I thought of a number. If I add 30/7 to it, then subtract 22/7 from the result, and then subtract that difference from 59/7, I get 19/7. What is my number

The angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

Given sinz = -4/5 for pi < z < (3pi)/2, we need to find the value of cosz. We can use the trigonometric identity of Pythagorean theorem to find the value of cosz.

According to Pythagorean theorem, sin2θ + cos2θ = 1, where θ is the angle in the right-angled triangle and sin, cos are the trigonometric ratios.

The negative sign for the given sinz indicates that the angle z is in the third quadrant. So, we can take the help of the unit circle to find the value of cosz as shown below:

Here, we have used the Pythagorean identity of sin2z + cos2z = 1 on the unit circle to find the value of cosz. Since the value of sinz is already given, we can find the value of sin2z as: sin2z = sinz x sinz = (-4/5) x (-4/5) = 16/25

Then, we can substitute the value of sin2z in the Pythagorean identity as: cos2z = 1 - sin2z = 1 - (16/25) = 9/25We need to find the value of cosz.

So, we can take the square root of cos2z as: cosz = ±(√(9/25)) = ±(3/5)The sign of cosz can be determined by considering the quadrant of the angle z.

Since the angle z is in the third quadrant, the value of cosz is negative. Hence, cosz = -3/5.So, the value of cosz is -3/5.

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Answer:

Road:

Distance to Greg's house = 3.2 + 1.7 =

4.9 miles

Time to get to Greg's house =

(4.9 mi)/(15 mi/hr) = about .327 hours = about 19.6 minutes (19 minutes, 36 seconds)

Shortcut:

Distance to Greg's house:

\( \sqrt{ {3.2}^{2} + {1.7}^{2} } = 3.6235 \)

Time to get to Greg's house:

(3.6235 mi)/(15 mi/hr) = about .242 hours = about 14.49 minutes (14 minutes, 30 seconds)

The shortcut is about 4.9 - 3.6235 = 1.28 miles faster (about 5.11 minutes, or 5 minutes, 6 seconds faster)

Tyshawn has 320 different outfits to choose from.

To calculate the number of different outfits Tyshawn can choose from, we need to multiply the number of choices for each category together.

Number of choices for pants = 8

Number of choices for t-shirts = 5

Number of choices for sweaters or hoodies = 4

Number of choices for shoes = 2

To find the total number of different outfits, we multiply these numbers together:

Total number of outfits = 8 × 5 × 4 × 2

Total number of outfits = 320

Therefore, Tyshawn has 320 different outfits to choose from.

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Answer:

x = 4

Step-by-step explanation:

6/x + 1/2 = 2

x(6/x + 1/2) = 2*x

x*6/x + x*1/2 = 2x

6 + x/2 = 2x

6 = 2x - x/2

6 = 4x/2 - x/2

6 = 3x/2

6*2/3 = x

12/3 = x

x = 4

probe:

6/4 + 1/2 = 2

3/2 + 1/2 = 4/2

Answer:

Set your calculator to Degree mode.

a² = 17² + 20² - 2(20)(17)cos(89°)

a² = 677.13236

a = 26.0 in.

sin(89°)/26.02177 = (sin B)/17

sin B = 17sin(89°)/26.02177

B = 40.8°

C = 50.2°

The three true statements are as follows:

In the list, there are several true statements and some of them include the facts that all triangles are polygons, they are closed figures and they have three straight sides.

A polygon is a shape with two or more sides. Triangles ahve three sides, so we can easily address them as polygons. Also, all triangles are closed figures and they also have three straight sides.

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Explanation:

The range is the set of y outputs of a relation. So we just list the y coordinates of the points shown.

We could sort the values to get {-1, 4, 11, 13}, but order doesn't matter in a set. So this step is optional.

Because the ratios between each set of numbers are equal, and the graph passes through the point, the linear relationship is proportionate (0,0).

Proportional connections are those in which the ratios of the two variables are equal. Another way to think about them is that one variable is always a constant value multiplied by the other in a proportional relationship. The "constant of proportionality" is the name given to this variable.

The origin, points (2,14.5), (4,29), and (6,43.5) are provided (0,0).

We are aware that the ratios are equivalent in a proportional connection, i.e.

So,

⇒ 14.5/2 = 29/4 = 43.5/6 = 7.25

The linear relationship is a proportionate relationship since the ratios are equal.

The given situation's graph has been drawn, and it is evident that the graph passes through its origin, or "zero," which is (0,0)

Since the ratios between each set of data are equal, the linear relationship can only be a proportional relationship because the graph passes through the point (0,0).

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A semicircle has been cut out of a rectangular paperboard that is 20 inches long and 12 inches broad, as seen below. After the semicircle is taken out, the paperboard's remaining perimeter is 34.58 inches.

The paperboard has a length of 20 inches and a width of 12 inches. A semicircle is cut out of it, which means we need to find the perimeter of the remaining part.

The diameter of the semicircle is equal to the width of the paperboard, which is 12 inches. So, the radius of the semicircle is half of the diameter, which is 6 inches.

The perimeter of the remaining part will be the sum of the length of the paperboard and the two straight sides of the semicircle.

The length of the paperboard is 20 inches, and the two straight sides of the semicircle are equal to the diameter of the semicircle, which is 12 inches. So, the perimeter of the remaining part is:

P = 20 + 12 + 12 = 44 inches

However, we also need to subtract the length of the curved part of the semicircle from the perimeter. The length of the semicircle can be found using the formula:

C = πr

where C is the circumference of the semicircle and r is the radius.

Since we have a semicircle, we need to divide the circumference by 2. So, the length of the curved part of the semicircle is:

C/2 = (π x 6) / 2 = 9.42 inches (rounded to two decimal places)

Therefore, the perimeter of the remaining part is:

P = 44 - 9.42 = 34.58 inches (rounded to two decimal places)

So, the perimeter of the remaining paperboard is 34.58 inches.

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Answer:

(1,2) and (x-2)-3 should be on the graph

Step-by-step explanation:

The measurements of the cylindrical (round and hollow) drum that minimize the fetched of development are roughly 10.19 yards by 2.46 yards.

Let's expect that the round and hollow drum includes a stature of h and a span of r.

The volume of a barrel is given by: V = πr^2h.

We know that the drum includes a capacity of 806 cubic yards, so able to compose:

πr^2h = 806

We need to play down the taken a toll of building the drum, which is given by the entirety of the fetched of the beat, foot, and side divider.

The zone of the beat and foot of the drum is given by: A = πr^2.

The fetched of fabric for the beat and foot is $2 per square yard, so the taken a toll of the best and foot is:

C_topbottom = 2A = 2πr^2

The cost of fabric for the side divider is $17 per square yard, and the region of the side divider is given by:

A_side = 2πrh

The whole fetched of building the drum is in this manner:

C = C_topbottom + C_side = 2πr^2 + 17(2πrh) = 2πr^2 + 34πrh

Presently we are able utilize the condition for the volume of the drum to kill h from the fetched condition:

h = 806/(πr^2)

Substituting this expression for h into the taken a toll condition, we get:

C = 2πr^2 + 34πr(806/(πr^2)) = 2πr^2 + 27404/r

To discover the least fetched, we got to take the subordinate of the fetched condition with regard to r and set it rise to to zero:

dC/dr = 4πr - 27404/r^2 =

Fathoming for r, we get:

r = (27404/(4π))^(1/3) ≈ 10.19 yards

Substituting this esteem of r back into the expression for h, we get:

h = 806/(π(10.19)^2) ≈ 2.46 yards

Hence, the measurements of the round and hollow drum that minimize the fetched of development are roughly:

Span: 10.19 yards

Stature: 2.46 yards

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The statement " when adding an entry to a binary search tree, the search ends at a leaf if the entry is not already in the tree" is true.

A tree is a type of data structure made up of nodes and contains the following features:

1- Every tree has a root node (also known as a parent node) at the top that contains some value (can be any datatype).

2- There are 0 or more child nodes of the root node.

3- There are zero or more child nodes for each child node, and so forth. As a result, the tree gains a subtree. Each node has a separate subtree that consists of its offspring and their offspring, etc. This implies that any node can function as a tree on its own.

In addition, a binary search tree (BST) has the following two features:

1- Each node has a maximum of up to two children.

2-For each node, the values of its left descendent nodes are less than that of the current node, which in turn is less than the right descendent nodes (if any).

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Given that 16 families went on a trip and the cost of the trip was Rs. 2,16,352.The amount paid by each family is to be determined by unitary method Hence each family paid Rs.13522

Now, let's solve this by using the method of unitary method. To find the cost of 1 family trip, we will divide the total cost of the trip by the number of families.2,16,352 / 16 = 13,522 So, the cost of the trip per family is Rs. 13,522.Hence, each family paid Rs. 13,522 for the trip.

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Answer:

Step-by-step explanation

1. The total cost of the trip for all 16 families is Rs 2,16,352.
2. To find out how much each family paid, we need to divide the total cost by the number of families: Rs 2,16,352 ÷ 16.
3. When we do the division, we get the result: Rs 13,522.

Now let's check if this result is correct:

1. If each family paid Rs 13,522 for the trip, then the total cost for all 16 families would be: 16 × Rs 13,522 = Rs 2,16,352.
2. This is exactly the same as the total cost given in the problem statement.

So we have shown that each family paid **Rs 13,522** for the trip

128Answer:

128

Step-by-step explanation:

vì 4+4=8

8+8=16

16+16=32

32+32=64

64+64=128

Answer:

let's try x = 1

f(x) = -2, g(x) = 1

g-f)(x) = -3

try = 2

-1, 4

continue with this concept

The polynomial simplifies to -x² + 8x + 1 with a highest degree of 2.

To simplify a mathematical expression is to represent it in the least complicated form possible.

In general the simplest form is one that has used the fundamental properties of numbers, exponents, algebraic rules, etc. to remove any duplication or redundancy from the expression.

The given expression;

= (3x²- x - 7) - (5x² - 4x - 2) + (x + 3)(x + 2)

The simplified form of the given expression is calculated as follows;

= 3x² - x - 7 - 5x² + 4x + 2 + x² + 2x + 3x + 6

= -x² + 8x + 1

Thus, the polynomial simplifies to -x² + 8x + 1 with a highest degree of 2.

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We can simplify cosec(t)tant(t) to sec(t). A trigonometric function is a mathematical function that relates the angles of a triangle to the ratios of its sides.

The most common trigonometric functions are sine (sin), cosine (cos), tangent (tan), cotangent (cot), secant (sec), and cosecant (csc).

To simplify the expression cosec(t)tant(t), we need to use the trigonometric identity:

cosec(t) = 1/sin(t)

tant(t) = sin(t)/cos(t)

Substituting these expressions into the original expression, we get:

cosec(t)tant(t) = (1/sin(t))(sin(t)/cos(t))

The sin(t) term in the numerator and denominator cancel out, leaving:

cosec(t)tant(t) = 1/cos(t)

Recalling the definition of secant, sec(t) = 1/cos(t), we can express the simplified expression as:

cosec(t)tant(t) = 1/sec(t)

Therefore, we can simplify cosec(t)tant(t) to sec(t).

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Answer:

what

Step-by-step explanation:

Answer:

um, sorry i dont speak gibberish

Step-by-step explanation:

Answer:

3.34 containers

Step-by-step explanation:

I always say: Recognize our numbers

8.35 2.5

"Holds 2.5 kg"

8.35 divided by 2.5

=3.34

Answer:

25

Step-by-step explanation:

5 x 5 is just a shorter way of saying 5 + 5 + 5 + 5 +5

Answer:

The main difference between a linear expression and a linear equation is that the linear equation has an equal sign in the expression. In the common core, you learn that a linear equation is the same thing as a linear function

Answer:

C. 162.5 sq ft.

Step-by-step explanation:

Given the following data;

S.A of smaller cylinder, S1 = 65 ft²

Ratio = 2:5 = 2 + 5 = 7

Let the total surface area be x.

S1 = 2/7 * x = 65

S1 = 2x = 65 * 7

S1 = 2x = 455

x = 455/2

x = 227.5 ft²

To find the surface area of the larger cylinder;

S2 = 5/7 * 227.5

S2 = 1137.5/7

S2 = 162.5 ft²

Answer:

2/3

Step-by-step explanation:

We solve with combination formula

C(n, r) = nCr = n!/r!( n - r)!

The selection will happen between four women and six men

Total number of people = Total number of possibly outcomes = Four women + six men

= 10 people

This can happen in two ways

a) 2 women

b) 1 man and 1 woman

The probability that at least one woman is selected =

4C2 ×(6C1 + 4C1)÷ 2 ways / 10C2

[6 × (6+ 4)] ÷ 2 / 45

= (6 × 10) ÷ 2/45

= 30/45

= 2/3

The triangle presented in the diagram drawn is known as equilateral triangle.

A triangle with angle 60 degrees is known as equilateral triangle because the sum of angles in a triangle is 180 degrees.

So if the total angles in a triangles is 180 degrees, and two known angles are 60 degrees, then the remaining side will be 60 degrees.

In an equilateral triangle, each of the interior angle measures 60 degrees.

Thus, the triangle presented in the diagram drawn is known as equilateral triangle.

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The height of the flagpole in this problem is calculated as follows:

12.9 feet.

The height of the flagpole in this problem is obtained using similar triangles, as shown by the image given at the end of the answer.

Similar triangles are used because the equivalent sides have proportional side lengths.

From the image given at the end of the answer, the equivalent sides of each triangle are given as follows:

Then the proportional equation is given as follows:

8/20 = 5.1667/x

Applying cross multiplication, the height of the flagpole is calculated as follows:

8x = 20 x 5.1667

x = 20 x 5.1667/8

x = 12.9 feet.

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Cotangent is the inverse of tangent:

cotΘ = 1/tanΘ

cotΘ = \(1/\frac{\sqrt{6} }{2}\)

         =\(\frac{2}{\sqrt{6}}\)

         =\(\frac{2}{\sqrt{6}}*\frac{\sqrt{6}}{\sqrt{6}}=\frac{2\sqrt{6}}{6}\) Rationalize the denominator

cotΘ = \(\frac{\sqrt{6}}{3}\)

Plug and solve.

\(\frac{\frac{\sqrt{6}}{2}+\frac{\sqrt{6}}{3} }{\frac{\sqrt{6}}{2}-\frac{\sqrt{6}}{3}}\)

We'll break the problem into 2, simplify the denominator, then simplify the numerator.

Simplify the denominator with the common denominator 6, of 2 and 3:

\({\frac{\sqrt{6}}{2}-\frac{\sqrt{6}}{3} = {\frac{3\sqrt{6}}{6}-\frac{2\sqrt{6}}{6} = {\frac{3\sqrt{6}-2\sqrt{6}}{6} = {\frac{\sqrt{6}}{6}\)

Simplify the Numerator with the common denominator 6, of 2 and 3:

\({\frac{\sqrt{6}}{2}+\frac{\sqrt{6}}{3} = {\frac{3\sqrt{6}}{6}+\frac{2\sqrt{6}}{6} = {\frac{3\sqrt{6}+2\sqrt{6}}{6} = {\frac{5\sqrt{6}}{6}\)

Back in original equation with simplified numerator and denominator:

\(\frac{\frac{5\sqrt{6}}{6}}{\frac{\sqrt{6}}{6}}\)

Multiply by reciprocal and simplify:

\(\frac{5\sqrt{6}}{6}*\frac{6}{\sqrt{6}} = \frac{5\sqrt{6} * 6}{6\sqrt{6}} = 5*\frac{6\sqrt{6}}{6\sqrt{6}} = 5*1 = 5\)

When listing all the pairs of factors for a particular term, the factorization process is used.

This process is fundamental in number theory and is used to break down composite numbers into their simplest building blocks: prime numbers.

For example, if we want to find all pairs of factors for the number 24, we could follow these steps:

Start with 1 and the number itself (in this case 24), as these are always factors.

Check if 2 divides 24 evenly. If it does, then 2 and 24/2 (which is 12) are a pair of factors.

Continue this process with increasing numbers. Check 3 (yes, it works, with the pair being 3 and 8), 4 (yes, with the pair being 4 and 6), and so on.

When the numbers you're testing exceed the square root of the original number (approximately 4.9 for 24), you can stop, as you'll have found all pairs.

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Answer:

3/8

Step-by-step explanation:

After spending 3/8 of her money on a bag, she has 5/8 of the original amount of money left. As she gave 2/5 of the remaining amount of money to her sister, she gave 1/4 of the original amount of money to her sister (5/8 × 2/5 = 1/4). Therefore, there's only 3/8 (1 - 3/8 - 1/4 = 3/8) of the original amount of money left in her bag.