Hi, I don't get what to do here I tried using vietas theorem, but I still can't get it. 55 points
Answers
Answer:
x^3 - 6x^2 + 12x - 8 = 0
Step-by-step explanation:
Let the roots of the equation x^3 - 8x + 3 = 0 be a, b, and c. Then, we know that the squares of the roots are a^2, b^2, and c^2.
By Vieta's formulas, we know that the sum of the roots of x^3 - 8x + 3 = 0 is 0, since there is no x^2 term:
a + b + c = 0
We also know that the product of the roots is 3/1 = 3:
abc = 3
Using the fact that the squares of the roots are a^2, b^2, and c^2, we can write:
a^2 + b^2 + c^2 = (a + b + c)^2 - 2(ab + ac + bc)
Since a + b + c = 0, this simplifies to:
a^2 + b^2 + c^2 = -2(ab + ac + bc)
Now, let's try to find a cubic equation with roots a^2, b^2, and c^2. We can start with:
(x - a^2)(x - b^2)(x - c^2) = 0
Expanding the left side, we get:
x^3 - (a^2 + b^2 + c^2)x^2 + (a^2b^2 + b^2c^2 + c^2a^2)x - a^2b^2c^2 = 0
Using the identity we found earlier for a^2 + b^2 + c^2, we can simplify this to:
x^3 + 2(ab + ac + bc)x - 3a^2b^2c^2 = 0
Now, we can substitute in the values we know for ab, ac, and bc:
ab = (a + b + c)(ab + ac + bc) - (a^2b + ab^2 + c^2a)
ac = (a + b + c)(ab + ac + bc) - (a^2c + ac^2 + b^2a)
bc = (a + b + c)(ab + ac + bc) - (b^2c + bc^2 + a^2b)
Plugging in these values and simplifying, we get:
x^3 - 6x^2 + 12x - 8 = 0
Therefore, the cubic equation we're looking for is:
x^3 - 6x^2 + 12x - 8 = 0
And the roots of this equation are the squares of the roots of x^3 - 8x + 3 = 0.
Related Questions
43. Patrick has a cylindrical coffee cup and a cylindrical glass with the dimensions
shown below.
What is the difference in the volumes of the two cylinders? (Use pi= 3.14)
A. 61pi mm^3
B. 124pi mm^3
C. 244pi mm^3
D. 541pi mm^3
Answers
The difference in volumes for the two cylinders is given as follows:
A. 61π mm³.
How to obtain the volume of the cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
For Cylinder 1, the parameters are given as follows:
r = 0.5 x 8 = 4 mm, h = 10 mm.
Hence the volume is given as follows:
V = π x 4² x 10
V = 160π mm³.
For Cylinder 2, the parameters are given as follows:
r = 0.5 x 6 = 3 mm, h = 11 mm.
Hence the volume is given as follows:
V = π x 9² x 11
V = 99π mm³.
Hence the difference is given as follows:
160π mm³ - 99π mm³ = 61π mm³.
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The matrix equation below can be used to solve a system of when your equation what is the solution to the system? [6,4][x]=[1], [9,6][y]=[3]
Answers
There is no solution from the given matrix equation.
Solving two by two matrix equations.
In a two by two matrix equation system, two matrices can be multiplied if and only if the number of columns in the first matrix is equal to the number of rows in the second matrix. It implies that the first matrix is 2×2 and the second matrix is 2×1.
Given that:
[tex]\left[\begin{array}{cc}6&4\\9&6\end{array}\right] \left[\begin{array}{c}x\\y \end{array}\right] = \left[\begin{array}{c}1 \\ 3 \end{array}\right][/tex]
We multiply each row in the first matrix by each column in the second matrix, so we get:
[tex]\left[\begin{array}{c}6x+4y\\9x+6y\end{array}\right] = \left[\begin{array}{c}1 \\ 3 \end{array}\right][/tex]
Then, we can express it as a system of linear equations:
6x + 4y = 1 --- (1)
9x + 6y = 3 --- (2)
Here, we decided to use the substitution method to solve the system of equations.
From equation (1)
x = 1/6 - 2y/3
Replace the value of x into equation (2) and solve for y, we get:
9(1/6 - 2y/3) + 6y = 3
By solving it, we get:
3/2 = 3
Thus, since 3/2 = 3 is not a true solution, then we can conclude that there is no solution.
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The list represents the ages of students in a gymnastics class.
8, 8, 8, 9, 9, 10, 10, 10, 11, 12
If another student of age 10 joins the class, how is the mean affected?
The mean will remain the same at 10.
The mean will remain the same at about 9.5.
The mean will increase to about 10.2.
The mean will decrease to about 9.
Answers
Answer:
The list represents the ages of students in a gymnastics class.
-------
8, 8, 8, 9, 9, 10, 10, 10, 11, 12
If another student of age 10 joins the class, how is the mean affected?
The mean will remain the same at 10.
The mean will remain the same at about 9.5.The mean will increase to about 10.2.
The mean will decrease to about 9.
-------
Step-by-step explanation:8 + 8 + 8 + 9 + 9 + 10 + 10+ 10 + 11 + 12
= 95
95 ÷ 10
=9.5
8 + 8 + 8 + 9 + 9 + 10 + 10 + 10+ 10 + 11 + 12
= 105
105 ÷ 11
= 9.54.....
You're welcome.HELP ASAP
The histogram below shows information about the hours students spent exercising in a week:
A histogram is titled Weekly Exercise, the horizontal axis is labeled Hours of Exercise, and the vertical axis is labeled Students. The range on the horizontal axis is 0 to 4, 5 to 9, and 10 to 14. The values on the vertical axis are from 0 to 10 at intervals of 1. The first bin goes to 4, the second bin to 9, the third bin to 5.
Which information is provided in the histogram? (4 points)
a
The number of students who exercised 4 hours or more
b
The number of students who exercised 9 hours or fewer
c
The mean hours of exercise
d
The median hours of exercise
Answers
The information from the histogram are as follow,
Students exercised for 4 or more hours are 14.
Students exercised for 9 or fewer hours are 13.
Mean of the data = 7.3.
median of the data = 6.33.
The histogram provides information about the distribution of hours students spent exercising in a week.
The number of students who exercised 4 hours or more,
= adding up the counts in the first and second bins.
= 9 + 5
= 14 students
The number of students who exercised 9 hours or fewer,
= adding up the counts in the first and second bins
= 9 + 4
= 13 students
The mean hours of exercise is not provided by the histogram
use the formula,
Mean = Σ[tex]x_{i} y_{i}[/tex] / N
where
[tex]x_{i}[/tex] is the midpoint of the ith bin
[tex]y_{i}[/tex] is the frequency of the ith bin
N is the total sample size
Mean = [(2)(4) + (7)(9) + (12)(5)] / 18
= 7.3
The median hours of exercise is not provided by the histogram.
Median = L + ( (n/2 – F) / f ) × w
where
L=The lower limit of the median group
n = The total number of observations
F = The cumulative frequency up to the median group
f =The frequency of the median group
w = The width of the median group
median = 5 + ( ( 14/2 - 4 ) /9 × 4
= 6.33
Therefore, from the histogram the number of students exercised for ,
4 hours or more are 14.
9 hours or fewer are 13.
mean = 7.3
Median = 6.33
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(₁4) Quadrilateral ABCD is graphed on a coordinate grid with vertices at A (-2, 0), B (-1, 3), C (3, 4), and D (4, -3). Quadrilateral ABCD is dilated by a scale factor of u with the origin as the center of dilation to create quadrilateral A'B'C'D'. What is the ordered pair that would represent the coordinates of vertex D'?
Answers
The ordered pair that would represent the coordinates of vertex D' is given as follows:
D'(4u, -3u).
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The scale factor for this problem is given as follows:
k = u.
The coordinates of each vertex are multiplied by y, hence the ordered pair that would represent the coordinates of vertex D' is given as follows:
D'(4u, -3u).
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9. a) 'Prime numbers less than 10' is a given collection. (i) Is this collection a set? Give reason. (ii) Name the method of describing this collection. (iii) Rewrite this collection in listing method. Approved by Curriculum Development Centre, Sanothimi, Bhaktapur 11 Vedanta Excel
Answers
Yes, this collection is a set because it has a well-defined and finite number of elements, namely {2, 3, 5, 7}.
What are the responses to other questions?(ii) The method of describing this collection is the roster method or tabular method, where the elements of the set are listed within curly braces and separated by commas.
(iii) {2, 3, 5, 7}
In mathematics, a set is a collection of conspicuous objects or elements, taken as an object in its own right. These elements can either be numbers, letters, symbols, or even other sets. A set is defined by listing its elements or by specifying a property that its elements satisfy.
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help me right answers only quick. here is screenshot
Answers
Answer:
Option 2 is correct. The function is increasing on the set of all positive real numbers.
Which equations are true for x = –2 and x = 2? Select two options x2 – 4 = 0 x2 = –4 3x2 + 12 = 0 4x2 = 16 2(x – 2)2 = 0
Answers
The equations that are true for x = -2 and x = 2 are x² + 4 = 0 and 4x² = 16. So, the correct option is A) and D).
To determine which equations are true for x = -2 and x = 2, we simply substitute these values into each equation and check if the equation is true or not. Here are the results
x² - 4 = 0
Substituting x = -2 gives (-2)² - 4 = 0, which is true. Substituting x = 2 gives 2² - 4 = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.
x² = -4
Substituting x = -2 gives (-2)² = -4, which is not true. Substituting x = 2 gives 2² = -4, which is also not true. Therefore, this equation is not true for either x = -2 or x = 2.
3x² + 12 = 0
Substituting x = -2 gives 3(-2)² + 12 = 0, which is true. Substituting x = 2 gives 3(2)² + 12 = 24, which is not equal to zero. Therefore, this equation is true for x = -2 but not for x = 2.
4x² = 16
Substituting x = -2 gives 4(-2)² = 16, which is true. Substituting x = 2 gives 4(2)² = 16, which is also true. Therefore, this equation is true for both x = -2 and x = 2.
2(x - 2)² = 0
Substituting x = -2 gives 2(-2 - 2)² = 0, which is true. Substituting x = 2 gives 2(2 - 2)² = 0, which is also true. Therefore, this equation is true for both x = -2 and x = 2.
Therefore, the two equations that are true for both x = -2 and x = 2 are x² - 4 = 0 and 4x² = 16. So, the correct answer is A) and D).
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1. Find the surface area of a right square pyramid if the area of the base is 169 cm² and the slant height of the pyramid is 13 cm.
Answers
The surface area of the right square pyramid with the given base area and slant height would be = 221cm²
How to calculate the surface ares of the right square pyramid?To calculate the surface area of the right square pyramid, the formula that should be used would be given below as follows. That is;
Surface area = a²+ 2al
where;
a² = area of base = 169cm²
a = side length of base = √169 = 13
l = slant height = 13 cm
S.A = 169+ 2(13×13)
= 169 + 52
= 221cm²
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find the domain range and function
Answers
The domain of this relation is [0, 5].
The range of this relation is [-4, 3].
No, this relation is not a function.
What is a domain?In Mathematics and Geometry, a domain refers to the set of all real numbers (x-values) for which a particular function (equation) is defined.
How to identify the domain any graph?In Mathematics and Geometry, the horizontal portion of any graph is used to represent all domain values and they are both read and written from smaller to larger numerical values, which simply means from the left of any graph to the right.
By critically observing the graphs shown in the image attached above, we can reasonably and logically deduce the following domain and range for graph 4:
Domain = [0, 5].
Range = [-4, 3].
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Please calculate this...
Answers
The solution of the expression is 3.659
First, we will start with the expression inside the brackets, i.e., [(3 1/3 * 1.9) + (19.5 / (4 1/2)]. Here, we have two operations - multiplication and division. According to PEMDAS, we need to perform multiplication before division.
To simplify this expression, we will first convert 3 1/3 to an improper fraction. 3 1/3 is the same as 10/3. Therefore, the expression inside the brackets becomes
=> [(10/3 * 1.9) + (19.5 / (9/2)].
Next, we will simplify the multiplication first -
=> 10/3 * 1.9 = 19/3.
Now, let's simplify the division operation
=> 19.5 / (9/2) = 4.33
Therefore, the expression inside the brackets becomes
=> [(19/3) + 4.33] = 8.99
Moving on to the denominator of the given expression
=> [62/75 - 0.16]. Here, we need to perform subtraction first as it comes before division in PEMDAS.
62/75 = 0.8266
Therefore, the denominator of the given expression becomes
=> [0.8266 - 0.16] = 0.6666
Now, let's simplify the numerator of the given expression. We have
=> [(3.5 + 4 2/3 + 2 2/15) / (0.5 * (1 1/20 + 4.1))].
Let's first convert all the mixed fractions to improper fractions.
3.5 can be written as 7/2, 4 2/3 can be written as 14/3, and 2 2/15 can be written as 32/15.
Therefore, the numerator becomes
=> [(7/2 + 14/3 + 32/15) / (0.5 * (21/20 + 4.1))].
Let's first simplify the expression inside the brackets
=> 21/20 + 4.1 = 5.15.
Therefore, the numerator becomes
=> [(7/2 + 14/3 + 32/15) / (0.5 * 5.15)].
Now, let's simplify the addition operation in the numerator. We need to find a common denominator to add the fractions.
The common denominator for 2, 3, and 15 is 30.
Therefore, (7/2 + 14/3 + 32/15) can be written as
=> (105/30 + 140/30 + 64/30).
Adding the fractions, we get (309/30).
Therefore, the numerator becomes [(309// (0.5 * 5.15)].
Next, let's simplify the expression inside the brackets - 0.5 * 5.15 = 2.575.
Therefore, the numerator becomes
[(309/30) / 2.575] = 3.68
Now that we have simplified the numerator and denominator of the given expression separately, we can simplify the entire expression.
[(8.99) / (0.6666)] / [3.68]
Let's first simplify the expression inside the first set of brackets.
(8.99) / (0.6666) = 13.486
Therefore, the given expression becomes 13.486 / 3.68 = 3.659
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kiran added 4.7x10 √4 and 1.2 x 10 √5. select all possible answers
Answers
The possible sum of Kiran adding 4.7x10 √4 and 1.2 x 10 √5 is 94 + 1.2 x 10 √5
Evaluating the sum of the expressionsFrom the question, we have the following parameters that can be used in our computation:
Kiran added 4.7x10 √4 and 1.2 x 10 √5
This means that we have
4.7 * 10√4 + 1.2 x 10 √5
Evaluate the square root of 4
So, we have
4.7 * 10 * 2 + 1.2 x 10 √5
When the products are evaluated, we have
94 + 1.2 x 10 √5
Hence, the possible result of the summation is 94 + 1.2 x 10 √5
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In a bag of marbles there are 2 blue marbles, 4 red marbles, and 4 green marbles. You pick three marbles out of a bag one at a time without replacement. How many ways can you pick two green marbles first and one red marble last?
Answers
There are 24 ways to pick two green marbles first and one red marble last.
The probability of picking a green marble on the first draw is 4/10, and then 3/9 on the second draw since there are only 3 green marbles left out of 9 total marbles remaining.
The probability of picking a red marble on the third draw is 4/8 since there are 4 red marbles left out of 8 total marbles remaining.
So the probability of picking two green marbles first and one red marble last is (4/10) x (3/9) x (4/8) = 2/45.
To calculate the number of ways to pick two green marbles first and one red marble last, we need to use combinations.
There are [tex]^4C_2[/tex] = 6 ways to choose two green marbles from four, and there are 4 ways to choose one red marble from four.
So there are 6 x 4 = 24 ways to pick two green marbles first and one red marble last.
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Please answer the question
Answers
Answer:
23,850 cubic inches
Step-by-step explanation:
I think I know your dad officer Chau he works at my middle school in Navarre. this was also kind of a basic and easy question I would recommend trying to figure it out yourself before turning to the internet.
In the context of this problem, which solutions to the polynomial equation can you eliminate because they do not make sense? x = –8 x = –4 x = 6
Answers
In the context of this problem all the solutions to the polynomial equation is correct because they all make sense.
What is the solution to the equation?The given polynomial equation can be expressed as ;
x³ + 6x² - 40x = 192 and the given solutions can be written as ; x = -8, x = -4, and x = 6
We can test if the solution is the best for the given euation because this will help us to know if these valueas are the solution for the equation
x = -8
[(-8)³ + 6(-8)² - 40(-8)]
= 192
[-512 + 384 + 320]
= 192
x = -4,
[(-4)³ + 6(-4)² - 40(-4)]
[-64 + 96 + 160 ]
= 192
x = 6
[(6)³ + 6(6)² - 40(6) ]
216 + 216 - 240
= 192
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Answer:
Step-by-step explanation:
A,B
x = –8
x = –4
the equation that best models the linearized data for a particular data set is log y=-0.02396x+4.8153.
a. what does the number -0.02296 tell you about the pattern exhibited by the points in the scatterplot of the original data set?
b. based on the equation, what is the value of y when x=0? show your work.
Answers
The number -0.02396 tell us about the slope of the pattern and the value of y when x = 0 is 4.8153
What does the -0.02396 tell you about the patternGiven that
y = -0.02396x + 4.8153
In the equation y = -0.02396x + 4.8153, we have
Slope = -0.02396
This means that the slope of the data is -0.02396
And as such it means that as the x values increase, the y values of the pattern decrease
The value of y when x = 0We have
y = -0.02396x + 4.8153
Set x = 0
So, we have
y = -0.02396 * 0 + 4.8153
Evaluate
y = 4.8153
Hence, the value of y when x = 0 is 4.8153
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Not drawn to scale
: Find the value of x in the figure at the right. Round your answer to the nearest tenth.
MUST SHOW WORK.
Answers
The value of x from the given isosceles triangle is 5.6 units.
Given that, the measure of equal sides of an isosceles triangle is 6 units and the base measures 5.9 units.
Draw perpendicular bisector to base, so we get halves as 5.9/2 =2.95
Let the length of perpendicular bisector be x.
By using Pythagoras theorem, we get
6²=2.95²+x²
36=8.7025+x²
x²=36-8.7025
x²=27.2975
x=5.2 units
We know that, sinθ=Opposite/Hypotenuse
sin68°=5.2/x
x=5.6 units
Therefore, the value of x from the given isosceles triangle is 5.6 units.
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The capacity of a water tank is 1000 gallons. Don uses a bucket that can hold 2 gallons to fill the tank. It takes him 3 minutes to fill the bucket with water and pour it into the tank.
Answers
Don would take 1500 minutes to fill the 1000-gallon water tank using the 2-gallon bucket.
If the capacity of the water tank is 1000 gallons and Don uses a bucket that can hold 2 gallons to fill the tank, we can calculate the number of buckets Don needs to fill the tank.
Let's assume the number of buckets Don needs to fill the tank is represented by 'n'.
Capacity of the tank = 1000 gallons
Capacity of each bucket = 2 gallons
Number of buckets needed to fill the tank, n = Capacity of the tank / Capacity of each bucket
n = 1000 gallons / 2 gallons
n = 500
So, Don needs 500 buckets, each holding 2 gallons, to fill the 1000-gallon water tank.
Given that it takes Don 3 minutes to fill the bucket with water and pour it into the tank, the total time taken by Don to fill the tank would be the product of the number of buckets (500) and the time taken to fill each bucket (3 minutes).
Total time taken to fill the tank = Number of buckets × Time taken to fill each bucket
Total time taken = 500 × 3 minutes
Total time taken = 1500 minutes
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Please help im struggling, if you can explain
Answers
The exponential function representing the lifting time on day n is given as follows:
a(n) = 2^(n - 1).
How to define an exponential function?An exponential function has the definition presented as follows:
y = ab^x.
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.On the first day, the time is of one minute, while the amount doubles each day, hence the parameters a and b are given as follows:
a = 1, b = 2.
We take the day one at the reference day, not day zero, meaning that the function was shifted right one unit, hence the rule is given as follows:
a(n) = 2^(n - 1).
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{V49 + [V81 - x 9x - 14)]}
Answers
The solution is, the simplification of the expression is:
{16 - 9x^2 + 14x}
Here, we have,
given that,
the expression:
{√49 + [√81 - x (9x - 14)]}
now, we have to simplify this expression:
{√49 + [√81 - x (9x - 14)]}
={7 + [9 - x (9x - 14)]}
={7 + [9 - 9x^2 + 14x]}
={7 +9 - 9x^2 + 14x}
={16 - 9x^2 + 14x}
Hence, The solution is, the simplification of the expression is:
{16 - 9x^2 + 14x}
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HELP ME ITS DUE TODAY!!!!! The scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
1 7, 9
2 1, 5, 9
3 0, 1, 2
4 6, 9
Key: 2|1 means 21
What is the appropriate measure of variability for the data shown, and what is its value?
The IQR is the best measure of variability, and it equals 32.
The range is the best measure of variability, and it equals 11.
The IQR is the best measure of variability, and it equals 11.
The range is the best measure of variability, and it equals 32.
Answers
Answer:
The answer to your problem is, D. The range is the best measure of variability, and it equals 32.
Step-by-step explanation:
We know the scores earned in a flower-growing competition are represented in the stem-and-leaf plot.
1 7, 92 1, 5, 93 0, 1, 24 6, 9The key will equal 2|1 means 21
Which we conclude to 17, 19, 21, 25, 29, 30, 31, 32, 46, 49.
Quartile:
Quartile 1, Q1 = 21Quartile 2, Q2 = 29.5Quartile 3, Q3 = 32Third Quartile, Q3 = 32Median, Minimum, Maximum, & Range:
Median, Q2 = 29.5Minimum, Min = 17Maximum, Max = 49Range, R = 32Thus the answer to your problem is, D. The range is the best measure of variability, and it equals 32.
Find the amount of air needed to fill a basketball whose diameter is 9.45 in. Use 3.14 for
Answers
Answer:
The amount of air needed to fill the basketball is approximately 533.16 cubic inches
Step-by-step explanation:
To find the amount of air needed to fill a basketball, we need to first calculate its volume. We can use the formula for the volume of a sphere, which is V = (4/3)πr^3, where π is approximately 3.14 and r is the radius of the sphere.
Since the diameter of the basketball is given, we need to first find the radius by dividing the diameter by 2:
r = 9.45 in / 2 = 4.725 in
Now we can plug in the value of r into the formula for the volume:
V = (4/3)πr^3 = (4/3)π(4.725 in)^3 = 533.16 in^3
Therefore, the amount of air needed to fill the basketball is approximately 533.16 approx cubic inches.
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Drag the tiles to the boxes to form correct pairs. Not all tiles will be used.
Match each logarithmic equation to its corresponding x-value.
Answers
The logarithm equations and corresponding x-value are
[tex]log_{2}x=5[/tex] has x=32
[tex]log_{10}x=3[/tex] then x=1000
[tex]log_{4}x=2[/tex] then x=16
[tex]log_{3}x=1[/tex] then x=1
We know that [tex]log_{a}x=b[/tex]
Then [tex]x=a^b[/tex]
(1) [tex]log_{2}x=5[/tex]
x=2⁵
=32
So [tex]log_{2}x=5[/tex] has x=32
(2) [tex]log_{10}x=3[/tex]
Then by using the above property of logarithmic function we have:
x=10³
x=1000
So [tex]log_{10}x=3[/tex] then x=1000
(3) [tex]log_{4}x=2[/tex]
x=4²
x=16
so [tex]log_{4}x=2[/tex] then x=16
(4) [tex]log_{3}x=1[/tex]
x=1³
=1
So [tex]log_{3}x=1[/tex] then value x=1
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Carter was out at a restaurant for dinner when the bill came. He wanted to leave a tip of 31%. What number should he multiply the cost of the meal by to find the total plus tip in one step?
Answers
The total cost of the meal is $65.50, with tip included.
Here, in this question we need to find the percentage Value, to find the total cost of the meal plus the tip, Carter needs to multiply the cost of the meal by a factor of 1 + the tip percentage, which is 1 + 31% = 1.31.
So, the number Carter should multiply the cost of the meal by to find the total plus tip in one step is 1.31.
For example, if the cost of the meal was $50, then the total cost including the tip would be addition of cost of meal and tip.
Total cost = Cost of meal + Tip
Total cost = $50 + 31% of $50
Total cost = $50 + $15.50
Total cost = $65.50
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what to write in the boxes/ answer’s please
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The missing sides of the right triangle were obtained below.
What is the Pythagoras theorem?Pythagoras' theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
We have that;
1) x = √26^2 - 10^2
x = 24
2) x = √20^2 + 14 ^2
x = 24.4
3) x = √50^2 - 30^2
x = 40
4) x = √15^2 + 5^2
x = 15.8
5) x = √12^2 + 20^2
x = 23.3
These are the sides that are missing.
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A population is growing according to the exponential model given by, P(t)=500^0.25t where t is measured in years. How many years will it take for the population to reach 1500? (Round your answer to one decimal place.)
Answers
It will take approximately 8.6 years for the population to reach 1500.
We have,
We are given that the population is growing exponentially according to the model, P(t) = 500^(0.25t),
where t is measured in years.
We need to find the value of t when the population reaches 1500.
So we can set P(t) = 1500 and solve for t:
1500 = 500^(0.25t)
Taking the natural logarithm of both sides:
ln(1500) = ln(500^(0.25t))
Using the logarithmic identity, ln(a^b) = b ln(a):
ln(1500) = 0.25t ln(500)
Solving for t:
t = ln(1500) / (0.25 ln(500))
Using a calculator, we get:
t ≈ 8.6 years
Therefore,
It will take approximately 8.6 years for the population to reach 1500.
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Houghton Mifflin Harcourt Publishing Company
the years
2. The margin by which Madison wins her sprint races are shown below.
Time (in seconds): 0.5, 0.3, 04, 0, 0, 0, 05, 0.8, ols, 0.4, 0.5, 0.6, 0.9,
0.2, 0.3, 0.5, 04, Q.3, Q.1, 06
A. Make a dot plot to show the time margins.
Time Margins
17
3
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Seconds
B. What is the average margin of victory?
5 second
C. What is the most common margin of victory?
D. By which margins did Maddie never win?
ㄱ
Answers
D. Maddie never won by margins of 0.1, 0.2, 0.4, or 0.7 seconds.
Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0). Determine the coordinates of the vertices for the image if the preimage is translated 3 units up.
A′(−3, 0), B′(0, 4), C′(−3, −3)
A′(−3, 6), B′(0, 10), C′(−3, 3)
A′(−6, 3), B′(−3, 7), C′(0, 0)
A′(0, 3), B′(3, 5), C′(0, 0)
Answers
The coordinates of the vertices for the image of the triangle are A(−3, 6), B(0, 10), and C(−3, 3)
Determining the coordinates of the vertices for the imageFrom the question, we have the following parameters that can be used in our computation:
Triangle ABC has vertices at A(−3, 3), B(0, 7), and C(−3, 0)
If the preimage is translated 3 units up, then the transformation rule is
(x, y) = (x, y + 3)
Substitute the known values in the above equation, so, we have the following representation
A(−3, 3 + 3), B(0, 7 + 3), and C(−3, 0 + 3)
Evaluate
A(−3, 6), B(0, 10), and C(−3, 3)
Hence, the coordinates of the vertices for the image are A(−3, 6), B(0, 10), and C(−3, 3)
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write the equation of a function whose parent function, f(x)= x+6, is shifted 4 units to the right
Answers
The transformed fuction shifted 4 units to the right of the parent function is g(x)= x + 2
Writing the equation of the transformed functionFrom the question, we have the following parameters that can be used in our computation:
Parent function, f(x)= x+6,
Transformation: shifted 4 units to the right
The rule of the above transformation is
g(x) = f(x - 4)
Substitute the known values in the above equation, so, we have the following representation
g(x)= x - 4 + 6,
Evaluate the terms
g(x)= x + 2
Hence, the transformed fuction is g(x)= x + 2
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PLEASE HELP ASAPP !!!!!!!!!!!!!!!!!!!!!
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The quadratic equation has only one solution if m = 14
Which is the value of m such that the equation has only one solution?For a quadratic equation:
ax² + bx + c = 0
The discriminant is:
D = b² - 4ac
If the discriminant is zero, then the quadratic has only one solution, here we have the equation:
2x² - 28x + 7m = 0
Then the discriminant is:
D = (-28)^2 - 4*2*7m
Now we need to solve:
(-28)^2 - 4*2*7m = 0
784 - 56m = 0
Solving that for m:
784/56 = m
14 = m
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