Note that the graphing form and vertex of each quadratic function are given as follows:
a) for f(x)=x² +6x+15, the graphing form of the quadratic function is f(x) = (x + 3)² + 6. The vertex is (-3, 6).
b) for y= x²-4x+9 the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).
c) for f(x)= x² +8x, the graphing form of the quadratic function is f(x) = (x + 4)² - 16. The vertex is (-4, -16).
d) for . y=x² - 4x+9, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).
a. To complete the square for the quadratic function f(x)=x² +6x+15, we add and subtract the square of half of the coefficient of x, which is (6/2)² = 9:
f(x) = x² + 6x + 15
= (x² + 6x + 9) + 6
= (x + 3)² + 6
Therefore, the graphing form of the quadratic function is f(x) = (x + 3)² + 6. The vertex is (-3, 6).
b. To complete the square for the quadratic function y= x^2-4x+9, we add and subtract the square of half of the coefficient of x, which is (-4/2)² = 4:
y = x^2 - 4x + 9
= (x^2 - 4x + 4) + 5
= (x - 2)² + 5
Therefore, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).
c. To complete the square for the quadratic function f(x)= x² +8x, we add and subtract the square of half of the coefficient of x, which is (8/2)² = 16:
f(x) = x² + 8x
= (x² + 8x + 16) - 16
= (x + 4)² - 16
Therefore, the graphing form of the quadratic function is f(x) = (x + 4)² - 16. The vertex is (-4, -16).
d. To complete the square for the quadratic function y=x² - 4x+9, we add and subtract the square of half of the coefficient of x, which is (-4/2)² = 4:
y = x² - 4x + 9
= (x² - 4x + 4) + 5
= (x - 2)² + 5
Therefore, the graphing form of the quadratic function is y = (x - 2)² + 5. The vertex is (2, 5).
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You are making an initial deposit of $1000 in an account that yields 5% interest quarterly (four times a year).
Following the pattern given above, find your year-end balance. (Show calculations for all four quarters and round to the nearest
penny) 15 pts
Answer: The interest rate per quarter is 5%/4 = 1.25%.
At the end of the first quarter, the balance is:
$1000 + $1000(1.25%) = $1000 + $12.50 = $1012.50
At the end of the second quarter, the balance is:
$1012.50 + $1012.50(1.25%) = $1012.50 + $12.66 = $1025.16
At the end of the third quarter, the balance is:
$1025.16 + $1025.16(1.25%) = $1025.16 + $12.82 = $1037.98
At the end of the fourth quarter, the balance is:
$1037.98 + $1037.98(1.25%) = $1037.98 + $13.00 = $1050.98
Therefore, the year-end balance is $1050.98 (rounded to the nearest penny).
Step-by-step explanation:
Use the method of cylindrical shells to find the volume generated by rotating the region bounded by the curves x=√y, x=0, and y=4 about the x-axis.
The volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells is [tex]$4\pi$[/tex] cubic units.
What is the formula for the volume of the cylinder?The formula for the volume of a cylinder is V = πr²h, where V is the volume, r is the radius, and h is the height.
According to given information :To find the volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells, we need to follow these steps:
Sketch the region and the axis of rotation. The region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] is a quarter-circle with radius 2 centered at the origin. The axis of rotation is the x-axis.
Choose a vertical strip with width $\Delta x$ that runs parallel to the y-axis and intersects the region. The height of this strip is given by the equation $y = 4 - x^2$.
Imagine rotating this strip around the x-axis to form a cylindrical shell with thickness [tex]$\Delta x$[/tex], height [tex]$4 - x^2$[/tex], and radius [tex]$x$[/tex].
The volume of this cylindrical shell is given by the formula [tex]$V = 2\pi x(4-x^2)\Delta x$[/tex].
To find the total volume of the solid, we need to add up the volumes of all the cylindrical shells. This can be done by taking the limit as the width of the strips $\Delta x$ approaches zero and summing up the volumes of the resulting shells. This gives us the integral:
[tex]$V = \int_{0}^{2} 2\pi x(4-x^2) dx$[/tex]
We can simplify this integral by expanding the expression inside the parentheses, which gives us:
[tex]$V = \int_{0}^{2} 8\pi x - 2\pi x^3 dx$[/tex]
We can then integrate each term separately to get:
[tex]$V = [4\pi x^2 - \frac{1}{2}\pi x^4]_{0}^{2}$[/tex]
[tex]$V = (4\pi \cdot 2^2 - \frac{1}{2}\pi \cdot 2^4) - (4\pi \cdot 0^2 - \frac{1}{2}\pi \cdot 0^4)$[/tex]
[tex]$V = 8\pi - 4\pi = 4\pi$[/tex]
Therefore, the volume generated by rotating the region bounded by the curves [tex]$x = \sqrt{y}$[/tex], [tex]$x = 0$[/tex], and [tex]$y = 4$[/tex] about the x-axis using the method of cylindrical shells is [tex]$4\pi$[/tex] cubic units.
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To qualify for a police academy, candidates must score in the top 10% on a general abilities test. The test has a mean of 200 and a standard deviation of 20. Find the lowest possible score to qualify. Assume the test scores are normally distributed.
Can someone give a step by step explanation on how to find the Z score? I know how to find X but I need help with mostly Z.
So the lowest possible score to qualify for the police academy is 225.6.
What is mean?In statistics, the mean is a measure of central tendency that represents the average value of a set of data. It is calculated by adding up all the values in the data set and then dividing by the total number of values.
Here,
To find the Z-score, you will need to use the following formula:
Z = (X - μ) / σ
where:
X = the raw score you are trying to find
μ = the population mean (in this case, 200)
σ = the population standard deviation (in this case, 20)
To find the lowest possible score to qualify, you need to find the score that corresponds to the 90th percentile (i.e., the top 10%).
To do this, you can use a standard normal distribution table or a calculator that has a normal distribution function.
Here are the steps:
Find the Z-score that corresponds to the 90th percentile.
You can use a standard normal distribution table to find this value. Look for the row that corresponds to the first digit(s) of the percentile (in this case, 9) and the column that corresponds to the second digit (in this case, 0.0). This will give you the Z-score that corresponds to the 90th percentile, which is approximately 1.28.
Alternatively, you can use a calculator that has a normal distribution function. For example, in Excel, you can use the formula =NORM.S.INV(0.9) to find the Z-score that corresponds to the 90th percentile.
Plug in the values for μ, σ, and Z into the formula for Z-score:
Z = (X - μ) / σ
Rearranging the formula, we get:
X = Z * σ + μ
Substituting the values we know, we get:
X = 1.28 * 20 + 200
X = 225.6
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Find the area of the triangle, round to the nearest tenths if necessary. *Hint: You will need to use Pythagorean Theorem to find the base of the triangle
Answer:
(c) 42.9 ft²
Step-by-step explanation:
You want the area of the right triangle with hypotenuse 17.3 ft and long side 16.5 ft.
Pythagorean theoremThe Pythagorean theorem tells you the relationship between the side lengths is ...
c² = a² +b²
The missing side, b, can be found as ...
b² = c² -a²
b = √(c² -a²) = √(17.3² -16.5²) = √27.04 = 5.2
AreaThe area of the triangle is ...
A = 1/2bh
A = 1/2(16.5 ft)(5.2 ft) = 42.9 ft²
The area of the triangle is 42.9 square feet.
Consider a sequence generated by the
formula f(n) = 4n - 7 starting with n =3.
Generate the terms f(1), f(2), f(3), f(4), f(5)
Can you please give a detailed explanation so I can understand
The sequence generated by the formula f(n) = (4n - 7) starting with n = 1 is: -3, 1, 5, 9, 13
What is functions?A function is typically denoted by a symbol, such as "f(x)", where "x" is the input value and "f(x)" is the output value. The input value is sometimes referred to as the "argument" of the function.
The formula f(n) = (4n - 7) generates a sequence of numbers when we plug in different values of "n". To generate the terms f(1), f(2), f(3), f(4), f(5) we need to substitute each value of n into the formula and evaluate the expression.
Starting with n = 1, we can generate the terms as follows:
f(1) = (4 × 1 - 7) = -3
f(2) = (4 × 2 - 7) = 1
f(3) = (4 × 3 - 7) = 5
f(4) = (4 × 4 - 7) = 9
f(5) = (4 × 5 - 7) = 13
So the sequence generated by the formula f(n) = (4n - 7) starting with n = 1 is: -3, 1, 5, 9, 13
Each term in the sequence is found by plugging in a different value of "n" into the formula f(n) = (4n - 7). The first term, f(1), is found by plugging in n = 1, the second term, f(2), is found by plugging in n = 2, and so on.
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The number of animals in a population at the start of year t is Pt
The number of animals at the start of year 1 is 400
Given that
Pt + 1 = 1.01Pt
work out the number of animals at the start of year 3
Therefore, the number of animals at the start of year 3 is approximately 408.04.
What is equation?An equation is a mathematical statement that shows the equality of two expressions, usually with an equal sign "=" in between them. An equation can contain variables, constants, and operators. The variables are represented by letters and can take on different values, while constants are fixed values that do not change. Operators include mathematical symbols like plus, minus, multiplication, and division, as well as exponents and logarithms.
Here,
We are given that the population at the start of year 1 (P1) is 400. Using the recurrence relation Pt + 1 = 1.01Pt, we can find the population at the start of year 2 (P2) and year 3 (P3) as follows:
P2 = 1.01 * P1 = 1.01 * 400 = 404
P3 = 1.01 * P2 = 1.01 * 404 = 408.04
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Translate and solve: 5 less than m is at most 70.
Write your solution in interval notation
The interval notation for the inequality statement "5 less than m is at most 70" is (-∞, 75].
What is an inequality?
In Algebra, an inequality is a mathematical statement that uses the inequality symbol to illustrate the relationship between two expressions. An inequality symbol has non-equal expressions on both sides. It indicates that the phrase on the left should be bigger or smaller than the expression on the right, or vice versa.
The statement given is - 5 less than m is at most 70.
The given sentence can be translated into a mathematical inequality as -
m - 5 ≤ 70
To solve for m, we can add 5 to both sides of the inequality -
m - 5 + 5 ≤ 70 + 5
m ≤ 75
Therefore, m is less than or equal to 75.
In interval notation, we can represent this solution as -
(-∞, 75]
Therefore, the interval value is (-∞, 75].
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reagan wanted to paint so she invested $500 several years later,she has earned $2000 in interest. how long did reagan invest the money if she earned a simple interest rate of 5% ?
Regan invested the money for 8 years at simple interest to earn $2000.
What is the difference between simple interest and compound interest?Simple interest is calculated on the loan amount or principle amount, whereas compound interest is calculated using both the principal amount and the interest that has accrued over the course of a prior period or particular time. Simple interest is based on the principal amount, which is the main distinction between it and compound interest. Contrarily, compound interest is calculated using the principle sum and interest that has been compounded over the course of a period.
The simple interest is given as:
SI = Prt
where I is the interest earned.
P is the principal, = 500.
is the interest rate = 5% = 0.05.
t is the time (in years).
Substituting the values:
2000 = 500 * 0.05 * t
t = 8 years
Hence, Regan invested the money for 8 years at simple interest to earn $2000.
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I WILL GIVE BRAINLIEST AND 5 STARS
Triangle ABC is similar to triangle DEF.
What is the length of AC?
Answer:
a
Step-by-step explanation:
16÷4 is 4 and 12÷4 is 3. I matched up the angles.
After calc, the lenght of AC segment is 3 cm. Alternative A
Similarity of trianglesThe similarity of triangles property has a way of calculating how much an unknown segment of the triangle is worth through measures of available equivalent segments of the two triangles and matching angles.
Let's see calc[tex]\begin{array}{l}\raisebox{8pt}{$\sf \dfrac{AC}{BC}=\dfrac{DF}{EF}$}\\\raisebox{8pt}{$\sf \dfrac{AC}{4}=\dfrac{\red{\diagup\!\!\!\!\!\!12}^{\div4}}{\red{\diagup\!\!\!\!\!\!16}^{\div4}}$}\\\raisebox{8pt}{$\sf \dfrac{AC}{\red{\diagup\!\!\!\!4}}=\dfrac{3}{\red{\diagup\!\!\!\!4}}$}\\\bf\therefore AC=3\end{array}[/tex]
Found the length of segment AC, which is 3cm
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The Gross Domestic Product (GDP) of a country in the first quarter of 2014 was $1.5489*107. Rewrite the GDP in standard notation
We can write the number in scientific nοtatiοn as: $1.5489*107 = 1.5489 * 10 pοwer 7$ This is the standard nοtatiοn fοr the given number.
What is Algebraic expressiοn ?Algebraic expressiοn can be defined as cοmbinatiοn οf variables and cοnstants.
In scientific nοtatiοn, a number is expressed as the prοduct οf a decimal number between 1 and 10 (called the cοefficient) and a pοwer οf 10 (called the expοnent). The expοnent indicates hοw many places the decimal pοint needs tο be mοved tο οbtain the οriginal number.
In the given number, $1.5489*107$, the cοefficient is 1.5489, and the expοnent is 7, which means the decimal pοint needs tο be mοved 7 places tο the right tο οbtain the οriginal number.
Therefοre , we can write the number in scientific nοtatiοn as: $1.5489*107 = 1.5489 * 10 pοwer 7$ This is the standard nοtatiοn fοr the given number.
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find the distance between each pair of points on the coordinate plane
Answer:
give full question please its not full
help with this example, I'm from Kazakhstan, sorry, help in any way you can
The inequalities are factorized to;
1. x > 5 and x > -1
x > 2 and x > -6
2. x < 2
x < -4 and x < 2
3. x > 7
x> 1 and x> 3
How to solve the inequalitiesFrom the information given, we have the inequalities;
(x - 5)(x + 1)> 0
expand the bracket, we get;
x² + x - 5x - 5> 0
x(x + 1) - 5(x + 1) > 0
x > 5 and x > -1
2. x-2/x + 3 < 0
cross multiply the values
x - 2< 0
make 'x' the subject
x < 2
3. x -7/x + 4 > 0
cross multiply the values
x - 7> 0
make 'x' the subject
x > 7
x² + 4x - 12 > 0
x² + 6x - 2x - 12> 0
Factorize
x(x + 6) - 2(x + 6)> 0
x > 2 and x > -6
x² - 2x - 8< 0
x² -2x + 4x - 8 < 0
Factorize
x(x - 2) + 4(x -2 )< 0
x < -4 and x < 2
x² - 4x + 3 > 0
x² - 3x - x + 3> 0
factorize
x(x - 3) - 1(x - 3)> 0
x> 1 and x> 3
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the lowest form of 28 upon 36 is ........... ( with explanation pls)
Answer:
To find the lowest form of 28 upon 36, we need to simplify or reduce the fraction to its lowest terms. This can be done by finding the greatest common factor (GCF) of the numerator (28) and the denominator (36) and dividing both by it.
First, we can find the prime factors of 28 and 36:
28 = 2 × 2 × 7
36 = 2 × 2 × 3 × 3
Next, we can identify the common factors, which are 2 and 2.
To find the greatest common factor, we need to multiply the common factors together. In this case, 2 × 2 = 4, so the greatest common factor is 4.
Now we can divide both the numerator and the denominator by the GCF:
28 ÷ 4 = 7
36 ÷ 4 = 9
Therefore, the lowest form of 28 upon 36 is 7/9.
Step-by-step explanation:
What is the approximate (use 3.14 for pi) volume of this cylinder?
(Diameter is 10 in and height is 12.2 in)
A)383.1 cubic inches
B)957.7 cubic inches
C)122cubic inches
D)3830.8 cubic inches
Answer: B
V=957.7 cubic inches
Step-by-step explanation:
V=Hxpixr^2
V=12.2x3.14x5^2 r=5 because it is half of the diamter, which is 10.
V=12.2x3.14x25
V=957.7 cubic inches
Martin has a spinner that is divided into four sections labeled A, B, C, and D. He spins the spinner twice. PLEASE ANSWER BOTH RIGHT HELP EASY THANK UU
Question 1
Part A
Drag the letter pairs into the boxes to correctly complete the table and show the sample space of Martin's experiment.
Question 2
Part B
If Martin repeats this experiment 400 times, how many times should he expect to spin C and then A?
Enter the correct answer in the box.
Which algebraic expression is equivalent to the expression below? 3 ( 5 x + 7 ) − 6 ( 4 − 2 x )
Answer:
3(5x+7)-6 (4-2x)
15x+21-24+12x = 27x-3
or
15x+21-6+4-2x = 13x+19
Data shown in a frequency table could be displayed in which of the following graphs?
A) line graph
B)line plot
C)bar graph
D)stem-and-leaf plot
Multiple choice
Answer: I think line plot and bar graph
Step-by-step explanation:
Select ALL the correct answers.
Chris is taking a trip to a certain town and wants to know what the residents of the town think about the restaurants there. It would not be possible to ask all 500 residents, so Chris plans on surveying a random sample of 50 residents in the population.
Select the survey methods that would result in Chris obtaining a random sample.
Surveying the first 25 women and 25 men he met at a grocery store.
Surveying every 10th woman and every 10th man at a local diner.
Surveying every 10th woman and every 10th man from a list of people living in the town.
Surveying one person from every 10th home in the town.
Surveying the first 50 people he saw at the airport as he got off the plane.
Chris can obtain a random sample of 50 residents by surveying the first 25 women and 25 men at a grocery store, surveying every 10th woman and every 10th man from a list of people living in the town, surveying one person from every 10th home in the town, or surveying the first 50 people he saw at the airport as he got off the plane.
Random sampling is an important method used to obtain a representative sample of the population of interest. Random sampling involves selecting a sample of elements from a population in such a way that each element has an equal probability of being selected. This ensures that the sample is not biased in any way and that it is representative of the population.In order to obtain a random sample, Chris could use a variety of methods. He could survey the first 25 women and 25 men he met at a grocery store, survey every 10th woman and every 10th man from a list of people living in the town, survey one person from every 10th home in the town, or survey the first 50 people he saw at the airport as he got off the plane.Each of these methods would result in a sample of 50 people that is randomly selected from the population of 500 residents. This would ensure that the sample is representative of the population and that the results of the survey are not biased in any way. Furthermore, the sample size of 50 is large enough to be considered representative of the population of 500.
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A city currently has 138 streetlights. As part of a urban renewal program, the city council has decided to install 2 additional streetlights at the end of each week for the next 52 weeks.
How many streetlights will the city have at the end of 30 weeks?
streetlights
Answer:
The number of additional streetlights installed every week is 2, and this will continue for 52 weeks. Therefore, the total number of streetlights added during this period will be:
2 streetlights/week x 52 weeks = 104 streetlights
If the city currently has 138 streetlights, then after 30 weeks, the total number of streetlights will be:
138 streetlights + 2 streetlights/week x 30 weeks = 198 streetlights
Therefore, the city will have 198 streetlights at the end of 30 weeks.
Step-by-step explanation:
1. The problem states that the city currently has 138 streetlights.
2. The city council has decided to install 2 additional streetlights at the end of each week for the next 52 weeks. This means that every week, the city will add 2 streetlights to its total.
3. To find out how many streetlights will be added in total over the 52-week period, we can multiply the number of additional streetlights per week (2) by the number of weeks (52):
2 streetlights/week x 52 weeks = 104 streetlights
Therefore, over the 52-week period, the city will add 104 streetlights.
4. To find out how many streetlights the city will have at the end of 30 weeks, we need to calculate how many additional streetlights will be added during this time period. Since the city is adding 2 streetlights per week, we can multiply 2 by the number of weeks (30):
2 streetlights/week x 30 weeks = 60 streetlights
This means that over the course of 30 weeks, the city will add 60 streetlights.
5. To find out the total number of streetlights at the end of 30 weeks, we need to add the current number of streetlights to the number of streetlights added during the 30-week period. Therefore, we can add 138 (the current number of streetlights) and 60 (the number of streetlights added during the 30-week period):
138 streetlights + 60 streetlights = 198 streetlights
Therefore, the city will have 198 streetlights at the end of 30 weeks.
HELP ASAP!
Your boss hands you a memo with a summary of the monthly data. The number of imports is shown as f(x), and the number of exports is shown as g(x). Use the data in the table below, representing both functions, to explain to your boss the solution to the system of equations and what that solution represents. Use complete sentences.
Month f(x) = No. of imports g(x) = No. of exports
January (1) 3 1
February (2) 4 3
March (3) 5 5
April (4) 6 7
The system of equations modeling the number of imports and the number of exports is given as follows:
f(x) = x + 3.g(x) = 2x + 1.The solution f(x) = g(x) represents the month at which the number of imports and the number of exports was the same.
How to model the system of equations?The system of equations is modeled by linear functions in slope-intercept form, as follows:
y = mx + b.
In which:
The slope m represents the rate of change.The intercept b represents the initial amount.Hence the equations are given as follows:
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Which of the following explains how to find the area of the shaded region shown?
Find the area of the inner and outer trapezoids, and add them together.
Find the area of the outer trapezoid and then subtract the area of the inner trapezoid.
Count the shaded grid squares and estimate the number of partially shaded squares.
Find the area of the outer trapezoid.
Part B
Find the area in square units.
Answer:
Step-by-step explanation:
Find the area of the outer trapezoid and then subtract the area of the inner trapezoid.
[tex]A=\frac{1}{2} (a+b)h[/tex]
[tex]A_o=\frac{1}{2} (6+2)6=24[/tex]
[tex]A_i=\frac{1}{2} (4+2)3=9[/tex]
Total area = 24 - 9 =15 square units
need to Graph y≥13x−3.
The dοtted line is the line y=13x3, and the shaded area is abοve it.
what the slοpe οf the line?As is well knοwn, the equatiοn fοr a straight line is y = mx + c. Where 'c' is the y-axis intercept and 'm' is the slοpe οn the y-axis. The fοrmula fοr a hοrizοntal line is y = 3.
In οrder tο graph the inequality y≥13x−3, we can first plοt the line y=13x3
(which has a slοpe οf 13 and a y-intercept οf -3) as a dοtted line.
Since the inequality is y≥13x−3, we must shade the area abοve the line.
The dοtted line is the line y=13x3, and the shaded area is abοve it.
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115°
70°
X
Solve for x.
Finally, solve for x.
115 + × = 70
2
= [? ]°
Enter
Answer:
X= 25
Step-by-step explanation:
The answer is shown above!
50x212 with steps like
212
x 50
1 )Use the algorithm method.
5 0
× 2 1 2
1
100
500
1
10000
10600
2) Therefore,50×212=10600
10600
Question 4 of 10
The graphs below have the same shape. What is the equation of the blue
graph?
g(x) = ?
g(x) =
10
|f(x)=x²
6
E
Option B. g(x)=(x-2)²is the equation of blue graph.
A graph: what is it?A graph is a visual representation or diagram that displays facts or values in an organized manner in mathematics.
The red graph is represented by the function:
f(x)=x²
Also, we need the formula for the blue graph.
We can see that the blue graph is just the red graph with the horizontal axis moved 2 units to the right.
An example of a horizontal transition is:
f(x-h) where h is the quantity we shift (to the right).
h = 2 since we moved two units to the right.
Our new role will thus be:
g(x)=f(x-2)=(x-2)²
Therefore:
g(x)=(x-2)²
Our response is B.
Notes:
A denotes a downward vertical movement of two units.
C (assuming it is x²) denotes a two-unit vertical displacement upward.
And D (if you let h = -2, then f(x - (-2)) = f(x + 2) = (x + 2)²) is a horizontal shift of two units to the left.
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the complete question is:
The graphs below have the same shape. What is the equation of the blue
graph?
f(x) = x2
g(x) = ?
9(x) =
O A. g(x) = x² - 2
B. g(x) = (x - 2)2
c. g(x) = x + 2
D. Q(x) = (x + 2)2
Image is attached below;
PLEASE HELP WILL GIVE BRAINLISET WORHT 30 POINTS !!
The mapping of the functions h(x) = |x|/2, f(x) = 2x + 8, and f(x) = x² - 5x + 2 is defined at;
1). -2, f(-2) = 1
2). 6, f(6) = 20
3). 2, f(2) = -4
What is a functionA function is a rule that defines a relationship between one variable. It is the mapping whose codomain is the set of real numbers
For x = -2;
h(-2) = |-2|/2
h(x) = 2/2 {absolute value of -2 is 2 units}
h(x) = 1
for x = 6;
f(6) = 2(6) + 8
f(6) = 12 + 8
f(6) = 20
for x = 2;
f(2) = (2)² - 5(2) + 2
f(2) = 4 - 10 + 2
f(2) = -4
Therefore, the mapping of the functions h(x) = |x|/2, f(x) = 2x + 8, and f(x) = x² - 5x + 2 is defined at;
1). -2, f(-2) = 1
2). 6, f(6) = 20
3). 2, f(2) = -4
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If 80% of a number is 304 and 15% of the same number is 57, find 95% of that number.
Answer:
95% of that number is 361
Step-by-step explanation:
Let's start by finding the actual value of the number.
If 80% of a number is 304, we can set up the equation:
0.8x = 304
To solve for x, we can divide both sides by 0.8:
x = 380
So the number is 380.
Now we can use the second piece of information to find 15% of the number:
0.15(380) = 57
This confirms that our value for x is correct.
Finally, we can use this information to find 95% of the number:
0.95(380) = 361
Therefore, 95% of the number is 361.
reflection across x=1 Graph has GHIJ and yx at points
The vertices of the image after the transformation are G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)
How to perform the transformationGiven that
G = (1, -3), H = (5, -2), I = (3, -5) and J = (3, -1)
The reflection is given as
Reflection across x = 1
The rule of this reflection is
(x, y) = (-(x - 2a), y)
Where
Reflection across x = a = 1
So, we have
G' = (-(1 - 2), -3), H = (-(5 - 2), -2), I' = (-(3 - 2), -5) and J' = (-(3 - 2), -1)
Evaluate
G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)
Hence, the image of the reflection are G' = (1, -3), H = (-3, -2), I' = (-1, -5) and J' = (-1, -1)
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Complete questionWhat are the coordnate of the reflection across x = 1 of GHIJ such that
G = (1, -3), H = (5, -2), I = (3, -5) and J = (3, -1)
Two boats are headed to a lighthouse from
opposite directions. From point A, the crew
of boat A (red boat) measures the angle of
elevation to the top of the lighthouse as 45°.
On the other hand, from point B, the crew
of boat B (green boat) measures the angle
of elevation to the top of the lighthouse as
30°. The lighthouse is at a height of 300 ft
above the water.
A
45°
L
300 FT
30
a) How far is boat A from the
lighthouse? (the horizontal distance)
b) How far is boat B from the
lighthouse? (the horizontal distance)
c) And hence, find the total horizontal
distance between the two boats.
Hypotenuse equals opposite/tan(45°) = 300/1 = 300 feet. Boat A is therefore 300 feet horizontally away from the lighthouse.
what is distance ?The numerical measurement of distance is the separation between two objects or points. Typically, it is expressed in terms of metres, kilometres, miles, or feet. Distances can be calculated either along a simple path (the Euclidean distance) or along a more complicated one (such as a curved surface or a circuitous route). Distance is a crucial notion that is used to define the separation between things, the length of a route or path, and the displacement of an object through time in many disciplines, including physics, mathematics, geography, and engineering.
given
We may utilise trigonometry and create some equations based on the provided angles and distances to solve this problem.
a) We can use the tangent function to calculate the separation between boat A and the lighthouse:
opposite/hypotenuse = tan(45°)
where the hypotenuse is the distance between boat A and the lighthouse, the other side is the lighthouse's height (i.e., the horizontal distance we want to find). By calculating the hypotenuse, we obtain:
Hypotenuse equals opposite/tan(45°) = 300/1 = 300 feet. Boat A is therefore 300 feet horizontally away from the lighthouse.
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6 typists working 5 hours a day can type the manuscript of a book in 16 days. How many days will 4 typists take to do the same job? each working 6 hours a day?
Answer:
Let's begin by finding the total work required to complete the manuscript of the book:
Total work = (Number of typists) x (Number of hours per day) x (Number of days) = 6 x 5 x 16 = 480
Now let's find the work done by 4 typists working 6 hours per day:
Work done by 4 typists = (Number of typists) x (Number of hours per day) x (Number of days) = 4 x 6 x d
where d is the number of days required to complete the manuscript.
Since the amount of work done is the same in both cases, we can set the two equations equal to each other and solve for d:
6 x 5 x 16 = 4 x 6 x d
Simplifying this equation, we get:
480 = 24d
Dividing both sides by 24, we get:
d = 20
Therefore, it will take 4 typists working 6 hours per day a total of 20 days to complete the manuscript of the book.
Step-by-step explanation: