Answer:
Step-by-step explanation:
The formal definition of a common difference is d = a_(n + 1) - a_n)
so
d = ?
a_(n+1) = a_2 = 14
a_n = a_1 = 24
d = 14 - 24
d = - 10
-10
Step-by-step explanation:In the question, it is asking you to find the common difference between the numbers 24, 14, 4,...
In order to find the common difference between the numbers, we would nee to find the change between them.
In other words, we need to find out how much it's changing by between each number.
When you look at the sequence 24, 14, 4, you would know that it is decreasing each time. This means that the common difference would be a negative number.
Now, we need to figure out how much it is decreasing by.
When you subtract 24 and 14, [tex]24-14=10[/tex], you would get 10. When you subtract 24 by 10, you would get 14. So we know that the difference would be -10.
We can also check the next number. When you subtract 14 by 4, [tex]14-4=10[/tex], you would get 10. Then, when you subtract 14 by 10, you would get 4.
This means that the common difference of the sequence is -10
I hope this helps you out.Good luck on your academics.Have a fantastic day!Find the annual percentage yield (APY) in the following situation. A bank offers an APR of 4.4% compounded daily. The annual percentage yield is (blank) %
Step-by-step answer:
APY (annual percentage yield) is the amount of interest in percent one would actually earn by investing a sum of money in a year.
It takes into account the interest rate expressed in any particular form, and the compounding period.
In the current market, most interest rates (for example, credit cards) are expressed in APR (Annual percentage rate) which is an underestimate of the actual amount to be paid, by NOT taking into account the compounding period, monthly (instead of annually) most of the time. The shorter compounding period increases the APY.
Here the APR is 4.4%. to take into account the compounding period, we divide the interest rate by 12 to give the monthly rate, 4.4%/12=0.044/12.
This rate will then be compounded 12 times to give the APY, or the future value after 12 months.
Future value = (1+0.044/12)^12 = 1.044898
Therefore the APY is 1.044898 less initial deposit, or
1.044898-1 = 0.044898, or 4.4898%, or 4.49% (rounded to 2 decimal places)
2 Points
If y = 12x - 7 were changed to y = 12x + 1, how would the graph of the new
function compare with the original?
O
A. It would be steeper.
O
B. It would be shifted down.
O
c. It would be shifted up.
O
D. It would be less steep.
The graph's y intercept would be shifted up.
Intercept of the graphThe intercept of the original point is determined as follows;
y = 12x - 7, when compared to , y = mx + c
where;
c is the intercept = -7
The intercept of the second graph is determined as follows;
y = 12x + 1
New intercept = 1
The graph's y intercept will move from -7 to +1, thus, It would be shifted up.
Learn more about intercept here: https://brainly.com/question/1884491
Final answer:
The graph of the new function y = 12x + 1 would not be steeper or less steep than the original but would be shifted up compared to the graph of y = 12x - 7.(Option C)
Explanation:
Changing the equation from y = 12x - 7 to y = 12x + 1 does not alter the slope of the line, which remains 12 in both cases. The slope of a line represents the steepness and direction of the line, and since the slope (the coefficient of x) has not changed, the steepness and direction of the line will remain the same.
The change that does occur involves the y-intercept. The original line has a y-intercept at -7, while the new equation has a y-intercept at +1. This means the entire line is shifted vertically upwards by 8 units (from -7 to +1). Therefore, the correct answer to how the graph of the new function would compare with the original is that it would be shifted up.
Which of the following does not factor as a perfect square trinomial? A. 16a^2-72a+81 B. 169x^2+26xy+y^2 C. x^2-18x-81 D. 4x^2+4x+1
Answer:
The correct option is C.
Step-by-step explanation:
Lets solve each option one by one
A) 16a^2-72a+81
According to whole square formula:
a²-2ab+b² =(a-b)²
We have to take the square root of first and third term of each equation.
a² shows the first term = 16a^2
The square root of 16a^2 is 4a.. because 4 is the number which can be multiplied two times to give 16 and when we multiply a two times it gives us a².
b² shows the third term = 81
The perfect square of 81 is 9.
2ab shows the middle term.
2ab = 2(4a)(9) = 72a
Thus we can factor it as a perfect square trinomial:
a²-2ab+b² =(a-b)²
16a²-72a+81 =(4a-9)²
B) 169x^2+26xy+y^2
a²+2ab+b² =(a+b)²
The square root of 169x² is 13x
Square root of y² is y
The middle term 26xy =2ab= 2(13x)(y)= 26xy
Thus we can factor it as a perfect square trinomial:
a²+2ab+b² =(a+b)²
169x^2+26xy+y^2 = (13x+y)²
C) x^2-18x-81
We can not factor it as a perfect square trinomial because the third term is negative.
D) 4x^2+4x+1
a²+2ab+b² =(a+b)²
The square root of 4x² is 2x
Square root of 1 is 1
The middle term 4x=2ab=2(2x)(1)= 4x
Thus we can factor it as a perfect square trinomial:
a²+2ab+b² =(a+b)²
4x^2+4x+1 = (2x+1)²
Thus the correct option is C....

Transversal  cuts parallel lines  and  at points X and Y as shown in the diagram. If m∠CXP = 106.02°, what is m∠SYD?
A.
73.98°
B.
90°
C.
106.02°
D.
180°
Answer:
m<SYD = 106.02°. Reason: alternate exterior angles are equal.
Step-by-step explanation:
Answer:
m<SYD = 106.02°. Reason: alternate exterior angles are equal.
Step-by-step explanation:
x = -2y - 5
4x – 3y = 2
How to solve this linear system?
rewrite the fraction using the least common denominator
4/9 7/15
Answer:
20/45 & 21/45
Step-by-step explanation:
Find a common denominator. What you do to the denominator, you do to the numerator. In this case, the smallest denominator is 45.
(4/9)(5/5) = 20/45
(7/15)(3/3) = 21/45
The two fractions you have is:
20/45 for 4/9
21/45 for 7/15
~
Answer:
20/45 for 4/9 and 21/45 for 7/15
Step-by-step explanation:
The least common denominator of 4/9 is 20/45.
The least common denominator of 7/15 is 21/45.
Which relationship in the triangle must be true?
sin(B) = sin(A)
sin(B) = cos(90 - B)
cos(B) = sin(180 - B)
COS(B) = COS(A)
Mark this and return
Save and Exit
Sube
Answer:
sin(B)=cos(90-B)
Step-by-step explanation:
sin(B)=cos(90-B) is a co-function identity.
We can also prove it using the difference identity for cosine.
Let's do that:
cos(90-B)
equals
cos(90)cos(B)+sin(90)sin(B)
0cos(B)+1sin(B)
0+sin(B)
sin(B)
Therefore cos(90-B)=sin(B).
Use synthetic substitution to find g(3) and g(-6) for the function g(x)=x^5-5x^3-10x+4
Answer:
g(3)=82
g(-6)=-6632
Step-by-step explanation:
To find g(3) we are going to use synthetic division for dividing the polynomial x^5-5x^3-10x+4 by x-3.
So this means 3 goes on the outside.
Also since we are missing x^4 and x^2 term, we will need to put a 0 placeholders there.
3 | 1 0 -5 0 -10 4
| 3 9 12 36 78
|_____________________
1 3 4 12 26 82
So g(3)=82
To find g(-6) we will put -6 on the outside:
-6 | 1 0 -5 0 -10 4
| -6 36 -186 1116 -6636
--------------------------------------
1 -6 31 -186 1106 -6632
So g(-6)=-6632
Let f(x) = -2x - 7 and g(x) = -4x + 6. Find (fxg)(-5).
a. -59
b. 3
c. 26
d. -6
Answer:
78
Step-by-step explanation:
The given functions are:
[tex]f(x) = - 2x - 7[/tex]
and
[tex]g(x) = - 4x + 6[/tex]
[tex](f \times g)(x) = f(x) \times g(x)[/tex]
[tex](f \times g)(x) = ( - 2x - 7)( - 4x + 6)[/tex]
When we plug in x=-5, we get:
[tex](f \times g)( - 5) = ( - 4 \times - 5 + 6)( - 2 \times - 5 - 7)[/tex]
[tex](f \times g)( - 5) = ( 20 + 6)( 10 - 7)[/tex]
[tex](f \times g)(5) = ( 26)( 3) =7 8[/tex]
X+1
-
and h(x) = 4 - X, what is the value
Oil CD
Nior
wla
olo
Answer:
8/5
Step-by-step explanation:
[tex](g\circ h)(-3)[/tex] means [tex]g(h(-3))[/tex].
Start with the inside first: h(-3).
h(-3) means use the function called h and replace the x with -3. The expression that is called h is 4-x.
4-x evaluated at x=-3 gives us 4-(-3)=4+3=7.
So the value for h(-3) is 7, or h(-3)=7.
Now this is what we thus far:
[tex](g\circ h)(-3)=g(h(-3))=g(7)[/tex].
g(7) means use the function called g and replace x with 7. The expression that is called g is (x+1)/(x-2).
(x+1)/(x-2) evaluated at x=7 gives us (7+1)/(7-2)=(8)/(5)=8/5.
This is our final answer:
[tex](g\circ h)(-3)=g(h(-3))=g(7)=\frac{8}{5}[/tex].
The function f(x) = 2.54 can be used to represent the curve through the points (1, 10), (2, 50), and (3, 250). What is the
multiplicative rate of change of the function?
Answer:
So the multiplicative rate of change is increased by a factor of 5 per 1 unit increase in x.
Step-by-step explanation:
I think your function is off... but I can look at your ordered pairs.
(1,10)
(2,50)
(3,250),..
As the x increases by 1 the y is being multiply by a factor of 5 each time.
So the multiplicative rate of change is increased by a factor of 5 per 1 unit increase in x.
COMPLETE
the equation x2 - 9 = 0 has
real solution(s).
Answer:
Step-by-step explanation:
x^2-9 = 0
x^2 = 0+9
x^2=9
Take square root at both sides:
√x^2 =+/-√9
x =+/- 3
This equation has 2 real solutions, x=3 , x=-3....
Find the distance from Point A (4,2) to Point B (-3,2).
Answer:
7
Step-by-step explanation:
You can use the distance formula, but since both points have the same y-coordinate, they lie on a horizontal line. Just find the difference between the x-coordinates and take the absolute value.
distance = |-3 - 4| = |-7| = 7
Answer:
The distance is:
[tex]d=7[/tex]
Step-by-step explanation:
The distance d between two points [tex](x_1, y_1)[/tex] and [tex](x_2, y_2)[/tex] is calculated using the following formula:
[tex]d=\sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}[/tex]
In this case the points are:
A (4,2), B (-3,2).
Then the distance is:
[tex]d=\sqrt{((-3)-4)^2 + (2-2)^2}[/tex]
[tex]d=\sqrt{((-7)^2 + (0)^2}[/tex]
[tex]d=\sqrt{49}[/tex]
[tex]d=7[/tex]
PLEEEEEEASE HELP ME:D
Answer:
{ (1,1),(2,9),(4,8) } is the right answer. Mentioned relation has all the ordered pairs of x and y in the form of set, shown in the table.
Step-by-step explanation:
Tables can be used to describe functions. i.e. in given table two coordinates x,y used as ordered pairs and their values mentioned, the value x-coordinate comes first and than value of its corresponding y-coordinate .According to the table, if we take value of x=1 than we need to take corresponding value of y=1 written as ( 1,1 ), Similarly for if x=2, its corresponding value of 'y' will be y=3 written as ( 2,3 ) and so onThe entire table expressed in ordered pair gives set { (1,1),(2,9),(4,8) }.Answer details
Grade: Middle
Subject: Mathematics
Chapter: Representing Functions and relations
Keywords: relations, ordered pairs, tables and functions, set etc
Which is an exponential growth function f(x)=6(0.25)x
f(x)=0.25(5.25)x
Answer: Second Option
[tex]f(x)=0.25(5.25)^x[/tex]
Step-by-step explanation:
The exponential growth functions have the following form:
[tex]f(x) = a(b)^x[/tex]
Where a is the main coefficient, b is the base and x is the exponent.
For this type of functions the base b must always be greater than 1. Otherwise it would be an exponential decay function
Among the options given, the only function whose base is greater than 1 is the second option:
[tex]f(x)=0.25(5.25)^x[/tex]
Answer:
The correct answer option is B. [tex] f ( x ) = 0 . 2 5 ( 5 . 2 5 ) ^ x [/tex].
Step-by-step explanation:
If the numbers are positive along with the base of the exponent which must be greater than 1, then it an exponential growth function.
1. [tex]f(x)=6(0.25)^x[/tex]:
Here the numbers are positive but the base of the exponent is 0.25 which is less than 1 so it is not an exponential growth function.
2. [tex] f ( x ) = 0 . 2 5 ( 5 . 2 5 ) ^ x [/tex]:
Positive numbers with base of the exponent greater than 1, therefore it is an exponential growth function.
riangle XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z'. What is the distance between any two corresponding points on ΔXYZ and ΔX'Y'Z′?
Answer:
5 units
Step-by-step explanation:
According to the given statement Δ XYZ is translated 4 units up and 3 units left to yield ΔX'Y'Z' which means that each point in ΔXYZ is moved 4 units up and moved 3 units left.
To find the distance of each corresponding point we will use the Pythagorean theorem which states that the square of the length of the Pythagorean of a right triangle is equal to the sum of the squares of the length of other legs
The square of the required distance = 4^2+3^2 = 16+9 =25
By taking root of 25 we get:
√25 = 5
Thus, we can conclude that the the distance between any two corresponding points on ΔXYZ and ΔX′Y′Z′ is 5 units. ..
What is the location of the point on the number line that is 3/5 of the way from a=2 to b=17
Answer:
11
Step-by-step explanation:
The distance that a is to b is b-a=17-2=15.
The line segment from a=2 to b=17 has length 15.
We need to know what is 3/5 of 15.
3/5 of 15 means what is 3/5 times 15?
(3/5)(15)=3(3)=9
So this means we are looking to make a line segment that is 9 units from 2 which is 2 to 11.
So 11 is 3/5 the way from a=2 to b=17.
Let's check from 2 to 11 that is a length of 9 and from 2 to 17 that is a length of 15.
Is 9/15 equal to 3/5?
Yes, 9/15 can be reduced to 3/5.
Which set of numbers is included in the solution set of the compound inequality?
{-7,5, 18, 24, 32}
{-9, 7, 15, 22, 26}
{16, 17, 22, 23, 24}
{18, 19, 20, 21, 22}
Answer:
It's the first set.
Step-by-step explanation:
X ≤ 18 or x > 22.
The first set is included in the solution.
Its not the second because 22 is not included.
Nor the third also because of the 22.
Nor the third because of the 19, 20, 21 and the 22.
A set is a mathematical model for a collection of items; it contains elements or members, which can be any mathematical object.
What is Compound inequality ?A compound inequality is created when two simple inequalities are combined. This article explains how to graph and solve compound equations.
How to solve?Compound inequality includes number not included in selected region given in graph hence including numbers 18,19,20,21,22
Which is option D
Hence correct option is {18,19,20,21,22}
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A television video game company has the following total expenses E and total incomes I for producing x number of games.
E=200+11x
I=120+x2
Write an equation to represent the profit p for selling x videos.
Ms. Lund placed a 7 foot ladder against a wall with the base of the ladder 4 feet away from the wall . she decided that a different , 10 foot ladder needed to be used . for if Ms. Lund wants the longer ladder to rest against the wall at the same angle as the shorter ladder , about how far away from the wall should she place its base ?
ladders leaning against the wall form triangles. If two of these triangles share the same angle (except the one between wall and floor), they're similar. (The angle between wall and floor is the same, and the sum of all angles in a triangle is 180 degrees)
[tex] \frac{7}{10} = \frac{4}{x} \\ x = \frac{40}{7} [/tex]
The distance the wall should place its base will be 5.71 feet.
What is trigonometry?Trigonometry is the branch of mathematics that set up a relationship between the sides and angle of the right-angle triangles.
ladders leaning against the wall form triangles. If two of these triangles share the same angle (except the one between the wall and floor), they're similar. (The angle between wall and floor is the same, and the sum of all angles in a triangle is 180 degrees)
The distance will be calculated as below:-
( 7 / 10 ) = ( 4 / x )
x = ( 10 x 4 ) / 7
x = 5.71 feet
Therefore, the distance the wall should place its base will be 5.71 feet.
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What is the explicit formula for this sequence?
-7,-3, 1, 5,...
A. an = -7 + (n - 1)(-4)
B. an = 9+ (n - 1)(-4)
C. an = -7 + (n - 114
D. an= -4 + (n - 1)(-7
Answer:
[tex]a_n=-7+4(n-1)[/tex]
or
[tex]a_n=-7+(n-1)(4)[/tex]
Step-by-step explanation:
-7,-3,1,5,... is a arithmetic sequence.
Arithmetic sequences have a common difference. That is, it is going up by 4 each time.
When you see arithmetic sequence, you should think linear equation.
The point-slope form of a line is [tex]y-y_1=m(x-x_1)[/tex].
m is the common difference, the slope.
Any they are using the point at x=1 in the point slope form. So they are using (1,-7).
So let's put this into our point-slope form:
[tex]y-(-7)=4(x-1)[/tex]
[tex]y+7=4(x-1)[/tex]
Subtract 7 on both sides:
[tex]y=-7+4(x-1)[/tex]
So your answer is
[tex]a_n=-7+4(n-1)[/tex]
The explicit formula for the sequence -7, -3, 1, 5,... is an = -7 + (n - 1)(4), which corresponds to an arithmetic sequence with a common difference of 4.
The student is looking for the explicit formula for the sequence -7, -3, 1, 5,.... To find the explicit formula for a linear sequence, we look for a pattern in the increments between successive terms. In this sequence, each term increases by 4 from the previous term (-7 + 4 = -3, -3 + 4 = 1, etc.), so the common difference is 4. Using the formula for an arithmetic sequence, which is an = a1 + (n - 1)d, where an is the nth term, a1 is the first term, n is the term number, and d is the common difference, we can find the explicit formula:
an = -7 + (n - 1)(4)
Since the common difference in the question is positive and we are adding it to the first term which is negative, it is clear that choice A is the correct formula representing the given sequence:
an = -7 + (n - 1)(4)
assume this graph is a transformation from f(t)=-6t^2 what does the term -3.7 do to the rocket’s graph? what does the value t=3.7 represent and what happens to the rocket
@jdoe0001
Answer:
Eq.
y = -6(x-3.7)^2 + 82.14
the value t = 3.7 represents the maximum amplitude of the rocket in-flight.
Step-by-step explanation:
The standard equation of the parabola is written as
ax^2 +bx +c = 0
But we can rewrite it in vertex form. (See attached picture.)
y = a(x-h)^2 + k
If we look at the question, we can see that the vertex is
(h,k) = (3.7 , 82.14)
y = -6(x-3.7)^2 + 82.14
the value t = 3.7 represents the maximum amplitude of the rocket in-flight.
Answer:
t = 3.7 represents the time at which the rocket will reach at the maximum height.
Step-by-step explanation:
In the diagram,
We have a downward parabola having vertex (3.7, 82.14),
Since, a downward parabola is maximum at its vertex,
That is, the maximum value of the graph is 82.14 at 3.7,
Here, the graph shows the path of a rocket,
That is, it shows the distance covered by the rocket in different time,
Hence, the maximum distance covered is 82.14 unit at 3.7 time.
How can you estimate 33 percent of 87?
Answer:
28.71
Step-by-step explanation:
The easiest way I do this is by taking the smaller number (33) changing it to a decimal form of .33, and then multiplying it by 87 to get 28.71
JK Rowling is autographing some of the new Harry Potter books. A store sells 56 books and she is able to autograph 5/8 of the books sold. How many books will have her autograph?
Answer:
35 books
Step-by-step explanation:
56/8 = 7
7 x 5 = 35
5/8 of 56 = 35
J.K. Rowling will autograph 35 of the 56 books sold, which is calculated by multiplying the total number of books by 5/8.
To find out how many books J.K. Rowling will autograph, we need to calculate 5/8 of the 56 books sold. Here's the step-by-step calculation:
Find out what 5/8 of the total amount is by multiplying the total number of books (56) by 5/8.
To do this, first multiply 56 by 5, which equals 280.
Then divide that number by 8, which equals 35.
Therefore, J.K. Rowling will autograph 35 books.
I'm not exactly a geek at math and measurements is one of the things I have always messed up at.
Anyone mind helping me?
Check the picture below.
well, √180 is about 13.4, and √72 is about 8.5, clearly 2*8.5 ≠ 13.4.
Solve the following system of equations: 3x − 2y = 6 6x − 4y = 12 (0, 0) (6, 12) Infinitely many solutions No solutions
Answer:
The correct answer option is: infinitely many solutions.
Step-by-step explanation:
We are given the following system of equations:
[tex] 3 x - 2 y = 6 [/tex] --- (1)
[tex] 6 x - 4 y = 1 2 [/tex] --- (2)
Dividing equation (2) by 2 to get:
[tex] 3 x - 2 y = 6 [/tex] --- (3)
As the equation (3) is same as the equation (1), therefore the system will have infinitely many solutions.
Answer:
infinitely many solutions
Step-by-step explanation:
Note that if you multiply the first equation by 2, you get 6x - 4y = 12, which is exactly the same as the second equation. These two lines coincide, and so there are infinitely many solutions.
Use the discriminant to describe the roots of each equation. Then select the best description.
x2 - 4x + 4 = 0
Answer:
see explanation
Step-by-step explanation:
Given a quadratic equation in standard form
ax² + bx + c = 0 : a ≠ 0, then
The nature of it's roots can be determined by the discriminant
Δ = b² - 4ac
• If b² - 4ac > 0 then roots are real and distinct
• If b² - 4ac = 0 then roots are real and equal
• If b² - 4ac < 0 then roots are not real
For x² - 4x + 4 = 0 ← in standard form
with a = 1, b = - 4, c = 4, then
b² - 4ac = (- 4)² - (4 × 1 × 4) = 16 - 16 = 0
Hence roots are real and equal
This can be shown by solving the equation
x² - 4x + 4 = 0
(x - 2)² = 0
(x - 2)(x - 2) = 0, hence
x - 2 = 0 or x - 2 = 0
x = 2 or x = 2 ← roots are real and equal
PQ is the perpendicular
bisector of AB
In the construction shown, the two arcs with points P and Q have the same radius. What must be true of PO?
Answer:
PQ must bisect AB
Step-by-step explanation:
Which information would best fill the blanks in row 3?
1.metallic bond and low melting point
2.metallic bond and high melting point
3. covalent bond and low melting point
4.covalent bond and high melting point
Answer:
covalent bond and low melting point- 3.
Answer:
C)
Step-by-step explanation:
egdenuity 2020
Which of the following correlation coefficients represents the strongest correlation?
O 0.043680937
0 -0.313535265
O-0.922107932
O 0.854423006
Answer:
Option C (-0.922107932)
Step-by-step explanation:
Correlation is a concept which explains a linear relationship between two variables. The correlation constant lies between -1 and 1. 0 lies in the center of the interval. A negative correlation means an inverse relationship, and a positive correlation means a direct relationship. 0 technically means no linear relation between the variables. Further the correlation constant lies from 0, more the strength of the relationship. This means that closer the correlation to 1, stronger the positive relationship, and closer the correlation to -1, stronger the negative relationship. It can be seen that Option C (-0.922107932) is the correlation coefficient which is the largest in terms of the magnitude. Therefore, Option C is the correct choice!!!