Lesson Performance Task
The image shows the angles formed by a pair of scissors. When the
scissors are closed, m<1= 0°. As the scissors are opened, the measures
of all four angles change in relation to each other. Describe how the
measures change as m<1 increases from 0° to 180°.

The complex number in rectangular form is 17√2 / 2 - i 17√2 / 2. (Correct choice: A)

In this problem we have a complex number in polar form, whose formula is described below:

z = r · (cos θ + i sin θ)

Where:

And the rectangular form of the complex number is represented by:

z = a + i b, where a = r · cos θ and b = r · sin θ.

If we know that r = 17 and θ = 315°, then the rectangular form of the complex number is:

a = 17 · cos 315°

a = 17√2 / 2

b = 17 · sin 315°

b = - 17√2 / 2

The rectangular form of the complex number is 17√2 / 2 - i 17√2 / 2.

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Step-by-step explanation:

1+2+3+4+5=15

180÷15=12

12x1=12

12x2=24

12x3=36

12x4=48

12x5=60

The system of inequalities that models this situation is given as follows:

The variables of the system of inequalities are presented as follows:

Gwen charges $3.50 each time she walks a dog. Julia charges $1.25 each time she waters the flowers, and they need to raise at least $250, hence the first constraint is of:

3.5x + 1.25y ≥ 250.

The number of times Julia plans to water the flowers is no more than six times the number of dogs Gwen plans to walk, hence:

y ≤ 6x.

Gwen plans to walk no less than 12 dogs, hence:

x ≥ 12.

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We must combine 3 servings of Ta-sty Pocket, 2 serving of P-ita Roll, and 1 serving of In-sta Pancake to get 754 calories, 19.2 g of f-at, and 78.9 g of carbohydrates.

According to the question,

Three brands of breakfast food represents the calories , f-at, and carbohydrates.

To get 754 calories, we should combine

= 450 + 238 + 66

= 3 (150) + 2 ( 119) + 1 (66)

= 3 serving of Ta-sty Pocket + 2 serving of P-ita Roll + 1 serving of In-sta Pancake

To get 19.2g of f-at, we should combine

= 14.4 + 4.6 + 0.2

= 3(4.8) + 2( 2.3) + 1(0.2)

= 3 serving of Ta-sty Pocket +2 serving of P-ita Roll +1 serving of In-sta Pancake

To get 78.9 g of carbohydrates, we should combine

= 29.4 + 28 + 21.5

= 3(9.8) + 2( 14) + 1 (21.5)

= 3 serving of Ta-sty Pocket +2 serving of P-ita Roll +1 serving of In-sta Pancake

Hence, we should combine 3 serving of Tasty Pocket, 2 serving of P-ita Roll, 1 serving of In-sta Pancake

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Answer:

8

Step-by-step explanation:

Corresponding sides of similar triangles are proportional, so:

[tex]\frac{A'B'}{12}=\frac{4}{6} \implies A'B'=8[/tex]

Using the given inequality we can calculate that this is equivalent to

(B) x ≤-1 or x ≥1

The given inequality is |8x| ≥ 2 .

Now we have to solve this inequality to find the range of the value of x.

|8x| ≥ 2

now we will try to remove the modulus function.

either 8x ≥ 2 ⇒ x ≥ 1/4

or, -8x ≥ 2 ⇒ x ≤ -1/4

Therefore the solution of the inequality is x ≤ -1/4 or x ≥ 1/4

Now of the given options the most plausible option or inequality that also satisfies this inequality is given by B)  x ≤-1 or x ≥1

In mathematics, an inequality is a connection that makes an unequal comparison between two numbers and maybe other mathematical expressions. On the number line, size comparisons between two numbers are typically conducted.

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The GCF: x

answer: x(x+2)

The area of the base and curved surface area is 15400mm²  and 22000 mm² respectively, of the cylindrical surface.

What is the cylindrical surface?

The amount of space that is covered by the curved surface and flat surface of a cylinder's bases is known as the cylinder's surface area. In addition to the area of the curved surface, the cylinder's total surface area also comprises the areas of its two circular bases. Units of surface area are stated as squares, such as square millimeters, square inches, square feet, and so on. Two circular bases joined by a curving face form a 3-D solid object known as a cylinder.

The curved surface area of a cylinder is 2πrh

A = 2 * 22/7*140/2*50

A = 22000 mm²

The base are will be π r²

B= 22/7 * 140/2*140/2

B= 15400mm²

Hence the area of the base and curved surface area is 15400mm²  and 22000 mm² respectively.

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Answer:Yes, the obtuse angles for both triangles are equailateral

Step-by-step explanation:

Options B and C are the following conclusions that are true about the transformation of quadrilateral BLUE.

A four-sided polygon having four edges and four corners is referred to as a quadrilateral in geometry. The name is a combination of the Latin words quadri, which is a variation of four, and latus, which means "side." It is sometimes referred to as a tetragon, which is derived from the Greek words "tetra" for "four" and "gon" for "corner" or "angle," in comparison to other polygons (e.g. pentagon). Because "gon" means "angle," it is sometimes referred to as a quadrangle or 4-angle.

Either simple (not self-intersecting) or complicated quadrilaterals exist (self-intersecting, or crossed). Convex or concave surfaces characterize simple quadrilaterals.

From the given figure,

The points in the quadrilateral BLUE are

B(-8,5), L(-5,5), U(-3,4), E(-6,1)

If the quadrilateral BLUE is rotated 270° then,

B(-8,-5), L(-5,-5), U(-3,-4), E(-6,-1)

Now, the image is reflected

So, the points are switched as,

B'(-5,-8), L'(-5,-5), U'(-4,-3), E'(-1,-6)

Distance of BE is,

√(x₂-x₁)²+(y₂-y₁)²

√(-1+5)²+(-6+8)²

=√16+4

=√20

Distance of B'E' is,

√(-6+8)²+(1-5)²

=√4+16

=√20

∴BE=B'E'

And the quadrilateral B'L'U'E' will be located entirely on third quadrant.

Therefore, B and C are the appropriate choices.

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Answer:

m1 = 33 degrees ; m3 = 33 degrees

Step-by-step explanation:

m8 = m4 = 147 degrees

m4 + m1 = 180

147 + m1 = 180

m1 = 180 - 147

m1 = 33 degrees

m1 = m3 (vertical angles)

Using the GCF to factor and the distributive property 28 + 24 = 4(7 + 6)

28 + 24 as a product of the two factors using greatest common factor and the distributive property can be represented as follows:

The greatest common factor is defined as the largest number that is a factor of two or more numbers.

The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC.

Therefore, lets solve 28 + 24 using GCF and the distributive property.

The GCF of 28 and 24 is 4. Hence,

28 + 24 = 4(7 + 6)

Therefore,

28 + 24 = 4(7 + 6)

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Answer:

9:5

5:14

Step-by-step explanation:

Answer:

5.267

Step-by-step explanation:

Let's do long division to figure this out.

Answer: 5.26666666667

Step-by-step explanation:

If your asking for the decimal answer, than it is 5.26666666667, or you can round it to 5.3. :)

The total number of votes which is reduced by the ratios of yes and no votes will be: 4580; + 6412 = 10992;

What are Ratios?

Comparing two amounts of the same units and determining the ratio tells us how much of one quantity is in the other. Two categories can be used to categorize ratios. Part to whole ratio is one, and part to part ratio is the other. The part-to-part ratio shows the relationship between two separate entities or groupings. For instance, a class has a 12:15 boy-to-girl ratio, whereas the part-to-whole ratio refers to the relationship between a particular group and the entire. For instance, five out of every ten people enjoy reading. As a result, the ratio of the part to the whole is 5: 10, meaning that 5 out of every 10 people enjoy reading.

In the given question, we have:

The ratio of yes votes to no votes was 7 to 5.

Total Number of Yes votes = 6412;

So, Let us assume the total number of no votes be x;

So, according to the question,

[tex]\frac{7}{5} = \frac{6412}{x}[/tex]

Cross Multiplying the terms:

⇒7 × x = 6412 ×5

⇒x = 4580;

So, The total number of no votes is 4580;

So, The total number of votes will be: 4580; + 6412 = 10992;

Hence,

The total number of votes will be: 4580; + 6412 = 10992;

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Using Euler'formula, the difference between maximum and minimum possible numbers of faces is 96.

A polyhedron is a 3D shape with flat faces, straight edges, and sharp vertices (corners). "polyhedron" meaning "many" and "polyhedron" meaning "area". Therefore, when many planes are joined, they form a polyhedron.

Because all faces are triangles. So on a triangular base with triangular faces on both sides that meet at the vertex.

Therefore, the minimum number of triangular faces of a regular polyhedron is = 4

Next, the double pyramid has "2n" triangular faces. where n is a natural number greater than 2 and 'n' represents the number of sides of the base of the pyramid.

A polyhedron having equal quadrilateral faces is known as regular hexahedron.

quadrilateral faced polyhedron with total sides 100 and vertices 6 , then using Euler's formula

F + V-E = 2

=> F + 6- 100= 2 => F = 96 maximum faces possible = 96

Now the difference between maximum and minimum number of faces = 100 - 4 = 96

So the difference between maximum and minimum faces is 96.

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The polar form of the complex number z = - 2√3 - i 6 is z = (4√3) · (cos 4π / 3 + i sin 4π / 3). (Correct choice: D)

Complex numbers are numbers of the form z = a + i b, where a and b are real numbers. This form is known as rectangular form. The polar form equivalent to that number is:

z = r · (cos θ + i sin θ)

Where:

The norm and the direction of the complex number are, respectively:

r = √(a² + b²)

θ = tan⁻¹ (b / a)

If we know that a = - 2√3 and b = - 6, then the polar form of the complex number is:

r = √[(- 2√3)² + (- 6)²]

r = 4√3

θ = tan⁻¹ [(- 6) / (- 2√3)]

θ = 4π / 3

z = (4√3) · (cos 4π / 3 + i sin 4π / 3)

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Answer:

27

Step-by-step explanation:

45/5=9

9*3=27

Answer: 27

Step-by-step explanation:

45/5=9

9x3=27

Answer:

$250

Step-by-step explanation:

He expected to collect 37.5% less than $400.

First, we find 37.5% of $400.

Then we subtract that amount from $400.

37.5% of $400 is:

37.5% of $400 = 0.375 × $400 = $150

Now, subtract $150 from $400:

$400 - $150 = $250

Answer: $250

The AER on the savings account, based on the interest rate and the period it is paid is 8.16%

The AER stands for Annual Equivalent Rate which shows the periodic rate of an interest rate, based on the number of compounding periods of the savings account or investment.

The formula for Annual Equivalent Rate (AER) is:

= ( 1 + interest rate / number of payment or compounding periods) ^ number of payment or compounding periods - 1

The AER on the savings account is therefore:

= ( 1 + 8% / 2 semi annual periods) ² - 1

= 0.0816

= 8.16%

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The function for the arithmetic sequence (fn) = 8n

The domain is {1,2,3,…10}

An arithmetic sequence is a series of numbers in which each term (save the first) is obtained by adding a constant number to the preceding term. For example, 2, 4, 6, 8,... is an arithmetic sequence because each term is created by adding 2 (a constant integer) to the previous term.

Given that

The arithmetic sequence is 8, 16, 24, 32, 40, 48, 56

Common difference = 16-8 = 8

The sequence is increasing so the common difference is positive 8

fn = 8 + (n-1)d

fn = 8 + (n-1)8

fn = 8 + 8n – 8

fn = 8n

So the function for the arithmetic sequence (fn) = 8n

b. The points to the graph are represented by (nfn). So the points are (1,8);(2,16);(3,24);(4,32);(5,40);(6,48);(7,56)

The domain of the function is the number 10

So, the domain is {1,2,3,…10}

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According to the Pythagoras theorem, the value of the slope of the ramp is 10.44

Pythagoras theorem

Pythagoras theorem states that the sum of squares of the sides equal to the square of the hypotenuse.

The general form of the Pythagoras theorem is,

c² =  a² + b²

where

c refers the hypotenuse

a and b refers the sides of the triangle.

Given,

Here we have the ramp with the side values 3 and 10.

Now, we have to find the value of the slope.

Let us consider x be the hypotenuse or slope of the ramp.

We know that the Pythagoras theorem states that the square of the hypotenuse is equal to the sum of square of the sides.

So, it can be written based on these,

x² = 3² + 10²

x² = 9 + 100

x² = 109

x = √109

When we simplify this one then we get the value of slope as 10.44.

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Answer:

4 or -8

Step-by-step explanation:

180-148=x(x+4)

32=x^2 + 4x

x^2 +4x - 32

x = 4 or -8

Using equivalent equations to equate both caterer A and B need to serve 10 guests to have equal pay

Equivalent equations are systems of equations that have the same solutions. Equations are said to be equivalent when they have the same solution set. For example, x + 2 = 6 and 2x = 8 are equivalent equations, because when we solve each of them as follows, they have the same solution set: x + 2 = 6. Subtract 2 from both sides. x = 4.

In this case, we can set up two equations and equate them to know how many people they need to serve in order to earn equally.

For caterer A;

y = 15x + 100 ...eq(i)

y = 20x + 50 ...eq(ii)

For the equation to be equivalent, equation(i) and (ii) must be equal

15x + 100 = 20x + 50

x = 10

They both need to serve 10 guests to earn equally.

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Answer:

1) 1 = 120 degrees and 2 = 60 degrees

2) x = 25

3) p = 32

Step-by-step explanation:

1) Angle 1 is 120 degrees, since it is congruent to the corresponding angle below it (because lines a and b are parallel) Angles 1 and 2 are supplementary, meaning they add up to 180, so to find angle 2 we do 180 - 120 to get 60. Angle 1 = 120 degrees and angle 2 = 60 degrees.

I did 2 and 3 on paper, let me know if anything is confusing :))

2) the two lines are parallel, so we know those two angles are congruent since they're corresponding. If they're congruent we can just set them equal to each other to find x. x = 25.

3) the little square mark means a right angle, which is 90 degrees. The two lines are parallel, so we know that the angle below is corresponding and congruent to 90 degrees. So to find p, set 3p - 6 equal to 90. p = 32.

if anythings confusing let me know :-)

Answer:

∠DEA
I think, adjacent means "next to, or adjoining something else."
Since ∠BEC, and ∠DEA are sharing point E, I think they are adjacent.

(I haven't done this kind of math in forever..)

The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

In the question ,

it is given that ,

the equation is given as |y [tex]+[/tex] 6| [tex]=[/tex] 2 ,

after removing the modulus  , we get the two equations , that are

y + 6 = 2 and y + 6 = -2

Solving y + 6 = 2 , we get

y + 6 = 2

Subtracting 6 from both LHS and RHS ,

we get

y = 2 - 6

y = -4

On Solving y + 6 = -2 ,

we get

y + 6 = -2,

Subtracting 6 from both LHS and RHS ,

we get

y = - 2 - 6

y = -8 .

the two solutions are y = -8 and y = -4 .

Therefore , The conclusion from the equation |y + 6| = 2 is that it has two solutions , the correct option is (b) .

The given question is incomplete , the complete question is

Consider this equation. |y + 6| = 2 what can be concluded of the equation? check all that apply.

(a) There will be one solution

(b) There will be two solutions.

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The 45° and 55° base angles of the triangle that share a vertex with the inverted triangle that have the vertex angle (at the shared vertex) marked x, indicates that x is 80°

A shared vertex is a common point to two or more figures that is also a vertex to the figures that share the point.

The measure of the vertex angle of the triangle at the top which is inverted = x

The measure of the base angles of the triangle at the bottom are;

45° and 55°

The measure of the vertex angle of the triangle at the base = y

From the diagram of a similar question, angle x and angle y are vertical angles (angle x and angle y are formed by the intersection of two lines)

45° + 55° + y = 180° (angle sum property of a triangle)

y = 180° - (45° + 55°) = 80° (subtraction property of equality)

y = 80°

x ≅ y (vertical angles theorem)

x = y (definition of congruent angles)

x = 80° (substitution property of equality)

The measure of angle x is 80°

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Answer:

Step-by-step explanation:

Comment

How many 3 digit numbers are divisible by 4, but do not contain the digit nine?

If you know a computer language, then the main line would be

for x = 100 to 999 do

12x³ - 39x² -   111x + 30 is polynomial in standard form .

What in mathematics is a polynomial?

Using mathematical operations like addition, subtraction, multiplication, and division, a polynomial is an expression made up of variables, constants, and exponents.

standard form g(x) = 3(x + 2)(4x - 1)(x - 5)

                      g(X) = 3[ 4x² - x + 8x - 2 )( x - 5 ) ]

                             = 3[ ( 4x² + 7x - 2 ) ( x - 5 )]

                             = 3 [ 4x³ + 7x² - 2x - 20x² - 35x + 10 )]

                             = 3[ 4x³ - 13x² - 37x + 10 ]

                             = 12x³ - 39x² -   111x + 30

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