A members-only speaker series allows people to join for $19 and then pay $4 for every
event attended. What is the maximum number of events someone can attend for a total
cost of $31

With the gradient and one coordinates of the line, Using the formula of equation of line with gradient and a coordinates, The answer is

[tex](y-y_1) = m (x-x_1)[/tex] .

A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is used. A formula that expresses the connection between two expressions on each side of a sign. Typically, it has a single variable and an equal sign. Like this: 2x - 4 Equals 2.

In mathematics, a line's slope, also known as its gradient, is a numerical representation of the line's steepness and direction. Divide the difference in elevation between two points by the distance between them to find the percent slope, then multiply the result by 100. The term "rise" refers to the difference in elevation between two sites. The run is the separation between the points. Percent slope is therefore equal to (rise / run) x 100.

coordinates = ([tex]x_1,y_1[/tex])

gradient =slope =m

Required equation,

[tex](y-y_1) = m (x-x_1)[/tex]

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Answer:

7

Step-by-step explanation:

-(-4) + 3

= 4 + 3

= 7

A reflection preserves the size and shape of the prior original image, acting as a congruence transition.

A reflection in mathematics is a mapping from a Euclidean space to itself that is an isometry with a set of fixed points known as the hyperplane, also known as the axis or plane of reflection.

The mirror image of a figure in the axis or plane of reflection is the image produced by a reflection.

A reflection keeps the pre-original image's size and shape, making it a congruent transition.

A figure that has been flipped over a line of reflection is a reflection.

The position of the x- and y-coordinates simply changes in a reflection across the line y = x.

Consider the case when the point (6, 7) is reflected across the line y = x. The reflected point's coordinates are (7, 6).

Therefore, a reflection preserves the size and shape of the prior original image, acting as a congruence transition.

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Answer:

A) 9

B) 53

Step-by-step explanation:

A:

-6 + 15 = 9

- - - - - -

+++++++++++++++

There are 9 more +  signs then - signs.

B:

37 - -16

37 + 16 = 53

+++++++++++++++++++++++++++++++++++++

We want to take away 16 negative signs, but we do not have any negative signs, so we add 16 zero pairs.  A zero pair has a value to zero

++++++++++++++++

- - - - - - - - - - - - - - -   If we now take away the 16 - signs, we are left with 53 + signs.

The angle formed by the two sides of a triangle is acute and obtuse respectively.

What is an area of a triangle?

In a two-dimensional plane, the area of a triangle is the region enclosed by it. A triangle, as we all know, is a closed shape with three sides and three vertices. Thus, the area of a triangle is the total space occupied by the triangle's three sides. The general formula for calculating the area of a triangle is half of the product of its base and height.

The first point to mention is that they are not orthogonal. A triangle's area is equal to 1/2 * base * height. The base * height for this triangle would be 16 * 2 = 32.

There are two options from here:

1. The angle formed by the two sides is acute. Determine the angle as follows:

Use the 10" side as the foundation.

Use the area formula to calculate the height, h = 32 / 10 = 3.2, and trig to calculate the acute angle: tan(Θ) = 3.2 / 10

2. The angle formed by the two sides is obtuse.

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By factorizing x² + 16  we get the factors as (x + 4i) • (x − 4i).

Here given the equation x² + 16 .

To factor x² + 16 with our imaginary number, we will use the sum of squares formula:

a2 + b2 = (a + bi) • (a − bi)

We begin by defining our problem in mathematical terms, as follows:

x² + 16

As you can see, our problem does not match the left side of the formula, so we must first convert it to match the left side, as follows:

x² + 16 = x² + 4²

Now that it corresponds, we can simply enter x for a and 4 for b into the formula to obtain the factors of x² + 16:

(x + 4i) • (x − 4i)

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If the function f(x) = x² - 2x + 3  and g(x) = log(x) + 3 , then f(x) is a polynomial function and g(x) is the logarithmic function .

A Polynomial Function is defined as a function that involves only non-negative integer powers of a variable in equation ,

For Example : quadratic equation , cubic equation .

By the definition of polynomial function ,

we can say that the given function f(x) = x² - 2x + 3 is a polynomial function , that is having degree 2 .

A Logarithmic function is defined as a function that involves log in the equation , such as log x , ln x .

According to the definition of Logarithmic function , the given function g(x) = log(x) + 3 is a type of Logarithmic function .

Therefore , f(x) is a polynomial function and g(x) is a logarithmic function .

The given question is incomplete , the complete question is

If the function f(x) = x² - 2x + 3  and g(x) = log(x) + 3 , then what kind of function is f(x) and g(x) ?

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Answer:

Natalie has $1.11 right now.

Step-by-step explanation:

1. Create an equation that represents Natalie's situation. Let x = the money Natalie has right now.

        [tex]x+ 10 = 9(x)^2[/tex]

2. This equation is a quadratic, so we need to factorise to solve for x, the amount of money Natalie has right now.

3. [tex]x + 10 = 9x^2[/tex]

4. [tex]0 = 9x^2 -x - 10[/tex]

5. [tex]0 = 9x^2 + 9x -10x - 10[/tex]

6. [tex]0 = 9x(x+1) -10(x+1)[/tex]

7. [tex]0 = (9x-10) (x+1)[/tex]

8. [tex]x+ 1 = 0\\\\x = -1[/tex]

9. [tex]9x - 10 = 0\\9x = 10\\x = 10/9, 1.11[/tex]

10. The amount of money Natalie has now cannot be negative. Therefore, Natalie has $1.11 right now.

A car is being driven at a rate of 40 mph when the brakes are applied. the car decelerates at a constant rate of 10 ft/sec2.The car will stop after 5.87 seconds.

1 mile = 5280 ft (approx)

1 hr = 3600 sec

The car is driven at a rate of 40 mph when the breaks are applied , then,

v(0)=40 m/hr

v(0)=40 5280 / 3600

v(0)=58.67 ft/sec2     [rounded to two decimal places] .............. (i)  

The car decelerate at a constant rate of 10 ft/sec²

So, acceleration function,

a(t)=-10 m/sec2  

Now, velocity function,

v(t)= a(t) dt    (ft/sec²)

v(t)= -10 dt   (ft/sec²)

v(t)=-10t+C1   (ft/sec²)   [where c is integrating constant]............ (ii)

Putting t=0 in this function,

v(o)=-10(0)+C1   (ft/sec²)    (ft/sec²)

v(0)=C1   (ft/sec²)

58.67=C1

C1=58.67

Putting this value of C1 in equation (ii) velocity function becomes,

v(t)=-10t+58.67      ......... (iii)

Car will stop when v(t) =0 . Then,

-10t+58.67=0

10t=58.67

t=58.67/10

t=5.867    [rounded to 2 decimal places]

So after 5. 87 sec the car will stop.

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As per the concept of probability, the number of students read two books is 6.

The term probability  in statistics referred as the possible way of occurring the event.

Here we have given that Mrs. Dominguez asked her students to plot the number of books they read over the summer.

And we need to calculate the number of students who read two books.

While we looking into the given question, we have clearly know that the total number of students is

=> 1 + 3 + 6 + 2 + 3 + 1 + 2

=> 18

And the number of student is who can read two books are represented by the dots in 2.

Therefore, the resulting number is 6.

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The tools that would be used to make header 1 appear and look like header 2 is the alignment tool icon and the Bold tool icon.

Microsoft Excel is a spreadsheet that can be used for a variety of features such as:

As a Microsoft software, Microsoft Excel can also be used to edit sheets. In the image attached, the required tool icons needed to change the header 1 into header 2 is the alignment tool icon and the Bold tool icon. The two tools can be seen in the image as the two lower left icons.

Electronic spreadsheet programs were originally based on paper spreadsheets used for accounting. As such, the basic layout of computerized spreadsheets is the same as the paper ones. Related data is stored in tables — which are a collection of small rectangular boxes or cells organized into rows and columns.

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Answer:

Lola can buy 12 DVD's,

Step-by-step explanation:

Lola's dad gives each of his 5 children an equal part of $340, which means that each child receives $340 / 5 = $68. Lola adds $28 to her portion, so she has a total of $68 + $28 = $96 to spend on gifts.

Lola finds classic DVDs for $8 each, and she has $96 to spend, so she can buy a total of $96 / $8 = 12 DVDs. Therefore, Lola can buy 12 classic DVDs with the money she received from her dad and the additional money she added.

I did some stuff I hope you get the bar graph or a diagram of sorts

The number of DVDs Lola can buy if, Lola's dad gives each of his 5 children an equal part of $340 to buy gifts, is 12.

One of the fundamental mathematical operations is division, which involves breaking a bigger number into smaller groups with the same number of components.

Given:

Lola's dad gives each of his 5 children an equal part of $340 to buy gifts,

Lola adds $28 to her portion. She finds classic DVDs for $8 each,

Calculate the money each child gets as shown below,

The money each child gets = Total money/number of children

The money each child gets = 340 / 5

The money each child gets = 68

The total money Lola has after adding extra money,

The total money Lola has = 68 + 28

The total money Lola has = 96

Calculate the number of DVDs as shown below,

The number of DVDs = total money/price of each DVDs

The number of DVDs = 96 / 8

The number of DVDs = 12

Thus, the number of DVDs Lola can buy is 12.

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Answer:

16

Step-by-step explanation:

because 8 x 2 is 16

If she had 1 more quarter, the average value would be twenty one cents. There will be 0 dimes in her purse

                                             

Let p, n ,d and q be the number of pennies, nickels, dimes and quarters.

(p + 5n + 10d +25q)/(p+ n + d +q) = 20      

Adding 1 more quarter makes the average 21, so:

[p+5n+10d+25 (q+1)]/[p+n+d+q+1] = 21                                                                                    

The mean would not change even if the new coin cost $20 cents. The new number of coins must be $5 since the extra $5 raises the mean by $1. There were $4 coins, which were worth a total of $4 times 20 cents, or 80 cents.

We get to the same conclusion as in the previous solution: $25+25+25+5 is the only combination of $4 coins that will yield $80 cents. Having three quarters, one nickel, and no dimes results in a boxed math (A) score of 0. $

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Approximately 19.8% of the students have grade point averages that are greater than 1.66.

We can use the empirical rule to calculate that approximately 68% of the students have grade point averages that are within one standard deviation of the mean. So, the remaining 32% of the students have grade point averages that are either less than 1.66 or greater than 3.46.

To find the percentage of students with grade point averages greater than 1.66, we need to subtract the percentage of students with grade point averages less than 1.66 from 32%. To do this, we need to find the z-score corresponding to 1.66.

To find the z-score we can use the formula:

z = (x - μ) / σ

Where x is the value we are trying to find the z-score for (in this case, 1.66), μ is the mean of the distribution (in this case, 2.56), and σ is the standard deviation of the distribution (in this case, 0.45).

Plugging in the values, we get:

z = (1.66 - 2.56) / 0.45 = -1.22

We can use a z-table to find the percentage of values less than -1.22 in a standard normal distribution. The percentage is approximately 12.2%. So, the percentage of students with grade point averages greater than 1.66 is 32% - 12.2% = 19.8%.

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We can determine the value of height (h) by 2x of area gives the value of base height and the volume can be determined by dividing the base area by the height.

The product of the length and width of the rectangle forming the base of a cuboid would yield the area of the base.

Any solid's capacity is represented by its volume. It is the measurement of the interior volume of a particular shape and is only calculable for three-dimensional shapes.

The cuboid's base area is (l × b) sq. units, and its volume is (l × b × h) cu. units.

It is simple to determine the value of height (h) by taking the ratio of these two quantities. As the result of length and width would no longer be the standard term.

If you know the area and you have to find the volume:

Since the base area is known, the volume can be determined by dividing the base area by the height. (Remember that volume is expressed in cubic units.)

If you know the area and you have to find the base height:

Now that you know the area of the triangle

Area=1/2*base*height

Then if we want to know base height so 2x of area gives the value of base height.

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A collection of paired data consists of the number of years that students have studied Spanish and their scores on a Spanish language proficiency test.  r = 0.91; There is a significant linear correlation. Option A

Generally, The value of the linear correlation coefficient r is given in the display as 0.91. To determine whether there is significant linear correlation between years of study and test scores, we need to conduct a hypothesis test.

The null hypothesis for this test is that there is no linear correlation between years of study and test scores, and the alternative hypothesis is that there is linear correlation.

To test the null hypothesis, we can use the value of r and the sample size (10 pairs of data) to calculate a p-value. If the p-value is less than our significance level of 0.05, we can reject the null hypothesis and conclude that there is significant linear correlation between the variables.

Since r is given as 0.91 and the sample size is 10, we can conclude that there is significant linear correlation between years of study and test scores.

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Answer: 1. Infinitely many solutions. 2. No solution. 3. Infinitely many solutions.

Step-by-step explanation:

What is infinitely many solutions and No Solution ?

Infinitely many solutions means that there are an infinite number of solutions to a particular problem or equation. No solution means that there are no solutions to a particular problem or equation.

In the case of infinitely many solutions, this occurs when the equation or problem has an infinite number of possible solutions. This can happen when the equation has a variable with no coefficient (e.g. x=5x+3), or when the equation has a coefficient of 0 (e.g. 0=5x+3).

In the case of no solution, this occurs when the equation or problem has no possible solutions. This can happen when the equation is contradictory (e.g. x=5x+3 and x=-5x-3) or when the equation has no solutions within the specified domain (e.g. x^2=9 in the domain of x<0).

3/5+2x=3x-x+_

This equation has infinitely many solutions because the x term is eliminated on both sides of the equation, leaving a true statement regardless of the value of x. The blank can be filled with any value.

8x+5=2x+3+_

This equation has no solution because the left side is 8x+5 and the right side is 2x+3, which are not equal for any value of x. The blank cannot be filled in to make the equation true.

4n-6(3-n)+_=10n-15

The equation can be simplified to 4n-18+=10n-15, which can be further simplified to -14+=6n-15. Adding 15 to both sides gives 1+=6n, which can be simplified to _=6n-1. This equation has infinitely many solutions because the value of _ is dependent on the value of n. For example, if n=2, then _=11. If n=3, then _=17. There are an infinite number of values for n that can be plugged in to find a corresponding value for _.

Therefore,  3/5+2x=3x-x+_  has infinitely many solutions, 8x+5=2x+3+_  has no solution and 4n-6(3-n)+_=10n-15 also has infinitely many solutions.

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1. Infinitely many solutions. 2. No solution. 3. Infinitely many solutions.

What is infinitely many solutions and No Solution?
Infinitely many solutions means that there are an infinite number of solutions to a particular problem or equation. No solution means that there are no solutions to a particular problem or equation.

In the case of infinitely many solutions, this occurs when the equation or problem has an infinite number of possible solutions. This can happen when the equation has a variable with no coefficient (e.g. x=5x+3), or when the equation has a coefficient of 0 (e.g. 0=5x+3).
In the case of no solution, this occurs when the equation or problem has no possible solutions. This can happen when the equation is contradictory (e.g. x=5x+3 and x=-5x-3) or when the equation has no solutions within the specified domain (e.g. x^2=9 in the domain of x<0).
3/5+2x=3x-x+_
This equation has infinitely many solutions because the x term is eliminated on both sides of the equation, leaving a true statement regardless of the value of x. The blank can be filled with any value.
8x+5=2x+3+_
This equation has no solution because the left side is 8x+5 and the right side is 2x+3, which are not equal for any value of x. The blank cannot be filled in to make the equation true.
4n-6(3-n)+_=10n-15
The equation can be simplified to 4n-18+=10n-15, which can be further simplified to -14+=6n-15. Adding 15 to both sides gives 1+=6n, which can be simplified to _=6n-1. This equation has infinitely many solutions because the value of _ is dependent on the value of n. For example, if n=2, then _=11. If n=3, then _=17. There are an infinite number of values for n that can be plugged in to find a corresponding value for _.
Therefore,  3/5+2x=3x-x+_  has infinitely many solutions, 8x+5=2x+3+_  has no solution and 4n-6(3-n)+_=10n-15 also has infinitely many solutions.

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Answer:

Step-by-step explanation:

[tex](ax - 2)^{2} = 100[/tex]

([tex]3a-2)^{2}[/tex]=[tex]100[/tex]

[tex]Using\\ the\\ formula (a + b)^{2} = a^{2} + b^{2} + 2ab[/tex]

([tex]3a)^{2}[/tex][tex]+ (2)^{2} +2(3a)(2)[/tex][tex]=100[/tex]

[tex]9a^{2}+4^{2} + 12a[/tex]=[tex]100[/tex]

[tex]9a^{2}+ 12a+16=100[/tex]

[tex]9a^{2} +12a+116[/tex]=[tex]0[/tex]

[tex]9a^{2} +3a+29[/tex]

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E*V = T where E = Eve's peaches P = Perry's peaches V = Varying amount of peaches T = Total peaches is an expression that shows how many peaches tara picked.

How do you define expression in math?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division. The structure of an expression is: Expression is (Number/variable, Math Operator, Number/variable)

Perry picked p peaches.

Tara picked 3 times as many peaches as perry

E = Eve's peaches

P = Perry's peaches

V = Varying amount of peaches

T = Total peaches

P = E*V

E*V = T

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Answer: x=9

Step-by-step explanation:

15-4x=42-7x

Move 15 to the right side

-4x=-7x+27

Move 7x to the left side

3x=27

3x/3=27/3

x=9

The equation x² + 4x - 7 can be written in the form (x + a)² - b as (x + 2)² - 11.

It follows from the task content that the equation x² + 4x - 7 is to be written in the vertex form; (x + a)² - b.

Since the given equation is; x² + 4x - 7 in which case, b is a constant.

b = constant

x² + 4x - 7

We therefore have an equivalent expression using the completing the square method as follows;

(x + 2)² - 4 - 7

= (x + 2)² - 11

Hence,

x² + 4x - 7 = (x + 2)² - 11

To Check:

= (x + 2) (x + 2) - 7

= x² + 2x + 2x + 4 - 11

= x² + 4x - 7

Therefore, the obtained equation; (x + 2)² - 11 is another form the equation x² + 4x - 7 can be written.

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The amount of ascent, or vertical distance, divided by the run, or horizontal distance, is how slope is commonly expressed as a percentage.

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The value of p is 13.

Mean is the average of the given numbers and is calculated by dividing the sum of given numbers by the total number of numbers.

The basic formula to calculate the mean is calculated based on the given data set. Each term in the data set is considered while evaluating the mean. The general formula for mean is given by the ratio of the sum of all the terms and the total number of terms.

Given,

The mean of 6,7,4,p,10 is 8

We know,

Mean = sum of observations/ no. of observations

8 = 6+7+4+p+10 / 5

40= 27+p

p=13

Hence, the value of p is 13.

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The true values of x and y in the system of inequalities are (2/3, 10/3)

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

y ≥ 2

x + y ≤ 4

y ≤ 2x + 2

Express the inequalities as equations

So, we have the following representation

x + y = 4

y = 2x + 2

Substitute y = 2x + 2 in the equation

x + y = 4

So, we have the following representation

x + 2x + 2 = 4

Evaluate the like terms

So, the equation becomes

3x = 2

Divide by 3

x = 2/3

Substitute x = 2/3 in y = 2x + 2

y = 2 x 2/3 + 2

Evaluate

y = 10/3

In y ≥ 2, we have

10/3 ≥ 2

The above inequality is true

Hence, the values of x and y are (2/3, 10/3)

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Only when we can map one figure onto the other using stiff transformations can we say that two figures are congruent.

While the image's size and shape are unaffected by rigid body motion, its location and orientation are. The three fundamental movements of a rigid body are translation, reflection, and rotation. Prior to movement, archetypes depict points or forms.

Only when we can map one figure onto the other using stiff transformations can we say that two figures are congruent. All related sides and angles are congruent because stiff transformations maintain the measure of both distance and angle.

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The possible base and height of a second triangle is 12&7

The base is inversely proportional to Height

[tex]B & \propto \frac{1}{H} \Rightarrow B=\frac{K}{H} \\[/tex]

14=[tex]\frac{K}{6}[/tex]

K=36

Now,

Let base and height of second triangle be x and y.

So,

[tex]& x=k / y[/tex]

yx=84

Area[tex]=\frac{1}{2} \times 14 \times 6 \\[/tex]

[tex]\frac{1}{2} \times x \times y=42 \\[/tex]

xy=84

Therefore, the base is 12 and height is 7.

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Shirley is drawing triangles that have the same area. The base of each triangle varies inversely with the height. What are the possible base and height of a second triangle if the first triangle's base is 14 and its height is 6?

options:

i. 12 and 8

ii. 120 and 70

iii. 50 and 34

iv.12 and 7