Question 12
If a car tries to stop on ice, the distance the car slides can be modeled by the equation s= 50d + 25 where s stands
for speed in mph and d stands for distance in feet. What distance will you slide if your car is traveling at a speed of
55 mph?

The 3D distance formula is represented as √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

The 3D distance formula, also known as the Euclidean distance formula, is used to calculate the distance between two distinct points in three-dimensional space. The formula is the square root of the sum of the squares of the differences in the x, y, and z coordinates of the two points. Mathematically it can be represented as:

Distance = √((x2 - x1)² + (y2 - y1)² + (z2 - z1)²)

Where (x1, y1, z1) and (x2, y2, z2) are the coordinates of the two points.

It's used to measure the distance between two points in 3-D space. It's the straight-line distance between two points. This formula can be applied in various fields such as physics, computer graphics, and robotics.

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The coordinates of the vertices after a dilation with a scale factor of 1/3 centered at the origin is E'(0, -2), F'(3, -2), G'(3, 1) and H'(0, 1).

Dilation is  a type of transformation where the figure is enlarged or made smaller such that it preserves the shape but not size.

Every dilated image are similar figures to the original figure.

Given that center of the dilation is origin.

Any coordinate (x, y) when dilated to a scale factor k is (kx, ky).

The coordinates of the quadrilateral are E(0, -6), F(9, -6), G(9, 3) and H(0, 3).

Dilation is with a scale factor of 1/3.

So all the coordinates become (1/3x, 1/3y).

E(0, -6) becomes E'(0, -2)

F(9, -6) becomes F'(3, -2)

G(9, 3) becomes G'(3, 1)

H(0, 3) becomes H'(0, 1)

Hence the coordinates are E'(0, -2), F'(3, -2), G'(3, 1) and H'(0, 1).

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If each of the quadrilateral is a trapezoid, then the measure of ∠Q = 89 and ∠S = 153.

A polygon with only one set of parallel sides is called a trapezoid. The parallel bases of a trapezoid are another name for these parallel sides. Trapezoids have two additional sides that are not parallel and are referred to as their legs.

Given that in a trapezoid, the angle T is 91 and the angle R is 27.

For a trapezoid the measure of angle are as follows:

∠T + ∠Q = 180

∠R + ∠S = 180

Substituting the measures of ∠T and ∠R in the above equations we have:

91 + ∠Q = 180

∠Q = 89

27 + ∠S = 180

∠S = 153

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The reduced form of 14/10 is 7/5. The answer is obtained using the method of simplifying fractions.

What is meant by simplifying fractions?

Making a fraction as simple as possible is referred to as simplifying (or reducing) a fraction.

To do this, we divide the denominator and numerator by the biggest number that can be divided exactly into both numbers. In other words, we choose the biggest common number between the top and bottom and divide it by that.

In a fraction, the numerator and denominator are referred to as the "terms." Thus, when we simplify a fraction, we cast it in its most basic mathematical form.

Now, to reduce 14/10, we will find the highest common factor of 14 and 10.

The highest common factor is 2 i.e. both numerator and denominator are divisible by 2.

So, on dividing both the terms by 2, we get

(14÷2)/(10÷2)= 7/5

Hence, the reduced form of 14/10 is 7/5.

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Answer:

"Substitution comes in three flavors: nominal, verbal or clausal, depending on the item being substituted.

Step-by-step explanation:

Hope it helps!

The length of rectangle :10 feet

               The width of rectangle :  4 feet

       Given

        perimeter of the rectangle :28 feet

       let  width of the rectangle be :x

         and  length  of the rectangle be :  6+x   (as per given condition)

      therefore  

                      perimeter = 2(length +width)

                               28 = 2(6+x+x)

                               28 = 2(6+2x)

                               28 = 12+4x

                               28-12 = 4x

                                16  = 4x

                                 x = 4

  as width of rectangle  is : 4

similarly  length : 6+x

                            6+4

                            :10

The dimensions of the rectangle are : length =10

                                                               width = 4

verification :

perimeter =2(l+w)

28 = 2(10+4)

28 = 28

Answer: multiplying by denominators

Step-by-step explanation: not sure if this is the right answer in this context but i hope it helps

technically cross multiplying basically is multiplying by denominators, but depending on the math level they are sometimes considered different methods

again, this may not be correct so if you want a more clear answer could you provide a bit of context? sorry, hope it helps anyway though.

The formula for a sector's area is: 1. A = (sector angle / 360 ) * (pi *r2)

2. A = (sector angle / (2*pi)) * (pi * r2) 3. A = (fraction of the circle) * (pi * r2)

The ratio used to find the area of the sector is that of how to know what fraction of the circle is the sector.

Ratio = (θ/360°)

θ is the angle subtended at the center of the circle by the arc, measured in degrees.

For this question,

θ = 60°

Ratio = (θ/360°) = (60°/360°) = (1/6)

Area of a circle is given as

Area of a circle = πr²

where

π = pi

r = radius of the circle = 8

Area of the circle = πr²

Area of the circle = π (8²) = 64π square units

Area of the sector is given as

Area of the sector = (Ratio) × (Area of the circle)

Ratio = (1/6)

Area of the circle = 64π square units

Area of the sector = (Ratio) × (Area of the circle)

Area of the sector = (1/6) × (64π) = (64π/6) = (32π/3) square units

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Completing a square is a method for transforming a quadratic equation’s form so that its LHS becomes a perfect square, commonly known as vertex form. This is accomplished by rearranging the phrase.

X2 is x multiplied by itself, which is symbolized by and may be expressed as xx or x(x) as an algebraic term. 2 is an exponent in. It denotes that x has been multiplied by itself twice. x 2 = x .

heres the answer is, X squared is a helpful notation that we use in math. It can be used in different kinds of algebraic expressions. It simplifies our calculations and allows us to develop formulas to solve problems quicker!

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Aira should must score a total of 179 combined in her next two quizzes in order to make the average of all the marks of the quizzes as 83.

Aira has got 76, 85, 81 and 77 marks in her 4 quizzes.

I have to give two more quizzes and the marks obtained in those two quizzes should be such that the average of all the quizzes should be 83.

We know that we can find the average of the data by taking the sum of all the given values and dividing that particular value by the number of data given to us.

Here in this case let assume that she obtained X marks in her next to test combined. Now this way total number of observation are 6.

Now, we can simply apply the formula to find the average of the data.

Average = (76 + 85 + 81 + 77 + X)/6

83 = (76 + 85 + 81 + 77 + X)/6

X = 179

So, Aira should obtain 179 marks in her next to quizzes in order to make the average of all the score equal to 83.

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Answer:U: 1.98 V: 1.4 And also the other side, square root symbol: 1.4

Step-by-step explanation:

I hope this helps man, i havnt done this stuff in a while...

In mathematics, the factor theorem mostly used when factoring the polynomials totally. factorial theorem is that links factors and zeros of the polynomial.

By to factor theorem, if f(x) is a polynomial of degree n ≥ 1 and ‘a’ is any real number, then, (x-a) is a factor of f(x), if f(a)=0.

including, we can say, if (x-a) is a factor of polynomial f(x), then f(a) = 0. This also proves that the converse of the theorem. Let us see the proof and example.

Factor theorem is mostly used for factoring a polynomial and searching the roots of the polynomial. It is an important case of a polynomial remainder theorem.

As examined in the introduction, a polynomial f(x) has a factor (x-a), if and only if, f(a) = 0. It is one of the processes to do the factorization of a polynomial.

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The steady state value of the system is determined using the final value theorem.

The main characteristics of the Laplace transform are the initial and final value theorems. Pierre Simon Marquis De Laplace, a French mathematician and scientist, presented these theorems. Limiting theorems refer to both the initial and final value theorems.

The final value theorem asserts that one can compute a system's ultimate value using. The function's Laplace transform is

[tex]\lim_{t\rightarrow\infty}f(t) = \lim_{s\rightarrow0}sF(s)[/tex]

(1) Final value theorem prerequisites are the functions f(t) and f(t)' should be Laplace transformable.

(2) sF(s), where F(s) is the Laplace transform of f(t), has no pole on the j-w axis and right half plane.

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The term "congruent" refers to having exactly the same shape and size. Even if we flip, turn, or rotate the shapes, the shape and size should remain the same.

SSS (Side-Side-Side) (Side-Side-Side) SAS (Side-Angle-Side) (Side-Angle-Side) ASA (Angle-Side-Angle) (Angle-Side-Angle) AAS (Angle-Angle-Side) (Angle-Angle-Side) RHS (Right angle-Hypotenuse-Side) (Right angle-Hypotenuse-Side)

The first two postulates, Side-Angle-Side (SAS) and Side-Side-Side (SSS), emphasise the side aspects, whereas the following lesson discusses two additional postulates that emphasise the angles. The Angle-Side-Angle (ASA) and Angle-Angle-Side (AAS) postulates are what they are.

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Answer: the only line crossed is called a transversal line. x +3 would be vertically opposite to the other angle,and 2x-61 would also be vertically opposite. if you look at alternate and corresponding angles you would find the exact answer. this angle does not have a kind i guess.

hope it helps you!!!

Step-by-step explanation:

Answer:

Below

Step-by-step explanation:

Solutions are where the graphs intersect....they are equal at these points

(2,-3)  and (4,-1)  

There is likely one more point of intersection down and to the left which is not shown on the graph

The formula for the area of a square is A = s², where A is the area of the square and s is the length of one of its sides.

To calculate the area of a square, multiply the length of one side by itself. For example, if the side of a square is 5 meters, the area of the square would be 25 square meters (5² = 25). If the side of a square is 8 feet, the area of the square would be 64 square feet (8² = 64). The area of a square is always equal to the length of one side multiplied by itself.

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Answer:

It is called the perimeter

Step-by-step explanation:

What we can conclude by the given triangle about similarity is;

ΔPQR ∼ ΔPST

Similar triangles are defined as triangles that have the same shape, but their sizes may vary. Thus, if two triangles are similar, then it means that their corresponding angles are congruent and corresponding sides are in equal proportion.

Now, there are three types of similarity theorems for triangles namely;

Angle Angle(AA) Similarity

Side Angle Side(SAS) Similarity

Side Side Side(SSS) Similarity

We see that both triangles PQR and PST have equal angle R and angle T which are both 36 degrees. Thus, they are both similar by the AA Similarity theorem

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The total number of books that Jarrod packed into boxes can be represented by 84 + x*12.

The total number of books that Jarrod packed into boxes can be found by multiplying the number of boxes he packed with the number of books per box.

In this case, Jarrod packed 6 boxes of science textbooks with 14 books per box, so the number of books in the science boxes is 614 = 84. He also packed math textbooks with 12 books per box, so the number of books in the math boxes can be represented by x*12, where x represents the total number of boxes he packed.

So the total number of books that Jarrod packed into boxes can be represented by 84 + x*12.

Therefore, the equation that can be used to find the total number of books that Jarrod packed into boxes is: 84 + x*12 = Total number of books.

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The percentage of the tip that she leaves will be 20.02%.

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

Mrs. Peterson had lunch at Lunchee's. She paid $12.99 for her meal. She left a tip of 2.60.

Then the percentage is given as,

P = [2.6 / 12.99] x 100

P = 0.2002 x 100

P = 20.02%

The percentage of the tip that she leaves will be 20.02%.

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The measure of four angles of quadrilateral is 360°.

What is quadrilateral?

A closed quadrilateral has four sides, four vertices, and four angles.

It is a type of polygon.

In order to create it, four non-collinear points are joined.

Quadrilaterals always have a total interior angle of 360 degrees.

A polygon with four sides, four angles, and four vertices is called a quadrilateral.

The Latin words quadri, which means four, and latus, which means side, were combined to create the English word quadrilateral.

A quadrilateral is shown in the above image as an example.

A quadrilateral is a polygon with four vertices and four sides that each contain four angles, the sum of which is 360 degrees.

Two triangles are created when we draw a diagonal to a quadrilateral. These two triangles have a 180° angle sum.

As a result, the quadrilateral's total angle sum is 360°.

Hence, the measure of four angles of quadrilateral is 360°.

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Answer:

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

Graph each line:

The intersection of the lines is the solution:

By using the triangle inequality theorem, the possible side lengths for the third side is equal to: D. 4 < c < 42.

In Euclidean geometry, the Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than or equal (≥) to the third side of the triangle.

Mathematically, the Triangle Inequality Theorem is represented by this mathematical expression:

b - c < a < b + c

Where:

a, b, and c represent the side lengths of this triangle.

By applying the Triangle Inequality Theorem, the possible side lengths of the triangle's third side is given by:

b - c < a < b + c

23 - 19 < a < 23 + 19

4 < a < 42.

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Answer:

A. Function 1 has the lowest minimum value, and its coordinates are (−1, −3).

Step-by-step explanation:

To find the minimum value for f(x), set its first derivative to 0 and solve for x.

First derivative of f(x) is

f'(x) = 8x + 8 + 0 = 8x + 8

Setting this equal to 0 gives

8x + 8 = 0

8x = -8

x = -1

Plugging in this value for x in 4x² + 8x + 1 gives

f(x) = 4(-1)² + 8(-1) = 4 · 1 - 8 + 1

= 4 - 8 + 1

-4 + 1

= -3

So minimum for f(x) occurs at (-1, -3)

For g(x) the minimum is 0 and is at x = -1

So f(x) has minimum of -3 at x = -1

g(x) has minimum of 0 and occurs at x = -1

Answer:

A. Function 1 has the lowest minimum value, and its coordinates are (−1, −3).

The nearest whole number to which the new height of the image is enlarged is 9cm.

By scaling, we can create a drawing of an object that corresponds to the object's true size. In geometry, scaling refers to either growing or reducing figures in order to preserve their fundamental shape. Similar figures are what we call scaled figures.

Given that the original size was in the ratio 4: 3.

When the image is enlarged the enlarged image will be in the similar ratio to the original size.

Hence, the ratio in which the enlarged image will be increased is 4x : 3x.

The new width is given as 12,

The value of 4x = 12

x = 3

Then the new height of the image is:

3 (3) = 9cm.

Hence, the new height of the image is 9cm.

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Answer:

except 7/4

Step-by-step explanation:

The ratio of 4 to 7 is the same as the fraction 4/7

7/4 is not equal to 4/7 and therefore they cannot be written in the same way.