Describe a series of transformations Matt can perform to device if the two windows are congruent
Answers
Combining the three different transformations—rotations, reflections, and translations—will result in congruent shapes. Actually, any pair of congruent shapes can be matched to one another using a combination of one or more of these three transformations.
What are transformation ?There are four possible transformations of a point, line, or geometric figure, each of which changes the object's shape and/or location. Pre-Image denotes the shape of the object before transformation, while Image denotes the final position and shape of the object.
We now know that during rigid transformations, the size and shape of the figures are maintained (reflections, translations, and rotations). The pre-image and the image are always in agreement.
Matt has the following transformational abilities:
Reflection (Flip)
A reflection keeps its original shape because the comparable points from the pre-image to the image stay at the same distance from the line of reflection.
Rotations as a Congruence Transformation
Rotations as a Congruence Transformation
A figure twists when it rotates. The figurine looks to have fallen over, although being the same size and shape. A great illustration of a rotation in the actual world is a clock. The connecting arms of a clock rotate around its axis every hour or every day. A rotation is defined by its degree; common rotations include 90 degrees, 180 degrees, and 270 degrees. The figure completes a full 360-degree rotation before returning to its starting point. A rotation must include indicate the clockwise or counterclockwise direction. This information can be used to calculate the degree, quantity, and direction of a revolution.
Translational congruence transformation
We refer to a movement as a translation when an object or shape is moved from one place to another without changing its size, shape, or orientation. Every point on an item or shape is moved by the same amount and in the same direction during a translation, sometimes referred to as a slide.
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Related Questions
List the improper fractions in order from greatest to least:9/7, 7/6, 17/14, 26/21
Answers
Answer:
[tex]\frac{9}{7},\frac{26}{21},\frac{17}{14},\frac{7}{6}[/tex]Explanation:
Given the improper fractions:
[tex]\frac{9}{7},\frac{7}{6},\frac{17}{14},\frac{26}{21}[/tex]In order to arrange the fractions, first, find the lowest common multiple of the denominators.
• LCM of 7, 6, 14, and 21 = 42
Next, rewrite each fraction as an equivalent fraction using the LCM as the new denominator.
[tex]\begin{gathered} \frac{9}{7}=\frac{9\times6}{7\times6}=\frac{54}{42} \\ \frac{7}{6}=\frac{7\times7}{6\times7}=\frac{49}{42} \\ \frac{17}{14}=\frac{17\times3}{14\times3}=\frac{51}{42} \\ \frac{26}{21}=\frac{26\times2}{21\times2}=\frac{52}{42} \end{gathered}[/tex]Since all the denominators are the same, order the numerators from the greatest to the least:
[tex]\begin{gathered} \frac{9}{7}=\frac{9\times6}{7\times6}=\frac{54}{42} \\ \frac{26}{21}=\frac{26\times2}{21\times2}=\frac{52}{42} \\ \frac{17}{14}=\frac{17\times3}{14\times3}=\frac{51}{42} \\ \frac{7}{6}=\frac{7\times7}{6\times7}=\frac{49}{42} \end{gathered}[/tex]Thus, the fractions ordered from greatest to least is:
[tex]\frac{9}{7},\frac{26}{21},\frac{17}{14},\frac{7}{6}[/tex]
a certain linear function can be described by the equation below
Answers
We are given the information that the equation of the line is of the form:
y = a x + b
where a is a negative number and b is a positive number.
And we are asked to select among a number of options that represent the situation.
SInce b is a positive number (being "b" what is understood as the y-intercept) the line DOESN'T pass through the origing of coordinates. So the first option is discarded.
SInce "a"is a negative number (this is the so called "slope' of the line) the line must be slanted, and dropping from left to right Therefore option b is also discarded because that represents a line going up from left to right.
Option c is also discarded, because a is a negative number (not a zero) and lines parallel to the x axis have slope zero.
The last option is the correct one, since the intercept oo the y-axis is at a positive value for y, the line must be going down due to the negative slope, and therefore going across the II, I and IV quadrant as shown below: (give me a few minutes to draw a line with this characteristics)
Then, please mark the last option (d) as the correct answer.
Given the following information, determine which lines, if any, are parallel. State the converse that justifies your answer.
Answers
1. Angle j and k
j || k is a result of the Converse of Corresponding Angles Postulate.
2. The alternating inner angles of the lines j and k are angles 2 and 5. If angle 2 = angle 5, then
Alternate Interior Angles in Reverse According to the theorem, j || k.
Alternate interior angles are conversed by J and K.
How do parallel angles work?
3. Similarly Angle 3 equals Angle 10.
Angle 3 and Angle 10 are the exterior angles of the lines l and m, respectively. Angle 3 equals angle 10 according to the Converse of Alternate Exterior Angles Theorem, therefore l || m.
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Which statement is true regarding the functions on the graph? 6 9) O f2) = g(2) O fO) = g(0) O f2) = g(0) Of(0) = g(2) 2 5 6 -421
Answers
F(x) is blue and G(x) is red
Have to find at which point both functions have the same value, or the same in which point both lines intercept
and looking at the graph ,theres only one point where both are equal. Its the point x= 2 y=0.
so the correct answer is f(2) = g(2)
3 1 1 1 Evaluate 2 when n = 10 5 1 3 3 2 10 10 1 3 3 + + 2 10 10 (Type integers or fractions.)
Answers
The given expression is
[tex]\frac{1}{2}n+\frac{3}{10}[/tex]Where n = 1/5.
Let's replace the variable for its value.
[tex]\frac{1}{2}(\frac{1}{5})+\frac{3}{10}[/tex]First, we solve the product.
[tex]\frac{1}{10}+\frac{3}{10}[/tex]Then, we sum fractions. Notice that we just have to sum numerators because the denominators are equal.
[tex]\frac{1+3}{10}=\frac{4}{10}=\frac{2}{5}[/tex]Therefore, the answer is 2/5.The figure below is a parallelogram. Find RQ.-1+4xPeO 15O 1004O 123x+3SR
Answers
We have a parallelogram and we have to find the length of side RQ.
Opposite sides of a parallelogram besides being parallel, they also have the same length.
Then, we can write:
[tex]PS=QR[/tex]We can use that to find the value of x as:
[tex]\begin{gathered} PS=QR \\ -1+4x=3x+3 \\ 4x-3x=3+1 \\ x=4 \end{gathered}[/tex]Knowing x = 4, we can find RQ as:
[tex]QR=3x+3=3(4)+3=12+3=15[/tex]Answer: QR = 15
Ghost, Inc., has no debt outstanding and a total market value of $395,600. Earnings before interest and taxes, EBIT, are projected to be $53,000 if economic conditions are normal. If there is strong expansion in the economy, then EBIT will be 13 percent higher. If there is a recession, then EBIT will be 22 percent lower. The company is considering a $195,000 debt issue with an interest rate of 8 percent. The proceeds will be used to repurchase shares of stock. There are currently 8,600 shares outstanding. The company has a tax rate of 21 percent, a market-to-book ratio of 1.0, and the stock price remains constant. Calculate earnings per share (EPS) under each of the three economic scenarios before any debt is issued.
a-1.
Calculate earnings per share (EPS) under each of the three economic scenarios before any debt is issued. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
a-2. Calculate the percentage changes in EPS when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
b-1. Calculate earnings per share (EPS) under each of the three economic scenarios assuming the company goes through with recapitalization. (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.)
b-2. Given the recapitalization, calculate the percentage changes in EPS when the economy expands or enters a recession. (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)
Answers
EPS for recession is $3.7975, EPS for normal is $4.8686, EPS for expansion is $5.5015, and Percentage change in EPS for expansion is 13% and for recession is -22%, EPS under each of the three scenarios after recapitalization is 4360 and percentage change in EPS after the recapitalization is -31.17% and 18.42% for recession and expansion respectively.
A-1) Calculation of EPS under each scenario:
EBIT for expansion condition,
= EBIT × 113%
= $53,000 × 113%
= $59,890
EBIT for recession conditions,
= EBIT × 78%
= $53,000 × 78%
= $41,340
Tax = EBT × 21%
Net income = EBT - Taxes
EPS = Net income ÷ No. of shares
EPS for recession = $3.7975
EPS for normal = $4.8686
EPS for expansion = $5.5015
A-2) Calculation of Percentage change in EPS,
For Expansion = (Expansion EPS - Normal EPS) ÷ Normal EPS
= (5.05 - 4.86) ÷ 4.86
= 13%
For Recession = (Recession EPS - Recession EPS) ÷ Recession EPS
= (4.86 - 3.79) ÷ 4.86
= -22%
B-1) Calculation of EPS under each of the three scenarios after recapitalization,
Market to Book ratio (l) = Market value ÷ Book value
l = $395,600 ÷ Book Value
Book Value = $395,600
Stock Price = Book Value ÷ No. of outstanding shares
= $395600 ÷ 8,600
= 46
No. of shares repurchased = Debt ÷ Stock Price
= $195,000 ÷ 46
= 4240
No. of shares after repurchasing = No. of outstanding shares - No. of shares repurchased
= 8,600 - 4240
= 4360
B-2) Calculating percentage change in EPS after recapitalization,
For Recession = (Recession EPS - Recession EPS) ÷ Recession EPS
= (4.66 - 6.77) ÷ 6.77
= -31.17%
For Expansion = (Expansion EPS - Normal EPS) ÷ Normal EPS
= (8.02 - 6.77) ÷ 6.77
= 18.42%
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Mr. Coffey bought a house for $195,000. He made a 20% down payment. The interest rate is 5.25% for 30 years. How much does he need to borrow? What is his monthly payment?
Answers
Explanation:
Mr. Coffey bought a house for $195,000 with a 20% down payment.
A 20% down payment, would be 0.20, so $195,000 times 0.20 equals $39,000. Then $195,000 - $39,000 = $156,000.
He bought the bouse for $156,000.
5.25% is 0.525, because you move the decimals back. Understanding the total cost of the house is $156,000 now, we can do $156,000 times 5.25% (0.0525) which equals $8,190.
He would pay $8,190 every 30 years. (if this was the interest rate.)
Assuming if the cost was 20% down payment with the 5.25% interest rate then it would have been: $39,000 times 5.25% = 2047.5.
He would pay $2,047.50 every 30 years. (if this was the interest rate.)
There was no context between the interest rate, so let's assume the obvious which is $2,047.50 every 30 years.
8x^2+8x-22 In (x-p)^2=q
Answers
The given function 8x^2+8x-22 rewritten using the completing the square method is (x+1/2)^2 = 3
Completing the square methodBy altering the equation's form so that the left side is a perfect square trinomial, a quadratic equation can be solved using the "Completing the Square" approach.
Given the quadratic equation below;
8x^2+8x-22 = 0
This can be simplified into the equation below;
8x^2+8x-22 = 0
4x^2+4x-11 = 0
Add 11 to both sides of the equation
4x^2+4x-11 + 11= 0 + 11
4x^2+4x = 11
Factor out 4x from the expression;
4(x^2+1) = 11
(x+1/2)^2 = 11/4 + 1/4
(x+1/2)^2 = 12/4
(x+1/2)^2 = 3
Hence the expression in the form of (x-p)^2=q is (x+1/2)^2 = 3
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NEED ASAP PLS QUESTION IS IN THE PICTURE IF CORRECT ILL GIVE BRAINLIEST
Answers
The vertex and range of y = (x + 2) - 3 is [tex]$(0,-1) ;-3 \leq y < \infty[/tex]
What is vertex and range?We only need to think about the k as the vertex is determined by the coordinates (h, k). Consider the function f(x)=3(x+4)26 as an illustration. All real integers greater than or equal to 6 fall within the range since an is positive and the vertex lies at (4,6).A vertex is a place where two line segments come together at an acute angle or where two curved lines come together to form a parabola. Depending on the direction, a parabola's vertex is either its highest or lowest point.The set of values that a function can accept as input is known as its range.. After we enter an x value, the function outputs this sequence of values.To learn more about vertex and range refer to :
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Round your answer to two
decimal places.
7X = 77
Answers
Answer:
x = 11
Step-by-step explanation:
7X = 77
divide both sides by 7
x = 11
In ΔJKL, \overline{JL} JL is extended through point L to point M, \text{m}\angle KLM =(7x+3)^{\circ}m∠KLM(7x+3) ∘,\text{m}\angle LJK = (2x+12)^{\circ}m∠LJK=(2x+12)∘,and \text{m}\angle JKL = (3x+7)^{\circ}m∠JKL=(3x+7) ∘.Find \text{m}\angle LJK.m∠LJK.
Answers
Applying the exterior angle theorem, the measure of angle LJK is: 28°.
What is the Exterior Angle Theorem?Where an external angle is formed by an extended side of a triangle, its measure is equal to the two remote angles of the triangle, according to the exterior angle theorem.
Given the following:
m∠KLM = (7x + 3)°m∠LJK = (2x + 12)°m∠JKL = (3x + 7)°Angles LJK and JKL are remote angles of the triangle which are opposite the exterior angle KLM.
Therefore:
m∠LJK + m∠JKL = m∠KLM
Substitute
2x + 12 + 3x + 7 = 7x + 3
Combine like terms and find the value of x:
5x + 19 = 7x + 3
5x - 7x = -19 + 3
-2x = -16
-2x/-2 = -16/-2
x = 8
Find
m∠LJK = 2x + 12
Plug in the value of x:
m∠LJK = 2(8) + 12
m∠LJK = 28°
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What is the slope of a line perpendicular to the
line whose equation is 6x - 9y = 216. Fully
simplify your answer.
Answers
Answer:
Slope is 2/3
Step-by-step explanation:
NEEEEEEEEDDDDDD HELPPPPP ASAPPPPPPP
Answers
Matching the specific Polygons with their descriptions, we have;
15-gon → An exterior angle measures 24°
16-gon → The Sum of interior angles is 2520°
12-gon → An interior angle measures 150°
18-gon → An interior angle measures 160°
What is the sum of interior angles of a Polygon?The formula for sum of interior angles of a Polygon is;
S = (n - 2) * 180
where n is number of sides of polygon. Thus;
1) For a 15 sided polygon;
Sum = (15 - 2) * 180
Sum = 13 * 180
Sum = 2340
Sum of exterior angles of a polygon is; 360°
Thus, external angles = 360/15 = 24°
2) For a 16 sided polygon;
Sum of interior angles = (16 - 2) * 180 = 2520°
3) The value of the interior angles of a polygon with 12 sides is;
(12 -2) * 180/12 = 150°
4) The value of the interior angles of a polygon with 18 sides is;
(18 - 2) * 180/18 = 160°
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Which of the following is a solution of the inequality h + 9 < 20?
Answers
Answer:
h < 11
Step-by-step explanation:
Thats what i get when i work it out lol
A cell of some bacteria divides into two cells every 30 minutes. The initial population is 3 bacteria.
(a) Find the size of the population after t hours
y(t)
(function of t)
=
(b) Find the size of the population after 7 hours.
y(7)=
=
(c) When will the population reach 21?
T =
Answers
After t hours, the population is 3(2^2t).
After 7 hours, the population is 3(2^14).
In 2.33 minutes, the population would be 21.
What is the function representing bacterial growth?The following formula is used to calculate the bacteria population:
The formula for calculating future value is as follows:
FV = P (1 + r)^n
Where:
FV stands for Future Value.
P = Present value of three
R = growth rate = 100%
(hours x 60 minutes) / 30 = 2t = time
3(2^2t) = population in t hours
3(2 ^14) = population in 7 hours
The population of time would be 21 =[( FV /PV) / r] X 30.
2.33 minutes = ( 21 / 3) / 3.
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hii i have a question on the question below . in the photo
Answers
Solution
For this case we need to sort the values and we have:
Studied
79, 83, 84, 88, 89, 89, 91, 92, 93, 94, 95, 95, 96, 99, 100, 100, 100, 100
Q3= 98.25
Q1= 89
Therefore IQR = 98.25-89= 9.25
Not Studied
45, 58, 65, 72, 73, 77, 82, 83, 87, 89, 90, 91
Q3= 87.5
Q1= 70.25
Therefore IQR = 87.5-70.25= 17.25
From the results obtained we can conclude that the students who not studied havve larger variability compared to those who studied
which candy is better to buy $4.12 for 4 bars of 7.14 for 7 bars?
Answers
Its better to buy second set of candy. That is, candy which is $7.14 for 7 bars.
Given,
The cost for first candy = $4.12 for 4 bars.
The cost for second candy = $7.14 for 7 bars.
We have to determine which candy is better to buy.
For that we have to find the cost of one candy.
That is,
The cost for one candy in first candy set = 4.12/4 = 1.03
The cost for one candy in second candy set = 7.14/7 = 1.02
Here,
1.02 is less than 1.03.
That is, second set of candy has lesser cost than first set.
So, its better to buy second set of candy. That is, candy which is $7.14 for 7 bars.
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Line j has an equation of y=–
9
7
x+
10
7
. Line k is parallel to line j and passes through (–
4,4). What is the equation of line k?
Answers
The equation of the line k parallel to line j and passes through (-4, 4) is
y = - 9 / 7 x - 8 / 7
How to find equation of a line?Equation of a line can be represented as follows:
y = mx + b
where
m = slopeb = y-interceptTherefore, the line k is parallel to the line j, y = - 9 / 7 x + 10 / 7 and passes through (-4, 4),
Parallel lines have the same slope.
Hence, let's find the y-intercept of the equation k using (-4, 4)
4 = - 9 / 7 (-4) + b
4 - 36 / 7 = b
b = - 8 / 7
Therefore,
the equation is y = - 9 / 7 x - 8 / 7
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five friends earn a total of $33.75 shovellimg snow. How much does each friend earn
Answers
Given:
Number of friends = 5
Total amount they earn = $33.75
Let's find how much each friend earn.
To find the amount each friend earn, take the formula below:
[tex]\text{ Amount each friend earn = }\frac{Total\text{ amount they earn}}{\text{Number of friends}}[/tex]Substitute values into the equation above and evaluate:
[tex]\text{ Amount each friend earn = }\frac{33.75}{5}=6.75[/tex]Therefore, each friend earns $6.75
ANSWER:
$6.75
Answer: $6.75
Step-by-step explanation: Divided 33.75 by 5 which is equal to $6.75
A chord of a circle is 56cm long. The distance of the chord to the centre of the circle is 20cm. a) calculate the radius of the circle b) calculate the length of a chord which is 24cm from the center of the circle.
Answers
Answer:
a) 34.4 cm,b) 49.4 cmStep-by-step explanation:
The distance from the center to the chord is the perpendicular bisector of the chord.
The three segments form a right triangle:
The radius - hypotenuse,The half-length of the chord - leg,The distance to the chord - another leg.a) Use Pythagorean to find the radius:
r² = (56/2)² + 20²r² = 28² + 20²r² = 1184r = √1184r = 34.4 cm (rounded)b) Let the half-chord is x cm long. Use Pythagorean to find the missing leg:
34.4² = x² + 24²1184 = x² + 576x² = 1184 - 576x² = 608x = √608x = 24.7 cm (rounded)The length of the chord is:
24.7*2 = 49.4 cmGraph the line with slope 1/3
and y-intercept -2.
Answers
The equation of a straight line is y = mx + b where m is the slope and b is the y-intercept then the two points exist (0, -2) and (6, 0).
What is meant by the equation of a straight line?A straight line's general equation is y = mx + c, where m denotes the gradient and y = c denotes the point at which the line crosses the y-axis. On the y-axis, this value c is referred to as the intercept. Y = mx + c represents the equation of a straight line with gradient m and intercept c on the y-axis.
The equation of a straight line is:
y = mx + b where m is the slope and b is the y-intercept.
Therefore, the equation for this line is:
y = (1/3)x - 2
To graph it we can identify two points on the line and connect them.
If x = 0, then y = -2 this is the y-intercept given in the problem.
If x = 6, then y = 0 this is the x-intercept
Therefore, the two points exist (0, -2) and (6, 0).
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Tina's kitchen has an area of 54 square feet the kitchen is 9 times as many square feet does Tina's pantry if the pantry is 2 feet wide what is the length of the Pantry in feet
Answers
From the information given, the area of the kitchen is 54 square feet and it is 9 times as many square feet as does Tina's pantry. This means that the area of Tina's pantry is
54/9 = 6 square feet
If the pantry is 2 feet wide, we would determine its length by applying the formula for determining the area of a rectangle which is expressed as length * width
Therefore,
2 * length = 6
length = 6/2 = 3 feet
Length of the pantry is 3 feet
Name the number of degrees in the monomial.8abcd
Answers
Given: 8abcd
The number of degrees is the sum of the exponent of each variable in the monomial
The answer is 4
6 singles, 7 fives, 3 twenties, and 2 hundred dollar bills are all placed in a hat. If a player is to reach into the hat and randomly choose one bill, what is the fair price to play this game?
Answers
Fair price to play this game is $16.72
Explanation:[tex]\begin{gathered} \text{Given:} \\ 6\text{ singles, 7 fives, 3 twenties and 2 hundred dollar bills in a hat} \\ \end{gathered}[/tex]To find the fair price, we divide the total amount by the number of bill denominations given
[tex]\text{fair price = }\frac{total\text{ amount in the hat}}{nu\text{mber of bills in the hat}}[/tex][tex]\begin{gathered} nu\text{mber of bills = }6\text{ + 7 + 3 + 2 = 18} \\ \\ \text{singles = 1} \\ 6\text{ singles = 6 }\times\text{ 1} \\ 7\text{ fives = 7}\times\text{ 5} \\ 3\text{ twenties = 3}\times20 \\ 2\text{ hundred = 2 }\times\text{ 100} \\ \\ \text{Total amount in the hat = 6 }\times\text{ 1 + 7}\times\text{ 5 + 3}\times20\text{ + 2 }\times\text{ 100} \\ \text{Total amount = 6 + 35 + 60 + 200 = 301} \end{gathered}[/tex][tex]\begin{gathered} \text{fair price = }\frac{301}{18} \\ \text{fair price = 16.72} \end{gathered}[/tex]Fair price to play this game is $16.72
14 more than greg’s savings is 58
translate into equation
Answers
Answer:
1-4<58
Step-by-step explanation:
poor Greg is broke and yea
A. 8 + 8 + 8 + 8B. 2 + 4C. 4 + 4 + 8 + 8 + 1 + 1D. 8 + 8 + 4 + 4 + 2 + 2These Are The Choices
Answers
The surface area of a rectangular prism can be represented below
[tex]\begin{gathered} A=2(lw+wh+lh) \\ l=4 \\ w=2 \\ h=1 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} A=2(8+2+4) \\ A=8+8+4+4+2+2 \end{gathered}[/tex]3x+7x-28+31-8x for x=2043
Answers
The value of the function when x is equivalent to 2043 is 4089.
Solving linear equationLinear equations are equation that has a leading degree of 1. Given the linear equation;
3x+7x-28+31-8x
Collect the like terms
3x+7x-28+31-8x
3x+7x-8x-28+31
10x-8x-28+31
2x+3
If the value of x is 2043, substitute;
2x+3 = 2(2043) + 3
2x + 3 = 4086 + 3
2x + 3 = 4089
Hence the value of the function when x is equivalent to 2043 is 4089.
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Please show work as if you didn’t have a calculator
Answers
SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given function.
[tex]f(x)=\frac{1}{(x+3)}-2[/tex]STEP 2: Explain the means to use to find the required values
Since we were given a graph and can not use a caculator, we will be using the graph to get the values.
STEP 3: Plot the given function on a graph
STEP 4: Get the domain of the function
Domain: The domain is all x-values or inputs of a function. The domain of a graph consists of all the input values shown on the x-axis.
[tex]\begin{gathered} The\text{ domain from the graph is given as:} \\ x<-3\text{ or }x>-3 \\ \text{The interval notation is given as:} \\ (-\infty,-3)\cup(-3,\infty) \end{gathered}[/tex]STEP 5: Get the Range of the function
The range is all y-values or outputs of a function.
[tex]\begin{gathered} \mathrm{The\: set\: of\: values\: of\: the\: dependent\: variable\: for\: which\: a\: function\: is\: defined} \\ \text{The range of the graph is given as:} \\ f(x)<-2\text{ or }f(x)>-2 \\ \text{The interval notation is given as:} \\ (-\infty,-2)\cup(-2,\infty) \end{gathered}[/tex]STEP 6: Get the value on which the function is increasing on
[tex]\begin{gathered} \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)>0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: increasing.} \\ \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)<0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: decreasing.} \end{gathered}[/tex]STEP 7: Get the value on which the function is decreasing on
[tex]\begin{gathered} \mathrm{If}\: f\: ^{\prime}\mleft(x\mright)<0\: \mathrm{then}\: f\mleft(x\mright)\: \mathrm{is\: decreasing.} \\ It\text{ can be s}een\text{ that the function on the graph decreases on the point betw}een\text{ negative infinity} \\ \text{and -3 and the point betw}een\text{ -3 and infinity. }\therefore This\text{ can be written as:} \\ \: \\ \mathrm{Decreasing}\colon-\infty\:STEP 8: Get the values of the asymptotes
An asymptote is a line that a graph approaches without touching. Similarly, horizontal asymptotes occur because y can come close to a value, but can never equal that value. In the previous graph, there is no value of x for which y = 0 ( ≠ 0), but as x gets very large or very small, y comes close to 0.
[tex]\mathrm{Vertical}\colon\: x=-3,\: \mathrm{Horizontal}\colon\: y=-2[/tex]
find the length of the base if the area of the trapezoid is 198 M2.
Answers
The area of a trapezoid is given by:
[tex]A=\frac{1}{2}(b_1+b_2)h[/tex]where b1 and b2 are the bases of the trapezois and h is the height. In this case we have that A=198, b1=15 and h=12, plugging this values into the equation above and solving for b2 we have:
[tex]\begin{gathered} 198=\frac{1}{2}(b_2+15)12 \\ 2\cdot198=12(b_2+15) \\ 396=12(b_2+15) \\ \frac{396}{12}=b_2+15 \\ 33=b_2+15 \\ b_2=33-15 \\ b_2=18 \end{gathered}[/tex]Therefore b2 is equal to 18 m