The width of the garden is 18 feet. In this case, the length of the diagonal of the rectangular garden is the hypotenuse, and the length and width of the garden are the other two sides. Let's denote the width of the garden as "w".
Given:
Length of the garden = 24 feet
Diagonal of the garden = 30 feet
Using the Pythagorean theorem, we can set up the following equation:
[tex]24^2[/tex] + [tex]w^2[/tex] = [tex]30^2[/tex]
Simplifying:
576 + [tex]w^2[/tex] = 900
Subtracting 576 from both sides:
[tex]w^2[/tex] = 900 - 576
[tex]w^2[/tex] = 324
Taking the square root of both sides:
w = √324
w = 18
So, the width of the garden is 18 feet.
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we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324 Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.
Using the Pythagorean theorem, we can find the width of the garden. If the length is 24 feet and the diagonal is 30 feet, then the width can be found by taking the square root of (30^2 - 24^2), which is approximately 18.97 feet.
Therefore, the garden is about 18.97 feet wide. We can use the Pythagorean theorem to find the width of the rectangular garden.
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the diagonal across the garden is the hypotenuse, and the length and width of the garden are the other two sides.
The diagonal is 30 feet, and the length is 24 feet. We need to find the width (w).
The Pythagorean theorem formula is:a² + b² = c²Where 'a' and 'b' are the two shorter sides, and 'c' is the hypotenuse.
In this case, we have:24² + w² = 30²Solve the equation:576 + w² = 900Subtract 576 from both sides:w² = 324Take the square root of both sides:w = √324w = 18So, the width of the rectangular garden is 18 feet.
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Can someone help me asap? It’s due tomorrow. I will give brainiest if it’s all correct.
Answer:
1.a
2.c
3.d
4.b
Step-by-step explanation:
the slope of a graphed line is -8/7. Write the standard-form equation of the line using the coordinates of the labeled point.
The standard-form equation of the line using the coordinates of the labeled point is: B. 8x + 7y = 60.
How to determine an equation of this line?In Mathematics and Geometry, the point-slope form of a straight line can be calculated by using the following mathematical equation (formula):
y - y₁ = m(x - x₁)
Where:
m represent the slope.x and y represent the points.At data point (4, 4) and a slope of -8/7, a linear equation in slope-intercept form for this line can be calculated by using the point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = -8/7(x - 4)
By multiplying all through by 7, we have:
7(y - 4) = -8(x - 4)
7y - 28 = -8x + 32
7y + 8x = 32 + 28
8x + 7y = 60.
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6. Anchorage (southern coast of Alaska) is several hundred miles north of Helena, Montana, yet its January temperatures are similar to Helena's. Explain why.
Helena experience similar temperatures during January due to their subarctic climate regime, but the moderating effect of the oceanic currents on Anchorage's climate makes its winters milder than those of Helena.
what is temperatures ?
"Temperatures" refers to the degree of hotness or coldness of a substance, usually measured in degrees Fahrenheit (°F) or Celsius (°C). In the context of the original question, "temperatures" refers to the measure of how hot or cold it is in a particular location, specifically in Anchorage and Helena.
In the given question,
Anchorage and Helena are both located in high latitude regions where the climate is dominated by polar or subarctic air masses. The prevailing westerly winds carry these cold air masses from the Arctic towards the continental interiors, affecting the climate of both Anchorage and Helena. Although Anchorage is located further north than Helena, it is situated along the coast of the Gulf of Alaska, which is influenced by the relatively warm oceanic currents such as the North Pacific Current and the Alaska Current. These currents help to moderate the cold air masses coming from the north, resulting in a maritime subarctic climate in Anchorage.
In contrast, Helena is situated in the interior region of Montana, which is far away from any major water bodies, leading to a continental subarctic climate with relatively colder and drier conditions compared to Anchorage. Therefore, despite their different latitudes, both Anchorage and Helena experience similar temperatures during January due to their subarctic climate regime, but the moderating effect of the oceanic currents on Anchorage's climate makes its winters milder than those of Helena.
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ten families were randomly selected and their daily water usage (in gallons) before and after viewing a conservation video was recorded. the sample mean difference was found to be 4.8 and the corresponding standard deviation 5.25, where differences were found (before - after). assume the data is normally distributed. if the resulting 95% confidence interval is (1.04,8.55), we have evidence to suggest that the conservation videos would be effective in reducing water use in the general population. true false
True. The question states that ten families were randomly selected and their daily water usage (in gallons) before and after viewing a conservation video was recorded.
The sample mean difference was found to be 4.8 and the corresponding standard deviation 5.25, with differences
calculated as (before - after).
Assuming the data is normally distributed, the resulting 95% confidence interval is (1.04, 8.55).
Since the entire 95% confidence interval is positive (i.e., all values are greater than zero), this indicates that there is a
significant difference between water usage before and after viewing the conservation video.
This provides evidence to suggest that the conservation videos would be effective in reducing water use in the general population.
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Dilate point S by a scale factor of 1/2
PLEASE JUST TELL WHERE THE POINT MUST BE LOCATED DONT GIVE A LONG EXPLANATION AND IF U CAN UPLOAD A PIC OF THE ANSWER
The position of point S after dilating will be half of the original. The dilated point S' has been shown below.
What is dilation?
Using a modification known as dilation, an object can be resized. Through dilatation, the objects can be resized or enlarged. This transformation results in a shape that is a perfect replica of the original image. The form's dimensions do vary, though. An expansion or contraction of the original form is required for a dilatation. This shift is referred to as a scale factor.
We are given a graph showing position of point S.
Now, on dilating the point by a scale factor of [tex]\frac{1}{2}[/tex], we get that the point will be located at half of the original.
The point has been located and attached in the image below.
Hence, the required solution has been obtained.
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Mr. K drove to Milwaukee, Wisconsin for spring break. He left at 1:25pm and arrived at 3:00pm. How long did it take him to get there? Also, he spent $285 on basketball game tickets, $5 on parking, $15.90 on concessions at the game, $20 on dinner after the game, $26.69 in UBER rides to and from the game, and $35 in gas. How much money did he spend IN ALL? and if he started the trip with $400, how much money does he have left over?
Answer:
A.) 1 hour and 35 minutes
B.) $387.59
C.) $12.41
Step-by-step explanation:
Question 1 answer — 1 hour and 35 minutes
Question 2 answer — $387.59
Question 3 answer — $12.41
Hope my answer helps you.
:)
Please mark my answer as the BRAINLIEST. Plssssssssssssssssssss
can someone answer my new math questions please
Answer:
yes
Step-by-step explanation:
Leah is an administrator for a large
school district. She wants to know how
many hours students spend on
homework each week. She asks the
question to 250 randomly selected eighth
grade students. The results are shown in
the table. Which of the following
inferences about the eighth grade
students in the school district are valid?
Hours. Students
Less than 2 44
2 to less than 4 88
4 to less than 6 90
At least 6 28
A. There are more students who spend at least 4 hours per week on homework than students who spend less than 4 hours per week on homework.
B.About 11% of students in the school district spend at least 6 hours per week on homework.
C. About 50% of students who spend less than 4 hours per week on homework spend less than 2 hours per week.
D.About 1 of every 3 students who spend at least 4 hours per week on homework spend at least 6 hours per week.
Based on the data provided in the table, the valid inferences are A, B and C, while inference D cannot be confirmed.
What is a valid inference?A conclusion that is logical, rational, and backed by solid reasoning, statistical analysis, or scientific principles is considered to be a valid inference when it is derived from the available facts or evidence. It should be founded on trustworthy and pertinent data and adhere to accepted rules of statistical or scientific reasoning.
In addition to being compatible with accepted theories, guiding principles, or previous research findings, a valid inference should take into account any constraints and potential sources of mistake in the data or evidence. In other terms, a valid inference is a plausible and convincing conclusion that may be reached using acceptable statistical or scientific techniques from the relevant information or evidence.
A. Valid: There are more students who spend at least 4 hours per week on homework than students who spend less than 4 hours per week on homework.
B. Valid: Approximately 11% of students in the school district spend at least 6 hours per week on homework, based on the "At least 6" category which has 28 students out of the total 250 students surveyed.
C. Valid: About 50% of students who spend less than 4 hours per week on homework spend less than 2 hours per week, based on the total number of students in the "Less than 2" and "2 to less than 4" categories compared to the total number of students in the "Less than 4" category.
D. Not valid: The table does not provide data specifically about students who spend at least 4 hours per week on homework and their hours of homework beyond 4 hours, so this inference cannot be made.
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Help with algebra 2 homework
a) The inverse function is given as follows: [tex]r = \sqrt{\frac{3v}{40\pi}}[/tex]
b) The radius of the cone with a volume of 4190 cubic inches is given as follows: r = 10 inches.
How to obtain the inverse function?The function for this problem is defined as follows:
v(r) = 40/3πr²
We want to find the radius as a function of the volume for the inverse function, hence:
[tex]r^2 = \frac{3v}{40\pi}[/tex]
[tex]r = \sqrt{\frac{3v}{40\pi}}[/tex]
Then the radius of the cone with a volume of 4190 cubic inches is given as follows:
[tex]r = \sqrt{\frac{3 \times 4190}{40\pi}}[/tex]
r = 10 inches.
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what does the red line on the graph represent? what does the red line on the graph represent? the average amount of solid waste generated by each household in the united states per year the total amount of solid waste generated by all people in the united states per year the average amount of solid waste generated by each person in the united states per year the period of time in years
The red line on the graph may also include other lines that represent related data, such as the total amount of solid waste generated by all people in the United States per year, or the period of time in years being measured.
Red line on the graph represents the average amount of solid waste generated by each person in the United States per year.
The red line on the graph is a useful tool for understanding the impact of solid waste on the environment and society as a whole.
It helps us to identify areas where we can make changes to reduce waste and improve our overall environmental performance and serves as a reminder of the importance of responsible consumption and waste management practices.
Red line on the graph represents the average amount of solid waste generated by each person in the United States per year.
This is a key metric in measuring the environmental impact of waste production in the country.
The average amount of solid waste generated per person is an important figure because it provides a more accurate picture of individual behavior and consumption patterns.
It takes into account factors such as population growth, changes in household size, and shifts in lifestyle and consumption habits.
By tracking this metric over time, policymakers and environmental advocates can gain insight into trends and patterns in waste generation and identify opportunities for reducing waste and promoting sustainability.
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an expression is well-defined if you can compute its value without any illegal operations. examples of expressions that are not well-defined include $1/0$ and $\sqrt{-10}$. for what values of ${}x$ is the expression \[\frac{\sqrt{x 1} \sqrt{1 - x}}{\sqrt{x}}\]well-defined? express your answer in interval notation.
To exclude the value [tex]$x=0$[/tex] since division by zero is not allowed.
The expression is well-defined for [tex]$x \in (0,1]$[/tex].
Expression is well-defined for [tex]$0\leq x\leq 1$[/tex].
In interval notation, we can write this as [tex]$[0,1]$[/tex].
Therefore, the expression [tex]$\frac{\sqrt{x\cdot 1} \sqrt{1 - x}}{\sqrt{x}}$[/tex] is well-defined for [tex]$ x\in [0,1]$[/tex].
Expression to be well-defined, we need to ensure that we do not perform any illegal operations.
This means that we cannot take the square root of a negative number, and we cannot divide by zero.
Let's consider each of the factors in the expression separately.
The first factor is.
[tex]$\sqrt{x\cdot 1}=\sqrt{x}$[/tex].
To ensure that this is well-defined, we need.
[tex]$x\geq 0$[/tex] since we cannot take the square root of a negative number.
The second factor is
.[tex]$\sqrt{1-x}$[/tex].
To ensure that this is well-defined, we need.
[tex]$1-x\geq 0$[/tex], or equivalently, [tex]$x\leq 1$[/tex], since we cannot take the square root of a negative number.
The denominator is.
[tex]$\sqrt{x}$[/tex].
To ensure that this is well-defined, we need.
[tex]$x\geq 0$[/tex], since we cannot divide by zero.
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Identify the expression that is not equivalent to 6x + 3.
Answer:
distribute x as 3:
3²+10(3)+24
=63
Which graph shows the solution to the inequality Negative 3 x minus 7 less-than 20 Group of answer choices A number lines goes from negative 10 to positive 10. An open circle appears at positive 9. The number line is shaded from positive 9 through negative 10. A number line goes from negative 10 to positive 10. An open circle appears at positive 9. The number line is shaded from positive 9 through positive 10. A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through positive 10. A number line goes from negative 10 to positive 10. An open circle appears at negative 9. The number line is shaded from negative 9 through negative 10.
The solution is all values of x greater than -9.
What is the correct graph for the given inequality?The correct graph for the given inequality "Negative 3x - 7 < 20" is:
From negative 10 to positive 10, a number line runs. An open circle shows up at negative 9. From negative 9 to positive 10, the number line is shaded.
To chart the arrangement, we initially confine the variable by adding 7 to the two sides of the imbalance:
Negative 3x - 7 + 7 < 20 + 7
Negative 3x < 27
Next, we divide both sides by -3, remembering to flip the inequality sign since we're dividing by a negative number:
Negative 3x/-3 > 27/-3
x > -9
Therefore, the arrangement is all upsides of x more prominent than - 9. Since these are the values that satisfy the inequality, we graph this by drawing an open circle at -9 on the number line and shading all values to the right of -9.
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Need help on 3 and 4
[3] Vertical
➜ These angles are opposite angles created by two intersecting lines. They are also congruent, another quality of vertical angles.
[4] Neither
➜ While these angles are "opposite" of each other, they are incongruent angles. Since the angles are not adjacent or vertical, they are neither.
Jonah subscribed to a new movie streaming service. The service costs Co $14.99 per month, but Jonah's rate is reduced by $0.75 for each new subscriber that he signs up. If there is no limit to the discount, how many users must Jonah recruit in order from him to use the service for a cost of at most $5.00?
Last Friday, AT&T closed at $41.68. AT&T pays an annual dividend of $1.98. Calculate the dividend yield
Answer: The dividend yield is the annual dividend payment divided by the stock's current market price, expressed as a percentage.
Dividend yield = (Annual dividend payment / Stock's current market price) x 100%
In this case:
Annual dividend payment = $1.98
Stock's current market price = $41.68
Dividend yield = ($1.98 / $41.68) x 100% = 4.75%
Therefore, the dividend yield for AT&T is 4.75%.
Step-by-step explanation:
Sky Launch Trampoline Park charges customers $9.50 per hour they spend jumping. Each customer must
also pay $2.50 for grip socks. Create a table or t-chart. Write an equation in slope-intercept form to represent this linear function.
Answer:
2.50 + 9.50h
Step-by-step explanation:
Sky Launch Trampoline Park charges customers $9.50 per hour they spend jumping. Each customer must also pay $2.50 for grip socks.
Let the number of hours be h.
The equation will be:
= 2.50 + (9.50 × h)
= 2.50 + 9.50h
I need a bit of help please
The slope of the line in the reduced form is 4 / 7.
How to find the slope of a line?The slope of a line is the change in the dependent variable with respect to the change in the independent variable.
Therefore,
slope = m = change in y / change in x
slope = m = y₂ - y₁ / x₂ - x₁
P = (2, 3)
Q = (9, 7)
x₁ = 2
x₂ = 9
y₁ = 3
y₂ = 7
Therefore,
slope = 7 - 3 / 9 - 2
slope = 4 / 7
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-2(8x-5) + 2x =4(x+5)
Answer:
x = -5/9
Step-by-step explanation:
-2(8x - 5) + 2x = 4(x + 5)
-16x + 10 + 2x = 4x + 20
-16x + 2x + 10 = 4x + 20
-14x + 10 = 4x + 20
+14x = +14x (Add 14 to both sides)
10 = 18x + 20
-20 = -20 (Subtract 20 from both sides)
-10 = 18x
18 = 18 (Divide by 18)
-10/18 = x
Simplified:
-5/9 = x
Answer:
Step-by-step explanation: Distribute -2 to the parenthasis, and 4 to the other parenthasis. two double negatives make a positive. Combine like terms. get the x and regular numbers on different sides of the equal sign, and divide to find the x=
-16x +10 +2x=4x+20
-14x+10=4x+20
-14x -20
-10x= -10
/-10 /-10
x=1
Describe a situation with two variables that you can represent w it’s an equation that uses two operations. Write the equation. Explain the relationships between the variables
An equation uses two operations is equal to C = n × p + T.
Relationship between variables is C represents total cost where as 'n × p' is cost of meal per person and T is additional cost.
Total cost of a meal at a restaurant is a function of the number of people and the price per dish.
Represent the variables as follows,
Let us use the variable 'C' to represent the total cost of the meal.
Let us use the variable 'n' to represent the number of people at the table.
Let us use the variable 'p' to represent the price per dish.
An equation that uses two operations, use multiplication and addition.
C = n × p + T
'n × p' represents the cost of the meal per person,
'T' represents any additional costs, such as taxes or tips.
By adding these two values together, total cost of the meal.
Relationship between the variables is as follows,
Total cost of the meal C is directly proportional to both the number of people n and the price per dish p.
Increase either n or p, total cost of the meal will increase proportionally.
For example,
Double number of people at the table n,
Total cost of meal C will also double,
Assuming price per dish p remains constant.
Similarly,
Double the price per dish p,
Total cost of the meal C will also double,
Assuming number of people at the table n remains constant.
Constant term T represents any additional costs.
That are independent of n and p, such as taxes or tips.
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4 m
7 m
…..help please
The total surface area of the composite shape is 40.57 square m
Calculating the surface areasThe surface area of composite shapes can be found by breaking the composite shape down into simpler shapes and then finding the surface area of each individual shape.
Once the surface areas of all the individual shapes are found, they can be added together to find the total surface area of the composite shape.
Here, we have
Area = Area of rectangle + circle
So, we have
Area = 4 * 7 + 22/7 * (4/2)^2
Area = 40.57 square m
So, the area is 40.57 square m
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Identify the circumscribed angle in the picture below.
Answer:
A.) LGJ
Step-by-step explanation:
An airplane is flying at a height of 3 miles above the ground. The distance along the ground from the
airplane to the airport is 7.5 miles. What is the angle of depression from the airplane to the airport?
Round to the nearest degree.
Answer:
the angle of depression is approx 22 degrees
Step-by-step explanation:
Model drawn below to visualize
I represented the angle of depression as x
Since two side lengths are given, we can use tangent to find the angle of depression
tan x= 3/7.5
We then use inverse tangent to find the angle measure:
m<x=[tex]tan^{-1}[/tex](3/7.5)
m<x is approx 21.8 or 22 when rounded to the nearest degree
(when using tan, inverse tan, sin, cos, inv... use deg on calculator when finding angle of depression, solving triangles, etc.)
‼️WILL MARK BRAINLIEST‼️
This level of granularity can be particularly useful when analyzing complex datasets or when trying to identify subtle relationships between variables.
What is a graph?
In computer science and mathematics, a graph is a collection of vertices (also known as nodes or points) connected by edges (also known as links or lines).
One advantage of being able to see each individual data point in a graph when comparing two data sets is that it allows for a more accurate and detailed analysis of the similarities and differences between the two sets. By examining the distribution and spread of the data points, it is possible to identify patterns and trends that may not be immediately apparent from a simple comparison of summary statistics, such as means or medians.
Additionally, by seeing each individual data point, it becomes possible to detect outliers or anomalies that may be skewing the data, which can lead to more informed decision-making and a deeper understanding of the underlying trends and patterns in the data. This level of granularity can be particularly useful when analyzing complex datasets or when trying to identify subtle relationships between variables.
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two pollsters will canvas a neighborhood with 20 houses. each pollster will visit 10 of the houses. how many different assignments of pollsters to houses are possible?
There are 92,378 different assignments of pollsters to houses where two pollsters will canvas a neighborhood with 20 houses.
There are 20 houses to choose from for the first pollster, and then 19 houses remaining for the second pollster.
However, since the order in which the pollsters visit the houses does not matter, we need to divide by the number of ways of arranging the 10 houses that each pollster will visit evaluated using probability.
Therefore, the total number of different assignments of pollsters to houses is:
(20 choose 10) * (10 choose 10) / 2! = (184,756) * (1) / 2 = 92,378
So there are 92,378 different assignments of pollsters to houses.
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five rectangles, and have integer side lengths. rectangle has a width of , rectangle has a width of rectangle has a length of rectangle has a length of and rectangle has a length of if all five rectangles have the same area , what is the least possible value of ?
All five rectangles have the same area of 60, and the sum of their dimensions is:
2 + 30 + 4 + 15 + 6 + 10 + 8 + 7.5 + 10
Let the width of rectangle 1 be w1, the width of rectangle 2 be w2, and so on. We know that all five rectangles have the same area, so we can set up an equation:
[tex]w1 * l1 = w2 * l2 = w3 * l3 = w4 * l4 = w5 * l5[/tex]
We can simplify this equation by dividing both sides by w1 * l1, which gives:
[tex]1 = (w2 * l2) / (w1 * l1) = (w3 * l3) / (w1 * l1) = (w4 * l4) / (w1 * l1) = (w5 * l5) / (w1 * l1)[/tex]
Let's define a new variable x = w2 * l2 = w3 * l3 = w4 * l4 = w5 * l5. Then we have:
[tex]w1 * l1 = xw2 * l2 = xw3 * l3 = xw4 * l4 = xw5 * l5 = x[/tex]
Now we need to find the least possible value of w1 + l1 + w2 + l2 + w3 + l3 + w4 + l4 + w5 + l5. Since w1 * l1 = x, we can rewrite this as:
[tex]w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x)[/tex]
To find the minimum value of this expression, we can take its derivative with respect to w1, set it equal to zero, and solve for w1:
[tex]d/dw1 (w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x)) = 1 - 2 * sqrt(x) / w1^1.5 + 2 * sqrt(x) / w1^2.5 = 0[/tex]
Solving for w1, we get:
[tex]w1 = 2 * x^(1/4)[/tex]
Substituting this back into our expression for the sum of the rectangle dimensions, we get:
[tex]w1 + l1 + 4 * sqrt(x / w1) + 4 * sqrt(w1 / x) = 2 * x^(1/4) + 2 * x^(3/4) + 8 * (x / 2)^(1/4)[/tex]
To find the minimum value of this expression, we can take its derivative with respect to x, set it equal to zero, and solve for x:
[tex]d/dx (2 * x^(1/4) + 2 * x^(3/4) + 8 * (x / 2)^(1/4)) = 1/2 * x^(-3/4) + 3/2 * x^(1/4) + 2 / (2 * x)^(3/4) = 0[/tex]
Solving for x, we get:
x = 4
Therefore, the least possible value of w1 is:
w1 =[tex]2 * x^(1/4) = 2[/tex]
And the dimensions of the rectangles are:
Rectangle 1: 2 x 30
Rectangle 2: 4 x 15
Rectangle 3: 6 x 10
Rectangle 4: 8 x 7.5
Rectangle 5: 10 x 6
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A rectangular prism has a width of 4, a length of 6, and a height of 8. What is the diagonal height of the rectangular prism? Round the decimal to the nearest tenth.
Answer:
add 2
Step-by-step explanation:
just adding 2
Can someone help me out fast please!?!?!
Pamela purchased a new laptop for her schoolwork. She plans to sell it sometime in the future; however, its value depreciates monthly. The expression below shows the depreciated sales value of the laptop. What does the second term of the expression represent?
A. The number of months Pamela will wait to sell the laptop.
B. The original value of the laptop.
C. The total depreciation value of the laptop.
D. The monthly depreciation value of the laptop.
The second term of the expression represent the total depreciation value of the laptop. Therefore, the answer is C.
How to find the terms of an expression?Pamela purchased a new laptop for her schoolwork. She plans to sell it sometime in the future; however, its value depreciates monthly.
The expression below shows the depreciated sales value of the laptop.
856 - 17mTherefore, the meaning of the second term in the expression can be calculated as follows:
Therefore,
856 = The amount she bought the laptop
The second term 17m is the total depreciation value of the laptop where m = number of months.
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Help
Please show your work .
Answer:
QR=8
Step-by-step explanation:
When two lines are perpendicular, they form two 90-degree angles. So:
m∠QSR = m∠QSP = 90°
We also know that the line segment PS is congruent to the line segment SR.
Lastly, by the reflexive property, QS is congruent to itself.
Thus, ΔPSQ ≅ ΔRSQ by SAS (side-angle-side).
Now that we know these triangles are congruent, we can further state that PQ is congruent to QR by CPCTC (corresponding parts of congruent triangles are congruent).
If PQ is congruent to QR, then their measures are also congruent, and we can get this equation (by using substitution and algebra):
[tex]3n-1=5n-7=\\6=2n=\\n=3[/tex]
Plug in n to the length of QR:
[tex]5n-7=\\5(3)-7=\\15-7=\\8[/tex]
So, QR=8.
Consider a sequence whose first five terms are:-1.75, -0.5, 0.75, 2, 3.25
Which explicit function (with domain all integers n ≥ 1) could be used to define and continue this sequence?
Step-by-step explanation:
+ 1.25
every new term is the previous term + 1.25.
with starting value -1.75
f(n) = 1.25n - 1.75