To comply with the triangle inequality theorem, the smallest possible length of the congruent sides in an acute isosceles triangle with the longest side being 8 centimeters, would be slightly greater than 4 centimeters, rounded to the nearest tenth (4.1 centimeters).
Explanation:In the context of an acute isosceles triangle, the longest side is the base and the other two sides are congruent or have equal length. The smallest possible length of the congruent sides comes into play in respect of the triangle inequality theorem, stating that the sum of the lengths of any two sides must be greater than the length of the third side. Thus, for the smallest possible length, each of the congruent sides must hence be just slightly larger than half the length of the longest side. So for an 8 centimeter base, the smallest length for the congruent sides should be slightly more than 4 centimeters, let's call it 4.1 centimeters, when rounded to the nearest tenth.
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What is the equation of the blue graph?
State two reasons why including the p-value is prudent when you are reporting the results of a hypothesis test.
Which person in the high rise building is closest to the street level?Moira is in her doctor’s office on the fourth floor.Geoffrey is in the elevator between the second and third floors.Sandy is in the laundry room on the –2 basement floor.Hasim is leaving the parking garage and is currently between –1 and –2 levels.
Answer
Hasim is the closest... I just took the test
The trees at a national park have been increasing in numbers. There were 1,000 trees in the first year that the park started tracking them. Since then, there has been one fifth as many new trees each year. Create the sigma notation showing the infinite growth of the trees and find the sum, if possible.
1 1000
2 200
3 40
Answer:
A
Step-by-step explanation:
Find the volume of each figure to the nearest tenth. Show your work.
The sum of three numbers is 91. the third number is 2 times the first. the first number is 7 less than the second. what are the numbers?
To solve for three unknown numbers with given relationships, we set up algebraic equations. Using substitution, we find the three numbers by solving the linear system. The numbers are 21, 28, and 42.
Explanation:The problem presented is a typical linear equation problem found in mathematics where we need to find the values of three unknown numbers with the given relationships between them. To find the three numbers, we set up algebraic equations based on the information provided. Let's denote the first number as x, the second number as y, and the third number as z.
According to the problem:
The sum of the three numbers is 91: x + y + z = 91.The third number is 2 times the first: z = 2x.The first number is 7 less than the second: x = y - 7.Let's now use substitution to solve for the numbers. Substituting the value of x from the third equation into the second equation, we get z = 2(y - 7). Plugging the expressions for x and z back into the first equation, we have y - 7 + y + 2(y - 7) = 91. Simplifying this equation gives us 4y - 21 = 91, which solves to y = 28. Using y = 28, we find x = 21 and z = 42.
Therefore, the three numbers are 21, 28, and 42.
Two lines are perpendicular. if one line has a slope of 0, what is the slope of the other line?
which residual plot shows that the line of best fit is a good model?
The residual plot with a line of best fit that is a good model is the third residual plot.
Which line of best fit is a good model?The line of best fit should cut across data points in such a way that the data points on each side are relatively the same number.
The data points on both sides should also be roughly the same distance away from the line. The third residual plot fits these parameters and so shows the line of best fit as a good model.
Find out more on the Line of Best fit at https://brainly.com/question/21241382.
Answer:
the 3rd one
Step-by-step explanation: took the test on edu
Hillary rolls 2 number cubes numbered 1 through 6 while playing her favorite board game. She will get a second turn if she rolls a sum that is an odd number greater than 10. What are Hillary's chances of getting a second turn when she rolls the number cubes?
the area of a rectangle with width x and length 7x is 7x^2 what does the coefficient 7 mean in terms of the problem
A square with an area of 64 in2 is rotated to form a cylinder. What is the radius of the cylinder?
points (0,0) and (3,3) lie on line k what is the slope of the line that is perpendicular to k
Which number line represents the solution set for the inequality 2x – 6 ≥ 6(x – 2) + 8?
what way do you shade in
Answer:
x < = -1/2 or -0.5
Step-by-step explanation:
that's the answer
The function below shows the number of car owners f(t), in thousands, in a city in different years t: f(t) = 0.25t2 − 0.5t + 3.5 The average rate of change of f(t) from t = 2 to t = 6 is ______ thousand owners per year. Answer for Blank 1:
Choose the correct simplification of (6x4y2z3)(3x4y3z5).
18x16y6z15
18x8y5z8
9x8y5z8
9x16y6z15
Answer:
18 x 8y 5z 8 witch is answer choice B
Step-by-step explanation:
A carpet cleaning business has 100 customers when they charge $125 for a cleaning. Research shows that every $5 reduction in price attracts another 20 customers. What price should the business implement to maximize its revenue?
a $75
b $100
c $120
d $90
The linear relationship is c(p) = -4p + b. Then the price that maximizes revenue is $75.
What is the linear system?It is a system of an equation in which the highest power of the variable is always 1.
A carpet cleaning business has 100 customers when they charge $125 for cleaning.
Research shows that every $5 reduction in price attracts another 20 customers.
Since a $5 decrease in price increases customers by 20, we can say that we have two options.
(120, 100) and (120, 120) from these we can find the slope or rate of change of customers as a function of price.
[tex]\rm m = \dfrac{20}{-5}\\\\ m = -4[/tex]
Then we have
[tex]\rm c(p ) = -4 p +b[/tex]
Now, we can use (125, 100) to solve for b
100 = -4(125) + b
b = 600
So our number of customers as a function of price is
[tex]\rm c(p) = 600 - 4p[/tex]
Revenue will simply be the number of customers times the price charged per customer will be
[tex]\rm r(p) = 600 p -4p^2[/tex]
We can find a price that creates maximum revenue by finding when the derivative is equal to zero.
[tex]\rm \dfrac{dr}{dp} = 600 - 8p\\\\[/tex]
WE know that for maximum,
[tex]\rm \dfrac{dr}{dp} = 0\\\\0 = 600 - 8p\\\\p = 75[/tex]
So, the price that maximizes revenue is $75.
More about the linear system link is given below.
Find the value of X.
what is the range of f(x)=log0.6x
On Mars, if you hit a baseball, the height of the ball at time "t" would be modelled by the quadratic function h=-1.85t^2+20t+1, where t is in seconds and h is in metres. When will the ball hit the ground?
If the tangent line to y = f(x) at (7, 4) passes through the point (0, 3), find f(7) and f '(7).
Final answer:
To find f(7) and f'(7) of y = f(x) given a point on the tangent line passing through another point.
Explanation:
Given:
Equation of tangent line to y = f(x) at (7, 4) passes through (0, 3).
To find:
f(7) and f'(7).
The graph below shows a line segment PQ: graph of line PQ going through ordered pairs negative 1, 3 and 2, negative 3 Which of the following equations best represents the line segment PQ?A: y = −3x + 2B: y = −2x + 1C: y = −3x − 2D: y = −2x − 1
Answer:
y = -2x + 1. The answer is B.
Step-by-step explanation:
Ted and Meg have each drawn a line on the scatter plot shown below:
Which line best represents the line of best fit?
Line P, because it is closest to most data points
Line P, because it shows a positive association
Line R, because it is closest to most data points
Line R, because it shows a negative association
line P is the best fit, since the data points are closest to it,
so the first answer.
The line which best represents the line of best fit is:
Line P, because it is closest to most data points
Step-by-step explanation:The line of best fit is a line which best represents the data and the data points are closely related to it.It is also known as a trend line.The line of best fit may pass through, some , none or all of the data points.Also if the scatter plot does not pass through all the data point then the magnitude of positive residual must be approximately equal to the magnitude of negative residual of the data points.Hence, by looking at the scatter plot we see that all the data points lie above Line R.
Hence, the Line R will not be a line of best fit.
But all the data points lie close to the line P , hence it act as a line of best fit.
Describe the graph of the function.y = |x – 4| – 7
We are given a function as:
[tex]y=|x-4|-7[/tex]
We know that this function is a transformation of the parent function y=|x| i.e. the modulus function.
The rule that holds in this transformation is:
It is a translation of the parent function 4 units to the right and 7 units down.
Also, the graph of the function is attached to the answer.
The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2). The answe is x_ _= something
Which is an equation of a circle with center (2, -1) that passes through the point (3, 4)?
1. (x + 2)2 + (y - 1)2 = 26
2. (x + 2)2 + (y - 1)2 = 13
3. (x - 2)2 + (y + 1)2 = 26
4. (x - 2)2 + (y + 1)2 = 13
To make bread dough, a baker mixes flour, eggs, yeast and salt by weight in pounds in the ratio of 11:9:3:2, respectively. how many pounds of yeast are required to make 20 pounds of bread dough?
Which line is parallel to the line y=12x+5 and passes through the point (-2, 1)?
The equation of the line parallel to y=12x+5 that passes through the point (-2, 1) is y=12x+25.
Since the two lines are parallel, they will have the same slope. The slope of the given line is the coefficient of x, which is 12. Therefore, the line we are looking for also has a slope of 12.
To find the equation of the new line, we'll use the point-slope form of a line equation, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the given point.
Substituting the given point and the slope into this form we get:
y - 1 = 12(x + 2)
Expanding and simplifying this, we have:
y - 1 = 12x + 24
Finally, adding 1 to both sides to solve for y, we get:
y = 12x + 25, which is the equation of the line that is parallel to y=12x+5 and passes through the point (-2, 1).
A key code must contain 6 numerals. There are 10 numerals available. Using these numerals, how many different key codes may be created? A. 151,200 B. 340 C. 210 D. 3,480
Answer: Option A, 151,200 possible combinations.
Explanation:
The code must contain 6 numbers, and there are a total of 10 numbers avaible. Here we must assume that the numbers must be different, because of the word "avaible" and the options avaible.
This means that for the first number, we have 10 options, for the second number, we have 9 options (because we already took 1), in the third number, we have 8 options, and so on.
The total number of combinations is equal to the product between the number of options for each number in the code.
10*9*8*7*6*5 = 151,200
Then the right option is A.
Okay before i even ask, everyone should i suck at math. so: Michelle went to Spain for 22 days in June. What fraction of the month June did Michelle spend in Spain?
What is the simplified form of 3 over 4x plus 3 + 21 over 8 x squared minus 14x minus 15
6 times the quantity 2 x plus 5 end quantity over the quantity 2x minus 5 end quantity times 4 x plus 3
6 over the quantity 4 x plus 3
6 times the quantity x plus 1 end quantity over the quantity 2x minus 5 end quantity times 4 x plus 3
6 times the quantity x plus 1 end quantity over the quantity 2x plus 5 end quantity times 4 x plus 3
Answer: Third Option is correct.
Explanation:
Since we have given that
[tex]\frac{3}{4x+3}+\frac{21}{8x^2-14x-15}[/tex]
Now, we will simplify it, step by step:
First we take 3 as common factor :
[tex]3[\frac{1}{4x+3}+\frac{7}{8x^2-14x-15}][/tex]
Now, we will do the method " Splitting the middle term" we get,
[tex]3[\frac{1}{4x+3}+\frac{7}{8x^2-20x+6x-15}]\\\\3[\frac{1}{4x+3}+\frac{7}{4x(2x-5)+3(2x-5)}]\\\\3[\frac{1}{4x+3}+\frac{7}{(4x+3)(2x-5)}]\\\\3[\frac{2x-5+7}{(2x-5)(4x+3)}]\\\\=3[\frac{2x+2}{(2x-5)(4x+3)}]\\\\=\frac{6(x+1)}{(2x-5)(4x+3)}[/tex]
Hence, 6 times the quantity x plus 1 end quantity over the quantity 2x minus 5 end quantity times 4x plus 3.
Therefore, Third Option is correct.