Triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4). Determine the translation direction and number of units of the image of triangle JKL if vertex J′ is at (−3, −5).
4 units down
4 units up
2 units to the right
2 units to the left
A triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4) and J′ at (−3, −5). The translation direction is 2 units to the left. The number of units of the image of triangle JKL is 2 units to the left only.
Given that a triangle JKL has vertices at J(−1, −5), K(−2, −2), and L(2, −4) and J′ at (−3, −5). We have to determine the translation direction and the number of units of the image of triangle JKL. Let's first find the translation direction to determine the image of triangle JKL.
Seeing the position of J and J', we can determine that the translation was made in the left direction because J has moved from the point (-1,-5) to (-3,-5). Thus, the translation direction is 2 units to the left. Now, let's calculate the number of units of the image of triangle JKL.
Let's draw a rough sketch of the triangle JKL and locate its vertices J(-1,-5), K(-2,-2), and L(2,-4).To find the number of units of the image of triangle JKL, we need to find the horizontal and vertical distances between the vertices of the original triangle and its image.
We can use the horizontal distance between J and J′ as a reference to calculate the remaining distances. J has moved 2 units to the left, so the horizontal distance between J and J′ is 2. Now, let's calculate the vertical distance between J and J′. The coordinates of J and J′ are (-1,-5) and (-3,-5), respectively.
The difference between the y-coordinates of J and J′ is 0, which means that J and J′ are on the same horizontal line. Therefore, the vertical distance between J and J′ is 0. Hence, the image of the triangle JKL has moved 2 units to the left and 0 units vertically. Thus, the number of units of the image of triangle JKL is 2 units to the left only.
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How does the graph of g(x) = - 1/x compare to the graph of f(x) = 1/x?
Answer:
The answer is B) g(x) is shift 5 units to the right and 2 units up from f(x).
Step-by-step explanation:
The equation that is given in this item can be written for clarity as follows:
g(x) = 1/(x - 5) + 2
It can be seen that the x-component is subtracted with 5 and the g(x) which would lie in the y-axis is added with two. This suggests that the graph of this equation is shifted to the right by 5 units and upwards by 2 units compared to the graph of the parent function.
The Graph for both function is attached below.
What is Translation?A translation in mathematics does not turn a shape; instead, it moves it left, right, up, or down. They are congruent if the translated shapes (or the image) seem to be the same size as the original shapes. They have only changed their direction or directions.
Given:
g(x) = - 1/x
and, f(x) = 1/x
The Graph shown below.
From the Graph we can see that the graph of g(x)= -1/x and f(x)= 1/x
shows the same graph but the position is changed in opposite of each other.
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Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $10,400 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,400.
Required:
a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
b. Suppose you bid $14,000. What is the probability that your bid will be accepted (to 2 decimals)?
c. What amount should you bid to maximize the probability that you get the property (in dollars)?
Answer:
a) 0.32 = 32% probability that your bid will be accepted
b) 0.72 = 72% probability that your bid will be accepted
c) An amount in excess of $15,400.
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The probability that we find a value X lower than x is given by the following formula.
\(P(X \leq x) = \frac{x - a}{b-a}\)
Assume that the competitor's bid x is a random variable that is uniformly distributed between $10,400 and $15,400.
This means that \(a = 10400, b = 15400\)
a. Suppose you bid $12,000. What is the probability that your bid will be accepted (to 2 decimals)?
You will win if the competitor bids less than 12000. So
\(P(X \leq 12000) = \frac{12000 - 10400}{15400 - 10400} = 0.32\)
0.32 = 32% probability that your bid will be accepted
b. Suppose you bid $14,000. What is the probability that your bid will be accepted?
You will win if the competitor bids less than 14000. So
\(P(X \leq 14000) = \frac{14000 - 10400}{15400 - 10400} = 0.72\)
0.72 = 72% probability that your bid will be accepted
c. What amount should you bid to maximize the probability that you get the property (in dollars)?
His bid is uniformly distributed between $10,400 and $15,400.
So, to maximize the probability that you get the property, you should bid an amount in excess of $15,400.
inequalities of x + 9 < 12 I need help solving this
What is the value of the expression when a = 5 and b = 2?
2a+b−3
A. 6
B. 9
C. 11
D. 24
9
Step-by-step explanation:Hi there !
2a + b - 3 =
replace a = 5 ; b = 2
= 2(5) + 2 - 3
= 10 + 2 - 3
= 12 - 3
= 9
Good luck !
Answer: 9
2a and b - 3 = ?
a = 5 ; b = 2
2(5/a) + 2/b - 3
Now we solve this.
10 + 2/b - 3
Subtract 3.
12 - 3
The answer is 9.
what is the equation of the line that is paralle to y=3x-8 and passes thur the point (4,-5)
⊰_________________________________________________________⊱
Answer:
The equation is-: y=3xStep-by-step explanation:
\(\large\displaystyle\text{$\begin{gathered} \sf{Substitute \ the \ values \ into \ the \ formula \ y-y_1=m(x-x_1)} \\ \sf {parallel \ lines \ have \ same \ slopes, \ thus} \\ \sf{slope \ of \ the \ 2nd \ line = 3}\\ \sf{now \ substitute \ the \ values} \\ \sf {y-(-5)=3(x-4)}\\ \sf{y+5=3(x-4) (It's \ Point-Slope\;Form, \ see \ below \ for \ slope-intercept)}\\ \sf {y+5=3x-12} \\ \sf{y=3x-12-5} \\ \sf{y-3x-17} \end{gathered}$}}\)
\(\pmb{\tt{done \ !!}}\)
⊱_________________________________________________________⊰
Find the distance around each figure. Use 3.14 as an approximation for π(pie)
30. The figure is made up of a rectangle and two identical semicircles.
Answer:
Step-by-step explanation:
I need help where do I plot the point help asap please
Answer:
Plot the point at the minimum of the graph.
Step-by-step explanation:
If you keep moving the graph down, pick the point with the lowest y value that is still on the blue.
Martin is two years younger than three times his daughter Ada’s age. The sum of their ages is 54. If Ada’s age is given by a, then which equation below fully models in the information given in this problem?
Answer:
Martin is 40 and Ada is 14Step-by-step explanation:
Martin's age = mAda's age = aMartin is two years younger than three times his daughter Ada’s age:
m = 3a - 2The sum of their ages is 54:
m + a = 54Solving this equation for m:
m = 54 - aEliminate m:
3a - 2 = 54 - aSolve for a:
3a + a = 54 + 24a = 56a = 56/4a = 14Find m:
m = 54 - 14 = 40Martin is 40 and Ada is 14
What rectangle described has the same perimeter as this shape but different area
The formula for calculating the perimeter of a rectangle is
perimeter = 2(length + width)
Perimeter of the given rectangle = 2(15 + 5) = 40
Area = 5 x 15 = 75
Looking at the given options,
A) Perimeter = 2(11 + 7) = 36
Area = 11 x 7 = 77
B) Perimeter = 2(11 + 9) = 40
Area = 11 x 9 = 99
Thus, the correct option is B
Which of the following equations represents a linear function?
2x − 4 = 6
x = −2
y equals one half times x squared
y equals two thirds times x plus 4
Answer:
y equals 2/3 x plus 4 is correct.
The equation y= 1/3x + 4 represents a linear function.
What is Linear Equation?A linear function is a function that can be represented by a straight line. The equation of a linear function is typically in the form y = mx + b, where m represents the slope and b represents the y-intercept.
1. 2x − 4 = 6 is a linear equation, but it is not a function because it does not isolate y.
2. x = −2" represents a vertical line with a slope of infinity, but it does not have the form y = mx + b.
3. y = 1/2x² represents a quadratic function because it contains x raised to the power of 2.
4. y= 1/3x + 4 represents a linear function.
Therefore, the equation y= 1/3x + 4 represents a linear function.
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Explain why multiplying by 8/3 gives the same result as first multiplying by 8 and then multiplying by 1/3
The outcome of multiplying by 8/3 is the same as multiplying with 8 and then by 1/3.
Explain multiplication of fraction?The two fractions that want to multiply come first when multiplying fractions.
You multiply both denominators (the lower numbers) by the sum of the numerators (this same top numbers). Finding the sum of two or maybe more fractions is known as multiplying fractions. When multiplying fractions, a different approach is taken than when adding and subtracting fractions.For the stated number.
The number given is 8/3.
Other set of numbers are-
Multiplying 1/3 with 8.
= 1/3*8
= (1*8)/3
= 8/3, which is equal to the stated number.
Thus, the outcome of multiplying by 8/3 is the same as multiplying with 8 and then by 1/3.
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You roll a die 2 times. What is the probability or rolling a 6 and then a 2?
Answer:
1 out of 6
Step-by-step explanation:
Each roll of the die is an independent event. This means that the second roll does not rely on the first roll. The probability of rolling a six is one out of six. The probability of rolling a two is also one out of six. Since the two events are independent of each other, you would take the average of the two probabilities, which since they are both one out of six, the probability of rolling a six and then a two is one out of six.
Please help on both!!!!!
Answer:
\(14\pi\) and \(16\pi\)
Step-by-step explanation:
The equation for the circumference of circles is either \(d\pi\) or \(2r\pi\), with r being the radius and d being the diameter.
Question A
The diameter is stated as 14. Plug into the equation to get:
\(14\pi\)
This is your answer in exact form.
Question B
The radius is stated as 8. Plug into the equation to get:
\(2(8)\pi\)
\(16\pi\)
This is your answer in exact form.
Answer:
1) 43.98
2) 50.27
Step-by-step explanation:
I hope this helps!
Write 3 expressions containing exponents so that each expression equals 81
Answer:
9x9= 81
3x3x3x3=81
81 to the first power.
Step-by-step explanation:
I hope this helps in any way:)
Select a personal or professional example of a measurement you use routinely. Convert the measurement either from U.S customary units to metric units, or from metric units to U.S. customary units. You may choose more than one measurement and may choose among weight, length, temperature, etc. Show each step of your conversion and be sure to include all units from the original and converted measurements (for example, yards to meters, degrees Celsius to degrees Fahrenheit).
A personal example of a measurement I use routinely is converting weight from U.S. customary units to metric units. Let's convert pounds to kilograms.
To convert pounds to kilograms, we use the conversion factor of 1 pound = 0.453592 kilograms.
For example, if I have a weight of 150 pounds, I can calculate the equivalent weight in kilograms as follows:
150 pounds * 0.453592 kilograms/pound = 68.0388 kilograms
Therefore, 150 pounds is approximately equal to 68.0388 kilograms.
In this conversion, we multiply the weight in pounds by the conversion factor to obtain the weight in kilograms. By using the appropriate conversion factor, we can accurately convert weights from U.S. customary units to metric units.
It's important to note that conversion factors may vary slightly depending on the rounding used and the exact value of the conversion factor.
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30 points I need an answer asap please
Answer:
D. 0.05
Step-by-step explanation:
5 x 10 = 50
50 as a decimal
0.5
Hope it helps!!!Brainliest pls!!!Two cars leave town at the same time going in the same direction on the same road.One travels 32 mi/h and the other travels 47 mi/h.In how many hours will they be 69 miles apart?
Yes i know there are already answered questions but i need like an answer with a graph and then the work under the graph . Please help , you can earn 30 points from me .
Thanks
4 hours and about 23-30m
Answer:
4.6 hours
Step-by-step explanation:
i will send a picture of my graph and work to you directly, check your brainly inbox (it may take me a few minutes to get logged in on my phone)
How would you express 42 + 36 using the GCF and the distributive property
Teresa started to run on a treadmill after setting its timer for 78 minutes. The display says that she has finished 57% of her run. How many minutes have gone by? Round your answer to the nearest tenth
The nearest tenth, 44.5 minutes have gοne by.
What is time?Time is the οngοing prοgressiοn οf existence and events that take place in what appears tο be an irreversible οrder frοm the past thrοugh the present tο the future. It is οne οf the quantities that make up variοus measurements that are used tο cοmpare the lengths οf events οr the gaps between them, tο cοmpare hοw lοng they last, tο οrder events, and tο measure hοw quickly certain quantities in the physical wοrld οr in cοnsciοus experience change. The fοurth dimensiοn, in additiοn tο the three spatial dimensiοns, is frequently referred tο as time.
If Teresa has finished 57% οf her run, then she has 43% left tο cοmplete.
Let x be the number οf minutes that have gοne by.
Since 57% οf the run is cοmpleted in 78 minutes, we can set up the fοllοwing prοpοrtiοn:
57/100 = x/78
Sοlving fοr x, we get:
x = (57/100) * 78
x = 44.46
Therefοre, tο the nearest tenth, 44.5 minutes have gοne by.
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if 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is _.
Answer: If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate 7-i5.
Step-by-step explanation:
We know that when a complex number \(z=a+ib\) is a root of a polynomial with degree 'n' , then the conjugate of the complex number (\(\overline{z}=a-ib\)) is also a root of the same polynomial.Given: 7+5i is a zero of a polynomial function of degree 5 with coefficients
Here, 7+5i is a complex number.
So, it conjugate (\(\overline{7+5i}=7-5i\)) is also a zero of a polynomial function.
Hence, if 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate 7-i5.
If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate which is 7 - 5i
The standard form of writing complex numbers with real and imaginary values is expressed as:
z = x + iy
The conjugate of the complex number will be y = x - iy
A complex number and its conjugate both have the same degree with coefficient.Given the polynomial 7 + 5i. If 7+5i is a zero of a polynomial function of degree 5 with coefficients, then so is its conjugate which is 7 - 5i
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Nathaniel would like to establish a trust fund that will provide R380 000 a year, forever, for his descendants. The trust fund will be invested very conservatively, so the expected rate of return is only 6,45%. How much money must he deposit today, to fund this gift for his descendants?
Answer:
Step-by-step explanation:
To calculate the amount of money Nathaniel needs to deposit today to fund this gift for his descendants, we can use the present value formula for a perpetuity:
Present Value = Annual Payment / Discount Rate
In this case, the annual payment is R380 000 and the discount rate (expected rate of return) is 6.45% in decimals, or 0.0645 as a fraction. So we can plug these values into the formula:
Present Value = R380 000 / 0.0645
This gives us a present value of approximately R5,899,225.68. Therefore, Nathaniel would need to deposit R5,899,225.68 today into the trust fund to provide R380 000 a year forever for his descendants, assuming a 6.45% expected rate of return.
find the missing angle
Answer:
? = 77°
Step-by-step explanation:
the 3 angles in a triangle sum to 180° , that is
? + 35° + 68° = 180°
? + 103° = 180° ( subtract 103° from both sides )
? = 77°
Answer:77
Step-by-step explanation:
180-103=77
Triangle ABC is similar to triangle DEF. what is the length of AC?
Help quick please look at pic to solve
The required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.
Given the diagram of the hanger which one side has 10 + 5x and other side has 11.
To find the equation, equate the expression of one side to the numerical value of the other side. On solving the equation gives the value of x.
Thus, the equation is 10 + 5x = 11.
Consider the equation 10 + 5x = 11
On subtracting 10 from each side gives,
5x = 1
Divide each side by 5 gives,
x = 1/5.
Hence, the required equation that represent the hanger is 10 + 5x = 11 and the value of x is 1/5.
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help me pls i needd this right now
What is the total surface area for the figure shown below?
11
8
17
14
10
pls help me guys and pls answer this correctly!
Answer:
Step-by-step explanation:
1) 1 7/9 = 9*1+7/9 = 16/9
2) 6 3/4 = 6*4+3/4 = 27/4
3) 11 1/5 = 11*5+1/5 = 56/5
4) 5 2/6 = 5*6+2/6 = 32/6
5) 10 3/7 = 10*7+3/7 = 73/7
Hope you understood!!
Change 9/3 to percentage
Answer:
300%
Step-by-step explanation:
because 9/3×100=900/3=300 so it is 300%
Answer:
300%
Step-by-step explanation:
9/3 * 100%
900%/3 = 300%
29.4.3 Quiz: Parabolas with Vertices at the Origin
Question 5 of 10
The equation below describes a parabola. If a is negative, which way does the
parabola open?
y=ax²2²
O A. Right
B. Down
OC. Up
OD. Left
SUBMIT
The equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. option B.
The equation y = ax² represents a parabola with its vertex at the origin. In this case, if the coefficient 'a' is negative, it determines the direction in which the parabola opens.
When 'a' is negative, the parabola opens downward. This means that the vertex, which is at the origin (0, 0), represents the highest point on the graph, and the parabola curves downward on both sides.
To understand this concept, let's consider the basic equation y = x², which represents a standard upward-opening parabola. As 'a' increases, the parabola becomes narrower. Conversely, when 'a' becomes negative, it flips the parabola upside down, resulting in a downward-opening parabola.
For example, if we have the equation y = -x², the negative coefficient causes the parabola to open downward. The vertex remains at the origin, but the shape of the parabola is now inverted.
In summary, when the equation of a parabola with its vertex at the origin includes a negative coefficient 'a', the parabola opens downward. This can be visually represented as a U-shape curving downward from the origin. So Optyion B is correct.
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