope up the y-axis 7.5, making the y-intercept (7.5,0)

The probability that all three wires will meet the specifications is approximately 0.173 .

Expected value (mean) of wire resistance = 0.13 ohms Standard deviation of wire resistance = 0.005 ohms

the probability for each wire, we need to standardize the range of resistance values using the expected value and standard deviation. We can use the Z-score formula:

Z = (X - μ) / σ

Z is the standard score (Z-score) X is the observed value (resistance) μ is the mean (expected value) σ is the standard deviation

For the lower specification of 0.10 ohms

Z1 = (0.10 - 0.13) / 0.005

For the upper specification of 0.17 ohms

Z2 = (0.17 - 0.13) / 0.005

Using a standard normal distribution table , we can find the probability associated with each Z-score.

Lower bound of standardized range = (0.10 - 0.13) / 0.005 = -0.06

Upper bound of standardized range = (0.17 - 0.13) / 0.005 = 0.80

Let's calculate the probabilities for each wire

P(z < -0.60) ≈ 0.2743

P(z < 0.80) ≈ 0.7881

Since we want the probability that all three wires meet the specifications, we need to multiply these probabilities together since the wires are selected independently.

P(all three wires meet specifications) = P(z < -0.60) × P(z < 0.80) × P(z < 0.80)

P(all three wires meet specifications) ≈ 0.2743 × 0.7881 × 0.7881 ≈ 0.1703

Therefore, the probability that all three wires will meet the specifications is approximately 0.173, or 17.3% .

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The 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

To find the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers, we can use the formula for the confidence interval for a proportion.

The formula for the confidence interval is:

CI = p1 ± Z * √((p1 * (1 - p1)) / n)

Where:

CI is the confidence interval,

p1 is the sample proportion (proportion of accidents involving teenage drivers),

Z is the Z-score corresponding to the desired confidence level (95% confidence level corresponds to Z ≈ 1.96),

n is the sample size (number of accidents checked).

Given:

Number of accidents checked (sample size), n = 582

Number of accidents involving teenage drivers, x = 91

First, we calculate the sample proportion:

p1 = x / n = 91 / 582 ≈ 0.1566

Now we can calculate the confidence interval:

CI = 0.1566 ± 1.96 * √((0.1566 * (1 - 0.1566)) / 582)

Calculating the standard error of the proportion:

SE = √((p1 * (1 - p1)) / n) = √((0.1566 * (1 - 0.1566)) / 582) ≈ 0.0184

Substituting the values into the formula:

CI = 0.1566 ± 1.96 * 0.0184

Calculating the values:

CI = 0.1566 ± 0.0361

Finally, we can simplify the confidence interval:

CI = (0.1205, 0.1927)

Therefore, the 95% confidence interval for the true proportion of all auto accidents involving teenage drivers is approximately (0.1205, 0.1927).

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The total area of the region bounded by the graph of y = x times the square root of \((1 - x^2)\) and the x-axis is 1/2.

Let the region bounded by the graph of y = x times the square root of\((1 - x^2)\) and the x-axis be the region R.

The total area of region R is given by A as;\(A = 2∫_0^1▒〖ydx〗\)

The boundary of the given region is given by y = x times the square root of\((1 - x^2)\) and the x-axis.

Thus, for any x in the interval [0, 1], the boundary of the region R can be represented as;\(∫_0^1▒〖x√(1-x^2)dx〗\)

Let \(u = 1 - x^2,\)

therefore, du/dx = -2x.

It implies that\(dx = -du/2x.\)

The integral becomes;\(∫_1^0▒〖(-du/2)√udu〗=-1/2 ∫_1^0▒√udu\)

=-1/2 2/3

= -1/3

Therefore the total area of the region bounded by the graph of y = x times the square root of \((1 - x^2)\)and the x-axis is 1/2. Hence, option B) 1/2 is the correct answer.

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Answer:

  375

Step-by-step explanation:

You want to know the number of integers from 1 to 1000 that are multiples of 4 or 6.

Assuming the ends of the range are not multiples of interest, we can find the number of multiples of a given number by dividing the range by that number. Doing this for 4, 6, and (4×6), we find that in [1, 1000], there are ...

The number of multiples of 4 or 6 will be the total of multiples of 4 and multiples of 6, less the number of multiples of both 4 and 6. That is, the first sum counts those multiples of 24 twice.

  250 +166 -41 = 375

There are 375 multiples of 4 or 6 in the range 1 to 1000.

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The alteration has an effect on (K) I, II and III

The function is given as:

\(h = -at^2 + bt + c\)

When the constant term (c) is altered, i.e. changed, the function becomes a different function entirely.

Take for instance, the new function is:

\(h = -at^2 + bt + c+ 1\)

The functions \(h = -at^2 + bt + c\) and \(h = -at^2 + bt + c+ 1\) are different, and both functions will have different intercepts and vertices.

Hence, the alteration has an effect on (K) I, II and III

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Answer: number 3 is the answer!!!

Step-by-step explanation:

number 3!!!

1) To find the missing ordered pair of a rectangle, we can use the fact that opposite sides of a rectangle are parallel and equal in length. This means that the x-coordinate of D must be equal to the x-coordinate of A, and the y-coordinate of D must be equal to the y-coordinate of C. Therefore, D(-3, -3).

2) Similarly, we can use the fact that opposite sides of a rectangle are parallel and equal in length. This means that the x-coordinate of H must be equal to the x-coordinate of E, and the y-coordinate of H must be equal to the y-coordinate of F. Therefore, H(0, 0).

3) To find the missing ordered pair of a square, we can use the fact that all sides of a square are equal in length and all angles are right angles. This means that the distance between J and K must be equal to the distance between K and L, which is 4 units. Therefore, the distance between L and M must also be 4 units. Since L has an x-coordinate of 2, M must have an x-coordinate of 2 + 4 = 6. Similarly, since L has a y-coordinate of -2, M must have a y-coordinate of -2 + 4 = 2. Therefore, M(6, 2).

4) To find the missing ordered pair of an isosceles right triangle, we can use the fact that two sides of an isosceles triangle are equal in length and two angles are equal in measure. This means that the distance between P and Q must be equal to the distance between Q and R, which is 6 units. Therefore, R must be 6 units away from Q along the x-axis. Since Q has an x-coordinate of 0, R must have an x-coordinate of 0 + 6 = 6. Similarly, since Q has a y-coordinate of 6, R must have a y-coordinate of 6 - 6 = 0. Therefore, R(6, 0).

-\frac{92}{27}}

The matrix form of the given system of linear equations is:

\left[\begin{array}{cccc}3 & 1 & 5 & 5 \\ 4 & -4 & 5 & 0 \\ -4 & -2 & -4 & 3 \\ -5 & 1 & -5 & -4\end{array}\right]\left\{\begin{array}{l}x_{1} \\ x_{2} \\ x_{3} \\ x_{4}\end{array}\right\}=\left\{\begin{array}{c}a \\ b \\ c \\ d\end{array}\right\}

The augmented matrix of the system can be obtained by concatenating the coefficient matrix and the constant matrix. \left[\begin{array}{cccc|c}3 & 1 & 5 & 5 & a \\ 4 & -4 & 5 & 0 & b \\ -4 & -2 & -4 & 3 & c \\ -5 & 1 & -5 & -4 & d\end{array}\right]

Now, we will perform the row operations on the augmented matrix in order to obtain the echelon form of the matrix.

\left[\begin{array}{cccc|c}3 & 1 & 5 & 5 & a

\\ 0 & -8 & -5 & -20 & b - 4a

\\ 0 & 0 & -27 & -27 & c + a + \frac{5}{4}b

\\ 0 & 0 & 0 & -\frac{92}{27} & d + 5a + \frac{23}{108}b + \frac{11}{27}c\end{array}\right]

We see that the echelon form of the given augmented matrix has four non-zero rows.

Therefore, we can say that the rank of the coefficient matrix is 4.

Also, we have only 4 variables.

Hence, the system is consistent and has a unique solution.

Now, we can use back-substitution to find the value of x_1, x_2, x_3, and x_4.

From the last row of the echelon form, we get x_4 = -\frac{92}{27}.

Substituting x_4 = -\frac{92}{27} in the third row of the echelon form,

we get -27x_3 = c + a + \frac{5}{4}b,

i.e., x_3 = -\frac{c}{27} - \frac{a}{27} - \frac{5}{108}b.

Substituting x_4 = -\frac{92}{27} and

x_3 = -\frac{c}{27} - \frac{a}{27} - \frac{5}{108}b in the second row of the echelon form,

we get -8x_2 - 5x_3 - 20x_4 = b - 4a,

i.e., x_2 = -\frac{1}{8}b + \frac{1}{4}a + \frac{5}{32}x_4 + \frac{5}{27}c.

Finally, substituting x_4

= -\frac{92}{27}, x_3

= -\frac{c}{27} - \frac{a}{27} - \frac{5}{108}b, and x_2 = -\frac{1}{8}b + \frac{1}{4}a + \frac{5}{32}x_4 + \frac{5}{27}c in the first row of the echelon form, we get 3x_1 + x_2 + 5x_3 + 5x_4 = a,

i.e., x_1 = -\frac{1}{3}x_2 - \frac{5}{3}x_3 - x_4 + \frac{1}{3}a

Therefore, the solution of the given system of linear equations is given by \boxed{x_1

= -\frac{1}{3}x_2 - \frac{5}{3}x_3 - x_4 + \frac{1}{3}a, \quad x_2

= -\frac{1}{8}b + \frac{1}{4}a + \frac{5}{32}x_4 + \frac{5}{27}c, \quad x_3

= -\frac{c}{27} - \frac{a}{27} - \frac{5}{108}b, \quad x_4

= -\frac{92}{27}}

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Hello !

An infinity value is generated for an operation whose result is less than the smallest numeric value.

it's true!

The best approximation of the number of yellow markers in the box is 30.

The first step is to express the sample of markers picked as a fraction of the total markers in the box.

Sample of markers picked = markers in the sample / total number of markers in the box

= 50 / 300 = 1/6

The second step is to divide the number of yellow markers by the fraction gotten in the previous step

Number of yellow markers in the box = 5 ÷ 1/6

= 5 x 6 = 30 markers

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(a) The population proportion of success is given as 53%. This means that 53% of the population is expected to have a successful outcome from the flu shot.

To calculate the population proportion of success, we are given that the flu vaccine is effective for 53% of patients administered the shot. This means that 53% (or 0.53) of the entire population is expected to have a successful outcome from the flu shot.

(b) The mean of the sampling distribution of the sample proportion is also 53%.

The mean of the sampling distribution of the sample proportion can be calculated using the same population proportion of success, which is 53%. The sampling distribution represents the distribution of sample proportions if multiple samples of the same size are taken from the population. Since the mean of the sampling distribution is equal to the population proportion, the mean in this case is also 53%.

(c) The standard deviation of the sampling distribution of the sample proportion is approximately 0.017.

To calculate the standard deviation of the sampling distribution of the sample proportion, we use the formula:

\(\sigma = \sqrt{\frac{p \cdot q}{n}}\)

where σ represents the standard deviation, p is the population proportion of success (0.53), q is the complement of p (1 - p, which is 0.47), and n is the sample size (85).

Plugging in the values, we get:

\(\sigma = \sqrt{\frac{0.53 \cdot 0.47}{85}}\)

Calculating this expression, we find:

\(\sigma \approx \sqrt{\frac{0.0251}{85}} \approx \sqrt{0.000295} \approx 0.0171\)

Rounding this value to three decimal places, the standard deviation of the sampling distribution of the sample proportion is approximately 0.017.

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a) The mean of the distribution is 40 minutes.

b) The standard deviation of the distribution is approximately 5.77 minutes.

c) The probability that the next room will require exactly 34 minutes to clean is zero.

d) The probability that the next room will require less than 45 minutes to clean is 0.75 or 75%.

e) The probability that the next room will require more than 45 minutes to clean is 0.25 or 25%.

f) The probability that the next room will require between 34 and 45 minutes to clean is 0.55 or 55%.

g) The 70th percentile of the distribution is 44 minutes, which means that 70% of the cleaning times will be less than or equal to 44 minutes.

a) The mean of a continuous uniform distribution is given by the average of the minimum and maximum values:

Mean = (Minimum + Maximum) / 2

         = (30 + 50) / 2

Mean = 40 minutes.

b) The standard deviation of a continuous uniform distribution is calculated using the following formula:

Standard Deviation = (Maximum - Minimum) / √12

                                = (50 - 30) / √12

                                ≈ 5.77 minutes.

c) The probability that the next room will require exactly 34 minutes to clean is zero because the continuous uniform distribution assigns zero probability to any single point within the range.

d) To calculate the probability that the next room will require less than 45 minutes to clean, we need to find the area under the probability density function (PDF) curve up to 45 minutes. Since the distribution is uniform, the probability is equal to the proportion of the range from the minimum to 45 minutes:

Probability = (45 - 30) / (50 - 30)

                  = 15 / 20

                  = 0.75.

e) The probability that the next room will require more than 45 minutes to clean is equal to 1 minus the probability calculated in part (d):

Probability = 1 - 0.75 = 0.25.

f) To calculate the probability that the next room will require between 34 and 45 minutes to clean, we need to find the area under the PDF curve between these two points. Again, since the distribution is uniform, the probability is equal to the proportion of the range between these values:

Probability = (45 - 34) / (50 - 30)

                  = 11 / 20

                  = 0.55.

g) The 70th percentile represents the value below which 70% of the data falls. For a continuous uniform distribution, this can be calculated using the formula:

Percentile Value = Minimum + (Percentile / 100) * (Maximum - Minimum)

Percentile Value = 30 + (70 / 100) * (50 - 30) = 30 + (0.7 * 20) = 30 + 14 = 44 minutes.

Therefore, the 70th percentile of this distribution is 44 minutes.

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\(b \leq -1\) is written in the Interval notation = (-∞, -1)

Given that \(b \leq -1\)

To prove that it is a inequality:

What is Inequality?

In mathematics, a relationship between two expressions or values that are not equal to each other is called 'inequality. ' So, a lack of balance results in inequality.

It can be considered as Interval notation for that is (-∞, -1)

What is Interval Notation?

We can use interval notation to show that a value falls between two end points.

Hence the answer is, \(b \leq -1\) is written in the Interval notation = (-∞,-1).

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29.

\(f(x) = -x^2-7x-6\)

As \(x \to \pm \infty\), \(y \to - \infty\).

This can be easily verified by looking at the graph (graph of a quadratic equation).

30.

The growth of a population is not linear, it's exponential.

31.

Exponential growth > polynomial, so \(y = 3^x\).

35.

\(V(t) = 30\cdot (25)^{\frac{t}{20}}\)

The question is asking V(t) for t = 40.

\(V(40) = 30\cdot (25)^{\frac{40}{20}} \\~\\V(40) = 30\cdot 25^2 \\~\\V(40) = 30\cdot 625 \\~\\V(40) = 18750\)

36.

The point of symmetry of a quadratic equation \(y = ax^2+bx+c\) is at its vertice:

\(V_x = \dfrac{-b}{2a}\)

\(V_x = \dfrac{6}{2}\)

\(V_x = 3\)

The line is x= 3.

Answer:

4 blue 5 purple 8 red

40

Step-by-step explanation:

8*5=40 40 can be devied by 10

Answer:

yes

Step-by-step explanation:

I think it the relation between arrow daigram or matrix

9514 1404 393

Answer:

Step-by-step explanation:

The conjugate is found by changing the sign of the square root term.‡ (For this purpose, i = √-1.)

a) the sign of 3i is changed: 2 + 3i

b) the sign of sqrt(-5) is changed: 8 -sqrt(-5) = 8 -i√5

c) the sign of 2i is changed: 7 +2i

d) the sign of sqrt(7) is changed: 4 +√7

_____

‡ Actually, the conjugate of a binomial is formed by changing the sign between terms. The purpose is to allow the product of the binomial and its conjugate to be the difference of squares.

Conventionally, the conjugate of a complex number is the value with the sign of the imaginary part reversed. That is why (-2i+7)* = 7+2i.

The x-component of the vector ⃗ is -9.98 and the y-component is 8.53.

We can find the x and y components of the vector ⃗ by using trigonometry. The magnitude of the vector is given as 13.1, and the direction of the vector is 50∘ counter-clockwise from the -axis. We can use the cosine and sine functions to find the x and y components, respectively.

cos(50∘) = -0.6428, sin(50∘) = 0.7660

x-component = magnitude x cos(50∘) = 13.1 x (-0.6428) = -9.98

y-component = magnitude x sin(50∘) = 13.1 x (0.7660) = 8.53

Therefore, the x-component of the vector ⃗ is -9.98, and the y-component is 8.53.

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The x-component of the vector is approximately 8.375 and the y-component is approximately 9.955.

To find the x- and y-components of the vector, we can use trigonometry.

Given that the magnitude of the vector is 13.1 and the direction is 50° counter-clockwise from the - axis, we can determine the x- and y-components as follows:

The x-component (horizontal component) can be found using the formula:

x = magnitude * cos(angle)

x = 13.1 * cos(50°)

x ≈ 8.375

The y-component (vertical component) can be found using the formula:

y = magnitude * sin(angle)

y = 13.1 * sin(50°)

y ≈ 9.955

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Answer:

3 bottles

Step-by-step explanation:

you equation is 7x-5=16

you add 5 to both sides which gets you 7x=21

then you divide 7 by both sides that gets you x=3

The expression −√3 sin x + cos x can be written in terms of sine only as 2 sin(x + π/3).

To express the given expression in terms of sine only, we can use trigonometric identities. We know that sin(x + π/2) = cos(x), and sin(x + π/3) = (√3/2) sin x + (1/2) cos x.

To rewrite the expression, we can rearrange the terms and substitute the values:

−√3 sin x + cos x = −√3 sin x + (√3/2) sin(x + π/3) - (1/2) sin(x + π/2)

= −√3 sin x + (√3/2) sin(x + π/3) - (1/2) cos x

Now, we can use the sum-to-product formula for sine, which states that sin(A) + sin(B) = 2 sin((A + B)/2) cos((A - B)/2):

−√3 sin x + (√3/2) sin(x + π/3) - (1/2) cos x = -√3 sin x + 2(√3/2) sin((x + π/3 + x)/2) cos((x + π/3 - x)/2) - (1/2) cos x

= -√3 sin x + 2 sin((2x + π/3)/2) cos(π/6) - (1/2) cos x

= -√3 sin x + 2 sin((2x + π/3)/2) (√3/2) - (1/2) cos x

= -√3 sin x + √3 sin((2x + π/3)/2) - (1/2) cos x

Finally, simplifying further:

-√3 sin x + √3 sin((2x + π/3)/2) - (1/2) cos x = √3 [sin((2x + π/3)/2) - sin x] - (1/2) cos x

= √3 [2 sin((x + π/6)/2) cos((x - π/6)/2)] - (1/2) cos x

= 2√3 sin((x + π/6)/2) cos((x - π/6)/2) - (1/2) cos x

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Answer:

t = 44 years

Step-by-step explanation:

t = (1/r)(I/P-1)

t = (1/0.05) {(8000/2500) - 1}

t = 44

Answer:

y=2x+3

Step-by-step explanation: The line intersects the y axis at 3 and the slope of the line is 2/1

goirtj seirdhrtijtshr rtsdh  hh h h hh h hh  hh

Answer:

a. 1.00 minute (rounded to 2 decimal places)

b. 0.7568 (rounded to 4 decimal places)

c. 0.2432 (rounded to 4 decimal places)

Step-by-step Explanation:-

a. To calculate the expected arrival time, we multiply the total time range (3.7 minutes) by the probability of the elevator arriving at any given time within that range. Since the arrival time is equally likely at any time, the probability is uniformly distributed. Thus, the expected arrival time is:

Expected arrival time = (3.7 minutes) * (1/3.7) = 1.00 minute (rounded to 2 decimal places)

b. To find the probability that the elevator arrives in less than 2.8 minutes, we divide the desired time range by the total time range:

Probability = (2.8 minutes) / (3.7 minutes) = 0.7568 (rounded to 4 decimal places)

c. To find the probability that the wait for an elevator is more than 2.8 minutes, we subtract the probability from 1 since it is the complement event:

Probability = 1 - 0.7568 = 0.2432 (rounded to 4 decimal places)

Therefore, the probability that the wait for an elevator is more than 2.8 minutes is 0.243 (rounded to 3 decimal places).

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Answer:

A ≈ 418.9 cm²

Step-by-step explanation:

the area (A) of the sector is calculated as

A = area of circle × fraction of circle

  = πr² × \(\frac{120}{360}\) ( r is the radius )

 = π × 20² × \(\frac{1}{3}\)

 = \(\frac{400\pi }{3}\)

 ≈ 418.9 cm² ( to the nearest tenth )

Answer:

The average rate of change of the function for the interval [-4, 0] is  \(\frac{3}{4}\) ⇒ A

Step-by-step explanation:

The average rate of change of the function is the slope of the line that represents the function, m = Δy/Δx, where

From the given figure

→ The values of x in the interval [-4, 0] are -4 and 0

∵ The point (-4, 0) and (0, 3) lie on the line

∴ x1 = -4 and x2 = 0

∴ x2 = 0 and y2 = 3

∵ Δx = 0 - (-4) = 0 + 4 = 4

∵ Δy = 3 - 0 = 3

→ By using the rule of the slope above

∴ m = \(\frac{3}{4}\)

∵ The average rate of change of the function = the slope of the line

∴ The average rate of change of the function for the interval [-4, 0] is  \(\frac{3}{4}\)

Slope

Answer:

The answer is x= 31

Step-by-step explanation:

(5x-16)+ (x+10)= 180 (Linear Pair)

Now, open the brackets

5x-16+x+10= 180

Arrange the like terms together

5x+x-16+10= 180

=> 6x-6= 180

=> 6x= 180+6

=> 6x= 186

=> x= 186/6 = 31

∴x= 31

Hope it helps!!

Answer:

(-4,5)

Step-by-step explanation:

just count from zero horizontally for the first number and vertically for the second number.

Answer:

sorry, I'm here for points

Answer:

B

Step-by-step explanation: