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2 years ago

Which of the following steps is included in the construction of a perpendicular line through a point on a line?

Mathematics

1 answer:

Molodets [167]2 years ago

6 0

Answer:

Connect arcs that are above the original line with a straightedge ⇒ 2nd

Step-by-step explanation:

* Lets revise how to construct a perpendicular line through a point

on the line

- Given: line AB and point P lies on it

1. Place your compass pin at P and draw an arc of any size below

AB that crosses the line twice at points C and D

2. Stretch the compass to a larger distance

3. Place the compass pin on point C and draw a small arc above

the line

4. Without changing the distance of the compass place the

compass pin on point D and draw another small arc intersects

the small arc from C at point E

5. Using a straightedge, to join P which is on the original line and E

which is the intersection point of the two small arcs above the

original line, then PE is perpendicular to AB at E

- From the steps up the step is including in the construction of a

perpendicular line through a point on a line is:

Connect arcs that are above the original line with a straightedge

* Remember:

- The step of Connect arcs that are above and below the given line

with a straightedge is in the construction a perpendicular from a

point off the line

- The step of Create arcs on either side of a point that is off the

given line is in the construction of a perpendicular bisector

of a line

- The step of Create a copied angle by using the first two lines as the

original angle in the construction of the parallel lines

- Look to the attached figure to help you

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Which graph can be used to find the solution(s) to x2 - 4x + 4 = 2x + 1 + x??

SVETLANKA909090 [29]

Where are the graphs? And the solutions are the 2 points that intersect with the x-axis I don’t know if that’s the correct equation but i only got 1 solution once i put the equation into Desmos

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2 years ago

Which of the following is a radical equation? x + StartRoot 5 EndRoot = 12 x squared = 16 3 + x StartRoot 7 EndRoot = 13 7 Start

d1i1m1o1n [39]

Answer:

x = 3

Step-by-step explanation:

$(8x-8)^{3/2}=64$

Multiply both sides by the exponent 2/3.

$8x - 8 = 64^{2/3}$

Solve for the exponent.

$8x-8=16$

Add 8 to both sides.

$8x = 16+8$

$8x=24$

Divide 8 into both sides.

$x=24/8$

$x=3$

6 0

2 years ago

During a field trip, 60 students are put into equal-sized groups. Describe two ways to interpret 60÷5 60 ÷ 5 in this context. Fi

Afina-wow [57]

The second question:

Consider the division expression $7\frac{1}{2} / 2$ . Select all multiplication equations that correspond to this division expression.

$2 * ? = 7\frac{1}{2}$ $7\frac{1}{2} * ?= 2$ $? * 2 = 7\frac{1}{2}$

$2* 7\frac{1}{2} = ?$ $? * 7\frac{1}{2} = 2$

Answer:

1. See Explanation

2. $2 * ? = 7\frac{1}{2}$ and $? * 2 = 7\frac{1}{2}$

Step-by-step explanation:

Solving (a):

Given

$Students = 60$

$Group = Equal\ Sized$

Required

Interpret $\frac{60}{5}$ in 2 ways

Interpretation 1: Number of groups if there are 5 students in each

Interpretation 2: Number of students in each group if there are 5 groups

Solving the quotient

$Quotient = \frac{60}{5}$

$Quotient = 12$

For Interpretation 1:

The quotient means: 12 groups

For Interpretation 2:

The quotient means: 12 students

Solving (b):

Given

$7\frac{1}{2} / 2$

Required

Select all equivalent multiplication equations

Let ? be the quotient of t $7\frac{1}{2} / 2$

So, we have:

$7\frac{1}{2}/2 = ?$

Multiply through by 2

$2 * 7\frac{1}{2}/2 = ? * 2$

$7\frac{1}{2} = ? * 2$

Rewrite as:

$? * 2 = 7\frac{1}{2}$ --- This is 1 equivalent expression

Apply commutative law of addition:

$2 * ? = 7\frac{1}{2}$ --- This is another equivalent expression

8 0

2 years ago

Show that the given set of functions is orthogonal with respect to the given weight on the prescribed interval. Find the norm of

AnnyKZ [126]

Answer/Explanation

The complete question is:

Show that the set function {1, cos x, cos 2x, . . .} is orthogonal with respect to given weight on the prescribed interval [- π, π]

Step-by-step explanation:

If we make the identification For ∅° (x) = 1 and ∅n(x) = cos nx, we must show that ∫ lim(π) lim(-π) .∅°(x)dx = 0 , n ≠0, and ∫ lim(π) lim(-π) .∅°(x)dx = 0, m≠n.

Therefore, in the first case, we have

(∅(x), ∅(n)) ∫ lim(π) lim(-π) .∅°(x)dx = ∫ lim(π) lim(-π) cosn(x)dx

This will therefore be equal to :

1/n sin nx lim(π) lim(-π) = 1/n [sin nπ - sin(-nπ)] = 0 , n ≠0 (In the first case)

and in the second case, we have,,

(∅(m) , ∅(n)) = ∫ lim(π) lim(-π) .∅°(x)dx

This will therefore be equal to:

∫ lim(π) lim(-π) cos mx cos nx dx

Therefore, 1/2 ∫ lim(π) lim(-π)( cos (m+n)x + cos( m-n)x dx (Where this equation represents the trigonometric function)

1/2 [ sin (m+n)x / m+n) ]+ [ sin (m-n)x / m-n) ] lim(π) lim(-π) = 0, m ≠ n

Now, to go ahead to find the norms in the given set intervals, we have,

for ∅°(x) = 1 we have:

//∅°(x)//² = ∫lim(π) lim(-π) dx = 2π

So therefore, //∅°(x)//² = √2π

For ∅°∨n(x) = cos nx , n > 0.

It then follows that,

//∅°(x)//² = ∫lim(π) lim(-π) cos²nxdx = 1/2 ∫lim(π) lim(-π) [1 + cos2nx]dx = π

Thus, for n > 0 , //∅°(x)// = √π

It is therefore ggod to note that,

Any orthogonal set of non zero functions {∅∨n(x)}, n = 0, 1, 2, . . . can be normalized—that is, made into an orthonormal set by dividing each function by its norm. It follows from the above equations that has been set.

Therefore,

{ 1/√2π , cosx/√π , cos2x/√π...} is orthonormal on the interval {-π, π}.

6 0

2 years ago

W hich of these scales is equivalent to the scale 1 cm to 5 km? Select all that apply. (Lesson 1-11) A. 3 cm to 15 km D. 5 m

nordsb [41]

The equivalent scales are:

3 cm to 15 km is equivalent to 1 cm to 5 km ⇒ answer A

5 mm to 2.5 km is equivalent to 1 cm to 5 km ⇒ answer D

1 mm to 500 m is equivalent to 1 cm to 5 km ⇒ answer E

Step-by-step explanation:

To solve this problem do that

1. The given scale is 1 cm represents 5 km, then all given answer must

be change to cm and km

2. Find the equivalent scales to the given scale

∵ 3 cm represents 15 km

- Divide both of them by 3

∴ 1 cm represents 5 km

3 cm to 15 km is equivalent to 1 cm to 5 km

∵ 1 mm represents 150 km

- Change mm to cm

∵ 1 cm = 10 mm

∴ 1 mm = $\frac{1}{10}$ cm = 0.1 cm

∴ 0.1 cm represents 150 km

- Multiply both by 10

∴ 1 cm represents 1500 km

1 mm to 150 km is not equivalent to 1 cm to 5 km

∵ 5 cm represents 1 km

- Divide both my 5

∴ 1 cm represents 0.2 km

5 cm to 1 km is not equivalent to 1 cm to 5 km

∵ 5 mm represents 2.5 km

- Change mm to cm

∵ 1 cm = 10 mm

∴ 5 mm = $\frac{5}{10}$ cm = 0.5 cm

∴ 0.5 cm represents 2.5 km

- Divide both by 0.5

∴ 1 cm represents 5 km

5 mm to 2.5 km is equivalent to 1 cm to 5 km

∵ 1 mm represents 500 m

- Change mm to cm

∵ 1 cm = 10 mm

∴ 1 mm = $\frac{1}{10}$ cm = 0.1 cm

- Change m to km

∵ 1 km = 1000 m

∴ 1 m = $\frac{1}{1000}$ = 0.001 km

∴ 500 m = $\frac{500}{1000}$ = 0.5 km

∴ 0.1 cm represents 0.5 km

- Multiply both by 10

∴ 1 cm represents 5 km

1 mm to 500 m is equivalent to 1 cm to 5 km

Learn more:

You can learn more about the equivalent quantities in brainly.com/question/120752

#LearnwithBrainly

3 0

2 years ago