The 25th term is 137
Explanation:[tex]\begin{gathered} \text{Given:} \\ a_1\text{ = -7} \\ a_{18}\text{ = 95} \\ a_{25}\text{ = ?} \end{gathered}[/tex]To get the 25th term, we need to find the common difference.
An arithmetic sequence is given as:
[tex]\begin{gathered} a_n=a_1\text{ + (n - 1)d} \\ \text{where a}_1\text{ = first term} \\ n\text{ = number of terms} \\ d\text{ = co}mmon\text{ difference} \end{gathered}[/tex]The formula for the 18th term will be used to find the common difference:
[tex]\begin{gathered} \text{where n = 18} \\ a_{18}=a_1\text{ + (18 - 1)(d)} \\ 95\text{ = -7 + 17d} \\ 95\text{ + 7 = 17d} \\ 102\text{ = 17d} \\ d\text{ = }\frac{102}{17} \\ d\text{ = 6} \end{gathered}[/tex]Now we can find the 25th term:
[tex]\begin{gathered} \text{where n = 25} \\ a_{25}=a_1\text{ + (25 - 1)d} \\ a_{25}=a_1\text{ + 24d} \\ a_{25}=\text{ -7 + 24(6) }=\text{ 144 - 7} \\ a_{25}=\text{ }137 \end{gathered}[/tex]The 25th term is 137
What is the slope of this line?
6
10
Answer: 0.6
Step-by-step explanation:
m = 6/10
m = 0.6
MATH please solve it now and let it be correct please i am dropping 30 points so please help me
The matrix X is [tex]X = A^{-1} B[/tex]
What are invertible matrix?
A square matrix is invertible if and only if the determinant is not equal to zero. A n × n matrix is only invertible if the determinant of the matrix is not zero and has inverse. If the determinant is zero, then the matrix is not invertible and has no inverse.
Given that the two matrix A, B are invertible, therefore the inverse of the matrix exists.
Now given that,
AX = B …(1)
Multiplying [tex]A^{-1}[/tex] on both the side of the equation (1), we get
[tex]A^{-1} A X = A^{-1} B[/tex]
We know that [tex]AA^{-1} = 1[/tex]
⇒ [tex]X = A^{-1} B[/tex]
Therefore, the matrix will be [tex]X = A^{-1} B[/tex]
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A plane traveled 880 miles to Ft. Worth and back. The trip there was with the wind. It took 11hours. The trip back was into the wind. The trip back took 20 hours. What is the speed of theplane in still air? What is the speed of the wind?Please help:):):)
Let the following variables represent the velocities of the plane and the wind:
[tex]\begin{gathered} \text{Velocity of the plane: }v_p \\ \text{Velocity of the wind: }v_w \end{gathered}[/tex]When the plane travels with the wind, the total velocity is the sum of both velocities. When the plane travels against the wind, the resulting velocity will be the difference of both velocities.
When the plane travels with the wind, the following condition is satisfied:
[tex]v_p+v_w=\frac{880\text{ miles}}{11\text{ hours}}[/tex]When the plane travels against the wind, the following condition is satisfied:
[tex]v_p-v_w=\frac{880\text{ miles}}{20\text{ hours}}[/tex]This is a 2x2 system of equations. To solve it by the elimination method, add both equations:
[tex](v_p+v_w)+(v_p-v_w)=\frac{880\text{ miles}}{11\text{ hours}}+\frac{880\text{ miles}}{20\text{ hours}}[/tex][tex]\begin{gathered} \Rightarrow v_p+v_w+v_p-v_w=\frac{880\text{ miles}}{\text{hour}}(\frac{1}{11}+\frac{1}{20}) \\ \Rightarrow2v_p=\frac{880\text{ miles}}{\text{ hour}}(\frac{31}{220}) \\ \Rightarrow2v_p=124\cdot\frac{\text{miles}}{\text{hour}} \\ \Rightarrow v_p=62\cdot\frac{\text{ miles}}{\text{ hour}} \end{gathered}[/tex]Solve for the velocity of the wind from the first equation:
[tex]\begin{gathered} v_w=\frac{880\text{ miles}}{11\text{ hours}}-v_p \\ =\frac{880\text{ miles}}{11\text{ hours}}-62\cdot\frac{\text{miles}}{\text{hour}} \\ =18\cdot\frac{\text{miles}}{\text{hour}} \end{gathered}[/tex]Therefore, the velocity of the plane is 62 miles per hour and the velocity of the wind is 18 miles per hour.
please tell me what I'm doing wrong. I'm still not understanding the subject after 1 hour of practicing.
Here, we want to aolve for the value of x
We proceed by cross-multiplying
We have this as follows;
[tex]\begin{gathered} \frac{1}{x+3}\text{ = }\frac{x+10}{x-2} \\ \\ 1(x-2)\text{ = (x+3)(x+10)} \\ x-2\text{ = x(x+10) + 3(x+10)} \\ x-2=x^2+10x+3x+30 \\ x-2=x^2+13x+30 \\ x^2+13x-x+30+2\text{ = 0} \\ x^2+12x+32\text{ = 0} \\ x^2+4x+8x+32\text{ = 0} \\ x(x+4)\text{ + 8(x+4)= 0} \\ (x+4)(x+8)\text{ = 0} \\ x\text{ + 4 = 0 or x + 8 = 0} \\ x\text{ = -4 or -8} \end{gathered}[/tex]what is the general formula for quadratic equation
Answer:
ax^2 + bx + c = 0
Step-by-step explanation:
a, b, are the coefficients, c is the constant term, and x is the variable
Hope that helps
Anyone know the answer
P(x) = (x4+2x3-7x2+4x) = 0.1 or an expression of more than two algebraic terms, particularly the sum of numerous phrases that contain different powers of the same variable, p(x)=0.1 x4 + 0.2 x3 - 0.7x2 + 0.4x (s).
What is polynomials?Zero polynomial function, linear polynomial function, quadratic polynomial function, and cubic polynomial function are the four most prevalent types of polynomials used in precalculus and algebra.
For instance, the polynomial 2x+5 has an exponent of 1.
The following are a few illustrations of each kind of polynomial function:
continuous operation. Example: The linear polynomial function y = 1. For instance, the quadratic polynomial function 5y + 10 Consider the Cubic Polynomial Function 14x2 + 2x – 6. Example: Quartic polynomial function 4y3 + 5y2 + 2. Eg: 3y4 + 5
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Which number line shows the inequality n < -1? {++ -5-4-3-2 -1 0 1 2345 {++++++ -5-4-5-2-10 1 2 395 {+++++ -5-4-5-2 -1 0 1 2 3 日 5 +++++++++ -5-4-3-2 -1 0 1254 5
Given:
[tex]n\leq-1[/tex]Since n is greater or equal to -1, we are to use a closed dot.
To draw the number line, make a closed circle at point -1, and move the red line left (because n is less than or equal to -1).
Therefore the number line that shows the inequality is the third number line.
The diagram is below
3 What is the area of the parallelogram? Show your work.
0.36 m
0.09 m
Answer:
0.0324
Step-by-step explanation:
0.36x0.09=0.0324
How many kilometers is 2,400,000 meters?
Answer:
2,400 km
Step-by-step explanation:
1 km = 1000 m or 1 m = 10^-3 km
so 2,400,000 x 10^-3 = 2,400 km
What will the new demensions of the rectangle below be after a dilation within scale factor of 9\4
Answer
The new dimensions of the rectangle after dilation by scale factor of (9/4) include
New length = 72 feet
New width = 18 feet
Explanation
The relationship between new length, original length and scale factor of dilation is given as
New length = (Original length) × (Scale factor)
For this question,
Scale factor = (9/4)
Original length = 32 feet
New length = (Original length) × (Scale factor)
New length = 32 × (9/4) = 72 feet
New width = (Original width) × (Scale factor)
Original width = 8 feet
Scale factor = (9/4)
New width = (Original width) × (Scale factor)
New width = 8 × (9/4) = 18 feet
Hope this Helps!!!
An equation is shown below:6(2x − 11) + 15 = 3x + 12Part A: Write the steps you will use to solve the equation, and explain each step. (6 points)Part B: What value of x makes the equation true? (4 points)Can you answer part a and part b in written form please?
Given:
[tex]6(2x-11)+15=3x+12[/tex]Required:
To write the steps to solve the given equation and to find the value of x.
Explanation:
(A)
Consider
[tex]6(2x-11)+15=3x+12[/tex]First multiply 6,
[tex]12x-66+15=3x+12[/tex]Next subtract 15 from 61, we get
[tex]12x-51=3x+12[/tex]Add 51 to the above equation
[tex]\begin{gathered} 12x-51+51=3x+12+51 \\ 12x=3x+63 \end{gathered}[/tex]Subtract 3x we get
[tex]\begin{gathered} 12x-3x=3x-3x+63 \\ 9x=63 \end{gathered}[/tex]Divide 9 on both side, we get
[tex]\begin{gathered} \frac{9x}{9}=\frac{63}{9} \\ \\ x=7 \end{gathered}[/tex](B)
[tex]\begin{gathered} 6(2x-11)+15=3x+12 \\ 12x-66+15=3x+12 \\ 12x-3x=12-15+66 \\ 9x=63 \\ x=\frac{63}{9} \\ x=7 \end{gathered}[/tex]x = 7 makes the equation true.
Final Answer:
The value of x = 7 makes the equation true.
Emerson wants to fence in a rectangle play area for his dog. He decides to make the length 2 feet longer than the width. He has 32 feet of fencing to use for this project and will use it all. What will the dimensions of the dog’s play area be?
If Emerson wants to fence a rectangular play area for his dog where he decides to make the length of the fence, 2feet more than the width, and he uses the complete 32feet fencing he had with himself, for this project, then the dimensions of the play area are 9ft in length and 7ft in width.
As per the question statement, Emerson wants to fence a rectangular play area for his dog and he decides to make the length of the fence, 2feet more than the width, for which, he uses the complete 32feet fencing he had with himself.
We are required to calculate the dimensions the play area from the above-mentioned data.
To solve this question, we need to know the formula to calculate the perimeter of rectangle which goes as [p = 2(l + b)]
Where, "p" is the perimeter of the rectangle, "l" is the length and "b" is the breadth of the rectangle.
Here given that, length of the fence will be 2feet more than width of the same. So, let us assume that width of the fence is "x" ft, and the length of the fence should be (x + 2)ft.
Also since, Emerson uses the complete 32feet fencing he had with himself, the perimeter of the play-area will be 32ft.
Substituting our assumptions in the above mentioned formula to calculate the perimeter of rectangle, we get, [32 = 2{x + (x + 2)}], which is a linear equation. Therefore, solving this equation for x, we will obtain our desired answer.
[32 = 2{x + (x + 2)}]
Or, [32 = 2(x + x + 2)]
Or, [32 = 2(2x + 2)]
Or, (32 = 4x + 4)
Or (4x = 32 - 4)
Or, (4x = 28)
Or, [x = (28/4)]
Or, (x = 7).
Therefore, (x + 2) = (7 + 2) = 9ft.
Rectangle: Any four-sided, closed polygon (quadrilateral) having right angles at all four interior angles, and two pairs of equal and parallel opposite sides, is known as a rectangle.To learn more about Perimeter of rectangles, click on the link below.
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.Which expression is equivalent to 45 ÷ (2 - x)?
A
45
2-X
B (2-x) = 45
C 45+ (x - 2)
D
2-x
45
The equivalent expression to 45÷(2-x) is 45/(2-x).
According to the question,
We have the following expression:
45÷(2-x)
Or in other words, it can be said that 45 is divided by (2-x).
Now, when we are finding the equivalent expression of any expression for that matter then the final expression after solving any expression should be equal to the original one.
For example, the equivalent expression for 3/5 is 6/10 because when we divide the second fraction by we will get 3/5.
Now, in this case, the equivalent expression will be:
45/(2-x)
Because the fraction also means division.
Hence, the correct option is A.
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Korey’s comic book store has been up and running for 4 years. Korey feels that his store has been successful and is considering moving to a larger property to allow for greater inventory and customer opportunities in his business. He would like investors to cover the cost of his expansion. The profits of Korey’s comic book store for its first four years are outlined below. According to this information, what would be the best estimate for Korey to quote as expected profits in the next year in his new business plan? Year Net Profits 1 $14,250.00 2 $15,390.00 3 $16,621.20 4 $17,950.90 5 a. $20,550.19 b. $19,090.90 c. $19,280.60 d. $19,386.97
The next year's expected profit to quote is $19,386.97
Given,
Net profit for 1st year = $14,250
Net profit for 2nd year = $15,390
Net profit for 3rd year = $16,621.21
Net profit for 4th year = $17,950.90
We have to find the expected profit in the next year.
For that, first we have to find the profit percentage of 4 years.
Profit % for 1st year =( 15,390 - 14,250 )/14250 × 100 = 0.08 × 100 = 8%
Profit % for 2nd year =( 16,621.21 - 15,390 )/15,390 × 100 = 0.08 × 100 = 8%
Profit % for 3rd year =( 17,950.90 - 16,621.21)/16,621.21 × 100 = 0.08 × 100 = 8%
So the profit percentage is consistent for the years.
Then we can find next years profit by;
Net profit for 4th year × 1.08 = 17,950.90 × 1.08 = 19,386.97
That is,
The next year's expected profit to quote is $19,386.97
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Answer:
d. $19,386.97
How many ways can 5 students be assigned a seat in a classroom if there are 9 seats in a row?
a) 45
b) 14
c) 362,880
d) 15,120
e) 126
f) None of the above.
Answer: I believe it is D! hope this helps
Step-by-step explanation:
g3-h²+8, when g = 3, h = 5
I think it's 8- I did this before
ХBased on the table, which best predicts the end behaviorof the graph of f(x)?f(x)-6-20-5-4-3-2-101As xoo, fx) - 00, and as x, f(x) – 00.As X-oo, f(x) - oo, and as X - -co, f(x) – 4.O As X - co, f(x) – oo, and as X - oo, f(x) - 09.As x - 00, f(x) ---, and as Xoo, f(x) = -0.440-2.-6-1023
Given the table:
x f(x)
-5 -6
-4 -2
-3 0
-2 4
-1 4
0 0
1 -2
2 -6
3 -10
Let's find the best behaviour if the graph.
From the table, as the values of x increases, the values of f(x) decreases and as the values of y decreases, the values of f(x) decreases.
From the table of values, we can see that as x approaches negative infinity, f(x) approaches negative infinity.
Also, as x approaches infinity, f(x) approaches negative infinity.
Thus, we have the statement that best predicts the behaiour of the graph f(x):
As x ==> ∞, f(x) ==> -∞, and as x ==> -∞, f(x) ==> -∞
ANSWER:
this box is packed with cubes that measure one cubic footenter the volume of the box in cubic feer
The box has the shape of a cuboid.
The volume of the box is given by the formula:
[tex]\text{ volume = length}\times\text{ width}\times\text{ height}[/tex]We now find the number of cubes that make up the length, width, and height
[tex]\begin{gathered} \text{length = 6 ft.} \\ \text{width = }3\text{ ft.} \\ \text{height = 4 ft.} \end{gathered}[/tex]Hence, the volume of the box can be calculated by:
[tex]\begin{gathered} \text{ volume = 6 ft. x 3 ft. }\times\text{ 4ft.} \\ \text{ volume = 72 ft}^3 \end{gathered}[/tex]Therefore, the volume is 72 ft³
I need some help please
Then
4 | x + 1| + 2 > 6
Substract 2 , at left and right
4 |x+1 | > 6-2 = 4
Now divide by 4
(4 |x + 1| )/4 > 4/4
Then
| x + 1| > 1
Now solve this equation, by way of 2 equations
x + 1 > 1
and
- (x + 1) < 1
Solution for first iis
x > 1 - 1
x > 0
And solution for second inequality is
- x - 1 < 1
x < -1 - 1
x < -2
THEN ANSWER interval for this is
(-OO, -2) U (0, OO)
ANSWER IS OPTION B)
Interval notation is
x > 0 ( 0, infinite)
x < -2 ( - infinite, -2)
help meeeeeeeeeeeeeeeeeee please
Answer: 539.9
Step-by-step explanation: Since 2004 is our starting year, 9 years have passed since 2004 and 2013. 9 would be the “x” in the equation.
y = 20.1(9) + 359
y = 180.9 + 359
y = 539.9
what undoes the Sine function
In this problem we have that
In the given right triangle
sin(x)=15/24 ------> by opposite side divided by the hypotenuse
using a calculator
x=38.68 degrees
sin(x)=15/24 ------> simplify
sin(x)=5/8
1 shown. If the diameter of a circle is of an inch, what 4 is its radius? 1 What is the radius r of a circle with a diameter of 4 a r in (Simplify your answer. Type an integer or a fraction.) Enter your answer in the answer box е e Save for ater
Given
d = 1/4 inch
d = diameter
Procedure
[tex]\begin{gathered} r=\frac{1}{2}d \\ r=\frac{1}{2}\cdot\frac{1}{4} \\ r=\frac{1}{8}\text{ inch} \end{gathered}[/tex]
The graph of a function h is shown below. Find h(-1) and find one value of x for which h(x) =5
We have the graph of the function h.
First, we must find h(-1)
To find h(-1) we must see which value takes the function when x = -1
In this case
We can see that when x = -1, the function is equal to 2.
So,
[tex]h(-1)=2[/tex]Second, to find one value of x for which h(x) = 5 we must see which value takes x when the function is equal to 5.
In this case
We can see when h(x) = 5, x takes the value of 1.
So,
[tex]\text{ One value of x for which h(x) = 5 : }1[/tex]2. What is the solution point for the system below?
Answer
The point of intersection is the solution point for the system equation
The point of intersection is the solution
The final answer
x = 4
y= -3
[tex](x,y)=(4,-3)[/tex]Can you please help me my friend says it’s not $6.17 but I think it is what is the right answer please give an explanation cuz my friend wants why it’s $6.17 lol she think it’s $3.25
1.
In order to calculate how much is 5% of the original value, let's use the following rule of three:
[tex]\begin{gathered} 6.50\to100\text{\%} \\ x\to5\text{\%} \\ \\ \frac{6.5}{x}=\frac{1}{0.05} \\ x=0.05\cdot6.5 \\ x=0.325 \end{gathered}[/tex]So the amount taken off is $0.32.
2.
Subtracting this amount from the original price, we have:
[tex]6.50-0.32=6.18[/tex]So the final value is $6.18.
3.
A solution in a sentence would be:
The final value after the discount is 0.95 * 6.5 = $6.18.
What is the explicit formula for this sequence?
-9, -3, 3, 9, 15,
A. an= (-9) + (n − 1)(-6)
B. an=6+ (n − 1)(-9)
C. an=21+ (n-1)6
D. an= (-9) + (n-1)6
The explicit formula for this sequence exists as = (-9) + (n-1)6
Explain about the explicit formula ?We can use an explicit formula, as previously discussed, to determine the nth term in a series. The simplest meaning of explicit is precise or unambiguous. The reason the formula is explicit is that, if properly used, it can be used to find the nth term.
An arithmetic sequence can be expressed explicitly as a = a + (n - 1)d, and each term of the sequence can be computed without knowledge of the other parts. The nth term of an arithmetic, geometric, or harmonic series is usually the explicit formula.
Given: -9, -3, 3, 9, 15.
Because it is an arithmetic series, the supplied sequence.
Therefore, there is no difference between two consecutive terms.
For example, 3-(-3)=6 and (-3)-(-9)=6.
The nth term is now equal to a+(n-1)d.
as, a=-9
So, = -9+(n-1)6
= -9+6n-6
= 6n-15
so that =-9+(n-1)6.
The answer is option D
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Before solving any of the following problems: identify the variables that are given and which one is unknown. Then solve the problem, rounding to two decimal places. 7) Tyrone deposits his yearly bonus of $1000 into an account that earns 2% interest compounded annually . How much will he have in the account after 20 years of working at his job?
Explanation
For a sum compounded annually, the Annuity formula is given by:
[tex]\begin{gathered} A=P\times\frac{1-(1+r)^{-n}}{r} \\ \\ where\text{ P =Initial deposit =\$1000} \\ r=rate\text{ of interest=2 \% =0.02} \\ n=the\text{ number of years compounded =20} \end{gathered}[/tex]Thus, we will compute the amount that will be in his account as:
[tex]A=1000\times\frac{1-(1+0.02)^{-20}}{0.02}[/tex][tex]\begin{gathered} A=1000\times\frac{0.3270}{0.02} \\ \\ A=16351.43 \end{gathered}[/tex]Therefore, after 20 years, he will have had the sum of $16351.43 in his account
find the domain and range of the graph below
Answer:
DOMAIN: (-∞,-2)U(-2,∞) RANGE (-∞,-4)U(-4,∞)
Step-by-step explanation:
Domain x values
(-∞,-2)U(-2,∞)
Range y values
(-∞,-4)U(-4,∞)
Solve the following equation in two different ways. Explain what you did differently.
5(x + 2) = 45
5(x + 2) = 45
The following equations can be solved in two different ways
On solving the equation we get the value as [tex]x=7[/tex]
What is an equation?
An equation is a formula that represents the equality between two expressions.
Method 1) : We are given an equation
[tex]5(x+2)=45[/tex]
Divide both sides by 5, we get
[tex]x+2=9[/tex]
Subtracting 2 from both sides we get,
[tex]x=7[/tex]
Method 2)
We are given an equation
[tex]5(x+2)=45[/tex]
On simplifying the equation we get
[tex]5x+10=45[/tex]
Subtracting 10 from both sides
[tex]5x=35[/tex]
Dividing both sides by 5 we get
[tex]x=7[/tex]
In the first method we first perform division then subtraction and in the second method we simplify the right side of the equation then subtract 10 and finally divide by 5.
Hence We solve the equation by 2 ways And in both cases we get the answer as 7
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Given the sequence: 1,-4, 9, -16, ... The next term is 25.TrueFalse
it's true
the next term is 25
