4. A town has an initial population of 75,000. It grows at a constant rate of 2,500 per year for five years
a. Find the linear function that models the town's population P as a function of the year, t where t is the number of years since the model began
b. Graph y==p(t) Interpret the meaning of the Intercepts.
c. When does the model expect the population to reach 100,000?
5. The weight of a newborn baby is 7.5 pounds. The baby gained one-half pound a month in its first year.
a. Find the linear function that models the baby's weight W as a function of the age of the baby t, in months
b. Fine a reasonable domain and range for the function W
Answers
The city has an initial population of 75,000.
Grows at a constant rate of 2,500 per year for five years
a) We must find a linear function that models the P population of the city according to the years.
This function has the following form:
[tex]P=P_{0}+ at\\[/tex]
Where
P is the population as a function of time
[tex]P_{0}[/tex] is the initial population
"a" is the constant rate of growth of the function.
"t" is the time elapsed in units of years.
Then the function is:
[tex]P=75,000+2500t[/tex]
b) Before plotting the function, let's find its intercepts with the "t" and "P" axes
To find the intercept of the function with the t axis we do P = 0
[tex]0 =75000+2500t[/tex]
[tex]t=\frac{-75 000}{2500}[/tex]
[tex]t = -30[/tex]
Now we make t = 0 to find the intercept with the P axis
[tex]P =75000[/tex]
The intercept with the P axis at P = 75 000 means that this is the initial population, therefore, for a period of 0 to 5 years, the population can not be less than 75,000.
The intercept at t = -30 does not have an important significance for this problem, since we are evaluating population growth for a period of [tex]0 \leq t \leq 5[/tex].
The graph of the function is shown in the attached figure.
c) To answer this question we must do P = 100 000 and clear t.
[tex]100000=75000+2500t [/tex]
[tex]25 000=2500t [/tex]
[tex]t =10years[/tex].
The second problem is solved in the following way:
The weight of a newborn baby is 7.5 pounds
The baby earns half a pound a month in its first year
a) To find the function that models the weight of the baby we follow the same procedure as in the previous problem.
[tex]W = W_{0} + at[/tex]
Where
W is the baby's weight according to the months
[tex]W_{0}[/tex] is the initial weight in pounds
"a" is the rate of increase
"t" is the time elapsed in months.
So:
[tex]W = 7.5 + 0.5t[/tex]
b) The domain of the function is [tex]0 \leq t \leq 12\\[/tex]
Since the function only applies for the first year of growth of the baby, and one year has 12 months.
The range of the function is [tex]7.5 \leq W\leq 13.5[/tex]
The towns' population and the baby's weight can be modeled by linear functions, which have a constant growth rate and an initial starting value. For the population to reach 100,000, we need to solve for t in our linear equation. Linear relationships are common in population growth, but are often approximations as they ignore limiting factors.
Explanation:In both scenarios, we're dealing with linear functions. The towns' population, P, can be represented by a linear function as follows: P(t) = 2,500*t + 75,000 where t is the number of years passed. For the baby's weight, use the similar linear function: W(t) = 0.5*t + 7.5, where t is the baby's age in months. Both functions have an initial value (intercept at t=0) and a constant growth rate (the slope of the line). For the town's population to reach 100,000, solve the equation 100,000 = 2,500*t + 75,000 for t. Similarly, the baby's weight will depend on how many months have elapsed.
To graph either function, start at the intercept (t=0) and use the slope to find additional points (i.e., for each year that passes, add 2,500 to the population, or for each month that passes, add 0.5 to the baby's weight).
Linear relationships like these are common in Population Growth and other Population Models but are often approximates as they ignore factors that may limit growth (such as resources).
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Related Questions
Compare 9.36 and 9.359
Answers
Try this option (this is not the only way!):
1. the rule: if 'number_1' - 'number_2' > 0, then number_1>number_2. If 'number_1'-'number_2'<0, then number_2>number_1.
2. according to the rule above: 9.36-9.359=0.001. 0.001>0, it means, 9.36>9.359.
Which of the following describes how to translate the graph y = |x| to obtain the graph of y = |x - 1| - 1? 1 unit left and 1 unit down 1 unit left and 1 unit up 1 unit right and 1 unit down 1 unit right and 1 unit up
Answers
Answer:
1 unit right and 1 unit down
Step-by-step explanation:
When you replace x with x - h, you translate the graph h units horizontally.
When you replace y with y - k, you translate the graph k units vertically.
y = |x - 1| - 1
y + 1 = |x - 1|
y - (-1) = |x - 1|
Compare the last equation above with y = |x|. x was replaced by x - 1, so h = 1, and the translation is 1 unit horizontally. Since 1 is positive, it is a 1 unit translation to the right. y was replaced by y - (-1), so k = -1, and the vertical translation is 1 unit down.
Answer:
1 unit right and one unit down
Step-by-step explanation:
Math problem please help!
and if you could explain how you got your answer that would be very helpful thanks!
Answers
-110 = 13 + 3(4h -6) . . . . . . given
-110 = 13 + 12h -18 . . . . . . . eliminate parentheses using the distributive property
-110 = 12h -5 . . . . . . . . . . . . collect terms
-105 = 12h . . . . . . . . . . . . . . add 5 to both sides of the equation
-105/12 = h = -8.75
______
There are many ways you can solve this. Another is to undo the operations done to h. The variable h is ...
multiplied by 4has -6 added to the producthas the sum multiplied by 3has 13 added to the productWhen you undo these, you do it in reverse order:
-110 -13 = 3(4h -6) . . . . subtract 13
-123/3 = 4h -6 . . . . . . . divide by 3
-41 +6 = 4h . . . . . . . . . .add 6
-35/4 = h . . . . . . . . . . . divide by 4
h = -8.75
Write a ratio for each situation 310 beats per minute
Answers
The obvious one is (310 beats)/(1 minute).
A circle has an area of 324π cm2. What is the radius?
Answers
Final answer:
To find the radius of a circle, use the formula A = πr² and solve for r by dividing the area by π and then taking the square root of the result.
Explanation:
The radius of a circle can be found using the formula for the area of a circle, A = πr².
Given A = 324π cm², substitute this value into the formula: 324π = πr².
Solve for r by dividing both sides by π: r² = 324, r = √324, r = 18 cm.
One ordered pair (a,b) satisfies the two equations ab^4 = 12 and a^5 b^5 = 7776. What is the value of 'a' in this ordered pair?
Answers
Answer:
a = 4.762203156
Step-by-step explanation:
Given:
ab^4 = 12 and a^5b^5 = 7776
Making the equations a subject of a;
a = 12/b^4 and a^5 = 7776/b^5
Finding fifth root on both sides of equation two;
a = [tex]\sqrt[5]{7776}[/tex]/b
You will get a = 6/b
Equating the two equations;
12/b^4 = 6/b
Multiplying both sides by b^4 gives:
b = [tex]\sqrt[3]{2}[/tex] = 1.25992105
We had that a = 12/b^4 so;
a = 12/1.25992105^4 = 12/2.5198421 = 4.762203156
one type of insect is 0.0052 meter long. what is the length in scientific notation.
Answers
Here, we need to write the length of the insect in scientific notation.
The given length of the insect is 0.0052 meter
Now, to write 0.0052 meter in scientific notation we need to follow this:
Scientific notation always start with non-zero digit followed by a decimal point.
Since in our number the decimal is needed to be moved three places to the right to get the first non-zero digit.
The exponent of the 10 is [tex]-3[/tex].
[tex]10^{-3}=\frac{1}{1000} =0.001[/tex]
Therefore, our number 0.0052 can be written as:
[tex]5.2 \times 10^{-3}[/tex]
Hence, the require scientific notation is [tex]5.2 \times 10^{-3}[/tex].
What system of linear inequalities is shown in the graph?
Enter your answers in the boxes.
two boxes
Answers
Try this option:
1) to difine the equations of the lines given in the picture. They are: y= -0.5x+2 (for the left line, see the attached picture) and y=2x-3 (for the right line).
2) according to the condition (dark area and type of the line) the 1st inequation is y≥ -0.5x+2, the 2d inequation is y>2x-3.
3) the required system is
[tex]\left \{ {{y>2x-3} \atop {y\geq -0.5x+2}} \right.[/tex]
Classify the following triangle. Check all that apply.
Answers
Step-by-step explanation:
A triangle can be of many types like right angled triangle, isosceles triangle, scalene triangle, obtuse, acute etc.
A right angle can be defined as the triangle in which one of the angle is 90 degrees.
An obtuse angle is that type of triangle in which the the angle is more than 90 degrees and less than 180 degrees.
An isosceles triangle is one in which two sides are equal.
An acute angle is the triangle in which the angle is less than 90 degrees.
The attached triangle is :
1. Right angle triangle
2. Isosceles triangle
A bag of marbles contains 7 red, 5 blue, 4 green, and 2 yellow marbles. Jon selects a marble, replaces it, then selects another marble. What is the probability that Jon selects a red marble and then a yellow marble?
Answers
Answer: about 0.0432 or 4.32%
Step-by-step explanation:
Given : A bag of marbles contains 7 red, 5 blue, 4 green, and 2 yellow marbles.
Total marbles = 7+5+4+2=18
Let R : Event of getting first marble as red .
Y= Event of getting second marble as yellow.
Jon selects a marble, replaces it, then selects another marble.
⇒Both events are independent .
Probability of getting first marble as red = [tex]P(R)=\dfrac{\text{Number of red marbles}}{\text{Total marbles}}[/tex]
[tex]\\\\=\dfrac{7}{18}[/tex]
Probability of getting second marble as yellow = [tex]P(Y)=\dfrac{\text{Number of yellow marbles}}{\text{Total marbles}}[/tex]
[tex]\\\\=\dfrac{2}{18}[/tex]
Now, the probability that Jon selects a red marble and then a yellow marble :
[tex]P(R)\times P(Y)=\dfrac{7}{18}\times\dfrac{2}{18}\approx0.0432=4.32\%[/tex] [ ∵ Event R and Y are independent .]
Hence, the probability that Jon selects a red marble and then a yellow marble is about 0.0432 or 4.32%.
I really need some help with this, it's confusing me something fierce. Could you do a step by step if possible, please.
Choose the correct answer.
Mike Morgan has a $83,098.59 loan. He paid $1,000 in fees and $4,900 in total interest the first year. If the APR is the finance charge (interest plus fees) for one year ÷ amount financed, what was the APR for that year?
A) 7.5
B) 7.1
C) 7.3
Answers
Total of fees: 1,000 + 4,900 = 5,900
You are told the APR is the total fees divided by the amount financed, so divide the total fees by the amount financed:
5,900 / 83,098.59 = 0.71
0.71 x 100 = 7.1% APR.
The answer is B.
Vanessa wants to buy a new iPod that costs $239.25. She earns $7.25 per hour at work.
Answers
Answer:
She would have to work for 33 hours.
Step-by-step explanation:
239.25/7.25=33. Since we are going with hours, this would be 33.
What if Randy needs an equal number if bowls and cups for his picnic how many packs of each will he need to buy bowls number 1 pack is 6 cups number of pack is 8
Answers
So therefore
Bowls: 4 packs of 6
Cups: 3 packs of 8
To have equal numbers of bowls and cups, Randy should buy 4 packs of bowls and 3 packs of cups, as the least common multiple of 6 (number of bowls per pack) and 8 (number of cups per pack) is 24.
Explanation:If Randy needs an equal number of bowls and cups for his picnic and one pack consists of 6 bowls and another pack consists of 8 cups, the least common multiple (LCM) of 6 and 8 must be found to ensure an equal number of both items. The LCM of 6 and 8 is 24, because 24 is the smallest number that both 6 and 8 can divide evenly into. Therefore, Randy will need to buy 4 packs of bowls (4 packs × 6 bowls per pack = 24 bowls) and 3 packs of cups (3 packs × 8 cups per pack = 24 cups) to have an equal number of each for his picnic.
Wolves have good endurance and have been known to travel long distances-up to about 60 miles-in one night.If a wolf trots 18 4/5 miles in 2 1/3 hours,what is its speed?
Answers
Answer:
8 2/35 miles per hour
Step-by-step explanation:
We are given distance traveled and the time required. We can use those directly in the relation that gives speed:
speed = distance / time
... = (18 4/5 miles)/(2 1/3 hours)
... = (94/5 miles)/(7/3 hours) . . . . . . converte mixed numbers to improper fractions
... = (94/5×3/7) miles/hour . . . . . . . "invert and multiply"
.. = 282/35 miles/hour . . . . . . . . . . improper fraction result
... = 8 2/35 miles/hour . . . . . . . . . . as a mixed number
6x5-3x3x3 divide by 3
Answers
I will interpret and evaluate your expression following order of operations rules strictly. 6*5 (multiplication) and 3*3*3 / 3 (division) must be done first, before subtraction. Then we have 30 - 9, or 21. If you truly meant 3*3*3, why not write that as 3^3?
factor the expression 1.5x+6
Answers
There is no way to factor this so i would assume the answer is no solution.
Does anyone know these?
Answers
You seem to generally have the right idea, and you seem to be able to solve the equations you write. However, your choice of equations for the problem sometimes needs a little work.
12.Given∠DBC = (12x -3)°∠DBE = (5x +12)°∠EBC = (3x +13)°∠DBC = ∠DBE + ∠EBCFind∠EBCSolution∠DBC = ∠DBE + ∠EBC
(12x -3) = (5x +12) + (3x +13) . . . . . substitute given values
12x -3 = 8x +25 . . . . . . . . . collect terms
4x = 28 . . . . . . . . . . . . . . . add 3-8x
x = 7 . . . . . . . . . . . . . . . . . . divide by 4
3x +13 = 3·7 +13 = 34
∠EBC = 34°
__________
13.Given∠FBC = (10x -9)°∠CBE = (4x +15)°∠FBC = ∠CBE = (1/2)∠FBEFind∠FBESolution∠FBC = ∠CBE
10x -9 = 4x +15 . . . . . substitute given values
6x = 24 . . . . . . . . . . . .add 9-4x
x = 4 . . . . . . . . . . . . . . divide by 4
∠FBC = (10·4 -9)° = 31°
∠FBE = 2·∠FBC = 2·31°
∠FBE = 62°
__________
14.Given∠1 = (7x -19)°∠2 = (x +5)°∠1 + ∠2 = 90°Find∠2Solution∠1 +∠2 = 90°
(7x -19) +(x +5) = 90 . . . . . . substitute the given values
8x -14 = 90 . . . . . . . . . . . . . collect terms
8x = 104 . . . . . . . . . . . . . . . add 14
x = 13 . . . . . . . . . . . . . . . . . . divide by 8
∠2 = (13 +5)°
∠2 = 18°
__________
15.Given∠1 = (6x +25)°∠4 = (10x -11)°∠1 = ∠4 . . . . . . they are vertical anglesFind∠1Solution∠1 = ∠4
6x +25 = 10x -11 . . . . substitute the given values
36 = 4x . . . . . . . . . . . add 11-6x
9 = x . . . . . . . . . . . . . .divide by 4
∠1 = (6·9 +25)°
∠1 = 79° . . . . . . matches your answer
can u answer this mathematics question and show your work
Answers
See this solution/explanation (answer is '7 meters'):
1. According to the condition 'y' means the height, and 'x' - the length from the start of the lift hill.
2. The phrase 'height of 343 meters' means y=343.
3. From the another side y=x³. If to substitute 343 instead of 'y': 343=x³, - it is possible to find the value of 'x'.
x=7 [m] - how far from the start of the lift hill...
which set of ordered pairs is a function?
[(-5, 1), (-3, 2), (-1, 3) (1, 4), (3, 5) or
[(-2, 1), (-4, 2), (0,3), (4, 1), (-2,5)]
[(-1, 5), (-1,4), (-1, 3), (-1, 2) (-1, 1)]
[(-6, -4), (-4, -2), (0, 0), (-4, 2) (-6, 4)]
Answers
Functions can't have multiple y values have the same x value.
[(-5, 1), (-3, 2), (-1, 3) (1, 4), (3, 5)] ** No repeating x-values.
[(-2, 1), (-4, 2), (0,3), (4, 1), (-2,5)]
[(-1, 5), (-1,4), (-1, 3), (-1, 2) (-1, 1)]
[(-6, -4), (-4, -2), (0, 0), (-4, 2) (-6, 4)]
Answer:
[(-5, 1), (-3, 2), (-1, 3) (1, 4), (3, 5)]
Write an equation of the line passing through each of the following pairs of points. c (4, 0), (−2, 8)
Answers
Moving from -2 to 4 is a gain of 6 in the x-direction and a drop of 8 in the y-direction. Thus, the slope of this line is m = -8/6, or m = -4/3.
Then, using the point-slope formula, y - 0 = (-4/3)(x-4), or y = (-4/3)x + 16/3
y=-1 1/3x+5 1/3
I hope this helps
Volume of triangular prism
Answers
Answer:
216
Step-by-step explanation:
9 * 6 = 54
54 * 8 = 432
432/2 = 216 is the answer
The volume of a triangular prism is the area of the base multiplied by the height. This can be represented as volume = base × height
Let's first identify our values:
9 m = height of the prism
6 m = base of the triangle
8 m = height of the triangle
First, we need to calculate the area of the triangle. To calculate the area of a triangle, the formula is base × height ÷ 2.
The base of the triangle is 6 and the height of the triangle is 8 so 6 multiplied by 8 will give us a product of 48. Next, we need to divide 48 by 2 and we will get a quotient of 24.
Finally, we need to multiply the area of the triangle by the height of the prism.
24 × 9 = 216
Therefore, the volume of the triangular prism is 216[tex]m^{3}[/tex]
Jacob has a mean score of 78 after his first four math tests. He wants to make a B, or an average of 80, in math. What does he need to score on the fifth test to have a mean score of 80?
A.
82
B.
88
C.
94
D.
108
I also have another one.
Which of the following is a valid conclusion from the pie chart?
A.
If 60 students read four books, then 15 students read five or more books.
B.
More than half the students read fewer than 3 books.
C.
If 60 students read four books, then 120 students read two books.
D.
Twenty-two percent of the students read four or more books.
Answers
Answer:
1) B. 88
2) C. If 60 students read four books, then 120 students read two books.
Step-by-step explanation:
1) Solution
Step 1: Let "x" be the 5th test score.
Scores upto the 4th tests = 4*78 = 312
Step 2: Mean of the five tests = 80
(x + 312)/5 = 80
x + 312 = 80*5
x + 312 = 400
Step 3: Now find the value of x.
x = 400 - 312
x = 88
Therefore, Jacob scored 88 in the 5th test.
2) Solution
Step 1: 60 students read four books.
Now find the number of students.
Percentage of students read four books = 12% = 0.12
Total number of students = 60/0.12 = 500
Percentage of students reads two books = 24% = 24/100 = 0.24
Number of students read two books = 0.24*500
= 120
Hope you will understand the concept.
Thank you.
Hello,
Please, see the attached files.
Thanks.
Here are the numbers of times 14 people ate out last month. 7, 6, 5, 4, 3, 6, 5, 6, 5, 4, 4, 4, 6, 5 Find the modes of this data set. If there is more than one mode, write them separated by commas. If there is no mode, click on "No mode."
Answers
the mode of the data is 4.
mode is the number repeats in the data set the most.
Answer:
6782
Step-by-step explanation:
A student has passed 60 percent of the 20 quizzes he has written so far successfully. If the student writes 50 quizzes during the year and passes 80 percent of the remaining quizzes successfully, what is the percent of all successful quizzes for the entire year?
PLS HELP QUICK
Answers
The student’s total percent of all successful quizzes for the entire year is 72%.
To determine the percent of all successful quizzes for the entire year, we need to follow these steps:
Calculate the number of quizzes passed so far: The student has passed 60% of 20 quizzes. This is calculated as follows:
0.60 x 20 = 12 quizzes passed.
Determine the number of quizzes remaining: The student needs to write 50 quizzes in total, so the remaining quizzes are 50 - 20 = 30 quizzes.
Calculate the number of additional quizzes passed: The student is expected to pass 80% of the remaining quizzes.
0.80 x 30 = 24 quizzes passed.
Calculate the total number of quizzes passed: Add the quizzes passed so far to the additional quizzes passed.
12 + 24 = 36 quizzes passed in total.
Determine the percentage of successful quizzes for the entire year: Divide the total number of successful quizzes by the total number of quizzes.
(36 / 50) x 100 = 72% successful quizzes.
Thus, the student’s total percent of all successful quizzes for the entire year is 72%.
Need help ASAP please!
Answers
x | - 8 - 4 0 4 8
y | 28 16 4 - 8 - 20
to calculate the values of y, substitute the given values of x into the equation
x = - 8 : y = (- 3 × - 8 ) + 4 = 24 + 4 = 28
x = - 4 : y = (- 3 × - 4 )+ 4 = 12 + 4 = 16
x = 0 : y = (- 3 × 0 ) + 4
0 + 4 = 4
x = 4 : y = (- 3 × 4 ) + 4 = - 12 + 4 = - 8
x = 8 : y = (- 3 × 8 ) + 4 = - 24 + 4 = - 20
Graph x <17/5+7/20 on number line
Answers
The open circle at 3.75 and the arrow pointing left represents the values of x that are less than 3.75.
To graph [tex]\(x < \frac{17}{5} + \frac{7}{20}\)[/tex] on a number line, we'll first simplify the expression:
[tex]\(\frac{17}{5} + \frac{7}{20}\)[/tex]
To add these fractions, find a common denominator, which in this case is 20:
[tex]\(\frac{17}{5} = \frac{17 \times 4}{5 \times 4} = \frac{68}{20}\)[/tex]
Now, add the fractions:
[tex]\(\frac{68}{20} + \frac{7}{20} = \frac{75}{20}\)[/tex]
So, the expression simplifies to [tex]\(x < \frac{75}{20}\)[/tex].
To simplify [tex]\(\frac{75}{20}\)[/tex]:
[tex]\(75 \div 20 = 3.75\)[/tex]
This means the inequality is [tex]\(x < 3.75\)[/tex].
Now, to graph this on a number line, mark a point at 3.75, but as it is "less than" <, make sure to have an open circle at 3.75, indicating that it does not include the value itself. Then, draw an arrow to the left, signifying all values less than 3.75.
```
0-------------------o-------------------3.75------------------->
```
Here, the open circle at 3.75 and the arrow pointing left represents the values of x that are less than 3.75.
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Use the continuous change function A(t) = Pe^rt to answer the question.
You invest $2,500 in an account that grows 5% each year. What will be your investment amount after 6 years?
A.
$2,699.72
B.
$3,374.65
C.
$15,769.07
D.
$13,272.96
Answers
B
A(6) = 2500 × [tex]e^{(0.05(6))}[/tex] = 2500 × [tex]e^{0.3}[/tex] = $3, 374.65
My investment amount will be 3374.65 rupees after 6 years.
So, option B is the correct answer.
What is Euler's number ?
A(t) [tex] = p {e}^{rt} [/tex] is known as Euler's number.
A is the desired amount per account/price/population/etc. equal
P is the principal or amount you start with.
e is a particular irrational number that is approximately 2.718. Just as pi is a concrete irrational number, so is e. The Euler number is often used as a title for e. Just as pi is an infinite non-repeating decimal, so is e. And just as many people use 3.14 to approximate pi, some use 2.718 for e. However, using the special π button on the calculator gives a more accurate answer than 3.14, and using the e button on the calculator is more accurate than using 2.718.
r is a rate written as a decimal, not a percentage.
t is time.
Let's say you have a population of bacteria that is constantly growing at a rate of 15% per hour. If there were 40 bacteria at the beginning of the experiment, how many bacteria will there be after 8 hours?
A is the amount after 8 hours, it's unknown, so I'll just use the variable A.
P initially has 40 bacteria.
e I use the “e” button on my calculator.
r is the hourly rate of 15%, I write it as 0.15
t is time, in this case 8 hours.
A = 40•e^(0.15•8)
A = 132.8, you need to round down because you haven't reached the next whole number of bacteria.
132 bacteria after 8 hours.
Here given,invest amount is $2,500 and rate of interest is 5% and total time period is 6 years.
Here we need to use continuous function A(t)[tex] = p {e}^{rt} [/tex]
Where P is principal,r rate of interest is interest and t is time.
Now,
[tex]p = 2500 \\ r = 5\% = 0.05\\ t = 6 \: years[/tex]
So,after 6 years the amount become ,A(6)
= [tex]2500 \times {e}^{0.05 \times 6} \\ = 2500 \times {e}^{0.3} [/tex]
[tex] = 2500 \times 1.34986 \\ = 3374.65[/tex]
Therefore,my investment amount will be 3374.65 rupees after 6 years.
The continuous change function related one more question:
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Free Brainliest! **PLEASE HELP**
Use the equation to find the length of the missing leg measure.
a^2 + 16^2 = 20^2
1. Evaluate Powers: A^2 + 256 = 400
2. Undo addition: a^2 = 144
3. Undo The square: a= 144 ( Square root )
What is the length of the missing leg measure?
a = ________ units
Answers
[tex] a^2+16^2=20^2[/tex]
[tex] a^2+256=400[/tex]
Subtracting 256 from both sides
[tex] a^2=144[/tex]
Taking squareroot both sides
[tex] a= \sqrt144[/tex]
[tex] a = \sqrt2.2.3.2.2.3[/tex]
[tex] a=12[/tex]
Therefore length of missing leg is
[tex] a = 12 units[/tex]
a^2+16^2=20^2
a^2+256=400
Subtracting 256 from both sides
a^2=144
Taking squareroot both sides
a= \sqrt144
a = \sqrt2.2.3.2.2.3
a=12
Therefore length of missing leg is
a = 12 units
(f ∘ g)(x) so if g(4) = 8 and f(8) = 22, then (f ∘ g)(4) =
Answers
Final answer:
To evaluate (f ∘ g)(4), we substitute the value of g(4) into f(x) which gives us 22.
Explanation:
To find (f ∘ g)(4), we need to first evaluate g(4) and then plug that value into f(x). Given that g(4) = 8 and f(8) = 22, we can substitute 8 into f(x) as follows:
(f ∘ g)(4) = f(g(4))
(f ∘ g)(4) = f(8)
(f ∘ g)(4) = 22
find the distance CD rounded to the nearest tenth C=(7,-4) D=(-8,-5)
Answers
15.0 ( to the nearest tenth )
calculate the distance (d) using the distance formula
d = √(x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (7, - 4 ) and (x₂, y₂ ) = (- 8, - 5 )
d = √(-8 - 7 )² + (- 5 + 4 )² = √(225 + 1 ) = √226 ≈ 15.0