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3 years ago

Describe the congruence transformation that maps ΔABC onto ΔA′B′C′ in the given figure. Question 9 options:

Mathematics

1 answer:

hodyreva [135]3 years ago

3 0

Answer:

B) Reflection along y-axis; Translation: (x, y) → (x, y – 3)

Step-by-step explanation:

A transformation is the movement of a point from its initial position to a new position. If an object is transformed, all its points are also transformed. Types of transformation are dilatation, rotation, reflection and translation.

The point of triangle ABC are A(-4, 4), B(-7, 1) and C(-3, -2) while for triangle A'B'Ç' is at A'(4, 1), B'(7, -2) and C'(3, -5)

If a point C(x, y) is reflected along y axis, the y coordinates is the same and the x coordinate is opposite (negated), i.e C'(-x, y). If a point C(x, y) is translated 3 units down, the new point is (x, y - 3).

ΔABC transformation to ΔA'B'C', the x coordinate is opposite and the y coordinate is 3 units downward, therefore this is a Reflection along y-axis; Translation: (x, y) → (x, y – 3)

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Heidi has an average score of 78 for her first six chemistry tests. If Heidi"s scores for the first four tests were 82,78,87, an

elixir [45]

Answer:

(A)74

Explanation:

Let her average score on the last two tests = x.

The six scores will now be: 82,78,87,73, x and x.

Since the average score for her first six chemistry tests = 78

$\frac{82+78+87+73+x+x}{6}=78$

We then solve for x.

$\begin{gathered} 320+2x=78\times6 \\ 320+2x=468 \\ 2x=468-320 \\ 2x=148 \\ x=\frac{148}{2} \\ x=74 \end{gathered}$

Her average score for the last two tests is 74.

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1 year ago

I need help please!!!

Setler79 [48]

Do you need help with the whole worksheet ?

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2 years ago

If y varies directly with x and y = 10 when k = 10, what is the value of x?

Damm [24]

y = k *x
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10 = 10*x
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x =1

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3 years ago

£8658 is shared equally between 9 people. How much does each person get? £

valkas [14]

Answer:

962

Step-by-step explanation:

8658/9

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2 years ago

Read 2 more answers

Let x be the average number of employees in a group health insurance plan, and let y be the average administrative cost as a per

Step2247 [10]

A scatter diagram has points that show the relationship between two sets of data.

We have the following data,

$\left\begin{array}{ccccccc}\mathrm{x}&3&7&15&32&74\\\mathrm{y}&40&35&30&25&17\end{array}\right$

where x is the average number of employees in a group health insurance plan and y is the average administrative cost as a percentage of claims.

To make a scatter diagram you must, draw a graph with the independent variable on the horizontal axis (in this case x) and the dependent variable on the vertical axis (in this case y). For each pair of data, put a dot or a symbol where the x-axis value intersects the y-axis value.

Linear regression is a way to describe a relationship between two variables through an equation of a straight line, called line of best fit, that most closely models this relationship.

To find the line of best fit for the points, follow these steps:

Step 1: Find $X\cdot Y$ and $X\cdot X$ as it was done in the below table.

Step 2: Find the sum of every column:

$\sum{X} = 131 ~,~ \sum{Y} = 147 ~,~ \sum{X \cdot Y} = 2873 ~,~ \sum{X^2} = 6783$

Step 3: Use the following equations to find intercept a and slope b:

$\begin{aligned} a &= \frac{\sum{Y} \cdot \sum{X^2} - \sum{X} \cdot \sum{XY} }{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 147 \cdot 6783 - 131 \cdot 2873}{ 5 \cdot 6783 - 131^2} \approx 37.05 \\ \\b &= \frac{ n \cdot \sum{XY} - \sum{X} \cdot \sum{Y}}{n \cdot \sum{X^2} - \left(\sum{X}\right)^2} = \frac{ 5 \cdot 2873 - 131 \cdot 147 }{ 5 \cdot 6783 - \left( 131 \right)^2} \approx -0.292\end{aligned}$

Step 4: Assemble the equation of a line

$\begin{aligned} y~&=~a ~+~ b \cdot x \\y~&=~37.05 ~-~ 0.292 \cdot x\end{aligned}$

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3 years ago