Simplify.

12.13 - 3.2 × 2.3 + 0.5^2

The word sentence that represents the equation 6(x + 3) = 42 is option A: The sum of 3 and six times some number is 42.

The word sentence that represents the equation 6(x + 3) = 42 is option A. The sum of 3 and six times some number is 42.

To understand why, let's break down the equation step-by-step:

So, option A correctly expresses the equation by stating that the sum of 3 and six times some number is 42.

23*2 = 46

5x-4 =46

5x = 50

x = 50/5 = 10

x = 10

Corresponding sides are congruent is not the correct answer here.

Similar triangles has same corresponding angles and the corresponding sides are in proportion and for the congruent triangles the corresponding angles and the corresponding sides are same.

Two triangles is similar if their corresponding angles are congruent and their corresponding sides are in equal proportion.

We can can think of a triangle having x°,  y°,  z° as it's interior angle and for the other triangle to be similar it must also have x°,  y°,  z° as it's interior angle and the first triangle has length of the 3 sides equal to some values the other triangle to be similar it's side must have values in the same multiples of the previous values of the first triangle.

Learn more about similar and congruent triangles here :

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The maximum value of the quadratic function f(x)=-[tex]x^2+8x-20[/tex] is -4, which occurs at x=4. This value can be found by using the vertex formula for parabolas.

The function in question is f(x)=-[tex]x^2[/tex]+8x-20. This is a quadratic function, and since the coefficient of [tex]x^2[/tex] is negative, the graph of the function will be a downward-opening parabola. To find the maximum value of this function, we need to determine the vertex of the parabola.

The vertex of a parabola in the form of f(x)=[tex]ax^2[/tex]+bx+c is given by the formula h=-b/(2a). Plugging in our coefficients a=-1 and b=8, we find the x-coordinate of the vertex to be h=-8/(2(-1))=4. To find the corresponding y-coordinate, which is the maximum value, we substitute x=4 into the original function [tex]ax^2[/tex]+bx+c:

f(4)=[tex]-4^2+8\times4-20[/tex]

f(4)=-16+32-20

f(4)=-4

Therefore, the maximum value of the function f(x)=-[tex]x^2+8x-20[/tex] is -4, which occurs at x=4.

Final answer:

It is inefficient to use a key where each symbol represents the value 1 in a picture graph because it can make the graph cluttered and hard to interpret, especially with large data sets. Picture graphs should simplify visualization of data, yet remain clear and easily comprehensible.

Explanation:

Using a key where each symbol stands for 1 in a picture graph might not be a good idea because picture graphs are meant to represent larger sets of data visually and efficiently. If each symbol represents only 1, the graph could quickly become cluttered and hard to read, especially if the data set is large. This defeats the purpose of a picture graph, which is to provide a clear and simplified visual representation of the data. Moreover, the choice of symbols in a mathematical context is arbitrary; they are placeholders that have no intrinsic significance, and what matters is the concept they represent.

For instance, when dealing with large quantities, using symbols that represent 10, 100, or any other convenient large number makes the graph much more readable and helps to emphasize important relationships and comparisons between different data sets. Similarly, when using equations, symbols are used as stand-ins for numbers, and changing a symbol does not affect the underlying relationship they represent. Introducing more effective representations pictures the concept that equations capture. Likewise, the practicality of picture graphs can be compared to other types of graphs, like pie graphs, bar graphs, and line graphs, each of which serves a different purpose and has its own best use scenario.

Using a key where each symbol stands for 1 in a picture graph can make it cluttered and confusing, especially for large data sets. It is advisable to use symbols to represent larger values or to choose different types of graphs for readability and clear communication of the data's relationships.

Using a key where each symbol stands for 1 in a picture graph could be inadvisable in some situations. For large quantities, having one symbol represent a single unit could make the graph cluttered and difficult to read. It is more effective to have symbols represent larger, rounded values so the graph remains clear and interpretable. The use of symbols in mathematics and graphs is generally arbitrary, and they can be chosen to best represent the data being visualized. For example, in equations or graphs illustrating one-dimensional kinematics, symbols are chosen to present information on position, velocity, and acceleration over time in a way that makes relationships between these physical quantities easily understandable.

When considering how to best display data, it's crucial to think about readability and the ease of extracting useful information from the graph. If a picture graph with one symbol representing 1 becomes too complex, it might be better to opt for other types of graphs like bar graphs or line graphs, depending on the data's characteristics. Furthermore, the real purpose of graphs is to capture and represent relationships or trends, which is often better achieved with symbols that represent more suitable quantities, especially when dealing with large numbers.

The glossary of key symbols and notation in mathematics reaffirms the concept that the symbols themselves are not inherently meaningful, but are placeholders to facilitate understanding of the relationships and quantities they represent. Therefore, when creating picture graphs, the key chosen should enhance the viewer's ability to quickly grasp the depicted information.

The jigsaw puzzle has a total of 1050 pieces, with 126 edge pieces and 924 inside pieces, based on the ratio 3:22 provided in the question.

To calculate the total number of pieces in the jigsaw puzzle, we need to use the given ratio of edge pieces to inside pieces, which is 3:22. If there are 924 inside pieces, and the ratio of edge pieces to inside pieces must remain constant, we can set up a proportion where the number of edge pieces is represented by x and the number of inside pieces by 924.

3:22 = x:924

To find the value of x, we can cross-multiply:

3 * 924 = 22 * x

This gives us :

2772 = 22x

Now, we can solve for x by dividing both sides of the equation by 22:

x = 2772 / 22

x = 126

This means there are 126 edge pieces. To find the total number of pieces in the jigsaw puzzle, we add the edge pieces to the inside pieces:

Total pieces = edge pieces + inside pieces = 126 + 924 = 1050

Answer:

The GCF is [tex]11j^{2} k^{4}[/tex]

Step-by-step explanation: I did the assignment on edge.

[tex]5x-2y=8\ \ \ \ |-5x\\\\-2y=8-5x\ \ \ |:(-2)\\\\y=-4+2.5x\\\\\boxed{y=2.5x-4}[/tex]

it would be -32/21 because if you multiple 4/7 -8/3 it would be -32/21  

divide 15 hours by 75%

15 / 0.75 = 20

he was scheduled for 20 hours

Answer:

he sold 450 horses and 650 cows

Step-by-step explanation:

number of horses he sell =total horses - sold horses

number of cows he sell = total cows- sold cows

To solve the equation 2/3s + 5/6s = 21, you first combine the fraction terms into 1.5s = 21, then solve for s by dividing both sides of the equation by 1.5, giving you s = 14.

To solve for s, you need to first combine like terms on the left-hand side of the equation 2/3s + 5/6s = 21.

To add these fractions, you first need to find a common denominator, which is 6 in this case. So, the equation becomes 4/6s + 5/6s = 21, which simplifies to 9/6s = 21 or 1.5s = 21.

Now you can solve for s by dividing both sides of the equation by 1.5, resulting in s = 21 / 1.5.

So, the solution for s is 14, which can be entered as a whole number.

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Answer:

12.75 and 13x

Step-by-step explanation:

took the test (k12)