The set of parametric equations are
[tex]x=\sqrt{t}[/tex]
[tex]y=\sqrt{3+t[/tex]
Parametric Equations:A parametric equation uses a parameter, which is an independent variable (often represented by the notation t), and dependent variables, which are expressed as continuous functions of the parameter and are independent of other variables.
Using one or more independent variables known as parameters, a parametric equation defines a set of quantities as functions.
Given the equation:
[tex]x= \sqrt[]{y^{2}-3 }[/tex]
Let's find a set of parametric equation for the given equation given the parameter:
[tex]x = \sqrt{t}[/tex]
From the parameter:
[tex]x = \sqrt{t}[/tex]
Now, substitute [tex]\sqrt{t}[/tex] for x in the given equation:
[tex]x=\sqrt{y^2-3} \\\\\sqrt{t} = \sqrt{y^2 - 3} \\\\t=y^2-3\\\\y^2=3+t\\\\y=\sqrt{3+t}[/tex]
Therefore, the set of parametric equations is:
• [tex]x=\sqrt{t}[/tex]
• [tex]y=\sqrt{3+t}[/tex]
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How does deforestation increase the warming of Earth?
A. It releases more oxygen into the atmosphere.
B. It increases the presence of methane in the atmosphere.
C. It decreases the removal of carbon dioxide from the atmosphere.
D. It decreases the production of ozone in the atmosphere.
Answer:
C. it decreases the removal of carbon dioxide from the atmosphere
Answer:
Step-by-step explanation:
it decreases the production of ozone in the atmosphere
What type of triangle is this triangle?
obtuse scalene
obtuse isosceles
acute scalene
acute isosceles
Answer: obtuse scalene triangle
Step-by-step explanation:
A scalene triangle has three different sides.
An isosceles triangle has 2 of the same sides and 1 different side.
Answer:
Its a obtuse scalene triangle!
A stereo that regularly sells for $330 is on sale at 15% off. How much will a customer save on the stereo during the sale?
Answer: 49.5 dollars
Step-by-step explanation: the original price is 330, but the sale takes 15 percent off
so we turn 15% into a decimal so we can multiply 330 and 15%
we get 0.15 × 330 = 49.5
Leon is standing 67 feet from a telephone pole. As he looks up, a red-tailed hawk lands on the top of the
pole. Leon's angle of sight up to the bird is 24° and his eyes are 5.1 feet above the ground. How fall is th
pole?
The pole is 34.93 feet tall. The solution has been obtained by using trigonometry.
What is trigonometry?
Trigonometry is the branch of mathematics that focuses on the study of the sides, angles, and connections of the right-angle triangle.
We are given that Leon is standing 67 feet from a telephone pole. Leon's angle of sight up to the bird is 24° and his eyes are 5.1 feet above the ground.
From this, a figure is obtained which is attached below.
Using trigonometry,
We know that tan theta = opposite side/ adjacent side
So,
⇒tan θ = x/67
Here, θ = 24°
So,
⇒tan 24° = x/67
⇒x = 67 tan 24°
⇒x = 67 * 0.4452
⇒x ≈ 29.83
The height of the pole = 29.83 + 5.1 = 34.93 feet
Hence, the pole is 34.93 feet tall.
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the mean of the sample group of answer choices is always smaller than the mean of the population from which the sample was taken can never be zero none of these alternatives is correct. can never be negative
The mean of a sample is the average of all values in the sample. The mean of a sample is generally always smaller than the mean of the population from which the sample was taken, since the sample is only a small subset of the population.
The mean of a sample can never be zero or negative, since it is an average of all the values in the sample. The mean of a sample can also never be greater than the mean of the population. None of these alternatives is correct.
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How does the quantity of shares you own impact your dollar gains and losses?
how does the length of time you hold the shares impact your rate of return?
How does the quantity of shares you own impact your rate of return?
The quantity of shares you own can impact your dollar gains and losses, but not your rate of return. The length of time you hold the shares can have a significant impact on your rate of return, with longer holding periods generally leading to higher returns.
Investing in stocks can be a great way to earn money, but it's important to understand how your investments can impact your gains and losses. Two key factors that can impact your returns are the quantity of shares you own and the length of time you hold the shares. In this article, we'll explore how these factors can affect your rate of return.
Impact of Quantity of Shares:The quantity of shares you own can have a direct impact on your dollar gains and losses. When the stock price goes up, the value of your shares also increases. Similarly, when the stock price goes down, the value of your shares also decreases. If you own more shares, the dollar amount of your gains and losses will be greater.
But, how does the quantity of shares impact your rate of return? Rate of return is the percentage change in the value of your investment over a certain period of time. It takes into account the gains and losses as well as the length of time you held the investment.
Impact of Length of Time:The length of time you hold the shares can have a significant impact on your rate of return. Generally, the longer you hold the shares, the higher your rate of return will be. This is because the stock market tends to go up over time, and the longer you hold the shares, the more time you have to benefit from this growth.
Impact of Quantity and Time on Rate of Return:So, how does the quantity of shares you own impact your rate of return? As we mentioned earlier, the rate of return is only impacted by the percentage change in the stock price, not the quantity of shares. However, owning more shares can provide you with a higher dollar amount of gains, which can lead to a higher rate of return.
Additionally, the longer you hold the shares, the higher your rate of return will be. This means that if you own more shares and hold them for a longer period of time, you can potentially earn a higher rate of return.
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In a simple linear regression model we use the normal quantile plot of the residuals to evaluate if it is reasonable to assume the _____ come from a normal distribution.
a. Response Variable
b. Explanatory Variable
c. Observations
d. Errors
To determine whether the errors from the linear regression model are from a normal distribution, examine the normal quantile plot of the residuals.
Calculating the regression equation is the first step in a straightforward linear regression model. The link between the explanatory variable (x) and the response variable is modelled using this equation (y). A linear function of the explanatory variable, an intercept term, and an error term make up the regression equation. The errors or residuals (e), which indicate the difference between the observed and expected values of the response variable, are calculated as the following step. To evaluate the regression model's accuracy, the residuals are crucial. The residuals are then plotted using a normal quantile to see whether it is acceptable to believe that the errors are derived from a normal distribution. Because linear regression models presume that the errors are regularly distributed, this is significant. The residuals' normal quantile plot shows the distribution of the mistakes graphically, making it simpler to determine whether the errors follow a normal distribution. The linear regression model might not be the optimal one to employ if the errors do not follow a normal distribution.
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help pls! i don’t as much need the answer but to know how to do it?
Step-by-step explanation:
an inscribed angle has its vertex on the circle, and the sides of the angle are two chords of the circle.
the inscribed angle is half the size of the arc angle (the angle at the center of the circle) of the arc that the two sides cut out of the circle.
110° is the arc angle (at the center of the circle) of the arc GJ.
for the inscribed angle GFJ the vertex is F, and the angle there is half of the arc angle :
angle GFJ = 110/2 = 55°
the second problem is the opposite "direction".
we have the inscribed angle FJH = 36°.
and we want the arc angle FH.
now, since the inscribed angle is half of the arc angle, the arc angle is twice the inscribed angle :
arc angle FH = 36×2 = 72°
4. Suppose the account in 3 above paid interest quarterly instead of annually. Find the
account balance after 5 years
The account's balance after 5 years is given as follows:
[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]
In which:
P is the principal.r is the interest rate.What is compound interest?The amount of money earned, in compound interest, after t years, is given by:
[tex]A(t) = P\left(1 + \frac{r}{n}\right)^{nt}[/tex]
In which:
P is the principal, which is the value of deposit/loan/....r is the interest rate, as a decimal value.n is the number of times that interest is compounded per year, annually n = 1, semi-annually n = 2, quarterly n = 4, monthly n = 12.
Quarterly compounding means that the value of n is given as follows:
n = 4.
Then the balance of the account after 5 years, when t = 5, is given as follow:
[tex]A(5) = P\left(1 + \frac{r}{4}\right)^{20}[/tex]
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1. You need to dig a tunnel. You begin at the surface of the ground. The tunnel slopes downward for 83 meters. The final depth below ground is 52 meters. Find the angle of depression of the tunnel's descent. Round your answer to the nearest tenth. Draw a diagram to illustrate your problem.
Answer: 38.8°
Step-by-step explanation:
See the attached diagram:
From it we can tell that the tunnel forms a right triangle, with the length of a leg and the hypotenuse given. We can use the sine function to easily answer this, (letting θ be the angle we need to find)
sinθ = 52/83
.: θ = arcsin(52/83)
(Note: arcsin is the inverse of the sine function)
.: θ ≅ 38.8°
A 90° rotation around the origin followed by a reflection across the line x = 3 maps △JKL, with coordinates J(–2, 2), K(–2, 6), and L(–8, 2), to △PQR. Find the area of △PQR.
The area of the triangle PQR is 12 square units
How to determine the area of PQRFrom the question, we have the following parameters that can be used in our computation:
J(–2, 2), K(–2, 6), and L(–8, 2),
Reflection and rotation are rigid transformation
This means that
Area of PQR = Area of JKL
So, we have
Area = 1/2 * |x1y2 - x2y1 + x2y3 - x3y2 + x3y1 - x1y3|
So, we have
Area = 1/2 * |-2 * 6 + 2 * 2 + -2 * 2 + 8 * 6 - 8 * 2 + 2 * 2|
Evaluate
Area = 1/2 * |24|
So, we have
Area = 12
Hence, the area is 12 square units
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A vector with magnitude 7 points in a direction 10 degrees counterclockwise from the positive x axis.
Write the vector in component form.
Vector
Give each value accurate to at least 1 decimal place
The vector in component form is given as follows:
v = (6.9, 1.2).
How to write the vector in component form?Considering a vector with a magnitude of M and an angle of x, the component form notation for the vector is given as follows:
v = (Mcos(x), Msin(x)).
The parameters for this problem are given as follows:
M = 7.x = 10º.Hence the components are given as follows:
7 x cosine of 10 degrees = 6.9.7 x sine of 10 degrees = 1.2.Hence the vector is of:
v = (6.9, 1.2).
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The slope of a staircase is 0. 95 if it rises 210 what is the run?
If the slope of a staircase is 0. 95 and rises with 210, then the run is:
221.05 units.
In this problem, we can use the formula for the slope of a staircase, which is given by:
slope = rise / runwhere "rise" is the vertical height of the staircase and "run" is the horizontal distance of the staircase.
We are given the slope of the staircase as 0.95 and the rise as 210. We can substitute these values in the formula and solve for the run:
0.95 = 210 / runMultiplying both sides by run, we get:
0.95 * run = 210Dividing both sides by 0.95, we get:
run = 210 / 0.95Simplifying the expression, we get:
run = 221.05 (rounded to two decimal places)Therefore, the run of the staircase is approximately 221.05 units.
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a system if equations y=x-6 and y=-x-2 grap the sytsem then write the solution you can also awnser no soloution or infinite solutions.
the solution is where they intercept; (2,-4)
A survey was conducted among some people. The survey showed 120 like to listen radio, 80 don't like to listen radio. If 50 people like to listen radio but not like to watch television and 110 don't like to watch television then C. Find the total number of people who took part in the survey. b. Find the number of people who like to watch television only. a. Illustrate the information in a venn-diagram.
Answer:
a) See the attachment for the completed Venn diagram.
b) The number of people who liked to watch television only is 20.
c) The total number of people who took part in the survey was 200.
Step-by-step explanation:
Draw a Venn diagram with two overlapping circles.
Label one circle "Radio" and the other circle "TV".
Given that 50 people like to listen to the radio but not like to watch television, place the number 50 in the part of the radio circle that does not overlap the TV circle.
Given that 120 people like to listen to the radio, and 50 people like to listen to the radio but not like to watch television, then the number of people who like to listen to the radio and watch tv is:
Radio & TV = 120 - 50 = 70Therefore, place the number 70 in the part where the two circles overlap.
Given that 110 people don't like to watch television, and 50 people like to listen to the radio but not like to watch television, then the number of people who don't like to listen to the radio or watch television is:
Neither radio or TV = 110 - 50 = 60Therefore, place the number 60 in the area outside the two circles.
Given that 80 people don't like to listen to the radio, and 60 people don't like to listen to the radio or watch television, then the number of people who like to watch the television only is:
TV only = 80 - 60 = 20Therefore, place the number 20 in the part of the TV circle that does not overlap the radio circle.
Now the Venn diagram has been completed, we can find the total number of people who took part in the survey by adding all the numbers in the Venn diagram:
Total number of people = 50 + 70 + 20 + 60 = 200Therefore, there was a total of 200 people who took part in the survey.
Helppp i need to find the transformations needed.
The transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.
What is a transformation?A transformation is a general term for four specific ways to manipulate the shape and/or position of a point, a line, or geometric figure. The original shape of the object is called the Pre-Image and the final shape and position of the object is the Image under the transformation.
The given functions are f(x)=x³ and g(x)= -(x-4)³+1.
To find the transformation, compare the function to the parent function and check to see if there is a horizontal or vertical shift, reflection about the x-axis or y-axis, and if there is a vertical stretch.
Horizontal Shift: Right 4 Units
Vertical Shift: Up 1 Units
Reflection about the x-axis: None
Reflection about the y-axis: Reflected
Vertical Compression or Stretch: None
Therefore, the transformations from the function f(x) to g(x) is horizontal shift: Right 4 Units and vertical shift: Up 1 Units.
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An art teacher is making packages
a. The greatest number of packages the teacher can make using all the paintbrushes and paint is 8
b. The number of paintbrushes in each package would be 3 and the number of tubes of paints would be 5
How do we determine the number of packages?In order to determine the greatest number of packages the teacher can make using all the paintbrushes and paint, we have to determine the highest common factor of the number of brushes and the number of tubes of paint
Highest common factor is the highest factor that is common to two or more numbers:
Factors of 24 = 1,2,3,4,6,8,12 and 24
Factors of 40 = 1, 2, 4, 5, 8, 10, 20 and 40.
Common factors of 24 and 40 = 1, 2, 4, 8
Therefore, the highest common factor is 8.
The number of paintbrushes in each package:
= Number of brushes / number of package
= 24/8
= 3 brushes
The number of tubes of paint:
= number of tubes of paints / number of package
= 40 / 8
= 5 tubes of paints
Full question "An art teacher is making packages of paint brushes and paint for his. He has 24 brushes and 40 tubes of paint. Each package will have the same number An art teacher is making packages of paintbrushes and paint for his students. of brushes and the same number of tubes of paint. Part a. What is the greatest number of packages that the art teacher can make using all the paintbrushes and paint? Show your work Part b. How many paintbrushes and tubes of paint are in each package?".
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A boat heading out to sea starts out at Point A, at a horizontal distance of 724 feet from a lighthouse/the shore. From that point, the boat’s crew measures the angle of elevation to the lighthouse’s beacon-light from that point to be 16 ∘ . At some later time, the crew measures the angle of elevation from point B to be 5 ∘ . Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
The distance from point A to point B is 1496 ft.
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.
Given that, a boat is at point A which at 724 ft distance from a lighthouse making an angle of elevation to the lighthouse’s beacon-light of 16°, when moved to some distance B making an angle of elevation to the lighthouse’s beacon-light of 5°, we need to find the distance from point A to point B.
Refer to the figure attached,
The whole scene is creating two right triangles, rt Δ CDA and rt Δ CDB
Using the trigonometric functions, in rt Δ CDA,
We have,
tan 16° = CD/DA
CD = tan 16° × 724
CD = 207.6
Therefore, the height of the lighthouse is 207.6 ft
Now,
tan 5° = CD/DB
DB = CD / tan 5°
DB = 2373
The distance between A and B = DB-DA = 2373 - 724 = 1496
Hence, the distance from point A to point B is 1496 ft.
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What would be the answer?
a) Sin2θ = 22/20 = 11/10
b) cos 2θ = 2(17/20) = 17/10
c)tan 2θ = 2(11/17) = 22/17
What are the trigonometric ratios?The trigonometric ratios are six functions that relate the angles of a right triangle to the lengths of its sides. The six trigonometric ratios are: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot).
Sine (sin): The sine of an angle is the ratio of the length of the side opposite the angle to the length of the hypotenuse.
Cosine (cos): The cosine of an angle is the ratio of the length of the adjacent side to the length of the hypotenuse.
Tangent (tan): The tangent of an angle is the ratio of the length of the side opposite the angle to the length of the adjacent side.
If sin θ = 11/20
The missing side of the triangle is;
b = √20^ - 11^2
b = 17
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when a new baby is born to the johnsons the family decides to invest $5000 in an account that earns 7% interest
The amount in the college fund is $16,899.66
How to determine the amount in the college fund?In order to determine the amount in the college fund, we need to find the future value of the money.
The formula for the future value of money is:
FV = PV * (1 + r)^t
where:
FV = future value
PV = present value (initial amount)
r = interest rate (as a decimal)
t = time (in years)
PV = $5000, r = 7% = 0.07, t = 18
FV = PV * (1 + r)^t
FV = 5000 * (1 + 0.07)¹⁸
FV = 5000 * (1.07)¹⁸
FV = $16,899.66
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Complete Question
When a new baby is born to the Johnsons, the family decides to invest $5000 in an account that earns 7% interest as a way to start the baby's college fund. If they do not touch that investment for 18 years, how much will there be in the college fund?
Jayla’s parents are replacing their bathroom floor with square tiles. The tiles will be laid side by side to cover the entire bathroom with no gaps, and none of the tiles can be cut. The floor is a rectangle that is `48` inches by `60` inches. What is the side length of the largest possible tile they could use?
The largest possible side length of the tiles that can be used is `12` inches as it can cover the entire bathroom without any gaps or cutting of tiles.
The largest tile that can be used is a square tile. To calculate the side length of the largest possible tile, divide the length and width of the bathroom by 4.
`48/4 = 12`
`60/4 = 15`
The largest possible side length of the tiles that can be used is `12` inches. Jayla's parents are replacing their bathroom floor with square tiles. The floor is a rectangle that is `48` inches by `60` inches. To cover the entire bathroom with no gaps, and without having to cut any of the tiles, they need to use a tile that is the same size as the largest possible tile that can cover the entire floor without any gaps.
To calculate the side length of the largest possible tile, divide the length and width of the bathroom by 4. This is because a tile needs to cover 4 sides of the floor without any gaps, so the side length of the tile needs to be equal to the length divided by 4, or the width divided by 4.
In this case, the side length of the largest possible tile is `12` inches. This is because `48/4 = 12`, and `60/4 = 15`. As `15` is larger than `12`, the side length of the largest possible tile is `12` inches. This means that the tiles need to be `12` inches by `12` inches in size to cover the entire bathroom without any gaps.
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While racking a circuit breaker in energized gear, what means could be used to reduce the arc flash hazard to 0 incident energy exposure to a worker?
The only way to completely eliminate the risk of arc flash is to de-energize the equipment before performing any maintenance or testing.
Racking a circuit breaker in energized gear poses a significant arc flash hazard to workers due to the potential for electrical energy to be released and cause an arc flash.
If it is not possible to de-energize the equipment, the following means could be used to reduce the arc flash hazard to 0 incident energy exposure to a worker:
Use remote racking: Remote racking systems allow workers to rack circuit breakers from a safe distance, reducing the risk of exposure to the arc flash hazard.Wear personal protective equipment (PPE): Workers should wear appropriate PPE.Implement an energy control program: An energy control program should be in place to ensure that workers are properly trained.Use a remote video camera: A remote video camera can be used to monitor the racking process from a safe distance, allowing workers to rack circuit breakers without being in the line of fire.Learn more about circuit breaker here:
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4. Triangle WXY with vertices W(-4, 8),
X(10, 0), and Y(-2, -8): k = 1
itblib
Slot
blib
brit d
W': C
X': (85
Y':
piqot
OM
The dilated points are:
W': (-1, 2)
X': (2.5, 0)
Y': (-0.5, -2).
What is dilation?Resizing an item uses a transformation called dilation. Dilation is used to enlarge or shorten the structures. The result of this transformation is an image with the same shape as the original. However, there is a variation in the shape's size. The initial form should be stretched or contracted during dilatation.
Given:
Triangle WXY with vertices W(-4, 8), X (10, 0), and Y(-2, -8).
And the scale factor is 1/4.
So, the image points are,
W': (-4/4, 8/4) = (-1, 2)
X': (10/4, 0/4) = (2.5, 0)
Y': (-2/4, -8/4) = (-0.5, -2)
Hence, the image points are given above.
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2/5 of a gal used 1/4 for coffee. How much milk in cups
The cups of milk required for the ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee is given by 2.4 cups.
Here,
( 2 / 5 ) of a gallons is equal to 0.4 gallons.
( 1 / 4 ) of gallons used for coffee that is equal to 0.25 gallons.
Total gallons left after coffee is equal to
= ( 0.4 ) - ( 0.25 )
= ( 0.15 )gallons
Conversion of gallons to cups is given by :
1 gallon = 16 cups
⇒ ( 0.15 )gallons = 0.15 × 16 cups
⇒ ( 0.15 )gallons = 2.4 cups of milk used.
Therefore, the 2.4 cups of milk is used when ( 2 / 5 ) of a gallons used ( 1 / 4 ) for a coffee.
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Marcia's cost, in dollars, to wash her car can be calculated using the expression below,
where m represents the number of minutes the car wash will run.
0.25m +1.50
Evaluate the expression for m = 20, and interpret the meaning of the result.
When m is 20 the value of expression is 6.5. The value 6.5 represent the cost which marcia has to pay for car wash for 20 mins.
What is Expression?An expression is combination of variables, numbers and operators.
Given that Marcia's cost, in dollars, to wash her car can be calculated using the expression
0.25m +1.50
Zero point two five plus one point five.
In the expression m represents the number of minutes the car wash will run.
We need to find the value of expression when m is 20
0.25(20)+1.50
5+1.50
6.5
When m is 20 the value of expression is 6.5. The value 6.5 represent the cost which marcia has to pay for car wash for 20 mins.
Hence, Marcias cost $6.5 to wash her car for 20 minutes.
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Classify each pair of angles as Complementary, Supplementary, or Neither. Drag and drop the choices into the boxes to correctly complete the table. Each category may have any number of pair of angles. Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response.
Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
Complementary Supplementary Neither
Answer:
Complementary is 2 angles that add up to 90 degrees and supplementary is 2 angles that add up to 180 degrees
48+32=80 so that would be neither
101+77=178 so that would be neither
107+73=180 so that would be supplementary
Step-by-step explanation:
have a nice day.
Answer:
only here for points
Step-by-step explanation:
A standard deck of 52 playing cards contains 13 cards in each of four suits: diamonds, hearts, clubs, and spades. Two cards are chosen from the deck at random. What is the approximate probability of choosing one club and one heart?
0. 0588
0. 0637
0. 1176
0. 1275
The probability of getting one club and one heart is 0.127.
p= [tex]\frac{13*13*2*1}{52*51}[/tex]=0.1275
One of the areas of probability theory is the estimation of the chance of experiments occurring. Using a probability, we can calculate everything from the likelihood of getting heads or tails when flipping a coin to the likelihood of making a research error, for example. It is essential to appreciate the most basic definitions of this branch, such as the formula for computing probabilities in equiprobable sample spaces, the likelihood of two events joining together, the probability of the complementary event, etc., in order to properly understand it .Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. Mathematics has incorporated probability to forecast the likelihood of various events.
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the original price of shoe is 80$. They are on sale 25% off. The sales tax is 6.25%. How much will you pay for the shoes?
Answer: The total amount paid for shoes = $63.75
Step-by-step explanation:
The original price of the shoes = $ 80
Sale Discount = 25 %
So, the discount offered = 25 % of 80 = 20
So, the Discounted Price = Marked price - discount
= $ 80 -$ 20 = $ 60
Now, we need to calculate the sale tax of 6.25 % on $ 60.
Also, we know that Sales Tax = Sales Tax rate x Sale Price
= $ 60 x 0.0625 = $ 3.75
Total Cost = Sale Price + Sales Tax
= $ 60 + $ 3.75 = $63.75
Hence, the total amount paid for shoes = $63.75 included sales tax
Do anybody know this?
The proof for the congruence of triangles GHI and GFJ are given below.
What is Congruence of Triangles?Two or more triangles are said to be congruent if and only if sides and angles of one triangle is equal to the corresponding sides and angles of another triangle.
From the figure,
1) Line segment FJ ⊥ line segment FH (given)
2) ∠HGI = ∠FGJ (It is also given)
3) HI = FJ (Given). So HI ≅ FJ
4) HI ⊥ FH (given)
5) Since both the angles F and H are right angles,
∠F ≅ ∠H (since all right angles are congruent)
6) So we get that two angles and a non included side of ΔGHI are equal to the corresponding two angles and a non included side of ΔGFJ.
So by AAS congruence theorem, ΔGHI ≅ ΔGFJ.
Hence the given two triangles are congruent.
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WILL GIVE BRAINLIEST, PLEASE HURRY
Which transformations take the graph of f(x)=6x to the graph of g(x)=6x−4+2?
Choose each correct answer.
Responses
The graph is translated to the right 4 units.
The graph is translated up 2 units.
The graph is translated down 4 units.
The graph is translated to the right 2 units.
The graph is translated to the right 2 units. This is because the expression inside the function is now 6x - 4, which means the function has a horizontal shift to the right by 4/6 = 2/3 units.
What is Graph?
In mathematics, a graph is a collection of points, called vertices or nodes, and a collection of lines, called edges, that connect pairs of vertices. Graphs are used to represent relationships between objects, such as the connections between different parts of a network or the dependencies between different variables in a system. They are commonly used in fields such as computer science, operations research, and engineering to model and solve problems involving complex systems.
The correct transformations are:
The graph is translated to the right 2 units. This is because the expression inside the function is now 6x - 4, which means the function has a horizontal shift to the right by 4/6 = 2/3 units.
The graph is translated up 2 units. This is because there is a constant term of +2 added to the function, which means the function has a vertical shift upwards by 2 units.
Therefore, the correct answers are:
The graph is translated to the right 2 units.
The graph is translated up 2 units.
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