Which functions represent the arithmetic sequence 8, 1.5, –5, –11.5... ?
Answer:
-6.5n+14.5 and 8,f(n+1)=f(n)-6.5
Step-by-step explanation:
Indicate the equation of the given line in standard form. The line that is the perpendicular bisector of the segment whose endpoints are R(-1,6) and S(5,5)
The equation of the perpendicular bisector of the segment with endpoints R(-1,6) and S(5,5) is found by calculating the midpoint, slope, and using the negative reciprocal for the perpendicular slope. It is then written in point-slope form and converted to standard form, resulting in 12x - 2y = 13.
Explanation:To find the equation of a line that is the perpendicular bisector of a segment with endpoints R(-1,6) and S(5,5), we need to take the following steps:
Determine the midpoint of the segment RS which will be a point on our bisector.Calculate the slope of the line segment RS.Find the negative reciprocal of the slope from step 2, which will give us the slope of our perpendicular bisector.Write the equation of the bisector line using the point-slope form and then convert it into standard form.The midpoint of RS is given by ((-1+5)/2, (6+5)/2) = (2, 5.5). The slope of RS is (5-6)/(5-(-1)) = -1/6. The negative reciprocal of -1/6 is 6. Thus, the slope of our bisector is 6.
Using the point-slope form with the midpoint, y - 5.5 = 6(x - 2). Expanding and rearranging to standard form, we get:
6x - y = 12 - 5.5 -> 6x - y = 6.5.
Multiplying through by 2 (to clear the decimal), we obtain:
12x - 2y = 13, which is the standard form equation of the perpendicular bisector of segment RS.
Standard form of 210 million, 64 thousands, and fifty
The standard form of 210 million, 64 thousands, and fifty is 210,064,050. This is found by adding the values of each place: 210,000,000 for million, 64,000 for thousand, and 50 for the units.
The standard form of a number is a way of writing numbers that is commonly used in mathematics, especially in arithmetic and place value studies. To write the number 210 million, 64 thousands, and fifty in standard form, one combines these values considering their place values.
The value of 210 million is simply 210,000,000. The value of 64 thousands is 64,000, and the value of fifty is 50. When these are combined, we get:
210,000,000 (Two hundred and ten million)+ 64,000 (Sixty-four thousand)+ 50 (Fifty)Adding these together:
210,000,000 + 64,000 + 50 = 210,064,050
Therefore, the standard form of 210 million, 64 thousands, and fifty is 210,064,050.
A restaurant uses 8 1/4 pounds of carrots to make 6 carrot cakes. Frank wants to use the same recipe. How many pounds of carrots does Frank need to make one carrot cake?
Frank needs [tex]\( \frac{11}{8} \)[/tex] pounds of carrots to make one carrot cake.
To find out how many pounds of carrots Frank needs to make one carrot cake, we first need to determine how many pounds of carrots are used per carrot cake in the original recipe.
Given that the restaurant uses 8(1)/(4) pounds of carrots to make 6 carrot cakes, we divide the total pounds of carrots by the number of cakes to find the amount per cake.
[tex]\( \text{Carrots per cake} = \frac{8\frac{1}{4}}{6} \)[/tex]
First, we convert the mixed number [tex]\(8\frac{1}{4}\)[/tex] to an improper fraction:
[tex]\(8\frac{1}{4} = \frac{(8 \times 4) + 1}{4} = \frac{33}{4}\)[/tex]
Then, divide by 6:
[tex]\( \frac{33}{4} \div 6 = \frac{33}{4} \times \frac{1}{6} = \frac{33}{24} = \frac{11}{8} \)[/tex]
So, Frank needs [tex]\( \frac{11}{8} \)[/tex] pounds of carrots to make one carrot cake.
NEED HELP 25 POINTS PLEASE HELP.The students at Harrison Middle School are being split into groups for a community service project. The school faculty has decided that each grade (6th, 7th, and 8th) will be split up into their own set of groups. The faculty has also decided that it is important for each grade to be split evenly into groups, with no leftover students, so that each group in a grade has exactly the same number of boys and girls. For each of the following grades, determine the largest number of groups that can be made and the number of boys and girls that will be in each group. The 6th grade has 64 girls and 72 boys. The 7th grade has 81 girls and 63 boys. The 8th grade has 68 girls and 60 boys. Please list down how many groups each grade has for both boys and girls.
what times what equals 46
What times what equals 46 is 2 times 23, or 2 x 23 = 46.
We have,
To find what times equal 46, we can look for pairs of numbers that, when multiplied together, result in 46.
We can start by listing the factors of 46:
1 x 46 = 46
2 x 23 = 46
From these factor pairs, we can see that 2 and 23 are the numbers that multiply to 46.
Therefore,
What times what equals 46 is 2 times 23, or 2 x 23 = 46.
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21.12 subtracted by 12.2
4000 is 1/10 as much as what number
To find a number that is 1/10 as much as 4000, you would multiply 4000 by 10, resulting in 40000.
To find the number that is 1/10 of 4000, you need to divide 4000 by 1/10, which is the same as multiplying by its reciprocal, 10.
Step 1: Write down the expression:
Let ( x ) be the number we're looking for.
Step 2: Set up the equation:
[tex]\[ x = \frac{4000}{\frac{1}{10}} \][/tex]
Step 3: Multiply by the reciprocal:
x = 4000 \times 10
Step 4: Solve:
x = 40000
So, the number that is 1/10 as much as 4000 is 40000.
The ratio of a quarterback completed passes to attempted passes is 7 to 8. If he attempted 24 passes, how many did he complete? Round to nearest whole number if needed.
If he attempted 24 passes, he completes 21 pass.
What is ratio?The numerical association of two values that shows how frequently one value includes or is contained inside another is called ratio.
Given, The ratio of a quarterback completed passes to attempted passes is 7 to 8.
If he attempted 24 passes.
To find the number of passes, he completes:
24 x 7/8
= 3 x7
= 21
Hence, he completes 21 passes.
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Describe sets of two or more matching integer cards that satisfy the criteria in each part below:
a. Cards increase the score by eight points.
b. Cards decrease the score by 9 points.
c. Removing cards that increase the score by 10 points.
d. Positive cards that decrease the score by 18 points.
Answer:
a. Removing two (-4)'s
b. Picking up three (-3)'s or removing three 3's
c. Removing two (-3)'s and one (-4)'s
d. Removing three 5's and one 3's
Step-by-step explanation:
Cards available: 5, -3, -4, & 3
a. Score can be increased picking up positive cards or removing negative cards.
b. Score can be decreased picking up negative cards or removing positive cards.
c. As stated before, in order to increase the score removing cards, positive cards have to be removed.
d. As stated before, in order to decrease the score with positive cards, those cards have to be removed.
The force of an object (f) is equal to its mass (m) times its acceleration (a). Thus, the formula for calculating force is f = ma.
Based on this information, which of the following equations would be used to calculate acceleration?
A. a = fm B. a = f + m C. a = f − m D. a = f ÷ m
Answer:
D. [tex]a=f\div m[/tex].
Step-by-step explanation:
We are given that force of an object and we have to find the equation would be used to calculate the acceleration
Mass of object=m
Acceleration of an object= a
Force of an object=f
We are given that force of an object is equal to its mass times its acceleration.
Therefore , the formula for calculating force
f=ma
Because we are given this formula
Now , we have find the equation which is used to calculate acceleration
Then by division property of equality we have
[tex]a=f\div m[/tex]
Hence, the equation would be used to calculate acceleration [tex]a=f\div m[/tex].Therefore, option D is true.
A town's population is 43,200. About 100 people move out of the town each month. Each month, 125 people on average move into town. A nearby town has a population of 45,000. It has no one moving in and an average of 200 people moving away every month. In about how many months will the populations of the towns be equal?
a real estate developer is looking to find help fund a new condo complex.he promises 145% return on investment in four years. if youre interested in investing $30,000 and the developer follows through on his promise, how much money will you get back in four years?
Evaluate the integral. 2 (6t i − t3 j + 2t3 k) dt 0
The integral of the vector field 2 (6t i − t3 j + 2t3 k) from 0 to t can be broken down into three separate integrals for each component, yielding the resulting integral vector of (6t^2)i - (0.5t^4)j + (t^4)k.
Explanation:The integral you're asking about is a vector field integral, which comes up primarily in physics-related problems. The integral of a vector field, in this case, 2 (6t i − t3 j + 2t3 k) with respect to time, can be broken down into three separate integrals, each corresponding to a different component.
To solve, you would perform each integral separately:
Integral from 0 to t of 2*6t dt = 6t^2 between 0 and t = 6t^2 Integral from 0 to t of 2*-t^3 dt = -0.5*t^4 between 0 and t = -0.5t^4 Integral from 0 to t of 2*2t^3 dt = t^4 between 0 and t = t^4Combine these answers to yield the integral vector (6t^2)i - (0.5t^4)j + (t^4)k as the solution. Please remember to always check your calculations to ensure accuracy!
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If the force is f=-30 units and the acceleration is a=6 units, find the mass, m
When a decimal is written in word form, what indicates that the equivalent form is a mixed number and not a fraction
thw ration of two elements prontons is equivalent to 3 to 1. What are those two elements? A) gold to tin B)nein to tin C) platinum to iron D) silver to gold
When the r2 of a regression equation is very high, it indicates tha?
Pamela wants to buy a suitcase whose dimensions are 1 1/2 times those of her 28 times 16 times 8 inch suitcase. How is the ratio of the volumes related to the ratio of corresponding dimensions? What is the ratio of the volumes?
Thus the required ratio is 3.375
Pamela wants to buy a suitcase whose dimensions are 1 1/2 times of her 28 times 16 times 8 inch suitcase.
What is the ratio of the volumes?
The ratio can be defined as the comparison of the fraction of one quantity towards others. e.g.- water in milk.
volume of former suitcase = 28 x 16 x 8
=3584 cubic inches
volume of latter suitcase
=1.5x28 x1.5x16 x1.5x8
=12096
ratio of volumes
= 12096/3584
=3.375
Thus the required ratio is 3.375 of volumes of suitcase.
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What scale of measurement is being used when a teacher measures the number of correct answers out of 50 on a quiz for each student?
A rectangular rug is 12.5 feet long and 10 feet wide. The rug needs to be reduced by a factor of 1/5 to be placed near a door. What is the area of the reduced rug in square feet?
_______ft2
The perimeter of a college athletic field is 92 meters and the length is 18m more than the width. Find the length and width.
Solve for y 1.2x - 4y = 28
Ricky is taking out a personal loan for $12,000 to remodel his kitchen. He would like the lowest monthly payment possible, even if it means a bigger finance charge in the end. His bank has offered him a loan at 13% interest for 36 months or 12% interest for 60 months, both of which are compounded monthly. Which of the following statements most accurately describes what Ricky should be thinking? a. More payments with the 60 month loan will give him the lowest monthly payment. b. Fewer payments with the 36 month loan will give him the lowest monthly payment. c. The 60 month loan comes with a bigger finance charge and, thus, a bigger monthly payment. d. The 36 month loan comes with a bigger finance charge and, thus, a bigger monthly payment.
Answer : The correct Option is A.
Step-by-step Explanation :
To solve this we are going to use the monthly payment formula:
[tex]\text{Payment = }\frac{Rate\times Principal}{1-(1+Rate)^{-n}}}[/tex]
where, Principal is the amount of the loan
n is the number of periods.
Option A. 13% interest for 36 months compounded monthlyRicky is taking out a personal loan for $12,000 and term of the loan is 36 months ⇒ n = 36. To find the rate per period, we first need to convert the interest rate to decimal form ⇒ Rate = 0.13.
Now since the bank is charging him the interest rate for the 36 months, we just need to divide the interest rate (in decimal form) by the number of months (36) to find the rate per period
[tex]\implies\text{Rate per period = }\frac{0.13}{36}[/tex]
So, putting all these values in the formula, We get monthly payment of loan A = $356.07
Option B : 12% interest for 60 months compounded monthlyinterest rate in decimal form = 0.12
By replacing the values in formula the monthly payment of loan B is $212.44
Option C and Option D are obviously denied as the financial charge is not effected by the monthly payments so ricky will not be thinking about the financial charge.Now, Monthly payments of loan B are significantly low than that of monthly payments of loan A.
So, we can conclude that the correct answer is a. More payments with the 60 month loan will give him the lowest monthly payment.
Answer:
A
Step-by-step explanation:
What value of x will give the minimum value for x^2- 14x + 3?
Please help me!!
Anyone knows the answer
What is the difference between 7,001 and 433?
Graph the following lines and write the equation in slope-intercept form. Through the point (−8,1) with a slope of 3.
Round 527 to the nearest hundred
3.74 rounded to the nearest
hundredth