JL is a common tangent to circles M and K at point J. If angle MLK measures 61ᵒ, what is the length of radius MJ? Round to the nearest hundredth. (Hint: Show that triangles LMJ and LKJ are right triangles, and then use right triangle trigonometry to solving for missing sides of the right triangles.)

Answer:

The required form of the given expression is : (a + 4)(b + 1)

Step-by-step explanation:

The given expression is : ab + 4 + a + 4b

We need to factor he given expression and arrange the factors in the alphabetic order.

To find the factors of the given expression, we need to use the concept of algebra :

ab + 4 + a+ 4b

First rearranging the terms in order to form the factors :

= ab + 4b + 4 + a

= b(a + 4) + 1(4 + a)

= b(a + 4) + 1(a + 4)

= (b + 1)(a + 4)

Now, the factors in the alphabetic order :

= (a + 4)(b + 1)

Hence, the required form of the given expression is : (a + 4)(b + 1)

Linear pair Postulate. Two angles are a linear pair if the angles are adjacent and the two unshared rays form a line. Below is an example of a linear pair: The linear pair postulate states that two angles that form a linear pair are supplementary.

We will see that the exact value is √2/2 = 0.707, and the reference angle is 45°.

We know that for any angle θ we have that:

sin(θ) = sin(θ + n*360°)

Where n is an integer value.

To find the reference angle of a given angle θ, we just need to find a value of n such that:

0 ≤  θ + n*360° ≤ 360°

So we can write our angle in the normal range.

in this case, our angle is -135°

Then we can write:

0 ≤  -135° + n*360° ≤ 360°

Is immediate to notice that we must take n = 1

0 ≤  -135° + 1*360° ≤ 360°

0 ≤  -135° + 1*360° ≤ 360°

0 ≤  225° ≤ 360°

Now we know that θ = 225°.

Ok, this lies on the third quadrant, when an angle lies on the third quadrant, to get the reference angle you just need to subtract 180°.

We will get:

225° - 180° = 45°

So the reference angle is 45°.

Finally, to get the exact value we use:

sin (-135°) = sin(225°) = cos(45°) = √2/2 = 0.707

If you want to learn more about trigonometry, you can read:

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A. The figure given in A is a square pyramid and the formula for the surface area of this figure is:

A = l w + l sqrt [(w/2)^2 + h^2] + w sqrt [(l/2)^2 + h^2]

where l and w are the lengths of the base and h is the height of the pyramid. Since the base is square, so:

l = w = 16 in

h = 15 in

Substituting:

A = 16 * 16 + 16 sqrt [(16/2)^2 +15^2] + 16 sqrt [(16/2)^2 + 15^2]

A = 256 + 272 + 272

A = 800 in^2

B. We are given a cone, the formula for surface area is:

A = πr (r + h^2 + r^2)

where h is the height = 8 in and r is the radius = 3 in

Substituting:

A = π * 3 (3 + sqrt (8^2 + 3^2))

A = 34.63π in^2 = 108.80 in^2 

so use a basic formula here:

area of a circle = πr²

and the circumference of a circle = πd

a)

therefore the area of the pool cover is π multiplied by the radius² (which is the diameter of the pool cover plus the extra 12 inches divided by two, so the radius is 21/2 or 10.5) is 346.36(to two decimal places.)

b)

Using the same diameter, we can work out the length of the rope by multiplying the diameter (10.5) by π, which is 32.99 (to two decimal places).

Answer: 10, 15, 24 is your answer

Step-by-step explanation:

Answer: The answer is [tex]1\dfrac{28}{99}.[/tex] .

Step-by-step explanation: The given rational number is

[tex]R=1.\bar{28}.[/tex]

We are to select the correct expression from the options  that is equivalent to the given rational number.

Let us consider that

[tex]x=1.\bar{28}\\\\\Rightarrow x=1.28\bar{28}\\\\\Rightarrow 100\times x=100\times 1.28\bar{28}\\\\\Rightarrow 100x=128.\bar{28}\\\\\Rightarrow 100x=128+.\bar{28}\\\\\Rightarrow 100x=127+x\\\\\Rightarrow 100x-x=127\\\\\Rightarrow 99x=127\\\\\Rightarrow x=\dfrac{127}{99}\\\\\Rightarrow x=1\dfrac{28}{99}.[/tex]

Thus, the correct option is [tex]1\dfrac{28}{99}.[/tex]

The value of the digit 4 in the number 943,268 is 40,000 because it is in the ten thousand place.

The value of the digit 4 in the number 943,268 depends on its place value in the number.

In 943,268:

- The digit 4 is in the ten-thousands place.

So, the value of the digit 4 in 943,268 is:

4 × 10,000 = 40,000

Therefore, the value of the digit 4 in 943,268 is 40,000.

Final answer:

In art, vertical lines suggest stability and structure, contrasting with calming horizontal lines and dynamic diagonal lines. These lines help define shapes, indicate motion, and guide the viewer through the composition.

Explanation:

The term vertical lines in the context of art and design, refers to lines that run up and down the canvas or design space, perpendicular to the horizon. These lines can convey a variety of meanings and emotions in visual compositions. According to a description by Oliver Harrison, vertical lines are seen as visually stable and can be associated with structures like tree trunks or classical columns, suggesting strength and stability.

Answer:

B. Square

D. Rhombus

Step-by-step explanation:

If you take a rhombus ABCD, its all sides are congruent. Lets take E as the point where the diagonals of a rhombus meet. Now it is known fact that the point where diagonals meet, they bisect each other.

Since, for sides, AB , CD,AD and CB are congruent

For diagonals, AC = BD

As E is the bisecting point for diagonals,

AE = EC and ED = EB

Now by SSS postulate, we can prove that all four triangles formed by rhombus are congruent

ΔAED , ΔBEC , ΔEDC and ΔAEB are congruent

Now the angles

∠AED, ∠AEB, ∠CED and ∠CEB are congruent as well,

So, we know that sum of interior angles of any quadrilateral is 360°

So each angle is 360/4 = 90°

This calculation is valid for square as well.

Answer:

B and D

Step-by-step explanation:

cya

You are given the graph of four straight lines, P, Q, R, and S. You are asked to find which line corresponds to the function of f(x) = 4x - 3. The easiest way to answer this is to plug in the values of the coordiante points used for each graph.

f(x) = 4x - 3 = y

y = 4x - 3

for graph of line S we have the coordinates (0, -3) and (2, 5)

(0, -3)

-3 = 4(0) - 3

-3 = -3

(2,5)

5 = 4(2) - 3

5 = 8 - 3

5 = 5

So the answer is the graph of line S.

To complete the square for the expression x^2 - 18x, add 81 to become a perfect square trinomial in the form (x - 9)^2.

To complete the square for the expression x^2 - 18x, we need to add a constant term to the expression in such a way that it can be factored as a perfect square trinomial. First, we take half of the coefficient of the linear term and square it:

Half of -18 is -9, and when we square it we get 81. Therefore, adding 81 to the expression gives us x^2 - 18x + 81. This can be factored as (x - 9)^2. So the value that completes the square is 81.

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Answer:

Option 4th is correct

the domain of the following relation R is:

[tex]\{-3, 1, 6\}[/tex]

Step-by-step explanation:

Domain is the set of all values of x-coordinates where function is defined.

Given the Relation:

[tex]R = \{(6, -2), (1, 2), (-3, -4), (-3, 2)\}[/tex]

The ordered pairs are in the form of (x, y)

Domain = Set of all values of x.

In the given relation:

x-values = { 6, 1, -3}

⇒[tex]\text{Domain} = \{-3, 1, 6\}[/tex]

therefore, the domain of the following relation R is:

[tex]\{-3, 1, 6\}[/tex]

Answer:

[tex]x^2-4[/tex]

Step-by-step explanation:

Sally found that a solution of x = 2 was extraneous for her function.

Extraneous solution is a solution that makes the denominator 0

Possible denominator are given . LEts plug in 2 for x and check which option gives us 0

[tex]4x+8=4(2)+8= 16[/tex]  

[tex]2x+12=2(2)+12=4+12= 16[/tex]

[tex]x^2-4= (2)^2-4= 4-4=0[/tex]

[tex]x^2-16= (2)^2-16= 4-16= 12[/tex]

[tex]x^2-4[/tex] gives us 0 when we plug in 2 for x.

So x=2 was extraneous solution for [tex]x^2-4[/tex]

Answer with explanation:

It is given that ,

  In two triangles, ΔWAS and ΔNOT

1. WA = NO

2. W S = NT

3. ∠W=∠N

≡ΔWAS ≅ ΔNOT

The Angle is included between two sides .

So,these two triangles are congruent by ,SAS.

Option B:→ S AS

Variable 1: X= number of craft activities

Variable 2: Y= number of sports activities

Equation: X + Y=15

Answer:

option C is correct

[tex]8x^5+24x^3+48x^2[/tex]

Step-by-step explanation:

As per the statement:

The length(l), width(w) and height(h) of the rectangular prism are:

l = 4x

w = 2x

[tex]h = x^3+3x+6[/tex]

We have to find volume.

Use the formula:

[tex]V = lwh[/tex]

Substitute the given values we have;

[tex]V = 4x \cdot 2x \cdot (x^2+3x+6)[/tex]

⇒[tex]V = 8x^2 \cdot (x^3+3x+6)[/tex]

Using distributive property, [tex]a\cdot (b+c) = a\cdot b+ a\cdot c[/tex]

then;

[tex]V = 8x^5+24x^3+48x^2[/tex]

Therefore, the volume of the rectangular prism is, [tex]8x^5+24x^3+48x^2[/tex]