The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.
Slope of a line:The slope of a line is defined as the change in y- coordinate with respect to x - coordinate. The slope of a line represents the direction and steepness of a line. The formula for the slope of a line that passes through the points (x₁, y₁) and (x₂, y₂) is given by
Slope (m) = [ y₂ - y₁]/ [x₂ - x₁]Here we have
The pair of points (11, 8), (- 13, 11)
By the given formula,
Slope (m) = [ y₂ - y₁]/ [x₂ - x₁]
The slope from (11, 8) to (- 13, 11) can be calculated as follows
Slope = [ 11 - 8 ]/ [ -13 -11 ] = 3/-24 = -1/8
Therefore,
The slope of the line through each pair of points (11, 8), (- 13, 11) is -1/8.
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What is the solution to the following system of equations
4x+2y=6
X-y=3
Answer:
The solution of the equation 4x + 2y = 6 and x − y = 3 will be D. (2, –1)
Step-by-step explanation:
4x + 2y = 6 ....… (1)
x − y = 3 …..... (2)
Example, for equation 2 is:
x - y = 3
x = 3 + y
Put in equation 1:
4(y + 3) + 2y = 6
4y + 12 + 2y = 6
6y = -6
y = -6/6
y = -1
We have the value of y, then the value of x will be:
x = 3 + y
= 3 + (-1)
= 3 - 1
= 2
So, the solution of the equation 4x + 2y = 6 and x − y = 3 will be (2, –1)
Select the correct answer from each drop-down menu.
Observe the given functions.
Complete the sentences to compare the two functions.
Over the interval ____, the average rate of change of g is greater than the average rate of change of f. As the value of x increases, the average rates of change of f and g _________, respectively. When the value of x is equal to 7, the value of _________
It can be further generalized that a quantity increasing exponentially will ___ exceed a quantity increasing linearly.
The correct answer for each of the math expressions is given below:
1. (4,5)2. remain constant and increase3. g(x) exceeds the value of f(x)4. eventuallyWhat is a Graph?The graph of a function f in mathematics is the collection of ordered pairs where displaystyle f(x)=y.
These pairs are Cartesian coordinates of points in two-dimensional space and so form a subset of this plane in the typical situation when x and f(x) are real integers.
Hence, given that in the graph,
f(x) = 4x + 3
g(x) = [tex]\frac{5}{3} ^x[/tex]
Over the interval (4,5), the average rate of change of g is greater than the average rate of change of f.
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HELP DUE IN 20 MINS!!!!!
Boris's company makes solid balls out of scrap metal for various industrial uses. His current task is to make a batch of lead balls with radius 3 in. If he has a 3 total of 28,260 in³ of lead, how many balls can he make? Use 3.14 for , and do not round your answer.
The number of balls that he can make is given as follows:
249 balls.
How to obtain the volume of a sphere?The volume of a sphere of radius r is given by the equation presented as follows:
V = 4πr³/3.
Considering the radius of 3 inches, the volume of each ball is given as follows:
V = 4π x 3³/3
V = 113.1 in³.
He has a total of 28,260 in³ of material, hence the number of balls that he can make is given as follows:
28260/113.1 = 249 balls.
(rounding down, as there will not be enough material for the 250th ball).
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the hockey surface at a community centre is 61 m by 30.5m.FIeld hockey is played outdoors on a surface 91.5 by 54.9m.Which surface has the larger area and by how much?
The area of field hockey is larger by 3162.85 [tex]m^2[/tex].
What is Area ?The amount of unit squares that cover an enclosed figure's surface is its area. Square units like [tex]cm^2[/tex] and [tex]m^2[/tex] are used to measure area. A shape's area is a two-dimensional measurement. The space inside the perimeter or boundaries of a closed shape is known as the "area."
The hockey surface given here is in rectangular shape, so,
Area = length x breadth
Area of the hockey surface at a community centre is,
= 61 m x 30.5 m
=1860.5 [tex]m^2[/tex]
Area of field hockey played at outdoors,
= 91.5 m x 54.9 m
= 5023.35 [tex]m^2[/tex]
Clearly, we can see that area of field hockey is larger.
Difference between both the areas = 5023.35 -1860.5 = 3162.85 [tex]m^2[/tex].
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The area of an equi
Lateral triangle having height 12 cm is
The area of an equilateral triangle having height 12 cm is 83.136 sq.cm.
An equilateral triangle in geometry is a triangle with equal-length sides on all three sides. In the well-known Euclidean geometry, an equilateral triangle is also equiangular, meaning that each of its three internal angles is 60 degrees and congruent with the others. It is sometimes referred to as a regular triangle because it is a regular polygon.
if height h is given in equilateral triangle then first we have to find the length of side which can be solve by this formula like a right angle triangle where side of equilateral triangle is a and another side is a/2 and next is height which is given 12 cm.
[tex]a^{2} -(a/2)^{2} = 12^{2}[/tex]
[tex](3/4)a^{2} = 144[/tex]
[tex]a^{2} = 192\\a = \sqrt{192}[/tex]
a = 13.85
area of equilateral triangle = [tex]((\sqrt{3})/ 4 )a^{2}[/tex]
= 1.732*192/4
83.136 sq.cm
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relationship btw three set( in a market survey 100traders sell fruit, 40sell Apple, 46 sell Orange, 50 mango, 15sell Apple and Mango, 10 sell the three
fruit draw a venn diagram
Number of student that sell mango and orange
Answer:
7 traders sell oranges and mangoes alone.
Step-by-step explanation:
(21 + 4 + 5 + 10 + x + 35 – x + 32 – x = 100)
(107 – x = 100)
(x = 107 – 100 = 7)
Therefore, 7 traders sell oranges and mangoes alone.
(b) (312_{four} + 52_{x} = 96_{ten})
(312_{4} = 3 times 4^{2} + 1 times 4^{1} + 2 times 4^{0})
= (48 + 4 + 2 = 54_{10})
(52_{x} = 5 times x^{1} + 2 times x^{0})
= ((5x + 2)_{10})
(therefore 54 + (5x + 2) = 96)
(56 + 5x = 96 implies 5x = 96 – 56 = 40)
(x = 8)
(therefore 312_{4} + 52_{8} = 96_{10})
a lamppost, cab, bent at point a after a storm. the tip of the lamppost touched the ground at point c, as shown below: triangle abc has measure of angle c equal to 55 degrees, measure of angle abc equal to 90 degrees, and length of bc equal to 20 feet. what is the height, in feet, of the portion ab of the lamppost?
The height of the portion AB of the lamppost is approximately 27.8 feet, as calculated using the tangent function with angle 55 degrees and length BC 20 feet.
Based on the given information, we can use trigonometry to find the height of the portion AB of the lamppost.
Let's call the height of AB "x". We can use the tangent function to solve for x:
tan(55) = x/20
Multiplying both sides by 20:
x = 20 tan(55)
Using a calculator, we get:
x ≈ 27.8 feet
Therefore,
The height of the portion AB of the lamppost is approximately 27.8 feet.
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Answer: 20 tan 55
Step-by-step explanation:
took test and got it right
suppose x is the number of times a woman is selected when 3 people are randomly chosen (without replacement) from a group of 2 women and 2 men. what are the possible values of x?
Suppose x is the number of times a woman is selected when 3 people are randomly chosen from a group of 2 women and 2 men, the possible values of x are 0, 1, 2, and 3.
When 3 people are randomly chosen without replacement from a group of 2 women and 2 men, there are a total of 4C₃ = 4 possible outcomes, which we can list as follows:
WWx (two women and one of either gender)
WMx (one woman, one man, and one of either gender)
MWx (one man, one woman, and one of either gender)
MMx (two men and one of either gender)
In each of these outcomes, x represents the number of times a woman is selected. We can see that the possible values of x are 0, 1, 2, and 3, depending on which outcome occurs.
In outcome 1 (WWx), a woman is selected twice, so x = 2.
In outcomes 2 (WMx) and 3 (MWx), a woman is selected once, so x = 1.
In outcome 4 (MMx), no women are selected, so x = 0.
Therefore, the possible values of x are 0, 1, 2, and 3.
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a researcher divided subjects into three groups according to whether or not they have brown, blue or green eyes, and then selected members from each group for her sample. what sampling method was the researcher using? group of answer choices random systematic cluster stratified
If the researcher divided subjects into three groups according to whether or not they have brown, blue or green eyes, then the researcher was using a stratified sampling method.
Here a researcher divided subjects into three groups according to whether or not they have brown, blue, or green eyes.
The selected members from each group for their sample
The stratified sampling method is defined as the sampling method that divides the total population into the smaller group
Here the total population is divided into three groups according to whether they have brown, blue or green eyes.
Therefore, researcher was using stratified sampling method
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which of the following statements about approaches to political risk management is not true? question 26 options: passive political risk management discourages managers from fully or partially hedging their bets against exposure to political hazards. passive political risk management assumes that it is difficult, if not impossible, to systematically model political risk. active political risk management assumes that positive and negative political events in any country are neither independent nor random events. active political risk management assumes that political events unfold in observable patterns that statistical methods can detect.
The statement which is not true is a. Passive political risk management discourages managers from fully or partially hedging their bets against exposure to political hazards
Passive political risk management does not deter managers from fully or partially hedging their bets against political risk exposure. This management describes a strategy for controlling political risk that involves altering how a firm carries out a business to reduce political risk. This is generally performed without necessarily using financial instruments to safeguard against any degree of political risk.
It may entail taking necessary steps to spread the firm's operations across other geographies and regions, choosing joint venture partners with strong political influence, determining local contacts, and preserving strong ties with local individuals associated with politics. Even if a firm doesn't use active hedging tactics, these activities can efficiently assist it to lessen its exposure to political risk.
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three vertices of ABCD are A(2,4) b(5,2) c(3,-1) find the coordinates of vertex D
The coordinates of vertex D of the parallelogram is; (0, 1)
How to find the coordinates of a Parallelogram?We are given the coordinates of the parallelogram as;
A(2,4), B(5,2) and C(3,-1)
Now, we know that the diagonals of a parallelogram bisect each other. So, the midpoint of AC is same as the mid point of BD.
The formula for the midpoint between two coordinates is;
(x1 + x2)/2, (y1 + y2)/2
Thus;
Midpoint of AC = (2 + 3)/2, (4 - 1)/2 = 5/2, 3/2
Midpoint of BD = (5 + x)/2, (2 + y)/2
Thus;
(5 + x)/2 = 5/2
x = 0
(2 + y)/2 = 3/2
2 + y = 3
y = 1
Coordinate of D = (0, 1)
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In a class of 55 student 21 study Physic, 24 study geography, 23 study econs, 6study both phy and geo, 4 study both geo and econs, 5 both econs and phy, if X study all the three subject and 20 study non of the three subject
find the value of X
find the Number of student that study phy only
No of student that study one of the 2 subject
X = 2 (two) students study all three subjects (physics, geography, and economics). This can be found by adding the number of students who study only two subjects (6 + 4 + 5 = 15) and subtracting that from the total number of students who study at least one subject (55 - 20 = 35), since each of these 15 students who study two subjects is counted twice in the totals for each subject.
How do we get the responses to other questions?The number of students who study physics only is 10. This can be found by subtracting the number of students who study physics and at least one other subject (21 - 6 - 5 - 2 = 8) from the total number of students who study physics (21).
The number of students who study exactly one of the two subjects is 25. This can be found by adding the number of students who study each subject only (10 + 11 + 9) and subtracting that from the total number of students (55 - 20 = 35).
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Please help me by finding the degree measure of angle x
Triangle ABC is the term used to refer to a triangle with the vertices A, B, and C. When the three points are not collinear, a unique plane and triangle in Euclidean geometry are discovered [tex]A^2 = B ^2 + c^2[/tex] => AC = [tex]\sqrt{115}[/tex]
What is the Pythagorean theorem?Given that it has three sides and three vertices, a triangle qualifies as a polygon. It belongs to the fundamental geometric shapes.
Triangles are polygons because they have three sides and three corners. The points where the three sides of the triangle converge are referred to as the triangle's corners. 180 degrees is obtained by multiplying three triangle angles.
Here, in this triangle by Pythagorean theorem
[tex]A^2 = B ^2 + c^2[/tex]
AC = [tex]\sqrt{14^2- 9^2}[/tex]
AC = [tex]\sqrt{196- 81}[/tex]
Ac = [tex]\sqrt{115}[/tex]
Therefore, We can state that this triangle conforms to the Pythagorean theorem after answering the offered question.
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you could measure arrival delay by recording the amount of time between actual arrival time and scheduled arrival time (with positive numbers representing delays and negative numbers representing early arrivals). is this variable categorical or quantitative? if the variable is quantitative, classify it as discrete or continuous.
It is a continuous variable, as it can take on any value within a certain range (i.e., any value between a positive delay and a negative early arrival).
The variable described is quantitative, as it represents a numerical measurement of time, which is a continuous variable that can take on any value within a certain range. The range includes both positive values, representing delays, and negative values, representing early arrivals. This variable is a useful metric for tracking the performance of transportation systems or airlines, as it provides an objective measure of the amount of time a flight is delayed or arrives early. By analyzing the distribution of arrival delay times, policymakers and transportation providers can identify patterns, trends, and potential areas for improvement in their service delivery.
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A coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50%.
The statement, coin is flipped 14 times and lands on heads 8 times. The theoretical probability that the next coin flip will be heads is 50% is True.
What is probability?The probability of an occurrence is a figure that represents how likely it is that the event will take place. In terms of percentage notation, it is expressed as a number between 0 and 1, or between 0% and 100%. The higher the likelihood, the more likely it is that the event will take place. A definite occurrence has a chance of 1 while an impossible event has a probability of 0.
When a coin is flipped the probability of getting a heads and a tail is 50%.
Hence, without the consideration of the flips and the result the theoretical probability that the next coin flip will be heads is 50%.
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How many terms are in this expression?
4n + 6m
Answer:
2
Step-by-step explanation: this is because the plus sign splits the terms so simply 2 terms
assume that earth is a sphere with radius 3960 miles a town is at latidtude 32 n find the distance in miles from the town to the north pole
The distance from the town to the North Pole is approximately 2290 miles.
To find the distance in miles from the town to the North Pole, we need to calculate the length of the meridian arc from the town to the North Pole. The meridian arc is a portion of a great circle passing through the town and the North Pole.
The length of the meridian arc can be calculated using the formula:
Length = (π/180) x radius of the Earth x angle in degrees
where π is approximately 3.14159, and the radius of the Earth is 3960 miles.
Since the town is located at latitude 32°N, the angle between the town and the North Pole is 90° - 32° = 58°.
Plugging in these values into the formula, we get:
Length = (π/180) x 3960 miles x 58°
Length = (3.14159/180) x 3960 miles x 58
Length ≈ 2290 miles
Therefore, the distance from the town to the North Pole is approximately 2290 miles.
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From the top of a canyon, the angle of depression to the far side of the river is 52°, and the angle of depression to the near side of the river is 71°. The depth of the canyon is 230 feet. What is the width of the river at the bottom of the canyon? Round to the nearest foot.
Trig question
Answer:
49ft
Step-by-step explanation:
Sketching out the problem, we get something like the diagram below. Assuming the canyon makes a roughly 90° angle with the ground, we can see that we have two right-angled triangles formed.
Focusing on the first triangle: since we have the angle, and we know the height of the canyon is 230ft, we can also find the combined width of the ground and river (let's call this y) using cos:
cos38=230/y
0.7880107536=230/y
y=230/0.7880107536= 291.874189467ft
Focusing now on the first triangle: since we have the angle, and we know the height of the canyon is 230ft, we can find the width of the ground (let's call this x) using cos:
cos19=230/x
0.94551857559=230/x
x=230/0.94551857559= 243.252756673ft
Therefore, the width of the river must be the difference between the combined width of the ground and river, minus the width of the ground:
291.874189467ft - 243.252756673ft = 48.621432794ft ≈ 49ft
the school swimming pool is 50m long and 21 m wide. The pool is divided lengthwise into six lanes for a swim meet. what is the area of each lane?
Answer:
175m²
Step-by-step explanation:
Total area (of pool):
50 × 21 = 1050
Area of each lane:
1050 ÷ 6 = 175
A total of 709 tickets were sold for the school play. They were either adult tickets or student tickets. There were 59 more student
tickets sold than adult tickets. How many adult tickets were sold?
Solving the Question
First, assign variables to the given information:
Let the number of student tickets sold be x.Let the number of adult tickets sold be y.We're given:
[tex]x+y=709[/tex][tex]x=59+y[/tex]Plug the second equation into the first and solve using substitution:
[tex]x+y=709\\59+y+y=709\\59+2y=709\\2y=650\\y=325[/tex]
Therefore, 325 adult tickets were sold.
Answer325 adult tickets were sold.
in nine bernoulli trials, what is the probability that there will be more than the expected number of failures?
The probability of having more than the expected number of failures (i.e., at least five failures) in a set of nine Bernoulli trials is 0.2461, assuming that the probability of failure is 0.5.
In the field of probability, it is essential to understand the expected number of successes or failures in a given set of trials. However, what happens when we observe more or fewer outcomes than expected? In this scenario, we need to calculate the probability of observing a specific number of failures in a set of Bernoulli trials.
Let's assume that the probability of failure is denoted by "p," and the probability of success is denoted by "q." Thus, the expected number of failures in nine Bernoulli trials is given by:
E(X) = np
where n is the number of trials, and p is the probability of failure. In this case, n = 9, and we need to determine the probability of having more than the expected number of failures. This means we are interested in finding the probability of observing at least five failures since the expected number of failures is given by:
E(X) = 9p
If we assume that the probability of failure is 0.5 (i.e., p = 0.5), then the expected number of failures is 4.5 (i.e., E(X) = 9 * 0.5 = 4.5). Therefore, we are interested in finding the probability of observing at least five failures in nine Bernoulli trials.
To calculate this probability, we need to use the binomial distribution formula, which is given by:
[tex]P(X = k) = (^n_k) \times p^k \times q^{n-k}[/tex]
where P(X = k) is the probability of observing k failures in n trials, (n choose k) is the binomial coefficient, which is calculated as n! / (k! (n-k)!), p is the probability of failure, q is the probability of success (i.e., q = 1 - p), and k is the number of failures we are interested in observing.
Using this formula, we can calculate the probability of observing at least five failures in nine Bernoulli trials as follows:
P(X >= 5) = P(X = 5) + P(X = 6) + P(X = 7) + P(X = 8) + P(X = 9)
= (9 choose 5) x 0.5⁵ x 0.5⁴ + (9 choose 6) x 0.5⁶ x 0.5³ + (9 choose 7) x 0.5⁷ x 0.5² + (9 choose 8) x 0.5⁸ x 0.5¹ + (9 choose 9) x 0.5⁹ x 0.5⁰
= 0.2461
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29. A racket is propelled upward from the top of a building 210 feet tall at an initial velocity of 112 feet per secon
The function that describes the height of the rocket in terms of time t is S(t) = - 16+2 + 112t + 210.
Determine the time at which the rocket reaches its maximum height.
a. 2.8 seconds
b. 3.5 seconds
C. 7 seconds
d. 5.6 secands
The time at which the rocket reaches its maximum height is 3.5 seconds. Therefore, b. is the correct answer.
What is function f(x)?An equation describing the relationship between the input (x) and the output (f(x)) is called the function f(x). Any equation that represents the connection between an input x and an output f is referred to as the function f(x) (x).
A function can be expressed as a graph or table in addition to the standard form of an equation. Functions can be stated using symbols and phrases in addition to equations. A function could be expressed, for instance, as "the square of x" or "f of x equals x squared."
Whatever form a function takes, it's critical to keep in mind that the input (x) always yields the same result (f(x)).
In the given question,
The maximum height of the rocket is achieved at the point when the velocity of the rocket is 112 feet. This can be determined by taking the derivative of the function S(t).
S'(t) = 112
Therefore, when S'(t) = 112, t = 3.5.
This means that the rocket reaches its maximum height at t = 3.5 seconds.
Therefore, the time at which the rocket reaches its maximum height is 3.5 seconds.
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Jody is picking a movie to watch this evening.
Of the movies in her cabinet, 9 are romantic
comedies. She will pick one movie at random.
If the probability of the selected movie being
a romantic comedy is 25%, how many movies
are on the shelf?
The number of movies on the shelf is given as follows:
36 movies.
How to calculate a probability?A probability is calculated as the division of the desired number of outcomes by the total number of outcomes.
For this problem, the parameters are given as follows:
Probability of 25% = 1/4.Number of desired outcomes is of 9.Hence the total number of outcomes, representing the number of movies on the shelf, is obtained as follows:
1/4 = 9/x
x = 9 x 4
x = 36 movies.
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Doranda was given two paid vacation days by her employer when she started her new job. She will receive an additional three days per year of paid vacation for each year she remains with the company up to a maximum of four work weeks of paid vacation time. Part A
The expression for the number of paid vacation days for x years is
2 + 3x.
What is an expression?An expression contains terms with addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number of paid vacation days = 2
Now,
She will receive an additional three days per year of paid vacation for each year she remains with the company.
This means,
For x years,
Number of paid vacation days = 2 + 3x
Now,
The expression for x years.
= 2 + 3x
Thus,
2 + 3x is the expression for the number of paid vacation days for x years.
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The complete question.
A)
Write an expression for the number of paid vacation days for x years.
Assignment
E
7m
K
6m 20 m
A
28 m
F
5 m J
24 m
G
Intro
LL
L
Mai enlarges a triangular sign by a multiple of 4
creating similar triangles. The bottom of the original
sign is side EG. Which side of the enlarged sign
corresponds to side EG?
If she wanted to turn the sign so that side JK was on the
bottom, what side of the original sign would this
correspond to?
Done
See below for the description of the enlarged shapes when dilated
How to determine the side of the enlarged sign corresponds to side EG?From the question, we have the following parameters that can be used in our computation:
Scale factor = 4
This means that if Mai enlarges the triangular sign by a multiple of 4,
Then the corresponding side in the enlarged sign to side EG is 4 times the length of side EG.
i.e Corresponding side = 4 * Original side
If Mai wanted to turn the sign so that side JK was on the bottom,
Then the corresponding side of the original sign would be the side that was previously opposite to JK.
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In the diagram below, RA is parallel to ET, and RT is 21 units long. Find the length of ST.
Answer:
ST = 12 units
Step-by-step explanation:
Δ STE and Δ SRA are similar ( AA postulate ) , then the ratios of corresponding sides are in proportion, that is
[tex]\frac{ST}{SR}[/tex] = [tex]\frac{TE}{RA}[/tex] ( substitute values )
[tex]\frac{ST}{21-ST}[/tex] = [tex]\frac{8}{6}[/tex] ( cross- multiply )
6 ST = 8(21 - ST)
6 ST = 168 - 8 ST ( add 8 ST to both sides )
14 ST = 168 ( divide both sides by 14 )
ST = 12 units
I don’t how to solve it
Answer:
Step-by-step explanation:
Since they are congruent, you know that 8=x-3. 11-3=8. and 14=x+6=8. x is 8
In a triangle ABC, AB = 5cm , BC = 7cm and CA = 8cm. Id D and E are reep mid points of AB and BC, find the length of DE.
The measured length of DE will be 4 cm.
What is the similarity?Two objects are said to be comparable if they have the same shape. Therefore, two figures are said to be comparable in mathematics if they share the same shapes, lines, or angles.
Given that AB is 5 cm, BC is 7 cm, and CA is 8 cm in the triangle ABC. The reep midpoints of AB and BC are Ids D and E.
The two triangles ABC and ADE will be similar to each other. The measure of the length DE will be calculated as:-
AC = DE = 7 / 3.5
DE = AC / 2
DE = 8 / 2
DE = 4 cm
Hence, the value of the side DE will be 4 cm.
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Question 7. A boat rental shop rents paddleboats for a fee plus an additional cost per hour. * O
The cost of renting for different numbers of hours is shown in table. Use the table and the
variables to write an equation. Let y = cost and x = hours.
The equation of the given information is y(x) = 5x+10
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
A mathematical equation is a statement with two equal sides and an equal sign in between.
Given that cost of renting for different numbers of hours.
The initial cost, regardless of time, is; $10. then the cost will increase at a rate of $5 per hour that the boat is rented.
Therefore, the cost (y) of renting a paddle boat for 'x' hours is:
y(x) = 5x+10
here linear relationship between x and y, where 5 is the slope of the equation, 10 is the y-intercept, the number of hours is the independent variable, and the cost is the dependent variable.
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Hi. I need 8 expressions that are equivalent to 31(2760q - d)
Answer: is 1 of them 31(2760)q -d)
