What is the formula for midpoint of a line segment?

If the parent graph is made steeper or less steep (y = ½ x), the transformation is called a dilation.

And if the parent graph is changed so that it falls to the right instead of rising to the right (y = -x), the transformation is called a reflection.

If x is replaced by x/A in a formula and A>1, then the effect on the graph is to expand it by a factor of A in the x-direction (away from the y-axis). If A is between 0 and 1 then the effect on the graph is to contract by a factor of 1/A (towards the y-axis). We use the word "dilate'' to mean expand or contract.

f y is replaced by y/B in a formula and B>0, then the effect on the graph is to dilate it by a factor of B in the vertical direction. As before, this is an expansion or contraction depending on whether B is larger or smaller than one. Note that if we have a function y=f(x), replacing y by y/B is equivalent to multiplying the function on the right by B: y=Bf(x). The effect on the graph is to expand the picture away from the x-axis by a factor of B if B>1, to contract it toward the x-axis by a factor of 1/B if 0<B<1, and to dilate by |B| and then flip about the x-axis if B is negative.

When dilating a line, check if the center is on the line.  If the center lines on the line, the line remains the same.

The line whose equation is y = x + 3 is dilated by a scale factor of 2  centered at the origin. Write the equation of the line after the dilation.

M= 1 , b =3

0=0 +3

0 ≠ 3

center not on line

(0 ,3)→(0 ,6)        d2   y intercept

(1 ,4)→(2 ,8)        d2   y intercept

y = mx + b

y =x +6

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Sometimes we are given exponential equations with different bases on the terms. In order to solve exponential functions with different bases we must know logarithms and how to use them with exponentiation. We can access variables within an exponent in exponential equations with different bases by using logarithms and the power rule of logarithms to get rid of the base and have just the exponent.

Exponential equation is an equation whose power or base number (base) and power contains a variable.

An example of an exponential equation:

32^x-3 = 81^x+5   →   the exponential equation with the power contains the variable x

(2x - 5)^x = (2x - 5)^3x-4  →  the exponential equation with bases and powers contains the variable x

So, in the exponential equation, it can only be the exponent that contains the variable or it can also be the base and the exponent that contain the variable. This variable is denoted by a letter, it can be from a to z. But, in general, the variable symbol that is often used in questions is the letter x.

The solution to the exponential equation is the set of all x values that satisfy the exponential equation, or we can also call it a set of solutions. So, how to solve the exponential equation varies depending on the form of the equation. The two examples of equations above are two of several forms of existing exponential equations. This means that there are still other forms of exponential equations and each equation has its own way of solving it

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Answer:

no real solutions

Step-by-step explanation:

the easiest method would be to graph the equation and see how many intersection points with the x-axis there are; that represents the  number of solutions

when we graph the equation we first want to add 3 to each side of the equation to get the following:

y = 2x²-8x+11

what we see is that the parabola does not intersect the x-axis at all; therefore, there are no 'real' roots or solutions

Answer:

Step-by-step explanation:

x =(4-√24)/4=1-1/2√ 6 = -0.225.

The likelihood that all three marbles selected will be red is 0.0588 to the nearest 1000th.

The field of mathematics concerned with probability is known as probability theory. Although there are various distinct interpretations of probability, probability theory approaches the idea rigorously mathematically by articulating it through a set of axioms. The probability is a measure of the possibility that an event will occur. It assesses the event's certainty. P(E) = Number of Favourable Outcomes/Number of Total Outcomes is the probability formula. A probability is a number that represents the possibility or chance that a specific event will occur. Probabilities can be stated as proportions ranging from 0 to 1, as well as percentages ranging from 0% to 100%.

Here,

Total number of marbles=7+6+5

=18

the probability, to the nearest 1000th, that all three marbles drawn will be red,

=(7/18)*(7/18)*(7/18)

=0.0588

The probability, to the nearest 1000th, that all three marbles drawn will be red is 0.0588.

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If the equation [tex]ax^2+2hxy+by^2+2gx+2fy+c=0[/tex]  describes a pair of straight lines, then the equations m1+m2=-2h/b and m1m2=a/b, where m1 and m2 are the slopes of the straight lines, apply.

A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis.

Determine the coordinates of two points along the line that you choose.

Find the difference between these two points' y-coordinates (rise).

Find the difference between these two points' x-coordinates (run).

Divide the difference in x-coordinates (rise/run or slope) by the difference in y-coordinates.

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The solution to this system of linear equations y - x = 6 and y + x = -10 is (-8, -2).

y - x = 6

⇒y = x + 6

y + x = -10

⇒y = - x - 10

Since both equations are equal to y, equate them.

x + 6 = - x - 10

x + x = - 10 - 6

2x = - 16

Divide both sides by 2

x = -8

Put the value of x in either of the equations

y - x = 6

y - (-8) = 6

y + 8 = 6

y = 6 - 8

y = - 2

Therefore, the solution to the system of linear equations is (-8, -2).

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To calculate the percent change in David's water intake from Tuesday to Wednesday, we can use the following formula:

percent change = (new value - old value) / old value * 100

In this case, the old value is the number of cups of water David drank on Tuesday (16 cups) and the new value is the number of cups of water he drank on Wednesday (12 cups).

Plugging these values into the formula:

percent change = (12 - 16) / 16 * 100 = -25%

So David's water intake decreased by 25% from Tuesday to Wednesday.



_______________


The original amount in the problem is the amount of water David drank on Tuesday, which is 16 cups.

It was given in the problem as the base value to calculate the percent change in David's water intake from Tuesday to Wednesday.
_____________
The change in David's water intake in this problem is the difference between the amount of water he drank on Tuesday and the amount of water he drank on Wednesday.

On Tuesday, he drank 16 cups of water, and on Wednesday, he drank 12 cups of water.

So the change in David's water intake is:

16 cups - 12 cups = 4 cups

David drank 4 cups less water on Wednesday than on Tuesday.

Step-by-step explanation:

The original amount is 16 cups.

The new amount is 12 cups.

The amount of change is the difference of the two:

Percent change is the change from the original amount:

This is a drop or decrease in percent.

The triangle Illustrated shows that the correct option is 4. No, not similar

According to the SAS criterion for triangle congruence, two triangles are considered congruent if they have two pairs of congruent sides and if the included angle (the angle between the congruent sides) in one triangle coincides with the included angle in the other.

According to the SSS rule, two triangles are said to be congruent if all three sides of one triangle are equal to the corresponding three sides of the other triangle.

In this case, the triangles are different. The correct option is 4.

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By using the given table we can find the two solutions of the equation:

f(x) = g(x)

are:

x = 1

x = 0.

Here we have a table for the functions f(x) and g(x), and we want to solve the equation:

f(x) = g(x)

So we just need to find a value of x, such that both functions have the same output.

To check that, just look at the table and find a row (horizontal line) where the values of f(x) and g(x) are the same ones.

If you look when x = 0, we have:

f(x) = 1

g(x) = 1

So x = 0 is a solution.

And for the next row, when x = 1.

f(x) = 0.25

g(x) = 0.25

So x = 1 is also a solution.

These are the two solutions to the given equation.

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Answer:

The Mode Is:

7 and 4

Step-by-step explanation:

Both 7 and 4 shows up 3 times

Answer: 7 and 4

Step-by-step explanation: Mode is most reapeated

The length of the other leg of the right triangle is √70. The result is obtained by using the concept of the Pythagoras theorem.

The Pythagoras theorem states that the square of the hypotenuse of a right triangle is equal to the squares of the other length sides. It can be expressed as

a² + b² = c²

Where

Base altitude is also called as legs of the right triangle.

A right triangle has a leg length of √11 and hypotenuse of 9. Find the length of the other leg!

Let's say

The length of other leg is b, the shorter side of hypotenuse.

By using the Pythagoras theorem, we get b.

a² + b² = c²

(√11)² + b² = 9²

11 + b² = 81

b² = 81 - 11

b² = 70

b = √70

Hence, the length of the other leg of the right triangle is √70.

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The required 15th term will be 19 given rules for a sequence.

An arithmetic sequence is defined as an arrangement of numbers that is in a particular order.

Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions.

The term-to-term rule for the sequence is to subtract 3 each time. If the 13th term is 25, we can use this rule to determine the 15th term.

We know that the 13th term is 25 and the rule is to subtract 3 each time, so:

13th term: 25

14th term: 25 - 3 = 22

15th term: 22 - 3 = 19

Therefore, the 15th term will be 19.

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To write a function from a table of values, you can use the data in the table to determine the pattern or relationship between the input (x) and output (y) values. Once you have identified this pattern or relationship, you can use mathematical notation to express it as a function in the form of y = f(x).

For example, if you have a table of values that shows a linear relationship between x and y, you can use the slope-intercept form of a linear equation (y = mx + b) to write the function. You can use the values in the table to find the slope (m) and the y-intercept (b) and then plug them into the equation to get the function.

You may also use the interpolation method to estimate a function from a table of values with a non-linear relation.

It's helpful to plot the data points on a graph to help identify the pattern or relationship, and to check that the function you've written correctly represents the data in the table.

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Complete question is: How do you write a function from a table of values?

The value of x in the line is 0.5 units and the value of y is 1.7 units.

The length of the lines are indicated on the diagram. The line below is bisected into two equal halves.

Therefore, let's find the value of x in the line segments.

5x + 8 = 21x

5x - 21x = -8

-16x = -8

divide both sides of the equation by -16

x = -8 / -16

x = 1 / 2

Therefore, let's find the value of y in the line segments.

20y - 2 = 17y + 3

20y - 17y = 3 + 2

3y = 5

divide both sides of the equation by 3

y = 5 / 3

y = 5 / 3 = 1.66666666667 = 1.7

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The horizontal distance covered by the ball is 119.5 ft.

It is a polynomial with a degree of 2 or the maximum power of the variable is 2 in quadratic equations. It has two solutions as its maximum power is 2.

Given that the height of a kicked ball can be modeled by the quadratic function h = - 0 .01x² + 1.18x + 2. The horizontal distance traveled by the ball in feet is represented by x, and h is the height of the ball in feet.

The horizontal distance covered by the ball will be calculated as,

h = - 0 .01x² + 1.18x + 2

Equate h to zero and solve for the distance x,

- 0.01x² + 1.18x + 2 = 0

Use the quadratic formula,

[tex]x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}[/tex]

[tex]x = \dfrac{-1.18\om\sqrt{(1.18^2)-(4\times(-0.01)\times2}}{2\times-0.01}[/tex]

[tex]x=\dfrac{-1.18\pm\sqrt{1.4+0.08}}{-0.02}[/tex]

x = ( -1.18 - 1.21 ) / 0.02

x = 119.5 ft

The horizontal distance will be 119.5 ft.

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The required equation is 12.5n+7

Linear equations help in representing the relationship between variables such as x, y, and z, and are expressed in exponents of one degree. In these linear equations, we use algebra, starting from basics such as the addition and subtraction of algebraic expressions.

Given: Let the fixed convenience fee be t and price per ticket be x then we have the following equations:

2x+t=32

3x+t=44.50

solving these two equations we get x=12.5 and t=7

Hence, the required equation is y=12.5n+7 where n is the number of tickets.

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The Additive Inverse of 924 is -924

⇒ The number that, when added to 924, will result in a sum of zero is the additive inverse of 924. The formula to solve the issue where x is the additive inverse of 924 is as follows:

924 + x = 0

⇒ When we solve the preceding equation for x, we obtain x = -924. As a result, the answer to the question "What is the additive inverse of 924?" is -924.

∴Therefore Additive Inverse of 924 = -924

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Answer:

solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1

Step-by-step explanation:

To solve these simultaneous equations, we need to find the values of x and y that satisfy both equations.

Given:

y = x

y = x² - 6

We can substitute the first equation into the second:

x = x² - 6

we can subtract x from both sides to get:

0 = x² - 7x + 6

Then we can factor it:

(x-6)(x-1) = 0

Therefore x = 6 or x = 1

So the solutions for these simultaneous equations are x = 6 and y = x = 6, or x = 1 and y = x = 1

There are two solutions, (6,6) and (1,1)

Answer: 110 inches.

Step-by-step explanation: The length of a necklace that has 10 of each type of bead can be represented by the expression:

1310 + 2110 + 3210 = 30+20+60 = 110 inches

So the correct answer is 110 inches.

Answer:

The answer is 15.

Explanation:

Got it right on i-Ready!

We can see here that in order to restore stuff, here are some steps to take:

Restoration is the process of returning an object or structure to its original condition or a close approximation of it. This can include cleaning, repairing, and/or preserving items such as furniture, antiques, artwork, historic buildings, and more.

The goal of restoration is to preserve the integrity of the item and maintain its historical or sentimental value. This process can include various techniques such as carpentry, metalworking, painting, and conservation.

To still restore a stuff,

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The expression for the total miles Mala walks her dog each day is : 3/4 x 3.

Manifold is the fundamental definition of multiplicity.

For the stated question:

Total distance of 1 walk = 3/4 miles.

Total frequency = 3.

So,

Total distance = 3/4 x 3

Thus, the expression for the total miles Mala walks her dog each day is : 3/4 x 3 .

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The complete question is-

Mala walks her dog 3 times a day. Each walk 3/4 is mile. What expression tells how many miles Mala walks her dog each day?

The most common way to convert a base-2 number to base-3 number is to convert a base-2 number to decimal or base-10 number first then convert base-10 number to base-3 number. You actually can directly convert it to base-3 number, but it is more complicated to do.

There is two ways to convert base-2 number to decimal or base-10 number, using positional notation methods and doubling methods. Positional notation methods are done as follow:

       1     -   0  -   1   -  1   -  0   -   1

       2⁵       2⁴    2³    2²    2¹      2⁰

After we get base 10, then convert base-10 number to base-3 number like this:

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The two Ordered pairs given as (1,2) and (2 ,1) are not equal because the position of the elements in both the ordered pairs are not equal .

What are Ordered Pairs ?

The Pair of elements can be called as Ordered Pair if the pair of elements are written in specific order .

Two Ordered Pairs [tex](a_{1} ,b_{1} )[/tex] and [tex](a_{2} ,b_{2} )[/tex] are considered as equal if and only if the elements ; [tex]a_{1} =b_{1}[/tex] and [tex]a_{2} =b_{2}[/tex] .

The Ordered Pairs are given as : (1,2) and (2 ,1) ,

On comparing the elements of both the ordered pairs ,

we get that , [tex]1\neq 2[/tex] and [tex]2\neq 1[/tex] ,

Therefore , the ordered pairs (1,2) and (2 ,1) cannot be considered as equal ordered pairs .

The given question is incomplete , the complete question is

Are (1,2) and (2 ,1) equal Ordered Pairs ?

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The points that the cooking group leader did label are (0,15) and (30,0). Thus, the correct answer is C.

As your first step, find the function that best represents x and y:

Hence, the function is:

The group leader labeled (0,15) on the y-axis, which means that when the number of small jars is 0, the group can use 15 large jars. This means that 15 large jars can hold 240 oz of spaghetti sauce, which is true since:

The group leader also labeled (30,0) on the x-axis, which means that when the number of large jars is 0, the group can use 30 small jars. This means that 30 small jars can hold 240 oz of spaghetti sauce, which is true since:

The function that represents this line is 8x + 16y = 240, where x is the number of small jars and y is the number of large jars. The line passes through (0,15) and (30,0) as the two intercepts.

This question should be written as:

A cooking group made 240 oz of spaghetti sauce to sell at a county fair. The group can pour the sauce into small jars that hold 8 oz and large jars that hold 16 oz. The group leader made a sketch to show the line representing the different combinations of jar sizes the group can use. The x-axis represented the number of small jars and the y-axis represented the number of large jars. The group leader labeled only the intercepts. Which points did the group leader label?

The correct answer is C.

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Answer:

A = 154 cm² , C = 44 cm

Step-by-step explanation:

the area (A) of a circle is calculated as

A = πr² ( r is the radius )

given r = 7 , then

A = [tex]\frac{22}{7}[/tex] × 7²

  = [tex]\frac{22}{7}[/tex] × 49

  = 22 × 7

  = 154 cm²

the circumference (C) of a circle is calculated as

C = 2πr

  = 2 × [tex]\frac{22}{7}[/tex] × 7

  = 2 × 22

  = 44 cm

The Fundamental Theorem of Algebra asserts that this 2 n d degree polynomial must have precisely two roots.

According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots. Algebra is the branch of mathematics that aids in the representation of problems or situations using mathematical expressions. In algebra, we utilize integers with definite or fixed values such as 2, 7, 0.068, and so on. In algebra, we employ variables such as x, y, and z in addition to integers. Elementary algebra, advanced algebra, abstract algebra, linear algebra, and commutative algebra are all sub-branches of algebra. In algebra, an algebraic expression is composed of integer constants, variables, and the basic arithmetic operations of addition(+), subtraction(-), multiplication(), and division(/). 5x + 6 is an example of an algebraic expression.

Here,

According to the Fundamental Theorem of Algebra, this 2 n d degree polynomial must have precisely two roots.

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For the information in the table, a linear function rule is y = -2x + 3. Each function is assigned a domain and a codomain, or scope.

The study of mathematics covers numbers and their variations, equations and related structures, shapes and their locations, and locations where they can be found. The relationship between a group of inputs, each of which has a corresponding output, is referred to as a "function." A function is a relationship between inputs and outputs where each input produces a single, unique result. Each function is assigned a domain and a codomain, or scope. Typically, the symbol f is used to represent functions (x). input consists of an x. Based on the following criteria, there are four primary categories of functions that are available: on functions, one-to-one functions, many-to-one functions, within functions, and on functions.

given

we'll utilize the coordinates (0, 3), and (1, 1)

Access the slope

Slope = 1-3/1-0

Slope = -2

X = 0 is where the y-intercept is located, hence b = 3.

Find the needed equation:

Keep in mind that y = mx + b.

y = -2x + 3 .

For the information in the table, a linear function rule is y = -2x + 3.

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The best method to apply in solving the given equation x² = 9 is the factorization method.

Factorisation is defined as the breaking or deterioration of an entity (for example a number, a matrix, or a polynomial) into a product of another entity, or factors, which when multiplied together give the original number or a matrix, etc.

In x² = 9, we need to remove the power of 2 in order to separate just x.

This implies finding the square root √x² which is equal to x.

However, there are 2 possible answers to any square root, a positive or a negative answer.

x = √9

x = ± 3

0r we can solve this equation by the splitting method.

Rearrange the equation

x² = 9

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

On solving, we get

x = +3 and x = -3

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8.6 cm2 is the area of a triangle with a base of 4.8 cm and a height of 3.6 cm.

A triangle in geometry is a three-sided polygon with three edges and three vertices.

The fact that a triangle's internal angles add up to 180 degrees is its most crucial characteristic.

This characteristic is known as the triangle's angle sum property.

If ABC is a triangle, it is written as ABC, where A, B, and C represent the triangle's vertices.

In Euclidean geometry, a triangle is a two-dimensional shape that is represented by three non-collinear points in a single plane.

A closed, two-dimensional shape is a triangle. It is a polygon with three sides. Straight lines make up all of the sides.

The vertex is the intersection of two straight lines. The triangle therefore has three vertices.

According to our question-

Base: 4.8 cm.

Size = 3.6 cm

Area of triangle = base/height/half

= 1/2×4.8×3.6 cm^2

=8.6 cm^2.

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