Answer:
The garden is 14ft by 8ft.
The width of the walkway needs to be the same around each side of the garden, let's suppose that the width is X.
Then the area of the garden plus the walkway will be:
(14ft + X) by (8ft + X).
And we want that the total area of the garden and the walkway must be equal to 315 ft^2. Then we must solve the equation:
(14ft + X)*(8ft + X) = 315ft^2
Let's solve this for X.
112ft^2 + 14ft*X + 8ft*X + X^2 = 315ft^2
Let's move al the terms to the same side:
X^2 + (14ft + 8ft)*X + 112ft^2 - 315ft^2 = 0
X^2 + 22ft*X - 203ft^2 = 0.
Now to solve this we can use Bhaskara's equation:
[tex]X = \frac{-22ft +- \sqrt{(22ft)^2 - 4*1*(203ft^)} }{2} = \frac{-22ft +-36ft}{2}[/tex]
Then we have two solutions:
X = (-22ft - 36ft)/2 = -29ft
This solution is negative, and X represents a width, so must be positive, then we can discard this solution.
X = (-22ft + 36ft)/2 = 7ft
Then we can conclude that the width of the walkway must be 7ft.
Jill has not been able to maintain the $1,000 minimum balance required to avoid fees on her checking account. She wants to switch to a different account with a fee of $0.20 per check and a $12.50 monthly maintenance fee. Jill wants to estimate the fees for her new account. Below is a summary of the checks she has written from May to August. What is the mean number of checks Jill wrote per month during the last four months? Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account. Estimate the total monthly fees Jill will pay each month for the new checking account.
Step-by-step explanation:
Kindly find attached a summary of the checks she has written from May to August.
A. What is the mean number of checks Jill wrote per month during the last four months
mean= (14+19+23+24)/4
mean= 80/4
mean= 20 checks
B. Based on the mean, estimate how much Jill expects to pay in per-check fees each month after she switches to the new account.
the expression for the total is given as
y=12.50+0.2x
y=12.50+0.2(20)
y=12.50+4
y=16.5
=$16.5
C. Estimate the total monthly fees Jill will pay each month for the new checking account.
May= 12.50+0.2(14)
May=12.5+2.8= 15.3
June= 12.50+0.2(19)
June=12.5+3.8= 16.3
July= 12.50+0.2(23)
July=12.5+4.6= 17.1
August= 12.50+0.2(24)
August=12.5+4.8= 17.3
total will be = 15.3+16.3+17.1+17.3= $66
A:20
B:$4.00
C:$16.50
A: 14+19+23+24/4 = 20
B: 20/.2 = 4
C: 12.50+4= 16.50
Why do we use coordinate planes to do
transformations and dilations?
Answer: a coordinate plane is used in order to track the location of the object.
Translations are congruence transformations that move an object, without changing its size or shape
Dilations are transformations that generate an enlargement
Step-by-step explanation:
What is the value of x? Round to the nearest tenths place....
Answer:
x = 12.64911064
Step-by-step explanation:
a^2 + b^2 = c^2
8^2 + b^2 = 14^2
36 + b^2 = 196
Q. Alex is managing an assembly line
creating precision drill bits. The number of
drill bits created is in the chart above. What
is the mode number of drill bits created?
bits
Answer:
i put 65 but that was not the correct answer
Step-by-step explanation:
Answer: 20
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line y = x + 4?
The slope of the line is
Answer:
-1
Step-by-step explanation:
Answer:
- 1/6 is correct
perpendicular refers to the opposite of 1/6 therefor being negative 1/6
Step-by-step explanation:
What is the slope of a line that is perpendicular to the line y =-1/5
Answer:
The slope-intercept form is y=mx+b y = m x + b , where m m is the slope and b b is the y-intercept. Using the slope-intercept form, the slope is 0 0 . All lines that are parallel to y=−15 y = - 1 5 have the same slope of 0 .
Find constants a , b, and c such that the function
y = ax2 + bx + c satisfies the differential equation y′′ + y′ − 2y = 4x2.
Answer: a = -2, b = -2, c = 1.
Step-by-step explanation:
We know that:
y = a*x^2 + b*x + c.
Then:
y' = 2*a*x + b
y'' = 2*a.
Then we can write the equation:
y′′ + y′ − 2y = 4x^2.
as:
2*a + 2*a*x + b - 2*(a*x^2 + b*x + c) = 4*x^2
To solve this, the first step is moving all the terms to the same side:
2*a + 2*a*x + b - 2*a*x^2 - 2*b*x - 2*c - 4*x^2 = 0
Now let's group terms with the same power of x.
(-4 - 2*a)*x^2 + (-2*b + 2*a)*x + (-2c + b) = 0
Now, this must be zero for all the values of x, then the parenthesis must be equal to zero:
-4 - 2*a = 0
-2*b + 2*a = 0
-2*c + b = 0
From the first equation:
-4 - 2*a = 0
-4 = 2*a
-4/2 = a
a = -2
And from the second equation:
-2*b + 2*a = 0
2*a = 2*b
a = b
b = -2.
From the third equation we have:
-2c + b = 0
-2c = b
c = b/-2 = -2/-2 = 1.
c = 1
Then our equation is:
y = -2*x^2 - 2*x + 1.
If you pls help lol I only have 52 mins left
Step-by-step explanation:
[tex]2y + 106 = 180[/tex]
[tex]y = 106 \div 2 = 53[/tex]
[tex]y = 53[/tex]
[tex]4z + 16 = 180[/tex]
[tex]4z = 180 - 16[/tex]
[tex]z = 164 \div 4 = 41[/tex]
and the answer for x is 106
In 1998, Susie Maroney set a record for the longest ocean swim without flippers. She swam 122 miles from Mexico to Cuba. Use a conversion factor to find the distance in feet. 1mile=5280 feet
Answer:
it's 644160 u need to times it if she swam 122 miles and each mile is 5280 and u answer is 644160
A recipe calls for 18 ounces of cream cheese with 15 ounces of sugar." How many ounces of cream cheese are there per ounce of sugar?
PLEASE HELP
Answer:
1.2
Step-by-step explanation:
Just divide
Answer:
1.2
Step-by-step explanation:
Divide 18 by 15 and get the answer.
Can anyone tell me if u pass the ela state exam but u didn't pass the math state exam can u still go to 9th grade cuz im in 8th please answer and my grades are always good so does it help? and my classwork etc is always around 80-100 is it good
is 3/4 less than,greater than,or equal to -1/2 ?
Answer: Greater than
3/4 greater than -1/2
3/4 > -1/2
Any positive number is always larger than any negative number
On a number line, stuff on the right side is always larger than stuff on the left side.
Answer:
it"s greater then
Which of the expressions below will have a 8 in the thousandths place of the quotient? Select all that apply.
A) 765.812 ÷ 100
B) 98.14 ÷ 1,000
C) 18.723 ÷ 100
D) 22.38 ÷ 10
Answer:
A
Step-by-step explanation:
In 1980, the number of high school dropouts in a country was 5217 thousand. By 2008, this number had decreased to 3120 thousand. Find and interpret the average rate of change
per year in the number of high school dropouts.
Answer:
74893 students per year
Step-by-step explanation:
The Average rate of change is calculated as
= Difference in number of students / Difference in years
= 3120 thousand - 5217 thousands/ 2008 - 1980
= (3120000 - 5217000)/(2008 - 1980)
= -2097000/28
= -74892.857143 per year
Therefore, the average rate of change
per year in the number of high school dropouts is approximately 74893 students per year
Find two numbers who’s product is 132 and whose sum is 23
Answer : The two numbers are 11 and 12.
how to find the area figure of square inches
is -4 greater,less than or equal to +4 ?
pls help <3 thank you sm ;)
Help me out fast on this question.
The length of a rectangle is (3x − 5) inches, and its width is 2x inches. Find the area of the rectangle.
Hint: Area of a rectangle = length × width.
Answer:
A = 6x² - 10x
General Formulas and Concepts:
Area of a Rectangle: Length × Width
To expand, use FOIL - First, Outside, Inside, Last
Step-by-step explanation:
Step 1: Define variables
l = 3x - 5
w = 2x
Step 2: Find area
Substitute: A = (3x - 5)(2x)Expand (FOIL): A = 6x² - 10xAnswer: A=6x^2-10x ✅
Step-by-step explanation:
Hii, do you need to find the area of the rectangle? Let me help you out! (:
Luckily, there's a formula to find this! (:
AreaTo find the area of a rectangle, multiply its length times its width. This is shown below.
[tex]\LARGE\boldsymbol{A=L W}[/tex]
Here, "A" denotes the area
"L" denotes the length
"W" denotes the width
NB : "L" and "W" are interchangeable
Next, it's just a matter of sticking in the known values...
[tex]\twoheadrightarrow\sf A=2x(3x-5)[/tex]
===> it's perfectly legal to stick in the values the other way around, because they are interchangeable
Alright, the next step is to multiply the values...
[tex]\twoheadrightarrow\sf A=(2x\cdot3x)-(2x\cdot(-5)[/tex]
Then we need to simplify...
[tex]\twoheadrightarrow\sf A=6x^2-10x[/tex]
Voila! There's the area of this rectangle! (:
Cheers! (:_______________Hope I helped! Best wishes.
⚜ Reach far. Aim high. Dream big. ⚜
_______________At a sale this week, a suit is being sold for $306 . This is a 15% discount from the original price.
What is the original price?
Answer:
260.1
Step-by-step explanation:15% of 306=45.9
306-45.9=260.1
Answer:
351.9
Step-by-step explanation:
x/306=15/100. then I cross multiplied. And when I do I get 100x/100=4590/100.
I cross out the 100/100 and I leave with x, then I divide 4590 with 100 and get 45.9. So x=45.9.
Then I added the price it was sold..=306+45.9=351.9
The lines y = 3x + 4 and y = 3x - 17 are perpendicular
Answer: No
Step-by-step explanation: Here's something that I learned. Same slope different y-intercept (no solution). Same slope and same y-intercept (Infinitely many solutions). Different slope and same y-intercept (one solution). Different slope and different y-intercept (one solution).
Find the measure of the missing angle
Answer:
M1=108° M2=72°
Step-by-step explanation:
M1 and the original 108° angle are equal, and to calculate M2, which is on the same straight line as the original 108°, we must remember that all angles on a straight line add up to 180°. So, 180-108=72, making M2 72°
1.) 4x+2y-z=21
2.) -x-2y+2z=13
3.) 3x-2y+5z=70
Answer:
Step by Step Solution:
More Icon
Reformatting the input :
Changes made to your input should not affect the solution:
(1): Dot was discarded near "2.-".
(2): "133.3" was replaced by "(1333/10)".
Too Many Equal Signs
Step-by-step explanation:
An architect wants to build a scale model of a building that is in the shape of a rectangular prism. The building has a height of 500 ft., a width of 120 ft., and a length of 600 ft.The scale model is 1% of the size of the building based off its length and width, so the length of the scale model is and the height of the scale model is .
Height: 5ft.
Legnth: 6ft.
Width: 1.2 ft.
1% of 500 is 5ft
1% of 600 is 6ft
1% of 120 is 1.2ft
Can someone help me solve this?
Answer:
2313
Step-by-step explanation:
A bookshelf at a bookstore is 3 feet 9 inches wide. There are 18 copies of the same book on the shelf, which fit the shelf exactly. What is the width of 1 of the books?
Answer:
5 / 2 inches OR 2.5 in
Step-by-step explanation:
3 ft 9 in = 45 inches
45in/18 books
5 in / 2 book
A product's demand per period follows a normal distribution with mean of 60 and standard deviation of 10. The lead time is 3 periods. What order-up-to level should be used to achieve at least a 90% in-stock probability?
Answer:
209
Step-by-step explanation:
Since the lead time is 2 periods at the time of order, the stocks should last for 3 periods with the 90% probability.
The z-value of 90$ in stock probability = 1.7
Mean of the demand over is (1 + 1 + 1 ) or (2+1 which is 3)
= 60 x 3 = 180
Now the standard deviation of demand over the three periods = 17.3
Therefore, the order up level would be = 180 + ( 1.7 x 17.3 )
= 209
Which two numbers both round to 1,500 when rounded to the nearest hundred?
Answer:
C
Step-by-step explanation:
Just take it lol
The two numbers where both round to 1,500 when rounded to the nearest hundred is option c. 1457 and 1547.
What is Rounded number?
The rounded number should be that where the number should be rounded to the nearest tenth, hundred or thousand
Since the number is 1500
So for hundred the number should be likely 1457 and 1547.
hence, the option c is correct.
learn more about number here: https://brainly.com/question/21474983
Mike has at least 250 in his savings account.Which inequality represents this situation