. The Declaration of Independence is approximately 1,458 words including signatures, which Tewanda read in 9 minutes. How fast did she read the document?​

Now, According to the question:

Linear inequalities are defined as a mathematical expression in which two expressions are compared using the inequality symbol. The expression can be an algebraic expression or numerical expression or a combination of both.

Graph Linear Inequalities in Two Variables:

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A pair of right triangles are said to be congruent if the lengths of their respective sides and angles are the same.

If the size and shape of two right triangles match, they are said to be congruent. Alternatively said, two right triangles are said to be congruent if the length of their respective sides and angles are equal. Fig. 1 shows that ABC = RPQ since A = R, C = Q, and B = P.

No, not every right triangle has a congruent angle. If the hypotenuse and the leg of one right-angled triangle match the hypotenuse and the corresponding leg of the other triangle, the two triangles are said to be congruent. This circumstance, known as RHS congruence of two triangles, only applies to right angled triangles. An isosceles triangle is one that possesses two congruent sides.

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Answer:

 14 boys

Step-by-step explanation:

We know

The ratio of girls to boys is 5:2, which means for every 7 kids, there are 5 girls and 2 boys

So, 49 kids there are

2 x 7 = 14 boys

So, there are 14 boys

Answer:

length= 8x

width= x

perimeter of a rectangle= 2L+2W

=2(8x) + 2(x)

=16x + 2x

perimeter=18x

Answer:

2 / 3/7

2/1 x 3/7

Cross Multiply

14/3

Answer:

26. Scale Factor of A to B:    [tex]\boxed{\dfrac{3}{4}}[/tex]

27. Scale factor of B to A:  [tex]\boxed{\dfrac{4}{3}}[/tex]

Step-by-step explanation:

If two triangles are similar, the ratios of the side length to the corresponding side length  of the other must be the same for all sides

The first challenge is to figure out which side of triangle A corresponds to which side of triangle B

If you flip triangle A counterclockwise by 90° the angles will be aligned with each other and it is easier to see the corresponding sides of A and B

We see that ....

side length 24 of A matches with side length 18 of B

side length 36 of A matches with side length 27 of B

side length 32 of A matches with side length 24 of B

B is of smaller size than A so the scale factor of A to B is less than 1

26.

Therefore the scale factor of A to B is

[tex]\dfrac{18}{24} = \dfrac{27}{36} =\dfrac{24}{32}\\\\\\\dfrac{18}{24}= \dfrac{3}{4} \cdots \textrm { by dividing numerator and denominator by 6}[/tex]

[tex]\dfrac{27}{36} = \dfrac{3}{4} \cdots \textrm { by dividing numerator and denominator by 9}\\\\\\\dfrac{24}{32} = \dfrac{3}{4} \cdots \textrm { by dividing numerator and denominator by 8}\\\\\\[/tex]

So the scale factor of Figure A to Figure B is [tex]\dfrac{3}{4}[/tex]

----------------------------------------------------------------------------------------------

27.

The scale factor of Figure B to Figure A is the reciprocal of
[tex]\dfrac{3}{4}[/tex]

Reciprocal of
[tex]\dfrac{3}{4} \; is \; \dfrac{4}{3}[/tex]

So scale factor of B to A is

[tex]\dfrac{4}{3}[/tex]

The length in centimeters of the side of the square is 8 cm.

The area of a rectangle and a square are -

A{R} = Length x Breadth

A{S} = Side x Side

Given is that a square and a rectangle have the same area. The length of the rectangle is 32 cm and the width of the rectangle is 2 cm.

It is given that -

A{R} = A{S}

Length x Breadth = Side x Side

32 x 2 = (Side)²

(Side)² = 64

Side = 8

Therefore, the length in centimeters of the side of the square is 8 cm.

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The two bikers are 11.18 miles apart from each other according o the coordinate plane.

A surface with two dimensions made of two number lines is referred to as a coordinate plane. When the origin, the place where the X- and Y-axes intersect, is reached, it is produced. A coordinate grid's numbers are used to find points. For graphing points, lines, and many other things, a coordinate plane is helpful. It functions as a map and gives precise directions on how to get from one place to another.

Distance between two coordinates is given by

d = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]

Here, (x₁, y₁) is (5, 4) and (x₂, y₂) is (3,-7)

Putting the values in formula

d = [tex]\sqrt{(3-5)^2+(-7-4)^2}[/tex]

d = [tex]5\sqrt{5}[/tex]

d = 11.18 miles

Thus, The two bikers are 11.18 miles apart from each other according o the coordinate plane.

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Answer:

[tex]\boxed{-2x^2 -2x +24\\}\\\\[/tex]

Step-by-step explanation:

The standard form of a quadratic function is:

[tex]y = ax^2 + bx + c\\[/tex]

where a, b and c are constants

 [tex]\textrm{The given expression is $y=-2\left(x-3\right)\left(x+4\right)$}[/tex]

Expand the right side of this expression
[tex]-2\left(x-3\right)\left(x+4\right)[/tex]

First expand (x-3)(x+4) using the FOIL method:

[tex](x-3)(x+4)[/tex]

[tex]=x\cdot x+x\cdot \:4-3x-3\cdot \:4\\\\= x^2+x-12[/tex]

[tex]-2\left(x-3\right)\left(x+4\right)\\\\= -2(x^2+x-12)\\\\= \boxed{-2x^2 -2x +24\\}\\\\[/tex]

ANSWER

The ratios in a 45-45-90 triangle are as follows: 1 : 1 : 2 for angles (45 degrees: 45° : 90°); and. 1 : 1 : 2 on the sides (a: a : a√2).

In addition, the 45-45-90 triangle is an isosceles triangle, which indicates that each of its legs is the same length.

In a triangle, the trigonometric ratio Tan Theta is the same as opposite or adjacent.

A 45-45-90 triangle has side lengths that are 1: 1: .

As a result, tan45 has a value of 1.

According to the 45 45 90 triangle theorem, special right triangles with sides whose lengths are in a special ratio of 1: 1 : 2 1:1:sqrt2 1:1:2, two angles of 45 degrees, and one right angle of 90 degrees.

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The easiest way to combine a similar file that are all located in the same folder are:

Combine A Similar File

There are several ways to combine similar files that are located in the same folder, depending on the type of files and the operating system you are using. Some options include:

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These are the vertex, focus, directrix, and focal width

Vertex: (0, 0), Focus: (0, 7), Directrix: y = -7, Focal width: 28

The vertex, focus, directrix, and focal width of the parabola described by the equation x^2 = 28y are:

Vertex: (0, 0)

Focus: (0, 7)

Directrix: y = -7

Focal width: 28

The vertex of a parabola is the midpoint of the directrix and the focus, which in this case is (0, 0). The focus is the point on the parabolic curve that is closest to the directrix, which in this case is (0, 7).

The directrix is the line along which the distance between the parabolic curve and its focus is minimized, which in this case is y = -7. The focal width is the distance between the focus and the directrix, which in this case is 28.

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The measure of ∠V of the parallelogram is = 150.5°

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure

The four types are parallelograms, squares, rectangles, and rhombuses

Properties of Parallelogram

Opposite sides are parallel

Opposite sides are congruent

Opposite angles are congruent.

Same-Side interior angles (consecutive angles) are supplementary

Each diagonal of a parallelogram separates it into two congruent triangles

The diagonals of a parallelogram bisect each other

Given data ,

Let the measure of the angle ∠Y = 10x + 27

Let the measure of the angle ∠W = 2x + 29

Now , for a parallelogram the opposite sides are congruent and opposite angles are congruent

Substituting the values in the equation , we get

10x + 27 = 2x + 29

Subtracting 2x on both sides of the equation , we get

8x + 27 = 29

Subtracting 27 on both sides of the equation , we get

8x = 2

Divide by 8 on both sides of the equation , we get

x = 1/4

Let the measure of the angle ∠Y = 10 ( 1/4 ) + 27

Let the measure of the angle ∠Y = 2.5 + 27

Let the measure of the angle ∠Y = 29.5°

Now , same-side interior angles (consecutive angles) are supplementary

Substituting the values in the equation , we get

angle ∠Y + angle ∠V = 180°

29.5° + m∠V = 180°

Subtracting 29.5 on both sides of the equation , we get

m∠V = 150.5°

Hence , the measure of m∠V = 150.5°

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3x° - 3° = 2x° + 13°

They are vertically opposite angle...

3x° - 2x° = 13° + 3°

1x = 16°

x = 16°

hence...the value of x is 16°

The number of bags of pink beads that can be made from today's shipment is given as follows:

5 bags.

The number of bags is obtained applying the proportions in the context of this problem.

We have that each bag weights 1/10 of a pound.

The shipment was of 4/7 pounds of pink beads, hence the total number of bags of pink beads that can be made from today's shipment is calculated as follows:

4/7/(1/10) = 4 x 10/7 = 40/7 = 5.

(rounded down, as the number of bags is a countable amount).

The problem is given by the image presented at the end of the answer.

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Answer: 10

Hope this helps :)

Step-by-step explanation:

29b = 290

/29     /29

b = 10

Answer:

b = 10

Step-by-step explanation:

29b = 290

-----     ------

29        29

b = 10

Answer:

R875

Step-by-step explanation:

We know

R35 = 1kg of breakfast cereal

? = 25kg of breakfast cereal

35 times 25 = R875

So, 25kg of breakfast cereal will cost R875.

They will win 100 games if the team rate continues through a 148-game season.

We will solve our question with the help of the Multiplication rule.

As per the question, the baseball team has won 25 games and lost 12 games. This will give us a total of 25+12= 37 games.

It is given that if the baseball team rate continues through a 148-game season which is 37*4 = 148 games.

So, we should multiply our initial won matches by 4 to get the final won matches as per the given condition, we will get:

25*4 = 100 matches.

We can also find the answer by:

You would multiply 25 by 148 divided by 37 to determine the number of games won if you were comparing the 25 of the 37 games won to the total of 148 games played.

(148*25)/(25+12)

= 3700/37 = 100

Therefore if the baseball teams' rate continues through a 148-game season, then they will win 100 matches.

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Step-by-step explanation:

He starts at 8000 gallons      when he adds 2000 gals it will overflow

120 gal go out each hour       225 gal goes in each hour     net : 105 gal per hour IN

105 x = 2000 gal

x = 19.048 hours until overflow      

1 pm + 19 .048 hours =  8.048 AM  = ~~8 :03 AM   Since he checks every hour, he will first see the overflow at   9:00 AM

The zeroes of the polynomial f(x) are 7, 6 and -1. The solution is obtained by the method of polynomial long division.

What is polynomial long division?

A long division polynomial is a formula for dividing one polynomial by another of the same degree or lower. The divisor, quotient, dividend, and remainder are all components of the long division of polynomials, just like they are for long division of numbers.

We are given f(7) = 0.

This means that (x-7) is one factor of f(x).

Using Polynomial Long Division,

Dividing :  x^3 -12x^2 + 29x + 42 ("Dividend")

By         :    x-7    ("Divisor")

Dividend     x^3  -  12x^2  +  29x  +  42

- divisor  * x2   x^3  -  7x^2        

Remainder      -  5x^2  +  29x  +  42

- divisor  * 5x     -  5x^2  +  35x    

Remainder             -       6x           +  42

- divisor  * (-6)            -       6x           +  42

Remainder                                  0

Quotient :  x^2-5x-6  

Remainder:  0

Now, factoring x^2-5x-6 , we get

⇒x^2-6x+x-6

⇒x(x-6)+1(x-6)

⇒(x+1)(x-6)

Thus, the factors are (x+1), (x-6) and (x-7).

Hence, the zeroes of the polynomial f(x) are 7, 6 and -1.

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The conclusion we can reach is D. If Henry goes to the library, he looks for books on tape.

An inductive proof requires two cases. The first, or base case, establishes the proposition that n = 0 without requiring any prior knowledge of other situations. The second example, the induction step, demonstrates that if the assertion is true for any particular case where n = k, then it must also be true for the subsequent case when n = k + 1. These two actions prove that the statement is true for all n = 1 natural numbers. The base case establishes the truth of the statement for all natural numbers n N, but it does not always start with n = 0. Instead, it frequently starts with n = 1, and it may also start with any fixed natural number n = N.

Given, If Henry goes to the library, he reads a book.

If Henry reads a book, he becomes smarter.

If Henry becomes smarter, he becomes happier.

If Henry becomes happier, the world is a better place.

Now, The only statement that is valid is  If Henry goes to the library, he looks for books on tape.

As reading books only by henry won't make the world a better place.

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Answer:

Nick is 6 years old.

Erica is 18 years old.

Step-by-step explanation:

Hello!

We know that Erica is 12 years older than Nick, which also means she is 3 times older than Nick. We can represent this situation as two equations.

Let E be Erica's age, and x be Nick's age.

E = x + 12, and E = x* 3

Since E is equal to E, we can say that x + 12 = 3x.

The value of x is 6. Nick is 6 years old, and Erica is 18 years old.

The 3-Systems of Equations Calculator is an online tool that provides the answer for the unknown variables after solving three equations with three different variables each utilizing a different approach.

To resolve equations involving the three variables x, y, and z, use the 3 systems of equations calculator. A group of three equations with three variables make up the three systems of equations. Three equations are entered, the equations are rearranged, and the values of x, y, and z are solved for.

This calculator can also calculate equations of the second and third degree, which result in complex solutions for the variables x, y, and z. Three actual solutions are provided by the calculator if the equation system is linear.

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Answer:

it's a little blurry but i think the slope is 2/3 and the y-intercept is -2

Step-by-step explanation:

The mass when L = 0.6 is given as follows:

M = 68.57 kg.

The mass of the cube is modeled according to a proportional relationship, as follows:

M = kL.

In which k is the constant of proportionality.

The mass the cube is 40 kg when the length of its edge is 35 cm = 0.35 m, hence the constant is obtained as follows:

0.35k = 40

k = 40/0.35

k = 114.28.

Hence the mass when L is of 0.6 m is given as follows:

M = 114.28 x 0.6

M = 68.57 kg.

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The angle 360 degree is called as complete angle.

An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.

A form of angle that measures 360° is known as a full angle. When two lines meet at a point, an angle is created, and the angle is the width of the space created.

The angle generated in this case is referred to be the complete angle if, after one complete revolution, the final ray corresponds with the incident or initial ray. A round angle and a complete angle are the alternate names. The angle, which corresponds to the center of a circle, is 2 radians, or 360 degrees. A complete angle is made up of four right angles or two straight angles. The amount of rotation makes the angle different from a zero angle.

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Answer:

1. 8

2.3

Step-by-step explanation:

This for num 2

[tex] \sqrt{8} = \sqrt{2 \times 4} = 2 \sqrt{4} = 2[/tex]

6÷2=3

1.

To solve [tex]\sqrt[n]{16}=2[/tex], you need to turn the question around and ask what value of n makes [tex]2^n=16[/tex].

n = 4

2.

To simplify this, your teacher could mean two things, either "just simplify the radical" or "rationalize the denominator."

For the first option, [tex]\sqrt{8}=\sqrt{4\cdot2}=\sqrt{4}\cdot\sqrt{2}=2\cdot\sqrt{2}[/tex], so your overall expression becomes:

    [tex]\dfrac{6}{2\cdot\sqrt{2}} = \dfrac{3}{\sqrt{2}}[/tex]

Now if your teacher also wants the denominator rationalized, then you keep going and multiply that by [tex]\dfrac{\sqrt{2}}{\sqrt{2}}[/tex]:

    [tex]\dfrac{3}{\sqrt{2}}\cdot \dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{3\sqrt{2}}{2}[/tex]

Answer:

y = -4x + 2

Step-by-step explanation:

y-6=-4x+4

y = -4x - 4 + 6

y = -4x + 2

Answer:

Let's say Hamid's normal weight is x.

88kg = 110%x

88kg=11/10x

Divide by 11 on each side

8kg=1/10x

Multiply by 10 on each side

80kg=x

Hamid's normal weight is 80kg

Using multiplication, Correct option is B, Justin earned $144 in 4 weeks.

One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size.

The multiplicand, multiplier, and product are the components of a multiplication sentence. The first number is the multiplicand, the second number is the multiplier, and the result is the product. Let's examine a few various forms of multiplication sentences and discover how to finish them.

As per the question,

Each week they make a total of $72.00,

Money earned in 4 weeks = 72 × 4 = $288

They split in equal halves,

⇒ $288 / 2 = $144

∴ Justin earned $144 in 4 weeks.

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