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Topic 12 Reteaching

The procedure to simplify fractions is presented in this answer.

The steps to simplify a fraction are given as follows:

For example, let's say we want to simplify the fraction 12/24:

Another example, let's say we want to simplify the fraction 16/20:

Note that a fraction is in its simplest form when its numerator and denominator have no common factors other than 1.

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Explanation:

We have 5 green in the 1st row and 4 green in the 2nd row.

The LCM is 5*4 = 20.

The ratio [tex]6 \text{ yellow} = 5 \text{ green}[/tex] scales up to [tex]24 \text{ yellow} = 20 \text{ green}[/tex] after multiplying both sides by 4.

The ratio [tex]4 \text{ green} = 3 \text{ purple}[/tex] scales up to [tex]20 \text{ green} = 15 \text{ purple}[/tex] after multiplying both sides by 5.

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These set of ratios

[tex]6 \text{ yellow} = 5 \text{ green}\\\\4 \text{ green} = 3 \text{ purple}\\\\[/tex]

scale up to

[tex]24 \text{ yellow} = 20 \text{ green}\\\\20 \text{ green} = 15 \text{ purple}\\\\[/tex]

The key is the "20 green" on each line. This leads to the ratios linking up.

If A = B and B = C, then A = C (transitive property).

So we can say [tex]24 \text{ yellow} = 20 \text{ green} = 15 \text{ purple}\\\\[/tex]

That simplifies to [tex]24 \text{ yellow} = 15 \text{ purple}\\\\[/tex]

We can divide both sides by 3 to get [tex]8 \text{ yellow} = 5 \text{ purple}\\\\[/tex]

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We now have these set of ratios

[tex]8 \text{ yellow} = 5 \text{ purple}\\\\5 \text{ purple} = 2 \text{ red}\\\\[/tex]

Connect those two equations together to get

[tex]8 \text{ yellow} = 2 \text{ red}\\\\[/tex]

Lastly, divide both sides by 4

[tex]4 \text{ yellow} = 1 \text{ red}\\\\[/tex]

The equation that represents a quadratic function is option b: [tex]y=3x^2-5x+9[/tex]

What is a quadratic function ?

A quadratic function is a function that can be written in the form of f(x) = [tex]ax^2 + bx + c[/tex] , where a, b, and c are constants, and a is not equal to 0. The graph of a quadratic function is a parabola, which can open upwards or downwards, depending on the sign of the coefficient a.

In option b, we can see that the equation is in the form of [tex]f(x) = 3x^2 - 5x + 9[/tex] , which is a quadratic function. The coefficient of [tex]x^2[/tex] is a non-zero constant (a=3), which means that the graph of this function is a parabola.

Option a is not a quadratic function, as it is in the form of [tex]x=y^2-2y+4[/tex], which is a quadratic equation in terms of y, but not in terms of x.

Option c is a little more complicated, as it contains a radical term. However, if we simplify it, we can see that it is also a quadratic function, in terms of x.

Option d is a linear equation, not a quadratic function, because it does not have an [tex]x^2[/tex] term.

Therefore, the quadratic function is [tex]y=3x^2-5x+9[/tex], option b.

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Answer:

-72

Step-by-step explanation:

Because -32 + (2 - 6)(10). is -72

Using the inequality rule we know that 11 is greater than -11, (11 > -11).

Mathematical expressions with inequalities are those in which the two sides are not equal.

Contrary to equations, we compare two values in inequality.

Less than (or less than or equal to), greater than (or greater than or equal to), or not equal to signs are used in place of the equal sign.

Two expressions in inequality aren't always equal, which is denoted by the symbols >, <, ≤, or ≥.

So, let's say the inequality equation looks like this: A

Right now, A is valued at

Let p be used to representing the initial number.

P equals 11, so

Let q be used to representing the second number.

Q has a value of -11.

-11 and 11 are both numbers that are greater than zero.

Then, 11 > -11 ... (1)

A has a value of 11 > -11.

Therefore, using the inequality rule we know that 11 is greater than -11, (11 > -11).

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Correct question:
Is 11 greater than, equal to, or less than -11?

The probability that either event will occur is given as follows:

P(A or B) = 0.83.

A probability is calculated as the division of the desired number of outcomes by the total number of outcomes in the context of a problem/experiment.

The "or probability" is defined as follows:

P(A or B)=P(A) + P(B) - P(A and B).

From the Venn Diagram, the probabilities of each event are given as follows:

Hence the or probability is given as follows:

P(A or B) = 0.5 + 0.3333 + 0

P(A or B) = 0.83. (rounded to the nearest hundredth).

The Venn diagram is given by the image presented at the end of the answer.

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The evaluation of the expression consisting of surds indicates that we get;

(9·x + 42 - 69·√x)/(x - 49)

A surd is a value under a square root sign, which can not be further simplified into fractions or whole numbers.

The expression (9·√x - 6)/(√x + 7), can be simplified by using the rationalization of surds technique as follows;

(9·√x - 6)/(√x + 7) = ((9·√x - 6)/(√x + 7)) × ((√x - 7)/(√x - 7))

(√x + 7) × (√x - 7) = ((√x)² - 7²) = (x - 49)

(9·√x - 6) × (√x + 7) = 9·x + 42 - 69·√x

Therefore; (9·√x - 6)/(√x + 7) = (9·x + 42 - 69·√x)/(x - 49)

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The area of the irregular shape is 34m²

The area of a shape is the space occupied by the boundary of a plane figures like circles, rectangles, and triangles

The shape above can be divided into three rectangles and the sum of the area of this rectangles is the area of the shape.

Area of rectangle 1

= l× w

= 7×2 = 14 m²

Area of rectangle 2

= l× w

= 5×2 = 10 m²

Area of rectangle 3

= l×w

= 5×2 = 10m²

Therefore , the area of the irregular shape is

14+10+10 = 34m²

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The approximate time, compass heading, distance, and fuel consumed during the climb of the airplane are 18 minutes, 214°, 2,430 nautical miles, and 3.9 gallons, respectively.

To determine the approximate time, compass heading, distance, and fuel consumed during the climb of the airplane, we need to use some basic principles of navigation and aviation.

First, we need to calculate the climb time. Since the airplane is climbing at a rate of 500 ft/min and the cruise altitude is 9,500 ft, the time it takes to climb to the cruise altitude can be calculated as (9,500-1,000)/500 = 18 minutes.

To calculate the compass heading, we need to account for the variation and deviation. The true course is given as 215°, and the variation is 3° W, which means we need to subtract 3° from the true course to get the magnetic course.

Therefore, the magnetic course is 215° - 3° = 212°. Next, we need to account for the deviation, which is given as -2°, meaning we need to add 2° to the magnetic course to get the compass heading. Therefore, the compass heading is 212° + 2° = 214°.

The distance traveled during the climb can be calculated using the average true airspeed and the climb time. The distance is given by the formula: distance = airspeed x time. Therefore, the distance traveled during the climb is approximately 135 kts x 18 min = 2,430 nautical miles.

Finally, we can calculate the fuel consumed during the climb using the average fuel consumption rate. The fuel consumed is given by the formula: fuel consumed = fuel consumption rate x time. Therefore, the fuel consumed during the climb is approximately 13 gal/hr x 18 min/60 min = 3.9 gallons.

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According to the information, we can infer that the correct sentences about the graph is A person with annual income of at least $50,000 is more likely to be 45 years old or above.

To find the correct sentence we have to analyze the information of the graph and read the options. Once we make this procedure, we can compare each sentence with the information of the graph to establish the correct one.

According to the information the correct option would be A person with annual income of at least $50,000 is more likely to be 45 years old or above (option C).

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Answer:

Step-by-step explanation:

The total amount of money she spent on books and notebooks is:

2/3x + 1/6x = 5/6*x

Jessica had $30 left, so we can set up an equation:

x - 5/6*x = 30

Simplifying the equation:

1/6*x = 30

x = 180

When they are at the same altitude, the distance between the planes will be 3962 feet.

Because the air is less dense at high altitudes, planes can fly quicker and consume less fuel. Additionally, at altitudes of 30,000 feet or more, airplanes may steer clear of weather systems, improving the comfort level inside.

The majority of commercial airplanes are permitted to soar as high as 42,000 feet. This upper limit is frequently referred to as a "service ceiling."

The planes will be at the same altitude when t seconds have passed, in which case 25.25t + 2548 = 70.75t,

45.5t = 2548 t = 56 seconds,

and 70.75 * 56 = 3962 feet.

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Answer:

131072

Step-by-step explanation:

Answer: The answer is 131072.

Step-by-step explanation:

Using a calculator, we find that [tex]2^{17}=\boxed{131072}.[/tex]

Gold costs less than platinum per ounce because the slope of the graph for gold is less steeper than that of the chart for platinum. The slope of the graph tells you the unit rate in dollars.

In Mathematics, a steeper slope simply means that the slope of a line is bigger than the slope of another line. This ultimately implies that, a graph with a steeper slope has a greater (faster) rate of change in comparison with another graph.

In Mathematics and Geometry, the slope of any straight line can be determined by using the following mathematical equation;

Slope (m) = (Change in y-axis, Δy)/(Change in x-axis, Δx)

Slope (m) = rise/run

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

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Answer: 28.27m^2

Step-by-step explanation:

Area of a circle: [tex]A = \pi r^{2} \\[/tex]

Given the diameter of 6m, we can divide that by 2 to get the radius and plug that into the formula.

6/2 = 3m

[tex]A = \pi (3)^2\\A= 28.27m^{2}[/tex]

The equation of the reflected graph is y = -3ˣ.

To reflect a graph over the x-axis, we need to negate the y-coordinates of all the points on the original graph. In other words, if a point (x, y) is on the original graph, its reflection over the x-axis would be (x, -y).

Let's apply this concept to the exponential function f(x) = 3ˣ. The graph of this function is an upward sloping curve that passes through the point (0,1) on the y-axis. If we reflect this graph over the x-axis, the point (0,1) will be mapped to (0,-1), as the x-coordinate remains the same, but the y-coordinate changes sign.

To find the equation of the reflected graph, we need to replace y with -y in the equation of the original function f(x) = 3ˣ. This gives us:

-y = 3ˣ

To isolate y, we can multiply both sides by -1:

y = -3ˣ

This function is a downward sloping curve that passes through the point (0,-1) on the x-axis.

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The face value of the note is $9,000.

The face value of a note is the principal value mentioned or stated on the note.

The face value is different from the maturity value or the discounted value.

The maturity value refers to the face value plus accumulated interest.

The discounted value is a value less than the maturity value received for discounting the note before its maturity date.

The face value of the note = $9,000

Note period or maturity period = 60 days

Note interest = 8%

Note issuance date = April 15

Note maturity date = June 14

Maturity value = $9,120 ($9,000 + $9,000 x 8% x 60/360)

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Answer:

If a sample of 99 students is taken from a population of 352 students, the population variance, σ2, is the variance of the entire population, which includes all 352 students. Therefore, the answer is (B) 352.

It's worth noting that the sample of 99 students could be used to estimate the population variance if certain assumptions are met and appropriate statistical methods are used. However, the question specifically asks for the population variance, which refers to the variance of the entire population, not just the sample.

Answer:

If a sample of 99 students is taken from a population of 352 students, the population variance, σ2, is the variance of the heights of all 352 students in the population.

Therefore, the answer is B. 352.

The correct statements describing the area and perimeter of the patio are:

The area of a rectangle is given by the product of its length and width. So, the area of the patio is:

Area = length x width

Area = (1 + 2x)(2 - 3x)

Therefore, the area of the patio is (1 + 2x)(2 - 3x) square yards.

The perimeter of a rectangle is given by the sum of the lengths of all four sides.

So, the perimeter of the patio is:

Perimeter = 2(length + width)

Perimeter = 2(1 + 2x + 2 - 3x)

Perimeter = 2(3 - x)

Therefore, the perimeter of the patio is 2(3 - x) yards.

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Answer: Hi! Read the explanation below:

Brainliest?

Step-by-step explanation:

Student 1 correctly started the proof.

To complete the proof using the law of sines, student 1 should use the fact that the sum of angles in a triangle is 180 degrees to obtain an expression for angle C, and then use the fact that the sum of the lengths of the opposite sides of an angle in a triangle is equal to the length of the third side to obtain an expression for side c in terms of sin(A) and sin(B).

Here's the complete proof:

Starting with Student 1's work:

bsin(A) = h

asin(B) = h

Using the fact that the sum of angles in a triangle is 180 degrees:

C = 180 - A - B

Using the fact that the sum of the lengths of the opposite sides of an angle in a triangle is equal to the length of the third side:

a/sin(A) = b/sin(B) = c/sin(C)

Substituting in the expressions for c and sin(C) in terms of sin(A) and sin(B):

a/sin(A) = b/sin(B) = 2h/(sin(A)+sin(B))

Simplifying:

a = 2hsin(A)/(sin(A)+sin(B))

b = 2hsin(B)/(sin(A)+sin(B))

c = 2hsin(C)/(sin(A)+sin(B)) = 2hsin(180-A-B)/(sin(A)+sin(B)) = 2h*sin(A+B)/(sin(A)+sin(B))

Therefore, the law of sines is:

a/sin(A) = b/sin(B) = c/sin(C) = 2h/(sin(A)+sin(B))

1.The measure of the central angle is 90°.

2.Equation of x=12.

3.The measure of the angle that bisects the minor arc is 45°.

4.The measure of the major arc is 270°.

The circle in the example illustration has a radius of 10 units and a centre of O. AOB is a central angle that the minor arc AB intercepts.

The fact that the measure of a central angle is equal to the measure of its intercepted arc can be used to determine the measure of the central angle. So, we must determine the minor arc's measure, AB. The circle's diameter is 2r = 20 units because its radius is 10 units. The minor arc AB is one-fourth of the circle's circumference, or (1/4) * 20 = 5 units. As a result, the minor arc's measure is 5 radians.

Radians to degrees conversion

5π * (180/π) = 90° degrees

Therefore, the measure of the central angle AOB is 90° degrees.

To find  Equation of x,

8x=96°

x=96°/8

x=12

Hence, Equation of x will be 12.

The angle that bisects the minor arc AB is half the measure of the central angle AOB. So, the measure of the bisecting angle is:

(1/2) * 90° = 45°

The major arc ACB is the difference between the circumference of the circle and the minor arc AB. So, the measure of the major arc ACB is:

2πr - 5π = 15π

for major arc,

We must multiply by (180/) degrees/radian in order to convert the measure from radians to degrees. The main arc ACB's degree measurement is as follows:

15π * (180/π) = 270°

Therefore, the measure of the major arc ACB is 270°.

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Answer:

Jamie gets £9.60

Step-by-step explanation:

sum the parts of the ratio, 2 + 3 = 5 parts

divide the amount by 5 to find the value of one part of the ratio.

£24 ÷ 5 = £4.80 ← value of 1 part of the ratio , then

2 parts = 2 × £4.80 = £9.60 ← amount Jamie gets

Answer:

40 plus 19/ 9-3=40

5/6 can be rewritten with a least common denominator of 6 as 10/12.

Fracture is  part of the whole. A fraction consists of two parts, the numerator and the denominator. Numerator: The numerator represents the number  above the fraction bar. For example, for 6/7, 6 is the numerator. Denominator: The denominator shows the number  placed under the fraction bar.  

We can write 5/6 in the lowest common denominator, we need to find the common multiple of 6. The smallest multiple  is 2. So we can write 5/6 with the lowest denominator  6 as follows:

5/6 = (5/6) x (2/2) = 10/12

Therefore, 5/6 can be rewritten as 10/12 with a lowest common denominator of 6.

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I actually do not know because I am still in grade 6

The equation of a line that is perpendicular to the line y = –4x + 3 and passes through the point (8, 1) is y = 1/4(x) - 1

In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):

y - y₁ = m(x - x₁)

Where:

Since the equation of this line is perpendicular to the line y = –4x + 3, the slope is given by;

Slope, m = -4

m₁ × m₂ = -1

-4 × m₂ = -1

m₂ = -1/-4

Slope, m₂ = 1/4

At data point (8, 1) and a slope of 1/4, a linear equation for this line can be calculated by using the point-slope form as follows:

y - y₁ = m(x - x₁)

y - 1 = 1/4(x - 8)  

y = 1/4(x) - 1

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Answer:

75%

Step-by-step explanation:

99/132=0.75

Answer:

75% of the chairs are red

Step-by-step explanation:

99/132 chairs are red. When divided, that equals 0.75. 0.75 is equivalent to 75%.