Determine the general solution for sin(x-30°)=cos2x

The surface area of the cube given in the above diagram would be = 1922.46 in².

To calculate the surface area of the cube, the formula that should be used would be given below as follows:

Surface area of cube = 6(a)²

a = side length= 17.9

SA=6(17.9)²

= 6×320.41

= 1,922.46 in²

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Answer:

The answer is 6.72 x 10⁷

Step-by-step explanation:

The answer is 6.72 x 10⁷ because I solved it and I got this answer.

A rectangular prism is thought of as being created by stacking congruent polygons.

A solid (3-dimensional) object which has six faces that are rectangles. It has the same cross-section along a length, which makes it a prism.

Two geometric figures are said to be congruent, or to be in the relation of congruence, if it is possible to superpose one of them on the other so that they coincide throughout.

Stacking congruent figures means arranging the congruent figures on the top of the other until it become a large pile.

According to the given question.

We have to stack the congruent polygons.

As we know that stacking up means ​to keep increasing in quantity until we get a large pile.

Since, when we piled up of stack the congruent polygons we will get a prism.

For example when we stack congruent squares we will get cube or we can say a rectangular prism.

If we stack congruent octagons we will get an octagon prism.

Hence, a rectangular prism is thought of as being created by stacking congruent polygons.

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Answer:  x = -⁷⁰⁄₇₁

Steps: −6(−10x − 1) − 3 = 10 − 11 (x + 7)

Expand: 60x + 3 = -11x - 67

Subtract 3 from both sides: 60x + 3 - 3= -11x - 67 - 3

Simplify: 60x = -11x - 70

Add 11x to both sides: 60x + 11x = -11x - 70 + 11x

Simplify: 71x = -70

Divide both sides by 71:   71x ÷ 71 = -70 ÷ 71

Simplify:  x = -⁷⁰⁄₇₁

Plz mark brainliest:)

Step-by-step explanation:

-6( -10x - 1)-3 = 10- 11(x +7)

60x +6 -3= 10- 11x - 77

60x+11x = -67-3

71x = -70

x= -70/71

Examining the curve the information obtained are

vertex (3, 13)

axis of symmetry: x = 13

y intercept: (0, 5)

maximum

Domain (-∞, ∞)

Range (-∞, 12]

A parabolic curve, also known as a parabola, is a symmetrical U-shaped curve. It is defined by a mathematical equation of the form

y = ax^2 + bx + c,

where a, b, and c are constants, and x and y are the coordinates of points on the curve.

The graph of a parabolic curve is smooth and continuous, with no sharp corners or discontinuities.

The vertex is at the peak of the curve and the coordinates is (3, 13) where the axis of symmetry is where the curve is divided into two equal parts. This is represented by the equation x = 3

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The traveler must walk 17 blocks to reach the State Building.

The traveler needs to walk 8 blocks from the intersection of Orovada Street and Washington Avenue to the State Building.

She also knows that the intersection of Orovada Street and Washington Avenue is 5 blocks from the intersection of Wyoming Street and Washington Avenue, so she needs to walk 5 blocks from the intersection of Wyoming Street and Washington Avenue to the intersection of Orovada Street and Washington Avenue.

Also, the traveler had to walk 4 blocks to get from the intersection of Wyoming Street and Green Avenue to the intersection of Orovada Street and Green Avenue.

Therefore, the traveler must walk 8 + 5 + 4 = 17 blocks to reach the State Building.

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Answer: 4/33

Step-by-step explanation:

just divide

Answer:

The answer is 4/33.

Step-by-step explanation:

to get this you just have to divide.

you're welcome.

Answer:

\(x \leq -4\)

There will be a filled-in hole at -4.

Step-by-step explanation:

We can solve an inequality the same way we do for equations. The only thing to keep in mind, is that multiplying by a negative number will result in flipping the inequality sign (< to > and vice versa)

\(-7x + 13 \geq 41 \text{ //}-13\\-7x \geq 28 \text{ //}:-7 \text{ (Notice we multiply by a negative number.)}\\x \leq -4\)

The difference between a filled-in and an empty hole in terms of inequality graphs, is whether or not the number limiting the inequality is included in it.

For example, in x > 3, 3 is limiting the inequality, however, it is not included in it, therefore, x would always be greater than 3.

In another example, \(x \leq -4\), -4 is limiting inequality and is included in it. Therefore, x would always be less than or equal to -4.

A filled-in hole means the number is included in the inequality, while an empty one means it isn't.

In our cases, -4 is included in the inequality (notice the line under the inequality sign that resembles "less than or equal to"), therefore there will be a filled-in hole at -4.

Lee's TV costs $4.05 to operate for a month of 30 days.

To calculate the cost of operating Lee's TV for a month, we need to find out the total number of kilowatt-hours (kWh) of electricity consumed by the TV during that time.

First, let's find out how many watts Lee's TV consumes in a day:

250 watts/hour x 3 hours/day = 750 watts/day

To convert this to kilowatts, we divide by 1000:

750 watts/day ÷ 1000 = 0.75 kilowatts/day

Now, we can calculate the total number of kilowatt-hours consumed by the TV in a month:

0.75 kilowatts/day x 30 days = 22.5 kilowatt-hours

Finally, we can calculate the cost of operating the TV for a month:

22.5 kilowatt-hours x 18 cents/kilowatt-hour = $4.05

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Answer:

Step-by-step explanation:

Find 15 percent of 81.95 and add it to that.

The answer is 94.24 rounded.

The possible value of the side length of the plot of land that Abby owns, which is between 2200 and 2400 square meters is A. 48 meters.

The length is the quantitative measurement of a distance from one point to another position.

Length can also refer to the size of an object that has width or/and height.

The square of 2,200m² = 46.9 meters (√2,200)

The square of 2,400m² = 48.99 meters (√2,400)

The square of the median value of 2,200m² and 2,400m², which is 2,300m² is 48 meters approximateluy.

Thus, the possible value of the side length of the plot of land is A. 48 meters.

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A. 48 meters

B. 46 meters

C. 44 meters

D. 50 meters

The best interpretation of the slope of the linear regression equation is given as follows:

For each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.

The slope represents the rate of change of the output variable relative to the input variable of a linear relation.

Hence, it can be said that the slope states by how much the output variable y changes when the input variable x is increased by 1.

The variables in this problem are given as follows:

The negative slope of -0.7 means that for each increase of one degree of latitude, the average low temperature decreases by 0.70 degrees Fahrenheit.

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Answer:

B

Step-by-step explanation:

A counter-example to the given conclusion is the difference between the numbers 15 and 25, where both are positive, but the difference gives a negative result.

Here we are shown some differences between positive numbers:

7 - 3 = 4

8 - 5 = 3

9 - 8 = 1

And the conclusion is:

"The difference of two positive numbers is always positive".

To find a counter-example we just need to find two positive numbers such that the difference between these two positive numbers gives a negative number as a result.

An example of that can be the numbers 15 and 25, if we take the difference we will get:

15 - 25 = -10

Here we can see that the difference between two positive numbers gives a negative number as an outcome, so this is our counter-example.

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Answer:

Step-by-step explanation:

The full revolution is a full circle = 360°.

1/6 of a revolution:

(a) To meet the desired 20g protein and 80g carbohydrate intake, prepare 4 servings of Pork & Beans and combine with 15 slices of "lite" rye bread.

(b) Bread: A/4 slices, Beans: B/21 - (A/4) * (12/21) servings.

(a) To prepare a meal of "beans-on-toast" that supplies 20 grams of protein and 80 grams of carbohydrates, you can use the following combination:

- Servings of Campbell's Pork & Beans: 4 servings.

- Slices of "lite" rye bread: 15 slices.

By using 4 servings of Campbell's Pork & Beans, you will obtain a total of 20 grams of protein (5 grams per serving) and 84 grams of carbohydrates (21 grams per serving).

Combining this with 15 slices of "lite" rye bread will contribute an additional 60 grams of carbohydrates (12 grams per slice) and 4 grams of protein (4 grams per slice). Thus, your meal will meet the desired nutritional requirements of 20 grams of protein and 80 grams of carbohydrates.

(b) The formula to determine the number of slices of bread and servings of Pork & Beans needed to meet specific protein and carbohydrate requirements is as follows:

- Number of slices of bread (Bread): A divided by 4.

- Number of servings of Pork & Beans (Beans): (B divided by 21) minus ((A divided by 4) multiplied by (12 divided by 21)).

Using this formula, you can calculate the appropriate quantities of bread and beans based on the desired protein (A) and carbohydrate (B) values.

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We have prepared the table and drawn the graph.

What is a graph of a function?

A graph of a function is a visual representation of the relationship between the inputs (x-coordinates) and the outputs (y-coordinates) of a function. The inputs are typically represented on the x-axis and the outputs are represented on the y-axis.

Table:

x (days) y (number of cells)

0        1000

1        2000

2       4000

Graph:

The graph would be a line graph with x-axis showing the day passed and y-axis showing the number of bacteria cells,

The point (0,1000) would be plotted on the graph, representing the initial number of bacteria cells on the first day.

The point (1,2000) would be plotted on the graph, representing the second day and the number of bacteria cells.

The point (2,4000) would be plotted on the graph, representing the third day and the number of bacteria cells.

The graph would be a upward sloping line, representing the growth of bacteria cells.

Hence we have prepared the table and drawn the graph.

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The jumper is in free fall for 7.07 s if the parachute is opens at 1000 ft

The jumper is in free fall for 7.29 s if the parachute is opens at 950 ft

The reasonable domain for the function h is

0 ≤ t ≤ 10

The reasonable range for the function h is

0 ≤ h ≤ 1800

The duration of free fall is calculated using the given function

h = -16t² + 1800

the parachute is opens at 1000 ft

h = -16t² + 1800

1000 = -16t² + 1800

16t² = 1800 - 1000

16t² = 800

t² = 800 / 16

t² = 50

t = √50

t = 7.07 s

the time at this situation is 7.07s

the parachute is opens at 950 ft

h = -16t² + 1800

950 = -16t² + 1800

16t² = 1800 - 950

16t² = 850

t² = 850 / 16

t² = 53.125

t = √53.125

t = 7.2887 s

the time at this situation is 7.29s

reasonable domain

minimum t = 0

for maximum t, h = -16t² + 1800 = 0

16t² = 1800

t = 10.61

0 ≤ t ≤ 10

the reasonable domain is 0 ≤ t ≤ 10

reasonable range

h = -16t² + 1800

at t = 0, h = 1800

at t = 10.606, h = 0

0 ≤ h ≤ 1800

the reasonable range is 0 ≤ h ≤ 1800

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The derivative of the function cos(xº) in radians is y' = -sin(xπ/180)

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

cos(xº)

Changing the degree into radian, we have

cos(xπ/180)

Express as a function

So, we have

y = cos(xπ/180)

When the cosine function is differentiated, we have

y' = -sin(xπ/180)

Hence, the differentiated function is y' = -sin(xπ/180)

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By using the Unitary Method we get the number of children who went on an excursion was 63. Thus, the total number of children at school is 90.

We are given that,

No. of children who stayed at school is 27,

Also, 70% of the children went on an excursion.

Suppose, the total number of children in percentage is 100%

Out of which 70% went on an excursion

Thus, the children who stayed at school is 100% - 70% = 30%

By using the Unitary method, we can find out the number of 70% of children.

If 30% of the children are 27

Then 70% of the children are = 27 × 100

                                                        30

                                                 = 63

∴ the total no. of children in the school = 27 + 63

                                                                 = 90

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Answer:

320 ft^2

Step-by-step explanation:

Answer:

Computation of Grade Point Average (GPA):

GPA = Total Weighted Points divided by total credit hours

= 45/19

= 2.37 on 4.00 Grade Average

Step-by-step explanation:

a) Data and Computations:

Courses  Grade Letters  Credit Hours  Quality Points  Weighted Points

1                        B                     4                        3                      12

2                       B                     5                        3                      15

3                       A                     1                         4                       4

4                       C                     5                        2                     10

5                       D                     4                        1                       4

Total                                       19 credit hours                         45 Points

b) GPA = Total Weighted Points divided by total credit hours

= 45/19

= 2.37

c) The GPA for this student is the total weighted points (which is a product of the credit hours (loads) and the quality point) expressed as a ratio of the total credit hours for the courses she took.  The grade point average ensures that the each point used in calculating the GPA is weighed by the credit hours allocated to the course.  The resultant figure of 2.37 implies that out of 4.00 grade points, the student scored 2.37, translating to about 59%.

The equation of the possible way to begin solving for x is 2/5x - 7/20x = 3/4 - 1/2

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

-3/4 + 2/5x = 7/20x -1/2

The first step is to collect the like terms

So, we have

2/5x - 7/20x = 3/4 - 1/2

This represents an equation of the possible way to begin solving for x

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The orthogonal projection of vector v onto vector w in R^3 is (-54/14, -159/70, -159/35).

To find the orthogonal projection of v onto w, we need to calculate the scalar projection of v onto w and multiply it by the unit vector of w. The scalar projection of v onto w is given by the formula:

proj_w(v) = (v⋅w) / (w⋅w) * w

where ⋅ denotes the dot product.

Calculating the dot product of v and w:

v⋅w = (-7)(-5) + (6)(-3) + (-6)(-6) = 35 + (-18) + 36 = 53

Calculating the dot product of w with itself:

w⋅w = (-5)(-5) + (-3)(-3) + (-6)(-6) = 25 + 9 + 36 = 70

Now, substituting these values into the formula, we have:

proj_w(v) = (53/70) * (-5,-3,-6) = (-54/14, -159/70, -159/35)

Therefore, the orthogonal projection of v onto w is (-54/14, -159/70, -159/35).

In simpler terms, the orthogonal projection of v onto w can be thought of as the vector that represents the shadow of v when it is cast onto the line defined by w. It is calculated by finding the component of v that aligns with w and multiplying it by the direction of w. The resulting vector (-54/14, -159/70, -159/35) lies on the line defined by w and represents the closest point to v along that line.

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Answer: 22.4402

Step-by-step explanation:

Answer:

84.4% of 23 is 19.412.

Step-by-step explanation:

Let the unknown number be x.

Now, 84.4% of x = 19.412.

∴ (84.4 ÷ 100) × x = 19.412.

By simplifying the equation,

x = (19.412 × 100) ÷ 84.4

x = 1941.2 ÷ 84.4

∴ x = 23

Thus, 84.4% of 23 is 19.412.

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Answer:

400 litres

Step-by-step explanation:

Check the picture below.

The domain of the composite functions:

a). (f + g)(-2) = 23

b). (f - g) (-2) = 1

c). f(x) - g(x) = x² - 5x - 13

A function is composite when the co- domain of the first mapping is the domain of the second mapping

Given the functions f(x) = x² - 4x and g(x) = x + 13, we shall evaluate the domains of the functions as follows:

a). (f + g)(-2) = (-2)² - 4(-2) + (-2) + 13

(f + g)(-2) = 4 + 8 - 2 + 13

(f + g)(-2) = 23

b). (f - g) (-2) = (-2)² - 4(-2) - (-2) - 13

(f - g)(-2) = 4 + 8 + 2 - 13

(f - g) (-2) = 1

c). f(x) - g(x) = x² - 4x - x - 13

f(x) - g(x) = x² - 5x - 13

Therefore, the domain of the composite functions:

a). (f + g)(-2) = 23

b). (f - g) (-2) = 1

c). f(x) - g(x) = x² - 5x - 13

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