Does anyone know the answer?

The average rate of f(x), in [4,6], is equal to 20.

To find the average rate of change of a function over an interval, we use the formula:

Average rate of change = (f(b) - f(a))/(b - a)

Where f(x) is the function, a and b are the endpoints of the interval, and f(a) and f(b) are the values of the function at those endpoints.

In this case, our function is f(x) = 2x² - 9, and our interval is [4, 6]. So, we plug in the values into the formula:

Average rate of change = (f(6) - f(4))/(6 - 4)

First, we find f(6) and f(4):

f(6) = 2(6²) - 9 = 2(36) - 9 = 72 - 9 = 63

f(4) = 2(4²) - 9 = 2(16) - 9 = 32 - 9 = 23

Now we plug these values back into the formula:

Average rate of change = (63 - 23)/(6 - 4) = 40/2 = 20

In conclusion, the average rate is worth 20.

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Answer:

El coste de producir un juego de vídeo es de 125 dólares.

Step-by-step explanation:

(This exercise is written in Spanish and is incomplete. Complete statement will be presented below)

El costo de producir 10 juegos de video al día es de 350 dólares , mientras que producir 30 juegos del mismo tipo al día cuestan 850 dólares . Si suponemos un modelo lineal como el descrito anteriormente , determine:

¿Cuál es el costo de producir un juego de vídeo?

(Explanation will be held in Spanish)

El modelo lineal es un polinomio de primer orden de la forma:

\(y = a\cdot x + b\)

Donde:

\(x\) - Variable independiente (eje x - Cantidad de juegos de vídeo producidos - Adimensional)

\(y\) - Variable dependiente (eje y - Coste de producción de juegos de vídeo - Dólares)

\(a\) - Pendiente de la función.

\(b\) - Intercepto en el eje y.

Dados los dos costes para dos cuotas distintas de producción, se construye el siguiente sistema de ecuaciones lineales:

\(10\cdot a + b = 350\)

\(30 \cdot a + b = 850\)

Se resuelve el sistema con algo de manipulación algebraica:

\((30\cdot a + b) - (10\cdot a + b) = 850 - 350\)

\(20 \cdot a = 500\)

\(a = 25\)

Luego:

\(b = 850 - 30\cdot a\)

\(b = 100\)

La ecuación lineal es:

\(y = 25\cdot x +100\)

Finalmente, el coste de producir un juego de vídeo es:

\(y = 25 \cdot (1) + 100\)

\(y = 125\)

El coste de producir un juego de vídeo es de 125 dólares.

(a) To express the daily revenue from ticket sales, R, as a function of the number of $1.00 price increases, x, we can use the given information. We know that for each $1.00 increase in price, the park loses an average of 3,500 customers per day.

The number of customers can be calculated as follows:

Number of customers = 80,000 - (3,500 * x)

The revenue from ticket sales is determined by multiplying the number of customers by the ticket price. Since the initial ticket price is $12.00, we can express the daily revenue, R, as a function of x:

R = (80,000 - (3,500 * x)) * 12.00

(b) To find the ticket price that maximizes the revenue from ticket sales, we need to find the value of x that corresponds to the maximum point on the revenue function.

The revenue function can be expressed as R = -3,500x^2 + 80,000x - 960,000, which is a quadratic function. The coefficient of the x^2 term is -3,500, and the coefficient of the x term is 80,000.

To find the x-value of the maximum point, we can use the formula x = -b / (2a), where a and b are the coefficients of the quadratic function. In this case, a = -3,500 and b = 80,000.

x = -80,000 / (2 * -3,500)

x ≈ 11.43

Since x represents the number of $1.00 price increases and must be a whole number, we round the value of x to the nearest whole number. Therefore, the ticket price that maximizes the revenue from ticket sales is obtained with 11 price increases.

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Answer:

16

Step-by-step explanation:

one side is four the other is four 4x4 is 16

Answer:

8

Step-by-step explanation:

Since its 1/2 cm per cube, each side is 4 cubes, 4x1/2 = 2. 2x2x2 = 8

Answer:

-3

Step-by-step explanation:

dividing a positive and a negative equals a negative so put the 4.5 in parentheses with the 1.5 and put the negative outside the parentheses. then do what's in the parentheses and add your negative which makes you get a -3

Answer:

4a) 110 square centimetres

4b) 127 square centimetres

6) 292 square centimetres

8) 800 tiles

Step-by-step explanation:

4. We need to find the area of the large rectangle and then deduct the area of the unshaded part:

a) The large rectangle has dimensions 12 cm by 15 cm. Its area is:

A = 12 * 15 = 180 square centimetres

The unshaded part has a length of 15 - (3 + 2) cm i.e. 10 cm and a width of 7 cm. Its area is:

a = 10 * 7 = 70 square centimetres

Therefore, the area of the shaded part is:

A - a = 180  - 70 = 110 square centimetres

b) The large rectangle has dimensions 13 cm by 11 cm. Its area is:

A = 13 * 11 = 143 square centimetres

The unshaded part has dimensions 8 cm by 2 cm. Its area is:

a = 8 * 2 = 16 square centimetres

Therefore, the area of the shaded part is:

A - a = 143 - 16 = 127 square centimetres

6. The background area of the space not covered by the photograph is the area of the frame minus the area of the photograph.

The frame has dimensions 24 cm by 18 cm. Therefore, its area is:

A = 24 * 18 = 432 square centimetres

The photograph has dimensions 14 cm by 10 cm. Therefore, its area is:

a = 14 * 10 = 140 square centimetres

Therefore, the background area of the space not covered by the photograph is:

A - a = 432 - 140 = 292 square centimetres

8) The floor has dimensions 8 m by 4 m. The area of the floor is:

A = 8 * 4 = 32 square centimetres

Each square tile has dimensions 20 cm by 20 cm. In metres, that is 0.2 m by 0.2 m. The area of each tile is:

a = 0.2 * 0.2 = 0.04 square metres

The number of tiles that are needed is the area of the floor divided by the area of each tile:

A / a = 32 / 0.04 = 800 tiles

The Slope-Intercept form of an equation of the line is:

\(y=mx+b\)

Where "m" is the slope and "b" is the y-intercept.

Given this line:

\(x+4y=12\)

You need to solve for "y" in order to write it in Slope-Intercept form:

\(\begin{gathered} 4y=-x+12 \\ y=\frac{-1}{4}x+\frac{12}{4} \\ \\ y=-\frac{1}{4}x+3 \end{gathered}\)

So you can identify that the slope of that line is:

\(m_1=-\frac{1}{4}\)

By definition, the slopes of perpendicular lines are opposite reciprocals. Then, you can determine that the slope of the other line is:

\(m_2=4\)

Knowing that it passes through this point:

\(\mleft(7,-3\mright)\)

You can substitute the coordinates into the equation and solve for "b":

\(\begin{gathered} -3=4(7)+b \\ -3-28=b \\ b=-31 \end{gathered}\)

Knowing the value of "b" and knowing the slope, you can determine that the equatio of the line in Slope-Intercept for

Answer: $3

Step-by-step explanation: Sierra has $5 and plans to spend $2 on a notepad. If she uses the expression 5 - 2 to find how much money she will have left after buying the notepad, the result will be 3. This means that Sierra will have $3 left after buying the notepad.

$18.04

Easy math. Just multiply 11 by $1.64

A18.04 all you have to do is multiply the 2 numbers

Answer:

15,000

Step-by-step explanation:

Based on the given quadrilaterals and their angles, the following are true:

Square and x = 45°Trapezium and y = 120°Parallelogram and a = 15 cm. What are the quadrilaterals and variables given?

The first shape given is a square which means that all the angles have the equal number of 90°. The value of x is therefore:

x = 90 - 45

= 45°

The second quadrilateral is a Trapezium and adjacent angles will add up to 180°. The value of y is:

= 180 - 60

= 120°

The third shape is a parallelogram and the lengths of sides that are opposite each other are the same. This means that a will have the same value as the opposite side of 15 cm.

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It’s A:I hope that helps have a blessed day :))

Step-by-step explanation:

[(3x − 6) (4x² − 1)] – [(2x − 4) (4x² + 4x + 1)]

>[3(x-2) (2x+1)(2x-1)]-[2(x-2)(4x²+2x+2x+1)

>[3(x-2)(2x+1)(2x-1)]-[2(x-2){2x(2x+1)+1(2x+1)}]

> 3(x-2)(2x+1)(2x-1)-2(x-2)(2x+1)²

> (x-2)(2x+1) [3(2x-1)-2(2x+1)]

> (2x²-3x-2)(6x-3-4x-2)

> (2x²-3x-2)(2x-5).

hope this helps you.

Answer:

6

Step-by-step explanation:

3x6=18

Answer:

6

Step-by-step explanation:

18 divided by 3

hope this helps

-mercury

(a) To find the 3x3 matrix that produces the composite 2D transformation of translating by (2,2), rotating 90 degrees about the origin, and then reflecting in the y-axis using homogeneous coordinates, we can use the following steps:

1. Write the translation, rotation, and reflection matrices in homogeneous coordinates:

Translation matrix:
```
[1 0 2]
[0 1 2]
[0 0 1]
```

Rotation matrix:
```
[0 -1 0]
[1 0 0]
[0 0 1]
```

Reflection matrix:
```
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
```

2. Multiply the translation matrix by the rotation matrix, then multiply the result by the reflection matrix, both in that order:

```
[-1 0 0] [0 -1 0] [1 0 -2]
[ 0 1 0] * [1 0 0] * [0 1 -2]
[ 0 0 1] [0 0 1] [0 0 1]
```

3. The resulting matrix is the 3x3 matrix that produces the composite transformation:

```
[1 0 -2]
[0 I apologize for the incomplete answer in my previous message. Here are the complete answers for all four parts:

(a) To find the 3x3 matrix that produces the composite 2D transformation of translating by (2,2), rotating 90 degrees about the origin, and then reflecting in the y-axis using homogeneous coordinates, we can use the following steps:

1. Write the translation, rotation, and reflection matrices in homogeneous coordinates:

Translation matrix:
```
[1 0 2]
[0 1 2]
[0 0 1]
```

Rotation matrix:
```
[0 -1 0]
[1 0 0]
[0 0 1]
```

Reflection matrix:
```
[-1 0 0]
[ 0 1 0]
[ 0 0 1]
```

2. Multiply the translation matrix by the rotation matrix, then multiply the result by the reflection matrix, both in that order:

```
[-1 0 0] [0 -1 0] [1 0 -2]
[ 0 1 0] * [1 0 0] * [0 1 -2]
[ 0 0 1] [0 0 1] [0 0 1]
```

3. The resulting matrix is the 3x3 matrix that produces the composite transformation:

```
[1 0 -2]
[0 -1 2]
[0 0 1]
```

Therefore, the 3x3 matrix that produces the composite transformation of translating by (2,2), rotating 90 degrees about the origin, and then reflecting in the y-axis using homogeneous coordinates is:

```
[1 0 -2]
[0 -1 2]
[0 0 1]
```

(b) To find the 3x3 matrix that produces the composite 2D transformation of translating by (-1,2), scaling 2 in the x-coordinate and 3 in the y-coordinate using homogeneous coordinates, we can use the following steps:

1. Write the translation and scaling matrices in homogeneous coordinates:

Translation matrix:
```
[1 0 -1]
[0 1 2]
[0 0 1]
```

Scaling matrix:
```
[2 0 0]
[0 3 0]
[0 0 1]
```

2. Multiply the translation matrix by the scaling matrix in that order:

```
[2 0 0] [1 0 -1] [2 0 -2]
[0 3 0] * [0 1 2] = [0 3 6]
[0 0 1] [0 1 -] [-1 2 1]
[0 0 1] [0 0 1]

3. The resulting matrix is the 3x3 matrix that produces the composite transformation:

```
[0.5 -0.5 -1]
[-0.5 0.5 2]
[ 0 0 1]
```

Therefore, the 3x3 matrix that produces the composite transformation of reflecting in the original, translating by (-1,1), and then scaling 0.5 in the x-coordinate using homogeneous coordinates is:

```
[0.5 -0.5 -1]
[-0.5 0.5 2]
[ 0 0 1]
```

(d) To find the 3x3 matrix that produces the composite 2D transformation of translating by (2,3), reflecting in the line y=x, and then rotating 30 degrees about the origin using homogeneous coordinates, we can use the following steps:

1. Write the translation, reflection, and rotation matrices in homogeneous coordinates:

Translation matrix:
```
[1 0 2]
[0 1 3]
[0 0 1]
```

Reflection matrix:
```
[0 1 0]
[1 0 0]
[0 0 1]
```

Rotation matrix:
```
[cos(30) -sin(d) To find the 3x3 matrix that produces the composite 2D transformation of translating by (2,3), reflecting in the line y=x, and then rotating 30 degrees about the origin using homogeneous coordinates, we can use the following steps:

1. Write the translation, reflection, and rotation matrices in homogeneous coordinates:

Translation matrix:
```
[1 0 2]
[0 1 3]
[0 0 1]
```

Reflection matrix:
```
[0 1 0]
[1 0 0]
[0 0 1]
```

Rotation matrix:
```
[cos(30) -sin(30) 0]
[sin(30) cos(30) 0]
[0 0 1]
```

2. Multiply the translation matrix by the reflection matrix, then multiply the result by the rotation matrix, both in that order:

```
[0 1 0] [cos(30) -sin(30) 0] [ 0.5 0.866 -3.464]
[1 0 0] * [sin(30) cos(30) 0] * [-0.866 0.5 4.232]
[0 0 1] [ 0 0 1] [ 0 0 1 ]
```

3. The resulting matrix is the 3x3 matrix that produces the composite transformation:

```
[ 0.5 0.866 -3.464]
[-0.866 0.5 4.232]
[ 0 0 1 ]
```

Therefore, the 3x3 matrix that produces the composite transformation of translating by (2,3), reflecting in the line y=x, and then rotating 30 degrees about the origin using homogeneous coordinates is:

```
[ 0.5 0.866 -3.464]
[-0.866 0.5 4.232]
[ 0 0 1 ]
```

The matrices for the transformations (a) Translate, Rotate, and Reflect, (b) Translate and Scale, (c) Reflect, Translate, and Scale, and (d) Translate, Reflect, and Rotate are calculated.

(a) To find the matrix for the composite transformation of Translate, Rotate, and Reflect, we multiply the matrices for individual transformations. The translation matrix is:

T = [[1, 0, 2],

[0, 1, 2],

[0, 0, 1]]

The rotation matrix for 90° counterclockwise is:

R = [[0, -1, 0],

[1, 0, 0],

[0, 0, 1]]

The reflection matrix in the y-axis is:

F = [[-1, 0, 0],

[0, 1, 0],

[0, 0, 1]]

The composite transformation matrix is obtained by multiplying these matrices: C = T * R * F.

(b) For the composite transformation of Translate and Scale, we have the translation matrix:

T = [[1, 0, -1],

[0, 1, 2],

[0, 0, 1]]

The scaling matrix is:

S = [[2, 0, 0],

[0, 3, 0],

[0, 0, 1]]

The composite transformation matrix is C = T * S.

(c) For the composite transformation of Reflect, Translate, and Scale, we have the reflection matrix:

F = [[-1, 0, 0],

[0, -1, 0],

[0, 0, 1]]

The translation matrix is:

T = [[1, 0, -1],

[0, 1, 1],

[0, 0, 1]]

The scaling matrix is:

S = [[0.5, 0, 0],

[0, 1, 0],

[0, 0, 1]]

The composite transformation matrix is C = F * T * S.

(d) For the composite transformation of Translate, Reflect, and Rotate, we have the translation matrix:

T = [[1, 0, 2],

[0, 1, 3],

[0, 0, 1]]

The reflection matrix in the y = x line is:

F = [[0, 1, 0],

[1, 0, 0],

[0, 0, 1]]

The rotation matrix for 30° counterclockwise is:

R = [[√3/2, -1/2, 0],

[1/2, √3/2, 0],

[0, 0, 1]]

The composite transformation matrix is C = T * F * R.

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According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. The correct option is A. 34% and 26%.

According to recent data, women make up 34% and 26% of workers in science and technology (STEM) fields in Canada and the United States, respectively. This indicates that women are still underrepresented in STEM fields, despite the fact that there has been an effort to attract more women to STEM fields.

In both Canada and the United States, women have made significant progress in breaking down gender barriers in STEM fields. However, there is still work to be done to close the gender gap and increase representation of women in STEM fields.

Women's representation in STEM fields has increased in both Canada and the United States in recent years, but the percentage of women in STEM fields is still significantly lower than the percentage of men. More efforts are needed to close the gender gap in STEM fields and encourage more women to pursue STEM careers.

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The lower and upper limits of the confidence interval can be determined using the sample mean and sample standard deviation.

Given the sample readings of total calcium levels in mg/dl, we can calculate the sample mean (x) and sample standard deviation (s). Using these values, we can determine the lower and upper limits of the 99.9% confidence interval.

Calculating the sample mean:

x = (9.9 + 8.6 + 10.9 + 8.5 + 9.4 + 9.8 + 10.0 + 9.9 + 11.2 + 12.1) / 10 = 10.03 mg/dl

Calculating the sample standard deviation:

s = sqrt(((9.9 - 10.03)^2 + (8.6 - 10.03)^2 + ... + (12.1 - 10.03)^2) / (10 - 1)) = 1.16 mg/dl

To determine the 99.9%   confidence interval, we need to find the critical value corresponding to this level of confidence. Since the sample size is small (less than 30) and the population standard deviation is unknown, we can use the t-distribution. With a sample size of 10 and a desired confidence level of 99.9%, the critical value is approximately 3.250.

Calculating the margin of error:

Margin of error = critical value * (s / sqrt(n))

= 3.250 * (1.16 / sqrt(10))

≈ 1.19

The lower limit of the confidence interval is given by x - margin of error:

Lower limit = 10.03 - 1.19 ≈ 8.84 mg/dl

The upper limit of the confidence interval is given by x + margin of error:

Upper limit = 10.03 + 1.19 ≈ 11.22 mg/dl

Therefore, the 99.9% confidence interval for the population mean of total calcium in this patient's blood is approximately 8.84 mg/dl to 11.22 mg/dl.

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50%

since 98/2 = 49

Thats it

To determine when the motion is in the positive direction, we need to find the values of t for which the velocity function v(t) is positive.

Given: v(t) = \(3t^2\) - 36t + 105

a) To find when the motion is in the positive direction, we need to find the values of t that make v(t) > 0.

Solving the inequality \(3t^2\) - 36t + 105 > 0:

Factorizing the quadratic equation gives us: (t - 5)(3t - 21) > 0

Setting each factor greater than zero, we have:

t - 5 > 0   =>   t > 5

3t - 21 > 0   =>   t > 7

So, the motion is in the positive direction for t > 7.

b) To find the displacement over the interval [0, 8], we need to calculate the change in position between the initial and final time.

The displacement can be found by integrating the velocity function v(t) over the interval [0, 8]:

∫(0 to 8) v(t) dt = ∫(0 to 8) (3t^2 - 36t + 105) dt

Evaluating the integral gives us:

∫(0 to 8) (3t^2 - 36t + 105) dt = [t^3 - 18t^2 + 105t] from 0 to 8

Substituting the limits of integration:

[t^3 - 18t^2 + 105t] evaluated from 0 to 8 = (8^3 - 18(8^2) + 105(8)) - (0^3 - 18(0^2) + 105(0))

Calculating the result gives us the displacement over the interval [0, 8].

c) To find the distance traveled over the interval [0, 8], we need to calculate the total length of the path traveled, regardless of direction. Distance is always positive.

The distance can be found by integrating the absolute value of the velocity function v(t) over the interval [0, 8]:

∫(0 to 8) |v(t)| dt = ∫(0 to 8) |\(3t^2\)- 36t + 105| dt

To calculate the integral, we need to split the interval [0, 8] into regions where the function is positive and negative, and then integrate the corresponding positive and negative parts separately.

Using the information from part a, we know that the function is positive for t > 7. So, we can split the integral into two parts: [0, 7] and [7, 8].

∫(0 to 7) |3\(t^2\) - 36t + 105| dt + ∫(7 to 8) |3t^2 - 36t + 105| dt

Each integral can be evaluated separately by considering the positive and negative parts of the function within the given intervals.

This will give us the distance traveled over the interval [0, 8].

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Answer: Picture of the paitents?

Step-by-step explanation:

27 total apples in the bag

15 apples were in the bag. If 3 apples are 20%, you could multiply 3 by 5 and 20% by 5 to get 100%.

Answer:

Step-by-step explanation:

B

Answer:

13

Step-by-step explanation:

The range of a data set is the difference between the greatest and least values in the set. In this case, the greatest value is 15 and the least value is 2 so the range is 15 - 2 = 13.

Answer:

Step-by-step explanation:

ANSWER:

1 Whole 1/2

Explanation:

3 x 2 and 4 x 1 = 6/4

if we simplify 6/4 by dividing 2 it will be 3/2

if we simplify it it will be a mixed number 1 whole and 1/2

The first step is to find the probability value corresponding to z = - 0.82 and z = 2.10 from the standard normal distribution table. Looking at the table,

Probability value corresponding to z = - 0.82 = 0.20897

Probability value corresponding to z = 2.10 = 0.98214

The area under the curve is the difference between both probability values. Hence,

area under curve = 0.98214 - 0.20897 = 0.77317

The answer is not listed, but the correct answer is E, the limit exists and is equal to 3.

To evaluate the limit of 3cos(π/2x - π) as x approaches π/2, we can use the fact that the cosine function is continuous. This means that the limit of cos(π/2x - π) as x approaches π/2 is equal to cos(π/2(π/2) - π) = cos(0) = 1.

Then, we can multiply both sides of the equation by 3:

lim x->π/2 3cos(π/2x - π) = 3cos(π/2x - π) * lim x->π/2 1

Since the limit of 1 as x approaches π/2 is equal to 1, we can substitute:

lim x->π/2 3cos(π/2x - π) * lim x->π/2 1 = 3 * 1 = 3

Therefore, the limit exists and is equal to 3. The answer is not listed, but the correct answer is E, the limit exists and is equal to 3.

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Answer:

d = 55.5  

x = 1

c = 11

m = \(\frac{1}{122}\)

k = \(\frac{a}{(c + 5)}\)

Step-by-step explanation:

Sorry, the formatting is slightly hard to understand, but I think this is what you meant.

Q1.

\(\frac{1}{6}\)d - 8 = \(\frac{5}{8}\) x 2

Step 1. Simplify.

\(\frac{5}{8}\) x 2 = \(\frac{5}{8}\) x \(\frac{2}{1}\) = \(\frac{10}{8}\)

Step 2. Cancel out the negative 8.

\(\frac{1}{6}\)d - 8 = \(\frac{10}{8}\)

+ 8 to both sides (do the opposite: \(\frac{1}{6}\)d is subtracting 8 right now, but to cancel that out, we will do the opposite of subtraction, i.e. addition)

\(\frac{1}{6}\)d = \(\frac{10}{8}\) + 8

Step 3. Simplify.

\(\frac{10}{8}\) + 8 = \(\frac{10}{8}\) + \(\frac{8}{1}\) = \(\frac{10}{8}\) + \(\frac{64}{8}\) = \(\frac{74}{8}\) = \(\frac{37}{4}\)

Step 4. Cancel out the \(\frac{1}{6}\).

\(\frac{1}{6}\)d = \(\frac{37}{4}\)

÷ \(\frac{1}{6}\) from both sides (do the opposite: d is multiplied by \(\frac{1}{6}\) right now, but to cancel that out, we will do the opposite of multiplication, i.e. division)

÷ \(\frac{1}{6}\) = x 6

So....

x 6 to both sides

d = \(\frac{37}{4}\) x  6 = \(\frac{37}{4}\) x \(\frac{6}{1}\) = \(\frac{222}{4}\) = \(\frac{111}{2}\) = 55.5

Step 5. Write down your answer.

d = 55.5

Q2.

3x - 4 + 5x = 10 - 2x × 3

Step 1. Simplify

3x - 4 + 5x = 3x + 5x - 4 = 8x - 4

10 - 2x × 3 = 10 - (2x × 3) = 10 - 6x

Step 2. Cancel out the negative 6x

8x - 4 = 10 - 6x

+ 6x to both sides (do the opposite - you're probably tired of reading this now - right now it's 10 subtract 6x, but the opposite of subtraction is addition)

14x - 4 = 10

Step 3. Cancel out the negative 4

14x - 4 = 10

+ 4 to both sides (right now it's 14x subtract 4, but the opposite of subtraction is addition)

14x = 14

Step 4. Divide by 14

14x = 14

÷ 14 from both sides (out of the [14 × x] we only want the [x], so we cancel out the [× 14])

x = 1

Step 5. Write down your answer.

x = 1

Q3.

7(c - 3) = 14 × 4

Step 1. Expand the brackets

7(c - 3) = (7 x c) - (7 x 3) = 7c - 21

Step 2. Simplify

14 x 4 = 56

Step 3. Cancel out the negative 21

7c - 21 = 56

+ 21

7c = 56 + 21

7c = 77

Step 4. Cancel out the ×7

7c = 77

÷ 7

c = 77 ÷ 7

c = 11

Step 5. Write down your answer.

c = 11

Q4.

11(\(\frac{m}{22}\) + \(\frac{3}{44}\)) = 87m + m × 5

Step 1. Expand the brackets

11(\(\frac{m}{22}\) + \(\frac{3}{44}\)) = (11 x \(\frac{m}{22}\)) + (11 x \(\frac{3}{44}\)) = (\(\frac{11}{1}\) x \(\frac{m}{22}\)) + (\(\frac{11}{1}\) x \(\frac{3}{44}\)) = \(\frac{11m}{22}\) + \(\frac{33}{44}\) = \(\frac{m}{2}\) + \(\frac{3}{4}\)

Step 2. Simplify.

87m + m x 5 = 87m + 5m = 92m

Step 3. Cancel out the add \(\frac{3}{4}\)

\(\frac{m}{2}\) + \(\frac{3}{4}\) = 92m

- \(\frac{3}{4}\)

\(\frac{m}{2}\) = 92m - \(\frac{3}{4}\)

\(\frac{m}{2}\) = \(\frac{92m}{1}\) - \(\frac{3}{4}\)

\(\frac{m}{2}\) = \(\frac{368m}{4}\) - \(\frac{3}{4}\)

\(\frac{m}{2}\) = \(\frac{368m - 3}{4}\)

Step 4. Cancel out the ÷ 4

\(\frac{m}{2}\) = \(\frac{368m - 3}{4}\)

x 4

2m = 368m - 3

Step 5. Cancel out the 368m

2m = 368m - 3

- 368m

-366m = - 3

Step 6. Cancel out the × -366

-366m = -3

÷ -366

m = \(\frac{-3}{-366}\)

m = \(\frac{1}{122}\)

Step 7. Write down your answer.

m = \(\frac{1}{122}\)

Q5.

ck + 5k = a

Step 1. Factorise

ck + 5k = (c × k) + (5 × k) = (c + 5) x k = k(c + 5)

Step 2. Cancel out the × (c + 5)

k(c + 5) = a

÷ (c + 5)

k = a ÷ (c + 5)

k = \(\frac{a}{(c + 5)}\)

Answer:

We can start by using the tangent formula:

tan(P) = sin(P) / cos(P)

We are not given the values of sin(P) and cos(P) directly, but we can use the Pythagorean identity to relate them:

sin^2(P) + cos^2(P) = 1

We can rearrange this expression to solve for sin(P) in terms of cos(P):

sin^2(P) = 1 - cos^2(P)

sin(P) = ±√(1 - cos^2(P))

Now we can substitute this expression into the tangent formula:

tan(P) = ±√(1 - cos^2(P)) / cos(P)

Substituting the given values and simplifying:

tan(P) = ±√(1 - (2/√85)^2) / (1/√89)

tan(P) = ±√(1 - 4/85) * √89

tan(P) = ±√(81/85) * √89 / 1

We want to express tan P in simplest radical form, so we can simplify the square root by factoring out the greatest perfect square factor of the numerator:

tan(P) = ±(√9/√85) * (√89/1)

tan(P) = ±(3/√85) * (√89/1)

Therefore, the exact value of tan P in simplest radical form is ±(3/√85) * (√89/1).

De Morgan's laws are two rules in formal logic that involve negating statements. The first law states that the negation of a conjunction (an "and" statement) is equivalent to the disjunction (an "or" statement) of the negations of the individual components.

The second law states that the negation of a disjunction is equivalent to the conjunction of the negations of the individual components.

In this case, the given statement is "She makes the bed, or I do not make the bed." To apply De Morgan's laws, we need to negate this statement. According to the first law, the negation of the disjunction "She makes the bed, or I do not make the bed" is the conjunction of the negations of the individual components: "She does not make the bed, and I make the bed."

Therefore, the negation of the original statement is "She does not make the bed, and I make the bed." This means that both she does not make the bed and I make the bed must be true in order for the negation to be true.

To learn more about “De Morgan's laws” refer to the https://brainly.com/question/13258775

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