Answer:
1/2 • 1 = 1/2
Step-by-step explanation:
It shows that anything multiplied by 1 is itself.
Answer:
1/2· 1= 1/2
Step-by-step explanation:
When multiplying by 1, you will get the same number.
For a sequence an=3/n(n+1) what is the value of a 10
Answer:
[tex]\large\boxed{a_{10}=\dfrac{3}{110}}[/tex]
Step-by-step explanation:
Put n = 10 to the equation [tex]a_n=\dfrac{3}{n(n+1)}[/tex]
[tex]a_{10}=\dfrac{3}{10(10+1)}=\dfrac{3}{10(11)}=\dfrac{3}{110}[/tex]
For this case we have the following sequence:
[tex]a_ {n} = \frac {3} {n (n + 1)}[/tex]
We must find the value of[tex]a_ {10}[/tex], then, substituting [tex]n = 10[/tex] in the formula we have:
[tex]a_ {10} = \frac {3} {10 (10 + 1)}\\a_ {10} = \frac {3} {10 * 11}\\a_ {10} = \frac {3} {110}[/tex]
ANswer:
[tex]a_ {10} = \frac {3} {110}[/tex]
Use the tables to determine which function will eventually exceed the other, and provide your reasoning.
x f(x)
−1 −5
0 −6
1 −5
2 −2
x g(x)
−1 0.166
0 1
1 6
2 36
f(x) will eventually exceed g(x) because f(x) is an exponential function.
f(x) will eventually exceed g(x) because f(x) has a higher rate of change.
g(x) will eventually exceed f(x) because g(x) is an exponential function.
g(x) will eventually exceed f(x) because g(x) has a higher rate of change.
Answer:
g(x) will eventually exceed f(x) because g(x) is an exponential function.
Step-by-step explanation:
From the first table we can observe the following patterns:
[tex]f( - 1) = {( - 1)}^{2} - 6 = - 5[/tex]
[tex]f(0) = {( 0)}^{2} - 6 = - 6[/tex]
[tex]f( 1) = {( -1)}^{2} - 6 = - 5[/tex]
[tex]f(2) = {( 2)}^{2} - 6 = - 2[/tex]
In general,
[tex]f(x) = {x}^{2} - 6 [/tex]
From the second table we can observe the following pattern:
[tex]g( - 1) = {6}^{ - 1} = \frac{1}{6} [/tex]
[tex]g(0) = {6}^{ 0} = 1[/tex]
[tex]g(1) = {6}^{1} = 6[/tex]
[tex]g(2) = {6}^{2} = 36[/tex]
In general,
[tex]g( x) = {6}^{ x} [/tex]
Conclusion:
Since the f(x) represents a quadratic function and g(x) represents an exponential function, g(x) will eventually overtake f(x).
The correct answer is C.
Answer: C.
Step-by-step explanation:
Go it right on my test
Use the elimination method to solve the system of equations. Choose the
correct ordered pair,
2y = x + 2
x - 3y = -5
Answer:
x = 4, y = 3 → (4, 3)Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}2y=x+2&\text{subtract x from both sides}\\x-3y=-5\end{array}\right\\\\\underline{+\left\{\begin{array}{ccc}-x+2y=2\\x-3y=-5\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad-y=-3\qquad\text{change the signs}\\.\qquad\boxed{y=3}\\\\\text{put the value of y to the second equation:}\\\\x-3(3)=-5\\x-9=-5\qquad\text{add 9 to both sides}\\\boxed{x=4}[/tex]
one line segment is 5 cm more than four times the length of another the difference in their lengths is 35cm how long are they
Answer:
Length of the segments will be 10 cm and 45 cm.
Step-by-step explanation:
Let the length of one segment is x.
Then by the statement of this question,
"one segment is 5 cm more than four times the length of another".
Length of other segment = 4x + 5
(4x + 5) - x = 35
4x + 5 - x = 35
3x + 5 = 35
3x = 35 - 5
3x = 30
x = 10 cm
Length of other segment = 4(10) + 5 = 45 cm
Therefore, two segments are of length 10 cm and 45 cm.
meaningful use was created to help improve quality safety and efficiency true or false
Answer:
TRUE
Step-by-step explanation:
Meaningful use is used to define the minimum standards of the American government for electronic health records and it has five main objectives:
Provide privacy and security for personal health informationExpand public healthImprove care coordinationIncrease patient engagementImprove quality, safety, efficiency and reduce health disparities.Therefore, the statement is true.
Consider the polynomial p(x)=x^3-9x^2+18x-25, which can be rewritten as p(x)=(x-7)(x^2-2x+4)+3 . The number _[blank 1]_ is the remainder whenp(x) is divided by x-7, and so _[blank 2]_ a factor of p(x)
What is blank 1 and 2?
options:
a)7
b)is
c)is not
d)0
e)3
Answer:
Blank 1: 3 is the remainder
Blank 2: not a factor
Step-by-step explanation:
If p(x)=(x-7)(x^2-2x+4)+3, then dividing both sides by (x-7) gives:
[tex]\frac{p(x)}{x-7}=(x^2-2x+4)+\frac{3}{x-7}[/tex].
The quotient is [tex](x^2-2x+4)[/tex].
The remainder is [tex]3[/tex].
The divisor is [tex](x-7)[/tex].
The dividend is [tex]p(x)=x^3-9x^2+18x-25[/tex].
It is just like with regular numbers.
[tex]\frac{11}{3}[/tex] as a whole number is [tex]3\frac{2}{3}[/tex].
[tex]3\frac{2}{3}=3+\frac{2}{3}[/tex] where 3 is the quotient and 2 is the remainder when 11 is divided by 3.
Here is the division just for reminding purposes:
3 <--quotient
----
divisor-> 3 | 11 <--dividend
-9
---
2 <---remainder
Anyways just for fun, I would like to verify the given equation of
p(x)=(x-7)(x^2-2x+4)+3.
I would like to do by dividing myself.
I could use long division, but I have a choice to use synthetic division since we are dividing by a linear factor.
Since we are dividing by x-7, 7 goes on the outside:
x^3-9x^2+18x -25
7 | 1 -9 18 -25
| 7 -14 28
-------------------------------
1 -2 4 3
We have confirmed what they wrote is totally correct.
The quotient is [tex]x^2-2x+4[/tex] while the remainder is 3.
If p/(x-7) gave a remainder of 0 then we would have said (x-7) was a factor of p.
It didn't so it isn't.
Just like with regular numbers. Is 3 a factor of 6? Yes, because the remainder of dividing 6 by 3 is 0.
in triange ABC, AB=5 and AC=14. Find The measure of angle c to the nearest degree
Answer:
The answer is ∠C= 20 degree
Step-by-step explanation:
The answer is ∠C= 20 degree
We have given:
AB= 5
AC = 14
and we have to find ∠c to the nearest degree.
So,
We know that:
tan(C)= AB/AC
tan(C)= 5/14
tan(C)= 0.3571
C=20 degree
Thus the answer is ∠C = 20 degree ....
Instructions:Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s). The native bird population in a city is decreasing at a rate of 10% per year due to industrialization of the area by humans. The population of native birds was 14,000 before the decrease began. Complete the recursively-defined function to describe this situation. f(1) = f(n) = f(n - 1) · , for n ≥ 2 After 3 years, birds will remain.
Answer:
The recursive function is;
f(n)=f(n-1)×0.9 for n≥2
After 3 years, 11340 birds will remain.
Step-by-step explanation:
First the native population was 14,000 before decreasing started, hence this is your f(1)
f(1)=14000
⇒A decrease of 10% is similar to multiplying the native value of birds with 90%
New number of birds = native value × 90% ⇒f(1)×0.9
For second year , you multiply the value you get after the first decrease by 0.9 to get the new number of birds;
f(2)=f(1)×0.9= 0.9f(1)=0.9×14000=12600
For the 3rd year, the value of the second year,f(2) is then reduced by 10%. This is similar to multiplying value of f(1) by 90%
f(3)=f(2)×0.9=12600×0.9=11340
Apply the same for the 4th year and above, hence for nth year;
f(n)=f(n-1)×0.9 for n≥2
What is the ratio for the sine of Z ?
Answer:
55/73
Step-by-step explanation:
Soh Cah Toa gives us our definitions for the trigonometric ratios: sine, cosine, and tangent.
That is the first part means sine is opposite / hypotenuse.
The second part means cosine is adjacent / hypotenuse.
The last part means tangent is opposite / adjacent.
No matter what angle you are looking to label the right triangle from, the hypotenuse will always be the same. The hypotenuse is the side opposite the 90 angle. Opposite meaning not touching; across from.
The other two terms are adjacent and opposite and depending on what angle you are looking from these change.
Adjacent means touching (exclude the hypotenuse from this).
Opposite means across from; not touching.
So from Z:
The side that has measurement 55 is opposite to Z.
The side that has measurement 48 is adjacent to Z.
The hypotenuse is the side that has measurement 73.
So from Y:
The side that has measurement 48 is opposite to Y.
The side that has measurement 55 is adjacent to Y.
The hypotenuse is the side that has measurement 73.
We don't label are triangle with respect to the 90 degree, X.
Anyways we asked to find sin(Z).
[tex]\sin(Z)=\frac{\text{opposite to }Z}{\text{ hypotenuse}}=\frac{55}{73}[/tex]
f(x) = x3 – 2x + 6
g(x) = 2x3 + 3x2 - 4x + 2
Find (f – g)(x).
Answer:
-x^3-3x^2+2x+4
Step-by-step explanation:
Just calculate each coefficient of the polynomial separately.
x^3-2x+6-(2x^3+3x^2-4x+2) = (1-2)x^3+(0-3)x^2+(-2-(-4))x+(6-2) = -x^3-3x^2+2x+4.
Answer:
- x³ - 3x² + 2x + 4
Step-by-step explanation:
(f - g)(x) = f(x) - g(x)
f(x) - g(x)
= x³ - 2x + 6 - (2x³ + 3x² - 4x + 2) ← distribute by - 1
= x³ - 2x + 6 - 2x³ - 3x² + 4x - 2 ← collect like terms
= - x³ - 3x² + 2x + 4 ← in standard form
If 50% of days are sunny and 50% of days are rainy, what is the ratio of sunny days to rainy
days? (4 points)
Answer:
1:1
Step-by-step explanation:
Since both equal up to 100% and both are 50%, it's 1:1.
1 stands for 50% and the other 1 stands for 50% too.
The drama club you are part of is hosting a pancake breakfast. You are in charge of buying the sausage, which costs $5 per pound, and bacon, which costs $4 per
pound. The meat budget you are given totals $500 dollars. The inequality 5x + 4y < 500 represents the possible combinations of pounds of sausage (x) and bacon
(y) you can buy
A. 20 pounds of sausage and 90 pound of bacon
B. 40 pound of sausage and 40 pound of bacon
C. 60 pound of sausage and 80 pound of bacon
D. 80 pound of sausage and 20 pound of bacon
Answer:
C.Step-by-step explanation:
Look at the pictures.
x - sausage
y - bacon
A. 20 pounds of sausage and 90 pound of bacon
x = 20 → y = 100 > 90
B. 40 pound of sausage and 40 pound of bacon
x = 40 → y = 75 > 40
C. 60 pound of sausage and 80 pound of bacon
x = 60 → y = 50 < 80
D. 80 pound of sausage and 20 pound of bacon
x = 80 → y = 25 > 20
Option A (20 pounds of sausage and 90 pounds of bacon) and Option B (40 pounds of sausage and 40 pounds of bacon) are the possible combinations of pounds of sausage and bacon that you can buy.
Explanation:The inequality 5x + 4y < 500 represents the possible combinations of pounds of sausage (x) and bacon(y) you can buy.
Let's check each option to see if it satisfies the inequality:
Option A: 20 pounds of sausage and 90 pounds of baconTherefore, options A and B are the possible combinations of pounds of sausage and bacon that you can buy.
P is a prime number and q is a positive integers such that p + q = 1696 IF P and Q are co primes and their Lcm is 21879 Then find p and q
Answer:
P = 1 3
Q = 1 6 8 3
Step-by-step explanation:
through factorization of 21879
A 4cm cube is cut into 1 CM cubes. what is the percentage increase in the surface area after such cutting?
Answer:
400%.
Step-by-step explanation:
The surface area of a 4 cm cube = 6 * 4^2
= 96 cm^2.
The number of 1 cm cubes that can be cut from the larger cube is :
16 * 4 = 64.
The surface area of each of these smaller cubes is 6*1 = 6 cm^2.
The increase in surface area is a factor of (6*64) / 96
= 4 = 400%.
I don’t which one it is?
Answer:
7.4
Step-by-step explanation:
The information given is in from SAS.
This is a job for law of cosines.
This is the law of cosines [tex]a^2=b^2+c^2-2bc cos(A)[/tex]
The angle A is opposite side a and b,c are the other sides.
So 13 degrees is opposite the y there.
[tex]y^2=16^2+22^2-2(16)(22)\cos(13)[/tex]
Now I'm going to put 16^2+22^2-2*16*22*cos(13) in my calculator:
[tex]y^2=54.04347439[/tex]
Now one more step. To get rid of the square, you need to square root both sides:
[tex]y=\sqrt{54.04347439}=7.351426691[/tex]
Sp the answer is approximately 7.4
Answer:
7.351
I don't know how they have rounded; the closest answer is A
Step-by-step explanation:
The only way I know to do this is with the cos law
y^2 = x^2 + z^2 - 2*x*z cos(Y)
x = 22
z = 16
y = ?
I have serious doubts that this will make a triangle. I ran it though a calculator and it does work -- surprise for me. Substitute the givens.
y^2 = 256 + 484 - 2*10*22*cos(13)
y^2 = 740 - 704*cos(13)
y^2 = 740 - 704*0.9744
y^2 = 740 - 685.95
y^2 = 54.05 Take the square root of both sides
y = √54.05
y = 7.351
In triangle ABC, BG = 24 mm. What is the length of segment
GE?
12 mm
24 mm
36 mm
48 mm
Answer:
A. 12 mm
Step-by-step explanation:
May I have brainliest please? :)
Answer: A: 12 mm
Step-by-step explanation:
^^
Write the equation of the line in slope-intercept form that has the following points: (2, -1)(5, -3) y = -2x + 1/3 y = -2/3x + 1 y = -2x + 1 y = -2/3x + 1/3
Answer:
[tex]\large\boxed{y=-\dfrac{2}{3}x+\dfrac{1}{3}}[/tex]
Step-by-step explanation:
The slope-intercept form of an equation of a line:
[tex]y=mx+b[/tex]
m - slope
The formula of a slope:
[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
===============================================
We have the points (2, -1) and (5, -3). Substitute:
[tex]m=\dfrac{-3-(-1)}{5-2}=\dfrac{-2}{3}=-\dfrac{2}{3}[/tex]
We have the equation:
[tex]y=-\dfrac{2}{3}x+b[/tex]
Put the coordinates of the point (2, -1):
[tex]-1=-\dfrac{2}{3}(2)+b[/tex]
[tex]-1=-\dfrac{4}{3}+b[/tex] add 4/3 to both sides
[tex]\dfrac{1}{3}=b\to b=\dfrac{1}{3}[/tex]
Finally:
[tex]y=-\dfrac{2}{3}x+\dfrac{1}{3}[/tex]
An ant can travel 2 feet in 30 seconds and a beetle can travel 5 feet in 90 seconds. Which bug travels farther per second?
Answer:
The beetle does
Answer:
The Ant travels farther per second
Step-by-step explanation:
To Find how far the ant and beetle travels we have to find out how many feet per second the Ant and Beetle travel.
To find that out for the Ant I divided 30 by 2 and got 15 which means the ant travels 1 foot in 15 second.
To find that out for the beetle I divided 90 by 5 and got 18 which means the beetle travels 1 foot in 18 seconds.
Therefore the Ant travels faster.
there are 480000 books in two public libraries if each cupboard in the library hold 80 books then how many cupboard are required to keep all of the books if one library has 267112 books then how many books are there in the other library
Answer:
there would be 212,888 books in the 2nd library, and 6,000 cupboards needed to hold all the books.
Step-by-step explanation:
simple division is all you need to answer. 480,000 divided by 80 is 6,000. for the second part, if the total amount of books between both libraries is 480,000 and one library has 267,112 books, 480,00 - 267,112 is 212,888
Hope this helps :)
feel free to ask if you have any questions
I need the answer to a parts I-iii and the answer to b
Answer:
a)
i) Mean = 72
ii) Median = 72
iii) Mode = 72
b)
69, 70, 71, 72, 72, 72, 73, 74, 75
Step-by-step explanation:
a. To find mean, median and mode
It is given that all the 9 students get 72 marks.
Therefore the data set be,
72, 72, 72, 72, 72, 72, 72, 72 72
i) mean = (sum of data)/(total number of data)
= (9 * 72)/9 = 9
ii) Median - Central data in the data set when arranging ascending or descending order
72, 72, 72, 72, 72, 72, 72, 72 72
Median = 72
iii) Mode - Most repeating data in the data set
Here mode = 72
b). To find a data set
69, 70, 71, 72, 72, 72, 73, 74, 75
Here Mean, mode and median are all 72
1/2x+3 2/3x+1
What is the solution to the equation
Answer:
12
Step-by-step explanation:
Start by multiplying both sides by 2.
[tex]\frac{1}{2} x+3=\frac{2}{3} x+1\\x+6=\frac{4}{3} x+2[/tex]
Next, multiply both sides by 3.
[tex]x+6=\frac{4}{3} x+2\\3x+18=4x+6[/tex]
Combine like terms.
[tex]3x+18=4x+6\\18=x+6\\12=x[/tex]
Which point represent the location of the vertex of the
given function? *
f(x) = -2(x – 4)2 – 7?
Answer:
(4,-7) is the vertex
Step-by-step explanation:
The equation of the parabola is of the form
y= a(x-h)^2 +k
where (h,k) is the vertex
f(x) = -2(x – 4)^2 – 7
(4,-7) is the vertex
Answer:
The vertex point is (4, -7)
Step-by-step explanation:
Compare withe the general form of the vertex form:
f(x) = a(x - h)^2 + k where (h, k) is the vertex.
f(x) = -2(x - 4)^2 - 7.
- so the vertex is (4, -7).
What fraction of an hour is 33 minuets in the simplest form
Ok.
So an hour contains 60 minutes.
The fraction is therefore,
[tex]\dfrac{33}{60}=\boxed{\dfrac{11}{20}}[/tex]
Hope this helps.
r3t40
Answer:
33 minutes is 11/20 of an hour.
Explanation:
So we know that 30 minutes is equal to half an hour. 30÷60 = 0.5
0.5 as a fraction is equal to 1/2.
Now let's use that same method for 33.
33÷60= 0.55.
0.55×100== 55.
55 as a fraction would be 55/100.
Let's convert that to its simplest form.
55÷5 = 11
100÷5 = 20
33 minutes is 11/20 of an hour.
Describe an example of an augmented matrix.
Answer:
Step-by-step explanation:
When we join the columns of two or more matrices having the same number of rows it is known as augmented matrix.
Let A= [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right][/tex]
B= [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
Then the augmented matrix is(A|B)
Note that a vertical line is used to separate te columns of A from the columns of B
(A|B) [tex]\left[\begin{array}{ccc}1&6\\0&3\\\end{array}\right | \left\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]
This is a simple example of augmented matrix....
Answer:
An augmented matrix refers to a matrix formed by appending the columns of two matrices.
The perfect example to show this is a linear systems of equations, because there we have a matrix formed by the coeffcients of the variables only, and we have a second matrix formed by the constant terms of the system.
If we have the system
[tex]2x+3y=5\\x-4y=9[/tex]
The two maxtrix involved here are
[tex]\left[\begin{array}{ccc}2&3\\1&-4\end{array}\right] \\\left[\begin{array}{ccc}5\\9\end{array}\right][/tex]
However, to solve the system using matrices, we have to formed an augmented matrix
[tex]\left[\begin{array}{ccc}2&3&5\\1&-4&9\end{array}\right][/tex]
So, as we defined it at the beginning, an augmented matrix is the appending of colums from two matrices to form one.
Which sequence could be partially defined by the recursive formula f (n + 1) = f(n) + 2.5 for n 2 1?
2.5, 6.25, 15.625, 39.0625, ..
2.5, 5, 10, 20
-10,-7.5, -5, -2.5, ...
-10, -25, 62.5, 156.25
Answer:
Sequence 3
-10,-7.5,-5,-2.5,...
Step-by-step explanation:
So f(n+1)=f(n)+2.5 means a term can be found by adding it's previous term to 2.5. That means this is an arithmetic sequence with a common difference of 2.5.
f(n+1)=f(n)+d is the recursive form for an arithmetic sequence with common difference d.
So you are looking for a sequence of numbers that is going up by 2.5 each time.
Let's check sequence 1:
2.5+2.5=5 so not this one because we didn't get 6.25 next.
Let's check sequence 2:
2.5+2.5=5 is what we have for the 2nd term.
5+2.5=7.5 so not this one because we didn't get 10 next.
Let's check sequence 3:
-10+2.5=-7.5 is the 2nd term
-7.5+2.5=-5 is the 3rd term
-5+2.5=-2.5 is the 4th term
Sequence 3 is arithmetic with common difference 2.5 assuming the pattern continues.
Let's check sequence 4 for fun:
-10+2.5=-7.5 is not -25
So we are done. Sequence 3 is the only one that fits term=previous term+2.5 or f(n+1)=f(n)+2.5.
??help me how to do this
Answer:
x = sqrt( 4^2 + 7^2)
Step-by-step explanation:
They want the equation to solve the triangle
We can use the Pythagorean theorem
a^2 + b^2 = c^2
where a and be are the legs and c is the hypotenuse
4^2 + 7^2 = x^2
Take the square root of each side
sqrt(4^2 + 7^2) = sqrt(x^2)
sqrt( 4^2 + 7^2) = x
Answer:
[tex]\large\boxed{x=\sqrt{7^2+4^2}=\sqrt{65}}[/tex]
Step-by-step explanation:
Use the Pythagorean theorem:
[tex]leg^2+leg^2=hypotenuse^2[/tex]
We have
[tex]leg=7,\ leg=4,\ hypotenuse=x[/tex]
Substitute:
[tex]x^2=7^2+4^2\to x=\sqrt{7^2+4^2}[/tex]
[tex]x=\sqrt{49+16}\\\\x=\sqrt{65}[/tex]
Find the distance between the points (-3, 2) and (4, -5)
Answer:
[tex]\large\boxed{7\sqrt2}[/tex]
Step-by-step explanation:
The formula of a distance between two points:
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
We have the points (-3, 2) and (4, -5). Substitute:
[tex]d=\sqrt{(4-(-3))^2+(-5-2)^2}=\sqrt{7^2+(-7)^2}=\sqrt{49+49}=\sqrt{(49)(2)}\\\\\text{use}\ \sqrt{ab}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt{49}\cdot\sqrt2=7\sqrt2[/tex]
Find an ordered pair to represent t in the equation t=1/2u+v if u=(-1,4) and v=(3,-2)
Answer:
t=(2.5,0)
Step-by-step explanation:
Given that
[tex]t=\frac{1}{2} u+v[/tex]
and
u=(-1,4)
v=(3,-2)
Then,substitute value of u and v in the equation
[tex]t=\frac{1}{2} (-1)+3=-\frac{1}{2}+ (3)=2.5\\\\\\\\t=\frac{1}{2} (4)+-2=2+-2=0\\\\\\t=(2.5,0)[/tex]
Answer:
The answer on edge is C
Step-by-step explanation:
Does the quadratic function have a maximum or minimum? Give the value
Answer:
Max is 4.
Step-by-step explanation:
Maximum means it has a highest point and what is the highest point.
Minimum means it has a lowest point and what is the lowest point.
It doesn't have a minimum because it keeps going down forever and ever.
It does have a maximum because it does stop at the top. The y-value that is stops at is 4 so the max is 4.
What is the 20th digit after the decimal point of the sum of the decimal equivalents for the fractions 1/7 and 1/3?