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2 years ago

Plot triangle ABC on graph paper with points A(2,2). B(-2, -2) and C(8, -2).

Mathematics

1 answer:

bonufazy [111]2 years ago

4 0

9514 1404 393

Answer:

a) The new triangle is a reflection of the original across the origin. All angles, segment lengths, and line slopes have been preserved: the transformed triangle is congruent with the original.

b) The new triangle is a reflection of the original across the origin and a dilation by a factor of 2. Angles have been preserved: the transformed triangle is similar to the original. The transformation is NOT rigid.

Step-by-step explanation:

1. The transformed triangle is blue in the attachment. It is congruent with the original. The transformation is "rigid," a reflection across the origin. All angles and lengths have been preserved, as well as line slopes.

2. The transformed triangle is orange in the attachment. It is similar to the original, in that angles have been preserved and lengths are proportional. It is a reflection across the origin and a dilation by a factor of 2. Line slopes have also been preserved. A dilation is NOT a "rigid" transformation.

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Indicate whether the statement is true of false.

yawa3891 [41]

The statement is false, as the system can have no solutions or infinite solutions.

<h3>Is the statement true or false?</h3>

The statement says that a system of linear equations with 3 variables and 3 equations has one solution.

If the variables are x, y, and z, then the system can be written as:

$a_1*x + b_1*y + c_1*z = d_1\\\\a_2*x + b_2*y + c_2*z = d_2\\\\a_3*x + b_3*y + c_3*z = d_3$

Now, the statement is clearly false. Suppose that we have:

$a_1 = a_2 = a_3\\b_1 = b_2 = b_3\\c_1 = c_2 = c_3\\\\d_1 \neq d_2 \neq d_3$

Then we have 3 parallel equations. Parallel equations never do intercept, then this system has no solutions.

Then there are systems of 3 variables with 3 equations where there are no solutions, so the statement is false.

If you want to learn more about systems of equations:

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3 0

1 year ago

the doctor recommended that Matt increase the number of calories you consume from 2000 to 2800 by what percent did the number of

nikdorinn [45]

Answer:

40% number of calories have increased

Step-by-step explanation:

Old Value ( Calories consume before) = 2000

New Value (increase in Calories consumed) = 2800

We need to find by what percent did the number of calories increase

To find percent increase, the formula used is:

$Percent\: increase=\frac{New\:Value-Old\:Value}{Old\:Value}\times 100%$

Putting values in formula and finding percent increase

$Percent\: increase=\frac{New\:Value-Old\:Value}{Old\:Value}\times 100\%\:\\Percent\: increase=\frac{2800-2000}{2000}\times 100\%\: \\Percent\: increase=\frac{800}{2000}\times 100\%\: \\Percent\: increase=0.4\times 100\%\: \\Percent\: increase=40\%$

So, 40% number of calories have increased

8 0

2 years ago

A problem states: "There are 2 more horses than cows in a field. There are 15 animals in the field in all. How many horses are t

mash [69]

Let h = the number of horses in the field
Let c = number of cows in the field

There are 2 more horses than cows in the field. Therefore
h = c + 2
or
c = h - 2 (1)

There are 15 animals in the field. Therefore
h + c = 15 (2)

Substitute (1) into (2).
h + (h - 2) = 15
2h - 2 = 15

Answer:
The correct equation is
2h - 2 = 15

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2 years ago

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ycow [4]

Answer:

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2 years ago

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Please help on my hw, I'm not feeling good, and can't concentrate

sergiy2304 [10]

Answer:

Solution given:

f(x)=x²

g(x)=x+5

h(x)=4x-6

now

23:

(fog)(x)=f(g(x))=f(x+5)=(x+5)²=x²+10x+25

24:

(gof)(x)=g(f(x))=g(x²)=x²+5

25:

(foh)(x)=f(h(x))=f(4x-6)=(4x-6)²=16x²-48x+36

26:

(hof)(x)=h(f(x))=h(x²)=4x²-6

27;

(goh)(x)=g(h(x))=g(4x-6)=4x-6+5=4x-1

28:

(hog)(x)=h(g(x))=h(x+5)=4(x+5)-6=4x+20-6=4x-14

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2 years ago