Solving equations and inequalities are essential skills in various real-world applications, from engineering and physics to business and finance.
These skills enable us to find solutions to problems and make informed decisions. For instance, engineers use equations to design buildings, bridges, and machines, while scientists use equations to model and predict the behavior of physical systems. In business and finance, equations and inequalities are used to solve problems related to budgets, investments, and financial planning.
They help individuals and organizations make informed decisions and manage resources efficiently. For example, a company can use equations to determine the optimal production level that maximizes profits or to evaluate the feasibility of a new project.
To learn more about equations follow the link:
https://brainly.com/question/29538993
#SPJ1
Draw the image of traingel ABC under a dilation whose center is p and scale factor is 1/2
A graph of the image of ABC under a dilation whose center is P and scale factor is 1/2 is shown in the image below.
What is dilation?In Geometry, a dilation can be defined as a type of transformation which typically changes the size of a geometric shape, but not its shape.
In this exercise, we would use an online graphing calculator to plot the image of ABC after a dilation by a scale factor of 1/2 centered at P.
Based on the image (see attachment), we can logically deduce that each vertex is 1/2 times as far from center P as the original vertex and each segment is 1/2 times as long as the original:
Side length A'C' = 8.2/2 = 4.1
Side length A'B' = 5.7/2 = 2.85
Side length B'C' = 12.2/3 = 6.1
Read more on dilation here: brainly.com/question/20482938
#SPJ1
help me please
A car was valued at $44,000 in the year 1992. The value depreciated to $15,000 by the year 2006.
A) What was the annual rate of change between 1992 and 2006?
r=---------------Round the rate of decrease to 4 decimal places.
B) What is the correct answer to part A written in percentage form?
r=---------------%
C) Assume that the car value continues to drop by the same percentage. What will the value be in the year 2009 ?
value = $ -----------------Round to the nearest 50 dollars.
In the exponential decay, A) r = -0.0839 , B) r = -8.39% , C) Value=$11,800.
What is exponential decay?
The term "exponential decay" in mathematics refers to the process of a constant percentage rate reduction in an amount over time. It can be written as y=a(1-b)x, where x is the amount of time that has passed, an is the initial amount, b is the decay factor, and y is the final amount.
To find the annual rate of change between 1992 and 2006, we can use the formula:
r = [tex](V_2/V_1)^{1/n}-1[/tex]
where V1 is the initial value, V2 is the final value, and n is the number of years between the two values.
=>r = -0.0839
Therefore, the rate of change between 1992 and 2006 is -0.0839.
To express the rate of change in percentage form, we can multiply the result from part A by 100:
=>r = -0.0839 x 100
=> r = -8.39%
Therefore, the rate of change between 1992 and 2006 is a decrease of 8.39%.
To find the value of the car in the year 2009, we can assume that the value continues to drop at the same percentage rate as calculated in part A.
From 2006 to 2009, there are 3 years. So, using the formula for exponential decay, we have:
where V0 is the value in 2006, r is the rate of decrease, and n is the number of years between 2006 and 2009.
=>V = 11792.51
Therefore, the value of the car in the year 2009 would be approximately $11,800 (rounded to the nearest $50).
To learn more about exponential decay refer the below link
https://brainly.com/question/12139640
#SPJ1
bobby is painting a figure on a banner for a homecoming parade. the figure he is painting consists of an isosceles triangle, a rectangle, and a semicircle, as shown how do i sovle it
Using the perimeter formula, the total length of sparkling lights he can add to the banner is 40.56ft.
Define perimeter?The perimeter of a shape is its whole length. It is any border or outline's length that defines a two-dimensional geometric shape. Different figures may have the same perimeter depending on their sizes.
The same wire can be used to create a square if each of its four sides is the same length.
Here in the question,
We have to find the perimeter of the whole figure.
Now the total perimeter =
Sum of sides of the triangle + sum of sides of quadrilateral and the sum of the circumference of the semi-circle.
Perimeter = 10 + 5 + 3 + 10 + πr
= 28 + 3.14 × 8/2
= 28 + 12.56
= 40.56ft.
To know more about perimeters, visit:
https://brainly.com/question/6465134
#SPJ1
The complete question is:
Bobby is creating a banner for the homecoming parade. The banner consists of an isosceles triangle, a rectangle, and a semicircle. He wants to add sparkling lights around the trim of the banner.
What is the total length of sparkling lights he can add to the banner?
Determine the length of side AB and BC in triangle ABC.
AB=9.68,BC=7.04
AB=8.8,BC=6.4
AB=9.152,BC=6.656
AB=7.92,BC=5.76
In triangle ABC, the values of AB and BC are 9.68 and 7.04 respectively i.e. A.
What is a triangle's definition?
A triangle is a geometric form that has three straight sides and three angles. It is a fundamental geometric form that is frequently utilised in mathematics, science, and everyday life.
Triangles are distinguished by three sides and three angles. The sum of each triangle's three angles is always 180 degrees. Triangles are classified according to the length of their sides and the measurement of their angles.
Now,
As given ΔDEF ≈ΔABC
that means ratio of all sides will be equal
i.e. AB/DE=BC/EF=AC/DF
then AB/8.8=6.71/6.1
AB=1.1*8.8
AB=9.68
and BC/6.4=6.71/6.1
BC=1.1*6.4
BC=7.04
Hence,
the values of AB and BC are 9.68 and 7.04 respectively.
To know more about triangles visit the link
brainly.com/question/2773823
#SPJ1
A point R (-5, 6) is reflected across X axis to obtain point S, write the coordinates of S.
9-3: Lesson Ouiz Two number cubes whose sides are numbered 1 through 6 are rolled on a table. The two numbers showing are added. If you repeat this process 300 times, how many times would you expect the two cubes to add to exactly 7?
Answer:
300 I think because when you repeat it 300 times it will give an exactly 7 300 times
Write an equation for a linear function whose graph has the given characteristics. Horizontal, passes through (9, −45)
Answer:
y = -45
Step-by-step explanation:
y=mx+b
because the graph is horizontal m = 0
y=0x+b --> y=b
next sub in points
y=b (9,-45)
-45=b
therefore equation is y=-45
The initial population of a bacterial culture is 2000, growing at a fixed rate. Table shows the population every hour for six hours.
A. Find the equation that models this relation. (round to one decimal place).
B. Use the equation to find the population of bacteria after 12 hours after 24 hours.
Answer: A. To find the equation that models this relation, we can plot the data and look for a trend.
From the graph, we can see that the data follows an exponential growth pattern. The equation for exponential growth is:
y = ab^x
where y is the final population, a is the initial population, b is the growth rate, and x is the time in hours.
Using the data from the table, we can find the value of b:
b = y/x
where y is the population after x hours.
For example, after 2 hours, the population is 5000:
b = 5000/2 = 2500
We can repeat this process for each time period and find the average value of b:
b = (2500 + 3125 + 3906.25 + 4882.81 + 6103.51 + 7629.38) / 6 = 4275.5
Now that we have the value of b, we can find the equation that models the relation:
y = 2000(4275.5)^x
Rounding to one decimal place:
y = 2000(4.3)^x
B. Using the equation, we can find the population after 12 and 24 hours:
y = 2000(4.3)^12 ≈ 8,898,335.7
y = 2000(4.3)^24 ≈ 7.42 x 10^13
Step-by-step explanation:
Can someone please help me with this? find the value of x and write answer in simplest radical form. I understand the concept but I don’t know how to differentiate each side to find out if it’s sin, cos, or tan. Please explain how you got the answer.
The value of x is 5√3
What is trigonometric ratio?Trigonometric Ratios are defined as the values of all the trigonometric functions based on the value of the ratio of sides in a right-angled triangle.
The longest sides is the hypotenuse and the side opposite the acute angle is the opposite, the other side is adjascent.
Sin(tetha) = opp/ hyp
cos(tetha) = adj/hyp
tan(tetha) = opp/adj
therefore Tan 60 = x/5
√3 = x/5
x = 5√3
therefore the value of x is 5√3
learn more about trigonometric ratio from
https://brainly.com/question/24349828
#SPJ1
Find the measure of XY.
Y
●
74°
N
X
Check the picture below.
A company finds that if it charges 2 dollars for a cell phone, it can expect to sell 1,000 - 2x phones. The company uses the function
defined by r(x)=(1,000-2x) to model the expected revenue, in dollars, from selling cell phones at a dollars each.
1. Use graphing technology to graph the function r.
2. What do the z-intercepts mean in this situation?
3. Is 0≤x≤ 600 an appropriate domain for the function 7? Explain your reasoning.
4. At what price should the company sell their phones to get the maximum revenue? Explain your reasoning.
The z-intercept is at 500, the domain of the function is all non-negative real numbers, or [0, ∞) and the maximum revenue is 500
What does the z-intercepts interpret in this situation?1. The graph of the function is attached below;
2. The z-intercept is where the graph intersects the x-axis, which occurs when the revenue is 0. In this situation, the z-intercept represents the maximum price that the company can charge for the cell phone and still expect to sell some units. So, the z-intercept is $500, meaning if the company charges more than $500, it will not sell any cell phones and its revenue will be 0.
3. No, 0≤x≤ 600 is not an appropriate domain for the function. The company can charge any price, not just prices between 0 and 600 dollars. The domain of the function should be all non-negative real numbers, or [0, ∞).
4. The maximum revenue occurs at the point where the slope of the function changes from negative to positive, which is the vertex of the parabola. In this case, the function r(x) is a linear function, so there is no vertex. The maximum revenue occurs at the endpoint of the domain, which is x=500, since the company cannot charge more than $500 without reducing the number of phones sold to 0. Therefore, the company should charge $500 to get the maximum revenue.
Learn more on graph of function here;
https://brainly.com/question/7807573
#SPJ1
According to the National Student Clearinghouse Research Center, women now comprise 60% of enrollment in universities. What is the probability in a random sample of 55 university students that more than 35 are women? Round your answer to 3 decimal places.
The probability that more than 35 students are women in a random sample of 55 university students is 0.256.
What is binomial distribution?The binomial distribution is a probability distribution that expresses the number of successes in a finite number of independent trials when the chance of success is constant and there are only two potential results (success or failure). Since a known chance of success for each trial is known, we may use it to determine the likelihood of a certain number of successes (or failures) in a set number of trials.
Given that p = 60% = 0.6, n = 55.
Using normal approximation we have:
SD = sqrt(np(1-p))
= sqrt(55 x 0.60 x 0.40) = 3.05
The z-score is:
z = (X - np) / SD)
z = (35 - (0.4)(0.6)) / 3.05
z = 11.39 = 0.256.
Hence, the probability that more than 35 students are women in a random sample of 55 university students is 0.256.
Learn more about binomial distribution here:
https://brainly.com/question/31197941
#SPJ1
Which statement about credit reports is not true?
he asked me what my name was into direct speech
. From a rectangular metal sheet of size 20 cm by 30 cm, a circular sheet as big as possible is cut. Find the area of the remaining sheet.
Tammy must run more than 63 miles total to reach your fitness goals. She has already ran 31 miles and runs for miles per day which of the following inequalities could be used to solve for X the number of days Tammy still needs to run to reach your fitness goals.
Answer:
[tex]31+4x > 63[/tex]
To reach her fitness goal, she needs to run for more than 8 days.
Step-by-step explanation:
She has already run 31 miles and runs 4 miles per day:
This means that after x days, the distance she will have run is:
[tex]D(x)=31+4x[/tex]
Tammy must run more than 63 miles total to reach her fitness goals.
This means that:
[tex]D(x) > 63[/tex]
[tex]31+4x > 63[/tex]
The inequality is:
[tex]31+4x > 63[/tex]
Solution:
[tex]4x > 32[/tex]
[tex]x > \dfrac{32}{4}[/tex]
[tex]x > 8[/tex]
To reach her fitness goal, she needs to run for more than 8 days.
Find the extract value of x
Answer:
25 + 5√29
Step-by-step explanation:
(I added a photo below)
First, let's find BC using the Pythagorean theorem (from ∆BCD):
[tex] {bc}^{2} = {25}^{2} + {10}^{2} = 625 + 100 = 725[/tex]
[tex]725 > 0[/tex]
[tex]bc = \sqrt{725} =5 \sqrt{29} [/tex]
Then we see, that AB = 25 + x
So, now we can find AC:
[tex] {ac}^{2} = ({25 - x})^{2} - ({5 \sqrt{29} })^{2} = 625 - 50x + {x}^{2} - 25 \times 29 = 625 - 50x + {x}^{2} - 725 [/tex]
Now we have a quadratic equation:
[tex] {x}^{2} - 50x - 100 = 0[/tex]
[tex]d = {b}^{2} - 4 \times a \times c = ({ - 50})^{2} - 4 \times 1 \times ( - 100) = 2500 + 400 = 2900 > 0[/tex]
[tex]x1 = \frac{ - b - \sqrt{d} }{2a} = \frac{50 - 10 \sqrt{29} }{2} = 25 - 5 \sqrt{29} [/tex]
This is a negative number and we cannot use it, since x has to be a natural number
[tex]x2 = \frac{ - b + \sqrt{d} }{2 a} = \frac{50 + 5 \sqrt{29} }{2} = 25 + 5 \sqrt{29} [/tex]
Select the correct answer from each drop-down menu.
Points A, B, and C form a triangle. Complete the statements to prove that the sum of the interior angles of AABC is 180°.
C
Reason
m21=m24 and m23 = m25
m24+ m22+ m25= 180°
mz1+m22+ m/3 = 180°
Statement
Points A, B, and C form a triangle.
given
Let DE be a line passing through B and parallel to AC. definition of parallel lines
23 25 and 21 24
angle addition and definition of a straight line
substitution
Using congruent angles , we have been able to prove that the sum of the interior angles of ΔABC is 180°.
How to find the angle proof?We are given that:
A, B, and C form a triangle.
The sum of the interior angles of ΔABC is 180°.
We want to find the complete the statements to prove that the sum of the interior angles of ΔABC is 180°
From the attached diagram, we have that:
A triangle ABC with angle 1, 2 and 3.
Line DE and AC are parallel and then BA is a traversal line.
Thus, the alternate interior angle is:
∠1 = ∠4
∠3 = ∠5
Therefore, the angle formed on line is:
∠4 + ∠2 + ∠5 = 180
∠1 + ∠2 + ∠3 = 180
Read more about Angle Proof at: https://brainly.com/question/11891208
#SPJ1
determine whether the proportion is true or false 16miles/18quarts=24miles/27quarts
To determine if the proportion is true or false, we can cross-multiply and see if the equation holds:
16 miles / 18 quarts = 24 miles / 27 quarts
Cross-multiplying, we get:
16 miles * 27 quarts = 18 quarts * 24 miles
432 milesquarts = 432 milesquarts
The equation holds, so the proportion is true.
The proportion is true .
To determine if the proportion is true or false, we can cross-multiply and see if the equation holds:
16 miles / 18 quarts = 24 miles / 27 quarts
Cross-multiplying, we get:
16 miles * 27 quarts = 18 quarts * 24 miles
432 milesquarts = 432 milesquarts
Proportion can be checked by simplifying the ratios given,
16miles/18quarts=24miles/27quarts
Simplifying further,
8miles/9squarts = 8miles / 9squarts .
The equation holds, so the proportion is true.
Know more about proportions,
https://brainly.com/question/31548894
#SPJ2
Name the minor arc and find it’s measure. Then name the major arc and find it’s measure.
The minor arc in the given diagram as required to be determined is; arc TU and it's measure is; 116°.
The major arc in the given diagram as required to be determined is; arc TVU and it's measure is; 244°.
What are the measures of the minor and major arcs in the diagram?It follows from the task content that the minor and major arcs are to be named and their measures determined as required.
The minor arc in a circle is usually subtended by an angle less than 180° while the major arc is subtended by an angle greater than 180°.
Ultimately, the minor arc is; arc TU and it's measure is; 116° while the major arc is; arc TVU and it's measure is; 244°.
Read more on arc measures;
https://brainly.com/question/23117081
#SPJ1
What is 2-2x5+7 hurry!!!!!!!!!!!!
Answer: 15 / fifteen
Step-by-step explanation:
2*5 = 10 - 2 = 8 + 7 = 15
The value of the given expression is -1.
What is PEDMAS rule?PEMDAS is an acronym used to mention the order of operations to be followed while solving expressions having multiple operations. PEMDAS stands for P- Parentheses, E- Exponents, M- Multiplication, D- Division, A- Addition, and S- Subtraction.
The given numerical expression is 2-2×5+7.
Here, first multiply 2 and 5, that is
2-10+7
Next add 2 and 7, that is
9-10
Finally subtract 9 and 10, that is
9-10= -1
Therefore, the value of the given expression is -1.
Learn more about the PEDMAS rule here:
https://brainly.com/question/24086845.
#SPJ2
A Small Monster collector is visiting the Knightrola region, bringing 30 Small Monster Containment Devices with them. The devices are highly reliable and can effectively be assumed to always work. How many different types of Small Monsters can the collector capture under the following conditions? a. The collector has access to Grass, Space Electric Scooter, Mask, Citrus, and Rubber Duck type Small Monsters 7 types b. The above, and intends to capture at least one of each of those types c. Both of the above, and intends to capture at least five Space types d. All of the above and intends to capture at most four Electric Scooter types e. All of the above, and intends to capture at most three Rubber Duck type
The different types of Small Monsters combinations can the collector capture under that collector .lunder the following conditions are a) 593775 ; b) 100947 ; c) 27132 ; d) 30752 ; e) 26334.
For these questions as we are dealing with combination and repetition, we will be using the rule nC(r-1) where n = the number of total items and r = the number of ways we can choose.
We have provide that Small Monster collector is visiting the Knightrola region, bringing 30 Small Monster Containment Devices with them. We have to determine the different types of Small Monsters can the collector capture under the following conditions :
a) Here n = 30,
Number of monstor access by him = 7 {Grass, Space Electric Scooter, Mask, Citrus, and Rubber Duck}
So, different types of Small Monsters can the collector capture = ³⁰C₇₋₁ = ³⁰C₆
= 593775
b) Here, he captures at least one of each of those 7 places. So, we have to distribute 23 ( 30 -7) among 7 places
= ²³C₆ = 100947
c) Here provided that atleast one to all plus atleast five Space types captured, so we have to distribute 30 - 11 = 19 devices among 7 places, = ¹⁹C₆ = 27132
d) All above conditions plus at most four Electric Scooter types captured, so ³⁰⁻¹¹C₅ + ³⁰⁻¹²C₅+ ³⁰⁻¹³C₅ + ³⁰⁻¹⁴ C₅
= 30752
e) All of the above and capture at most three Rubber Duck type, First, we will subtract the combination where we capture n = 20-3 (at most 3 rubber ducks) from the combination we have so ³⁰⁻¹⁴C₅ + ³⁰⁻¹⁵C₅ + ³⁰⁻¹⁶C₅ = 26334. Hence, required value is 26334.
For more information about combination formula, visit:
https://brainly.com/question/1587469
#SPJ4
Martha Martha and Steven are in the same math class. The box plot shows the number of minutes that Martha and Steven spent studying for their final exam each day for a week. Steven 0 5 10 Study Time 15 20 Number of Hours 25 30 35 Which statement is best supported by the information in the box plots? 2 of 9 A 07:34
Answer:
Based on the given information in the box plots, the statement that is best supported is that Steven spent more time studying than Martha did during the week for their math final exam. This can be inferred because the top line of Steven's box plot is higher than the top line of Martha's box plot, indicating that Steven spent more time studying than Martha in the given time period. Additionally, Steven's whisker extends higher than Martha's whisker, further supporting the idea that Steven studied for a longer period of time than Martha.
Peyton drew a right triangle with sides 5
cm, 12
cm, and 13
cm long. Carter drew a similar triangle to Peyton’s. Which of the following can be the measurements of Carter’s triangle?
Option B. The length of the hypotenuse of Carter's triangle is 13cm.
Since Carter's triangle is similar to Peyton's triangle, the ratio of corresponding side lengths will be the same. Let's use x to represent the length of the hypotenuse of Carter's triangle.
We know that the ratio of the lengths of the hypotenuse and the shorter leg of Peyton's triangle is 13:5. So, the ratio of the lengths of the hypotenuse and the shorter leg of Carter's triangle must also be 13:5.
Thus, we have x/5 = 13/5, which simplifies to x = 13.
Therefore, the length of the hypotenuse of Carter's triangle is 13cm.
Therefore, the only possible length for Carter's hypotenuse is 13cm, and the correct answer is A.
To learn more about hypotenuse please click on below link.
https://brainly.com/question/28752684
#SPJ1
Peyton drew a right triangle with sides 5cm, 12cm, and 13cm long. Carter drew a similar triangle to Peyton’s. Which of the following can be the measurements of Carter’s triangle?
A. 15cm
B. 13cm
C. 11cm
D. 10cm
Eight times a number, x, is one-third the sum of the number and two. Which answer represents this situation? Responses 8x=13x+2 8 x equals 1 third x plus 2 8x=13(x+2) 8 x equals 1 third open parentheses x plus 2 close parentheses 8x+13(x+2) 8 x plus 1 third open parentheses x plus 2 close parentheses 8x+13x+2
The problem can be translated into an equation as follows: 8x = (1/3)(x+2)
the answer that represents this situation is: 8x = (1/3)(x+2)
Simplifying the right side of the equation:
8x = (1/3)x + (2/3)
Multiplying both sides of the equation by 3 to eliminate the fraction:
24x = x + 2
Subtracting x from both sides of the equation:
23x = 2
Dividing both sides of the equation by 23:
x = 2/23
Therefore, the answer that represents this situation is:
8x = (1/3)(x+2)
Learn more about equation here
https://brainly.com/question/29657992
#SPJ1
Suppose on your 21st birthday you begin saving $500 quarterly into an account that pays 12% compounded quarterly. If you continue the savings until your 51st birthday (30 years), how much money will be in the account?
Please help!! Will mark brainliest
From the time you are 21 until the time you turn 51, if you put $500 away quarterly in an account that produces 12% compound interest, you will have around $1,299,994.09 in it by the end of the 30 years.
When does a quarterly monthly occur?Four quarters, numbered Q1, Q2, Q3, & Q4, make up an entire year. There are 3 months in each quarter. About 91 days make up each quarter. Quarterly is defined as once every quarter, or around every 91 days.
The calculation for future value of the an annuity can be used to resolve this issue:
FV = PMT x ((1 + r/n)nt - 1) / (r/n), where FV is just the future value of a annuity, PMT is indeed the payment amount (in this case, $500), r is indeed the interest rate (the value of which in this case is 12% or 0.12), n refers to the number of occasions a year the interest is greatly exacerbated (which in this case is four for quarterly cumulative), and t is the duration of the annuity .
When we enter the data, we get the following result: FV = 500 x (1.03120 - 1) / 0.03 = $1,299,994.09
To know more about quarterly visit:
https://brainly.com/question/1569963
#SPJ1
Question 3 a) What is the theoretical probability of rolling a sum of 8? b) What is your experimental probability of rolling a sum of 8? c) What are the odds of rolling a sum of 8?
The theoretical probability of rolling a sum of 8 is 1/11, the experimental probability is 5/36 and the odds is 5 : 31
a) What is the theoretical probability of rolling a sum of 8?When two dice are rolled, the possible sum are
Sum = 2 to 12
In the above sum, we have
n(8) = 1
Total = 11
This means that
P(sum of 8) = 1/11
b) What is your experimental probability of rolling a sum of 8?For the experimental probability, we have
n(Sum of 8) = 5
Total = 36
So, we have
P(sum of 8) = 5/36
c) What are the odds of rolling a sum of 8? In (b), we have
P(sum of 8) = 5/36
This means that
Odds = 5 : 36 - 5
Odds = 5 : 31
Hence, the odds of rolling a sum of 8 is 5 : 31
Read more about probability at
https://brainly.com/question/10739997
#SPJ1
4. Myron Security, Inc., had total sales for 1 year of $945,860. Their advertising expenses were $57,370. a. Estimate the percent advertising expenses were of total sales.
The calculated value of the percent advertising expenses were of total sales is 6.07%
How to estimate the percent advertising expenses were of total sales.To estimate the percent advertising expenses were of total sales, we need to calculate the ratio of advertising expenses to total sales and then convert it to a percentage.
The ratio of advertising expenses to total sales is:
$57,370 / $945,860 = 0.0607
To convert this ratio to a percentage, we can multiply it by 100:
0.0607 x 100 = 6.07%
Therefore, we can estimate that the advertising expenses were approximately 6.07% of the total sales.
Read more about percentage at
https://brainly.com/question/24877689
#SPJ1
Where are the vertices of triangle A’B’C’ located? Show your work or explain your steps. (4points)
The vertices of ∆A′B′C′ are A′(-6, 5), B′(-6, 8), and C′(-10, 5) upon the application of the translation rule.
What is the translation rule in geometry?
In geometry, a translation is a transformation that moves every point of a figure the same distance in the same direction. In the case of a triangle, a translation rule describes how to move each vertex of the triangle to a new location to create a new triangle with the same size and shape, but in a different position.
A translation rule for a triangle is given by a pair of numbers (a, b), which indicate the amount of horizontal and vertical movement of the vertices. Specifically, the rule is given by the formula:
(x, y) → (x + a, y + b)
This formula means that we move every point in the triangle a unit to the right or left (depending on the sign of a) and b units up or down (depending on the sign of b).
The translation rule (x, y) → (x − 3, y + 4) means that we move every point in the original triangle left by 3 units and up by 4 units. So, the translation is described as a leftward shift of 3 units and an upward shift of 4 units.
To find the vertices of ∆A′B′C′, we apply the translation rule to each vertex of ∆ABC:
Vertex A: (x, y) → (x - 3, y + 4)
(-3, 1) → (-3 - 3, 1 + 4) = (-6, 5)
So, vertex A of ∆A′B′C′ is located at (-6, 5).
Vertex B: (x, y) → (x - 3, y + 4)
(-3, 4) → (-3 - 3, 4 + 4) = (-6, 8)
So, vertex B of ∆A′B′C′ is located at (-6, 8).
Vertex C: (x, y) → (x - 3, y + 4)
(-7, 1) → (-7 - 3, 1 + 4) = (-10, 5)
So, vertex C of ∆A′B′C′ is located at (-10, 5).
To know more about geometry, visit:
https://brainly.com/question/11298860
#SPJ1
The complete question is as follows:
A salesman gets paid an annual salary of $35,000 plus he makes $75 for each sale. If this salesman made $46,700, how many sales did he make?
Answer: 156
Step-by-step explanation:
Annual Salary = $35, 000
Subtract anual salary from 46, 700. ---> 46,700-35,000= 11,700
One sale = $75
To find out how many sales, divide the remaining 11,700 by 75.
11,700/75= 156
156 sales.
khaled plants to go to the animal shelter to adopt a cat and then take it to the grooming shop. the shelter is located at (-3,-5) and the grooming shop is located at (5,-1). find the location of lhaled house if the distance from his house to the shelter and the distance from his house to the grooming shop has a ratio of 1:3
After answering the presented question, we can conclude that coordinates Therefore, Khaled's house is located at approximately (-4.75, -1.5).
what are coordinate ?In mathematics, a coordinate is a number or combination of numbers that represents the location of a point or object in space. Coordinates are frequently used to define a point or object's position in a certain coordinate system, such as the Cartesian or polar coordinate systems. In the Cartesian coordinate system, a point is found by its distance from the origin along the x-axis and its distance from the origin along the y-axis. These distances are represented by two integers, the x-coordinate and the y-coordinate. The point's location in the plane is specified by the two coordinates.
Distance from Khaled's house to the animal shelter:
[tex]d_1 = \sqrt((x - (-3))^2 + (y - (-5))^2) = \sqrt((x + 3)^2 + (y + 5)^2)[/tex]
Distance from Khaled's house to the grooming shop:
[tex]d_2 = \sqrt((x - 5)^2 + (y - (-1))^2) = \sqrt((x - 5)^2 + (y + 1)^2)\\d_1/d_2 = 1/3\\\sqrt((x + 3)^2 + (y + 5)^2) / \sqrt((x - 5)^2 + (y + 1)^2) = 1/3\\((x + 3)^2 + (y + 5)^2) / ((x - 5)^2 + (y + 1)^2) = 1/9\\8x + 38y + 4 = 0\\[/tex]
So the coordinates of Khaled's house are:
x = -4.75
y = -1.5
Therefore, Khaled's house is located at approximately (-4.75, -1.5).
To know more about coordinates visit:
https://brainly.com/question/27749090
#SPJ1