Question 5
Describe the reflection that maps ST, with vertices S(-7, 1) and T(-7, 5), onto itself. Use decimals, if necessary.
reflection in the line y =______

The vector equivalent to the directed line segment from the point (x1, y1) to the point (x2, y2) is the vector <x2-x1, y2-y1>.

The vector of a directed line segment is the difference between the two endpoints of the line segment. In this case, the endpoints are the points (x1, y1) and (x2, y2). Therefore, the vector of the directed line segment is equal to the vector <x2-x1, y2-y1>.

The vector equivalent of a directed line segment from the point (x1, y1) to the point (x2, y2) is the vector with initial point (x1, y1) and terminal point (x2, y2). This vector is equal to the vector form <x2-x1, y2-y1>, which describes the displacement from the initial point to the terminal point. This vector can also be written in component form, meaning the magnitude of the vector in the x-direction is x2-x1, and the magnitude of the vector in the y-direction is y2-y1.

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A total of 12,000 dollars is made from the sale of 300 books at a price of $40 each. 25 fewer books are sold for every $5 increase in price.      R(x)=(40+5x)(300−25x) R ( x ) = ( 40 + 5 x ) ( 300 − 25 x )

Assumed in this instance is , At a price of 40 dollars apiece, [tex]$(300)(40 \$)=12,000 \$$[/tex] books generate $300 in revenue. The result is that 25 fewer books are sold if we raise the price of each book by $5. That's [tex]$(300-25 x)$[/tex]. Due to the fact that the price always rises by five times more than the number of books, the cost is [tex]$(40+5 x)$[/tex].

[tex]$R=(300-25 x) \cdot(40+5 x)$[/tex]

[tex]$R=12000+6000 x-1000 x-125 x^2$\\$R=-125 x^2+5000 x+12000$\\$R=125 x^2-5000 x-12000$[/tex]

The revenue R is expressed as a function of the number x as it approaches 5. R(x)=(40+5x)(30025x) is the necessary revenue function. R(x) = (40 + 5 x)(300 25 x) is the necessary revenue function.

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The cost of each box of candy is 31 cents and the cost of each bag of chips is 69 cents.

To find the cost of each box of candy, we first need to find the total cost for all items. We know that Rafael and his sister spent a total of $3.82 + $2.69 = $6.51 on snacks. Since Rafael bought 3 boxes of candy and 1 bag of chips, and his sister bought 2 bags of chips and 1 box of candy, there were a total of 3 + 2 = 5 bags of chips and 3 + 1 = 4 boxes of candy bought.

To find the cost of each box of candy, we divide the total cost for all boxes of candy by the number of boxes of candy: $6.51 / 4 = $1.63 or 163 cents. To find the cost of each bag of chips, we divide the total cost for all bags of chips by the number of bags of chips: $6.51 / 5 = $1.30 or 130 cents.

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Can be cracked within eight hours by the average hacker.

With spaces included in the character count, 8 characters equals between 1 and 2 words. If spaces are excluded from the character count, 8 characters equals between 1 and 3 words.

There are 8-character passwords with capital letters, lowercase letters, and numerals that begin and end with the same symbol.A password of eight characters with just lowercase and capital letters offers 200 billion potential permutations.“1uppercase” is an example of an 8-character password. This password has one uppercase, one lowercase, one number, and one special character.

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Answer:

x = -4

y = 29

Step-by-step explanation:

Let's take our two equations and turn the decimals into fractions for simplicity's sake. We get:

x/4 + 5y/100 = 9    x + y = 25

Simplifying a bit gives us:

x/4 + y/20 = 9       x + y = 25

Now, we will take the first equation and multiply it by 20 to get rid of the fractions. We get:

5x + y = 9

We will rearrange numbers to give us an answer to y that we can substitute in. we get:

y = 9 - 5x

Then, we will plug this into our second equation giving us:

x + 9 - 5x = 25

Combining like terms and subtracting 9 from both sides gives us:

-4x = 16

Dividing by -4 gives us:

x = -4

Then, we can substitute this into our second equation giving us:

-4 + y = 25

We will add 4 to both sides giving us:

y = 29

Hope this helped!

The coefficients in the expression [tex]12x^{3} (2x^{3}) + y^{3}[/tex] are , coefficient of of x⁹ is 24 and coefficient of of y³  is 1   .

The Coefficients are defined as a multiplicative factor in some term of a polynomial , series or an expression , the coefficient is usually a number .

the expression is given as [tex]12x^{3} (2x^{3}) + y^{3}[/tex] ;

to find the coefficients we first simplify the expression ,

we get ;

= [tex]12x^{3} \times2x^{3} + y^{3}[/tex]

= [tex]24x^{9} +y^{3}[/tex] ;

so , the numerical term with x⁹  is 24 and the numerical term with y³ is 1 .

Therefore , the coefficient of x⁹ is 24 and the coefficient of  y³ is 1 .

The given question is incomplete , the complete question is

What is the coefficient of x⁹ and y³ in the expression [tex]12x^{3} (2x^{3}) + y^{3}[/tex] ?

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The graph of a line with a slope of 3/5 has an equation of y = 3/5x + 1 and the graph is attached

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

Graph of a line with a slope of 3/5

This means that

Slope = 3/5

And it also means that the equation is a linear equation

A linear equation is represented as

y = mx + c

Where

m = slope

i.e. m = 3/5

So, we have

y = 3/5x + c

Assume that c = 1

So, we have

y = 3/5x + 1

Hence, the equation is y = 3/5x + 1

See attachment for graph

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Pick a random selection of students who attend the work lab.

Picking a random sample of students is the most effective strategy to ensure accurate results. The findings of a survey that the student conducts among those sat in the lab's front rows might be skewed.

The students seated in front of the lab could exhibit a certain trait (e.g., they might be particularly diligent students), which would undoubtedly yield a different outcome.  The survey is in good shape. No special equipment is required to evaluate our comprehension of statistical analysis.

Additionally, there won't be much of a difference if more students are included in the sample that are sat in front of the lab. Finally, it makes no sense to administer instruments to a group that does not visit the work laboratory. Effectiveness cannot be evaluated based on students who do not participate in class.

Therefore the correct option is B)  Select a random sample of students who go to the work laboratory

The complete question is:

A student researcher wishes to examine the effectiveness of a statistical work laboratory on graduate students' overall understanding of application of statistical analyses. The researcher administers a survey to 15 students who are seated at the front of the laboratory. How could this study be improved? Select all that apply.

A. Use an instrument to test statistical analysis understanding.

B. Select a random sample of students who go to the work laboratory

C. Use a larger sample size.

D. Administer instruments to a group who does not go to the work laboratory, as well.

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Therefore ,As a result, the answer to the provided equation is that a burrito costs $2.50 and a soft taco costs $1.50.

A number, a variable, or a mix of both plus certain operation symbols make up an expression. An equal sign separates two expressions that make up an equation. Word illustration The product of 8 and 3 is 11.

Here,

Let the price of a soft taco be set at s.

Let b be the price for one burrito.

Therefore, we have this system.

3s + 3b = 11.25

4s + 2b = 10.00 (1) (1)

By multiplying the first equation by 3, we get that.

If s + b = 3.75, take b off of both sides.

s = 3.75 - b (2) (2)

Subtract (2) from (1) and you get

Simplify 4 (3.75 - b) + 2 b = 10.00.

15 - 4b + 2b = 10.00

Subtract 15 from both sides (-2b + 15 = 10) to get the total.

Divide both sides by -2 to get -2b = - 5.00.

b = 2.50

as well as (2)

s = 3.75 - 2.50 = 1.50

As a result, the answer to the provided equation is that a burrito costs $2.50 and a soft taco costs $1.50.

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No. the sum of any two lengths of the triangle is greater than the third length.

Option (A) is correct.

A triangle is a polygon with three edges and three vertices. In Euclidean geometry, a triangle is completely determined by the three points that make up its vertices.

Kathy wants to place a printer 9ft from the filing cabinet. Can the other two distances are shown to be 7ft and 2ft.

No the sum of any two lengths of the triangle should be greater than the third side.

but 7 + 2 = 9, so the condition for a triangle is false.

Hence, the correct explanation would be "No. the sum of any two lengths of the triangle is greater than the third length."

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Kathy wants to place a printer 9ft from the filing cabinet. Can the other two distances shown be 7ft and 2ft? Identify the answer with the correct explanation. Printer Desk Filing Cabinet

O Yes; the sum of any two lengths is greater than the third length.

O No; the sum of any two lengths is not greater than the third length.

O Yes; the sum of any two lengths is equal to the third length.

O No; the sum of any two lengths is greater than the third length

Answer:

No; The sum of any two lengths is NOT greater than the third length

Step-by-step explanation:

It is given that three objects, a desk, a filing cabinet, and a printer, form a triangle.

Use the Triangle Inequality Theorem to determine whether the given distances can be the lengths of the sides of a triangle.

9+7=16>2

9+2=11>7

7+2=9=9

The sum of one pair of lengths is equal to the third length. Therefore, the distances between the desk, the printer, and the desk and the filing cabinet cannot be 7ft and 2ft since 7+2 equals 9.

The variable terms in the expression 3[tex]x^{3}[/tex]y + 5[tex]x^{2}[/tex] + y + 9 are [tex]x^{3}[/tex]y, [tex]x^{2}[/tex], and y.

The expression provided is

3[tex]x^{3}[/tex]y + 5[tex]x^{2}[/tex] + y + 9

In the expression, each variable is represented by a letter.

Let's look at the variables for each term.

The variable in the first term, 3[tex]x^{3}[/tex]y, is [tex]x^{3}[/tex]y.

The variable in the second term, 5[tex]x^{2}[/tex] , is [tex]x^{2}[/tex] .

Y is the variable in the third term.

There is no variable in term 9's final equation.

The variables in the expression are [tex]x^{3}[/tex]y, [tex]x^{2}[/tex] , and y.

As a result, the variables [tex]x^{3}[/tex] and y are the variable terms.

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The formula yields the radius $r$ of a circle that is inscribed within three circles with radii $a$, $b$, and $c$ that are mutually external tangents.

[tex][\frac{1}{r} = \frac{1}{a} + \frac{1}{b} + \frac{1}{c}][/tex]

The radius of the inscribed circle is related to the radii of the three mutually externally tangent circles using a method known as the radical centre formula. According to this equation, the reciprocals of the radii of the three externally tangent circles add up to the radius of the circle that is inscribed.

The power of point theorem states that the product of the distance between the point and the three points of tangency is equal to the product of the distance between the point and the centres of the circles. This formula is based on the fact that the circles are mutually externally tangent and their centres are collinear. It is crucial to note that the formula can only be used if the circles are mutually externally tangent; otherwise, it is invalid.

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The midpoint of the x-intercept is (0,0).

By looking at the equation, we may determine the y-intercept when the equation is expressed in the slope-intercept form (y=mx+b). The y-intercept is the value of b. This is due to the fact that the occurs when the x value is 0. Y = B when x = 0, since mx y-intercept = 0 at this point.

We set y = 0 and solve the equation for x to determine the x-intercept. This is due to the fact that the line crosses the x-axis at y=0. If an equation is not in the form y = mx + b, we can still solve for the intercepts by substituting 0 where necessary and then solving for the final variable.

The formula for the x-intercept is y = 0: The x-intercept(s) can be determined by factoring or by employing the quadratic formula because ax2 + bx + c=0.

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a) The total amount of pizzas that they ate is given as follows: 2.92 pizzas.

b) The difference between the number of cheese pizzas and the number of vegetarian pizzas is given as follows: 4/3, which is the amount that they ate more of cheese pizzas than vegetarian pizzas.

The fractions relative to the amount of each type of pizza eaten are given as follows:

The total amount of pizzas eaten is given by the addition of these fractions, hence:

1/4 + 2 + 2/3 = 3/12 + 24/12 + 8/12

(as the least common factor between 4, 1 and 3 is of 12).

3/12 + 24/12 + 8/12 = (3 + 24 + 8)/12

(3 + 24 + 8)/12 = 35/12

2.92 pizzas.

The difference between the number of cheese pizzas and the number of vegetarian pizzas is obtained as follows:

2 - 2/3 = 6/3 - 2/3 = 4/3.

(as the least common factor of 1 and 3 is of 3).

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Since the problem is about linear equation in the form of y = mx + b, initial number represents the value of b = 12, the number of days represents the value of x = 3, the daily collection of cupcakes represent the slope m = 24, then the value of y is:

So the matching pairs are:

10,000 randomly chosen registered users receive an email survey from the company. The survey findings are most susceptible to nonresponse bias.

A news website sends an email survey to 10,000 randomly chosen registered users in order to learn which other websites its readers visit for their technology news. The most common sort of bias that the survey results are vulnerable to is nonresponse bias. Because convenience sampling, which many researchers engage in, frequently leads to undercoverage bias in survey research, it is a widespread problem.

Coverage bias, like many other potential problems in survey research and data gathering in general, can significantly change your survey results and compromise the integrity of your research. This phrase describes the several circumstances and biases that may affect survey results. Regardless of whether the bias was deliberate or unintentional, erroneous survey results make the information less helpful.

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The factored form of quadratic equation 2x² + 7x + 3 is 2(x + 1/2) (x + 3)

A quadratic equation can be expressed in:

- Standard form: y = ax² + bx + c

- factored form: y = a(x - x₁) (x - x₂)

Here, x₁ and x₂ are the roots of the given function.

Suppose we are given a quadratic equation:

y = ax² + bx + c

To find the factored form, use the following properties:

x₁ . x₂ = c/a

x₁ + x₂ = - b/a

In this case, the quadratic function is:

y = 2x² + 7x + 3

We have to find x₁ and x₂ such that:

x₁ . x₂ = 3/2

x₁ + x₂ = - 7/2

Hence,

x₁ = - 1/2

x₂ = - 3

Therefore the factored form is:

y = 2(x + 1/2) (x + 3)

Your question is incomplete, but most probably your question was:

Which expression is the factored form of 2x² + 7x + 3?

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Answer:

The value of x is 2/7 or 0.285

Step-by-step explanation:

Here, we will make equivalent expressions in the equation that all have equal bases.

6²⁽⁶ˣ⁻¹⁾ = 6⁵ˣ

Since, The bases are the same i.e., 6. So, exponent are also same

2(6x - 1) = 5x

Solve for x

12x - 2 = 5x

12x - 5x - 2 + 2 = 5x - 5x + 2

7x = 2

7x/7 = 2/7

x = 2/7 = 0.285

Thus, The value of x is 2/7 or 0.285

For verification

36⁶ˣ⁻¹ = 6⁵ˣ

36⁶⁽⁰°²⁸⁵⁾ ⁻ ¹ = 6⁵⁽⁰°²⁸⁵⁾

36¹°⁷¹ ⁻ ¹ = 6¹°⁴²⁵

36⁰°⁷¹ = 6¹°⁴²⁵

12.7 = 12.7

Hence, L.H.S = R.H.S

VERIFIED!!

Answer:

1st, 4th and 5th are correct.

Step-by-step explanation:

Answer:t=-12

and if want step by step just look the equation up on the internet and it will be there step by step

Answer: In mathematics, the reciprocal of a number is 1 divided by that number. So the reciprocal of 7/9 is 1/(7/9) which can be simplified to 9/7.

Therefore, 9/7 is the number that when multiplied by 7/9 will result in the product of 1.

Another way of arriving at the same solution is to remember that the product of a number and its reciprocal is always 1. In this case, the number is 7/9, and its reciprocal is 9/7.

Step-by-step explanation:

Answer:

B. ST and TK intersect at a 90 degree angle.

I know this because you can see that in between STK, there is a square in the corner indicating a 90 degree angle.

Step-by-step explanation:

Hope it helps! =D

The graph of the linear equation 2x + 3y = 6 is a straight line that cuts the Y-axis at the point (0,2).

A linear equation is an equation in which the highest power of the variable is 1.

The general form of a linear equation is:ax + by = c where a, b and c are constants and x and y are variables. This equation represents a straight line when plotted on a graph.

The slope-intercept form of a linear equation is y = mx + b, where m is the slope of the line and b is the y-intercept

To find the points at which the line will intersect y-axis,

take x=0 and substitute in the linear equation 2x+3y=6

2(0) + 3y = 6

3y = 6

y = 2

So the point where the line cuts the Y-axis is (0,2)

The straight line of the linear equation 2x+3y=6 intersects the y-axis at (0,2).

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You can identify equivalent expressions if one of the expressions can be written like the other and it is usually written by combining any like terms on each side of the equation such as x-terms with x-terms and constants with constants.

These are the type of expressions that have similar value or worth but do not look the same.

This type of expression can be identified if one of the expressions can be written like the other and example can be seen below:

3(x + 3) and 3x + 9

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the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.

Therefore,

a) 1 mop cost $77.50

b) 1 broom cost $62.50

What is the system of equations?

A system of equations is a set of one or more equations involving a number of variables. The solutions to systems of equations are the variable mappings such that all component equations are satisfied in other words, the locations at which all of these equations intersect.

To find the cost of a mop and a broom, we can set up a system of equations using the information given:

Let x be the cost of a broom

Let y be the cost of a mop (which is $15 more than a broom)

From the problem, we know that:

y = x + 15 (since a mop costs $15 more than a broom)

5x + 7y = 855 (since 5 mops and 7 brooms cost a total of $855)

We can substitute the first equation into the second equation:

5x + 7(x + 15) = 855

5x + 7x + 105 = 855

12x = 750

x = 62.5

Hence, the cost of a broom is $62.50, and the cost of a mop is x + 15 = 62.5 + 15 = $77.50.

Therefore,

a) 1 mop cost $77.50

b) 1 broom cost $62.50

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70-70-40 is an isosceles triangle.

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The spring constant is 30 N/m and the stretch when the 420 N force is applied is 14 cm.

The force needed or applied to compress or extend a spring on any attached object is known as the spring force.

A spring exerts an equal and opposite force on an object when the object exerts a force on it. It always takes action to get mass back to where it should be for equilibrium. 

Given that when 180 N force is applied the spring stretched by 6 cm. The spring stretch when the 420 N force is applied is calculated as,

First, calculate the spring constant,

F = kx

180 = k x 6

k = 30 N / m

Calculate the deformation,

x = F / k

x = 420 / 30

x = 14 cm

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By the concept of the proportional method we determine that the height of the tower would be 48 feet.

In its most basic form, a ratio is a comparison between two comparable quantities.

There are two types of proportions One is the direct proportion, whereby increasing one number by a constant k also increases the other quantity by the same constant k, and vice versa.

If one quantity is increased by a constant k, the other will decrease by the same constant k in the case of inverse proportion, and vice versa.

The model given can be interpreted by the concept of proportional method

a : b : : c : d.

Therefore,

5 : 6 : : 40 : x.

5/6 = 40/x.

5x = 240.

x = 240/5.

x = 48 feet.

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Answer:

The slope of line r is -3/4

Step-by-step explanation:

First, let's find the slope of line q. We can find the slope by finding the change in y over change in x.

[tex]\displaystyle{m=\dfrac{y_2-y_1}{x_2-x_1}}[/tex]

Therefore, substitute in:

[tex]\displaystyle{m=\dfrac{8-4}{6-3}}\\\\\displaystyle{m=\dfrac{4}{3}}[/tex]

Therefore, the slope of line q is 4/3. Since we want to find the slope of line r and we know by the given that line r is perpendicular to line q. By the definition of perpendicular line is [tex]\displaystyle{m_1m_2=-1}[/tex].

Let [tex]m_1[/tex] be slope of the line q which is 4/3. Therefore, substitute in and solve for [tex]m_2[/tex] (slope of line r)

[tex]\displaystyle{\dfrac{4}{3}m_2=-1}\\\\\displaystyle{4m_2=-3}\\\\\displaystyle{m_2=-\dfrac{3}{4}}[/tex]

Therefore, the slope of line r is -3/4