The translation of the coordinate points on the graph by linear displacement in comparison of original points ( x , y ) get translated to ( x + h, y + k ) where h ∈R , k ∈R.
As given in the question,
Let us consider original coordinate point on a given graph be ( x ,y ).
Translation represents the change in the linear displacement or the location without changing the shape and size.
Shift of the point may be horizontally or vertically.
Let 'h' and 'k' be the horizontal and vertical shift.
If the horizontal shift is right then it is represented by x + h
If the horizontal shift is left then it is represented by x - h
If the vertical shift is up then it is represented by y +k
If the vertical shift is down then it is represented by y - k.
Therefore, the translation of the coordinate points on a given graph represented by original points ( x , y ) get translated to ( x + h, y + k ) where h ∈R , k ∈R.
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find the zeroes of the polynomial and verify the relations between coefficient and zeroes
3x²-x-4
Answer:
(-1) & 4/3
Step-by-step explanation:
Polynomial:3x² - x - 4
Sum = -1
Product = 3*(-4) = -12
Factors = -4 and 3 { (-4)*3 = -12 & (-4) + 3 = -1}
3x² - x - 4 = 3x² + 3x - 4x -4 {Rewrite the middle term using the factors}
= 3x(x + 1) -4(x + 1)
=(x + 1)(3x - 4)
x + 1 = 0 ; 3x - 4 = 0
x = -1 ; 3x = 4
x = 4/3
[tex]\sf Zeroes \ of \ the \ polynomial \ are \ (-1) \ and \ \dfrac{4}{3}[/tex]
Verification:
[tex]\sf 3x^2 - x - 4 = 0\\\\Divide \ the \ entire \ equation \ by \ 3\\\\\\\dfrac{3x^2}{3}-\dfrac{x}{3}-\dfrac{4}{3}=0\\x^2 - \dfrac{x}{3}-\dfrac{4}{3}=0[/tex]
Coefficient of x = sum of the zeroes
[tex]\sf = -1 + \dfrac{4}{3}\\\\=\dfrac{-3}{3}+\dfrac{4}{3}\\\\=\dfrac{1}{3}\\\\[/tex]
Constant = product of the zeroes
[tex]\sf = (-1)*\dfrac{4}{3}\\\\=\dfrac{-4}{3}[/tex]
Thus verified.
Select the correct answer. Which graph represents the solutions to this equation? x2 + 8x = -20 A. Linear-quadratic system graph shows upward parabola with vertex at (minus 2, 4) and passing through x and y-axis (minus 8, 0), and (0, 0) B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8) C. Linear-quadratic system graph shows upward parabola with vertex at (4, 0) and passing through (1, 4), and (6, 4) D. Linear-quadratic system graph shows a downward parabola with vertex at (0, 8) which intercepts the x-axis at 3 and minus 3 units.
A graph which represents the solutions to this equation x² + 8x = -20 include the following: B. Linear-quadratic system graph shows upward parabola with vertex at (minus 4, 4) and passing through (minus 2, 8), and (minus 6, 8).
What are quadratic functions?In Mathematics, the graph of every quadratic functions (equations) is either an upward or downward parabola, which is typically a u-shaped curve. This ultimately implies that, the graph of a quadratic function (equation) would always form a parabolic curve.
Next, we would re-write the given quadratic function in standard form by equating it to zero (0) as follows;
x² + 8x = -20
Adding 20 to both sides of the linear-quadratic equation, we have the following:
x² + 8x + 20 = -20 + 20
x² + 8x + 20 = 0
In this scenario, we would use an online graphing calculator to plot the graph of the given quadratic function and then determine the point of intersection and vertex.
y = x² + 8x + 20
By critically observing the graph of the given quadratic function, we can logically deduce that the solutions and vertex are as follows;
x = -6, y = 8.
x = -2, y = 8.
Vertex = (-4, 4).
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You buy clothing at a sale. You buy sneakers at 2 3 of their original price of $60, a sweater at 7 10 of its original price of $35, and a jacket at 5 6 of its original price of $45. Answer each question and show all your work. How much money did you spend
We spent a total of 40.2 + 24.5+ 37.8 = $102.50
Explain about the fractions?A fraction is a metric unit for describing a piece or component of a whole. It represents the appropriate parts of the totality. A fraction is made up of two parts: the numerator and the denominator. The number at the top is the numerator, and the number at the bottom is the denominator.
Fractions are used to represent the parts of an entity or collection of entities. The components of a fraction are two. The figure at the top of the line is the numerator. It provides information on how many equal sections from the total or collection were taken. The number that appears below the line is the denominator.
We multiply the initial price by the fractions' decimal conversions to determine how much we spent. The quantities are then combined.
You purchased sneakers for $60 and paid 2/3 of that amount, or $0.6666, for a total of $40.20, saving $19.80.
Sweater costs $35 and you paid $7.50 for it, saving you $10.50. 35(0.7)=$24.50.
You paid $45 for a jacket, and since 5/6=0.8333, 45(0.84)=$37.80, you made a $7.20 profit.
We spent a total of 40.2 + 24.5+ 37.8 = $102.50
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5
1 point
Eliana measures outdoor temperatures in an area each day for a week at exactly 2:00 p.m. The
temperatures she records are all between 25 °C and 30 °C. Eliana concludes that the climate of the
area is tropical.
What is the most important reason why her conclusion might not be correct?
she made her conclusion based only on temperature and not also on precipitation
she took the temperature readings at the same time each day
she made her conclusion based on only one week of data instead of over a long period of
time
she did not calculate the average of her data
It is possible for a valid argument to have a false conclusion as long as at least one premise is false.
Conclusions might be true or erroneous.?When the premises are genuine, validity guarantees a true conclusion; when the premises are wrong, validity provides no assurance. Even in a legitimate argument, faulty premises might lead to either a true or erroneous conclusion. In many cases, it was chance rather than reasoning that led to the correct conclusion.
Avoid including: Important evidence or analysis that was not provided in the main body for a stronger conclusion paragraph.Generic closing phrases (for example, “In conclusion…”)Weak remarks that undercut your argument (for example, “There are valid points on both sides of this debate.”)
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What is elimination method example?
The elimination method is used for solving linear equations. Here we make use of the addition property of equality, that is when same number is added on both sides of equation, it still remains equal.
Lets look into some examples.
Example 1x + y = 10
x - y = 2
By adding both equations,
x + y + x - y = 10 + 2
+ y and - y are cancelled or y term is eliminated.
2x = 12
x = 6
Example 22x + 3y = 10
-3x + 3y = 15
Here to eliminate y, we have to add the additive inverse of second equation.
2x + 3y + 3x - 3y = 10-15
5x = -5
x = -1
Example 3x + 4y = 5
3x - y = 2
To equalize the y term we multiply the second equation by 4
12x - 4y = 8
Adding both equations,
x + 4y + 12x - 4y = 5 + 8
13x = 13
x = 1
So elimination method is used for solving linear equations.
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please awnser the question below
The various statements regarding the given scatter plot is checked and found to be true or false.
What is a scatter plot?
A set of dots plotted on a horizontal and vertical axis is known as a scatter plot. Because they can demonstrate the degree of connection, if any, between the values of observed quantities.
1)The equation of the line is y = 2500x - 125.
From the graph we can take two points on the line,
( 2,2250) and ( 10,1250)
Standard equation of line is y = mx + b
where b is y - intercept and m is slope
m = [tex]\frac{y_{2} - y_{1} }{x_{2}-x_{1}}[/tex] = [tex]\frac{1250 - 2250}{10 - 2}[/tex] = -125
From graph, b = 2500
Equation of line is
y = -125x + 2500
Therefore the given equation is false.
2) The group of hikers descends about 250 feet every minute.
From the graph it is evident that for the interval between two points on y-axis is 250 feet and interval of x-axis is 1 minute.
So the hikers descend 250 feet every minute.
Therefore the given statement is true.
3) The hikers began at the elevation of 2500 feet.
The x-intercept of the graph is 2500 feet.
So the beginning elevation is 2500 feet.
Therefore the statement is true.
4) The graph shows a negative association.
Since the line in the graph is going down and the slope is negative, the graph shows a negative association.
Therefore the statement is true.
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Write a rule to describe each transformation.
S(1,-4), R(2,0), 2(3,0), P(3,-2)
to
S'(-5,-2), R'(-4, 2), Q'(-3, 2), P(-3,0)
The transformation of S(1,-4), R(2,0), 2(3,0), and P(3,-2) is S(-6, -2), R(-6, 2), as well as the category is rotation transformation.
what is transformation ?Four distinct approaches to modify the position and/or shape of a point, line, or geometric figure are collectively referred to as transformations. The Pre-Image, which refers to the object's initial shape, and the Image, which refers to the object's ultimate shape and location after transformation, are both terms. Transformations can be divided into three categories: translations, reflections, and dilations. There are two types of transformations that can be done to a function: vertical (which affects the y-values) and horizontal (affects the x-values). The four transformation variables are included in the equation of a function that is shown below (a, b, h, and k). changing the log. Take the log of every observation as an example. Transposition by the square root. The square root of each observation is what is need for this.
given
Translation or shift vector refers to the pair (tx, ty). Column vectors are another way to visualize the aforementioned equations.
S(1,-4), R(2,0), 2(3,0), P(3,-2) to S'(-5,-2), R'(-4, 2), Q'(-3, 2), P(-3,0)
is S (-6, -2) , R( -6 , 2)
The transformation of S(1,-4), R(2,0), 2(3,0), and P(3,-2) is S(-6, -2), R(-6, 2), as well as the category is rotation transformation.
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1. The population average fuel efficiency of U.S. light vehicles for 2005 was 21 mpg. If the standard deviation of the population was 2.9 and the gas ratings were normally distributed, what is the probability that the mean for a random sample of 25 light vehicles is under 20 mpg
The probability that the mean mpg for a random sample of 25 light vehicles is 0.042341
What is probability?Probability theory, a subfield of mathematics, gauges the likelihood of an occurrence or a claim being true. An event's probability is a number between 0 and 1, where approximately 0 indicates how unlikely the event is to occur and 1 indicates certainty. A probability is a numerical representation of the likelihood or likelihood that a particular event will occur. Alternative ways to express probabilities are as percentages from 0% to 100% or from 0 to 1. the percentage of occurrences in a complete set of equally likely possibilities that result in a certain occurrence compared to the total number of outcomes.
z = (x-μ)/σ/n, where
x is the raw score = 20 mpg
μ is the population mean = 21 mpg
σ is the population standard deviation = 2.9
n = random number of samples [tex]x < 20[/tex]
[tex]= z = 20 - 21/2.9/\sqrt{25} \\= z = -1/2.9/5\\= z = -1.72414\\[/tex]
P-value from Z-Table:
[tex]P(x < 20) = 0.042341[/tex]
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After learning how to fly, Wendy reduced her daily commute time by 75%. Previously, her commute took me minutes. Which of the following expressions could represent Wendy's commute time, in minutes, after she learned how to fly
The time taken by Wendy after she learned flying is m/4 minutes or 0.25m minutes.
We will solve this problem with the help of Percentages.
In the concept of percentages, we know that:
100% = 100/100 = 1
75% = 75/100 = 3/4
50% = 50/100 = 1/2
25% = 25/100 = 1/4
In our question, it is given that previously wendy took ‘m’ minutes to commute.
Now she reduced her daily commute by 75% after learning how to fly.
So, our new time = (100-75)% of previous time
= 25% of m minutes
= 25/100 of m minutes = ¼ of m minutes = m/4
So our final answer will be m/4 minutes or 0.25m minutes taken by wendy to commute now.
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What are the solutions of the quadratic equation 2x^2 5x 12 0?
The solutions of the given quadratic equation are 4 and -3/2. Solved using the factoring method to solve a quadratic equation.
what is a quadratic equation?
The definition of a quadratic as a second-degree polynomial equation demands that at least one squared term must be included. It also goes by the name quadratic equations. The quadratic equation's general form is ax^2 + b*x + c = 0.
where a, b, and c are constant terms and x is the unknown variable.
Here I am using the factoring method to solve a quadratic equation.
Given quadratic equation is
[tex]2x^2 - 5x -12 = 0.[/tex]
By comparing the General form of the quadratic equation we will get
a = 2, b = -5 and c = -12.
2x^2 - (8-3)x - 12 = 0.
2x^2 - 8x + 3x -12 = 0.
2x(x-4) + 3(x-4) = 0
(x - 4) (2x + 3) = 0.
x - 4 = 0 or 2x + 3 = 0
x = 4 or x = -3/2
Given Question is incomplete complete question here:
What are the solutions of the quadratic equation 2x^2-5x-12 = 0?
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PLEASE HELP ASAP
Combine like terms
8x + 3 - 5x + 9
Answer: B
Step-by-step explanation: [tex]8x-5x=3x\\3+9=12\\[/tex]
Hope this helps any
Answer:
B. 3x+12
Step-by-step explanation:
8x+3-5x+9
First combine the x. So, 8x-5x=3x
Next combine the 3 and the 9. So, 3+9=12
After you combined like terms your equation now looks like: 3x+12
Hope it helped you.
The tip of a minute-hand travels 103. 62mm in one hour. Find the length of the minute
hand
Using the concept of circumference of a circle, the length of the minute hand is 16.5mm.
What is circumference of a circle?
The measurement of the circle's perimeter, also known as the circle's boundary, is called its circumference . The radius of the circle is considered when applying the formula to determine the circumference of the circle.
Circumference of circle(C) = 2πR
where,
R represents the radius of the circle
π is a constant with an approximate value of 3.14
Now, it is given that the tip of a minute-hand travels 103. 62mm in one hour which means that the minute hand moves 360 degrees.
This means that C= 103.62
So, using the concept of circumference of a circle,
C= 2πR
103.62= 2*3.14*R
So, R= 103.62/6.28
R=16.5mm
Hence, the length of the minute hand is 16.5mm.
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-x+3y=6 in slope intercept form pls i need to know!!!
Answer:
[tex]\sf \bf y = \dfrac{1}{3}x + 2[/tex]
Step-by-step explanation:
Slope intercept form: y = mx + bWhere m is slope and b is y-intercept.
To write in slope intercept form isolate y.
To isolate y, first add 'x' to both sides,
-x + 3y = 6
3y = x + 6
Now, divide the entire equation by 3,
[tex]\sf \dfrac{3y}{3}=\dfrac{1}{3}x + \dfrac{6}{3}\\\\\\[/tex]
[tex]\sf \boxed{\bf y = \dfrac{1}{3}x + 2}[/tex]
Victor has a circular clock in his room. The long hand of the clock is the radius with a measure of 6 centimeters. The approximate circumference of the face of the clock is 37.68 centimeters. Which expression best represents the value of π ? Responses 37.686⋅6
The expression that best represents the value of π is 37.68 / 12.
What is the expression for π?The circumference of a circle is the distance round the circle. The radius of a circle is the distance from the center of the circle to any point on the circumference.
The formula for circumference of a circle = 2πr
Where:
π = pi
r = radius
π = circumference / 2r
π = 37.68 / (2 x 6)
π = 37.68 / 12
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If PQR measures 75°, what is the measure of SQR?
22°
45°
The measure of the angle ∠PQS will be 53°. Then the correct option is C.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360°.
Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.
If angle ∠PQR measures 75°. And angle ∠PQS measures 22°.
Angle ∠SQR and angle ∠PQS are the adjacent angles. Then we have
∠PQS + ∠SQR = ∠PQR
∠PQS + 22° = 75°
∠PQS = 53°
The measure of the angle ∠PQS will be 53°. Then the correct option is C.
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Complete question is attached below.
GIVING BRAINLIEST AND MANY POINTS FOR ANSWER I BEG PLEASE PLEASE
1. Use the Distributive Property to simplify the expression.
6(5 - q)
Group of answer choices
11 - 6q
11 - q
30 - 6q
1 - q
Answer:
C) 30 - 6q--------------------------
Distributive Property is:
a(b + c) = ab + acApply it to the given expression:
6(5 - q) = 6*5 - 6*q = 30 - 6qThe matching choice is C.
Answer:
[tex] \sf \: c) \: 30 - 6q[/tex]
Step-by-step explanation:
Given expression,
→ 6(5 - q)
Let's simplify the expression,
→ 6(5 - q)
→ 6(5) - 6(q)
→ (6 × 5) - (6 × q)
→ (30) - (6q)
→ 30 - 6q
Hence, option (c) is correct.
Identify the applications that involve percentages. SELECT ALL THAT APPLY.
Commission
Original Sale Price
Retirement
Sales Tax
Loans
Income
Income Tax
here in equation function, John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.
How do equations function?To create an equation, multiplying and dividing are used to separate constants and variables. In an equation, terms in various forms on each side of the equality sign are equal. John makes $8.00 per hour waiting tables, and after 40 hours he makes $530.50, including 210.50 in tips.To create an equation, multiplying and dividing are used to separate constants and variables.
so we have,
John had paid $8.00 an hour and waits tables
Therefore,
In 29 hours, he earns -
[tex]= 40 X 8\\= 320 $[/tex]
Via tups, he earned 210.50$
So, in total he earns
[tex]= 320 + 210.50\\= 530.50 $[/tex]
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whoever helps me with this will get 10 points.
Answer:
The answer is 1/4.
I wish you good luck.
Answer: it's hard i thought i could do it but nope dang it
A school is interested in the average GPA of the sophomore class. They sample 75 of the 500 sophomores, for a mean GPA of 3.26 with a standard deviation of 0.62. Calculate the margin of error to the nearest hundredth.
calculated margin of error = 0.376
What is margin of error?
It is a statistical term that implies the amount of permissible error within the survey data. This error indicates the difference between statistical result and actual result.
margin of error can be determined by multiplying the critical value to the standard deviation.
How to calculate the margin of error?given, mean GPA of 75 sophomores = 3.26 = Xi
standard deviation = 0.62 = s
sample number = 75 = n
total sophomores = 500
z value of the sophomores = mean / standard deviation = 3.26 / 0.62
Z value = 5.26
margin of error = Z value × standard deviation / (√number of sample)
margin of error = 5.26 × 0.62/ √ (75)
= 0.376
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please i really need help! anything will help at the moment
Answer:
-2 i think hope this helps
Step-by-step explanation:
in exercise 15, find the expectation if a person buys two tickets. assume that the players ticket is replaced after each draw and that the same tiket can win more than one prize answer
The expectation is -$9.6
What is probability?Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true.
Given that, a lottery offers one $1000 prize, two $700 prizes, three $300 prizes, and four $200 prizes.
Expected winning per ticket :
Σ(X × p(X)) = [(1000 × 1/1000) + (600 × 2/1000) + (300 × 2/1000) + (200 × 5/1000) - price per ticket
= 1 + 1.2 + 0.6 + 1 - 7
= 3.8-7
= -$3.2
Expected winning if 3 tickets are purchased :
3 × (-3.2) = -$9.6
Hence, the expectation is -$9.6
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A band wants to enter a contest that requires traveling expenses. They need at least $1,150 to cover all of the expenses. They have already saved $700. They are selling shirts with a profit of $7. 00 per shirt to earn the remaining money Part Which inequality represents the minimum number of shirts, n, the band must sell to earn the remaining money 1, 150
the number of shirts has to be an integer (you can not sell "part" of a shirt) n >= 65
They need at least $1,150
They have already saved $700
They are selling shirts with a profit of $7.00 per shirt
If they sell n number of shirts, they will earn n times $7.00
Since they have already 700, they will earn a total of 700 + 7n
If this quantity has to be equal or greater to 1,150, we can write:
1150 <= 700 + 7n
if we solve this inequality for n:
1150 <= 700 + 7n
1150 - 700 <= 7n
450 <= 7n
450/7 <= n
64.28 <= n
Since the number of shirts has to be an integer (you can not sell "part" of a shirt)
n >= 65
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The table below shows the number of animals at a local petting zoo.
Animal
Goats
Number
3
Ponies
3
Rabbits
8
Sheep
6
Write the ratio of ponies to sheep.
You may write the ratio in ANY of the three forms. Remember to REDUCE the ratio, if
possible.
Answer:
1/2
Step-by-step explanation:
You are comparing ponies to sheep, so you put the ponies on top(3)
and the sheep on the bottom(6)
3/6 reduces to 1/2
How to do 5 choose 3 on calculator?
To do 5 choose 3 on calculator, there are many methods including typing the input the mathematical expansion or in scientific calculators according to the model, there is way to represent 5C3.
The notation 5 choose 3 (also known as "5C3" or "5 comb 3") represents the number of ways to choose 3 items from a set of 5 items, also known as the binomial coefficient. It is equivalent to the formula:
5C3 = (5!) / (3! × (5-3)!)
Where "!" denotes factorial, which is the product of all positive integers up to that number.
To calculate 5C3 on a calculator, you can use the above formula and input it as follows:
5!/(3!×(5-3)!)
Most calculators have a button for factorial (symbolized by "!" or "n!"), so you can use that to calculate the factorials in the formula.
For example, on a basic calculator, you can input the following:
5!/(3!×2!)
and then press enter or the "=" button to get the result which is 10.
On some scientific or graphing calculators the notation is different, it could be represented as "comb(5,3)" or "5C3" and you just need to enter it as such.
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The figure was created by repeatedly reflecting triangle NMP.
A figure is created by continuously reflecting triangle N M P. The length of side N M is 6 inches, the length of side M P is 4 inches, and the length of side N P is 8 inches.
The scale factor of the dilation of segment HG is One-sixth.
Point P is the center of dilation. Line segment H G is dilated to form shorter line segment H prime G prime. The length of P G prime is 0.5
If PG' equals 0.5 units, what is PG?
2.5 units
3 units
4.5 units
6 units
The length of PG if PG' is 0.5 units is; 3 units.
What is dilation?The act or action of enlarging, expanding, or widening : the state of being dilated: such as. : the act or process of expanding (such as in extent or volume)
Here, given that,
Dilation is simply defined as the shrinking or enlarging of an object by a scale factor.
Now, we are told that Line HG is dilated to form a shorter line H'G'.
We are told that the scale factor is 1/6.
Point P is the center of dilation and if PG' is 0.5 units, then we can write the relation as follows;
Length of PG'/Length of PG = 1/6
Thus;
0.5/length of PG = 1/6
Length of PG = 0.5/(1/6)
Length of PG = 4 units
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When two lines make an angle of 90 degree is known as?
When the two lines makes angle of 90 degree , then the lines are known as Perpendicular Lines .
What are Perpendicular Lines ?
Two lines are said to be perpendicular to each other if the straight line makes an angle of 90 degree with another line. 90 degree is also called a Right Angle and is represented by a little square between two perpendicular lines .
when the two lines intersect at a right angle, they are said to be perpendicular to each other.
For Example : In a football field all the four corners of a football field are perpendicular to each other.
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David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour,
but realizes that he will be 1 hour late if he continues at this speed. He increases his speed by 15
miles per hour for the rest of the way to the airport and arrives 30 minutes early. How many miles
is the airport from his home?
(A) 140 (B) 175 (C) 210 (D) 245 (E) 280
If David drives from his home to the airport to catch a flight. He drives 35 miles in the first hour, but realizes that he will be 1 hour late if he continues at this speed. The number of miles that is the airport from his home is 210.
How to find the distance?Let d represent the distance that is needed to travel 1 hour
1 hour late decreased to 0.5 hours early = 1.5
Hence,
d/50 + 1.5 = d/35
Simplify
7d + 525 =10d
Collect like terms
525 = 10d - 7d
525 = 3d
Divide both side by 3d
d = 525/3
d = 175
Total number of miles :
Total number of miles = 175 + 35
Total number of miles = 210
Therefore we can conclude that the correct option is C.
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How do you know if its linear or linear?
Linear equations are equations that can be written in the form ax + b = c, where a, b, and c are real numbers and a ≠ 0.
The equation can be solved for the variable x by subtracting b from both sides and then dividing both sides by a. This will give the solution for x, which is x = (c - b) / a.
For example, consider the equation 2x + 4 = 10. This is a linear equation since it can be written in the form ax + b = c, where a = 2, b = 4, and c = 10. To solve for x, subtract b from both sides to get 2x = 6, and then divide both sides by a to get x = 3. Therefore, the solution to the equation is x = 3.
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The following equation has an error in one of the operations.
12(2x+6)+4(x+5)=5x−17
Which answer would correct the error?
A. Change 5x−17 to 5x+17.
B. Change 12(2x+6) to 12(2x−6).
C. Change (x+5) to (x−5).
D. Change +4(x+5) to −4(x+5).
The Correct change to make the Equation correct is Change (x+5) to (x−5).
The Correct option is (C).
What is Equation?Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given:
12(2x+6)+4(x+5)=5x−17
28x + 72= 5x-17
23x = 109
x= 4.73
First, change (2x+6) to 12(2x−6).
12 (2x - 6) + 4(x+5) = 5x- 17
24x - 72 +4x +20 = 5x- 17
28x -52 = 5x- 17
23x = 35
x= 1.52
Now, Change (x+5) to (x−5).
12 (2x + 6) + 4(x-5) = 5x- 17
24x + 72 +4x -20 = 5x- 17
28x + 52 = 5x- 17
23x = 69
x=3
Hence, Change (x+ 5) to (x-5).
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8. Find the measure of E in the trapezoid.
The measure of x = 5, in the given diagram of a trapezoid.
What is trapezoid?A trapezoid is a four-sided shape with one parallel pair of sides. It is essentially a two-dimensional shape or figure similar to a square, rectangle, or parallelogram. As a result, this shape, like other shapes, has a perimeter and an area.
When two parallel lines are intersected by a transversal, the pair of interior angles on the same side of the transversal are supplementary.
Therefore, ∠D + ∠E = 180°
17x - 10 + 21x = 180°
38x − 10 = 180°
38x = 180° + 10
38x = 190
x = 190/38
x = 5
Thus, The measure of x = 5, in the given diagram of a trapezoid.
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