solve the following equations by graphical method: 2x+y=7 and x-y=1​

Answer: y=3x

Step-by-step explanation: To find the equation of the line m, which is the image of line t after a dilation with a scale factor of 1/2 centered at the origin, we need to follow these steps:

Rewrite the equation of line t in slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept.

3X - Y = 6

-Y = -3X + 6

Y = 3X - 6

So the slope of line t is 3.

Apply the dilation with a scale factor of 1/2 centered at the origin. This means that every point on line t is multiplied by 1/2 in both the x and y directions. The origin (0,0) remains fixed.

The new coordinates of any point on line t after dilation are given by (1/2x, 1/2y).

Use the new coordinates to find the equation of line m. To do this, we need to find the slope of line m and a point on it.

The slope of line m is the same as the slope of line t, which is 3.

To find a point on line m, we can use the fact that the origin remains fixed after dilation. So the point (0,0) is on line m.

Using the slope-intercept form, y = mx + b, we can write the equation of line m as:

y = 3x + b

To find the value of b, we can use the point (0,0):

0 = 3(0) + b

b = 0

Therefore, the equation of line m is y = 3x.

The Equation of line m is y= 3x - 3.

A scale factor is a number that can be used to adjust the size of any geometrical figure or object in relation to its original size. It's used to draw the enlarged or reduced shape of any given figure, as well as to calculate the missing length, area, or volume of an enlarged or reduced figure. It should be noted that the scale factor only affects the figure's size and not its shape.

We have, Equation of line t

3x - y = 6

Take x= 0 then y = -6 and y= 0 then x = 2.

Now, dilate the coordinates by factor 1/2 as

(0, -3) and (1, 0).

So, the Equation of line m is

(x - 0) / (1- 0) = (y - (-3)) / (0 - (-3))

x/1 = y + 3 / 3

3x = y+ 3

y= 3x - 3

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Answer:

[tex]y = 7[/tex]

[tex]x = 7 \sqrt{2} [/tex]

Sο, if οur estimatiοns are reasοnably accurate, the likelihοοd that a chοsen student is a wοman οr a business majοr is rοughly 0.6.

It describes the likelihοοd οf a specific οccurrence οr grοup οf οutcοmes in a given envirοnment and is a key idea in mathematics and statistics. Prοbability is typically stated as a number between 0 and 1, with 1 denοting a certain event and 0 denοting an impοssibility. By dividing the number οf faοurable οutcοmesv by the tοtal number οf pοssible οutcοmes, οne can determine the prοbability οf an οccurring.

We must sum the prοbabilities οf twο events—the prοbability that the student is a wοman and the prοbability that the student is a business majοr—in οrder tο get the likelihοοd that a certain student is a wοman οr a business majοr.

P(A and B) equals P(A)*P (B)

Using this presumptiοn, we may calculate the likelihοοd that a chοsen student will majοr in business and be a wοman as fοllοws:

P (wοman) = 0.2 * P (business majοr) = 0.1 (10%)

After that, we can enter this value in the previοus equatiοn:

P (wοmen majοring in business) = 0.5 + 0.2 - 0.1 = 0.6 (οr 60%)

Sο, if οur estimatiοns are reasοnably accurate, the likelihοοd that a chοsen student is a wοman οr a business majοr is rοughly 0.6.

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Complete Question:

A college has an undergraduate enrollment of 3500. Of these, 860 are business majors, 1800 are women and 425 are women business majors.

a. Are the events "selecting a woman student" and "selecting a business major" mutually exclusive? Explain.

b. If a college newspaper conducts a poll and selects students at random to answer a survey, find the probability that a selected student is a woman or a business major.

Answer: I believe it is option (A): 4.5

Step-by-step explanation: If you look closely and examine DE and CE you will see they are the same length, and we know they are 5. But if you compare the lines from a diagonal perspective, BD is not equal to 5 and has to be a bit smaller. The closest option below 5 is therefore 4.5

Hope this helps! Please mark brainliest!

Answer:

Step-by-step explanation:

[tex]FV = (PMT * \frac{(1+i)^{n} -1}{i} )* (1 + i)[/tex]

FV = Future Value of the annuity

PMT = Amount of each annuity payment

i = Interest rate per period

n = Number of periods for which annuity will last

FV = ?

PMT = $4,500

i = 5.2% = 5.2/100 = 0.052

n = 3

[tex]FV = (4500 * \frac{(1+0.052)^{3} -1}{0.052} )* (1 + 0.052)[/tex]

[tex]FV = 14,953.30[/tex]

You will have $14,953.30 in 3 years.

Answer: b I believe.

Step-by-step explanation:

4,500 times 5.2% = 4,754 add that to the amount of money you have already. giving you b.

Substitute a=7, b=5, and c=3 into the expression ab+c:

ab+c = (7)(5) + 3

ab+c = 35 + 3

ab+c = 38

Therefore, ab+c is equal to 38 when a=7, b=5, and c=3.

Triangle ABC can be mapped onto triangle XYZ by a composition of transformations represented by (x,y) → (x+3,y-6) and followed by a dilation with center (0,0) and scale factor 1/3 represented by (x,y) → (x/3,y/3).

Dilation is a geometric transformation that involves changing the size of an object while maintaining its shape and proportions. In dilation, every point of the original figure is expanded or contracted away from a fixed point called the center of dilation.

The ratio of the distance between the center of dilation and each point of the original figure is the same for all corresponding points in the dilated figure. This ratio is called the scale factor, and it determines the degree of dilation.

If the scale factor is greater than 1, the figure is enlarged or dilated, while if the scale factor is less than 1, the figure is reduced or contracted. If the scale factor is negative, the figure is reflected across the center of dilation before being dilated.

Triangle ABC can be mapped onto triangle XYZ by a composition of transformations represented by (x,y) → (x+3,y-6) and followed by a dilation with center (0,0) and scale factor 1/3 represented by (x,y) → (x/3,y/3).

Triangle ABC is similar to Triangle XYZ.

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Answer:

y = 1/2 x

Step-by-step explanation:

y = mx + b

We need to find the m (slope) and the b (y-intercept)

The slope is the change in y over the change in x.  Use to points on the line to find the slope.

(4,2) and (6,3)

[tex]\frac{3-2}{6-4}[/tex] = [tex]\frac{1}{2}[/tex]

The slope (m) is 1/2.

Use the slope and one of the points to calculate b

I will use the point (4,2)

y = mx + b

2 = 1/2(4) +b

2 = 2 +b  Subtract 2 from both sides

0 = b

The y-intercept (b) is 0

y = _m + _

y = 1/2x + 0  

y = 1/2 x

Helping in the name of Jesus.

Thus, the number of buses needed to carry the 2177 tourists is found as 61.

A number can be divided into an equal amount of component parts.

People may display a variety of signs to denote division. The backslash / is additionally employed, though the character is more typical. Numerous numbers may occasionally be written with a line separating them. It is also known as a fraction.

A division calculation has a name for each component. The dividend, the divisor, and indeed the quotient are the three key terms.

Given data:

Number of tourists carried by 1 bus = 36.

Total number of tourists = 2177.

Number of buses = (Total number of tourists)/(Number of tourists carried by 1 bus)

Number of buses = 2177/36

Number of buses = 60.47

Number of buses =  61

Thus, the number of buses needed to carry the 2177 tourists is found as 61.

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Answer:

To calculate the monthly payment for the TV after the discount, sales tax, and financing, we need to follow these steps:

Step 1: Calculate the discount

Discount = 25% of $987.48

Discount = 0.25 x $987.48

Discount = $246.87

Step 2: Calculate the discounted price of the TV

Price after discount = $987.48 - $246.87

Price after discount = $740.61

Step 3: Calculate the sales tax

Sales Tax = 6.5% of $740.61

Sales Tax = 0.065 x $740.61

Sales Tax = $48.15

Step 4: Calculate the total cost of the TV after discount and sales tax

Total cost = Price after discount + Sales Tax

Total cost = $740.61 + $48.15

Total cost = $788.76

Step 5: Calculate the monthly payment on the 2-year loan with 15.6% annual interest rate using the following formula:

Monthly Payment = (P x r) / (1 - (1 + r)^(-n))

where P is the principal (total cost of the TV), r is the monthly interest rate (15.6% / 12), and n is the number of months (24).

Monthly Interest Rate = 15.6% / 12

Monthly Interest Rate = 0.013

Monthly Payment = ($788.76 x 0.013) / (1 - (1 + 0.013)^(-24))

Monthly Payment = $36.89

Therefore, the monthly payment on the 2-year loan for the TV is $36.89.

Step-by-step explanation:

The area of ΔQRS is 26.10 square units.

What is triangle?

A triangle is a closed, two-dimensional geometric shape with three straight sides and three angles.

To find the area of [tex]$\triangle QRS$[/tex], we can use the formula:

[tex]$Area = \frac{1}{2} \times base \times height$[/tex]

where the base and height are the length of two sides of the triangle that are perpendicular to each other. We can find these sides using trigonometry.

First, we need to find the length of side [tex]$QR$[/tex]. We can use the Law of Cosines:

[tex]$QR^2 = QS^2 + RS^2 - 2(QS)(RS)\cos(R)$[/tex]

where [tex]$R$[/tex] is the angle at vertex [tex]$R$[/tex]. Substituting the given values, we get:

[tex]$QR^2 = 9^2 + 5^2 - 2(9)(5)\cos(57^\circ)$[/tex]

[tex]$QR \approx 8.02$[/tex]

Next, we need to find the height of the triangle, which is the perpendicular distance from vertex [tex]$R$[/tex] to side [tex]$QS$[/tex]. We can use the sine function:

[tex]$\sin(R) = \frac{opposite}{hypotenuse}$[/tex]

[tex]$\sin(57^\circ) = \frac{height}{8.02}$[/tex]

[tex]$height \approx 6.51$[/tex]

Now we can find the area of the triangle:

[tex]$Area = \frac{1}{2} \times QR \times height$[/tex]

[tex]$Area = \frac{1}{2} \times 8.02 \times 6.51$[/tex]

[tex]$Area \approx 26.10$[/tex] square units

Therefore, the area of [tex]$\triangle QRS$[/tex] is approximately [tex]$26.10$[/tex] square units.

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To solve the equation a (a^2 - 16) (a - 2) = 0, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

So, we need to find the values of a that make each factor equal to zero.

a = 0 is a solution, since any number times zero is zero.

a^2 - 16 = 0 can be factored as (a - 4)(a + 4) = 0. So, a = 4 or a = -4 are solutions.

a - 2 = 0 gives us a = 2 as a solution.

Therefore, the possible solutions to the equation are a = 0, a = 4, a = -4, and a = 2.

So, the answers to select from are: 0, 6, 4, 16, 1, 2, -4, 8. Among these options, the possible solutions to the equation are 0, 4, -4, and 2.

The counting process was an essential component in evaluating the results and drawing conclusions based on the data gathered.

Hi! Bob and Aniyah's apples were counted by a designated individual, likely a teacher, supervisor, or event organizer, who was responsible for ensuring the accuracy and fairness of the counting process.

This person utilized their organizational skills and attention to detail to effectively tally the number of apples collected by both Bob and Aniyah.

By doing so, they were able to determine the final count, which was then used to either compare the performance of the two individuals or contribute to a larger total for a specific event or purpose.

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Answer: It would be 3:13

Step-by-step explanation:

Pls brainliest if this helped you! :D

Answer:

3:13

Step-by-step explanation:

First we have to find the GCF (greatest common factor of both numbers) which is 20

So 60 divided by 20 is 3 and 260 divided by 20 is 13

Your final answer should by 3:13 because you can't divide any further using those numbers or any other number

Hope this helps!

Also for your information to make things easier --> keep in mind that whenever it says "ratio" means "to divide" !!!

Answer:

Step-by-step explanation:

34,000,000,000=4,005,000(1+0.041)^x

(1.041)^x=(34,000,000,000)/4,005,000

(1.041)^x=34,000,000/4,005

xlog(1.041)=log34,000,000-log 4005

=7.15348-3.60260

=3.55088

x=3.55088/log(1.041)=3.55088/0.01745

\approx 203.5~years

The point that appears to be closest to the coordinates (29, 37.7) on the scatter plot is (29,37).

A scatter plot is a type of chart that displays values for two variables for a set of data. The data points in a scatter plot are represented by dots or circles, and their position on the chart represents the values of the two variables. One variable is usually plotted on the horizontal axis (x-axis) and the other variable is plotted on the vertical axis (y-axis). By analyzing the pattern of the scatter plot, you can see whether there is a relationship between the two variables, and what kind of relationship it is (positive, negative, or no relationship). Scatter plots are useful for identifying patterns, trends, and relationships in data, and are commonly used in scientific research, engineering, economics, and many other fields.

Here,

To find the foot length closest to 29, we need to look for the point on the scatter plot that has an x-value closest to 29.

Using the equation of the line provided (y=0.3x+29), we can see that when x=29, y=0.3(29)+29=37.7. Therefore, we are looking for the point on the scatter plot with an x-value close to 29 and a y-value close to 37.7.

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Complete question:

Here is a scatter plot that shows the lengths and widths of `20` left feet together with the graph of a model of the relationship between foot length and width. Circle the point that represents the foot length closest to `29`.

So the price that would maximize revenue is $2.75.

An equation is a mathematical statement that asserts the equality of two expressions. It typically contains one or more variables, which represent unknown values that can be solved for using algebraic methods. An equation can be represented symbolically using mathematical notation, such as using letters, numbers, and mathematical symbols like +, -, x, /, and =. Equations can be used to model and solve a wide variety of problems in mathematics, science, engineering, and other fields.

Here,

We can start by finding the linear equation that relates price and monthly sales. Let's use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where y is the monthly sales, x is the price, m is the slope, and (x1, y1) is a point on the line.

Using the two points we have:

(10, 19000) and (7, 25000)

We can find the slope:

m = (y2 - y1) / (x2 - x1)

m = (25000 - 19000) / (7 - 10)

m = 2000

Now we have:

y - 19000 = 2000(x - 10)

Simplifying:

y = 2000x - 11000

This equation represents the relationship between price and monthly sales.

To maximize revenue, we need to find the price that gives the highest value for the product of price and monthly sales. In other words, we need to find the maximum value of the function:

R(x) = x * y = x(2000x - 11000)

Expanding and simplifying:

R(x) = 2000x² - 11000x

To find the maximum, we need to take the derivative and set it equal to zero:

R'(x) = 4000x - 11000 = 0

Solving for x:

4000x = 11000

x = 2.75

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Answer: Actually, the correct answer is:

−0.1 + 1.7 = 1.6

So, y = 1.6.

Step-by-step explanation:

Bus 14 is therefore the more reliable bus as a result of its lower IQR.

The dot plot, which depicts the frequency with which each observation appears in the data set, is the first thing we take into account.

The difference between the data set's third and first quartiles is represented by the interquartile range, which is the next factor we take into account.

Because it ignores outliers, the interquartile range is a better indicator of a spread than a data set's range.

We have the following for classes of 15 students:

Since the first seven students make up the first half, the first quartile is represented by the fourth dot, which represents the first half's median.

The final seven students make up the second half, thus the eleventh dot—the first half's median—is in the first quartile.

So, the following are the Bus 14 quartiles:

Q1 = 12.

Q3 = 18.

The IQR is therefore of:

IQR = Q3 - Q1 = 18 - 12 = 6.

Hence, the IQR is:

Q1 = 9.

Q3 = 16.

The IQR is therefore of:

IQR = Q3 - Q1 = 16 - 9 = 7.

Therefore, bus 14 is therefore the more reliable bus as a result of its lower IQR.

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Correct question:

The line plots represent data collected on the travel times to school from two groups of 15 students. A horizontal line starting at 0, with tick, marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 10,16,20, and 28. There are two dots above 8 and 14. There are three dots above 18. There are four dots above 12. The graph is titled Bus 14 Travel Times. A horizontal line starting at 0, with tick, marks every two units up to 28. The line is labeled Minutes Traveled. There is one dot above 8, 9,18, 20, and 22. There are two dots above 6, 10, 12,14, and 16. The graph is titled Bus 18 Travel Times. Compare the data and use the correct measure of variability to determine which bus is the most consistent. Explain your answer. Bus 14, with an IQR of 6 Bus 18, with an IQR of 7 Bus 14, with a range of 6 Bus 18, with a range of 7

Therefore , the solution of the given problem of equation comes out to be the equation of the perpendicular bisector of that line segment (7, 3) and (-5, 9) is y = 2x + 4.

Complex algorithms frequently employ variable words to demonstrate coherence between two opposing assertions. Equations are academic expressions that are used to demonstrate the equality of different academic figures. In this case, leveling generates b + 7 rather than another algorithm that could analyze data provided by y + 7, split 12 into two parts, and create y + 7.

Here,

The midpoint formula can be used to determine the midpoint of the line segment whose ends are (7, 3) and (-5, 9):

=> ((7 + (-5))/2, (3 + 9)/2) = (1, 6)

the middle is thus (1, 6). The slope of the line going through (7, 3) and must now be determined. (-5, 9). The slope method is used to:

=>slope = (9 - 3)/(-5 - 7) = -6/12 = -1/2

The equivalent of -1/2 in the negative is 2.

=> y - y1 = m(x - x1)

where (x1, y1) is a location on the line and m denotes the slope. When we replace m = 2 with (1, x1, y1) = (1, 6), we obtain:

=> y - 6 = 2(x - 1)

By enlarging and condensing, we obtain:

=> y - 6 = 2x - 2

=> y = 2x + 4

the line segment whose ends are and the equation of the perpendicular bisector of that line segment (7, 3) and (-5, 9) is y = 2x + 4.

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Answer:
Morning shifts -

Evening shifts -

Step-by-step explanation:

Morning

mean: (8+15+16+18+18+20+21+21+21+56) / 10 = 21.4

median: 10 numbers + 1 / 2 =5.5th number is median. therefore that is 19 (numbers have to be in chronological order to start counting)

mode: (most common number) 21

Evening

mean: (3+11+12+14+22+22+30+33+34+47) / 10 = 22.8
median: 10 numbers + 1 / 2 =5.5th number is median. therefore that is 22
mode: 22

Answer:

what number is right before "of the students ordered chicken nuggets and the rest of the students are eating nachos." you cant answer the question otherwise.

Step-by-step explanation:

Answer: 2%

Step-by-step explanation: i looked it up

The selling price of the oranges was 472.5 dollars.

The profit is equal to the difference between the selling price and the original cost price.

We have been given that a basket containing 150 oranges costs 450 find the selling price of an orange if it is to be sold at a profit of 5%

Let's start with the profit.

Let's convert 5% to decimal form to find out.

[tex]\implies 5\% = \dfrac{5}{100} = 0.05[/tex]

Then double that by the starting price of 450.

[tex]450\times 0.05 = 22.5[/tex]

As a result, the profit is $22.5.

Now, add the profit to the beginning cost to get the selling price.

[tex]450 + 22.5 = 472.5[/tex]

Therefore, the selling price of the oranges was 472.5 dollars.

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The length of the circle is approximately 9.237 cm.

What are the diagonals of a rhombus?
A rhombus is a quadrilateral with all sides of equal length. It also has the following properties regarding its diagonals:

The diagonals bisect each other at 90 degrees.

The diagonals are perpendicular to each other.

The diagonals have the same length.

The diagonals divide the rhombus into four congruent triangles.

In a rhombus with a side of 8 cm and an angle of 60 degrees, the diagonals are equal in length.

The length of the diagonals can be found using the formula:

[tex]$D_1 = \frac{2a}{\sqrt{3}}$[/tex]

where a is the length of the side. Substituting the value of a as 8 cm, we get:

[tex]$D_1 = \frac{2(8)}{\sqrt{3}} \approx 9.237 \text{ cm}$[/tex]

The length of the circle inscribed in the rhombus is equal to the length of the diagonals.

Therefore, the length of the circle is approximately 9.237 cm.

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The expression that corresponds to the provided sentence is 2sinx cos²x.

As an illustration, the expression x + y is one where both x and y have words with an addition function in between. There are two kinds of expressions in mathematics: numerical expressions, which only comprise integers, and algebraic expressions, which also include variables.

In mathematics, an expression is a combination of one or more numbers, variables, and mathematical operations (such as addition, subtraction, multiplication, division, exponents, and roots) that can be evaluated or simplified to produce a single value.

For example, 2 + 3x is an expression that contains the variables x and the numbers 2 and 3, as well as the operations of addition and multiplication.

Another example is [tex](4a^2 - 3b)/c[/tex], which is an expression that contains the variables a, b, and c, as well as the numbers 4 and 3, and the operations of addition, subtraction, multiplication, and division.

sin2x cos x is equivalent to (2sinx cosx) cosx,

which simplifies to 2sinx cos²x.

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question-

Which of the following expressions is equal to sin(2x) 2(1 - cos^2(x))

The measures for the triangle are given as follows:

The Pythagorean Theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides.

The theorem is expressed as follows:

c² = a² + b².

In which:

The base is composed by two lengths of 6 and 25 - 6 = 19, hence the value of x is obtained applying the Geometric Mean Theorem as follows:

x² = 6 x 19

x = sqrt(6 x 19)

x = 10.7.

The value of y is then the hypotenuse of a right triangles of sides 10.7 and 6, hence:

y² = 10.7² + 6²

y = sqrt(10.7² + 6²)

y = 12.3.

The value of z is then the hypotenuse of a right triangles of sides 10.7 and 19, hence:

z² = 10.7² + 19²

z = sqrt(10.7² + 19²)

z = 21.8.

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Answer : 52.

Explanation : For Triangles ( 3 × 4 ) ÷ 2     Rectangle 10 × 4

The area of this quadrilateral is 52 square feet.

First, I noticed that the rectangle had sides which were 10 feet long and 4 feet tall. (10 × 4)

Second, I noticed that the triangles were 3 feet long and 4 feet tall. (3 × 4) Since this was a triangle, I then divided by 2. (3 × 4) ÷ 2 I then saw there were 2 triangles so I multiplied it by 2. [(3 × 4) ÷ 2] × 2

Lastly, the equation I was left with was (10 × 4) + {[(3 × 4) ÷ 2] × 2} = 5

—————

Please remember to revise this and make it in your own words if you want! I hope this helps you. -Doodle

—————

The average rate of change from year 1 to year 10 is 8.3 pounds per acre per year based on given function.

We must compute the change in crop yield (in pounds per acre) during that time period and divide by the number of years to determine the average rate of change from year 1 to year 10:

Average change rate is equal to (f(10) - f(1)) / (10 - 1)

where f(x): function that represents the crop yield over an x-year period in pounds per acre.

When we enter the numbers 10 and 1 as substitutes in the function, we obtain:

f(10) = [tex]-10^2[/tex] + 20(10) + 50 = 150

f(1) =[tex]-1^2[/tex] + 20(1) + 50 = 69

Thus, from year one to year ten, the average rate of change is:

(150 - 69) / (10 - 1), or 8.3 pounds per acre per year, is the average rate of change.

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