When salving an inequality, when must you reversed he inequality.

The  variable x represent the length of rectangle.

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Perimeter= 64 units

let the length be x.

So, width = x - 3

So, Perimeter of rectangle = 2 ( l + w)

64 = 2( x+ x -3)

32 = 2x -3

29= 2x

x= 29/2

Hence, the variable x represent the length of rectangle.

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Answer: I don't quite understand your question. Supplementary angles are angles that equal 180 degrees. You can find missing supplementary angles by adding the two that are given, and then subtracting them by 180.

Coupon STRIPS can be created from the given T-bond by removing the coupon payments from the bond and selling them as individual securities. Let's calculate how many coupon STRIPS can be created from this T-bond.

The bond has a 5% coupon, which means it will pay $5 million in interest every year. Over a period of 29 years, the total interest payments would be $5 million x 29 years = $145 million.

The par value of the bond is $100 million. After deducting the interest payments of $145 million, the remaining principal value is $100 million - $145 million = -$45 million.

Since there is a negative principal value, we cannot create any principal STRIPS from this bond. However, we can create coupon STRIPS equal to the number of coupon payments that will be made over the remaining life of the bond.

Therefore, we can create 29 coupon STRIPS of $5 million each from this T-bond. These coupon STRIPS will be sold separately and will not include the principal repayment of the bond.

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An event that is defined as impossible has a probability of zero. However, it is important to note that an event with an empirically approximated probability of zero does not necessarily mean it is impossible.

Empirical results are based on observations and data, which may be limited in scope or subject to measurement errors. Therefore, a probability approximation of zero based on empirical results does not provide absolute certainty that the event is impossible.

In probability theory, an event that is classified as impossible is one that has a probability of zero. This means that the event cannot occur under any circumstances. For example, if you roll a fair six-sided die and the event is defined as rolling a seven, which is not possible, then the probability of rolling a seven is zero.

On the other hand, when empirical results are used to approximate probabilities, it is crucial to consider the limitations of the data and the possibility of measurement errors. If an event has been observed to have a probability of zero based on empirical data, it means that it has not been observed to occur within the scope of the data collected.

However, it does not definitively prove that the event is impossible. There might be factors or conditions beyond the scope of the data that could lead to the occurrence of the event. Therefore, while an empirical approximation of zero probability suggests extreme unlikelihood, it does not guarantee that the event is impossible.

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A statement that creates a list is my_nums= [5,10,15]. This is also known as array.

An array is a grouping of identically typed elements that are stored in adjacent memory locations and may each be separately referred to using an index to a special identifier. There is no need to declare five distinct variables when declaring an array of five integer values (each with its own identifier).

The three types of arrays are index, multidimensional and associative array.

my_nums= [5,10,15] is an array that stores multiples of 5.

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A statement that creates a list is my_nums= [5,10,15]. This is also known as array.

What is an array?

An array is a data structure consisting of a collection of elements (values or variables), each identified by at least one array index or key. An array is a combination of a set of elements which are all of the same data type, organized in a particular way. Arrays are used to store multiple values in a single variable, structure data, and access data more efficiently. Arrays are generally used to represent data in a structured way, and they can be used to perform various mathematical operations and other calculations. Arrays are also useful for sorting and searching data in a predetermined order.

What are three types of array?
The three types of array are index, multidimensional and associative array.
my_nums= [5,10,15] is an array that stores multiples of 5.

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There are different consecutive ways that the flowers can be planted:

3,9,15,21 and so on.

Numbers that follow each other in a regular counting order or pattern are called consecutive numbers. They are written sequentially, where the difference between the numbers is fixed and no number in between is skipped.

Given that:

Roses plants in 1st, 2nd, row are:

3,9 ,.....

Since difference between consecutive terms is same:

It is an AP

We have to find number of row in the flower bed:

Lets assume there are n rows in the flowers bed.

We know that:

    aₙ = a + (n-1)d

and d = 9-3 = 6

Therefore, the next numbers can be:

3,9,15 ,21 ......

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Maryanne leaves a tip of $0.75 since she paid $2.00 and the coffee costs $1.25.  Maryanne leaves a 60% tip when she buys a medium coffee for $1.25 and brings $2.00 with her, leaving the change as a tip.

To find the percentage tip, you need to divide the tip amount by the cost of the coffee and then multiply by 100.$0.75 (tip) / $1.25 (cost of coffee) = 0.6
0.6 x 100 = 60
Therefore, Maryanne leaves a 60% tip.

To find the percentage tip Maryanne leaves when buying a medium coffee costing $1.25 with $2.00, we will follow these steps:
1. Calculate the change by subtracting the cost of the coffee from the amount she brings: $2.00 - $1.25 = $0.75
2. To find the percentage tip, divide the change (tip) by the cost of the coffee: $0.75 / $1.25
3. Convert the result to a percentage by multiplying by 100: (0.75 / 1.25) * 100
Now, let's calculate the percentage:
(0.75 / 1.25) * 100 = 60%

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The inverse function (or reciprocal function) is \(f(x) = \dfrac{1}{x}\).

The x-values you can use are everything except for 0, since 1/0 is undefined.

If you look at the graph, you'll also notice that the graph never touches the x-axis, meaning a y-value of 0 is never used.  So the range is also all real numbers, except for 0.  

So the domain is \(\{ \ x \ | \ x\in\mathscr{R}, \ x\neq0 \ \}\) and

the range is \(\{ \ y \ | \ y\in\mathscr{R}, \ y\neq0 \ \}\).

Answer:

Step-by-step explanation:

If the lengths of two sides of a triangle are given the third side must be less than the sum of those two sides, but more than the value of the difference between the given two sides.

So for #9, the answer is 4 (which is 12-8) <x<16 (which is 12+8)

#10. 10<x<16

#11. 19<x<61

#12. 6<x<16

Below are what would happen if the 3rd side was too big (left) or too small (right)

Answer in scientific notation: 8.3x10^-3

1 furlong, a unit used in horse racing, is equal to 40 rods and 10 chains, both units used in surveying and equal to 201.168 meters (660 feet).

A furlong is a unit of length used primarily in horse racing. It is equal to 201.168 meters (660 feet). A rod is a unit of length used in surveying and is equal to 5.5 yards (16.5 feet). A chain is also a unit of length used in surveying and is equal to 66 feet.

To calculate 1 furlong in rods, we multiply 1 furlong by the conversion factor of 40 rods per furlong:

1 furlong x 40 rods/furlong

= 40 rods

To calculate 1 furlong in chains, we multiply 1 furlong by the conversion factor of 10 chains per furlong:

1 furlong x 10 chains/furlong

= 10 chains

To convert from furlongs to rods, we multiply the number of furlongs by the conversion factor of 40 rods per furlong:

4.0 furlongs x 40 rods/furlong = 160 rods

And to convert from furlongs to chains, we multiply the number of furlongs by the conversion factor of 10 chains per furlong:

4.0 furlongs x 10 chains/furlong = 40 chains

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Answer:

Step-by-step explanation:

To convert degrees to radians, we can use the following formula:

Then, for 35 degrees:

The camper should take 3 units of food, 1 first-aid kit, and 1 piece of clothing within the given constraints.

To determine the optimal number of each item the camper should take, we need to maximize the total benefit while considering the capacity constraint of the backpack.

Let's assume the camper takes x units of food, y first-aid kits, and z pieces of clothing.

The backpack has a capacity of 9 ft^3, and each unit of food takes up 2 ft^3. Therefore, the constraint for food is 2x ≤ 9, which simplifies to x ≤ 4.5. Since x must be a whole number and the camper needs at least one unit of food, the camper can take a maximum of 3 units of food.

Similarly, for first-aid kits, since each kit occupies 1 ft^3 and the camper must take at least one, the constraint is y ≥ 1.

For clothing, each piece takes 3 ft^3, and the constraint is z ≤ (9 - 2x - y)/3.

Now, we need to maximize the total benefit. The benefit of food is assigned as 7, first aid as 5, and clothing as 6. The objective function is 7x + 5y + 6z.

Considering all the constraints, the possible combinations are:

- (x, y, z) = (3, 1, 0) with a total benefit of 7(3) + 5(1) + 6(0) = 26.

- (x, y, z) = (3, 1, 1) with a total benefit of 7(3) + 5(1) + 6(1) = 32.

- (x, y, z) = (4, 1, 0) with a total benefit of 7(4) + 5(1) + 6(0) = 39.

- (x, y, z) = (4, 1, 1) with a total benefit of 7(4) + 5(1) + 6(1) = 45.

Among these combinations, the highest total benefit is achieved when the camper takes 3 units of food, 1 first-aid kit, and 1 piece of clothing.

Therefore, the camper should take 3 units of food, 1 first-aid kit, and 1 piece of clothing to maximize the total benefit within the given constraints.

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Answer:

B. 4

Step-by-step explanation:

\(7 \sqrt{7x} = \sqrt{49 \times 7x} \)

49 × 7x = 343x

14√7 = √(1372)

1372 ÷ 343 = 4 this is the vaule of x.

Answer:   infinitely many solutions

Step-by-step explanation:

The system is only 1 line.  So it must be that there are 2 equations that are actually the same so they intersect infinitely many times.

The number of points the team scored in each game are 23, 23 and 17 points respectively.

There are three basic types of equation in mathematics. Namely:

Total points scored = 63 points

First game = (x + 6) points

Second game = (x + 6) points

Third game = x points

63 = x + (x + 6) + (x + 6)

63 = x + x + 6 + x + 6

63 = 3x + 12

63 - 12 = 3x

51 = 3x

x = 51/3

x = 17

Therefore,

First game = (x + 6) points

= (17 + 6)

= 23 points

Second game = (x + 6) points

= (17 + 6)

= 23 points

Third game = x points

= 17 points

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Answer:

X=-4

Step-by-step explanation:

16x^2+9=5

- 9 -9

16x^2= -4

16/-4 =

-4

The values of the angles based on the information will be:

From the information given, angle 1 is 110° and the horizontal lines n and m are intersected by lines q and p.

In this case, it should be noted that opposite angles are equal. Hence, angle 2 is also 110°.

Angle 3 will be:

= 180° - 110° = 70° (angle on a straight line).

Angle 4 will also be 70° as opposite angle to angle 3.

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Using translation concepts, it is found that the equations that represents the transformations formed by the following items are given by:

Item a:

The function is:

\(f(x) = \sqrt{x}\)

Horizontal shift of 4 units to the left, hence:

\(g(x) = f(x + 4) = \sqrt{x + 4}\)

Vertical compression by a factor of \(\frac{1}{3}\), hence a multiplication by \(\frac{1}{3}\), that is:

\(g(x) = \frac{1}{3}\sqrt{x + 4}\)

Item b:

Vertical stretch by a factor of 4, that is, a multiplication by 4, so:

\(4f(x) = 4\sqrt{3}\)

Vertical shift of 3 units up, hence addition of 3, that is:

\(g(x) = 4\sqrt{3} + 3\)

Item c:

Horizontal stretch by a factor of 2, that is:

\(g(x) = f(\frac{1}{2}x) = \sqrt{\frac{x}{2}}\)

Vertical shift of 3 units down, hence subtraction by 3, that is:

\(g(x) = \sqrt{\frac{x}{2}} - 3\)

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Answer:

The answer is m=-2 or m=7.

Step-by-step explanation:

The steps to solve this equation are below:

Factor: to get (m+2)(m−7)=0.

m+2=0 or m−7=0

m=−2 or m=7. So, your answer is m=-2 or m=7.

Answer:

m = 7

m = -2

Step-by-step explanation:

ax^2 + bx + c

1m^2 - 5m - 14

a = 1

b = -5

c = -14

-b ± √b^2 - 4ac/2a

-(-5) ± √(-5)^2 - 4(1)(-14)/2(1)

5 ± √25 + 56/2

5 ± √81/2

5 ± 9/2

5 + 9/2

14/2 = 7

5 - 9/2

-4/2 = -2

Answer: 1.48971 x 10^19

Step-by-step explanation: 1-light year is approximately 5.865 x 10^12 which is 5,865,000,000,000 kilometers or 6 trillion miles in 1-year. The Andromeda galaxy is indeed 2.54 million light-years from Earth which is the closest galaxy to our Milky Way Galaxy.

The best way to this is to put this into a scientific calculator. If it shows 1.48971E19, the E stands for exponent and the 19 next to the E stands to the 19th power. That is written as 1,489,710,000,000,000,000 miles!! from Earth. That's a lot of zeros. That's the reason scientific notation is used; to avoid all those zeros and express very small/large figures.

Hope this explanation helps.

13

Explanation:

Given: 52 divided by 4​

There should be an equal to sign in order to perform an inverse operation.

Let the answer we get after dividing 52 by 4 = x

52/4 = x

52 divided by 4​ becomes:

52 = 4x

x is multiplied by 4. The inverse operation of multiplication is division.

So, we will divide 4 on both sides of the equation:

52/4 = 4x/4

13 = x

x = 13

The answer is 13

Answer:

it’s false

Step-by-step explanation:

In an equilateral triangle, all sides are equal in length. Therefore, to find the side length of the yield sign, we can use the given height of 12 cm.

In an equilateral triangle, the height (h) divides the triangle into two congruent right-angled triangles. Each right-angled triangle will have a base equal to half of one side length, and the height equal to the given height.

Let's consider one of the right-angled triangles formed by the height and half of one side length of the equilateral triangle:

Using the Pythagorean theorem, we have:

s^2 = (0.5s)^2 + h^2

Substituting the given height of the yield sign (h = 12 cm):

s^2 = (0.5s)^2 + 12^2

s^2 = (0.25s^2) + 144

s^2 - 0.25s^2 = 144

0.75s^2 = 144

s^2 = 144 / 0.75

s^2 = 192

s = √192

s ≈ 13.856

Therefore, the approximate side length of the yield sign is approximately 13.856 cm.

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The total number of tasks Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed

The factor 'x' in the expression '90x - 20' represents the total number of tasks that Terrence completed in the game.

To understand why, let's break down the given information. It states that Shelly and Terrence completed a different number of tasks. Shelly earned 90 points on each task, so the total number of tasks she completed is not represented by 'x'.

On the other hand, Terrence's total points were 20 less than Shelly's total. This means that Terrence's total points can be calculated by subtracting 20 from Shelly's total points. Since Shelly earned 90 points on each task, her total points would be 90 multiplied by the number of tasks she completed.

So, the expression '90x - 20' represents Terrence's total points in the game, where 'x' represents the total number of tasks that Terrence completed. By substituting the value of 'x' with the number of tasks Terrence completed, we can calculate his total points.

Therefore, the correct answer is: The total number of tasks Terrence completed.

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The values of the variables, a, b, and c obtained from the equation of the circle and the coordinates of the point P are;

a) a = 2

b = -2

c = 4

The general equation of a circle is; (x - h)² + (y - k)² = r²

Where;

(h, k) = The coordinates of the center of the circle

r = The coordinates of the radius of the circle

The specified equation of a circle is; x² + y² = 9

The coordinates of the center of the circle, is therefore, O = (0, 0)

a) The coordinates of the points P  and O indicates that the gradient of OP, obtained using the slope formula is; ((3·√3)/4 - 0)/(3/2 - 0) = ((3·√3)/4)/(3/2)

((3·√3)/4)/(3/2) = (√3)/2

The specified form of the gradient is; (√3)/a, therefore;

(√3)/a = (√3)/2

a = 2

The value of a is 2

b) The gradient of the tangent to a line that has a gradient of m is -1/m

The gradient of OP is; (√3)/2, therefore, the gradient of the tangent at P is -2/(√3)

The form of the gradient of the tangent at P is b/(√3), therefore;

-2/(√3) = b/(√3)

b = -2

The value of b is; -2

c) The coordinate of the point on the tangent, (0, (7·√3)/c) indicates

Slope of the tangent = -2/(√3)

((7·√3)/c - ((3·√3)/4))/(0 - (3/2)) = -2/(√3)

((7·√3)/c - ((3·√3)/4)) = (3/2) × 2/(√3) = √3

(7·√3)/c = √3 + ((3·√3)/4) = 7·√3/4

Therefore; c = 4

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Answer:

i dont know sorry

Step-by-step explanation:

To find the height h of the Washington Monument in Washington, D.C., we can use the following equation:
h + 630 = height of the Gateway Arch .

We know that the height of the Gateway Arch is 630 feet taller than the height of the Washington Monument. So, if we subtract 630 feet from the height of the Gateway Arch, we will get the height of the Washington Monument.

Therefore, the equation becomes:

h + 630 - 630 = height of the Gateway Arch - 630

h = height of the Gateway Arch - 630

Since we do not have the exact height of the Gateway Arch, we cannot solve for the exact height of the Washington Monument. However, we know that it is 630 feet shorter than the Gateway Arch.

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Answer:

x=37

Angle P: 65 degrees

Angle Q: 78 degrees

Angle R: 37 degrees

Step-by-step explanation:

sum of all three angles of a triangle always equal 180 degrees

So we can add these and set it equal to 180

2x-9+2x+4+x=180

5x-5=180

   +5. +5

5x=185

/5.   /5

x=37

So now to find each  angle we just fill in X

Angle p: 2x-9

2(37)-9

74-9

Angle P is 65 degrees

Angle Q: 2x+4

2(37)+4

74+4

Angle Q is 78 degrees

And since angle r is just x and we already know X=37 then

Angle r is 37 degrees

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