Jorge is standing at a horizontal distance of 25 feet away from a building. his eye level is 5.5 feet above the ground and looking up he notices a window washer on the side of the building at an angle of elevation of 65, how high is the window washer above the ground
Write 9.79 x 10^5 in standard notation
What are the coordinates of the vertex of the table? Is it a minimum or a maximum?
X Y
0 1
-1 -2
-2 -3
Select the situation in which one quantity is changing at a constant rate in relation to the other quantity.
a. Barry spends $9 on lunch daily.
b. The market value of a new computer decreases by 6% every year.
c. Nathan's investments increase in value by 13.5% each month.
d. The number of ants in a colony doubles every 8 weeks.
Answer:
A. Barry spends $9 on lunch daily.
Step-by-step explanation:
We are required,
To find the situation in which one constant is changing at a constant rate in relation to the other quantity.
So, according to the options, we have,
A. Barry spends $9 on lunch daily.
Let x= number of days and as the cost of lunch each day is $9
Then, the total cost of the lunch y, is [tex]y=9x[/tex]
Thus, this situation changes the variable with constant rate.
B. The market value of a new computer decreases by 6% every year.
Let, a= fixed initial value of the computer and x= number of years.
Since, the rate of decrease in value = 6% = 0.06
Then, the market value of the computer per year, y, is given by,
[tex]y=a(1-0.06)^x\\\\y=a(0.94)^x[/tex]
Thus, this situation changes the variable exponentially.
C. Nathan's investments increase in value by 13.5% each month.
Let, a= fixed initial investment and x= number of months.
Since, the rate of increase = 13.5% = 0.135
Then, the investment per month, y, is given by,
[tex]y=a(1+0.135)^x\\\\y=a(1.135)^x[/tex]
Thus, this situation changes the variable exponentially.
D. The number of ants in a colony doubles every 8 weeks.
Let, x= number of weeks where 'x' belongs to the se {1,8,16,24,...}.
Since, the number of ants is doubling every 8 weeks.
So, the number of ants in the colony, y, is [tex]y=2^x[/tex]
Thus, this situation changes the variable exponentially.
Hence, the situation that changes the variables with a constant rate is A.Find the equation of the plane with the given description. contains the lines r1(t) = 2, 1, 0 + t, 2t, 4t and r2(t) = 2, 1, 0 + 4t, t, 15t .
The equation of the plane containing the two given lines is found by calculating the normal vector through the cross product of direction vectors and then using the normal vector with a point from the lines to form the plane's equation, which is 26x + y - 7z = 53.
To find the equation of a plane that contains two given lines, we must first find two direction vectors that represent the lines. In this case, we are given the lines r1(t) = (2, 1, 0) + t(1, 2, 4) and r2(t) = (2, 1, 0) + t(4, 1, 15). The direction vectors for these lines are (1, 2, 4) and (4, 1, 15), respectively. To find the normal vector to the plane, we take the cross product of these two direction vectors.
Let's calculate the cross product:
(1, 2, 4) * (4, 1, 15) = (2*15 - 4*1, 4*4 - 15*1, 1*1 - 2*4) = (26, 1, -7).
The normal vector to the plane is (26, 1, -7), which also represents the coefficients of the variables in the plane's equation. Since both lines pass through the point (2, 1, 0), we can use this point and the normal vector to find the plane's equation.
The general form of the plane's equation is 'Ax + By + Cz + D = 0', where (A, B, C) is the normal vector to the plane. Plugging in the point (2, 1, 0) and the normal vector (26, 1, -7), we get:
26*(x - 2) + 1*(y - 1) - 7*(z - 0) = 0
26x - 52 + y - 1 - 7z = 0
26x + y - 7z = 53
And this is the Equation to the required plane containing the two given lines.
What is the equivalent factored form of 12x4 – 42x3 – 90x2? 6x(x – 5)(2x + 3) 6x2(x – 5)(2x + 3) 6x(x + 5)(2x – 3) 6x2(x + 5)(2x – 3)
The equivalent factored form of 12x4 - 42x3 - 90x2 is 6x(x - 5)(2x + 3).
The equivalent factored form of 12x4 - 42x3 - 90x2 is 6x(x - 5)(2x + 3).
We can factor out the greatest common factor, which is 6x. That leaves us with 2x3 - 7x2 - 15x.
Then we can factor by grouping, which involves grouping terms that have a common factor. By factoring out an x from the first two terms, we get x(2x2 - 7x - 15). By factoring out a -5 from the last two terms, we get -5(2x2 - 7x - 15). This gives us the final factored form of 6x(x - 5)(2x + 3).
Learn more about Factoring here:https://brainly.com/question/34290719
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A bus travels 36 miles in 45 minutes enter the number of miles the bus travels in 60 minutes at this rate
Find an equation for the nth term of the arithmetic sequence.
9, 11, 13, 15, ...
Answer Choices
A) an = 9 + 2(n - 1)
B) an = 9 + 2(n + 1)
C) an = 9 + 2
D) an = 9 + 2(n)
the sum of two numbers is -12 one number is 3 less than twice the other what is the bigger number
Ming used the calculations shown to find out how much he would spend on 6 pounds of ground beef if 10 pounds of ground beef cost $25.00. What was Ming’s error?
10 pounds
_________
$25.00
=10 pounds/ 25
__________
$25. 00/25
=0.4
____
1
Unit Price=$0.40
$0.40 x 6 =$2.40
What was Ming’s error?
A. He determined pounds per dollar by dividing 10 by 25 but wrote the unit rate as a dollar value.
B. He divided the numerator and the denominator of the fraction by 25.
C. He made a mistake when finding the quotient of 10 pounds and 25 dollars.
D. He made a mistake when finding the product of $0.40 and 6.
Answer:
The answer would be A. He determined pounds per dollar by dividing 10 by 25 but wrote the unit rate as a dollar value.
Brian’s school locker has a three-digit combination lock that can be set using the numbers 5 to 9 (including 5 and 9), without repeating a number. The probability that the locker code begins with a prime number is %. The probability that the locker code is an odd number is %.
Given the information below, match the following items.
Given statement: If two angles add to 180°, then they are supplementary.
1.converse
2.inverse
3. contrapositive
If two angles are supplementary, then they add to 180°
If two angles do not add to 180°, then they are not supplementary. 3.contrapositive
If two angles are not supplementary, then they do not add to 180°.
Answer:
Converse- If two angles are supplementary, then they add to 180°
Inverse- If two angles do not add to 180°, then they are not supplementary.
Contrapositive- If two angles are not supplementary, then they do not add to 180°
Step-by-step explanation:
If 12 is replaced with 3 in the following set, what will happen to the value of the range?
28, 45, 12, 34, 36, 45, 19, 20
It will increase.
It will decrease.
It will stay the same.
Your correct answer is A: it will increase.
Hope this helps. :)
Which is the converse of the following statement? Statement: if today is Monday then tomorrow is my birthday
A. If tomorrow is not my birthday, then tomorrow is not Monday
B. If today is not Monday, then tomorrow is not my birthday
C. If tomorrow is my birthday, then today is Monday
D. If today is Monday, then tomorrow is not my birthday
I'm guessing its A:
If tomorrow is not my birthday, tomorrow is not Monday
What is the area of this triangle? A= bh 2 12/13/5 is what it shows and here are the answers [A] 17 m2, [B] 30 m2, [C] 60 m2, [D] 60 m2, [E] 120 m2,
Jeremy goes to the store where he buys 18 bananas. After two days, he notices that there are only 10 bananas that are left. Which equation below would Jeremy use to find the percent of bananas that he has left?
A. 10/18 = 100/x
B. 18/10 = x/100
C. 5/9 = x/100
D. 10/18 = x/55.5
1/7-3(3/7n-2/7)
I need help solving this problem...
To solve the expression 1/7 - 3(3/7n - 2/7), distribute the 3 to the terms inside the parentheses, simplify the expression inside the parentheses, and combine like terms to get the simplified form of 7n - 1/7.
Explanation:To solve the expression 1/7 - 3(3/7n - 2/7), we need to follow the order of operations which is Parentheses, Exponents, Multiplication and Division (from left to right), and finally Addition and Subtraction (from left to right).
First, distribute the 3 to the terms inside the parentheses: 1/7 - (9/7n - 6/7).
Next, simplify the expression inside the parentheses: 1/7 - 9/7n + 6/7.
Finally, combine like terms by subtracting and adding the fractions: 7n - 1/7.
So, the simplified form of the expression 1/7 - 3(3/7n - 2/7) is 7n - 1/7.
Final answer:
The algebraic expression 1/7 - 3(3/7n - 2/7) can be simplified by distributing the -3 and combining like terms to yield a final expression of 1 - 9/7n.
Explanation:
The student is asking for help in solving an algebraic expression. The problem given is 1/7 - 3(3/7n - 2/7). To solve this, we need to apply the distributive property and then simplify the expression. Here's how we can solve it step by step:
Distribute the -3 to the terms inside the parenthesis: -3 * (3/7)n = -9/7n and -3 * (-2/7) = 6/7.
The expression now becomes 1/7 - 9/7n + 6/7.
Combine like terms, which are the constant fractions: 1/7 + 6/7 = 7/7 = 1.
The final simplified expression is 1 - 9/7n.
Your friend asks you to make picture frames and will give you 5 5 nickels for the first frame. You agree to help if she multiplies your payment by 5 5 for each frame completed. After 2 2 frames, you will receive 25 25 nickels, and after 3 3 frames, you will receive 125 125 nickels. What is the number of nickels for tenth frame?
To find the number of nickels for the tenth frame, we calculate 5 imes 5^9, which equals 9,765,625 nickels. This is a geometric sequence where the common ratio is 5, and the first term for the first frame is 5 nickels.
Explanation:The question asks about the payment received for making picture frames where the payment is multiplied by 5 for each subsequent frame. To find out the number of nickels for the tenth frame, we can use the concept of geometric sequences, where each term is found by multiplying the previous term by a common ratio. The common ratio in this case is 5.
For the first frame, you get 5 nickels. For the second frame, 5 multiplied by 5 is 25 nickels. To find the payment for the tenth frame, we multiply the payment of the first frame by the common ratio to the power of the frame number minus one: 5 imes 5^(10-1) = 5 imes 5^9.
Calculating 5 to the power of 9 gives us 1,953,125. Multiplying this by 5 gives us 9,765,625 nickels for the tenth frame.
Solve each equation f over 28=24
Dominoes are small rectangular tiles with dots called spots or pips embossed at both halves of the tiles. a standard "double-six" domino set has 28 tiles: one for each of the unordered pair of integers from (0,0) to (6,6). in general, a "double-n" domino set would consist of domino tiles for each unordered pair of integers from (0,0) to (n,n). determine all values of n for which one constructs a ring made up of all the tiles in a double-n domino set.
If 8 identical blackboards are to be divided among 4 schools, how many divisions are possible? how many if each school must receive at least 1 black- board?
Which of the following is a rational number? square root 97 square root 98, square root 99, square root 100
A.)square root 97
B.)square root 98
C.)square root 99
D.)square root 100
Answer:
d
Step-by-step explanation:
Find the area and the circumference of a circle with radius 2m. use the value 3.14, and do not round your answers. be sure to include the correct units in your answers.
Final answer:
The area of a circle with a radius of 2m is 12.56 m² and the circumference is 12.56 m when using 3.14 for π, with both answers having two significant figures due to the radius given with two significant figures.
Explanation:
The area (A) and the circumference of a circle with radius 2m can be found using the formulas A = πr² and C = 2πr. Using 3.14 as the value for π, the calculations would be A = (3.14)(2m)² = 12.56 m² for the area, and C = 2(3.14)(2m) = 12.56 m for the circumference. It is important to note that when performing calculations, the result should have the same number of significant figures as the quantity with the fewest significant figures used in the calculation.
Help me find the surface area of a triangular prism with work please
Of the members of a student choir, 60% are boys. If there are 21 boys in the choir, how many members does the choir have in total?
Suppose there are x number of members in all.
Now we are given that 60% of these are boys.
So number of members who are boys = 0.6x
We are also given that there are 21 boys in the choir.
So making an equation ,
[tex] 0.6x =21 [/tex]
dividing both sides by 0.6,
x= 35
So there are total 35 members in the choir.
To stay healthy, Kevin’s doctor says he should try to consume at most 2000 inequality to show the amount of calories Kevin should consume
I will give you brainliest.
simplify the ratio 120 cm / 1 m.
A 1 / 1
B 2/1
C 5 / 6
D 6 / 5
A line and a plane are considered parallel if they have no points in common. True or False?
Camelle manages her soccer team. She needs to order 4 practice jerseys for each player. There are y players. How many total practice jerseys does she need to order?
Answer:
The required number of total practice jerseys does she need to order is '4y'.
Step-by-step explanation:
Given : Camelle manages her soccer team. She needs to order 4 practice jerseys for each player. There are y players.
To find : How many total practice jerseys does she need to order?
Solution :
Let the total practice jerseys does she need to order be 'x'.
According to question,
She needs to order 4 practice jerseys for each player.
Number of players are y.
So, Total jerseys she needs is
[tex]x=4\times y[/tex]
[tex]x=4y[/tex]
Therefore, The required number of total practice jerseys does she need to order is '4y'.
Find the 29th term of the following sequence. 21, 15, 9, 3, . . .
Answer:
The correct answer would be -147
Step-by-step explanation: