What are the 9 types of solution with example?.

Heather would have to work 4.6 hours to make $65.

Time and work is a branch of mathematics that deals with the relationship between the time required to complete a task and the amount of work done. The basic formula used in time and work is:

Work = Time x Rate

Where,

Work = amount of work done

Time = time taken to complete the work

Rate = the rate at which the work is done

We can calculate this by using the formula:

Hours = (Money earned / Hourly rate)

In this case, you can use the proportion:

(x hours) / (65) = (12 hours) / (156)

Solving for x you get:

x = (65 * 12) / 156 = 4.6 (approximately, rounded to the nearest tenth)

Therefore, Heather would have to work 4.6 hours to make $65.

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In this case, you can use the proportion:

(x hours) / (65) = (12 hours) / (156)

Solving for x you get:

x = (65 * 12) / 156 = 4.6 (approximately, rounded to the nearest tenth)

When each number is rounded to the nearest hundred, the difference I 100 the number could be 14,499 less 13,500 or 999

To the closest hundred, the biggest number that can be named 14,000 is 14,050. To the closest hundred, the least number that can be named 14,000 is 13,950. There is a 100 difference between the two.

This claim may be generalized as follows.

The difference between the upper and lower limits is m for any integer N that has been rounded to the nearest m.

The maximum is N+m/2.

N-m/2 is the lower limit.

(N+m/2) is the difference between the two. (N-m/2) = (N-N) +m/2 - (N-N) -m/2

= 0 + m/2 + m/2

= 2(m/2)

= m.

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EF as a decimal rounded to the nearest tenth is 60.9.

A, I looked online and came across this statistic.

OM is probably perpendicular to CD and EF is perpendicular to ON, and I'm assuming there's more information there.

The chords are similarly split in half by the diameters that intersect them at right angles, so CM = (1/2) CD = 28.

r2 = OM2 + CM2 = 202 + 282 = 1184 r = 474 b; FN is the leg of a right triangle with other leg ON=16 and hypotenuse OF=r because it is a radius; r2 = OM2 + CM2 = 202 + 282 = r = 474 b.

r2 - ON2 = 1184 - 162 = 1184 - 256 = 928 = FN2 = 928

C, By the perpendicular diameter bisecting a chord theorem, EF is twice as large as FN.

EF = 2√928

60.9

A, I looked online and came across this statistic. I'll venture a guess of 1.

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8 gigabytes would have to be used for the plans to cost the same. The cost will be $100.

Given is that Smart One smartphone plan cost $20 per month for talk and messaging and $10 per gigabyte of data used each month. A second smartphone plan cost $60 per month for talk and messaging and $5 per gigabyte of data used each month.

Let {C} represent the total cost in dollars and {D} represent the amount of data used in gigabytes. The system of equation can be used to represent this situation are -

C = 20 + 10d

C = 60 + 5d

For same cost -

20 + 10d = 60 + 5d

5d = 40

d = 8

The cost would be -

C = 20 + 10d

C = 20 + 10 x 8

C = 100

Therefore, 8 gigabytes would have to be used for the plans to cost the same. The cost will be $100.

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Answer:

Fraction form: [tex]\frac{10\sqrt{14} }{7}[/tex]

Decimal form: 5.34522483

Answer:

(-2, 3)

Step-by-step explanation:

The area of ​​the RMC triangle is 43.4.

3 sides, 3 corners, 3 corners form a closed triangle. The mathematical sign of a three-sided triangle is RMC. Triangle-shaped sandwiches and signs are the most common triangles.

Three sides and three interior angles together define a triangle (a rectilinear polygon). This symbol is used to represent one of the basic geometric shapes with three connected vertices.

Triangles are classified in different shapes depending on their sides and angles. Different parts form a triangle. It consists of 3 corners, and 3 sides.

If we round the area to the nearest 10th digit then it will be 116.

Use the Law of Cosines to find the length of the third side RC: RC = [tex]sqrt(19^2 + 27^2 - 2(19)(27)cos(27))[/tex]

Compute the semi-perimeter s = (19+27+RC)/2

Compute the area of the triangle with Heron's formula

A = [tex]sqrt(s(s-a)(s-b)(s-c))[/tex]

After the calculation, we can get the area is approximately 43.4

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No, thirty-two is not a prime number i.e., it is a composite number.

A prime number is a number that has only two divisors that is 1 and the number itself. Consider the number 7, which has only two factors, 1 and 7 so it is a prime number. As another example, let's take the example of 8, which has two or more divisors of 1, 2, 4, and 8. This means that 8 is not prime i.e., it is a composite number. I have a number 32 and I need to check if it is prime. To do this, we need to determine 32 factors. The factors of 32 are 1,2,4,8,32, so 32

= 1×2×2×2×2. Here we see that 2, 4, and 8 are factors of 32 that are different from 1 and 32. So there are more than two factors. Therefore it is not prime.

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Complete question:

Is 32 a prime number?

The Cartesian Product of sets A and B is defined as the set of all ordered pairs (x, y) such that x belongs to A and y belongs to B.

Now, According to the question:

Cartesian Product of Vector Spaces:

The Cartesian product U × V of two finite-dimensional vector spaces U and V consists of all pairs {u, v} of vectors u in U and v in V. The vector space operations are defined component wise: (1) (2).

The Cartesian product of two vectors is :

The Cartesian Product of sets A and B is defined as the set of all ordered pairs (x, y) such that x belongs to A and y belongs to B. For example, if A = {1, 2} and B = {3, 4, 5}, then the Cartesian Product of A and B is {(1, 3), (1, 4), (1, 5), (2, 3), (2, 4), (2, 5)}.

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the angle between 0 and 2pi in radians that is coterminal to 44pi/9 then terminal angle for 43pi/10 is 3pi/10.

How do you find Coterminal angles?

The coterminal angles can be positive or negative. To find the coterminal angles, simply add or subtract 360 degrees as many times as needed from the reference angle. All of these angles are coterminal angles.

The coterminal angle lie in between [0, 2pi].

Simplify the coterminal angle 43pi/10 to obtain in [0, 2pi].

43pi/10= 4pi+3pi/10

So coterminal angle for 43pi/10 is 3pi/10.

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Latitude is always presented before longitude when giving a coordinate. Degrees, minutes, and seconds are used to divide latitude and longitude. While a degree is made up of 60 minutes, a minute is made up of 60 seconds.

Latitude lines run parallel with each other from east to west. The more north you travel, the higher the latitude values. Last but not least, latitude values vary from -90 to +90. However, longitude lines run from north to south. Latitudes are lines that are horizontal and indicate how far away from the equator a location is. East and west directions with reference to the Greenwich, England, meridian are shown using longitudes, which are vertical lines. Cartographers and geographers. The grid system that enables us to locate precise or absolute locations on the surface of the globe is made up of latitude and longitude meridian. Drawing imaginary lines that circle the globe vertically (up and down) and connect at the North and South Poles is one step in the longitude calculation.

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For Identifying the Similar Triangles Here are three ways to show that two triangles are similar.

AA Similarity Two angles of one triangle are congruent to two angles of another triangle.

SSS Similarity The measures of the corresponding side lengths of two triangles are proportional.

SAS Similarity The measures of two side lengths of one triangle are proportional to the measures of two corresponding side lengths of another triangle, and the included angles are congruent.

Intervention is the The measures of two side lengths of one triangle are proportional to the measures of two corresponding side lengths of another triangle, and the included angles are congruent.

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The function that has the lowest minimum value is given as follows:

f(x) = 3/4|x - 8| - 3.

From the table, the minimum value of the function is given at the following coordinate:

(3,-2).

Hence the minimum value is of -2.

The parent absolute value function is given as follows:

f(x) = |x|.

After the vertical compression by a factor of 3/4, the function is given as follows:

f(x) = 3/4|x|.

Shifting 8 units right, the function is of:

f(x) = 3/4|x - 8|.

Shifting 3 units down, the function is of:

f(x) = 3/4|x - 8| - 3.

Meaning that the minimum value is of -3, which is lower than the minimum value of -2 of the function on the table.

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Answer:

The same thing to both sides.

Step-by-step explanation:

The correct way to write greater than B is A > B where it tells that B having greater value than A.

In mathematics,

→The greater than symbol (>) is used to indicate that one value is larger than another. For example, if we say "A > B," this means that the value of A is greater than the value of B.

→The less than symbol (<) is the opposite, it indicates that one value is smaller than another. For example, if we say "A < B," this means that the value of A is less than the value of B.

→The greater than or equal to symbol (≥) indicate that one value is larger than or equal to another. For example, if we say "A ≥ B," this means that the value of A is greater than or equal to the value of B.

→The less than or equal to symbol (≤) indicate that one value is smaller than or equal to another. For example, if we say "A ≤ B," this means that the value of A is less than or equal to the value of B.

These symbols are commonly used in mathematical expressions, equations, and inequalities.

To write "greater than B" in mathematical notation, you would use the greater than symbol (>) followed by the letter B. For example:

A > B

This means that A is greater than B.

Therefore, the correct way to write greater than B is A > B where it tells that B having greater value than A.

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The ​equation of the line is equal to y - 8 = 1/3 (x + 2).

y = mx + c

m = slope

c = y-intercept

Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given that the line has a slope 1/3 and passes through (-2,8). The equation of the line will be,

y - y₁ = m(x - x₁)

y - 8) = (1/3)(x + 2 )

Therefore, the ​equation of the line is equal to y - 8 = 1/3 (x + 2).

The complete question is,

Write an equation in point slope form for the line that has a slope 1/3 and passes through (-2,8)

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s = 990 / (-22)

s = -45

The answer is -45

Answer:

s = -45

Step-by-step explanation:

Now we have to,

→ find the required value of s.

The equation is,

→ -22s = 990

Then the value of s will be,

→ -22s = 990

→ s = 990/-22

→ s = -(990/22)

→ [ s = -45 ]

Hence, the value of s is -45.

Answer:

5x – 30 = 176

Step-by-step explanation:

The vertex of the given function g(x) = -3x² + 18x + 2 is (3, 29)

Function in math is defined as  a rule that gives value of a dependent variable that corresponds to specified values of one or more independent variables.

Here we have given the function called g(x)  has the expression -3x² + 18x + 2.

And here we need to find the vertex for the function that can be calculated as,

As we all know that vertex form of a parabola is written as,

=> y = a (x - h)² + k

Here we know that (h, k) is the vertex

Then the given expression is written as,

=> g(x) = -3x²  + 18x + 2

When we can be written by completing the square as follows,

=> y = -3x²  + 18x + 2

Here we have to take 3 as common term, then we get

=> -3(x²  + 6x)+ 2

now, we have to expand the expression within the brackets, then we get,

=> -3(x²  + 6x+ 9)+ 2 + 27

Then the resulting vertex form o the equation is written as

=> y = - 3(x - 3)2 + 29

While we comparing this with the standard form then we get the value of vertex is (3, 29).

Complete Question:

What is the vertex of the function g(x) = -3x² + 18x + 2?

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Solving the provided question, we can say that Pythagorean theorem to find the length of the paper as follows [tex]9.9^2 = 9.2^2 + (length)^2[/tex] => length = 3.656 inches

The Pythagorean Theorem, sometimes known as the Pythagorean Theorem, is the basic Euclidean geometry relationship between a right triangle's three sides. According to this rule, the area of a square with the hypotenuse side equals the sum of the areas of squares with the other two sides. The Pythagorean Theorem, often known as the generic algebraic notation a2 + b2 = c2, states that the square that crosses the hypotenuse of a right triangle opposite the right angle equals the sum of the squares that span the sides of a right triangle.

the Pythagorean theorem to find the length of the paper as follows:

[tex]9.9^2 = 9.2^2 + (length)^2\\length = \sqrt{9.9^2 - 9.2^2} \\length = \sqrt{98.01 - 84.64}\\ length = \sqrt{13.37} \\[/tex]

length = 3.656 inches

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MO is a perpendicular bisector of NP.The value of x is 3

Lines that cross each side's midpoint and are perpendicular to the specified side are known as a triangle's perpendicular bisectors.The circumcenter (Durell 1928), which is also the centre of the triangle's circumcircle,

Measuring the length of the line segment you need to bisect is an easy approach to discover a perpendicular bisector. Find the midway of the measured length by dividing it by two. From this midway, extend a line at a 90° angle.

6x−1=3x+8

⇒6x−3x=8+1

⇒3x=9

⇒x = 9 / 3 =3

∴x = 3.

MO is a perpendicular bisector of NP.The value of x is 3

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If O is the center of the circle in the figure, the value of x. is 80°.

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle has rotational symmetry around the center.

Simply put, a circle is a rounded shape without any edges or line segments. It has the geometric shape of a closed curve. The distance between the circle's points and its center is fixed. A circle is a spherical shape without boundaries or edges. A circle is a closed, curved object with two dimensions in geometry.

Given: ∠ BAC = 35°, ∠ DBC = 65°,

∠BDC = ∠BAC = 35° (Angle in same section).

∠BDC + ∠BCD + ∠DBC = 180° in ABCD.

35° + x + 65° = 180°

⇒ 100° + x = 180°

. '. x = 80°

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Complete question -

The area of the triangle xyz is 33.941...

To calculate area of triangle, we need to take the base and height's measurement.

Formula- 1/2 x Base x Height

However, Area may also be calculated when we know the 3 sides of the triangle.

It is known as "Heron's Formula"

Simply use this 2 step process :

Step 1-

Calculate "S" (which is half of the triangle's perimeter)

S = (side1 + side2 + side3) / 2

Naming the sides as a b and c respectively.

4 inches = a

5 inches = b

7 inches = c

 S = ( a + b + c ) / 2

S = ( 4 + 5 + 7 ) / 2

S = 16/2

S = 8

Step 2: Calculating the area of the triangle XYZ

Formula:

Area ( A ) = √S(S−a)(S−b)(S−c)

put the values and you will get the answer.

A = √8(8−4)(8−5)(8−7)

A = 33.941..

The area of the triangle xyz is 33.941...

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Answer:

14 square inches

Step-by-step explanation:

Area of triangle = (h.b)/2

The height and base aren't specified, and no pic is provided

So I'll assume that the height is 4 and base is 7 ( or the opposite)

Area = (4.7)/2

= 14 square inches

If the height is 5 and base 7 ( or the opposite)

Area = (5.7)/2

= 17.5 square inches

If the height is 4 and base is 5 ( or the opposite)

Area= (4.5)/2

= 10 square inches

Answer:

∠ PQS = 15°

Step-by-step explanation:

PQRS is a cyclic quadrilateral

• the opposite angles of a cyclic quadrilateral sum to 180° , then

∠ QPS + ∠ QRS = 180°

∠ QPS + 105° = 180° ( subtract 105° from both sides )

∠ QPS = 75°

the sum of the 3 angles in Δ PQS = 180° , that is

∠ PQS + ∠ PSQ + ∠ QPS = 180°

∠ PQS + 90° + 75° = 180°

∠ PQS + 165° = 180° ( subtract 165° from both sides )

∠ PQS = 15°

The average ticket price for the concert, expressed in dollars, is given by the equation P = (TP + PR)/(T + ).

The average ticket price, P, in dollars, of all tickets sold to the concert is represented by the equation P = (T + ηR)/(T + η) where T is the original ticket price, R is the price increase, η is the number of tickets sold on the day of the concert, and T + η is the total number of tickets sold to the concert.

In this scenario, before the concert, the theater sells T tickets at a price of P dollars each, and on the day of the concert, the theater increases the ticket price by R dollars and sells η tickets.

Therefore, the average ticket price for all the tickets sold is the sum of the original ticket price and the increased ticket price, divided by the total number of tickets sold.

P = (TP + η(P+R))/(T + η)

P = (TP + ηPR)/(T + η)

So, the equation P = (TP + ηPR)/(T + η) represents the average ticket price, in dollars, of all tickets sold to the concert.

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There were 192 birds in the aviary in total.

There were 16 habitats in the aviary at the zoo, and each habitat had 12 birds. To find out how many birds were in the aviary in total, we need to multiply the number of habitats by the number of birds in each habitat.

16 habitats * 12 birds/habitat = 192 birds

So there were 192 birds in the aviary in total.

This is done by using the distributive property of multiplication. Basically, if you have a certain number of groups, each containing a certain number of items, and you want to find the total number of items, you can multiply the number of groups by the number of items in each group. In this case, the number of groups is the number of habitats (16) and the number of items in each group is the number of birds (12). So by multiplying those two numbers together, we get the total number of birds in the aviary.

Therefore, There were 192 birds in the aviary in total.

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16 areas with 12 birds each equals 192 birds.

Thus, there were 192 animals in all in the aviary.

Utilizing multiplication's distributive principle, this is accomplished. Basically, you can increase the total number of groups by the total number of items in each group if you have a certain number of groups, each of which contains a specific number of items. In this instance, the number of objects in each group equals the number of birds, and the number of groups equals the number of habitats (16). (12). We can calculate the overall number of birds in the aviary by multiplying those two numbers.

Consequently, there were 192 animals in all in the aviary.

The possible solution to the system of linear inequalities is (40, 4)

An equation is an expression showing the relationship between numbers and variables.

An inequality shows the non equal comparison of two or more numbers and variables.

Given the inequalities:

x + y ≥ 35    (1)

and:

0.40x + 2y ≤ 30    (2)

The solution to the system of linear inequalities is the darker region shown in the graph. A possible solution is (40, 4)

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