The lengths of a rectangular garden, the inner rectangle, is 9ft more than its width. For the garden. Let x = width, x + 9 = length. It is surrounded by a brick walkway 4ft wide. Suppose the total area of the walkway is 400ft^2.
a. Write a polynomial to represent the length of PQ
b. What are the dimensions of the garden?
Answers
Answer:
[tex]PQ = x + 13[/tex]
The dimension of the garden is 52.5ft by 43.5ft
Step-by-step explanation:
Given
The shape above
Required
Determine PQ
Determine dimension of the garden
Calculating Length PQ
Represent the length of the inner rectangle as L
Represent the width of the inner rectangle as W
[tex]W = x[/tex]
[tex]L = x + 9[/tex]
The distance between the inner rectangle and the outer triangle is 4ft
This implies that;
[tex]PQ = L + 4[/tex]
Substitute [tex]x + 9[/tex] for [tex]L[/tex]
[tex]PQ = x + 9 + 4[/tex]
[tex]PQ = x + 13[/tex]
Also;
[tex]QR = W + 4[/tex]
Substitute [tex]x[/tex] for [tex]W[/tex]
[tex]QR = x + 4[/tex]
Calculating The Dimension of The Garden
First, we need to determine the Area of the inner rectangle
[tex]Area_1 = L * W[/tex]
Recall that [tex]W = x[/tex] and [tex]L = x + 9[/tex]
So;
[tex]Area_1 = x * (x + 9)[/tex]
For the bigger rectangle
[tex]Area_2 = PQ * QR[/tex]
Recall that [tex]PQ = x + 13[/tex] and [tex]QR = x + 4[/tex]
So;
[tex]Area_2 = (x + 13)(x + 4)[/tex]
Given that the Area of the walkway is [tex]400ft^2[/tex]
This implies that
[tex]Area_2 = Area_1 + 400[/tex]
Substitute [tex]Area_1 = x * (x + 9)[/tex] and [tex]Area_2 = (x + 13)(x + 4)[/tex]
[tex](x + 13)(x + 4) = x * (x + 9) + 400[/tex]
Open All Brackets
[tex]x^2 + 13x + 4x + 52 = x^2 + 9x + 400[/tex]
[tex]x^2 + 17x + 52 = x^2 + 9x + 400[/tex]
Collect Like Terms
[tex]x^2 - x^2 + 17x - 9x = 400- 52[/tex]
[tex]8x = 348[/tex]
Divide both sides by 8
[tex]\frac{8x}{8} = \frac{348}{8}[/tex]
[tex]x = \frac{348}{8}[/tex]
[tex]x =43.5[/tex]
Since the dimensions of the garden is [tex]W = x[/tex] and [tex]L = x + 9[/tex]
Substitute 43.5 for x in both cases
[tex]L = 43.5 + 9 = 52.5[/tex]
[tex]W = 43.5[/tex]
Hence, the dimension of the garden is 52.5ft by 43.5ft
Related Questions
Which expression is equivalent to
?
4 square root 6/ 3 square root 2
Answers
Answer:
Hope the picture helps
Please help me with geometry questions :((
Answers
Answer:
[tex]14.\:\:\overline{RT}=3.3\:ft[/tex]
Step-by-step explanation:
Using the definition of similar triangle, we have the equation for problem no. 14 as:
[tex]\frac{\overline{QT}}{\overline{RT}}=\frac{\overline{RT}}{\overline{TS}}\\\\\frac{5}{x}=\frac{x}{2.2}\\\\\Rightarrow x=3.3[/tex]
Best Regards!
Which expression is equivalent to *picture attached*
Answers
Answer:
[tex]\frac{35(1 + 35)}{2}[/tex]
Step-by-step explanation:
Given:
The attached
Required
Find the equivalent expression
The interpretation of is to add the sequence:
n = 1,2,3,......35
This can be done using the following formula (Sum of n terms of an AP)
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
Where n is the number of terms from 1 to 35; [tex]n = 35[/tex]
T1 is the first term; [tex]T_1 = 1[/tex]
Tn is the last term; [tex]T_n = 35[/tex]
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex] becomes
[tex]S_n = \frac{35}{2}(1 + 35)[/tex]
[tex]S_n = \frac{35(1 + 35)}{2}[/tex]
From the list of given options;
Option A is correct
[tex]\frac{35(1 + 35)}{2}[/tex]
30 POINTS GEOMETRY QUESTION
Answers
Answer:
2.25
Step-by-step explanation:
x/1 = (9+x)/5
9 + x = 5x
9 = 4x
x = 2.25
Answer:
x = 9/4
Step-by-step explanation:
We know that the triangles are similar
We can use ratios to solve
x x+9
----- = ----------------
1 5
Using cross products
5x = 1(x+9)
5x = x+9
Subtract x
5x-x = x+9-x
4x= 9
Divide by 4
4x/4 = 9/4
x = 9/4
Which equation represents the vertical asymptote of the graph? a curve asymptotic to y equals 0 from negative x to negative y near x equals 12. A curve asymptotic to y equals 0 from positive x to positive y near x equals 12. x = 0 y = 0 x = 12 y = 12
Answers
Answer:
The correct option is x = 12
Step-by-step explanation:
An asymptote of a function is a line to to which the function converges to as it tends to infinity such that the function gets infinitesimally close to its asymptote but the function will not reach or cross its asymptote. That is the separating distance between the function and the asymptote tends to zero as either the x or y coordinates, or both the x and y coordinates tend to infinity.
A vertical aymptote, is one parallel to the y-axis and it is given by the value of the x-coordinate where it occurs
In the graph of the question, the vertical asymptote occurs at x = 12 and it is the line x = 12.
From the given graph, it can be said that the vertical asymptote will be formed at x=12. Option C is correct.
The given curve represents a function which is defined for all value fo x except 12.
The following information can be extracted from the graph of the function;
The function is defined for all values of x except 12.The function has a horizontal asymptote at y=0.The function forms a vertical asymptote at x=12. The curve approaches negative infinity from the left of 12 and approaches positive infinity from right of 12.Based on the above conclusions, it can be said that the vertical asymptote will be formed at x=12. Option C is correct.
For more details, refer to the link:
https://brainly.com/question/23535769
Brainliest for whoever answers fully! Part A: Using the graph above, create a system of inequalities that only contains points C and F in the overlapping shaded regions. Explain how the lines will be graphed and shaded on the coordinate grid above. (5 points) Part B: Explain how to verify that the points C and F are solutions to the system of inequalities created in Part A. (3 points) Part C: Chickens can only be raised in the area defined by y > −4x + 3. Explain how you can identify farms in which chickens can be raised. (2 points)
Answers
Answer:
Hope this helps
Step-by-step explanation:
For part A, we want two inequalities that have F and D as solutions, but none of the other points. The easiest way to do this is construct two lines that pass through the origin, and then figure out which way the inequalities need to face based on the points we want to include. Our lines will be:
The first line intersects F and the second line intersects D, so we need to figure out which way to point the inequalities so both include the point they do not intersect:
So our system is:
Part B: To verify, plug in the x and y values for D and F and verify that it creates true statements in the system.
Part C: You can plug in the different x, y values for the points. The points which create true statements identify farms where chickens can be raised, while those which create false statements cannot raise chickens.
Five test scores have a mean (average score) of 90, a median (middle score) of 91 and a mode (most frequent score) of 94. Find the sum of the two lowest test scores.
Answers
Answer:
171
Step-by-step explanation:
If five test scores have a mean of 90, then the total 5x90=450. We already have the middle score (91) and the two top scores (94 and 94). So the equation is 450-91-94-94=171
Please help with step by step. Thank you.
Answers
Answer:
A) 90 degrees
B) 110 degrees
C) 78.5 in. sq.
D) 15.3 in. sq.
Step-by-step explanation:
A) 90 degrees by the two-tangent theorem
B) 360-90-90-70=110
C) A=pi r-squared
A=3.14x5x5
A=78.5
D) 70/360=0.1944
78.5x0.1944=15.3
Identify the types of number
Answers
Answer:
1 surds
2 fraction
3 decimal
4 negative
5 positive
nth term of this sequence please 18, 16, 14, 12
Answers
Answer:
[tex]\boxed{\sf -2n+20}[/tex]
Step-by-step explanation:
Let’s find the common difference.
The common difference can be found by subtracting a term in the sequence with the previous term.
[tex]\sf d=16-18\\d=-2[/tex]
Apply formula for the [tex]\sf n^{th}[/tex] term of an arithmetic sequence.
[tex]\sf a_n=a_1+dn-d[/tex]
[tex]\sf a_1[/tex] is the first term of the sequence.
[tex]\sf d[/tex] is the common difference.
[tex]\sf a_n=18+-2n-(-2)[/tex]
[tex]\sf a_n=18+-2n+2[/tex]
[tex]\sf a_n=-2n+20[/tex]
Questions are attached
Answers
Answer:
V = 32 in^3
Step-by-step explanation:
The area of the triangle is (1/2)(base)(height), which here comes to:
(1/2)(4 in)(8 in) = 16 in^2.
The volume is (16 in^2)(height) = (16 in^2)(2 in) = 32 in^3
The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collected, the sales te determines that the monthly profit is approximated by f(p)= -50p^2+1700p-12000, where p is the price per shirt and f(p) is the monthly profit on that price. A) Find the price that generates the maximum profit B) Find the maximum profit C) Find the price(s) that would enable the company to break even.
Answers
Answer:
Below
Step-by-step explanation:
You could just graph the equation for the answers....
Here is algebraic method
for Quadratic Equation - 50p^2 +1700p - 12000
the max profit occurs at p = - b/2a = - 1700 / (2* -50) = 17 dollars
A ) 17 dollars
B) use p =17 in the equation to find profit = 2450 dollars
C) Set the equation = 0 and solve for p
0 = -50p^2+1700p - 12 000
Use Quadratic Formula with a = -50 b = 1700 c = 12000
to find price = 40 dollars
Emily has driven 600 miles so far on her way to the beach. If her total trip will be 850 miles‚ about what percentage of the drive does she have left to complete? a) 15% b) 29% c) 40% d) 73%
Answers
Answer:
B) 29%
Step-by-step explanation:
First, we subtract 600 from 850 to get the distance she has left. 850 - 600 = 250. Next, we take 250 and divide it by 850 to get the decimal which is 0.294117647. We can round this answer to 0.29 and convert this answer to a percentage which is 29%.
Answer:
B. 29%
Step-by-step explanation:
Percentages can be found by dividing the part by the whole, then multiplying by 100.
(part/whole) * 100
We have to find the percentage of the drive she has left.
Therefore, the part is the miles she has left and the whole is the total trip.
(miles left/total trip) * 100
First, we need to find how many miles she has left. We must subtract the miles she has driven from the total trip.
total - miles driven
She has 850 total miles and has driven 600 miles.
850-600
250
She has 250 miles left.
Now we know the miles she has left.
(miles left/total trip) * 100
miles left = 250
total trip= 850
(250/850) * 100
Solve inside the parentheses first. Divide 250 by 800.
(0.29411765)*100
Multiply
29.411765
Round to the nearest whole number. The 4 in the tenth place tells us to leave the whole number as is.
29
Therefore, she has about 29% of her trip left.
Find the mean absolute deviation (MAD) of the data in the bar chart below.
Answers
Mean absolute deviation of the given data is 1.5
What is Mean absolute deviation?The average absolute deviation of a data set is the average of the absolute deviations from a central point.
What is Mean?The arithmetic mean, also known as arithmetic average, is a measure of central tendency of a finite set of numbers
From the given bar chart
Mean = Sum of the terms / Number of terms
Mean = [tex]\frac{4+5+6+1}{4}=4[/tex]
Mean absolute deviation = [tex]\frac{1}{n}[/tex]∑ | mean- x|
MAD = [tex]\frac{|4-4|+|4-5|+|4-6|+|4-1|}{4} =\frac{0+1+2+3}{4}=1.5[/tex]
Hence, Mean absolute deviation of the given data is 1.5
Learn more about Mean and Mean absolute deviation here
https://brainly.com/question/10528201
#SPJ2
Answer:
1.5
Step-by-step explanation:
Pls Help!! Jazzmin has 2/5 of a pie. How many 1/10's of a whole pie are there in 2/5 of a whole pie?
Answer options: a.) 1/25 b.) 1/4 c.) 25 d.) 4
PLS write the correct answer
Answers
Answer:
d
Step-by-step explanation:
2/5÷ 1/10 = [tex]\frac{2}{5}*\frac{10}{1}[/tex]
= 2 * 2
= 4
Answer:
b
Step-by-step explanation:
LCD of (5, 10): 10
2/5=4/10(multiply top and bottom by 2)
(4/10)/(1/10)= 4
Therefore, 1/10 is 1/4th of 2/5
Which of the following graphs represents the equation below? y= 0.666667x + 3
Answers
Answer:
the last graph
Step-by-step explanation:
the y intercept is clearly shown as three and then using rise over run you can see that the slope is 2/3 or 0.667
24 t 1,507 lb 12 oz + 7 t 938 lb 6 oz
Answers
Answer:
31t 2,446 lb 2oz
Step-by-step explanation:
24t+7t=31t
1,507+938=2,445 lb
12 oz+6 oz=18 oz = 1 lb + 2oz (16 oz in a pound)
31t+2,445 lb+1 lb + 2oz=
31t 2,446 lb 2oz
15 POINTS!!!!!!!
How is a linear function affected by a horizontal shift?
Answers
Answer:
horizontal shift can affect the linear function, because it is impossible to distinguish which transformation was applied by looking at the resulting graph.
Step-by-step explanation:
a horizontal shift is a movement left to right along the x-axis, and in equation of a function it's change in the value of x before it's multiplied by the slope.
Answer:
I agree with Lambina and added this answer so she could get brainliest
Step-by-step explanation:
pre-algebra !!!. A class contains 3 female and 9 male students. Find the probability that a student chosen at random is a male, and then a second student chosen at random from the remaining students is also male. 9/16 3/4 1/2 6/11 None of the above
Answers
Answer:
D
Step-by-step explanation:
The first student is from a class of 12.
The first student = 9/12 for the fist male.
The second male is 8 out of 11.
The probability of both being males is
9/12 * 8/11 = 3/4 * 8/11 = 6/11
how to convert m into mm
Answers
Answer:
Multiply value in mm by 1000
Step-by-step explanation:
For example, 3m = (3 * 1000)mm
= 3000mm
Answer:
multiply by 1000
Step-by-step explanation:
1m = 1000mm
If i need convert meter en mikimeters
i multiply meter by 1000, example:
7 meters:
7 * 1000 = 7000 milimeters
another example:
4.75m = 4.75*1000 = 4750 milimeters
The weights, in pounds, of the upper-class men offensive line players for a college are shown below: 322, 290, 321, 326, 330, 315, 311, 292, 290 What is the average, or mean, weight of the upper-class men offensive players? Provide your answer with 3 sig figs. -311 pounds -315 pounds -290 pounds -318 pounds
Answers
Answer: 311 pounds
Step-by-step explanation:
To find the average, add up all of the values and divide by the amount of values.
First add up all of the values.
322+290+321+326+330+315+311+292+290 = 2797
Now count how many values there are and divide your previous sum by it.
2797/9 = 310.78
Because you need to have 3 sig figs, round to the nearest one.
310.78 rounds up to 311.
answer-311
Step-by-step explanation:
322+290+321+326+330+315+311+292+290=2797
Count the number of values and divide by 2797
2797 divided by 9 =310.77777777777777
Nearest one-311
A rectangle is graphed on the coordinate grid.
Which represents the equation of the side that is parallel to sider?
y=-X+9
y=-x+ 5
y=x-3
y= X+3
Answers
Let’s see if I can help you :)!
With two points you can define a line.
So, the line parallel to s is q, which has these two pointS: (3,6) and (6,3)
There are different ways to get the line. For instance, this one:
Y = a*x+b
a = slope = difference_y/difference_x = (3-6)/(6-3) = -1,
y = -x + b,
Now use any point, say (3,6) to get b:
6 = -3+b-> b - 9.
Line is y = -x + 9,
It checks out in the other point: (6,3) —> 3 = -6+9 = 3. Good.
Other method:
y-y2 = a*(x-x2), where (x2,y2) is one of the two points and a is the slope as defined before.
Really hope this helped you!
Answer:
The answer is B
Step-by-step explanation:
calculate the radius and diameter of the circle
Answers
Answer:
radius is 12, diameter is 24
Step-by-step explanation:
it is a 15-12-9 triangle
Below are the distances that each of Davi the Dragon Keeper's four dragons can blow fire (in meters). 0.9, 0.5, 0.3, 1.1. Find the mean absolute deviation (MAD) of the data set.
Answers
Answer:
Step-by-step explanation:
MAD is simply the average distance that all of the numbers in your data set are from the mean. Your first step is to put your data in order, then determine the mean. Let’s look at this data set:0.3, 0.5, 0.9, 1.1
The mean of this data set is 0.7Starting with the lower extreme, and checking every number in your data set, determine how far each number is from the mean. First, put the numbers in numerical order, from least to greatest. Determine the distance each number is from 0.7. 0.3=0.40.5=0.20.9=0.21.1=0.4Add up all of the distances. Total distance from the mean (12) ÷ 4 numbers in our data set = a mean absolute deviation of 3.I added a PowerPoint that I made so that if you didn't understand it you could read off of it.
Answer:
[tex]0.3[/tex] - written in [tex]2/14/2021[/tex]
Step-by-step explanation:
The answer is [tex]0.3[/tex] because, [tex]\frac{0.9+0.5+0.3+1.1}{4} =\frac{2.8}{4} =0.7[/tex], so [tex]0.7[/tex] is the mean. After having found the mean, we have to subtract [tex]0.7[/tex] from the numbers, or the numbers from [tex]0.7[/tex]:
Data Point | Distance from the mean
[tex]0.9[/tex] | [tex]0.9-0.7=0.2[/tex]
[tex]0.5[/tex] | [tex]0.7-0.5=0.2[/tex]
[tex]0.3[/tex] | [tex]0.7-0.3=0.4[/tex]
[tex]1.1[/tex] | [tex]1.1-0.7=0.4[/tex]
After finding out the Distance from the mean we'll use their sums and add them all up: [tex]0.2+0.2+0.4+0.4[/tex], then divide them by [tex]4[/tex] because there are [tex]4[/tex] numbers combined together: [tex]\frac{0.2+0.2+0.4+0.4}{4}=\frac{1.2}{4}=0.3[/tex].
So that's why the answer is [tex]0.3[/tex] (Happy Valentines Day!)
8 elementary classes will be chosen to participate in a school lunch survey. There are 23 elementary classes in the school. In how many ways can the classes be chosen?
Answers
Answer:
490,314
Step-by-step explanation:
This is a combinations problem. The formula is n!/(n-r)!xr!
This is 23!/(23-8)!x8!=
23!/15!x8!=
19,769,460,480/40,320=
490,314
Using the combination formula, it is found that the classes can be chosen in 490,314 ways.
The order in which the classes are chosen is not important, hence the combination formula is used to solve this question.
What is the combination formula?[tex]C_{n,x}[/tex] is the number of different combinations of x objects from a set of n elements, given by:
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
In this problem, 8 classes are chosen from a set of 23, hence:
[tex]C_{23,8} = \frac{23!}{8!(15)!} = 490314[/tex]
The classes can be chosen in 490,314 ways.
More can be learned about the combination formula at https://brainly.com/question/25821700
Sam purchased 3 1/4 pounds of cheese. He used half of the purchased cheese for a casserole and 1/4 pound for sandwiches. Express as a mixed number the number of the number of pounds of cheese he has left.
Answers
Answer:
1 3/8 lbs.
Step-by-step explanation:
3 1/4 x 1/2 = 1 5/8
1 5/8-1/4=
1 5/8-2/8=
1 3/8
helppppp idk how to do that?
Answers
Explanation:
360 = POR + OPT + ORT + 44
OPT = ORT = 90 (line TP and TR tangent to the circle)
360 = POR + 90 + 90 + 44
POR = 360 - 224
POR = 136
B). OPTR is a kite because OP = OR and TP = TR
Definition of a kite:
A quadrilateral whose 4 sides can be grouped into two pairs of equal sides that are adjacent to each other.
help plz i want help
Answers
Answer:
1/3
Step-by-step explanation:
There are 9 possible outcomes
We want the ones that have the same color which are GG , YY or BB
P ( same color) = number of same color outcomes / total outcomes
= 3/9
=1/3
Answer:
1/3
Step-by-step explanation:
3/9, simplify to 1/3
Find the exact value of the following. The distance traveled by a car going 65 miles per hour for 3.5 hours is ____ miles.
Answers
Answer:
227.5
Step-by-step explanation:
D=ST so X= 65 x 3.5 = 227.5 miles
D=Distance = x
S=Speed = 65
T=Time = 3.5
PLEASE HELP! 10 POINTS Which relation is not a function?
Answers
Answer:
The first relation is not a function.
Step-by-step explanation:
If you see two points in which one is vertically above the other, then it is not a function. In other words, if in a relation, two points have the same x-coordinate and different y-coordinates, that relation is not a function. The only example in which this happens is the first graph.
The first relation is not a function.