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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. 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]

For two variable inequalities which has equal to inequal sign is shown in the graph as a solid line.

An algebraic expression of two variables having equal to inequal sign or inequal sign with it.  such as ≥ and ≤ are equal to inequal sign and < and > are inequal sign.

The way we solve linear equation is similar to solve the inequalities. The inequalities which have equal to inequal sign ≤ or ≥ is plotted on the graph and identify the boundary with solid line.

hence, we indicate an equal to inequality on a graph for variables by solid line.

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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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The value of x in the equation x² = 16 is  ± 4

        Here, x² = 16

        Taking square root on both sides,

        [tex]\sqrt{x^{2} } =\sqrt{16}\\[/tex]

        Simplifying the radicals,

         x = ± 4

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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:

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]

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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To get the SSS loan disbursement account approved follow these steps :

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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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answer- 5 watches

- you divide 1,500 by 300

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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To know it's AAS or ASA check, In ASA, the side is in between the two angles on the triangle i.e Its included side. In AAS, the S is listed at the end to indicate that the side is not in between the angles i.e it's not include side.

AAS stands for "Angle, Angle, Side" and means that there are two triangles whose two angles and sides that are not included are known to be equal. Triangles are congruent if two angles and not included sides of a triangle are equal to the corresponding angles and sides of another triangle.

ASA (Angle, Side, Angle) :

If two triangles are congruent, all three corresponding sides are congruent and all three corresponding angles are congruent. Triangles are congruent if two corresponding pairs of angles and the sides between them are known to be congruent. A triangle is congruent if two pairs of corresponding angles are congruent and the sides involved are also congruent. This criterion is known as Angle Side Angle (ASA). Another criterion is the angle-angle-side (AAS), which is known to congruent two pairs of angles and an absent side.

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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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(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.

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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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

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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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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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

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.

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!

Customers pay an amount of $259 for the tents. which is the correct answer would be an option (C).

The markup rate is computed by dividing a unit's gross profit (its sales price less its cost to create or buy for resale) by its cost.

To find the price that the customers pay for the tents, we need to first calculate the markup on the tents.

The markup is 40% of the purchase price, which is $185. So the markup is: ⇒ 40/100 × $185 = $74.

Now we can add the markup to the purchase price to find the selling price of the tents.

The selling price is :

$185 + $74 = $259.

Therefore, the customers pay $259 for the tents.

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The expressions which are equivalent to 35 + 30s - 45t are:

The correct answer options are options B and C

35 + 30s - 45t

Check all options

A. 7⋅(5+30s−45t)

= 35 + 210s - 315t

False

B. 5(7+6s−9t)

= 35 + 30s - 45t

True

C. (−35−30s+45t)×(−1)

= 35 + 30s - 45t

True

D. 10×(3.5+3s−4.5)

= 35 + 30s - 45

False

E. ( 35/2 - 15s + 45/2t) ⋅ (-2)

= (17.5 - 15s + 22.5t) (-2)

= -35 + 30s - 45t

False

Therefore, the equivalent expression is an expression which has an equal value to each other.

Complete question:

Which expressions are equivalent to 35 + 30s - 45t?

A. 7⋅(5+30s−45t)

B. 5(7+6s−9t)

C. (−35−30s+45t)×(−1)

D. 10×(3.5+3s−4.5)

E. ( 35/2 - 15s + 45/2t) ⋅ (-2)

choose 2 answers

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The discriminant of the equation 3x² - 6x + 5 = 0 is -24

Given,

The equation; 3x² - 6x + 5 = 0

We have to find the discriminant of the equation;

Discriminant of equation;

Any equation with the formula ax2 + bx + c = 0 and an alpha value of 0 is a quadratic equation. The discriminant is the expression b2 - 4ac for the quadratic equation ax2 + bx + c = 0. The discriminant's value reveals how many roots f(x) has: - The quadratic function has two unique real roots if b2 - 4ac > 0, otherwise it does not.

Here,

a = 3

b = -6

c = 5

Then,

Discriminant, D = b² - 4ac

D = -6² - 4 × 3 × 5

D = 36 - 60

D = -24

That is,

The discriminant of the equation is -24

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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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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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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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