15 POINT QUESTION
Francine solves the system of equations using the linear combination method. 4x+3y=−1
3x−5y=4
Which steps would allow her to eliminate the x terms in the system of equations?
A) Multiply 4x+3y=−1 by 4. Multiply 3x−5y=4 by 3. Add the resulting equations together.
B) Multiply 4x+3y=−1 by −4 . Multiply 3x−5y=4 by 3. Add the resulting equations together.
C) Multiply 4x+3y=−1 by 3. Multiply 3x−5y=4 by −4. Add the resulting equations together.
D) Multiply 4x+3y=−1 by 5. Multiply 3x−5y=4 by 3. Add the resulting equations together.

Answer:

The multiplicative identity shows us that any time you multiply something by the number 1, the result would be what you started with.

Ex: 1(m) or 1 x m.

The reason for thusbis that when you are multiplying you are representing groups of something, so 1 group of anything or m, would just be that anything or m in this case!Step-by-step explanation:

Answer:

A

Step-by-step explanation:

it makes the most sense

To solve this problem you must apply the proccedure shown below:

a) You must sum terms with same exponents, therefore, you have that the sum of these two polynomials is:

[tex] (x^{2}-4x+5)+(7x^{2}+2x-3) [/tex]

[tex] 8x^{2} -2x+2 [/tex]

b) First, you must mulitply the signs of the second polynomial by the negative sign, and them, you apply an algebraic sum. Therefore, the result is:

[tex] (7x^{2}+4x-6-2x^{2}+3x-1) \\ 5x^{2} +7x-7 [/tex]

The answers are: a)[tex] 8x^{2} -2x+2 [/tex]; b) [tex] 5x^{2} +7x-7 [/tex]

a)

x² - 4x + 5 + 7x² + 2x - 3

8x² - 2x + 2

b)

7x² + 4x - 6 - (2x² - 3x + 1)

7x² + 4x - 6 - 2x² + 3x - 1

5x² + 7x - 7

Final answer:

Calculate the percentage change in income, find a decrease of 22.92% from last year to this year.

Explanation:

Given:

Original income = $24,000
Current income = $18,500

Step 1: Calculate the change in income:
Change in income = New income - Original income = $18,500 - $24,000 = -$5,500

Step 2: Calculate the percentage change in income:
Percentage change = [(Change in income) / (Original income)] x 100
= [(-$5,500) / ($24,000)] x 100
= -22.92%

Step 3: Interpretation:
The percentage change is -22.92%, indicating a decrease in income by 22.92%.

The answer is a rectangular prism

The boxes of Fred's Fudge, made of 2 triangles and 3 rectangles, are most likely shaped as triangular prisms.

Each box of Fred's Fudge is constructed from 2 triangles and 3 rectangles. The shape of each box can be determined by visualizing how the triangles and rectangles are assembled. In most cases, packaging that includes triangles would imply the presence of triangular prism shapes, where the triangles serve as the ends and the rectangles connect the corresponding sides of the triangles. Hence, it's reasonable to conclude that the shape of each box is likely a triangular prism.

The third and fourth methods described are more likely to yield unbiased results, whereas the first and second methods are prone to bias.

The manager of a sawmill wants to find out what percentage of the boards that the mill produced are defective. To determine this accurately, the manager must use unbiased sampling methods.

Biased Sampling Methods

On 1 day, an hour after the sawmill begins production, 30 boards in a row are selected and examined: This method is likely to be biased because it only considers boards produced during a specific timeframe, which might not represent the entire production cycle.

The manager sends an email to 20 customers who buy lumber from the mill, asking each how many of the boards they bought the past week were defective. Results from the first 5 customers to respond are tallied: This method is biased due to its reliance on customer self-reporting and the fact that only the first few respondents are considered, which might not be representative.

Possibly Unbiased Sampling Methods

The manager selects 20 boards at random each day for 5 days and examines them: This sampling method is likely to be unbiased as it involves random selection across multiple days, covering a broader production span.

Every 40th board produced over the course of 1 week is selected and examined: This method is less likely to be biased as it systematically covers the production over a week, though it might miss defects that occur in clusters shorter than 40 boards.

In summary, the third and fourth methods described are more likely to yield unbiased results, whereas the first and second methods are prone to bias.

When translating a figure using two translations, the end result is a figure that is congruent to the original. This is due to the fact that translations move the shape without altering its size or orientation.

Yes, when translating a figure using a combination of two translations, the resulting figure is congruent to the original figure. When a figure is translated, it is moved without being turned or flipped, the size and shape remains the same, hence making it congruent. For example, consider a parallelogram. If two different vectors A and B are chosen to translate it, following the rules of vector summation, the figure moved, known as the resultant vector retains the dimensions and angles of the original parallelogram, albeit in a different location.

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The plane's actual speed is 135 miles/hour if the plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour option (C) 135 miles/hour is correct.

When two lines or rays converge at the same point, the measurement between them is called a "Angle."

The question in incomplete.

The complete question is:

A plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour. If the plane's resultant speed due to the wind is 180 miles/hour, what is the plane's actual speed, rounded to the nearest integer?

From the data given in the question:

Using Cosine Law:

c² = a² + b² - 2 ac cos C

180² = 50² + x² - (2×50)x  cos 150°

32400 - 2500 - x² = 86.6x

29,900 - x² = 86.6 x

x² + 86.6x - 29900 = 0

After solving the above quadratic equation:

x = 135 miles/hour

Thus, the plane's actual speed is 135 miles/hour if the plane is traveling due south. The wind is blowing 30° east of south at 50 miles/hour option (C) 135 miles/hour is correct.

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11 less implies: -11

two times a number (x) implies: 2x

equal to 27 implies: = 27

Set the equation together.

2x - 11 = 27 is your equation.

Solve for x. Note the equal sign. What you do to one side you do to the other. Add 11 to both sides

2x - 11 (+11) = 27 (+11)

2x = 38

Isolate the x. Divide 2 from both sides.

2x/2 = 38/2

x = 19

hope this helps