The slope of the tangent line to the graph y = x² - 4x + 8 at x = 3 is calculated as: 2.
How to Find the Slope of a Line Tangent to a Graph:To find the slope of the line tangent to the graph of y = x² - 4x + 8 at a given point x, we need to find the derivative of the function at that point.
The derivative of y = x² - 4x + 8 is:
y' = 2x - 4
To find the slope of the tangent line at a specific point x, we substitute x into the derivative expression:
slope = y'(x) = 2x - 4
For example, if we want to find the slope of the tangent line at x = 3, we substitute 3 into the derivative expression:
slope = y'(3) = 2(3) - 4 = 2
Learn more about slope of a line tangent to a graph on:
https://brainly.com/question/22744772
#SPJ1
Help!! Will give the amazing crown!!
Answer:
\( - \frac{58}{20} < - \sqrt{8} < \frac{17}{22} < 0.78\)
Step-by-step explanation:
There you go, have a good day
Please help I will give brainliest and a lot of points :)
The inequality shaded in the graph is given as follows:
y ≥ 5x/2 + 3.
How to define a linear function?The slope-intercept equation for a linear function is presented as follows:
y = mx + b
In which:
m is the slope.b is the intercept.The graph crosses the y-axis at y = -3, hence the intercept b is given as follows:
b = 3.
When x increases by 2, y increases by 5, hence the slope m is given as follows:
m = 5/2.
Then the equation of the line is given as follows:
y = 5x/2 + 3.
The line is a solid line, and values above it are plotted, hence the inequality is given as follows:
y ≥ 5x/2 + 3.
More can be learned about linear functions at https://brainly.com/question/15602982
#SPJ1
When testing a right-tailed hypothesis using a significance level of 0.025, a sample size of n=13, and with the population standard deviation unknown, what is the critical value? H0: u≥2 hours and H1:u<2 hours H0:u<2 hours and H1:u≥2 hours H0:u=2 hours and H1:u=2 hours H:u≤2 hours and H1:u>2 hours
The correct answer is a. H0: u≥2 hours and H1:u<2 hours. When testing a right-tailed hypothesis using a significance level of 0.025, a sample size of n=13, and with the population standard deviation unknown, the critical value is as follows:
To determine the critical value, we need to use the t-distribution since the population standard deviation is unknown.
Using a t-distribution table or calculator with 12 degrees of freedom (n-1), a one-tailed test, and a significance level of 0.025, the critical value is 2.1604.
If the test statistic is greater than or equal to this value, we can reject the null hypothesis in favor of the alternative hypothesis, which is a right-tailed hypothesis.
To learn more about right-tailed hypothesis, refer:-
https://brainly.com/question/17199362
#SPJ11
If 2x and (4x+30) are complementary angles. find the angles. Please answer it it's urgent.
Answer:
20 ,70
Step-by-step explanation:
Complementary angles sum up to 90
2x + 4x + 30 = 90
6x + 30 = 90
Subtract 30 from both sides
6x = 90 - 30
6x = 60
x = 60/6
x = 10
2x = 2*10 = 20
4x +30 = 4*10 +30 = 40 +30 = 70
Answer:
20 and 70
Step-by-step explanation:
2x + 4x + 30 =90
6x=90-30
6x=60
x=60/6x
x=10
so, 2x= 20 and 4x=40
20,70
Match each equation from Column I with the correct first step for solving it in Column II. Cube each side of the equation. Multiply each side of the equation by x(x + 5). Raise each side of the equation to the power UN Square each side of the equation. Let u = (x + 5) 1/3 and u? = (x+5)2/3 Drag each first step above to the corresponding equation below. Items may be used more than once. II 2x + 3 5 (a) + х X + 5 9 (b) VX + 5 = 9 (c) (x + 5) 5/2 = 32 2/3 1/3 (d) (x+5) - (x+5) -6= 0 (e) Vx(x+5) = -6
To match the equations in Column I with the correct first step for solving them in Column II, we need to identify the appropriate algebraic manipulation for each equation.
Equation (a) is 2x + 3 = 5. The correct first step for solving this equation is to subtract 3 from both sides to isolate the term with x, resulting in 2x = 2.
Equation (b) is √(x + 5) = 9. The correct first step for solving this equation is to square both sides of the equation, eliminating the square root, resulting in x + 5 = 81.
Equation (c) is (x + 5)^(5/2) = 32^(2/3). The correct first step for solving this equation is to raise both sides of the equation to the power 2/3, resulting in (x + 5)^(5/2)^(2/3) = 32.
Equation (d) is (x + 5)^(-6) = 0. The correct first step for solving this equation is to take the reciprocal of both sides, resulting in 1/(x + 5)^6 = 0.
Equation (e) is √(x(x + 5)) = -6. The correct first step for solving this equation is to square both sides of the equation, eliminating the square root, resulting in x(x + 5) = 36.
Matching the equations with their correct first steps:
(a) - Subtract 3 from both sides
(b) - Square both sides
(c) - Raise both sides to the power 2/3
(d) - Take the reciprocal of both sides
(e) - Square both sides
To learn more about algebraic manipulation click here :
brainly.com/question/12602543
#SPJ11
A worker has four different job offers, each with a contract for six years. Assuming the job descriptions are identical,
which offer will allow the worker to earn the most over six years?
O a starting salary of $49.000 with a 3% increase each year
O a starting salary of $51 000 with a 1% increase each year
O a starting salary of $48,000 with a 6% increase each year
a starting salary of $50,000 with a 2% increase each year
9514 1404 393
Answer:
$48,000 to start, with 6% raises
Step-by-step explanation:
The starting salaries are within a few percentage points of each other, so the majority of the difference in earnings will come because of the raises. The offer with the largest raise percentage is likely the best.
The earnings total can be figured as the sum of a geometric series with a first term of "starting salary" and a growth factor of (1+raise percentage). For starting salary 's' and raise percentage 'r', the total earnings in 6 years will be ...
S = s((1+r)^6 -1)/r
Here are the total earnings, in thousands, for each of the offers:
a) s = 49, r = .03, S = 316.95
b) s = 51, r = .01, S = 313.75
c) s = 48, r = .06, S = 334.82 . . . . best offer
d) s = 50, r = .02, S = 315.41
The worker can earn the most from a starting salary of $48,000 and 6% increases each year.
C) a starting salary of $48,000 with a 6% increase each year
Find the volume of the triangle
The volume of the pyramid will be 14 cubic meters.
The volume of the pyramid is defined as the space occupied by the triangular pyramid in three-dimensional space.
The volume of a pyramid is a measure of the amount of space it occupies and is defined as one-third the product of the area of the base and the height of the pyramid.
Calculate the area of the base of the pyramid,
Area = 1/2 x 4 x 3
Area = 6 square meters
Calculate the volume of the pyramid as
Volume = 1/3 x ( 6 x 7 )
Volume = 14 cubic meters
Therefore, the volume of the pyramid will be 14 cubic meters.
To know more about volume follow
https://brainly.com/question/30966073
#SPJ1
thank you for your help
The answer option that matches the graph I drew include the following: D. graph D.
What are the rules for writing an inequality?In Mathematics, the following rules are generally used for writing and interpreting an inequality or system of inequalities that are plotted on a graph:
The line on a graph should be a solid line when the inequality symbol is (≥ or ≤).The inequality symbol should be greater than or equal to (≥) when a solid line is shaded above.The inequality symbol should be less than or equal to (≤) when a solid line is shaded below.In this context, we can logically deduce that the most appropriate graph to represent the solution to the given inequality y ≤ - 2x is graph D because the solid boundary lines must be shaded below.
Read more on inequality here: brainly.com/question/27976143
#SPJ1
note: i dont want to answer the question below i want you to
explain only my questions i will ask now...
b1=10
62=8
b3-a=15
b3-b=10
b4=9
i want to ask... now in question i want to
calculate
The given information consists of a series of equations involving variables b1, b3, and b4, as well as the constant values 8, 9, and 10. The objective is to calculate the value of b3.
To find the value of b3, we need to analyze the given equations and use algebraic techniques to solve for the unknown variable.
From the equations given, we can observe that b1 = 10, b4 = 9, and 62 = 8. These values provide fixed points of reference.
Next, we examine the equations involving b3. We have two equations: b3 - a = 15 and b3 - b = 10. However, there is no information provided about the values of a and b. Without additional information or constraints, we cannot determine the specific value of b3.
It is important to note that the solution to the problem depends on having all the necessary information or additional equations that can be used to solve for the unknowns. In this case, the lack of information about the values of a and b prevents us from calculating the exact value of b3.
Learn more about equation here
https://brainly.com/question/29657983
#SPJ11
can someone plz help me with this question ASAP. drag the tiles to the correct boxes to complete the pairs. not all tiles will be used. the organizers of a founders day festival on main street surveyed local businesses to see if they would be offering any promotions to customers during the festival. the table contains the data gathered.
Answer:
hello the geinus has arrived
what is a simpler form of the radical expression 4 sqrt 1296 x^16y^12
So, the simpler form of the radical expression 4 sqrt 1296 x^16y^12 is 144x^14y^14 sqrt (x) sqrt (y).
To simplify the radical expression 4 sqrt 1296 x^16y^12, we need to first factor the number inside the radical. 1296 can be factored into 36 x 36, which simplifies to 6^4. So, the expression becomes 4 sqrt (6^4 x^16y^12).
Next, we can simplify the expression further by using the property of exponents that says a^m x a^n = a^(m+n). This means that we can combine the exponents of x and y, which gives us 4 sqrt (6^4 x^(16+12) y^(12+16)). Simplifying this, we get 4 sqrt (6^4 x^28 y^28).
Now, we can simplify the radical expression even further by using the property that says sqrt (a x b) = sqrt (a) x sqrt (b). Applying this to our expression, we get 4 x 6^2 x sqrt (x^28) x sqrt (y^28). Simplifying this further, we get 144x^14y^14 sqrt (x) sqrt (y).
To know more about radical visit:
https://brainly.com/question/14923091
#SPJ11
What is the measure of the reference angle for a 112° angle?
A.
22°
B.
68°
C.
67°
D.
78°
Answer:
B. 68
Step-by-step explanation:
180-112 = 68
just simple angle addition
crossin my fingers and hoping this helps
The measure of the reference angle for a 122° angle is 68°.
What is Reference Number?Reference number associated with t is defined as the shortest distance from the x axis to the terminal point t, along a unit circle.
So we have to find the shortest angle that the X axis make with the angle 112 degree.
112 degree lies on the second quadrant.
We know that,
Sum of the angles along the X axis = 180°
Reference angle of 112 degree = 180° - 112°
= 68°
Hence the reference angle for 112 degree is 68 degrees.
Learn more about Reference Angle here :
https://brainly.com/question/1603873
#SPJ2
i don’t know this answer i need help
Simplify. plsss
(-2)^-3
Answer:
-0.125
Hope this is right
Answer:- 1/8 as a fraction and - 0.125 as a decimal
Assume that the physical requirements of his/her job result in an average energy expenditure rate of 5 kcal/min over the hour shift. During his/her remaining non working, non sleeping hours, his/her activity level results in an energy expenditure rate that averages 1.7 kcal/min. time of rest per hour is 18.15 min and time of working per hour is 41.85. Calculate the worker daily metabolic rate?
The worker's daily metabolic rate is approximately 2169.28 kcal.
To calculate the worker's daily metabolic rate, we need to consider the energy expenditure during working hours and non-working hours.
Energy expenditure during working hours:
The worker's average energy expenditure rate during working hours is 5 kcal/min.
The worker works for 41.85 minutes per hour.
So, the energy expenditure during working hours is 5 kcal/min * 41.85 min = 209.25 kcal/hour.
Energy expenditure during non-working hours:
The worker's average energy expenditure rate during non-working hours is 1.7 kcal/min.
The worker has a rest time of 18.15 minutes per hour.
So, the energy expenditure during non-working hours is 1.7 kcal/min * 18.15 min = 30.955 kcal/hour.
Total daily metabolic rate:
The worker works for 8 hours per day (assuming a standard workday).
So, the total energy expenditure during working hours is 209.25 kcal/hour * 8 hours = 1674 kcal.
The remaining non-working hours in a day are 16 hours (24 hours - 8 hours).
So, the total energy expenditure during non-working hours is 30.955 kcal/hour * 16 hours = 495.28 kcal.
The daily metabolic rate is the sum of the energy expenditure during working hours and non-working hours:
Daily metabolic rate = Energy expenditure during working hours + Energy expenditure during non-working hours
Daily metabolic rate = 1674 kcal + 495.28 kcal = 2169.28 kcal.
To learn more about expenditure visit;
https://brainly.com/question/30063968
#SPJ11
The power, P (watts), of a car engine is proportional to the square of its speed, s(m/s) When s= 30 P= 1500 Work out the speed (to 1 DP) when the power is 1715 watts
Answer:
S = 32.1 m/s
Step-by-step explanation:
P = 1,500
S = 30
since P is proportional to S², then we must first determine S² = 900
900 / 1,500 = S² / 1,715
(900 x 1,715) / 1,500 = S²
1,543,500 / 1,500 = S²
S² = 1,029
S = √1,029 = 32.08 m/s ≈ 32.1 m/s
This sample is selected by dividing the population into subgroups and then taking a fixed number of units from each group using the simple random sample. simple random sample stratified random sample cluster random sample Voluntary random sample
The correct sampling method described in the question is a stratified random sample among the simple random sample, stratified random sample, cluster random sample and Voluntary random sample
The sampling method described in the question is a stratified random sample.
In a stratified random sample, the population is divided into subgroups or strata based on certain characteristics or criteria. Then, a random sample is selected from each stratum. The key idea behind this method is to ensure that each subgroup is represented in the sample proportionally to its size or importance in the population. This helps to provide a more accurate representation of the entire population.
In the given sampling method, the population is divided into subgroups, and a fixed number of units is taken from each group. This aligns with the process of a stratified random sample. The sample selection is random within each subgroup, but the number of units taken from each group is fixed.
Other sampling methods mentioned in the question are:
Simple random sample: In a simple random sample, each unit in the population has an equal chance of being selected. This method does not involve dividing the population into subgroups.
Cluster random sample: In a cluster random sample, the population is divided into clusters or groups, and a random selection of clusters is included in the sample. Within the selected clusters, all units are included in the sample.
Voluntary random sample: In a voluntary random sample, individuals self-select to participate in the sample. This method can introduce bias as those who choose to participate may have different characteristics than those who do not.
Therefore, the correct sampling method described in the question is a stratified random sample.
Learn more about sampling methods here:
https://brainly.com/question/15604044
#SPJ4
Deion loves to play the piano but doesn't like practicing the exercises his piano teacher
assigns. Deion knows the exercises will help him play better though, so he tries to motivate
himself using his favorite treat - chocolate chip cookies.
There is a proportional relationship between the amount of time (in hours) that Deion
practices the piano, x, and how many cookies he gives himself, y.
10
o
8
7
6
Cookies
3
2.
1
2
3
4
8
9
10
5 6 7
Hours
What is the constant of proportionality? Write your answer as a whole number or decimal.
cookies per hour
A car is traveling at 60 miles per hour from Boston, Massachusetts to Las Vegas, Nevada. If the two cities are about 2,750 miles apart, about how many hours will the trip take without any stops
Answer: 45.83
Step-by-step explanation: 2,750 / 60 = 45.8333333333
\/\/\/\/\/\/\/\/\/\/\/
45.83
Answer:
About 45.8333 hours
Step-by-step explanation:
\(\frac{D}{ST}\) is a chart for this. D= distance S= speed T= time.
Find distance by multiplying speed and time.
Find time by dividing distance by speed.
Find speed by dividing distance by time.
Hopefully this helps.
Find the specified areas for a Upper N left-parenthesis 0 comma 1 right-parenthesis density. (a) The area below z equals 1.04 Round your answer to three decimal places. areaequals the absolute tolerance is +/-0.001 (b) The area above z equals -1.4 Round your answer to three decimal places. areaequals the absolute tolerance is +/-0.001 (c) The area between z equals 1.1 and z equals 2.1 Round your answer to three decimal places. areaequals the absolute tolerance is +/-0.001
The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.
To find the area below z=1.04 for an Upper N(0,1) density, you will need to use the standard normal distribution table or a calculator with a z-table function. Here are the steps:
1. Locate the value of z=1.04 in the table or use the calculator's function.
2. Find the corresponding area value (which represents the probability or percentage of values below z=1.04).
The area below z=1.04 is approximately 0.851, rounded to three decimal places.
(b) To find the area above z=-1.4 for an Upper N(0,1) density, follow these steps:
1. Locate the value of z=-1.4 in the table or use the calculator's function.
2. Find the corresponding area value.
3. Since we need the area above z=-1.4, subtract the area value found in step 2 from 1.
The area above z=-1.4 is approximately 1 - 0.0808 = 0.919, rounded to three decimal places.
(c) To find the area between z=1.1 and z=2.1 for an Upper N(0,1) density, follow these steps:
1. Locate the values of z=1.1 and z=2.1 in the table or use the calculator's function.
2. Find the corresponding area values for both z=1.1 and z=2.1.
3. Subtract the area value of z=1.1 from the area value of z=2.1 to find the area between them.
The area between z=1.1 and z=2.1 is approximately 0.982 - 0.864 = 0.118, rounded to three decimal places.
Learn more about area
brainly.com/question/27683633
#SPJ11
(a) Write
\( {2}^{5} \div {2}^{5} \)
as a single power if 2.
Answer:
2^0
Step-by-step explanation:
When you are dividing 2 exponents with the same base (in this case, 2) you subtract them. 2^5 ➗ 2^5 => 2^(5-5) = 2^0 => which is equal to 1, but the answer here would be 2^0.
There are two ways to go about this problem.
The first way, the generic way, is to know that,
\(\frac{a^n}{a^m}=a^{n-m},a\neq0\).
So,
\(\frac{2^5}{2^5}=2^{5-5}=\boxed{2^0}\).
The second way is to realise that both numerator and denominator are equal and when diving two equal numbers you obtain 1. (except when diving zeros) aka,
\(\frac{a}{a}=1, a\neq0\)
And 1 equals to any number raised to the power of zero,
\(a^0=1,a\neq0\)
So we just have to say that the 1 we got is rewritten as some base to the power of zero.
Since our base needs to be 2, we just simply say,
\(2^0\).
Et Viola.
Hope this helps.
Find the area of triangle XYZ if length XY equals 7 and length XZ equals 4.3. You also
know that angle Y equals 79°.
Answer:
A ≈ 14.8 units²
Step-by-step explanation:
the area (A) of the triangle is calculated as
A = \(\frac{1}{2}\) yz sin Y ( that is 2 sides and the angle between them )
where x is the side opposite ∠ X and z the side opposite ∠ Z
here y = XZ = 4.3 and z = XY = 7 , then
A = \(\frac{1}{2}\) × 4.3 × 7 × sin79°
= 15.05 × sin79°
≈ 14.8 units² ( to 1 decimal place )
Simplify the following polynomial by adding. If the polynomial cannot be simplified, then enter the polynomial as it is currently written below
Given the expression:
\(30t^3+25t^3\)Let's simplify the polynomials by adding them.
Here, the polynomials have like terms because their variables are the same and the expoenents of the variables are also equal.
Since the polynomials have like terms, let's add the coefficients.
\(30t^3+25t^3=55t^3\)Therefore, the simplified expression after adding is:
\(55t^3\)ANSWER:
\(55t^3\)Help please will give brainly if answerd
Answer:
H
Step-by-step explanation:
The answer is graph H
Answer:
it`s H
Step-by-step explanation:
literaly it`s H
Suppose that an ounce of gold costs 15 U.S. dollar and 14.3028 Italian lira. An ounce of silver costs 0.7302 Italian lira and 0.1605 Swiss francs. How much Swiss franc can a U.S. dollar buy?
a. 0.23
b. 0.30
c. 0.11
d. 0.21
A U.S. dollar can buy approximately 0.21 Swiss francs (rounded to two decimal places). Thus, the answer is option d) 0.21.
To determine how much Swiss francs a U.S. dollar can buy, we need to use the given exchange rates between different currencies.
Given:
1 ounce of gold costs 15 U.S. dollars and 14.3028 Italian lira.
1 ounce of silver costs 0.7302 Italian lira and 0.1605 Swiss francs.
Let's calculate the exchange rate between the U.S. dollar and the Swiss franc using the given information:
1 ounce of silver = 0.7302 Italian lira
1 ounce of silver = 0.1605 Swiss francs
To find the exchange rate between the Italian lira and the Swiss franc, we can divide the price of 1 ounce of silver in Swiss francs by the price of 1 ounce of silver in Italian lira:
Exchange rate: 0.1605 Swiss francs / 0.7302 Italian lira
Simplifying this, we get:
Exchange rate: 0.2199 Swiss francs / 1 Italian lira
Now, let's find the exchange rate between the U.S. dollar and the Italian lira:
1 ounce of gold = 15 U.S. dollars
1 ounce of gold = 14.3028 Italian lira
To find the exchange rate between the U.S. dollar and the Italian lira, we can divide the price of 1 ounce of gold in Italian lira by the price of 1 ounce of gold in U.S. dollars:
Exchange rate: 14.3028 Italian lira / 15 U.S. dollars
Simplifying this, we get:
Exchange rate: 0.9535 Italian lira / 1 U.S. dollar
Finally, to find how much Swiss francs a U.S. dollar can buy, we multiply the exchange rate between the U.S. dollar and the Italian lira by the exchange rate between the Italian lira and the Swiss franc:
Exchange rate: 0.9535 Italian lira / 1 U.S. dollar * 0.2199 Swiss francs / 1 Italian lira
Simplifying this, we get:
Exchange rate: 0.2099 Swiss francs / 1 U.S. dollar
Therefore, a U.S. dollar can buy approximately 0.21 Swiss francs (rounded to two decimal places). Thus, the answer is option d) 0.21.
for such more question on dollar
https://brainly.com/question/24278371
#SPJ8
find a basis for the vector space of polynomials of degree at most two which satisfy the constraint . how to enter your basis: if your basis is then enter .
The basis for the vector space of polynomials of degree at most two which satisfy the constraint is {1 - 2x - 3x²}.
A basis for the vector space of polynomials of degree at most two which satisfy the constraint is {1 - 2x - 3x²}.To find a basis for the vector space of polynomials of degree at most two which satisfy the constraint, we use the following steps:Step 1: We let p(x) = a + bx + cx² and substitute it into the given constraint. That is,p(1) - 3p(0) + 2p(−1) = 0Thus, we get a + b + c − 3a = 0 and a − 2b + c = 0.
These equations can be rewritten as4a − b − c = 0 and a − 2b + c = 0.Step 2: We can solve for a, b, and c by setting up an augmented matrix as shown below:4 −1 −1 | 00 1 −2 | 0Using row reduction, we get the augmented matrix in row echelon form as follows:4 −1 −1 | 00 1 −2 | 0R2 → R2 + 2R1 −> 0 −1 −3 | 00 1 −2 | 0R1 → R1 + R2 -> 4 0 −4 | 00 1 −2 | 0R3 → R3 / (-4) -> 0 0 1 | 0R2 → R2 + 3R3 -> 0 1 0 | 0R1 → R1 + R3 -> 4 0 0 | 0
Therefore, the solution is a = 0, b = 0, and c = 0.Since the only polynomial of degree at most two that satisfies the constraint is the zero polynomial, the vector space of polynomials of degree at most two which satisfy the constraint is a trivial vector space, denoted by {0} Since the dimension of a trivial vector space is 0, then any set containing only the zero vector is a basis for the vector space.
Therefore, the basis for the vector space of polynomials of degree at most two which satisfy the constraint is {0}.Step 5: However, the question is asking for a basis for the vector space of polynomials of degree at most two which satisfy the constraint. Therefore, we need to redo the calculations to account for the fact that there is no nontrivial vector in the vector space of polynomials of degree at most two which satisfy the constraint.
In this case, we can take any non-zero vector as the basis for the vector space of polynomials of degree at most two which satisfy the constraint. For example, we can take p(x) = 1 - 2x - 3x² as the basis. Since p(x) is a polynomial of degree at most two, and it satisfies the constraint p(1) - 3p(0) + 2p(−1) = 0, then it is in the vector space of polynomials of degree at most two which satisfy the constraint. Therefore, the basis for the vector space of polynomials of degree at most two which satisfy the constraint is {1 - 2x - 3x²}.
Learn more about Vector space
brainly.com/question/13058822
#SPJ11
In two distinct acute triangles ABC and DEF, ZBZE. AABC A DEF are congruent when ther is a sequence of rigid motions that maps
which of the following?
ZA onto ZD, and ZC onto ZF
AC onto DF, and BC onto EF
Point A onto Point D, and AB onto DE
ZC onto ZF, and BC onto EF
The correct answer is Point A onto Point D, and AB onto DE.Since the triangles are congruent, we know that they have the same shape and size.
what is congruent?
In mathematics, congruent means having the same size and shape. In geometry, two figures are congruent if they have the same size and shape, which means that all corresponding sides and angles are equal.
In the given question,
Based on the given information, we know that triangle ABC and triangle DEF are distinct acute triangles such that ZBZE. We are also told that AABC is congruent to ADEF, and we need to determine which sequence of rigid motions maps the triangles onto each other.
The correct answer is Point A onto Point D, and AB onto DE.
Since the triangles are congruent, we know that they have the same shape and size. Therefore, we need to find a sequence of rigid motions that will map one triangle onto the other.
The first step is to map point A onto point D, which can be done with a translation. The second step is to map AB onto DE, which can be done with a rotation about point D. This sequence of rigid motions will map triangle ABC onto triangle DEF.
Option 1, ZA onto ZD and ZC onto ZF, does not necessarily map the rest of the triangles onto each other.
Option 2, AC onto DF and BC onto EF, is incorrect because it only maps two sides of the triangle and does not guarantee congruence.
Option 4, ZC onto ZF and BC onto EF, also does not necessarily map the rest of the triangles onto each other.
To know more about congruent, , visit:
https://brainly.com/question/12413243
#SPJ1
Given: e || f and g is a transversal Prove: 1 8 Given that e || f and g is a transversal, we know that 4 5 by the alternate interior angles theorem. We also know that 1 4 and 8 5 by the corresponding angles theoremalternate interior angles theoremvertical angles theoremalternate exterior angles theorem. Therefore, 1 8 by the transitive property
We also know that 1 4 and 8 5 by the vertical angles theorem.
Vertical angles, also known as vertically opposite angles, are the opposing angles formed when two lines converge. Angles that are vertically opposite one another are always equal to one another. A vertical angle and the angle it is near to are also supplementary angles, which means their combined angle is 180 degrees.
The opposite angle, for example, is 45° when two lines intersect to form an angle, say X=45°. And the angle next to angle X will be 180 – 45, or 135 degrees.
Correct Question :
Given: e || f and g is a transversal.
Prove: 1 8 Given that e || f and g is a transversal, we know that 4 5 by the alternate interior angles theorem. We also know that 1 4 and 8 5 by the (corresponding angles theorem / alternate interior angles theorem / vertical angles theorem / alternate exterior angles theorem). Therefore, 1 8 by the transitive property.
To learn more about vertical angles theorem here:
https://brainly.com/question/18868430
#SPJ4
What is even function and odd function?
If f(-x) = f(x) for all x in the domain of the function, then the function is said to be even function in mathematics. if a function meets the criterion that f(-x) = -f(x) for all x in the function's domain, then is said to be odd function .
An even function, then, is symmetric about the y-axis. The graph of an even function would look geometrically identical to its reflection across the y- axis if we were to plot it. The functions f(x) = x2, f(x) = cos(x), and f(x) = |x| are examples of even functions.
An odd function, then, is symmetric about the origin. If we were to draw the graph of an odd function geometrically, if we were to plot the graph of an odd function, it would appear to be identical to its reflection across the origin, after being rotated 180 degrees. Some examples of odd functions include f(x) = x³, f(x) = sin(x), and f(x) = 1/x.
It is also possible for a function to be neither even nor odd. In other words, a function does not need to exhibit either symmetry about the y-axis or the origin.
To learn more about Even function :
https://brainly.com/question/3762195
#SPJ4
Need help pls have no idea how to this
Answer:
The local minimum point of f(x) is at the point (-2,-2)
Step-by-step explanation:
the minimum point is located on the very bottom of the parabola!
so its cut off but its (-2,-2)
sorry I didnt see the 6,-2
so I am gussing the y-value is the minimum point so it should be -2....tell me if I am wrong but if your looking for a points it (-2,-2) if your looking for the value it would be -2
pls mark me brainliest