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3 years ago

The two triangles shown are congruent: ΔFHG ≅ ΔJKL. Based on this information, which of the following is a true statement?

Mathematics

2 answers:

alex41 [277]3 years ago

8 0

Answer is C this a math is subtracted and I know

julia-pushkina [17]3 years ago

5 0

Answer:

Answer is C) Angle G is congruent to Angle L

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1. Use precise mathematical language to justify and explain each mathematical process.

iris [78.8K]

Mathematical processes are the steps used to determine the result of operations

The perimeter of the rectangle is $10x^2 - 14x + 28$
The area of the rectangle is $5x^3 +17x^2 -31x + 45$

The dimension of the rectangle is given as:

$Length = 5x^2 - 8x + 9$

$Width = x + 5$

<u>(1) The perimeter of the triangle</u>

This is the sum of the side lengths of the rectangle.

So, we have:

$Perimeter = 2 \times (Length + Width)$

This gives

$Perimeter = 2 \times (5x^2 - 8x + 9 + x + 5)$

Collect like terms

$Perimeter = 2 \times (5x^2 - 7x + 14)$

Open brackets

$Perimeter = 10x^2 - 14x + 28$

Hence, the perimeter of the rectangle is $10x^2 - 14x + 28$

<u>(2) The area of the triangle</u>

This is the product of the dimensions of the rectangle.

So, we have:

$Area = Length \times Width$

This gives

$Area = (5x^2 - 8x + 9) \times (x + 5)$

Open brackets

$Area = 5x^3 - 8x^2 + 9x +25x^2 - 40x + 45$

Collect like terms

$Area = 5x^3 - 8x^2 +25x^2+ 9x - 40x + 45$

$Area = 5x^3 +17x^2 -31x + 45$

Hence, the area of the rectangle is $5x^3 +17x^2 -31x + 45$

Read more about areas and perimeters at:

brainly.com/question/15656646

6 0

2 years ago

The graph of f(x) is shown below. On a coordinate plane, a straight line has a negative slope and goes through (0, 6) and (3, 0)

Rudik [331]

Answer:

The intersection point is (2,2)

Step-by-step explanation:

First let's find the equation of f(x), using the linear model:

$f(x) = ax + b$

Using the point (0, 6), we have:

$6 = a*0 + b\\b = 6$

Using the point (3, 0), we have:

$0 = a*3 + 6\\3a = -6\\a = -2$

So we have that $f(x) = -2x + 6$

To find f'(x) (the inverse of f(x)), we can substitute f(x) by x and x by f'(x) in the equation of f(x) and then isolate f'(x):

$x = -2f'(x) + 6\\2f'(x) = -x + 6\\f'(x) = -x/2 + 3$

Now, to find the intersection point, we need to calculate f(x) = f'(x):

$-2x + 6 = -x/2 + 3\\3x/2 = 3\\3x = 6\\x = 2$

And the y-value is:

$y = -2x + 6 = -2*2 + 6 = 2$

So the point is (2,2)

4 0

3 years ago

Which angles are vertical angles?

shutvik [7]

Answer:

<DCA and <BCF

Step-by-step explanation:

The vertically opposite angles are the angles <DCA and <BCF. These angles are always equal.

When two lines cross, two angles that are vertical two one another are equal.
They are know as vertically opposite angles.
When two straight lines cross each other, four angles are produced.
The two vertically opposite have the same values.

6 0

3 years ago

What is the perimeter, in centimeters, of the figure

xeze [42]

Answer:

30 cm

Step-by-step explanation:

add all sides and use 7 for the bottom line because 5+2=7 and use 8 for the side because 5+3=8.

5 0

2 years ago

Lisa had $4.26 in her purse. She bought some school supplies for $2.75. How much money does Lisa have left?

Mama L [17]

Answer:

$1.51

Step-by-step explanation:

take 4.26 and subtract 2.75.

7 0

3 years ago