All categories

3 years ago

Use the figure to answer the questions.

Mathematics

1 answer:

Advocard [28]3 years ago

4 0

Answer:

a) Triangle ABE is similar to Triangle DCE by Angle-Angle-Angle postulate.

b) 4 cm

Step-by-step explanation:

a) angle A = angle D

And

angle B = angle C

(Alternate angles)

Angle AEB = Angle DEC

(Vertically opposite angles)

All three angles are equal, hence triangles are similar

AB/DC = AE/DE

6/15 = y/10

y = 6×10/15

y = 4

You might be interested in

I need help. See attachment for detail.

lesantik [10]

Answer:

4.5

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A right square pyramid is shown. The height of the pyramid is 6 units. The distance from the center of the base of the pyramid t

elena-14-01-66 [18.8K]

Answer:

AD is 6.5 units

Step-by-step explanation:

Find the diagram attached.

From the diagram, you can see that the dotted triangle is a right angled triangle with side AD as the hypotenuse.

To get AD, we will use the pythagoras theorem as shown;

Hyp² = Opp² + Adj²

AD² = 6²+2.5²

AD² = 36 + 6.25

AD² = 42.25

AD = √42.25

AD = 6.5

Hence the measure of length segment AD is 6.5 units

6 0

2 years ago

Which of the following is written as a rational function?

Brrunno [24]

We have to identify the rational function among the given functions.

Rational function is a function that is the ratio of two polynomials. It is rational because one polynomial is divided by the other polynomial, like a ratio.

1. Consider the first function $G(x)= -2x$ , since it is not a function that is the ratio of two polynomials. So, it is not a rational function.

2. Consider the second function $P(x)= 3x+4$ , since it is not a function that is the ratio of two polynomials. So, it is not a rational function.

3. Consider the third function $Q(x)= x^2-8x+1$ , since it is not a function that is the ratio of two polynomials. So, it is not a rational function.

4. Consider the fourth function $F(x)= \frac{x+2}{5x}$ , since it is a function that is the ratio of two polynomials (x+2) and (5x). So, it is a rational function.

So, Option D is the correct answer.

6 0

3 years ago

Read 2 more answers

A triangle is formed from the points L(-3, 6), N(3, 2) and P(1, -8). Find the equation of the following lines:

Dima020 [189]

Answer:

Part A) $y=\frac{3}{4}x-\frac{1}{4}$

Part B) $y=\frac{2}{7}x-\frac{5}{7}$

Part C) $y=\frac{2}{7}x+\frac{8}{7}$

see the attached figure to better understand the problem

Step-by-step explanation:

we have

points L(-3, 6), N(3, 2) and P(1, -8)

Part A) Find the equation of the median from N

we Know that

The median passes through point N to midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

$M(-1,-1)$

step 2

Find the slope of the segment NM

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

N(3, 2) and M(-1,-1)

substitute the values

$m=\frac{-1-2}{-1-3}$

$m=\frac{-3}{-4}$

$m=\frac{3}{4}$

step 3

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{3}{4}$

$point\ N(3, 2)$

substitute

$y-2=\frac{3}{4}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{3}{4}x-\frac{9}{4}$

$y=\frac{3}{4}x-\frac{9}{4}+2$

$y=\frac{3}{4}x-\frac{1}{4}$

Part B) Find the equation of the right bisector of LP

we Know that

The right bisector is perpendicular to LP and passes through midpoint segment LP

step 1

Find the midpoint segment LP

The formula to calculate the midpoint between two points is equal to

$M(\frac{x1+x2}{2},\frac{y1+y2}{2})$

we have

L(-3, 6) and P(1, -8)

substitute the values

$M(\frac{-3+1}{2},\frac{6-8}{2})$

$M(-1,-1)$

step 2

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 3

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

$m_2=\frac{2}{7}$

step 4

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{2}{7}$

$point\ M(-1,-1)$ ----> midpoint LP

substitute

$y+1=\frac{2}{7}(x+1)$

step 5

Convert to slope intercept form

Isolate the variable y

$y+1=\frac{2}{7}x+\frac{2}{7}$

$y=\frac{2}{7}x+\frac{2}{7}-1$

$y=\frac{2}{7}x-\frac{5}{7}$

Part C) Find the equation of the altitude from N

we Know that

The altitude is perpendicular to LP and passes through point N

step 1

Find the slope of the segment LP

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

we have

L(-3, 6) and P(1, -8)

substitute the values

$m=\frac{-8-6}{1+3}$

$m=\frac{-14}{4}$

$m=-\frac{14}{4}$

$m=-\frac{7}{2}$

step 2

Find the slope of the perpendicular line to segment LP

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is equal to -1)

$m_1*m_2=-1$

we have

$m_1=-\frac{7}{2}$

$m_2=\frac{2}{7}$

step 3

Find the equation of the line in point slope form

$y-y1=m(x-x1)$

we have

$m=\frac{2}{7}$

$point\ N(3,2)$

substitute

$y-2=\frac{2}{7}(x-3)$

step 4

Convert to slope intercept form

Isolate the variable y

$y-2=\frac{2}{7}x-\frac{6}{7}$

$y=\frac{2}{7}x-\frac{6}{7}+2$

$y=\frac{2}{7}x+\frac{8}{7}$

7 0

3 years ago

WILL GIVE BRAINLIEST

____ [38]

Answere:

its black

Step-by-step explanation:

black is better and im right

7 0

3 years ago