14/35 Marks
Which one of these grids is shaded red and blue in the ratio 1: 2?
B
C
E
F

Shapes that are identical to each other are considered congruent. There are no differences in the matching sides or angles.

What is a congruent shape?

Congruent refers to things that are exactly the same size and shape. Even if we flip, turn, or rotate the forms, the shape and size should remain the same.

Congruent refers to something that is "absolutely equal" in terms of size and shape. The shapes hold true regardless of how we rotate, flip, or turn them.

Shapes that are identical to one another are said to be congruent. Both the matching sides and the corresponding angles match. We must examine all of the shapes' angles and sides in order to accomplish this. Two shapes that are similar to one another can be stacked perfectly.

Here is the format you requested:

△ABC = △DEC due to AAS

Angle A = Angle D Given

Angle B = Angle E Alternate Interior

Angle C1 = Angle C2 Vertically Opposite

AB = DE Congruent Sides

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Answer:

m1 = 4, m2 = 176

Step-by-step explanation:

Using complementary angle rule you know the total angle is 180 thus:

[tex]180 - (x-18) = 8x\\198 - x = 8x\\198 = 9x\\x = 22[/tex]

m1 = (22 - 18) = 4

m2 = 8(22) = 176

The sixth term of the arithmetic progression is 94.

An arithmetic progression is a sequence of numbers such that the difference between any two successive members of the sequence is a constant.

Let's call the first term of the arithmetic progression "a" and the common difference "d". Then the nth term of the progression can be found using the formula:

an = a + (n-1)d

We know that the sum of the first four terms is 14, so we can set up the following equation:

a + (a+d) + (a+2d) + (a+3d) = 14

We also know that the sum of the first eight terms is 108, so we can set up another equation:

a + (a+d) + (a+2d) + (a+3d) + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108

Now we can use the first equation to substitute for the first four terms of the second equation:

14 + (a+4d) + (a+5d) + (a+6d) + (a+7d) = 108

This gives us:

a + 4d = 94

So the sixth term can be found by substituting n = 6 into the first formula:

a + (6-1)d = a + 5d = 94

Therefore, the sixth term of the arithmetic progression is 94.

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The probability of selecting an orange marble is 0.33.

Option B is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

The number of times each marble is selected.

Green = 4

Black = 6

Orange = 5

Total number of times all marbles are selected.

= 4 + 6 + 5

= 15

Now,

The probability of selecting an orange marble.

= 5/15

= 1/3

= 0.33

Thus,

The probability of selecting an orange marble is 0.33.

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An equation for the plane consisting of all points that are equidistant from the points (1,4,4) and (-4, 1, 2) is 5x+3y+2z-6=0

Given, the points are (1, 4, 4) and (-4, 1, 2).

We have to find an equation for the plane consisting of all points that are equidistant from the given points.

Let the parametric point be (x, y, z) on the plane which is equidistant from the given points.

Using the distance formula:

[tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2+(z_{2}-z_{1} )^2 } }[/tex]

Distance between the points (x, y, z) and (1, 4, 4)

=[tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}[/tex]

Distance between the points (x, y, z) and (-4, 1, 2)

=[tex]\sqrt{(x-(-4)^2+(y-1)^2+(z-2)^2}\\\\ \sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]

Given, [tex]\sqrt{(x-1)^2+(y-4)^2+(z-4)^2}=\sqrt{(x+4)^2+(y-1)^2+(z-2)^2}[/tex]

By using algebraic identity,

(a-b)² = a²-2ab+b²

(a+b)² = a²+2ab+b²

(x² - 2x + 1)+(y²-8y+16)+(z²-8z+16)=(x²+8x+16)(y²-2y+1)+(z²-4z+4)

x²+y²+z²-2x-8y-8z+1+16+16=x²+y²+z²+8x-2y-4z+16+1+4

By grouping,

-2x-8x-8y+2y-8z+4z+33-21

-10x-6y-4z+12=0

Dividing by -2 into both sides,

5x+3y+2z-6=0

Therefore, the equation of the plane is 5x+3y+2z-6=0

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The weight of the cat is equal to 24.5 Newton.

In Science, weight can be defined as the force acting on an object or a physical body due to the effect of gravity. Mathematically, the weight force on a physical body can be calculated by using this formula:

Fg = mg

Where:

Note: Acceleration due to gravity is equal to 9.8 m/s².

Substituting the given parameters into the weight formula, we have;

Weight, Fg = 2.5 × 9.8

Weight, Fg = 24.5 Newton.

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The solution to the inequality is x < 6

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

x - 8 < -2

Add 8 to both sides of the inequality

So, we have the following representation

x - 8 + 8 < -2 + 8

Evaluate the sum in the expression

x < -2 + 8

Evaluate the other sum

x < 6

Hence, the solution is x < 6

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The distributive property states that for any real numbers a, b and c, the following is true:

a(b + c) = ab + ac

To use the distributive property to write an expression that is equivalent to 6 - 9x, we can factor out the -9x from the second term:

6 - 9x = 6 - 9x + 0 - 0x = 6 - 9x + (-9x) = 6 + (-9x)

Therefore, using the distributive property, we can write an expression that is equivalent to 6 - 9x as:

6 + (-9x)

Answer:

-3 ( 3x - 2 )

Step-by-step explanation:

- 9x + 6

Answer:

c

Step-by-step explanation:

c

Here, b = 6 is a solution for the equations 8b = 48, b + 3 = 9 and 54  ÷ b = 9 but not a solution for 4 = b + 11 - 3b.

Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and typically consist of two expressions connected by an equals sign, is known as solving an equation in mathematics.

One or more variables are designated as unknowns when looking for a solution. An assignment of values to the unknown variables that establishes the equality in the equation is referred to as a solution.

To put it another way, a solution is a value or set of values (one for each unknown) that, when used to replace the unknowns, cause the equation to equal itself. The term "equation's root" is frequently used to refer to an equation's solution, especially but not exclusively for polynomial equations.

Given to prove b = 6

a. 8b = 48

   b = 48/8

   b = 6

b = 6 is a solution

b. 4 = b + 11 - 3b

   3b - b = 11 - 4

   2b = 7

   b = 7/2

   b = 3.5

b = 6 is a not solution

c. b + 3 = 9

   b = 9 - 3

   b = 6

b = 6 is a solution

d. 54  ÷ b = 9

   9b = 54

   b = 54/9

   b = 6

b = 6 is a solution

Thus,  b = 6 is a solution for the equations 8b = 48, b + 3 = 9 and 54  ÷ b = 9 but not a solution for 4 = b + 11 - 3b.

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the length of the sections will be 24 and 18 respectively.

Parallel lines are lines in a plane that are always the same distance apart. Parallel lines never intersect. Perpendicular lines are lines that intersect at a right (90 degrees) angle.

Given, Some pair of lines in that three lines are parallel and two of them are intersecting them.

Since, these are the the section made by two parallel lines. Thus, these given section will be Proportional to each other.

Thus,

20/15 = ( 7x - 11)/(4x - 2)

4/3 = ( 7x - 11)/(4x - 2)

16x - 8 = 21x - 33

5x = 25

x = 5

therefore, the length of the sections will be 24 and 18 respectively.

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Answer:

29x+20

Step-by-step explanation:

If 10 people share 3 brownies equally, each person will get the same amount. To find out how much each person will get, you can divide the total number of brownies by the number of people.

Unitary Method:

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

3 brownies / 10 people = 0.3 brownies per person

So, each person will get 0.3 of a brownie. Since a brownie is a solid object, it is not possible for each person to get 0.3 of a brownie, It would be best to cut the brownies into 10 equal pieces.

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The vertex of the graph of the quadratic function f(x )= x² located at the origin of the graph.

The function f(x)=x²  looks like a quadratic equation.

The most basic quadratic function is f(x) = x², Its shape should look familiar from Intermediate Algebra – it is called a parabola. The point (0,0) is called the vertex of the parabola.

To find the vertex of a quadratic function on a graph:

Get the equation in the form y = ax²+bx+c.

Calculate -b/2a. This is the x-coordinate of the vertex.

To find the y-coordinate of the vertex, simply plug the value of -b/2a into the equation for x and solve for y. This is the y-coordinate of the vertex.

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If and only if a function is a bijective function, it has an inverse that is also a function.

Only in the condition, if a function is bijective, meaning it is both onto (surjective) and one-to-one (injective), it has an inverse that is itself a function. If there are no two random input values resulting in a similar output value, then the function is said to be injective. As a result, there is only one x-value that can yield a given y-value.

A unique inverse function cannot be determined for a function if it is not injective. Whereas, a function is surjective if at least one input value is required to produce each output value. As a result, there is at least a single x-value in the domain of the function that yields each y-value in the function's range. A function's inverse would not be defined for values in the range if it were not surjective.

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Nora will have $ 4.05 money.

Given that, Sam has 3. 50 less than Junho and 2. 30 less than Nora. Junhao has 4. 25.

By using the unitary method

The unitary approach is a methodology for problem-solving that involves first determining the value of a single unit and then determining the necessary value by multiplying the single unit value.

The unitary method's formula is to get the value of a single unit and then multiply that value by the number of units to obtain the required value.

Junhao has $4.25

so, Sam has =$4.25-3.50

= $1.75

::NORA HAS = $ 1.75 +2.30

= $ 4.05

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Answer:I apologize, but I am not able to understand your question as it is written in a mix of mathematical notation and text that is not clear. Could you please rephrase your question or provide more context? I'll be happy to help you with your question.

Step-by-step explanation:

Step-by-step explanation:

since a ratio is a fraction with all calculation and comparison rules (but with a special overall meaning), we need to observe the main rule for transforming fractions : when multiplying one part of the fraction by a factor, we also need to multiply the other part by the same factor to keep the value of the fraction unchanged.

the basic ratio is here

145/52 (or written 145:52 - it has the same meaning)

290/104 is just (145×2)/(52×2)

435/156 is just (145×3)/(52×3)

to complete the table we simply have to keep following that structure :

580 = 145×4

so, 52×4 = 208

and the ratio is

580/208

725 = 145×5

52×5 = 260

and the ratio is

725/260

Answer: Expression - 10.2x
The weight carried by each hiker is 10.2 pounds.

Step-by-step explanation:

Hello! To find the answer, you have to add all of the weight together. Do 3.4 + 4.6 + 2.2 = 10.2.  You know the total combined weight that all hikers will have to carry is 10.2 pounds.  The expression will be 10.2x.  You can check this by putting a random number in for x to represent the number of hikers.  10.2 (2) = 20.4.  20.4 would be the total weight that two hikers would have to carry, so the expression is correct.  You already know the weight each hiker will have to carry, 10.2 pounds, so you can put that in for the second question.

The value of the number x such that the quotient of the number,x and 19 is 10 is; 190.

As evident in the task content, the value of x is to be determined such that the quotient of a number, x and 19 is 10.

Since the statement given above can be written algebraically as;

x / 19 = 10

By multiplying both sides of the equation by 19; we have that;

x = 10 × 19

x = 190.

Ultimately, the value of x is; 190.

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In common inverse meaning is “something that is contrary or reverses”. When we define inverse meaning we will talk mostly from the mathematics point of view where we find the inverse of different operations and functions

The inverse of a given number is equal to number that is obtained by solving the operation 1/x where x is the initial number.

The inverse operation of subtraction is addition, the inverse operation of division is multiplication.

The inverse of a number should not be muddled with its opposite. While the inverse is 1/x, the opposite is equal to -x. That is, the inverse of 3 is equal to 1/3 while its opposite will be equal to -3.

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Answer: To find the answer to the expression x(-2.54y+6y-3.77)+x, I followed these steps:

Distribute the x coefficient:

x(-2.54y+6y-3.77) = -2.54xy + 6xy - 3.77x

Combine like terms:

-2.54xy + 6xy - 3.77x + x = -2.54xy + 6xy - 2.77x

Simplify the expression:

-2.54xy + 6xy - 2.77x

The result is a polynomial with x and y as variables, and the coefficients -2.54, 6, -2.77.

It is a good practice to check the work by substituting the variables with some numbers to see if the output is correct.

Step-by-step explanation:

Answer:

he given expression can be simplified as:

X(-2.54y+6y-3.77)+x

= X(-2.54y + 6y) + X(-3.77) + x

= X(3.46y) - 3.77X + x

= 3.46xy - 3.77X + x

So, the simplified form of the given expression is 3.46xy - 3.77X + x.

The corresponding point on the unit circle for the angle θ = 5pi/3  is given by: (0,5, -0.866).

What is the unit circle?

Basically, the unit circle is a circle with a radius of 1. It is used in trigonometry to help define and understand angles and their associated trigonometric values. The unit circle is centered at the origin (0, 0) of the coordinate plane, and each point on the circle is defined by its distance from the origin and its angle from the positive x-axis.

What is area of circle ?

The area of circle can be defined as the product of pi and square of radius of a given circle.

In this problem, we have that θ = 5pi/3 , hence:

cos θ = 0.5

sin θ = -0.866

Thus the point is (0,5, -0.866).

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Answer:

Step-by-step explanation:

A vertical line has undefined slope, but will always have an x-intercept. In this case, since the line goes through the point (-2,-9) we know that x will always equal -2. So therefore the equation of this vertical line will be x=-2.

The cost of the shirt given the ticketed price is $16.66.

When the price of an item is marked down, it means that the price of the item is reduced. The item would become cheaper after the mark down. The shirt would become cheaper after it is marked down.

Price of the shirt after the mark down = (1 - fraction of mark down in price) x ticketed price

= (1 - 1/3) x $24.99

= 2/3 x $24.99

= $16.66

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Answer:

B.10

Step-by-step explanation:

Because it increases by 10

If 60 adults ages 18-29 made resolutions, and 10% of adults are ages 18-29, we can infer that 600 people were surveyed.

How to calculate percentages?

Percentages are a way to express a number as a fraction of 100. To calculate a percentage, you can use the following formula:

(Part/Whole) x 100 = Percentage

The question states that 60 adults ages 18-29 made resolutions, but does not provide information about the total number of people surveyed. In order to determine the total number of people surveyed, we would need additional information about the percentage of adults that fall within the age range of 18-29.

If the percentage of adults ages 18-29 is 10%, and 60 adults in that age range made resolutions, we can use that information to determine the total number of people surveyed.

We can use the following formula:

(Total number of people surveyed) = (Number of adults ages 18-29 who made resolutions) / (Percentage of adults ages 18-29)

(Total number of people surveyed) = (60) / (0.10) = 600

Hence. If 60 adults ages 18-29 made resolutions, and 10% of adults are ages 18-29, we can infer that 600 people were surveyed.

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From the given angles of the triangle, it was possible to find the angle x=29°.

Triangles are geometric figures with three (3) sides. They present different classifications regarding their sides or angles.

Like a classification for angles, it is possible to cite, a right triangle. A triangle is classified as a right triangle when it presents one of your angles equal to 90º.

For another side, an equilateral triangle whose classification is associated with the sides. An equilateral triangle presents the three  equal sides.

Regardless of its classification, the sum of the a triangle's angles will always be 180°.

The question gives two angles: 50° and 101°. And, it asks the value of angle x.

Therefore,

50+101+x=180

x+151=180

x=180-151

x=29°

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Answer:

9

Step-by-step explanation:

16 divided by 8 equals 2

11-2=9

The most likely happened in Sandy's experiment is that,

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

Option D is the correct answer.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Tossing a coin:

The probability of getting a head = 1/2

The probability of getting a tail = 1/2

This is the theoretical probability.

Now,

Experiment probability:

Virtual coins too have the same probability of getting a head and a tail as compared to the theoretical probability.

Thus,

Sandy's experimental probability was exactly the same as the theoretical probability for all three experiments.

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Answer:Not Sure but it is not D at all so please don't use that!

Step-by-step explanation: