Please answer the problem above

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]

No, 8 is  real number.

Real numbers are those that can be expressed in decimal form, can be represented on number lines, and include positive or negative numbers. Real numbers do not include imaginary numbers because they cannot be expressed on number lines.

Given to find 8 is real or not,

non real numbers: The numbers which are not genuine and are Fanciful are known as not genuine or non-genuine numbers. The number line cannot be used to represent non-real numbers.

Number lines assume a significant part in deciding if a number is genuine or non-genuine as the genuine numbers can be shown on the number lines while non-genuine numbers can't be addressed on the number lines as they are fanciful.

Examples of real number  −1, 4, 8, 9.5, −6, 3, etc.

example of non real number  √-2, √-6

Hence, 8 is real number.

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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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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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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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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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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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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.

Fraction (3x)/(x-3) + 5/(x²-9) after simplifying is  (3x²+9x+5) / (x²-9).

A fraction is a component of a whole. Mathematically, the number is expressed as a quotient, where the numerator and denominator are divided. In a simple fraction, both are integers. In a complex fraction, a fraction can be found in either the numerator or the denominator. A suitable fraction has a numerator that is smaller than its denominator.

Given, fraction expression;

(3x)/(x-3) + 5/(x²-9)

Simplifying,

(3x)/(x-3) + 5/(x²-9)

= (3x)/(x-3) + 5/(x-3)(x+3)

Taking LCM,

= {3x(x+3)+5} / {(x-3)(x+3)}

= (3x²+9x+5) / (x²-9)

Therefore, fraction's simplification is (3x²+9x+5) / (x²-9).

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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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Answer: 28

Step-by-step explanation:

   First, we will write what the first line of text represents:

3x + 5 = 7

   Then, we will solve:

3x + 5 = 7

3x = 2

x = [tex]\frac{2}{3}[/tex]

   Lastly, we will substitute this value of x into the expression and simplify:

12x + 20

12([tex]\frac{2}{3}[/tex]) + 20

8 + 20

28

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The median is the middle point in a dataset—half of the data points are smaller than the median and half of the data points are larger.

A data set's median value is the point where 50% of the data points have values that are lower or equal to it, and 50% of the data points have values that are higher or equal to it.

To arrange the data points in ascending order for a small data set, count the number of data points (n).

To get the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.

Example: The median of 4, 1, and 7 is 4 because when the numbers are put in order (1,4,7)the number 4 is in the middle.

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the rank of the data point whose value is the median when the number of data points is unequal, multiply the total by 1 and divide the results by 2.

The median of 4, 1, and 7 is 4 because when the numbers are put in order (1,4,7)the number 4 is in the middle.

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

Answer:

(x - 3) ( 2x+1)

Step-by-step explanation:

(x - 3) ( 2x+1)

2x^2 + x - 6x -3

2x^2 - 5x -3

So, my answer is right!

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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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 slope of the graph determines if a graph is positive or negative.

The slope is the ratio of change of the dependent variable with respect to the change in the independent variable.

It is calculated for both straight lines as well as curves.

for example, let us say , we have a straight line y = mx +c , then the coefficient of the dependent variable 'm' is the slope of the line. It is also calculated by (y2-y1)/ (x2-x1) where y2, x2 are the final positions and y1,x1 are the initial positions.

For curves, since the graph is not linear, the slope changes everywhere and hence we take the differential of y w.r.t. x i.e. dy/dx.

for example, we have a parabola  , y^2 =4ax .

So , here 2ydy= 4adx , so dy/dx = 4a/2y.

Hence , we can say that is the slope is positive, i.e. the graph extends upto right , its a positive graph; if the slope is negative, i.e. the graph extends down to y , its a negative graph .

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Answer:

16

Step-by-step explanation:

because 8 x 2 is 16

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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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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a. Finding equation of line passing through A and parallel to BC.

[tex]\quad[/tex]

Since our line is parallel to BC, slope of the line is,

[tex]\longrightarrow\rm{m_a=\dfrac{y_B-y_C}{x_B-x_C}}[/tex]

[tex]\longrightarrow\rm{m_a=\dfrac{7-4}{2-(-10)}}[/tex]

[tex]\longrightarrow\rm{m_a=\dfrac{1}{4}}[/tex]

Since our line passes through A, the equation will be,

[tex]\longrightarrow\rm{y-y_A=m_a(x-x_A)}[/tex]

[tex]\longrightarrow\rm{y-(-2)=\dfrac{1}{4}(x-5)}[/tex]

[tex]\longrightarrow\rm{\underline{\underline{x-4y-13=0}}\quad\quad\dots(1)}[/tex]

[tex]\quad[/tex]

b. Finding equation of line passing through B and perpendicular to AC.

[tex]\quad[/tex]

Since our line is perpendicular to AC, slope of the line is,

[tex]\longrightarrow\rm{m_b=-\dfrac{x_A-x_C}{y_A-y_C}}[/tex]

[tex]\longrightarrow\rm{m_b=-\dfrac{5-(-10)}{-2-4}}[/tex]

[tex]\longrightarrow\rm{m_b=\dfrac{5}{2}}[/tex]

Since our line passes through B, the equation will be,

[tex]\longrightarrow\rm{y-y_B=m_b(x-x_B)}[/tex]

[tex]\longrightarrow\rm{y-7=\dfrac{5}{2}(x-2)}[/tex]

[tex]\longrightarrow\rm{\underline{\underline{5x-2y+4=0}}\quad\quad\dots(2)}[/tex]

[tex]\quad[/tex]

c. Finding point of intersection of the above two lines.

[tex]\quad[/tex]

From (1),

[tex]\longrightarrow\rm{x=4y+13}[/tex]

Putting this value of x in (2),

[tex]\longrightarrow\rm{5(4y+13)-2y+4=0}[/tex]

[tex]\longrightarrow\rm{18y+69=0}[/tex]

[tex]\longrightarrow\rm{y=-\dfrac{23}{6}}[/tex]

Then,

[tex]\longrightarrow\rm{x=4\left(-\dfrac{23}{6}\right)+13}[/tex]

[tex]\longrightarrow\rm{x=-\dfrac{7}{3}}[/tex]

Hence the intersection point is [tex]\bf{\left(-\dfrac{7}{3},\ -\dfrac{23}{6}\right)}.[/tex]

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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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:

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.

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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(a) If your entire portfolio is now composed of stock a and you can add some of only one stock to your portfolio, you would choose stock D of corr(a, d) = .45.

(b) No, the answer to (a) would not change.

(c) No, you would not change your answers to parts a and b if the T-Bill rate is 8%.

A- Since all stocks have the same expected rate of return and standard deviation, we choose the stock that will result in the lowest risk. This leads to the intuitive result that the desired addition would be the stock with the lowest correlation with Stock A, which is Stock D.
B- The answer to (a) would not change, at least as long as investors are not risk lovers.

C- Treasury Bills (T-bills) 1.3 Treasury bills or T-bills, which are money market instruments, are short-term debt instruments issued by the Government of India. Treasury bills are zero coupon securities and pay no interest.

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A- Since all stocks have the same expected rate of return and standard deviation, we choose the stock that will result in the lowest risk. This leads to the intuitive result that the desired addition would be the stock with the lowest correlation with Stock A, which is Stock D.

B- The answer to (a) would not change, at least as long as investors are not risk lovers.

C- Treasury Bills (T-bills) 1.3 Treasury bills or T-bills, which are money market instruments, are short-term debt instruments issued by the Government of India. Treasury bills are zero coupon securities and pay no interest.

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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