Your answer is (C) !
The correct equation to find the amount of time they spent swimming laps is:
[tex]c. \( \frac{1}{2} \times 1 \frac{1}{2} \)[/tex]
To find the amount of time Paul and Krystal spent swimming laps, we need to determine what half of 1 1/2 hours is. This can be calculated by multiplying 1 1/2 by 1/2.
Let's look at the options:
a. [tex]\( 1 \frac{1}{2} - \frac{1}{2} \):[/tex] This would subtract 1/2 hour from 1 1/2 hours, which is not what we need.
b. [tex]\( 1 \frac{1}{2} \div \frac{1}{2} \):[/tex]This would divide 1 1/2 hours by 1/2, which is not what we need.
c. [tex]\( \frac{1}{2} \times 1 \frac{1}{2} \):[/tex]This is the correct operation, as it multiplies 1 1/2 hours by 1/2 to find half of the time.
d.[tex]\( \frac{1}{2} + 1 \frac{1}{2} \):[/tex] This would add 1/2 hour to 1 1/2 hours, which is not what we need.
So, the correct equation to find the amount of time they spent swimming laps is:
[tex]c. \( \frac{1}{2} \times 1 \frac{1}{2} \)[/tex]
Let's calculate it:
[tex]\[\frac{1}{2} \times 1 \frac{1}{2} = \frac{1}{2} \times \frac{3}{2} = \frac{3}{4} \text{ hours}\][/tex]
Therefore, Paul and Krystal spent [tex]\( \frac{3}{4} \)[/tex] hours (or 45 minutes) swimming laps.
Help me find x please
Trigonometry
[tex]Sine\frac{Opposite}{Hypotenuse} Cos\frac{Adjacent}{Hypotenuse} Tan\frac{Adjacent}{Opposite} \\S\frac{O}{H} C\frac{A}{H} T\frac{A}{O}[/tex]
Depending on which angle you use, decides which formula you use.
We'll use the top right angle.
9 is the adjacent.
x is the opposite.
So you need to use
[tex]Tan\frac{Adjacent}{Opposite} \\Tan45\frac{9}{x} \\x = \frac{9}{Tan45} \\x = 9[/tex]
x = 9If you solve y, you can check this is correct by doing pythagoras' theorem.
[tex]Cos\frac{Adjacent}{Hypotenuse} \\Cos45\frac{9}{y} \\y = \frac{9}{cos45} \\y = 9\sqrt{2}[/tex]
[tex]\sqrt{9^{2}+9^{2} } = 9\sqrt{2}[/tex]
Eva buys online tickets to a play for her family. Each ticket costs $45.00 and there is a fee of $17.99. The total cost for tickets including the fee is $422.99. How many tickets does Eva buy?
45.00x +17.99 = 422.99 (Setup Equation)
45.00x = 405 (Subtract 17.99 from both sides)
x = 9 (Divide both sides by 45.00)
Answer:
9
Step-by-step explanation:
First, you write out the equation. We don't know how many tickets Eva bought, so it can be represented by x. Each ticket costs 45 dollars. The amount of tickets times 45 plus the fee will equal 422.99, so the equation will look like this:
45x + 17.99 = 422.99
Subtract 17.99 from both sides:
45x = 405
Divide 45 on both sides:
x = 9
Eva bought 9 tickets
hope this helps :)
Help me please.......
Answer:
50%
Step-by-step explanation:
you need to figure out what percent ok AK is BG
so we know that AK is 20 units long 10-(-10)=20
and BG is 10 units long 8-(-2)=10
so then you can solve with a proportion
10/20 = x/100
cross multiply that out
20x=1000
divide by 20
x= 50
50%
Answer:
[tex]\frac{1}{2}[/tex]
Step-by-step explanation:
The container that holds the water for the football team is 4/9 full. After pouring in 4
gallons of water, it is 2/3 full. How many gallons can the container hold?
Answer: 18 gallons.
Step-by-step explanation:
Let's call the total gallons that the container can hold x.
Then, based on the information given in the problem, you can write the following expression:
[tex]\frac{4}{9}x+4=\frac{2}{3}x[/tex]
Now, you must solve for x, as you can see below. Therefore, you obtain the following result:
[tex]\frac{4}{9}x+4=\frac{2}{3}x\\\\4=\frac{2}{3}x-\frac{4}{9}x\\\\4=\frac{2}{9}x\\\\4*9=2x\\\\36=2x\\\\x=18\ gallons[/tex]
To solve the container problem, we set up a proportion based on the given fill levels and found that the total capacity of the container is 18 gallons.
Explanation:Understanding the Water Container ProblemTo solve how many gallons the container can hold, we need to set up a proportion based on the information given. The container was initially 4/9 full, and after adding 4 gallons of water, it became 2/3 full. We can use this ratio to find the total capacity of the container.
Steps for CalculationLets represent the total capacity of the container as C gallons.The amount by which the container's fullness increased is from 4/9 to 2/3. In terms of the container's total capacity, this increase can be represented mathematically as: (2/3)C - (4/9)C.This increase is known to be 4 gallons, so we have: (2/3)C - (4/9)C = 4.Now, find a common denominator to subtract the fractions: ((6/9)C - (4/9)C = 4).Then simplify: (2/9)C = 4.Finally, solve for C by multiplying both sides by the reciprocal of (2/9): C = 4 * (9/2), which gives us C = 18 gallons.Therefore, the container's total capacity is 18 gallons.
HELP PLEASE.........
Answer: [tex]\bold{\dfrac{41}{80}}[/tex]
Step-by-step explanation:
[tex]\dfrac{puppies}{total}+\dfrac{kittens}{total}+\dfrac{unicorns}{total}\\\\\\=\dfrac{15}{80}+\dfrac{16}{80}+\dfrac{10}{80}\\\\\\=\large\boxed{\dfrac{41}{80}}[/tex]
Alison had lost some puzzle pieces. She found 3
10
of them under the coffee table and another 4
10
of them under the couch. How much is she still missing?
A) 1
10
B) 3
10
Answer:
Correct Answer 7/10
Step-by-step explanation:
Evan spent 20 hours doing homework last week. This week he spent 25 hours doing homework. He says that he spent 125% more time doing homework this week. Is he correct? Show your work to justify your decision.
Answer:
False. He is not correct.
Step-by-step explanation:
To find the percent increase subtract the old time from the new time then divide that number by the old time. 25-20=5. 5/20=.25. There was a 25% increase in time worked. Evan worked 125% of the original time but only worked 25% more time.
Simplify. Consider all the cases |2x+7|
If x>___, then |2x+7|=___
If x=___, then |2x+7|=___
If x<___, then |2x+7|=___
*fill in the blanks
The absolute value |2x+7| simplifies differently depending on values of x. If x > -7/2, |2x+7|=2x+7. If x=-7/2, |2x+7|=0. If x<-7/2, |2x+7|= -(2x+7).
Explanation:The absolute value |2x + 7| measures the distance of the value 2x + 7 from zero on the number line. To simplify the equation and determine for what values of x the absolute value results are positive, negative or zero, we must consider the following conditions:
If x > -7/2, then |2x + 7| = 2x + 7.If x = -7/2, then |2x + 7| = 0.If x < -7/2, then |2x + 7| = -(2x + 7).In the first case, the inside of the absolute value is positive and thus its value is itself. In the second case, the inside of the absolute value equals to zero and the absolute value of zero is zero. In the third case, the inside of the absolute value is negative and thus its absolute value is the negation of it.
Learn more about absolute valuehttps://brainly.com/question/24368848
#SPJ11
Please see attached below.
Please explain.
Answer:
15 rentals
Step-by-step explanation:
You can (and may be expected to) set up an equation that equates the total cost at one store to the total cost at the other store. When you work through the solution of this equation, you find that the "break even" number of rentals is the ratio of the difference in fixed cost (setup fee) to the difference in per-use cost (rental charge).
Here, that ratio is ...
(15.00 -7.50)/(2.25 -1.75) = 7.50/0.50 = 15
15 rentals will make the total costs the same.
so after 15 movie sales they will be equal
Identify the determinants for the given
Explanation:
The first determinant is that of the matrix of coefficients:
[tex]|A|=\left|\begin{array}{cc}5&2\\-3&-5\end{array}\right|=(5)(-5)-(-3)(2)=-19[/tex]
The second determinant is the same as the above but with the constants substituted for the x-coefficients.
[tex]|A_x|=\left|\begin{array}{cc}14&2\\3&-5\end{array}\right|=(14)(-5)-(3)(2) =-76[/tex]
The third determinant is the same as the first but with the constants substituted for the y-coefficients.
[tex]|A_y|=\left|\begin{array}{cc}5&14\\-3&3\end{array}\right|=(5)(3)-(-3)(14)=57[/tex]
_____
The solution to the system of equations is then ...
[tex]x=\dfrac{|A_x|}{|A|}=\dfrac{-76}{-19} =4\\\\y=\dfrac{|A_y|}{|A|}=\dfrac{57}{-19} =-3[/tex]
What are the dimensions of this matrix?Help!!!
Answer:
The dimensions ⇒ 3 × 4
Step-by-step explanation:
* Any matrix has two dimensions
- Raw and column
- The dimensions very important in the operations on matrices
- We called the number of raw m and the number of column n
- We must write the number of raw before the number of column
- m × n is the dimensions of the matrix
* Example : If the dimension of a matrix is 2 × 3, that
means the matrix has 2 raw and 3 column
* Now lets look to our problem
∵ It has 3 raw and 4 column
∴ Its dimensions is 3 × 4
Answer:
Size of matrix = 3 × 4
Step-by-step explanation:
We are given the following matrix and we are to determine its dimensions:
[tex] \left [ \begin {array}{cccc} 1&-3&8&4\\7&5&3&0\\9&6&-2&-1 \end { array } \right ] [/tex]
We know that the dimension of a matrix is written in the form:
rows × columns
Here we have 3 rows and 4 columns. Therefore, the size of this matrix is 3 × 4.
What are the answers?
Answer:
10. 5556 discs per month
11. 3.33 hours; 0.196%
Step-by-step explanation:
I find "appropriate technology" for questions like these to be a graphing calculator.
10. Put the given function definitions into the formula for profit and look for the peak of the profit curve. It is found at x ≈ 5556.
___
11. The peak of the graph is found at t=3.333. The value of A(t) there is about 0.1962.
_____
If these are part of a calculus course, you can find the maximum values by differentiating the P(x) or A(t) functions and setting the derivative to zero. You get a linear equation in each case, so finding the independent variable value is not difficult:
10. 5 -.0009x = 0
11. (.16 -.048t)e^(-.3t) = 0
3/4 of a pan of brownies was sitting on the counter.Paul decided to eat 1/3 if the brownies in the pan.How much of the whole pan of brownies did Paul eat?
plz make a diagram/picture/model
Answer:
1/4 of the pan
Step-by-step explanation:
1/3 of 3/4 = 1/4
What is the right triangle definition of the cosecant function?
A. hypotenuse/adjacent
B. opposite/hypotenuse
C. adjacent/hypotenuse
D. hypotenuse/opposite
E. opposite/adjacent
D. hypotenuse/opposite
Step-by-step explanation:The mnemonic SOH CAH TOA reminds you that ...
Sin = Opposite/Hypotenuse
You know that
csc = 1/sin
so
csc = 1/(opposite/hypotenuse) = hypotenuse/opposite . . . . matches D
The correct answer to the definition of the cosecant function in a right triangle is D. hypotenuse/opposite, which is the length of the hypotenuse divided by the length of the opposite side.
The right triangle definition of the cosecant function is the length of the hypotenuse divided by the length of the side opposite the angle in question. According to this definition, the correct answer to the student's question is D. hypotenuse/opposite.
In a right triangle, suppose we have an angle 0 (theta), which is not the 90-degree angle. The side opposite this angle is called the 'opposite side', and the side that is not the hypotenuse or the opposite side is called the 'adjacent side'. The hypotenuse is the longest side, opposite the right angle, denoted by c in the Pythagorean theorem, a2 + b2 = c2. Therefore, the cosecant of angle 0 is given by c / opposite side, where c is the hypotenuse.
Please answer, really need help, will be very grateful to anyone who helps...
a) a^2+ 2ab+ b^2=25, find a+b
b) a^2− 8ab+ 16b^2=81, find a–4b
Answer:
a) ±5
b) ±9
Step-by-step explanation:
In each case, the expression on the left is the square of the expression you're asked to find the value of. Then the value of your expression is the square root of the constant on the right. That square root can be either positive or negative.
___
a) a^2 +2ab +b^2 = (a +b)^2 = 25
(a +b) = ±√25 = ±5
___
b) a^2 -8ab +16b^2 = (a -4b)^2 = 81
(a -4b) = ±√81 = ±9
Fill in the blank to make the expression a perfect square y^2-14y+__
y^2-14y+49
(y-7)(y-7)
Answer:
y^2-14y+49 I hope i can help you out
In circle o, which is the chord
Answer:
AC
Step-by-step explanation:
A chord is a line segment connecting two points on a circle.
Basically, it means that a chord is a line that has both endpoints on the edge of the circle.
Solve the system of equations: 7x−3y=13, x−2y=5
Answer:
{1;-2}
Step-by-step explanation:
[tex]...=\left \{ {{x=2y+5} \atop {7x-3y=13}} \right. =\left \{ {{x=2y+5} \atop {14y+35-3y=13}} \right.=\left \{ {{x=2y+5} \atop {y=-2}} \right.=\left \{ {{x=1} \atop {y=-2}} \right.[/tex]
What is the value of (j - k)(5)?
j(x) = 6 + x; k(x) = x^2 - 1
(j - k)(5) =
Answer: -13
j(5)=11
k(5)=24
11-24=-13
Can someone help me on this problem?? I think I’m setting the problem wrong...
Answer:
Message instructor about this question
Step-by-step explanation:
The question does not provide the appropriate information for a suitable answer. The equation tells you height above sea level, but the question asks when the height above ground level will be zero. No information is given as to where ground level is in relation to sea level.
The best choice is "Message instructor about this question." Ask the instructor where ground level is in relation to sea level.
___
In any event, the equation can be made somewhat simpler by factoring -16 ouf of it. Then you get ...
h(t) = -16(t^2 -7t -18) = -16(t -9)(t +2)
For h(t) = 0, solutions are ...
0 = -16(t -9)(t +2)
A product will be zero only when at least one of the factors is zero.
t = 9 or -2 . . . . . values that make the factors zero
The rocket comes back to sea level 9 seconds after launch.
___
If the rocket is launched from ground level (288 ft), then we want to find t when ...
h(t) = 288 = -16t^2 +112t +288
Subtracting 288 and factoring out -16, we get ...
0 = -16(t^2 -7t) = -16t(t -7)
Solutions are ...
t = 0 or t = 7
It is no surprise that the rocket is at ground level at t=0, since we have assumed that is where it is launched from. The other solution, t=7, tells us the rocket returns to gruond level 7 seconds after launch.
_____
Possible solutions are ...
9 seconds if "ground level" means "sea level."
7 seconds if "ground level" means "launch height."
... something else if "ground level" is not one of these
Which expression is equivalent to 15 - -5
Answer:
See below.
Step-by-step explanation:
15 - -5
= 15 - 1(-5)
= 15 + 5
= 20.
Answer:
15--5
add the negatives so its positive.
15+5=20
Step-by-step explanation:
what is 3m+8/8=m-1/3
3(m + -2) + -5 = 8 + -2(m + -4)
Reorder the terms:
3(-2 + m) + -5 = 8 + -2(m + -4)
(-2 * 3 + m * 3) + -5 = 8 + -2(m + -4)
(-6 + 3m) + -5 = 8 + -2(m + -4)
Reorder the terms:
-6 + -5 + 3m = 8 + -2(m + -4)
Combine like terms: -6 + -5 = -11
-11 + 3m = 8 + -2(m + -4)
Reorder the terms:
-11 + 3m = 8 + -2(-4 + m)
-11 + 3m = 8 + (-4 * -2 + m * -2)
-11 + 3m = 8 + (8 + -2m)
Combine like terms: 8 + 8 = 16
-11 + 3m = 16 + -2m
Solving
-11 + 3m = 16 + -2m
Solving for variable 'm'.
Move all terms containing m to the left, all other terms to the right.
Add '2m' to each side of the equation.
-11 + 3m + 2m = 16 + -2m + 2m
Combine like terms: 3m + 2m = 5m
-11 + 5m = 16 + -2m + 2m
Combine like terms: -2m + 2m = 0
-11 + 5m = 16 + 0
-11 + 5m = 16
Add '11' to each side of the equation.
-11 + 11 + 5m = 16 + 11
Combine like terms: -11 + 11 = 0
0 + 5m = 16 + 11
5m = 16 + 11
Combine like terms: 16 + 11 = 27
5m = 27
Divide each side by '5'.
m = 5.4
Simplifying
m = 5.4
Equation:
Variable:
Answer:
Step-by-step explanation:
Para la ecuación 2x+5y-3=0, halla la coordenada que falta (-3,?)
Answer:
[tex](-3, \frac{9}{5})[/tex]
Step-by-step explanation:
We have the equation [tex]2x + 5y-3 = 0[/tex].
The ordered pairs of this equation have the form [tex](x_0, y_0)[/tex]
Where x is the independent variable and y is the dependent variabe.
That is, the points belonging to the line [tex]2x + 5y-3 = 0[/tex] have the form [tex](x_0, f (x_0))[/tex]
For [tex]y = f(x)[/tex].
So, we need to find [tex]f(x_0)[/tex] for x_0 = -3.
Then we substitute x = -3 into the equation and clear the value of y.
[tex]2(-3) + 5y -3 = 0[/tex]
[tex]-6 + 5y = 3\\\\5y = 9\\\\y = \frac{9}{5}[/tex].
Then the ordered pair is:
[tex](-3, \frac{9}{5})[/tex]
A Pizza restaurant offers the following deals”
Deal #1: $8.99 for one large pizza and $5 for each additional large pizza on the same order
Deal#2: $6.00 per large pizza
At what number of pizzas does Deal #1 become a better deal?
What is the cost of 10 pizzas for each deal?
What is the cost per pizza in Deal #1? Which is the better deal and why?
Answer:
The least number of pizza make deal 1 better than deal 2 is 4
The cost of deal 1 is $53.99 and the cost of deal 2 is $60
The cost per pizza of deal 1 is $5.399
The better deal is deal 1
Step-by-step explanation:
* Deal 1 becomes better if it costs less than deal 2
- Assume that the number of pizza are n
* Deal 1:
∵ The cost of one large pizza = $8.99 for first 1 and = $5 for each
additional one
∵ They ordered n large pizza
∴ The cost = 8.99 + 5(n - 1)
- Multiply the bracket by 5
∴ The cost = 8.99 + 5n - 5
- Add like terms
∴ The cost = 3.99 + 5n
∴ The cost of deal 1 = 3.99 + 5n
* Deal 2:
∵ The cost of any large pizza is $6
∵ They ordered n large pizza
∴ The cost = 6 × n = 6n
∴ The cost of deal 2 = 6n
- We need Deal 1 better than deal 2
- Then, put the cost of deal 1 < the cost of deal 2
∵ 3.99 + 5n < 6n
- Subtract 5n from both sides
∴ 3.99 < n
∴ n > 3.99
∴ n = 4
* The least number of pizza make deal 1 better than deal 2 is 4
∵ n = 10
∴ The cost of deal 1 = 3.99 + 5(10) = 53.99
∴ The cost of deal 2 = 6(10) = 60
* The cost of deal 1 is $53.99 and the cost of deal 2 is $60
∵ The cost per one pizza = total cost ÷ the number of pizza
∴ The cost per pizza of deal 1 = 53.99 ÷ 10 = 5.399
* The cost per pizza of deal 1 is $5.399
∵ The unit price of deal 1 is $5.399
∵ The unit price of deal 2 is $6
∵ $5.399 < $6
∴ The unit rate of deal 1 is less than the unit price of deal 2
* The better deal is deal 1
Deal #1 becomes a better deal at 4 pizzas. The cost of 10 pizzas for Deal #1 is $43.99, and for Deal #2 is $60.00. The cost per pizza in Deal #1 is $8.99 for the first pizza and $5 for each additional pizza. Deal #1 is the better deal when ordering 4 or more pizzas because the cost per pizza decreases as more pizzas are added to the order.
To determine at what number of pizzas Deal #1 becomes a better deal than Deal #2, we need to compare the total cost of pizzas under each deal.
For Deal #1, the cost structure is as follows:
The first pizza costs $8.99.
Each additional large pizza on the same order costs $5.
For Deal #2, the cost is a flat rate of $6.00 per large pizza.
Let's first find out at what point the total cost of pizzas under Deal #1 equals the total cost under Deal #2. We'll denote the number of additional pizzas (after the first one) as 'n'.
The total cost for Deal #1 can be expressed as:
[tex]\[ C_1 = 8.99 + 5n \][/tex]
The total cost for Deal #2 is:
[tex]\[ C_2 = 6(n + 1) \][/tex]
We set [tex]\( C_1 \) equal to \( C_2 \)[/tex] to find the break-even point:
[tex]\[ 8.99 + 5n = 6(n + 1) \][/tex]
[tex]\[ 8.99 + 5n = 6n + 6 \][/tex]
[tex]\[ 8.99 - 6 = 6n - 5n \][/tex]
[tex]\[ 2.99 = n \][/tex]
Now let's calculate the cost of 10 pizzas for each deal:
For Deal #1:
[tex]\[ C_{10} = 8.99 + 5(10 - 1) \][/tex]
[tex]\[ C_{10} = 8.99 + 5 \times 9 \][/tex]
[tex]\[ C_{10} = 8.99 + 45 \][/tex]
[tex]\[ C_{10} = \$43.99 \][/tex]
For Deal #2:
[tex]\[ C_{20} = 6 \times 10 \][/tex]
[tex]\[ C_{20} = \$60.00 \][/tex]
The cost per pizza in Deal #1 is $8.99 for the first pizza and $5 for each additional pizza. As the number of pizzas increases, the average cost per pizza decreases.
Find the exact circumference of a circle with diameter equal to 8 ft. 8 ft. 16 ft. 64 ft.
ANSWER
8π ft
EXPLANATION
The circumference of a circle is calculated using the formula C=πd.
Where d=8 is the diameter of the circle.
We substitute d=8 into the formula to obtain,
C=8π ft.
Because we are looking for the exact circumference, we leave the answer in terms of π.
Answer:
The correct answer is,
circumference = 8π feet
Step-by-step explanation:
Formula:-
Circumference of a circle = 2πr
Or circumference = πd
Where 'r' is the radius of circle and 'd' is the diameter of circle
It is given that, diameter of circle is 8 feet
To find the circumference
Here d= 8 feet
Circumference = πd = π * 8 = 8π feet
∠ABC is a 40∘ angle. Point A is at (7, 1) Point B is at (3, 2) Point C is at (8, -1) If ∠ABC is rotated 180∘ about the origin, what are the new points on the image and what is the new angle degree measurement?
Answer:
The new points would be (-7, -1), (-3, -2) and (-8, 1). The angle would not change
Step-by-step explanation:
When you rotate points by 180 degrees, you simply change the sign on the ordered pairs. This will give you the new points.
Also, spinning the points will not change the angle between them. Therefore it stays the same.
Precalculus problem i need help :S
A)
recall that there are 180° in π radians.
[tex]\bf \textit{arc's length}\\\\ s=r\theta ~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ s=10\\ r=5 \end{cases}\implies 10=5\theta \implies \cfrac{10}{5}=\theta \implies \stackrel{\textit{radians}}{2=\theta } \\\\[-0.35em] ~\dotfill\\\\ \begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ x&2 \end{array}\implies \cfrac{180}{x}=\cfrac{\pi }{2}\implies 360=x\pi \\\\\\ \cfrac{360}{\pi }=x\implies 114.59\approx x[/tex]
B)
[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta r^2}{2}~~ \begin{cases} r=radius\\ \theta =angle~in\\ \qquad radians\\[-0.5em] \hrulefill\\ r=5\\ \theta =2 \end{cases}\implies A=\cfrac{(2)(5)^2}{2}\implies A=25[/tex]
Which of the following is the general term for the sequence m, -m, m, -m, . . .?
A. m(-1)^(n-1)
B. (-m)^n
C. (-1)m^(n + 1)
D. (-1)m^(n - 1)
the general term for the sequence m, -m, m, -m, . . . is
The correct option is (A).
The given sequence is: m, -m, m, -m, ...
Let's analyze the pattern:
1. For n = 1, the term is m.
2. For n = 2, the term is -m.
3. For n = 3, the term is m.
4. For n = 4, the term is -m.
5. And so on...
From the pattern, we can see that the sign alternates between positive and negative, and the term alternates between m and -m. This suggests that we can use [tex](-1)^(n-1)[/tex] to control the sign alternation and m to control the alternation between m and -m.
Now, let's check the options one by one:
A. [tex]m(-1)^(n-1)[/tex]
Substituting n = 1, we get[tex]m * (-1)^(1-1) = m * (-1)^0 = m * 1 = m[/tex]
Substituting n = 2, we get [tex]m * (-1)^(2-1) = m * (-1)^1 = m * -1 = -m[/tex]
This matches our sequence. So, Option A seems correct.
B.[tex](-m)^n[/tex]
This doesn't match our sequence because it would give us [tex](-m)^1 = -m,[/tex][tex](-m)^2 = m^2, (-m)^3 = -m^3[/tex], and so on, which doesn't alternate between m and -m.
C.[tex](-1)m^(n + 1)[/tex]
Substituting n = 1, we get [tex](-1)m^(1 + 1) = (-1)m^2 = -m^2[/tex]
Substituting n = 2, we get [tex](-1)m^(2 + 1) = (-1)m^3 = -m^3[/tex]
This doesn't match our sequence because it doesn't alternate between m and -m.
D.[tex](-1)m^(n - 1)[/tex]
Substituting n = 1, we get [tex](-1)m^(1 - 1) = (-1)m^0 = -1[/tex]
Substituting n = 2, we get[tex](-1)m^(2 - 1) = (-1)m^1 = -m[/tex]
This also doesn't match our sequence because it doesn't alternate between m and -m.
So, the correct answer is Option A:[tex]m(-1)^(n-1).[/tex]
help please .........
Answer:
17. 37 2/7
20. 3.4
Step-by-step explanation:
17. The scale factor of the smaller triangle PQR to the larger triangle LMN is given by the ratio of corresponding sides:
RP : NL = 18 : 28 = 9 : 14
The perimeter of LMN is the sum of the lengths of its sides:
16 + 14 + 28 = 58
So, the perimeter of PQR is ...
(9/14)×58 = 261/7 = 37 2/7 . . . . units
__
20. By the same reasoning as above, the sides of triangle RQP are 25/40 = 5/8 of those of triangle MNP. Then ...
RQ = (5/8)·MN
5x -2 = (5/8)·24 = 15 . . . . substitute the measures shown
5x = 17 . . . . . add 2
x = 17/5 = 3.4 . . . . . . divide by 5
The value of x is 3.4.
What happened when a bunch of numbers got lost in the desert and spent years wandering from oasis to oasis?
Answer:
they became "roamin' numerals"
Step-by-step explanation: