Answer:
Negative
Step-by-step explanation:
x + 5 = -8
Subtract 5 from both sides to get x by itself
x = -13
Answer:
X is negative
Step-by-step explanation:
A rectangle is twice as long as it is wide and has the same perimeter as a square whose area is 36 square feet larger than that of the rectangle. what are the dimensions of both the rectangle and the square?
Answer:
rectangle: 12 ft × 24 ftsquare: 18 ft squareStep-by-step explanation:
You want the dimensions of a rectangle and square such that they have the same perimeter, but the square has an area of 36 more square feet. The rectangle is twice as long as wide.
SetupLet x represent the side length of the square. Then its area is x², and the area of the rectangle is (x² -36).
This area is the product of length and width. The expression factors as ...
rectangle area = x² -36 = (x +6)(x -6)
SolutionIf we assume these factors are the dimensions of the rectangle, then the longer dimension is twice the shorter one:
(x +6) = 2(x -6)
18 = x . . . . . . . . . add 12-x to both sides
This is the side length of the square. The rectangle dimensions are ...
x+6 = 18+6 = 24 . . . . feet long
x -6 = 18 -6 = 12 . . . . feet wide
The rectangle is 12 feet wide and 24 feet long. The square is 18 feet on a side.
__
Additional comment
The perimeter in each case is 4x = 2((x+6) +(x -6)) = 72 ft.
The area of the rectangle is (12 ft)(24 ft) = 288 ft². The area of the square is (18 ft)² = 324 ft², a value that is 36 ft² more than the rectangle area.
Alternate solution
Using x for the width of the rectangle, the length is 2x and its area is x(2x) = 2x². The perimeter is 2(x +2x) = 6x, so the side length of the square is (6x)/4 = 3/2x and its area is (3/2x)² = 9/4x².
The difference is 36 square feet, so we have ...
9/4x² -2x² = 36 = x²/4 ⇒ x = √(36·4) = 6·2 = 12 . . . . width of rectangle
need help in algebra 2
Answer:(-2,2)
Step-by-step explanation:
1. Which of the following sequences are arithmetic?
For those sequences that are arithmetic, identify
d and write an expression for an, in terms of n, the
term number.
I. 100, 98, 96, 94, . . .
II.
64, 32, 16, 8, ...
III. 2¹+1, 22+1, 23 +1,24 + 1,...
IV.
3 13 17 7
4'12'12'4
.....
The arithmetic sequence from the collection is I
an = 100 +( n + 1) 2
What is an arithmetic sequence?For an arithmetic sequence, the difference between consecutive terms is always the same, and it is called common difference 'd'.
The nth term of an arithmetic sequence is expressed as;
[tex]an = a + ( n + 1) d[/tex]
Thus, the arithmetic sequences are given as follows:
100, 98, 96, 94, . . . d = 2For the other sequences, there are different differences between consecutive terms, hence the sequence is not arithmetic, for example:
The nth term is given as;
an = 100 +( n + 1) 2
Thus, the arithmetic sequence from the collection is I
Learn more about arithmetic sequences here:
https://brainly.com/question/6561461
#SPJ1
Translate this sentence into an equation.
The difference of Goran's height and 10 is 57
Use the variable g to represent Goran's height.
Answer:
g-10=57
Step-by-step explanation:
'Difference' means to subtract.
Andrew can paint the neighbor's house 5 times as fast as Bailey. The year Andrew and Bailey worked together, it took them 2 days. How long would it take each to paint the house?
Answer:
12 days for Bailey
2.4 days for Andrew
Step-by-step explanation:
If Andrew is 5 times as fast, then Andrew + Bailey are 6 times as fast as Bailey alone.
That means Bailey would take 2*6 = 12 days to paint alone.
Since Andrew is 5 times faster, he'd only take 12/5 = 2.4 days.
Evaluate and leave your answer in simplest form
(-4/3) (5/12) (9/10) step-by-step
Which expression has a greater value?
(2,040329) x 5
2,040329
Answer:
2,040329×5
Step-by-step explanation:
you are multiplying 5 more to the number so it will be 5 times larger than the other number
Answer: (2,040329) x 5 =10.201645
Step-by-step explanation:
they are both equal too so its neither is greater
write 336 mi in 11.2 h as a rate in simplest form
Answer:
30 mL/h
Step-by-step explanation:
You want the rate 336 ml in 11.2 h as a rate in simplest form.
Unit rateThe rate can be expressed in simplest form in a number of ways. We usually want rates involving time to be expressed with time units in the denominator:
(336 mL) / (11.2 h) = 30 mL/h
__
Additional comment
Medicine is often prescribed on a "per day" basis. In 24 hours, this rate would be ...
(30 mL/h)×(24 h/day) = 720 mL/day
The machine setup to dispense this medicine might use time units of minutes:
(30 mL/h) / (60 min/h) = (1/2) mL/min
Nora has a box of 1 hundred cubes she also has a bag of 70 cubes how many trains of 10 cubes can she make?
Answer:
17
Step-by-step explanation:
[tex]\begin{matrix}\:\:\:\:\:\:\:\:\emptyspace1\emptyspace7\:\:\:\:\:\:\:\:\:\:\:\:\\ 10\overline{|\smallspace170}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\underline{\emptyspace1\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\emptyspace7\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\underline{\emptyspace7\emptyspace0}\:\:\:\:\:\:\:\:\:\:\:\:\\ \:\:\:\:\:\:\:\:\:\:\emptyspace0\:\:\:\:\:\:\:\:\:\:\:\:\end{matrix}[/tex]
The length of a rectangle is 5 in longer than its width.
If the perimeter of the rectangle is 58 in, find its length and width.
Answer:
Length = 17 in
Width = 12 in
Step-by-step explanation:
Formula we use,
→ P = 2(L + W)
Then the value of L and W is,
→ P = 2(L + W)
→ 58 = 2(x + 5 + x)
→ 2(2x + 5) = 58
→ 4x = 58 - 10
→ x = 48/4
→ [ x = 12 ]
Then the width will be,
→ W = x = 12 in
Hence, the width is 12 in.
Now the length will be,
→ L = x + 5 = 12 + 5 = 17 in
Therefore, the length is 17 in.
Find the domain and range of the relation. Also determine whether the relation is a function.
{(6,3), (8,5), (-4,-4), (5,5)}
The domain is:
D: {-4, 5, 6, 8}
The range is:
R: {-4, 3, 5}
And yes, the relation is a function.
How to determine the domain and range?
For a relation that maps elements x into elements y (in the form (x, y)), we define the domain as the set of the inputs (values of x) and the range as the set of the outputs (values of y).
Here our relation is defined by: {(6,3), (8,5), (-4,-4), (5,5)}
The domain is the set of the first values of each pair, so we have:
D: {-4, 5, 6, 8}
The range is the set of the second values of each pair:
R: {-4, 3, 5}
Now, is this a function?
Yes, it is a function, because each input is mapped into only one output.
If you want to learn more about domain and range:
https://brainly.com/question/10197594
#SPJ1
Identify the lower class limits, upper class limits,
class width, class midpoints, and class boundaries for
the given frequency distribution. Also identify the
number of individuals included in the summary.
Age (yr) when
award was won
20-29
30-39
40-49
50-59
60-69
70-79
80-89
Frequency
27
32
15
3
5
1
1
The upper class limits are- 29, 39, 49, 59, 69, 79, 89
The lower class limits are- 20, 30, 40, 50, 60, 70, 80
The class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5
The class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5
And the number of individuals included in the summary is 84.
Here, we are given the following dataset-
Age (yr) when Frequency
award was won
20-29 27
30-39 32
40-49 15
50-59 3
60-69 5
70-79 1
80-89 1
Upper class limit is the largest data value that can go in a class.
Thus, the upper class limits are- 29, 39, 49, 59, 69, 79, 89
Lower class limit is the smallest data value that can go in a class.
Thus, the lower class limits are- 20, 30, 40, 50, 60, 70, 80
The class midpoint is the average of the upper and lower limits of a class. Class midpoint = (upper limit + lower limit)/ 2
Thus, the class midpoints are- 24.5, 24.5, 44.5, 54.5, 64.5, 74.5, 84.5
Class boundary is the midpoint of the upper class limit of a class and the lower class limit of the previous class.
Thus, the class boundaries are- 29.5, 39.5, 49.5, 59.5, 69.5, 79.5
Frequency gives us the number of individuals/ objects belonging to a particular class.
Thus, the number of individuals included in the summary = 27 + 32 + 15 + 3 + 5 + 1 + 1 = 84
Learn more about frequency distribution here-
https://brainly.in/question/1123422
#SPJ9
Simplify: 2.4 × 10-4
The four is a exponent
Answer: 20
Step-by-step explanation:
Multiply 2.4*10-4
Calculate 24-4
the answer is (12x^10000)/5
Emma is baking cookies for her sisters birthday. She is using a bowl in the shape of a hemisphere with a diameter of 11.5 inches. If the bowl is completely full of dough and each cookie is 8.295 cubic inches of dough, how many cookies can she make
Considering the volume of the hemisphere, it is found that she can make 48 cookies.
What is the volume of an hemisphere?The volume of an hemisphere of radius r is given as follows:
[tex]V = \frac{2\pi r^3}{3}[/tex]
The radius is half the diameter, hence, for this problem:
r = 11.5/2 = 5.75.
Hence the volume of the bowl in cubic inches is given as follows:
V = 2π(5.75)³/3 = 398.16 cubic inches.
Consider the volume of a single cookie, the number of cookies that she can make is given by:
398.16/8.295 = 48 cookies.
More can be learned about the volume of an hemisphere at https://brainly.com/question/24247548
#SPJ1
Trevor has a rectangular patch of dirt that has a length of 50 feet and a width of 30 feet. He wants to divide this area into two rectangular gardens as shown.
Write an expression to represent the area of the
garden on the left.
B. Write an expression to represent the area of the
garden on the right.
C. If the area of the garden on the left is greater, what
is the difference of the areas of the two gardens? Simplify your answer
Answer:
sweefe
Step-by-step explanation:
EFEFEEa
Suppose you make monthly mortgage payments of $1,345 and have 10 years left on the mortgage (next payment due next month). Assuming a 3.6% stated annual interest rate for the mortgage, how much would you need today to pay off the mortgage?
I will need $1,61,884.2 to pay off the mortgage.
This problem is related to simple interest and we have to calculate the amount after 10 years which is payable in the form of mortgage.
The monthly mortgage payment is $1,345.
Rate of interest is 3.6% per annum.
Time is given to be 10 years.
Simple interest for 10 years = 1345×3.6×10/100
= $ 484.2
So, the total money required to clear the mortgage
= $(1345×12×10) + $ 484.2
= $161400 + $484.2
= $ 1,61,884.2
To learn more about Simple Interest visit the link:
https://brainly.com/question/25845758
#SPJ9
compare the following numbers
2.7×1012;1.5×108
2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)
Given two numbers
1)2.7×1012
2) 1.5×108
Two numbers can be equal or one is greater than the other or one is less than the other. there will be no other case rather than these three.
1)2.7×1012=2,732.4
2) 1.5×108=162
The value of the 1st number is 2,732.4 and the value of the 2nd number is 162
1st given number is greater than the 2nd number i.e. 2,732.4>162
Therefore,2.7×1012 (i.e.2,732.4) is greater than 1.5×108 (i.e. 162)
Learn more about numbers here:
https://brainly.com/question/17429689
#SPJ9
List a and b for each of them
1) The intersection of sets A and B is; A ∩ B = {1, 3}
2) The complement of set A is; A' = {4, 5, 6, 9, 10}
How to interpret Mathematical Sets?
We are given the sets;
U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
A = {1, 2, 3, 7, 8}
B = {1, 3, 9, 10}
1) The intersection of sets A and B simply means the numbers that are common to both sets. Thus;
A ∩ B = {1, 3}
2) The complement of set A is defined as the set that contains the elements present in the universal set but not in set A. Thus;
A' = {4, 5, 6, 9, 10}
Read more about Mathematical Sets at; https://brainly.com/question/2166579
#SPJ1
Please help solve question
Answer:
a) [tex]x=\frac{15}{p}[/tex]
b) x=[tex]-3[/tex]
Step-by-step explanation:
First, you distribute the 4 to open the parentheses.
[tex]4px+4=64[/tex]
Subtract 4 to both sides:
[tex]4px=60[/tex]
Divide by 4p on both sides:
[tex]x=\frac{60}{4p}[/tex]
[tex]x=\frac{15}{p}[/tex]
For the second part, substitute the value of p.
[tex]x=\frac{15}{-5}[/tex]
[tex]x=-3[/tex]
Solve.
c = kny, for y
The solution of the equation c = kny, for y is y = c/kn
How to solve the equation c = kny, for y?The equation is given as
c = kny
Divide both sides of the given equation by k
So, we have
c/k = kny/k
Evaluate the quotient on both sides of the above equation
So, we have
c/k = ny
Divide both sides of the above equation by n
So, we have
c/kn = ny/n
Evaluate the quotient on both sides of the above equation
So, we have
c/kn = y
Rewrite as
y = c/kn
Hence, the solution of the equation c = kny, for y is y = c/kn
Read more about subject of formula at:
https://brainly.com/question/10643782
#SPJ1
How much must be the last repayment be made if the loan is terminated after 5 year for which a loan of K10,000 is taken at 12% p.a. flat, where the loan is repaid by equal quarterly repayments for 9 years?
Answer:
Step-by-step explanation:
How many degrees is the angle marked X?
Answer:
the angle marked X is 60 degree
A college football team will play 14 games next fall each game can result in 2 possible outcomes find the total possible number of outcomes for the season
There will be an outcome of 16380 times.
What is an outcome?
An outcome is a potential consequence of an event or trial in probability theory. A specific experiment can have any number of outcomes, and they are all distinct and unrelated to one another.The football team will play 14 games
and each game can result in one of 2
Hence, the total possible number of outcomes for the season is [tex]2^{14}[/tex].
Now, let us explain
Let the result can be represented by an 'ordered set" i.e. 14- box.
|1|2|3|4|5|6|7|8|9|10|11|12|13|14|
Hence, the first box can be filled in 2 ways.
Similarly, all boxes.
Hence, the total number of cases will be,
2*2*2*2.... 14 times
= [tex]2^{14}\\[/tex]
=16380 times.
Learn more about outcomes here:
https://brainly.com/question/8090596
#SPJ9
What is the image of image of the point (-7,-3) after a rotation of 180 degrees counterclockwise
PLEASE
The image of image of the point [tex](-7,-3)[/tex] after a rotation of [tex]180[/tex] degrees counterclockwise is [tex](7,3)[/tex]
According to the question statement, point [tex](-7,-3)[/tex] is rotated by [tex]180[/tex] degrees counterclockwise, we are supposed to find out the image of the point after the rotation.
Point [tex](-7,-3)[/tex] lies in the Third quadrant of the Cartesian Plane.
When it will be rotated by [tex]180[/tex] degrees counterclockwise, it will shift to the first quadrant of the Cartesian Plane.
Therefore the coordinates will become as [tex](7,3)[/tex].
Cartesian Plane: The cartesian plane is defined as a two-dimensional coordinate plane that is made or formed by the intersection of the x-axis and y-axis or horizontal and vertical axes.To learn more about coordinates and plane, click on the link given below:
https://brainly.com/question/27927590
#SPJ9
Martha has 9 feet of red ribbon and 6 feet of green ribbon. How many yards of
ribbon does she have altogether?
Answer:5
Step-by-step explanation:9 ft of red ribbon plus the 6 ft of green ribbon would make 15 feet of ribbon
1ft=3yds
Which mean you would have 5 yards of ribbon.(15 divided by 3=5)
What is the value of this expression if h 8, j = -1, and k = -12?
Value of the given expression j³k/h0 is 12
h = 8
j=-1
h = 8
In order to do this, we need to change the values of h, j, and k in the given statement = (-1)^3 (-12) / 8^0 ....(1)
Find the denominator by using (1)
(-1)³ (-12) / 1
Analyze each exponent.
= 12/1
Hence, j³k/h0 = 12
To learn more about expressions from given link
https://brainly.com/question/17586027
#SPJ9
Complete Question -
What is the value of this expression if h=8 ,j= -1 , and k= -12? j³k/h0
The sale price of a new refrigerator is $705 and sales tax is figured at 0.05 times the price. What is the total amount paid for the refrigerator?
The amount paid for the refrigerator is $740.25.
How to calculate the price?From the information, the sale price of a new refrigerator is $705 and sales tax is figured at 0.05 times the price.
The price of the refrigerator will be:
= $705 + (0.05 × $705)
= $705 + $35.25
= $740.25
Therefore, the amount paid for the refrigerator is $740.25
Learn more about price on:
brainly.com/question/1153322
#SPJ1
You buy a new computer for $1500. The value of the computer decreases by 6% every year. How much is the computer worth after 4 years?
Answer: Your computer will be worth $1,171.12
Step-by-step explanation:
[tex]a_n = 1500(0.94)^4\\a_n=\boxed{1171.12}[/tex]
The measure of the complement of an angle is double the
measure of the angle itself. Find the measures of both angles.
Answer: u need to send a pic of the angle
Step-by-step explanation:
Oliver threw the discus 43.82 feet. Jason threw the discus 50.02 feet. What is the difference between the two distances?
A 6 feet
B 6.2 feet
C 13.8 feet
D 16.02 feet
The difference between the distances thrown by Oliver and Jason while discus throwing is 6.2 feet.
The correct answer is Option B.
Given data:
Oliver threw the discus 43.82 feet.
Jason threw the discus 50.02 feet.
Oliver threw the discus a distance of 43.82 feet, while Jason's throw reached a distance of 50.02 feet. The difference is calculated by subtracting the shorter distance from the longer distance, resulting in 6.2 feet.
Difference = Longer distance - Shorter distance
Difference = 50.02 feet - 43.82 feet
On simplifying the equation:
Difference = 6.2 feet
This represents the variation in their performances, with Jason achieving a greater distance by 6.2 feet compared to Oliver's throw.
Hence, the difference is 6.2 feet.
To learn more about equations, refer:
https://brainly.com/question/19297665
#SPJ3