Gerald is constructing a line parallel to line l through point P. He begins by drawing line m through points P and Q. He then draws a circle centered at Q, which intersects line l at point N and line m at point S. Keeping the compass measure, he draws a congruent circle centered at point P, which intersects line m at point T.

Which next step will create point R, such that when a line is drawn through points P and R, the line will be parallel to line l?

Lines m and n intersect at point Q. A circle is drawn around point Q and forms point S on line m and forms point N on line l. Point P is also on line m. A circle is drawn around point P and forms point T on line m.
Use the compass to construct a circle centered at Q through point P.
Using the compass measure between points S and N, draw an arc to the right of line m, centered at T, intersecting the edge of circle P.
Using the compass measure between points S and N, draw an arc above line l, centered at N, intersecting the edge of circle Q.
Use the compass to construct a circle centered at P through point Q.
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The measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees

From the question given, we have the following parameters

Base of the building = 7feet

Height of the building = 18 feet

Required

angle of elevation

Using the SOH CAH TOA identity

tanФ = opp/adj

tanФ = 18/7

Ф = 68.73 degrees

Hence the measure of the angle of elevation from the ground to the top of the ladder is 68.73 degrees

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Question:

A ladder leans against a building. The top of the ladder reaches a point on the building, which is 18 feet above the ground. The foot of the ladder is 7 feet from the building. Find the measure of the angle of elevation from the ground to the top of the ladder.

Answer:

6√27 + √243

6√9 x 3 + √81 x 3  

6 x 3 √3 + 9√3

18√3 + 9√3

27√3

Answer:

72

Step-by-step explanation:

yhsvybybyvyyvtvvyyvvt

Answer:

number 9 is the answer for this question

Answer:

√2.236

Step-by-step explanation:

(2,0) (5,-2). 2 - 5 = -3. 0 - -2 = 2. -3 squared = -9. 2 squared = 4. -9 + 4 = -5. Square root of -5 = 2.236, so the distance would be √2.236

Answer:

its opposite

Step-by-step explanation:

The conversion of the following units are done below.

Conversion means to convert the same thing into different units.

We know the following unit's conversion.

1 km = 0.62 miles

6 km = 3.72 miles

    1 L = 0.26 gallons

2.5 L = 0.65 gallons

  1 lb = 0.45 kg

90 lb = 40.5 kg

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Answer:

I think the answer is B

Step-by-step explanation:

Answer:

45 degree=√2/2

√2/2=12√2

we use criss-cross method

√2x/√ 2=12√2/√ 2

×=24

Step-by-step explanation:

if it confused you this is (/)is dividing

hope I helped

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Answer:

B) the lines never intersect

Step-by-step explanation:

okay essentially, syllogism is formatted in a repetitive way

it's something like:

if "a" are "b"

and "b" are "c"

then "a" are "c"

(a = b

b = c

logically, c = a)

(idea, thing related to idea, conclusion relating the two)

hope this helps!!

Answer:

the lines never intersect

Step-by-step explanation:

Syllogisms are connected by a shared statement that connects a hypothesis to a different conclusion.

Answer:

vertex: (3,1)

y-intercept = (0,-8)

x-intercept- Smaller=2 Larger=4

Domain= all real numbers, identity, infinite

Range= 1 is greater than or equal to y

axis of symmetry=3

Step-by-step explanation:

Answer:

True

Step-by-step explanation:

Hope this helps :)

Answer:

Same, because they are parallel.

Step-by-step explanation:

More plainly, the sequence is defined recursively by

[tex]a_{n+1} = \begin{cases} 3a_n - 9 & \text{if } a_n \text{ is odd} \\ 2a_n - 7 & \text{if } a_n \text{ is even} \end{cases}[/tex]

and some starting value [tex]a_1[/tex].

We're given that the sequence alternates between two constants, [tex]a[/tex] and [tex]b[/tex], so that [tex]a_1 = a[/tex].

• If [tex]a[/tex] is even, then the second term [tex]b[/tex] must be odd, since

[tex]a_2 = 2a_1 - 7[/tex]

by the given rule, and 2×(even) - (odd) = (odd). So

[tex]a_2 = 2a-7 = b[/tex]

In turn, the third term is even, since we jump back to [tex]a[/tex]. From the given rule,

[tex]a_3 = 3a_2 - 9[/tex]

and so

[tex]3b-9 = 3(2a-7)-9 = a \implies 6a-30=a \implies 5a=30 \implies a=6[/tex]

[tex]3b-9 = 6 \implies 3b = 15 \implies b = 5[/tex]

Then the sum of the two integers is [tex]a+b=\boxed{11}[/tex]

• You end up with the same answer in the case of odd [tex]a[/tex], so I'll omit this part of the solution. (It's almost identical as the even case.)

Answer:

f(x)=15x+120

Step-by-step explanation:

trust

Answer:

Symmetric property

Answer: 8

Step-by-step explanation:

We know that scale factor = (image)/(preimage).

Substituting in what we have,

[tex]5=\frac{R'S'}{RS}\\\\5=\frac{40}{RS}\\\\RS=\boxed{8}[/tex]

Answer:

Step-by-step explanation:

We know that r's't' was formed by a scale factor of 5.

This means rst was multiplied by 5 to create r's't'.

Dividing the sides of r's't' by 5 will give us the sides of the

pre-image.  If r's' = 40 - dividing 40 by 5 = 8.

So rs is 8.

Answer:

(-4,-18) and (5,90)

Step-by-step explanation:

I'll assume the first equation is supposed to be y – 10 = 11x + x^2

This is a parabola.  The second equation is a straight line:  

y – 12x = 30

We want to find the points at which these lines intersect.  They will intersect for any (x,y) that

Let's rearrange the second equation to isolate y:

y – 12x = 30

y  = 30 + 12x

Now we can take the this value of y and substitute it into the first equation:

y – 10 = 11x + x^2

(30 + 12x) – 10 = 11x + x^2

20 + 12x = 11x + x^2

0 = x^2 -x -20

We can factor this into (x+4)(x-5)

That means x can be either -4 or 5.

Find the value of y using these values of x in both original equations:

For x = -4

y – 10 = 11x + x^2

y  = 11x + x^2 + 10

y = 11(-4)+(-4)^2 +10

y = -44 + 16 + 10

y = -18    The point both lines meet is at (-4, -18) which was already given in the problem.  

For x = 5

y – 10 = 11x + x^2

y  = 11x + x^2 + 10

y  = 11(5) + (5)^2 + 10

y  = 55 + 25 + 10

y = 90

The second point both lines meet is (5,90).

We should use both solutions in the second equation to verify these values, but I'll graph them, instead.  See the attached graph to prove these points are correct.

Considering the area of a rectangle, the equation that could be used to determine the width for which the costs are the same is:

125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)

The area of a rectangle of length l and width w is given by the multiplication of dimensions, that is:

A = lw

In this problem, the dimensions are given as follows:

w = x, l = x + 5.

Hence the area in square feet is:

A = x(x + 5) = x² + 5x.

Then the costs are given as follows:

The costs will be equal when:

A(x) = B(x)

125 + 2(x² + 5x) = 75 + 2.5(x² + 5x)

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Answer:

see photo

Step-by-step explanation:

Plato/Edmentum

I am assuming you meant to write b(x) = x-4.

[tex](b \circ a)(x)=b(a(x))=b(3x+1)=(3x+1)-4=\boxed{3x-3}[/tex]

Since this is a linear function, the domain is all real numbers.

Answer:

center = (-5, -7)

radius = 21

Step-by-step explanation:

Equation of a circle

[tex](x-a)^2+(y-b)^2=r^2[/tex]

where:

Given equation:

[tex](x+5)^2 + (y+7)^2 = 21^2[/tex]

Comparing the given equation with the standard equation of a circle:

Hence, the coordinates of centre is (-5,-2).

A circle is a closed, two-dimensional object where every point in the plane is equally spaced from a central point. The line of reflection symmetry is formed by all lines that traverse the circle. Additionally, every angle possesses rotational symmetry around the center.

The given equation  of circle,

(x+5)² + (y+7)² = 21²

We know that,

Equation of a circle is:

(x-a)² + (y-b)² = r²

where:

(a, b) is the center

And r is the radius

Comparing with the given equation we have,

center = (-5,-7)

And radius = 21 units

Thus,

Coordinates =  (-5,-7).

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Answer:

n = 7

Explanation:

[tex]\rightarrow \sf 3 + 5(2 + 7n) = 258[/tex]

apply distributive method: a(b + c) = ab + ac

[tex]\rightarrow \sf 3 + 10 + 35n = 258[/tex]

simply add the numbers

[tex]\rightarrow \sf 13 + 35n = 258[/tex]

subtract both sides by 13

[tex]\rightarrow \sf 13-13 + 35n = 258-13[/tex]

simplify the following

[tex]\rightarrow \sf 35n = 245[/tex]

divide both sides by 35

[tex]\rightarrow \sf n = 7[/tex]

Answer:

n = 7

Step-by-step explanation:

1) Subtract 3 from both sides.

5(2 + 7n) = 258 - 3

2) Simplify 258 - 3 to 255.

5(2 + 7n) = 255

3) Divide both sides by 5.

2 + 7n = 255/5

4) Simplify 255/5 to 51.

2 + 7n = 51

5) Subtract 2 from both sides.

7n = 51 - 2

6) Simplify 51 - 2 to 49.

7n = 49

7) Divide both sides by 7.

n = 49/7

8) Simplify 49/7 yo 7.

n = 7

Answer:

$15 is the answers

Step-by-step explanation:

please mark me as brainlest

Answer:

$ 35.00   is what you pay     $15.00 off original price

Step-by-step explanation:

30 % discount means you pay 70 %

$ 50 * .70 = $ 35 .00

Answer:

6

Step-by-step explanation:

The second rational number equals 2 1/3.

Adding the mixed numbers:

[tex]3 \frac{2}{3} + 2 \frac{1}{3} = 5 \frac{3}{3} = 6 [/tex]

The property of each given rational number operation are respectively; Commutative Property; Closure Property; Associative Property; Closure Property; Distributive Property

The main properties of rational numbers are:

a) The property used here is commutative property which says that;

a + b = b + a.

This tallies with the operation used on the rational numbers.

b) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.

c) The property used here is called associative property because it states that; a * (b * c) = (a * b) * c.

d) The property used here is called Closure Property. This is because for two rational numbers say a and b, the results of addition, subtraction and multiplication operations gives a rational number.

e)  The property used here is called distributive property because it states that; a * (b * c) = (ab * ac)

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[tex]3(8 - 4x) < 6(x - 5) \\ 24 - 12x < 6x - 30 \\ 24 + 30 < 6x + 12x \\ 54 < 18x \\ \frac{54}{18} < \frac{18x}{18} \\ x > 3[/tex]

Solution : ] 3 , + ♾️ [

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Answer:

D. 0 < x < 20

Explanation:

Domain is in the x axis, Range lies in the y axis.

Here it is seen that function's domain lies between 0 to 20.

Here, as the circle's are open. Domain: 0 < x < 20

Additionally,

Monica win 2 games.

In maths, an expression is a combination of numbers, variables, functions (such as addition, subtraction, multiplication or division etc.)

According to the question,

First we  look from the perspective of one player.

How many games does this person play? 5.

Now, each or the 6 people in the tournament played 5 games,

SO,  

[tex]^{6} C_{2} = \frac{6!}{2! * 4!} = \frac{6*5}{2} = 15[/tex]

Therefore,

We know that there were a total of 15 games played.

This means, there were 15 losses, and more importantly, 15 wins.

Not counting Monica, there were:

4 + 3 + 2 + 2 + 2 = 13 wins.

This leaves,

15 − 13 = 2 wins for Monica.

Hence, 2 games won by monica in a tournament.

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The volume of the cone is V = 381.15 cu.cm

The curved surface area of the cone is given by

A = πrl

The slant height given in the question is

l = 10.5 cm

A = 115.5 sq.cm

radius = ?

Height = ?

Volume = ?

Using the Curved Surface Area Formula

115.5 = π * r * 10.5

taking π = 22/7

r = 3.5 cm

The slant height is given by

[tex]\rm l = \sqrt{ r^2 + h^2}[/tex]

Therefore the height is

[tex]\rm h = \sqrt{ 10.5^2 -3.5^2}[/tex]

h = 9.9 cm

The volume of the cone is

V = π r²h

V = (22/7) * 3.5 * 3.5 * 9.9

V = 381.15 cu.cm

The volume of the cone is V = 381.15 cu.cm

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