Note that the function takes the trapezoid's area as input and returns as output the length of the other base is A(x)/7-5=x.
What is the area of a Trapezoid?Recall that the function for the trapezoid area is:
A(x)=(B+b)*h/2
where
B and b are the bases and
h is the height.
Thus, given a height of 14 and one base length of 5 with the length of its other base
With the given data: h=14 B and b =5 and x (it may vary which one is bigger)
So that function becomes:
A(x)=(5+x) * 14/2
A(x)=(5+x)*7
So if you want the inverse function, you have to operate to find x:
A(x)/7=5+x
A(x)/7-5=x
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Identify the initial amount a and the grwoth factor b in the exponential function f(t)=14^x
The initial amount A is 1 and the growth factor B is 1.4 in the Exponential function f(t)=14^x.
Given,
f(x) = 1.4^x
It is an exponential function.
y = a.b^x
where a is the initial quantity and b is the growth/ decay component.
Now we are able to examine the given feature with
A = 1
B = 1.4
An exponential function is a mathematical function that has the form f(x) = a^x, where a is a constant greater than zero and not equal to one, and x is a variable. This function is widely used in a variety of fields, such as finance, physics, and biology, due to its ability to model growth, decay, and change over time.
Exponential functions are essential in understanding various natural phenomena, from population growth to radioactive decay, and they play a crucial role in the advancement of scientific research.The exponential function has several unique properties, such as exponential growth, where the function grows at an increasing rate as x increases. Additionally, the function has an asymptotic relationship with the x-axis, meaning it never actually touches the x-axis but gets infinitely close to it.
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F(x) equals -3(x-1) to the power of 2 + 2 and g(x) equals -3(x-1) to the power of 2 -5 . The vertex of g(x) is
The vertex of the function g(x) is (1,-5).
What is the function?Functions are the fundamental part of the calculus in mathematics. The functions are the special types of relations. A function in math is visualized as a rule, which gives a unique output for every input x.
The given functions are f(x)=-3(x-1)²+2 and g(x)=-3(x-1)²-5.
Graph the parabola using the direction, vertex, focus, and axis of symmetry.
Direction: Opens Down
Vertex:
(1,-5)
Focus:
(1,-61/12)
Axis of Symmetry:
x=1
Directrix:
y= -59/12
Therefore, the vertex of g(x) is (1,-5).
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The graph of the sales of a new product at a candy store, where x is time in months and y is number sold in hundreds, goes through the points (4, 2) and (6, 8). What is the rate of change.
in candies sold per month?
A 200
B 300
C 400
D 600
The rate of change in candies sold per month can be found by finding the slope of the line that goes through the two points (4, 2) and (6, 8). The slope of a line can be found by using the formula:
slope = (y2 - y1) / (x2 - x1)
Plugging in the values from the two points, we have:
slope = (8 - 2) / (6 - 4) = 6 / 2 = 3
So the rate of change in candies sold per month is 3. This means that the number of candies sold is increasing by 300 (3 * 100) per month. Therefore, the answer is B) 300.
Klaus is cycling at a speed of -8 miles per hour. If he starts at the same position as Rachel (zero) , what will his position be after 60 minutes?
Klaus will be ____ miles be hind where he started, and ___ miles away from Rachel.
Klaus wil be behind where he started with a distance of 8miles
What is distance?Distance is the total movement of an object without any regard to direction. We can define distance as to how much ground an object has covered despite its starting or ending point.
Distance can also be defined as the space or gap between two points.
Velocity = distance/time
distance = velocity × time
time = 60minutes = 1hr
therefore the distance made by Klaus in 60 minutes =
= 8 ×1
= 8miles
therefore within 60 minutes Klaus will cover a distance of 8miles from where he started.
Klaus and Rachel will be at same position with the same speed
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Multiply (5x + 2) (7x + 3).
A. 35x + 7
B. 35^2 + 6
C. 35x^2 + 14x + 6
D. 35x^2 + 29x +6
The answer would be D. 35x² + 29x +6.
What is the Solution of an Equation?
The value of a variable in an equation is the answer that, when inserted into the equation, makes the equation true. It is discovered by relegating the variable to one side of the equation, with the value on the other side being the solution.
To multiply two polynomials, we use the distributive property.
Starting with the first term, we multiply 5x and 7x, then add 2 and 7x, and then add 2 and 3. The result is:
= (5x + 2)(7x + 3)
= 35x² + 33x + 14x + 6
= 35x² + 29x + 6
Therefore, The answer would be D. 35x² + 29x +6.
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Please help I’ll give brainliest!!!!!!!!
The solution set of the system of equations is {(2,2), (4,-2)}
What is the solution to an equation?
In order to make the equation's equality true, the unknown variables must be given values as a solution. In other words, the definition of a solution is a value or set of values (one for each unknown) that, when used as a replacement for the unknowns, transforms the equation into equality.
4x+2y =12------>(1)
Take some random values for x. Find the corresponding y values
Example: when x=0
(1) => 4(0)+2y = 12
=> 0+2y = 12
=> 2y =12
=> y= 12/2 = 6
The point obtained is (x,y) = (0,6)
This way, we get a line when we graph the equation 4x+2y =12.
Similarly, when we graph the equation y= -x² + 4x -2 , we get a parabola
Graph is attached:
In the graph, both graphs intersect at the points (2,2) and (4,-2)
Thus, the solution set of the system of equations is {(2,2), (4,-2)}
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Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your choices are correct. ? 1. ? 2. ? 3. ? 4. ? 5. ? 6. ? 7. ? 8
The differential equations given correspond to phase lines with slopes that depend on the power of the x term in the equation.
1. y' = x: This differential equation corresponds to a phase line with a slope of 1, since the y' term is equal to the x term.
2. y' = -x: This differential equation corresponds to a phase line with a slope of -1, since the y' term is equal to the negative of the x term.
3. y' = [tex]x^2[/tex]: This differential equation corresponds to a phase line with a slope of 2x, since the y' term is equal to the x squared term.
4. y' = [tex]-x^2[/tex]: This differential equation corresponds to a phase line with a slope of -2x, since the y' term is equal to the negative of the x squared term.
5. y' =[tex]x^3[/tex]: This differential equation corresponds to a phase line with a slope of [tex]3x^2[/tex], since the y' term is equal to the x cubed term.
6. y' = [tex]-x^3[/tex]: This differential equation corresponds to a phase line with a slope of [tex]-3x^2[/tex], since the y' term is equal to the negative of the x cubed term.
7. y' = [tex]x^n[/tex]: This differential equation corresponds to a phase line with a slope of [tex]nx^(n-1)[/tex], since the y' term is equal to the x to the power of n term.
8. y' = -[tex]x^n[/tex]: This differential equation corresponds to a phase line with a slope of [tex]-nx^(n-1),[/tex] since the y' term is equal to the negative of the x to the power of n term.
In summary, the differential equations given correspond to phase lines with slopes that depend on the power of the x term in the equation.
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Complete question:
Determine which differential equation corresponds to each phase line. You should be able to state briefly how you know your choices are correct. ?
1. y' = x
2. y' = -x
3. y' = [tex]x^2[/tex]
4. y' = [tex]-x^2[/tex]
5.y' =[tex]x^3[/tex]
6.y' = [tex]-x^3[/tex]
7. y' = [tex]x^n[/tex]
8. y' = -[tex]x^n[/tex]
Kile is choosing between two international phone plans for his upcoming business trip. Plan A costs $40 for unlimited calls and texts plus $10 per day for data. Plan B costs $28 for unlimited calls and texts plus $12 per day for data. a. Let x represent the number of days Kile will be on the trip and y represent the total cost of the plan. Write a system of equations to represent the problem situation.
The system of two equations can be represented as y = 10x + 40 and
y = 12x + 28.
What are the three types of solutions for a system of linear equations?The system's equation can be graphed, the graph will have two straight lines, and the intersection point(s) of those lines will be the system's solution if a system of equations only has two linear equations with two variables.
Because there are only three possible methods to graph two straight lines in the plane, there are only three matching forms of solution for a given system of equations.
Let, 'x' represent the number of days and 'y' represent the total cost.
Plan A can be represented as y = 10x + 40.
And, PlanB be can be represented as y = 12x + 28.
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alyssa likes to play roulette, but she doesn't like the low probability of betting on a single number. therefore, she bets on a block of 4 numbers, increasing her probability of winning to 438. she generally places a $5chip on her block of 4. if one her 4 numbers come up, she wins $40 (and gets to keep her bet!). what is the expected value for alyssa playing roulette? round to the nearest cent. do not round until your final calculation.
If one her 4 numbers come up, she wins $40 (and gets to keep her bet!). Alyssa can expect to lose 47 cents per bet over the long run.
The expected value of a game is the average amount that a player can expect to win or lose per bet, taking into account both the probabilities and the payouts of each possible outcome. To find the expected value, we multiply the probability of each outcome by the amount won or lost for that outcome, and then sum up these products.
In this case, Alyssa bets $5 on a block of 4 numbers, which gives her a probability of winning of 4/38, or approximately 0.1053. If one of her 4 numbers comes up, she wins $40, for a net gain of $35 (since she gets to keep her $5 bet as well). If none of her 4 numbers comes up, she loses her $5 bet.
Therefore, the expected value for each bet is:
(0.1053 × $35) + (0.8947 × -$5) = -$0.47
So if she plays many times, she can expect to lose money overall. It's important to keep in mind that expected value is not a guarantee of what will happen on any particular bet, but rather a long-term average based on probabilities.
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A scout troop raised money for a camping trip. They made a total of $1,498 at seven bake sales. They earned the same amount at each sale. Miguel thinks they made $215 at each bake sale. Explain why the amount Miguel said is reasonable. 1,498 ÷ 7 is about ÷ = and $215 is close to $
The actual amount of sale for each bake is $214. As Miguel said it is $215 which is very close to the actual amount, it is reasonable.
To determine if Miguel's estimate of $215 per bake sale is reasonable, we can start by calculating the average amount of money the scout troop made per bake sale. We do this by dividing the total amount they earned by the number of sales they had, as follows:
Total amount earned = $1,498
Number of bake sales = 7
Average amount earned per bake sale = Total amount earned ÷ Number of bake sales
= $1,498 ÷ 7
= $214
This calculation shows that the average amount the scout troop made per bake sale was $214. This means that if they had charged a consistent price for all of their baked goods at each sale, they would have made an average of $214 per sale.
Now, we can compare this average to Miguel's estimate of $215 per bake sale. Since his estimate is very close to the actual average, we can conclude that it is reasonable.
It is possible that the scout troop charged slightly different prices for their baked goods at each sale, which could explain the small discrepancy between the actual average and Miguel's estimate. However, given that the difference between the two values is only $1, it is likely that Miguel's estimate is a good approximation of the actual amount.
Moreover, it is reasonable to assume that the scout troop earned the same amount at each bake sale, especially if they had a set price for their baked goods.
If they had charged different prices at each sale, it would have been more difficult to estimate the average amount they earned per sale, and it would have been less likely that Miguel's estimate of $215 per bake sale would have been close to the actual average.
Therefore, based on the calculation and the context of the problem, we can conclude that Miguel's estimate of $215 per bake sale is reasonable.
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John has 2 books. Peter has twice books more then John. How many books they have together?
John has average 2 books and Peter has 4 books. Together, they have 6 books.
John has 2 books
Peter has twice books more than John = 2 * 2 = 4 books
Total books they have together = 2 + 4 = 6 books
John has 2 books, so Peter has twice books more than John. This means that Peter has 2 * 2 = 4 books. Together, John and Peter have 2 + 4 = 6 books. John’s books are the starting point of the problem, so it is important to keep track of John’s books. Since Peter has twice books more than John, we can calculate the number of books that Peter has by multiplying the number of books that John has by two. Once we have calculated the number of books that Peter has, we can add the number of books that John has to the number of books that Peter has and get the total number of books that they have together. In this example, the total number of books that John and Peter have together is 6. This can be arrived at by adding the number of books that John has (2) to the number of books that Peter has (4).
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Multiply the polynomials. (2x+y)·(4x^2-2xy+y^2)
Answer:
Step-by-step explanation:
The answer is 4x^2y+8x^3+y^2-2xy
The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
0 5
1 0, 3, 7
2 4, 6, 8
3 2
4
5 8
Key: 5|8 means 58
What is the appropriate measure of variability for the data shown, and what is its value?
The range is the best measure of variability, and it equals 18.5.
The IQR is the best measure of variability, and it equals 45.
The range is the best measure of variability, and it equals 45.
The IQR is the best measure of variability, and it equals 18.5.
For this data, the IQR is a superior measure of variability because it is less than the range. The greatest way to quantify variability is the IQR, and that number is 11.
How does interquartile range work?The interquartile range (IQR) in descriptive statistics is a measurement of statistical dispersion, or the spread of the data. The IQR is also known as the middle 50%, the fourth spread, or the H-spread. The difference between the data's 75th and 25th percentiles is how it is defined.
How do you determine IQR?The median (middle value) of the lower half and upper half of the data should be found first in order to determine the interquartile range (IQR). The quartile 1 (Q1) and quartile 3 values are these (Q3). The IQR is the difference between Q3 and Q1.
From the given stem-and-leaf plot, we can see that the lowest score is 5, and the highest score is 23. Therefore, the range of the data is:
Range = highest value - lowest value = 23 - 5 = 18
We also need to find the quartiles to calculate the IQR. The median (Q2) of the data is 18, which is the value that separates the lower 50% of the scores from the upper 50%. To find Q1 and Q3, we can split the lower and upper halves of the data, respectively, and find their medians.
The lower half of the data is: 5, 10, 13, 17, 18. The median of this half is (13 + 17)/2 = 15.
The upper half of the data is: 24, 26, 28. The median of this half is 26.
Therefore, Q1 = 15 and Q3 = 26, and the IQR is:
IQR = Q3 - Q1 = 26 - 15 = 11.
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Answer:
IQR 18.5
Step-by-step explanation:
I took the test
-4x+4y=-4 & 4x-24y=-16
Answer:
Hello if you are solving for x the for the equation -4x+4y=-4
your answer is x=y+1
Step-by-step explanation:
4y -4x= -4
subtract 4y from both sides
-4x = -4y- 4
divide both sides by -4
x= y+1
I HOPE THIS HELPS!
How can I find the population of the town? Many thanks
What is the distance between these two points?
(2,0) and (2,−5)
The distance between these two points (2,0) and (2,−5) is 5 unit.
The distance between two points is the length of the line segment connecting the two points on the plane. The formula for finding the distance between two points is usually d=√((x2 – x1)² + (y2 – y1)²). This formula is used to find the distance between any two points on the coordinate or x-y plane.
d=√((2 – 2)² + (-5 – 0)²)
d = √(0+25)
d = 5 unit
if the coordinates of two points P and Q are such that, (x1, 0) and (x2, 0), the distance between PQ will be given by:
PQ = |x2 – x1|
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b. how many such strings are if 2 of the ones are to be next to each other and the third is not next to the other two? (for example, 0011000100.
The total number of strings that satisfy the given conditions is 24.
Let us count the number of strings where the two ones that are next to each other are in the first two positions, and the third one is in the fifth position. There are two choices for the value of the fourth digit (0 or 1), and two choices for the value of the last digit (0 or 1). Therefore, there are 2 \cdot 2 = 4 strings with this property: 110010, 110100, 111010, and 111100.
We can obtain the same number of strings by considering the case where the two ones that are next to each other are in the last two positions, and the third one is in the fifth position.
Now, let us count the number of strings where the two ones that are next to each other are in the first two positions, and the third one is in the sixth position. There are two choices for the value of the third digit (0 or 1), and two choices for the value of each of the other digits (digits 4 and 5 must be different from each other and from digit 3). Therefore, there are 2 \cdot 2 \cdot 2 = 8 strings with this property: 1100010, 1101010, 1110010, 1111010, 1000110, 1001110, 1010110, and 1011110.
Again, we can obtain the same number of strings by considering the case where the two ones that are next to each other are in the last two positions, and the third one is in the sixth position.
Thus, the total number of strings that satisfy the given conditions is 4+4+8+8=24.
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how to solve the first order linear differential equation
The solution to the given differential equation is y = e⁽ˣ³⁾⁽²⁸ˣ ⁺ ᶜ⁾, where C is a constant.
To solve the first-order linear differential equation of the form y' + p(x)y = q(x), where p(x) and q(x) are functions of x:
Find the integrating factor (IF) = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾
Multiply both sides of the equation by the IF.
Apply the product rule to the left side and simplify the right side.
Integrate both sides with respect to x.
Solve for y.
Using this method, for the given equation:
y' - 3x²y = 28e⁽ˣ³⁾
Find the integrating factor (IF):
IF = e⁽∫ᵖ⁽ˣ⁾ᵈˣ⁾ = e⁽⁻³/¹ * ∫ˣ²ᵈˣ⁾ = e⁽⁻ˣ³⁾
Multiply both sides by the IF:
e⁽⁻ˣ³⁾y' - 3x²e⁽⁻ˣ³⁾y = 28
Apply the product rule to the left side and simplify the right side:
d/dx (e⁽⁻ˣ³⁾y) = 28
Integrate both sides with respect to x:
e⁽⁻ˣ³⁾)y = 28x + C, where C is the constant of integration.
Solve for y:
y = e⁽ˣ³⁾(28x + C)
Therefore, the solution to the given differential equation is y = e⁽ˣ³⁾(28x + C), where C is a constant.
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Complete question:
How to solve the first order linear differential equation
Y'- 3x²y=28eˣ³
12x (3+2’2) divided by 2-10
Answer:
-5.5
Step-by-step explanation:
[12*(3/(2^2))]/2-10 [Rewritten to add brackets.
Use PEDMAS to determine order of operation.
P =- parentheses first:
[12*(3/(2^2))]/2-10
[12*(3/(4))]/2-10 [squared the 2]
[12*(3/4)]/2-10 [Removed excess parentheses]
[12*(3/4)]/2-10 [Next parenthses: 12*(3/4) Divide and Multioply]
[9]/2 - 10 [Divide and Multiply]
4.5 - 10 [Add/Subtract]
-5.5 Result
The length of a cell phone is 1.41.4 inches and the width is 2.82.8 inches. The company making the cell phone wants to make a new version whose length will be 1.611.61 inches. Assuming the side lengths in the new phone are proportional to the old phone, what will be the width of the new phone?
Answer:
Step-by-step explanation:
Since the side lengths are proportional, the ratio of the width to length in the old phone will be equal to the ratio of the width to length in the new phone. That is:
(width of old phone) / (length of old phone) = (width of new phone) / (length of new phone)
We know the length of the old phone is 1.41.4 inches, and the width is 2.82.8 inches, so we can use that information to solve for the width of the new phone:
(2.82.8 inches) / (1.41.4 inches) = (width of new phone) / (1.611.61 inches)
Cross multiplying, we get:
(width of new phone) = (2.82.8 inches) * (1.611.61 inches) / (1.41.4 inches)
Using a calculator, we can find that the width of the new phone is approximately 3.23.2 inches.
Select the correct answer.
Which graph is the graph of f(x) = 3 log2 (x +1)?
The graph of the equation of function f (x) = 3 log₂ (x + 1) is shown in figure.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The equation of function is,
⇒ f (x) = 3 log₂ (x + 1)
Now, By using tool we can draw the graph of the equation of function
f (x) = 3 log₂ (x + 1) as shown in figure.
Thus, The graph of the equation of function f (x) = 3 log₂ (x + 1) is shown in figure.
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Identify the figure below. Select 2 names that apply
A. quadrilateral
B.parallelogram
C. Rhombus
D. Square
E. Trapezoid
P.S hurry I have to summit this soon (1-10 mins)
Answer: a and b
Step-by-step explanation: lol it obvious
Answer: Quadrilateral, Parallelogram
Step-by-step explanation:
A Quadrilateral is any closed 4 sided figure
A Parallelogram is a quadrilateral with two sets of parallel and opposite sides.
DUE FRIDAY NEED HELP NOW!!!
Let P, Q, R, and S be the midpoints of sides AB, BC, CD, and DA, respectively. Use a ruler to locate these points as precisely as you can, and join them to form a new quadrilateral PQRS. What do you notice about the quadrilateral PQRS?
ABCD is a rectangle, and P, Q, R, and S are mid points of the sides AB, BC, CD, and DA, respectively. show that the quadrilateral PQRS is a rhombus
Jack washes cars no monday he washed 18 cars for $90 on tusday he washed 9 cars for $45 on wadnesday he washed 12 cars for $60 what si the rate of change of jakes earnings
The rate of change of Jakes earning is, 0 or no change.
What is the rate?Rate is a ratio of change in one quantity w.r.t. change in another quantity. The net change in one quantity is written as, Δy and the net change in another quantity is written as, Δx.
So formula for the rate is,
m = change in one quantity/change in another quantity = Δy/Δx
On Monday, Jake earned $90 by washing 18 cars.
Therefore, his earning rate was:
= $90 / 18 cars
= $5 per car
On Tuesday, Jake washed 9 cars and earned $45.
Therefore, his earning rate was:
= $45 / 9 cars
= $5 per car
On Wednesday, Jake washed 12 cars and earned $60.
Therefore, his earning rate was:
= $60 / 12 cars
= $5 per car
We can see that Jake's earning rate remained constant over the three days at $5 per car.
Therefore, the rate of change of Jake's earnings is 0, or no change.
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a stairway with three steps has three risers that are each 8 inches high and three treads that are each 10 inches deep. what is the area, in square inches, of this figure that is the side panel of the stairway?
The area of the side panel of the stairway is 360 square inches.
The side panel of the stairway is essentially a right triangle with the three steps forming the three horizontal segments (treads) and the three risers forming the three vertical segments (risers).
The height of the side panel would be the total height of the three risers, which is -
3 risers x 8 inches/riser = 24 inches
The length of the side panel would be the total length of the three treads, which is -
3 treads x 10 inches/tread = 30 inches
Now, we can calculate the area of the side panel using the formula for the area of a right triangle:
Area = (base x height)/2
we have the base as the length of the side panel (30 inches) and the height is the total height of the three risers (24 inches).
Substituting these values into the formula we get,
Area = (30 inches x 24 inches)/2
Area = 360 square inches
Therefore, the area of the side panel of the stairway is 360 square inches.
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What is the answer to this equation (5+12i)+(7-5i)
The answer to the equation (5+12i) + (7-5i) is found to be 12-7i.
The provided equation is a simple algebraic relation between two complex numbers.
The given complex numbers are 5+12i and 7-5i.
We have to add these two complex numbers.
We will add the real part of the complex number to the real part and complex part of one complex number to the complex part of the complex number.
Sum of number = (5+12i) + (7-5i)
Sum of number = 12-7i
The sum of the two complex numbers is also complex number that has a real part has 12 and the imaginary or the complex part as -7.
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You order a pizza with a 12” diameter. What is the area of the pizza?
What is the radius of a pizza that is 25% larger??
Pls help
Answer:
1. The formula for the area of a circle is given by A = πr^2, where r is the radius of the circle. To find the area of the 12" pizza, we first need to find the radius:
r = 12 / 2 = 6 inches
The area of the pizza is then:
A = πr^2 = π * 6^2 = 36π square inches
2. To find the radius of a pizza that is 25% larger, we can first find the amount by which the radius will increase:
increase = 6 * 0.25 = 1.5 inches
The new radius will then be:
new_r = 6 + 1.5 = 7.5 inches.
Step-by-step explanation:
Answer:
113.1, 8
The equation to find the area of a circle is:
Area = π (d/2)^2Now we can input 12 into the equation:
Area = π (12/2)^2Area = 113.1To find the radius of a pizza that is %25 larger, we can use this equation:
Radius × 1.25 = new radiusWhy do we multiply by 1.25?Well, that's a good question! If we were to multiply by 0.25, the radius would get smaller, instead of bigger. We add the 1.0 because we have to add the original radius, not just the added length.
Fitting the radius into the equation:
6 × 1.25 = 8Therefore, the area of the pizza is 113.1, and the radius of a pizza that is %25 larger is 8.
In the previous problem, how does the angle of depression from the top of the taller building relate to the angle of elevation from the top of the shorter building? a. they are congruentb. they are complementaryc. they are supplementaryd. they are alternate interior anglese. they are alternate exterior anglesf. they are corresponding angles
The angle of depression from the top of the taller building and the angle of elevation from the top of the shorter building are alternate interior angles.
Alternate interior angles are the angles formed when a transversal intersects two coplanar lines. They lie on the inner side of the parallel lines but on the opposite sides of the transversal. The transversal crosses through the two lines which are Coplanar at separate points.
The angles of elevation and depression are formed by the line of sight and the horizontal line. When the line of vision is above the horizontal line, the angle is of elevation, and if the line of sight is below the horizontal, the angle is of depression.
If the angle of depression of the taller building is 15° the angle of elevation of the shorter building is 15° too.
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Answer: look at the image for the answer and solution
Step-by-step explanation:
Type the correct answer in each box. Use numerals instead of words.
Solve the equation by completing the square. x2 + 20x + 82 = 7
The solutions, in order from least to greatest, are x = and x = .
By completing the square, the equation. x2 + 20x + 82 = 7. The solutions are x = -15 and x = -5, going from least to largest.
What is meant by constant?In expression, a constant is a value or number that is consistently the same. Multiple meanings can be derived from the word "constant." Its meanings as a noun and an adjective, respectively, are non-variance and two: an unchanging integer or other non-changing mathematical entity that is fixed and well-defined. The value of a constant is fixed and does not alter over time. A shoe's, a piece of clothing's, or any other item of clothing's size, for instance, will never alter. Because 8 is a constant number and cannot be modified in an algebraic equation, x+y = 8 is a valid solution.The square of half the x-coefficient must equal the constant on the left:
(20/2)^2 = 100
To get it to that value, we can add 18 to both sides of the equation:
x^2 + 20x + 100 = 25 . . . add 18 to both sides of the equation
(x + 10)^2 = 25 . . . . . . . . write the left side as a square
x + 10 = ±√25 = ±5 . . . . . take the square root
x = - 10 ± 5 = {-15, -5}
The solutions are x = -15 and x = -5.
The attached graph shows the solutions to ...
x^2 + 20x + 82 -7 = 0 . . . . . the result of subtracting 7 from both sides
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