How to determine instantaneous rate of change with pi

A dilation is a transformation that changes the size of an object by a scale factor. To dilate a triangle by a scale factor of 2/3, you will need to follow these steps:

Note that the center of dilation C and the dilation factor are the same for all points on the triangle, also if the dilation factor is less than 1, the image is smaller than the original and if the dilation factor is greater than 1, the image is larger than the original.

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The complete question is -

How do you dilate a triangle by a scale factor of 2/3?

Answer:

45 cents

Step-by-step explanation:

Answer:

a)   Length of the parking lot: 98 m

b)   Width of the pool: 89 m

Step-by-step explanation:

a)   The formula for the area of a rectangle is [tex]A=lw[/tex].

We need to evaluate the length. Lets solve for [tex]l.[/tex]

[tex]A=lw[/tex]

Divide both sides of the equation by [tex]w[/tex].

[tex]\frac{A}{w} =l[/tex]

We are given

[tex]A=8428\\w=86[/tex]

Lets evaluate [tex]l[/tex].

[tex]\frac{8428}{86}=l[/tex]

[tex]l=98[/tex]

b)   The formula for the perimeter of a rectangle is [tex]P=2l+2w[/tex].

We need to evaluate the width. Lets solve for [tex]w[/tex].

[tex]P=2l+2w[/tex]

Subtract [tex]2l[/tex] from both sides of the equation.

[tex]P-2l=2w[/tex]

Divide each term by 2.

[tex]\frac{P}{2} -\frac{2l}{2} =\frac{2w}{2}[/tex]

Simplify.

[tex]w=\frac{P}{2}-l[/tex]

We are given

[tex]P=376\\l=99[/tex]

Lets evaluate [tex]w[/tex].

[tex]w=\frac{376}{2}-99[/tex]

[tex]w=188-99[/tex]

[tex]w=89[/tex]

Answer:

a) 98m , b) 89m

Step-by-step explanation:

(a) Given,

To Find : Length of the Parking lot

Length of a rectangle shape can be derived by the formula,

[tex]l = \frac{A}{w}[/tex]

[tex]l = \frac{8428}{86}[/tex]

[tex]l = 98m[/tex]

Hence , the length of a rectangular parking lot is 98m

(b) Given ,

To Find : The width of the rectangular pool

We take the width as variable 'x'

Now we plug it into the perimeter of a rectangle equation

[tex]376 = 2(99 + x)[/tex]

Using distributive property we,

[tex]376 = 198 + 2x[/tex]

We now flip the equation

[tex]2x + 198 = 376[/tex]

[tex]2x = 376 - 198[/tex] ( Transposing into the right hand side)

[tex]2x = 178[/tex]

[tex]x = \frac{178}{2}[/tex]

[tex]x = 89[/tex][tex]m[/tex]

Hence , the width of the rectangular swimming pool is 89m

The probability that the 2 marbles taken from the bag are the same color is 25/49.

It is the chance of an event to occur from a total number of outcomes.

The formula for probability is given as:

Probability = Number of required events / Total number of outcomes.

We have,

Number of red marbles = 3

Number of blue marbles = 4

Total marbles = 7

Now,

The probability of taking two blue marbles consecutively with replacement.

= 4/7 x 4/7

= 16/49

The probability of taking two red marbles consecutively with replacement.

= 3/7 x 3/7

= 9/49

Since the two marbles of the same color can be blue or red.

The probability that the 2 marbles taken from the bag are the same color.

= 16/49 + 9/49

= 25/49

Thus,

The probability that the 2 marbles taken are the same color is 25/49.

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Area of circle equals Area of produced rectangle equals 1/2 π(2r) r.

Since r is the circle's radius and is equal to 22/7 or 3.14, the area of the circle is equal to πr².

All points on a plane that are at a specific distance from a specific point, the center, form a circle. In other words, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.

The following is a list of a circle's attributes:

Look closely at the above illustration; if we divide the circle into smaller pieces and arrange them in a particular order, a parallelogram will result. The circle progressively becomes the shape of a rectangle as it is split into smaller and smaller segments. The likelihood that it will have the above-illustrated rectangle form increases with the number of parts it has.

A rectangle's area equals its length times its width.

The ratio of a circle's radius to a rectangle's width (r)

When we compare a rectangle's length to a circle's circumference, we can see that the length is equal to half the diameter of the circle.

Area of circle equals Area of produced rectangle equals 1/2 π(2r) r.

Since r is the circle's radius and is equal to 22/7 or 3.14, the area of the circle is equal to πr².

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The quadratic equation in standard form that has an axis of symmetry of x=-2 and y-intercept of (0,6) is x² + 4x - 6 = 0.

A quadratic equation in standard form is of the form ax² + bx + c, where a, b, and c are constants.

The axis of symmetry of a quadratic equation is given by the line x = -b/2a, so if the axis of symmetry is x=-2, we can set -b/2a = -2, which gives b = 4a.

To find the y-intercept of the quadratic equation, we can set x = 0 and substitute that into the equation: y = a(0)² + b(0) + c = c
So, if the y-intercept is (0,6) then c = 6.

By using above two information, we can write the quadratic equation in standard form as:

a(x+2)² + 4a(x+2) + 6 =0
=> a(x²+4x+4) + 6 = 0
=> a(x²+4x+4) = -6
=> a(x²+4x+4) = -6
=> x² + 4x + 4 = -6/a
=> x² + 4x + 4 = -6/a +10
=> x² + 4x - 6 = 0

So, the quadratic equation in standard form that has an axis of symmetry of x=-2 and y-intercept of (0,6) is x² + 4x - 6 = 0.

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The value of 0.55 hectometers expressed in decimeters is 550 decimeters. The result is obtained by using the concept of unit ladder system.

The common length units are kilometers to milimeter. The conversion can be described in a unit ladder system as follows.

km (kilometers)

  hm (hectometers)

     dam (decameters)

        m (meters)

           dm (decimeters)

              cm (centimeters)

                  mm (millimeters)

Every time the length unit goes down, it is multiplied by ten. Every time the length unit goes up, it is divided by ten.

We have 0.55 hectometers. Express that value in decimeters!

From hectometers to decimeters, it goes down 3 times. So,

0.55 hectometers = 0.55 × 10 × 10 × 10 decimeters

0.55 hectometers = 0.55 × 1000 decimeters

0.55 hectometers = 550 decimeters

Hence, 0.55 hectometers is equal to 550 decimeters.

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Reflection across the y = -x line is equivalent to a rotation of 180 degrees about the origin.

The coordinates of X(-4,-3) after reflecting across the y = -x line would be (3, 4)

The coordinates of M(-3,-2) after reflecting across the y = -x line would be (2, 3)

The coordinates of (-1,-5) after reflecting across the y = -x line would be (5,1)

So, after reflecting across the y = -x line, the coordinates of the points are flipped along the line x = y and they are moved to the opposite quadrant.

x using the change of base formula will be B) -0.207519.

What is logarithm ?

Logarithm, the exponent or power to which a base must be raised to yield a given number. Expressed mathematically, x is the logarithm of n to the base b if bx = n, in which case one writes x = logb n. For example, 23 = 8; therefore, 3 is the logarithm of 8 to base 2, or 3 = log2 8

Have given ,

4x + 2 = 12

equation. We can do this by subtracting 2 from both sides:

4x = 10

Next, we divide both sides by 4:

x = 2.5

So, the solution is x = 2.5

x using the change of base formula will be B) -0.207519.

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The equivalent expression is RootIndex 12 StartRoot 8 EndRoot Superscript x. Option C

An equivalent expression can be described as an expression that has the same solution as the original expression.

The equivalent always have a different arrangement of variables, terms and factors but the solution is the same with the initial expression.

From the information given, we have that;

3Root 8 Superscript one-fourth x

This is represented as;

[tex]\sqrt[3]{8}^\frac{1}{4} ^x[/tex]

Now, take the cube root of 8, we have;

[tex]8^\frac{1}{3} * \frac{1}{4}^x[/tex]

Multiply the exponents, we get;

[tex]8^\frac{1}{12}^x[/tex]

Now, represent in root for, we have;

[tex]\sqrt[12]{8} ^x[/tex]

Hence, the correct option is C

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Answer:

C

Step-by-step explanation:

;)

Answer:

Interest is $4185.00

Please give me brainliest

Step-by-step explanation:

[tex]i = \frac{p \: r \: t}{100} \\ i = \frac{6750 \times \frac{62}{3} \times 3 }{100} \\ i = \frac{418500}{100} \\ i = 4185[/tex]

Answer:

Step-by-step explanation:

Formula for simple interest =S= (P*R*T)/100

Here P=$6750,R=62/3% T=3Years

Simple interest for given is S= 41.85

The vertices of the new polygon A'B'C'D' is A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1) (optionB)

A vertex is a corner point of a polygon, polyhedron, or other higher-dimensional polytope, formed by the intersection of edges, faces or facets of the object.

The vertices of the polygons are given as B(−2, 2), C(4, −2), D(4, 4) . The polygon is reduced by using a scale factor one fourth. i.e 1/4.

This means that each coordinates of the vertices will be reduced by 4 to give the vertices of the new polygon.

A = (-4,6) , A' = ( -1, 1.5)

B = ( -2,2) B' = ( -0.5, 0.5)

C = ( 4, -2) C' = ( 1, -0.5)

D = ( 4,4) , D' = ( 1, 1)

Therefore the vertices of the new polygon is A′(−1, 1.5), B′(−0.5, 0.5), C′(1, −0.5), D′(1, 1)

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Answer:

its not b i tried and it was wrong

Step-by-step explanation:

Answer: y = -2x+3.

Step-by-step explanation:

To answer this question, you must first use the FOIL method.

now the equation is this

y+3=-2x+6, since a negative * a negative is equal to a positive.

subtract 6 from both sides.

y-3=-2x

add three to both sides

y=-2x + 3

Answer:

C

Step-by-step explanation:

There are 3 pairs of corresponding sides with proportional lengths.

The ratios of the lengths of corresponding sides are equal AB/XY = BC/YZ = AC/XZ, then ΔABC and ΔXYZ  proven similar through SSS .

To prove two triangles similar using the SSS (Side-Side-Side) similarity criterion, all three pairs of corresponding sides of the two triangles must be proportional .

The SSS similarity criterion states that if the ratio of the lengths of corresponding sides in two triangles is equal, then the triangles are similar.

Given that we have a list of triangles,  to compare the ratios of their corresponding sides to see if any pairs satisfy the SSS similarity criterion.

The three pairs of corresponding sides in the triangles are denoted as follows:

Side A: Sides that are corresponding in length between the two triangles.

Side B: Sides that are corresponding in length between the two triangles.

Side C: Sides that are corresponding in length between the two triangles.

Since the specific list of triangles is not provided, I cannot give you the exact pairs that  proven similar through SSS similarity. However, I provide with an example:

Example:

Consider two triangles, ΔABC and ΔXYZ, where the corresponding sides are as follows:

ΔABC: AB, BC, and AC

ΔXYZ: XY, YZ, and XZ

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The midpoint formula helps us to find the midpoint of a line given to us on a coordinate system.

The coordinate system in geometry is a plane space in which points are located using paired numerical values called coordinates. It is of two types Cartesian coordinate system and polar coordinate system

The cartesian coordinate system is further divided into majorly two parts i.e., 2-Dimensional and 3- dimensional systems. A 2-D system has 2 axis X and Y whereas a 3-D system has X, Y, and Z axes. The plane is divided into 4 quadrants

The midpoint formula is used to find the center of a line or a figure. It is a mathematical equation used in geometry and economics. On a line from point (x1,y1) to (x2,y2) the midpoint P= (x1+y1)/2 , (x2+y2)/2. It divides the line in a 1:1 ratio.

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The correct option regarding the domain and the range of the quadratic function y = (x + 3)² - 5 is given as follows:

B. Domain all real values, Range [-5, infinity.]

The function for this problem is defined as follows:

y = (x + 3)² - 5.

Which is a concave up quadratic function with vertex at (-3,-5).

The quadratic function has no restrictions regarding the input, hence the domain is composed by all real values.

The minimum value of the function is of -5 at the vertex, hence the range is all values that are -5 or greater.

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Answer:

6

5^2 + square root 11^2 = 36

square root 36= 5

The following statements are true for all the numbers. The proof is shown as follows.

A real number is multiplied by an imaginary unit, I whose feature i2 = 1 defines it as an imaginary number. Bi is an imaginary number, while b2 is its square. For instance, the square of the fictitious integer 5i is 25. Zero is regarded as both real and fictitious by definition.

We know z₁ = a + bi and zbar= a-bi

z1+z1bar=2a that is purely real. Similarly with z2 +z2bar

z1-z1bar=-2bi that is purely imaginary. Similarly with z2-z2bar

Again

z1bar+z2bar= a-bi+c-di

z1+z2(whole bar)=a+c-(b+d)i

Hence Z₁ + Z₂ = Z₁ + Z₂

Similarly

z1bar.z2bar=z1.z2(whole bar)

Hence proved

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If the farmer plotted a straight line graph of how many goats he had left over time, the slope of the line would be -14.

To find the slope of the line representing the number of goats the farmer has over time, we need to use the formula:

Where y2 and y1 are the number of goats the farmer has at the end of two different months, and x2 and x1 are the number of months that have passed since he started selling the goats.

In this case:

So the slope of the line is:

The slope of the line is -14, which means that the number of goats the farmer has decreases by 14 goats per month.

It's important to note that when the value of the slope is negative, it means that the line is going down; this means that the farmer is selling goats at a constant rate.

This question is incomplete and should be written as:

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Answer: y = 8x

Step-by-step explanation:

The line passes through points (1,8) and (2,16).

Using this, we can first find the slope.

Slope = Δy/Δx = 8/1 = 8

So the slope is 8.

The equation is now

y = 8x + b

Let's use the point (1,8) to find the value of b now.

8 = 8 +b

b = 0

Therefore, y = 8x is the answer.

(you can skip the last step by noticing that the graph passes through the origin)

Answer:

y = 8x

Step-by-step explanation:

[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]

From inspection of the given graph, two points on the line are:

Substitute the points into the slope formula to find the slope of the line:

[tex]\implies m=\dfrac{16-0}{2-0}=\dfrac{16}{2}=8[/tex]

[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]

The y-intercept is the y-value of the point where the line crosses the y-axis. From inspection of the given graph, the y-intercept is zero. So b=0.

Substitute the found slope and y-intercept into the slope-intercept formula to create an equation for the line:

[tex]\implies y=8x+0[/tex]

[tex]\implies y=8x[/tex]

Therefore, the equation for the line in slope-intercept form is:

Answer:

-4

Step-by-step explanation:

y=3x13

2x=y-9

2x=3x+13-9

2x=3x+13-9

2x=3x+4

-3  -3

-x=4

-x/ -x/

x=-4

(You said "3x13" so i'm going to guess you meant to say "3x+13").

(If you meant "3x-13" I can also help you with that too)!

The point that lies in the fourth quadrant is (1, -2).

The coordinates in a graph indicate the location of a point with respect to the x-axis and y-axis.

The coordinates in a graph show the relationship between the information plotted on the given x-axis and y-axis.

We have,

The coordinates are:

(1,−2), (1, 8), (-5, -4), and (-5, 2).

(1, -2) is in the fourth quadrant.

(1, 8) is in the first quadrant.

(-5, -4) is in the third quadrant.

(-5, 2) is in the second quadrant.

Thus,

(1, -2) lies in the fourth quadrant.

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Answer:   (5,−2) is the only point in the fourth quadrant.

Step-by-step explanation:

Mary is mistaken in her conclusion that the two triangles are not similar because size does not determine similarity. Similarity is determined by the proportionality of corresponding sides and the congruence of corresponding angles. Congruence is the equality of all the measures of the corresponding parts of two figures.

In order to determine if two triangles are similar, we must compare the ratios of corresponding sides. If the ratios of corresponding sides are equal, then the triangles are similar. In the diagram, it is not specified what the measures of the sides of the triangles are, so it is not possible to determine if the triangles are similar based on the information given. However, if the ratio of corresponding sides are same, then the triangles are similar.

It is important to note that similarity and congruence are different concepts. Congruence refers to the equality of all measures of corresponding parts of two figures, including side lengths and angles. Similarity refers to the proportionality of corresponding parts, including side lengths and angles. A triangle can be similar to another triangle without being congruent, and congruent triangles are always similar.

In summary, Mary is mistaken because the size of the triangle does not determine similarity, it is determined by the proportionality of corresponding sides and congruence of corresponding angles. Without knowing the measures of the sides of the triangles, it is impossible to determine if the triangles are similar based on the information given.

So, on solving the provided question we can say that coordinates are -

(6, -4.) and T (-1,2) y-y1 = m(x - x1) => 2x - y -16 =0

A coordinate system in geometry is a method that employs one or more integers or coordinates to identify the precise placement of points or other geometrical objects on a manifold, such as Euclidean space. Pairs of integers called coordinates are used to locate a point or object on a two-dimensional plane. The position of a point on a 2D plane is described by two integers known as the x and y coordinates. a group of numbers that represent precise positions. Usually, there are two numbers in the figure. The front-to-back distance is represented by the first number, while the top-to-bottom distance is represented by the second number. like in (12.5), when there are 12 units below and 5 above.

here,

coordinates are -

(6, -4.) and T (-1,2)

y-y1 = m(x - x1)

y +4 = 2(x -6)

y+ 4 = 2x - 12

2x - y -16 =0

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A "full table of 5" refers to a multiplication table that includes all of the products of the number 5 multiplied by the integers from 1 to some maximum value.

Here is an example of a full table of 5:

5 x 1 = 5

5 x 2 = 10

5 x 3 = 15

5 x 4 = 20

5 x 5 = 25

5 x 6 = 30

5 x 7 = 35

5 x 8 = 40

5 x 9 = 45

5 x 10 = 50

In this example, the maximum value for the multiplier is 10, but a full table of 5 can continue with any number of rows. This table is useful for memorizing the multiplication facts of 5, and also to see the pattern of the multiples of 5.

It's worth to mention that if you are looking for a way to calculate the products you could use a loop or a function that takes the maximum value of the multipliers as an input and prints the full table of 5.

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A function y = 10 a not linear function

We know that the general form of linear function is f(x) = a + bx

A linear function has one independent variable (for above function x) and one dependent variable(here, f(x)).

The graph of linear function is always a straight line.

Let y = f(x)

So, y = a + bx

where b is the slope of line

and a is the y-intercept

here, the independent variable is x and the dependent variable is y.

We have been given a function y = 10

The graph of y = 10 is a horizontal line parallel to x -axis and intersects y-axis at (0, 10)

There is no y-intercept and the slope is undefined.

Therefore, given function is not a linear function

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1. The value of the m∠2 is 67°.

2. The third length in the triangle is 10 cm.

3. It should be noted that this is a rotation.

An equation is a expression that shows the relationship between numbers and variables.1)

In the triangle:m∠1 + 21 + 46 = 180° (sum of angles in a triangle)

m∠1 = 113°m∠1 + m∠2 = 180 (angle in a staight line)1

113 + m∠2 = 180

m∠2 = 180 - 113

= 67°

2. Let x represent the third length:

x + 12 + 13 = 35 (perimeter)

x = 35 - 25

x = 10

3. It should be noted that the diagram illustrated is a a rotation.

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