It is the same distance from second base to first base, and from second base to third base. The angle formed by first base, second base, and home plate has the same measure as the angle
formed by third base, second base, and home plate. What can you conclude about the distance from first base to home plate, and from home plate to third base? Explain using your knowledge of congruent triangles.

A transformation that alters the size of a figure is called a dilation (similarity transformation). It needs a scale factor of k and a central point. Depending on the value of k, the dilatation is either an enlargement or a decrease. The dilation is an enlargement if |k|>1.

If two figures have the same shape but different sizes, they are said to be comparable. A stiff motion combined with a rescaling constitutes a similarity transformation. In other words, a similarity transformation can change shape without changing location or size.

A dilation is a transformation that yields a different-sized picture with the same general shape as the original. Enlargements are dilations that result in a bigger picture. Reduction is the name for a dilatation that shrinks the picture. The initial figure is stretched or contracted by a dilatation.

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The expected net gain E(X) in the context of this problem is given as follows:

E(X) = -$0.5.

The net gain for this problem is modeled for a discrete distribution, as there are only two possible outcomes, given as follows:

The probability of winning is of 1% = 0.01, while the probability of losing is of 99% = 0.99, hence the distribution of gains for this problem is given as follows:

The expected value of a discrete distribution is calculated as the sum of each outcome multiplied by it's respective probability.

Hence the expected net gain for this game is calculated as follows:

E(X) = -1 x 0.99 + 49 x 0.01.

E(X) = -$0.5.

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Therefore , As a result, the intersection of these two lines will be a necessary point in order to solve the specified scatter plot problem (-0.5,2).

Several dots are placed on a vertical and horizontal axis to form a scatter plot. In statistics, scatter plots are crucial because they can demonstrate the amount of correlation, if any, between both the quantities of observed quantities or occurrences (called variables).

Here,

Maria You've erred, you know that. You don't understand the points at all. The attachment can be used to your advantage.

The property of rational numbers, according to which there are an endless number of terminating decimals between any two terminating decimals, must be used in order to plot any terminating decimal on the coordinate plane.

On the X axis, indicate -0.5 between 0 and -1.

Mark integer 2 on the Y axis in a similar manner.

Draw a line perpendicular to the Y axis, passing through (-0.5,0), and a line perpendicular to the X axis, passing through (0,2).

These two lines must cross at the specified position (-0.5,2).

As a result, the intersection of these two lines will be a necessary point in order to solve the specified scatter plot problem (-0.5,2).

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[tex]sin(C)=\cfrac{\stackrel{opposite}{4}}{\underset{hypotenuse}{9}}\qquad \textit{let's find the \underline{adjacent side}} \\\\\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \sqrt{c^2 - b^2}=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ \sqrt{9^2 - 4^2}=a\implies \sqrt{65}=a \\\\[-0.35em] ~\dotfill[/tex]

[tex]tan(C)=\cfrac{\stackrel{opposite}{4}}{\underset{adjacent}{\sqrt{65}}}\implies tan(C)=\cfrac{4}{\sqrt{65}}\cdot \cfrac{\sqrt{65}}{\sqrt{65}}\implies tan(C)=\cfrac{4\sqrt{65}}{65}[/tex]

Answer: original price: £400

Step-by-step explanation:

20/100 × original price = £80

Original price = £80 ÷ 20/100

                      = £400

Therefore , the solution of the given problem of linear equation comes out to be x= -6 , y = 45 and z =60.

The algebraic equation y=mx+b stands in for a linear equation. The slope is m, and B is the y-intercept. The last phrase referred to a "simple formula with two elements" where both y and x are variables. Bivariate linear equations are calculations involving two variables. Here are a few examples: The outcomes are 2x - 3 = 0; 2y = 8; m + 1 = 0; x/2 = 3; x + y = 2; and 3x - y + z = 3. If the answer to a mathematical equation is in the form y=mx+b, where m denotes the slope and b the y-intercept, the equation is said to be linear.

Here,

Given :

According to parallelogram laws

adjacent side sum is 180 degree

=> 4y + 3x-18 = 180

=> 4y+3x = 162

and

2x+12+3z = 180

=> 2x + 3z = 168

and

=> 3x+3z = 162

=> x + z =54

=> z = 54-x

So,

2x + 3(54-x) = 168

=> 162 - 3x+2x =168

=> -x = 6

or x =-6

and

z = 60

and

y = 162 - 3x /4

=> y= 162 +18 /4

=> y =180/4

=> y = 45

Therefore , the solution of the given problem of linear equation comes out to be x= -6 , y = 45 and z =60.

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Answer:

Step-by-step explanation:

y=2x-5+2

then you do minus 2 on both sides

Hope this helped!

Answer:

The slope is 0.75.

The equation is y=0.75x-2

Step-by-step explanation:

The answer is:

- 1 < x < 1

I hope this is correct

When B is the circumcenter of  triangle ADG the lengths of AE and DG are 4 and 12 respectively

The intersection of the perpendicular bisectors of a triangle's sides is known as the circumcenter of that particular triangle.

In other terms, the circumcenter is the point at which the bisector of a triangle's sides coincides.

The perpendicular lines radiating from the sides of the triangle are the bisectors hence the line it radiates from shares the is shared into two halves at that point

Having this in mind

AE = DE = 4

and

DF = GF = 6

Also, DF + GF = DG

DG = DF + DF

DG = 6 + 6

DG = 12

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The algebraic expression for area of rectangle in terms of width(w) is w^2+2w.

What is algebraic expression?

In mathematics, an expression that incorporates variables, constants, and algebraic operations is known as an algebraic expression (addition, subtraction, etc.).

The expressions are mainly of 4 types that includes:

Let the width be w.

So, length of rectangle will be w+2

Now, area of rectangle is length*width

Area= (w+2)*w

= w^2+2w

Hence, a simplified algebraic expression for the area of the rectangle in terms of width (w) is w^2+2w.

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The horizontal distance that the boat is from the lighthouse is 920.31 feet

An equation is used to show the relationship between numbers and variables.

Trigonometric ratio shows the relationship between the sides and angles of a right angled triangle.

A beacon light is 113 feet above the water. The angle of elevation to the beacon is 7 degrees.

Let d represent the horizontal distance from the house.

Using trig ration:

tanФ = opposite/adjacent

Substituting:

tan(7) = 113 / d

d = 920.31 feet

The horizontal distance is 920.31 feet

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The schedule of her course in 120 ways.

A finite collection of symbols that are properly created in line with context-dependent criteria is referred to as an expression, sometimes known as a mathematical expression. Operations include addition, subtraction, multiplication, and division.

A mathematical expression is the collection of mathematical symbols that results from the proper combination of numbers and variables using operations like addition, subtraction, multiplication, division, exponentiation, and other as-yet-unlearned operations and functions.

The three different types of algebraic expressions are monomial, binomial, and polynomial.

According to the question there are five spaces for different subjects which are arranged in different order so the number of ways are

2(5,4)

= 5 * 4 * 3 *  2

=120 ways

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Answer:

Step-by-step explanation:

The simple explanation is that the hypotenuse and sides of a right triangle are always shorter than one another. Therefore, any side's to any hypotenuse's ratio will never be greater than 1. The figure is no longer a triangle when the angle is 0 or 90 degrees because one of the sides vanishes and the other side lines up with the hypotenuse. For this reason, sin and cosine have values of 0 or 1 in these extreme situations.

The duckweed increases by a percentage each day which is calculated by the equation

(1230.25t/16)/a - 1.

This equation can be further simplified to 1230.25t/16a - 1 and then multiplied by 100 to get a percentage.

So the percentage increase of duckweed each day is calculated by multiplying 1230.25t/16a - 1 by 100.

1230.25t/16a×100

This will give us the percentage of increase each day, rounded to the nearest whole number.

For example, if the initial number of fronds is 1000 and the number of days is 2, the percentage increase of duckweed will be (1230.25(2)/16(1000)) - 1 = 24.6%, rounded to the nearest whole number which is 25%.

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The equation that represents the length of the square dining room in feet is (1/4)x - 5/6.

The area of a square is a product of it's any two sides or a product of diagonals divided by two. If a side has a length 'a' then the diagonal is a√2.

The perimeter of a square is the sum of the lengths of all the sides.

We know the perimeter of a square is 4×side.

We also know that 1 foot is equal 12 inches.

Given, A square dining room table has a perimeter of (12x - 40)".

Now if we factor out a 4 we'll have the side inside the bracket which is,

4(3x - 10)'', This is in inches to convert it to feet we have to divide what is inside the bracket by 12 which is,

= (3/12)x - 10/12 feet.

= (1/4)x - 5/6 feet.

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Answer:

16p^12 q^4

Step-by-step explanation:

Open up the parenthesis and simplify.

2^4 is 16

p^3 times ^4 is p^12

q times ^4 is q^4

So your answer is 16p^12 q^4

Answer:

16p^12 q^4

Step-by-step explanation:

This is because the power 4 will multiple with all the variables inside

hence, p^3 will become p^12

and q^1 will become q^4

the power 4 will also change 2 into 2^4 which is 16

Answer:

x = 60 , y = 85

Step-by-step explanation:

assuming the figure is a trapezoid

• each lower base angle is supplementary to the upper base angle on the same side.

x + 2x = 180

3x = 180 ( divide both sides by 3 )

x = 60

and

y + y + 10 = 180

2y + 10 = 180 ( subtract 10 from both sides )

2y = 170 ( divide both sides by 2 )

y = 85

The zeroes of this polynomial equation is [tex]$4 x^2-4 x-3$[/tex] are [tex]\frac{3}{2}$[/tex] and [tex]$-\frac{1}{2}$[/tex].

First form the equation

As per the given data the given polynomial equation is [tex]$4 x^2-4 x-3$[/tex].

Here we have to determine the zeroes of a polynomial equation is [tex]$4 x^2-4 x-3$[/tex].

We know that the zeroes of a polynomial are evaluated by equating them with zero.

Therefore p(x)=0

[tex]& \Rightarrow 4 x^2-4 x-3=0[/tex]

Then solve to find the zeroes

[tex]& 4 x^2-4 x-3=0 \\[/tex]

[tex]& \Rightarrow 4 x^2-6 x+2 x-3=0 \\[/tex]

2x(2x - 3) + 1(2x - 3) = 0

(2x - 3) (2x + 1) = 0

[tex]& \Rightarrow x=\frac{3}{2},-\frac{1}{2}[/tex]

Then do verification

We know that for a given polynomial [tex]$a x^2+b x+c$[/tex]

Sum of the zeroes [tex]$=-\frac{b}{a}$[/tex] and product of the roots [tex]$=\frac{c}{a}$[/tex]

Sum of the zeroes [tex]$=\frac{3}{2}-\frac{1}{2}=1$[/tex]

Again, [tex]$-\frac{b}{a}=\frac{4}{4}=1$[/tex]

Product of the zeroes [tex]$=\frac{3}{2} \times-\frac{1}{2}=-\frac{3}{4}$[/tex]

Again, [tex]$\frac{c}{a}=-\frac{3}{4}$[/tex]

Thus, the relationship between the zeroes and the coefficients of the polynomial is verified.

Hence, the zeroes of this polynomial are [tex]\frac{3}{2}$[/tex] and [tex]$-\frac{1}{2}$[/tex].

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Answer:

The area of the shaded region is, [tex]24mm^{2}[/tex]

Step-by-step explanation:

First we have to calculate the area of ΔABC and ΔXYZ.

Area of ΔABC = [tex]\frac{1}2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]

Area of ΔABC = [tex]\frac{1}{2}[/tex]×[tex]5mm[/tex]×[tex]12mm[/tex]

Area of ΔABC =[tex]30mm^{2}[/tex]

and,

Area of ΔXYZ = [tex]\frac{1}{2}[/tex]×[tex]Base[/tex]×[tex]Height[/tex]

Area of ΔXYZ = [tex]\frac{1}{2} X3mmX4mm[/tex]

Area of ΔXYZ = [tex]6mm^{2}[/tex]

Now we have to calculate the area of the shaded region.

Area of the shaded region = Area of ΔABC - Area of ΔXYZ

Area of the shaded region = [tex]30mm^{2} - 6mm^{2}[/tex]

Area of the shaded region = [tex]24mm^{2}[/tex]

Therefore, the area of the shaded region is, [tex]24mm^{2}[/tex]

The equation of the linear function is A(t) = -975t + 15000

From the question, we have the following parameters that can be used in our computation:

The table of values

From the table of values, we have:

A(t)         t

11,100   4

7200   8

3300   12

From the above table of values, we can see that

As t increase by 4, the value of A(t) decreases by 3900

This means that the table of values is a linear relation, and the slope is

slope = -3900/4

slope = -975

A linear equation is represented as

y = mx + c

Where

slope = m

So, we have

A(t) = -975t + c

Using the points on the table, we have

11000 = -975 * 4 + c

Evaluate

c = 15000

So, we have

A(t) = -975t + 15000

Hence, the equation is A(t) = -975t + 15000

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Answer:

Y=54x−2y=54x−1

I hope this helps you!

Therefore, the players are 6.84 meters apart from each other.

An item that is propelled by the application of an external force and then travels freely while being affected by gravity and air resistance is referred to as a projectile. Projectiles are generally used in sports and combat, despite the fact that every item traveling through space is a projectile.

The straight line that traverses a point with a slope equal to the derivative of the curve at that location is said to be the tangent line to a plane curve at that point in geometry. It was described by Leibniz as the path connecting two points on a curve that are infinitely near together.

If we let x be the distance between the players, then we can use the tangent function to relate the angle of elevation to the distance between the player and the basket:

tan(40°) = 3.5/x

tan(50°) = 3.5/(x+1)

We can solve for x in both equations, and set them equal to each other, we get x= 6.84m

Therefore, the players are 6.84 meters apart from each other.

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There are three types of asymptotes solved in the following way:

1. Horizontal asymptotes is y = k  for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.

2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.

3. Slant asymptotes is y = mx + c.

Therefore, the three types of asymptotes solved in the following way:

1. Horizontal asymptotes is y = k  for x→∞ and x→ -∞ , when degree of denominator > degree of numerator.

2. Vertical asymptote is x = k for y→∞ and y→ -∞ , when degree of denominator < degree of numerator.

3. Slant asymptotes is y = mx + c.

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Answer:

one solution

Step-by-step explanation:

The two lines cross at exactly one point.  That means there is one solution.

Answer:

The answer is A

Step-by-step explanation:

When looking at this image, look at A, notice how it says y and the equal to symbol is facing it? then notice at the end of answer a is -4, look at the graph and the line intercepts -4, remeber, the end number, whether positive or negative will always be the on the y axis

The length of base ON of trapezoid LMNO is 17 units

We know that the median theorem of trapezoid, which states that the median of a trapezoid is parallel to each base. Also, the length of the median equals one-half the sum of the lengths of the two bases.

Consider the following diagram of trapezoid LMNO with bases LM and ON , and Median PQ.

Given that the equations for the bases and median of trapezoid LMNO .

PQ = t +6, LM = t +3 and ON = 3t – 7

From above theorem,

PQ = 1/2 (LM + ON)

t + 6 = 1/2 ( t + 3 + 3t - 7)

2(t + 6) = 4t + 3 - 7

2t + 12 = 4t - 4

4t - 2t = 12 + 4

2t = 16

t = 8 units

So, ON = 3t - 7

ON = 3(8) - 7

ON = 24 - 7

ON = 17 units

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Answer:

1 - 5 < y < 5

I hope you pass your assignment

The range of solutions for the given inequality is -5<y<5.

Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.

The given inequality is -6<1/3(6y + 12)<14.

Here, -6<(2y + 4)<14

-6<(2y + 4)

Subtract 4 on both the sides of an inequality, we get

-10<2y

Divide 2 on both the sides of an inequality, we get

-5<y

(2y + 4)<14

Subtract 4 on both the sides of an inequality, we get

2y<10

Divide 2 on both the sides of an inequality, we get

y<5

So, -5<y<5

Therefore, the range of solutions for the given inequality is -5<y<5.

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