Answer:
The determinant of an identity matrix is always 1.
Step-by-step explanation:
Given : An identity matrix.
We have to find the determinant of an identity matrix.
Consider an identity matrix,
Identity matrix is a matrix having entry one in its diagonal and rest all entries are zero.
Let us consider a 2 × 2 identity matrix,
[tex]I=\left[\begin{array}{cc}1&0\\0&1\end{array}\right][/tex]
We know determinant of a 2 × 2 matrix
[tex]I=\left[\begin{array}{cc}a&b\\c&d\end{array}\right][/tex]
is given by
D = ad - bc
Thus, here a = 1 , b = 0 , c= 0 d= 1
Thus, D = 1 - 0 = 1
Thus, The determinant of an identity matrix is always 1.
A writer charges $5 per word plus a start up fee of $50 per article.
From 2000-2010 a city had a 2.5% annual decrease in population. If the city had 2,950,000 people in 2000, determine the city's population in 2008.
The population of the city in the year 2008 is 2409122.
Important information:
Initial population in 2000 is 2,950,000.Decreasing rate is 2.5%.Exponential formula:According to the exponential decay formula:
[tex]f(t)=a(1-r)^t[/tex]
Where a is the initial value, r is the decay rate and t is the time period.
The difference between 2008 and 2000 is 8.
Substitute [tex]a=2950000, r=0.025, t=8[/tex] in the above formula.
[tex]f(8)=2950000(1-0.025)^8[/tex]
[tex]f(8)=2950000(0.975)^8[/tex]
[tex]f(8)=2409122.8208[/tex]
Round the value to the previous integer.
[tex]f(8)\approx 2409122[/tex]
Therefore, the population of the city in 2008 is 2409122.
Find out more about 'Exponential formula' here:
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tom has 6 quarters and 12 dimes in his pocket how many coins does he need to take out his pocket to make sure he has 4 quarters
What is the area of ABC below? If necessary, round your answer to two decimal places.
The answer I got from apex was- 106.26
in the diagram below Bd is parallel to XY . what is the value of x
Answer: The correct option is (B) 60.
Step-by-step explanation: Given that the line BD is parallel ti the line XY.
We are to find the value of x.
We know that
if two parallel lines are cut by a transversal, then the measures of the alternate interior angles are equal.
In the given figure, BD is parallel to XY and they are cut by a transversal.
So, the angles with measures x° and 60° are alternate interior angles.
Therefore, we must have
[tex]x^\circ=60^\circ\\\\\Rightarrow x=60.[/tex]
Thus, the value of x is 60.
Option (B) is CORRECT.
Subtract -34.7 from -7.85
A student gets paid to sell raffle tickets at the school basketball game. He earns $15 a day, plus an extra $0.25 for each raffle ticket he sells and $2 for each hour he works at the game. If d = days, r = raffle tickets, and h = hours, what function can he use to calculate his earnings?
Answer: C. [tex]T=15d+\frac{r}{4}+2h[/tex]
Step-by-step explanation:
Let d = days, r = raffle tickets, and h = hours.
Given: A student earns in a day = $15
Then his earning in d days =$15d
Also, he earns for each riffle = $0.25
Then his earning in for r riffles =$0.25r
And , he earns for each hour he works at the game = $2
Then his earning for h hours = $2h
Then the function he can use to calculate his earnings is given by :_
[tex]T=15d+0.25r+2h\\\\\Rightarrow\ T=15d+\frac{1}{4}r+2h[/tex]
Which statement best describes how to determine whether f(x) = 9 – 4x^2 is an odd function?
Determine whether 9 – 4(–x)^2 is equivalent to 9 – 4x^2.
Determine whether 9 – 4(–x^2) is equivalent to 9 + 4x^2.
Determine whether 9 – 4(–x)^2 is equivalent to –(9 – 4x^2).
Determine whether 9 – 4(–x^2) is equivalent to –(9 + 4x^2).
Answer:
Its CCCCCCCCCCCCCCC aka 3 aka third option
on dredful edge im going nuts
Step-by-step explanation:
Justine enrolls in a music program. The cost of the program includes a one-time registration fee of $45 and a fee of $9 per lesson. If the average cost per music lesson is $12 and Justine has taken x classes, which equation represents this scenario?
A.12=54/x
B.12=45+9/x
C.12=45+9x/x
D.12=45x+9/x
If Justine has taken x classes of $9 per lesson, then the total fee for these lessons is $9x.
The cost of the program includes a one-time registration fee of $45 and a fee of $9 per lesson. This means that the total cost of the program in terms of x is
$45 + $9x = $(45 + 9x).
If the average cost per music lesson is $12 (includes a registration fee), then the cost of the program is $12x.
Therefore,
12x = 45 + 9x.
Divide this equation by x:
[tex]12=\dfrac{45+9x}{x}.[/tex]
Answer: correct option is C
The correct option is C) [tex]\[12 = \frac{45 + 9x}{x}\][/tex]. The equation that represents this scenario is [tex]\[12 = \frac{45 + 9x}{x}\][/tex].
To understand why option D is correct, let's break down the costs associated with Justine's music program.
1. The registration fee is a one-time cost of $45. This is a fixed amount and does not depend on the number of classes taken.
2. The cost per lesson is $9, and Justine has taken x classes. Therefore, the total cost for the lessons alone is 9x.
3. The average cost per music lesson, including the registration fee, is $12. This average cost is calculated by taking the total cost (registration fee plus the cost of x lessons) and dividing by the number of classes x.
4. The total cost for x classes, including the registration fee, is the sum of the registration fee and the cost of the lessons, which is [tex]\(45 + 9x\)[/tex].
5. To find the average cost per lesson, we divide the total cost by the number of classes x. This gives us the equation [tex]\(\frac{45 + 9x}{x}\)[/tex].
6. We know that the average cost per lesson is $12, so we set the equation equal to 12: [tex]\(12 = \frac{45 + 9x}{x}\).[/tex]
Therefore, the equation that correctly represents the scenario is: c)
[tex]\[12 = \frac{45 + 9x}{x}\][/tex].
some of the fastest growing occupations in the United States are in which field
a. retail
b. agriculture
c. health care
d. manufacturing
A college writing seminar increased its size by 50% from the first to the second day. If the total number of students in the seminar on the second day was 15 how many students were in the class on the first day
a surveyor standing 64 meters from the base of a building measures the angle to the top of building and finds it to be 39 degrees . the surveyor then measures the angle to the top of the radio tower on the building and finds that it is 48 degrees. how tall is the radio tower?
To calculate the height of the radio tower, trigonometry is used to first determine the building height and then the total height including the tower. Subtracting the building height from the total height gives the height of just the radio tower.
Explanation:To determine the height of the radio tower, we must first use trigonometry to find the height of the building. We use the tangent of the angle and the distance from the surveyor to the building:
Tan(39°) = Height of Building / 64 metersHeight of Building = 64 meters * Tan(39°)After calculating the height of the building, we use the same approach to find the total height to the top of the radio tower:
Tan(48°) = Total Height / 64 metersTotal Height = 64 meters * Tan(48°)Finally, to find the height of the radio tower alone, we subtract the height of the building from the total height.
Height of Radio Tower = Total Height - Height of Building
By following these steps, we can calculate the height of the radio tower.
Which of the following represents this function written in intercept form?
y=x^2-8x+12
a. y=-(x+2)(x+6)
b. y=(x-2)(x-6)
c. y=(-x+3)(x-4)
d. y=-(x+2)(x-6) Which of the following represents this function written in intercept form?
y=x^2-8x+12
a. y=-(x+2)(x+6)
b. y=(x-2)(x-6)
c. y=(-x+3)(x-4)
d. y=-(x+2)(x-6)
Answer:
B. y = (x-2)(x-6)
Step-by-step explanation:
The quadratic function y = x²- 8x + 12 can be factored into intercept form as y = (x - 2)(x - 6), which corresponds to option (b).
The function given is y = x² - 8x + 12. To write this function in intercept form, we need to factor it as the product of two binomials, each representing its intersections with the x-axis where y=0.
To do this, we look for two numbers that multiply to give the constant term (12) and add up to give the coefficient of the middle term (-8). These two numbers are -2 and -6.
Thus, the factored intercept form is y = (x - 2)(x - 6). This corresponds to answer choice (b).
You drive your car for 3 hours at an average speed at 30 km per hour. how far did you go?
The axis of symmetry for the function f(x) = –2x2 + 4x + 1 is the line x = 1. Where is the vertex of the function located?
Answer:
(1, 3)
Step-by-step explanation:
You are given the h coordinate of the vertex as 1, but in order to find the k coordinate, you have to complete the square on the parabola. The first few steps are as follows. Set the parabola equal to 0 so you can solve for the vertex. Separate the x terms from the constant by moving the constant to the other side of the equals sign. The coefficient HAS to be a +1 (ours is a -2 so we have to factor it out). Let's start there. The first 2 steps result in this polynomial:
[tex]-2x^2+4x=-1[/tex]. Now we factor out the -2:
[tex]-2(x^2-2x)=-1[/tex]. Now we complete the square. This process is to take half the linear term, square it, and add it to both sides. Our linear term is 2x. Half of 2 is 1, and 1 squared is 1. We add 1 into the set of parenthesis. But we actually added into the parenthesis is +1(-2). The -2 out front is a multiplier and we cannot ignore it. Adding in to both sides looks like this:
[tex]-2(x^2-2x+1)=-1-2[/tex]. Simplifying gives us this:
[tex]-2(x^2-2x+1)=-3[/tex]
On the left we have created a perfect square binomial which reflects the h coordinate of the vertex. Stating this binomial and moving the -3 over by addition and setting the polynomial equal to y:
[tex]-2(x-1)^2+3=y[/tex]
From this form,
[tex]y=-a(x-h)^2+k[/tex]
you can determine the coordinates of the vertex to be (1, 3)
Answer:
(1,3)
Step-by-step explanation:
A curve passes through the point (0, 5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? (Use x as the independent variable.) ...?
if (3x^2)+7=0 then (x-1/3)^2
Estimate the tip on a $19.65 check using a tip rate of 15%
Add.
(5n^2+4n)+(3n^2+6n)
A cylinder has a volume of 175 cubic units and a height of 7 units. The diameter of the cylinder is
5 units
10 units
12.5 units
The diameter of the cylinder with a volume of 175 cubic units and a height of 7 units is 5 units.
To calculate the diameter of a cylinder, we first need to find the radius using the formula for the volume of a cylinder, V = πr²h. Given that the volume is 175 cubic units and the height is 7 units, the radius comes out to be 5 units. Since the diameter is twice the radius, the diameter of the cylinder is 5 units.
Simplify the expression: √18x^4y^3
Answer:
[tex]3x^2y\sqrt{2\cdot y}[/tex]
Step-by-step explanation:
We have been given an radical expression. We are asked to simplify our given expression.
[tex]\sqrt{18x^4y^3}[/tex]
We can rewrite terms of our given function as:
[tex]\sqrt{18\cdot x^4\cdot y^3}[/tex]
[tex]\sqrt{2\cdot 9\cdot x^4}\cdot y^2\cdot y}[/tex]
[tex]\sqrt{2\cdot 3^2\cdot (x^2)^2\cdot y^2\cdot y}[/tex]
Using radical rule [tex]\sqrt[n]{a^n}=a[/tex], we will get:
[tex]3x^2y\sqrt{2\cdot y}[/tex]
Therefore, the simplified form of our given expression would be [tex]3x^2y\sqrt{2\cdot y}[/tex].
Factor completely: 2x3 + 10x2 + 4x + 20
Prime
(2x + 10)(x2 + 2)
2[(x + 5)(x2 + 2)]
(x + 5)(2x2 + 4) ...?
Answer:
B) 2[(x + 5)(x2 + 2)]
Step-by-step explanation:
Given: 2x^3 + 10x^2 + 4x + 20
Here 2 is a common factor, so we take it out and write the remaining terms in the parenthesis.
2(x^3 + 5x^2 + 2x + 10)
Now let's take (X^3 + 5x^2 +2x + 10), we group and factor them as follows:
(x^3 + 5x^2 + 2x + 10) = x^2(x+5) + 2(x + 5) = (x+5)(x^2 +2)
When we combine them, we get
2x^3 + 10x^2 + 4x + 20 = 2(x+5)(x^2 +2)
Therefore, the answer is B) 2[(x + 5)(x2 + 2)]
Hope this will helpful.
Thank you.
What is the value of the expression below when r = 2?
9 – 3r
A.12
B.6
C.3
music in 2001, full length cassettes represented 3.4% of total music sales. between 2001 and 2006, the present decreased by about 0.5% per year
A laptop computer sells for $850. the sales tax is 7%. what is the total cost of the laptop?
Answer:
$909.50
Step-by-step explanation:
$850 x 7% = $59.50 (tax amount)
850 x (1+ 0.07) = $909.50
Check my answer? Will Upvote!
A scientist counts 35 bacteria present in a culture and finds that the number of bacteria triples each hour. The function y = 35 • 3x models the number of bacteria after x hours. Estimate when there will be about 550 bacteria in the culture.
I think it's about 2.5 hours.
Other answer options:
about 5.5 hours
about 4.5 hours
about 3.5 hours
Answer:
The answer to your question is about 5.5 hours.
Step-by-step explanation:
The equation is y = 35(3x)
Data
# of bacteria = 550 = y
time = ? h
Then 550 = 35(3x) substitution
550 = 105x simplifying
x = 5.23 h.
The ratio of boys to girls in Mrs. Ronilo's math class is 3 to 1. What PERCENT of the class is girls?
Answer:25 %
Step-by-step explanation: there are 4 parts and 1 of those is girls 1 divided by 4 is 0.25, which is 25%
The percent of the class that is girls is 75%
Ratios and proportionGiven the ratio of boys to girls in Mrs. Ronilo's math class is 3 to 1, the total ratio will be:
Total ratio = 3 + 1Total ratio = 4The percent of the class that is girls = 3/4 * 100
The percent of the class that is girls = 75%
Hence the percent of the class that is girls is 75%
Learn more on percentage here: https://brainly.com/question/24304697
lyn has as much money as jo. together they have $63.how much money does each have
take 63 and divide it by 2.
63÷2= 31.5
so they each had $31.5
A sequence of transformations maps ∆ABC onto ∆A″B″C″. The type of transformation that maps ∆ABC onto ∆A′B′C′ is a_______
.When ∆A′B′C′ is reflected across the line x = -2 to form ∆A″B″C″, _______vertex
of ∆A″B″C″ will have the same coordinates as B′.
Answer:The first one is a Reflection
The second one is B
Step-by-step explanation:
Henry has 523 baseball cards. He buys 24 each month. What is a explicit rule for the number of baseball cards Henry has in n months?
Answer:
the answer is a_n= 24n+499 just took the test :)
Step-by-step explanation: