Area of a rectangle = w*l
w = width
l = length
In our problem,
Area = 105mi^2
l = x
w = x - 8
Let's plug our values into the formula above.
105mi^2 = x(x - 8)
Distribute the x
105mi^2 = x^2 - 8x
Subtract 105mi^2 from both sides.
0 = x^2 - 8x - 105
Let's factor the right side.
0 = (x - 15)(x + 7)
Set both terms equal to 0
x - 15 = 0
Add 15 to both sides.
x = 15
x + 7 = 0
Subtract 7 from both sides.
x = -7
Since the length cant be a negative number, 15 is the correct answer.
Length = x = 15 mi
Width = x - 8 = 15 - 8 = 7 mi
The length of the rectangle is 15 miles while the width is 7 miles.
What is a rectangle?A rectangle is a geometrical figure in which opposite sides are equal.
The angle between any two consecutive sides will be 90 degrees.
The perimeter of rectangle = 2( length + width).
Suppose the length is L while the width is W.
Area of rectangle = length × width.
L x W = 105
W = L - 8
By substitution,
L x (L - 8) = 105
L² - 8L - 105 = 0
L² - 15L + 7L - 105 = 0
L(L - 15) + 7(L - 15) = 0
(L + 7)(L - 15) = 0
L = -7, L = 15
Since length will not be negative thus L = 15 miles.
W = 15 - 8 = 7 miles
Hence "The length of the rectangle is 15 miles while the width is 7 miles."
For more about rectangles,
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Introduction to interval notation
What is the domain and range?
Answer:
1,7
Step-by-step explanation:
you go up one and over seven and i'll be on the other point
Please help asap need to be done now
Answer:
15.71 is the perimeter.Step-by-step explanation:
Perimeter = Circumference
Step 1. Know and recognize what you have
C = pi*d
pi = 3.142
d = 10
Step 2. Solve for the circumference of whole circle
C = 3.142*10
C = 31.42
Step 3. Solve for the questions answer
C of semicircle = 31.42/2
C of semicircle = 15.71Hope this helped,
Kavitha
Camila is seamstress and is creating a wedding dresses. She has 144 yards of silk fabric. For each dress, the skirt requires 3 yards of silk and the bodice requires 1 yard of silk. How many dresses can she make with the amount of silk she has?
Answer:
either 36 or 24
Step-by-step explanation:
The number of dresses can she make with the amount of silk she has is 48.
Given that,
She has 144 yards of silk fabric. For each dress, the skirt requires 3 yards of silk and the bodice requires 1 yard of silk.Based on the above information, the calculation is as follows:
[tex]= 144 \div 3[/tex]
= 48
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Help ASAP I'm bad at solving this I will give out 20 points!
Answer:
(0,3/2), (0,2),(6,0),(9/4,0)
I hope it helpss..
Use a graphing utility to graph the equation. Use a standard setting. y = x2 − 5x + 6
WILL GIVE BRAINLIEST!!Deepak is a landscaper who charges $30 for each job he does plus an additional $15 for each hour he works. He only accepts jobs if he will earn at least $90 the job. He writes this inequality to determine x, the number of hours he must work during each job in order to accomplish this.
30 + 15 x greater-than-or-equal-to 90
Which best describes the restrictions on the jobs Deepak will accept?
He only accepts jobs that last 4 or more hours.
He only accepts jobs that last 5 or more hours.
He only accepts jobs that last 8 or more hours.
He only accepts jobs that last 9 or more hours.
Answer:
He only accepts jobs that last 4 hours or more.
Step-by-step explanation:The number of hours is x and so when you plug in 4 hours into the equation. 30+15 (4) it equals exactly 90
Solve for x x-23=17
a -40
b 40
c -6 d 6
Answer: It is B - 40
Step-by-step explanation:
40-23 = 17
Answer:
40
Step-by-step explanation:
x-23 =17
x=17 +23
x=40
Jasmine is in charge purchasing tubes of silicone sealant, used for finishing
restroom facilities. She finds that she is able to purchase silicone sealant in cone
tubes. She knows that a jumbo cone of sealant has a top diameter of 8 inches and
a height of 12 inches, and a regular cone of sealant has a top diameter of 4 inches
and a height of 6 inches. Jasmine believes that with her order of sealant, that she
can get the same amount of silicone sealant from two regular cones as from one
jumbo cone,
a) Is Jasmina correct about the silicone sealant cones?
If you think Jasmina is correct explain why.
If you think she is incorrect replace the statement with one that is correct.
Explain why your statement is correct.
b) If the price for a regular cone of sealant is $3.40, what is a 'fair price' for a
jumbo cone?
Answer:
a) Jasmine or Jasmina is correct about the silicone sealant cones.
If Jasmine orders two regular cones of regular sealant, it will be equal to the Jumbo cone of sealant, because the top diameter when put together in a Jumbo cone will give the same result as a Jumbo cone, since 4 * 2 = 8 inches (top diameter) and 6 * 2 = 12 inches (height).
b) If the price for a regular cone of sealant is $3.40, the 'fair price' for a jumbo cone should be $6.80 ($3.40 * 2).
Step-by-step explanation:
Jumbo cone of sealant has top diameter of 8 inches and a height of 12 inches
Regular cone of sealant has top diameter of 4 inches and a height of 6 inches
If Jasmine orders two regular cones of regular sealant, it will be equal to the Jumbo cone of sealant, because the top diameter when put together in a Jumbo cone will give the same result as a Jumbo cone, since 4 * 2 = 8 inches (top diameter) and 6 * 2 = 12 inches (height).
If the price for a regular cone of sealant is $3.40, the 'fair price' for a jumbo cone should be $6.80 ($3.40 * 2), since two of the regular cone will give the value of a Jumbo cone.
The projected number of people aged 65 and over in the U.S. population with Alzheimer's disease (in millions) is given byP(t) = −0.0002083t 3 + 0.0157t 2 – 0.093t + 5.2 (4 ≤ t ≤ 40);Where t is measured in years and t = 4 corresponds to the year 2014. This model does not claim validity for years 2051 and beyond. Nevertheless, the model does suggest that:
The missing part of the question is;
What is the projected number of people aged 65 and over with Alzheimer's disease in 2030 and in 2050
Answer:
In 2030, P(20) = 7.9536 (in millions)
In 2050, P(40) = 13.2688 (in millions)
Step-by-step explanation:
We are given that;
Number of people aged 65 and over in the U.S. population with Alzheimer's disease (in millions) as;
P(t) = −0.0002083t³ + 0.0157t² – 0.093t + 5.2 (4 ≤ t ≤ 40);
Where t is measured in years and t = 4 corresponds to the year 2014.
Now,
Since t = 4 represents 2014,therefore;
t = 20 would represent population in 2030
Thus in year 2030;
P(20) = −0.0002083(20)³ + 0.0157(20)² – 0.093(20) + 5.2
P(20) = 7.9536 (in millions)
Also, in year 2050, t will correspond to 40 years.
Thus;
P(40) = −0.0002083(40)³ + 0.0157(40)² – 0.093(40) + 5.2
P(40) = 13.2688 (in millions)
How many quarters are in $20
HELP ME PLEASE WHAT IS THE ANSWER TO THESE QUESTIONS
Answer:
question 3.3 Answer: Angle 3
question 3.4 Answer: ABD and DBC are complementary angles
question 3.5 Answer: x is 7 degrees (first answer option)
Step-by-step explanation:
First question:
Recall that suplementary angles are those whose addition gives 180 degrees. Therefore the supplementary angle to angle 8 is angle 3.
Second question:
Recall that complementary angles are those angles which added give 90 degrees. Therefore, the only correct answer for this question is the third one: ABD and DBC are complementary angles.
Third question:
Notice that the two angles added should render 90 degrees, therefore, their expression should as well add to 90 degrees. Such can be written in equation form as:
( 6 x - 20 ) + (4 x + 40 ) = 90
combining like terms and later solving for x we get:
6 x + 4 x - 20 + 40 = 90
10 x + 20 = 90
10 x = 90 - 20
10 x = 70
x = 7
Therefore x is 7 degrees
Find the first partial derivatives of the function f(x,y,z)=4xsin(y−z)
Answer:
[tex]f_x(x,y,z)=4\sin (y-z)[/tex]
[tex]f_x(x,y,z)=4x\cos (y-z)[/tex]
[tex]f_z(x,y,z)=-4x\cos (y-z)[/tex]
Step-by-step explanation:
The given function is
[tex]f(x,y,z)=4x\sin (y-z)[/tex]
We need to find first partial derivatives of the function.
Differentiate partially w.r.t. x and y, z are constants.
[tex]f_x(x,y,z)=4(1)\sin (y-z)[/tex]
[tex]f_x(x,y,z)=4\sin (y-z)[/tex]
Differentiate partially w.r.t. y and x, z are constants.
[tex]f_y(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial y}(y-z)[/tex]
[tex]f_y(x,y,z)=4x\cos (y-z)[/tex]
Differentiate partially w.r.t. z and x, y are constants.
[tex]f_z(x,y,z)=4x\cos (y-z)\dfrac{\partial}{\partial z}(y-z)[/tex]
[tex]f_z(x,y,z)=4x\cos (y-z)(-1)[/tex]
[tex]f_z(x,y,z)=-4x\cos (y-z)[/tex]
Therefore, the first partial derivatives of the function are [tex]f_x(x,y,z)=4\sin (y-z), f_x(x,y,z)=4x\cos (y-z)\text{ and }f_z(x,y,z)=-4x\cos (y-z)[/tex].
Given below are a collection of scores on a spelling test: 5,6,10,8,3,5,9,8,7,4,6,5,3,7,9,5,6,4,5,6,7,5,4,6 a.) construct a frequency distribution b.) compute the relative frequencies. c.) compute the culmuative frequencies.
Rafael wrote expressions equivalent to 8 using square roots and cube roots. All of the following could be one of Rafael’s expressions except:
Answer:
it's c
Step-by-step explanation:
Answer:
C.
[tex] \sqrt[3]{64} \times \sqrt[3]{8} [/tex]
asap Algebra 2 hon explanation would be greatly appreciated.
Answer:
option A
Step-by-step explanation:
f(3)=3*27-2*9-12-1
=81-18-12-1
=81-31
=50
HOPE IT HELPS
PLS MARK AS BRAINLIEST
is 1 (b+6) equivalent to (b+6)
Answer:
Yes.
Step-by-step explanation:
Step 1: Write out expressions
1(b + 6) = b + 6
Step 2: Distribute 1
b + 6 = b + 6
-100x5 + 90?????????????????????????
Answer:
-410
Step-by-step explanation:
:)
Answer:-410
Step-by-step explanation:
how would i simplify this?
The distance around the outside of a building is 0.5 mile. Eli biked 0.72 of the distance during his free period. How far did he bike?
Answer:
0.36 miles
Step-by-step explanation:
Suppose that a visitor to Disneyland has a 0.74 probability of riding the Jungle Cruise, 0.62 probability of riding the Monorail, 0.70 of riding the Matterhorn, 0.52 of going on both the Jungle Cruise and Monorail, 0.46 of going on the Jungle Cruise and Matterhorn, 0.44 of going on the Monorail and the Matterhorn, and 0.34 of going on all three rides. What is the probability that a person visiting Disneyland will go on at least one of these three rides
Answer: 0.98
Step-by-step explanation:
Let J denotes Jungle Cruise , M denotes Monorail and H denotes Matterhorn.
As per given ,
P(J) = 0.74, P(M) = 0.62, P(H) = 0.70
P(J∩M) = 0.52, P(J∩H)= 0.46 , P(M∩H)=0.44
P(J∩M∩H)=0.34
Now , the required probability:
P(J∪M∪H) = P(J) + P(M) + P(H) - P(J∩M) - P(J∩H) - P(M∩H)+ P(J∩M∩H)
= 0.74+0.62+0.70-0.52-0.46-0.44+0.34
= 0.98
Hence, the probability that a person visiting Disneyland will go on at least one of these three rides= 0.98 .
HELP!!! Need Some Homework Help!
Answer:
( -4, 7 )
Step-by-step explanation:
The difference between (2,3) and (-1,5) is (-3,2)
Because (-3,2) is the length of half the line we need to add that figure to M to get point S
(-1,5) plus (-3,2) is (-4,7)
4|m-n| if m= -7 and n=2
F(x)=x2-2x find f(x2)
answer
0
Step-by-step explanation:
you plug in the 2 into every xbox value
Answer:
f(x)= x²-2x
For finding f(x²), replace x with x²
f(x²)= (x²)²-2x²
= x⁴-2x²
Hope it helps :-)
The sum of two numbers is 10. The larger number is 4
times the smaller number.
The system of equations used to represent this
scenario is y = -x + 10 and y = 4x.
What is the larger number?
04
8
06
08
10
10
Answer:
y = -x + 10 and y = 4x.
4x = -x+10
5x = 10
x=2
largest number = 4x = 4*2 =8
Step-by-step explanation:
A certain medicine is given in an amount proportional to a patient's body weight. Suppose a patient weighing 162 pounds requires 216 milligrams of medicine.
What is the weight of a patient who requires 220 milligrams of medicine?
Answer:
It should be 176,
Step-by-step explanation:
hope this helps!
Can someone help pls ??:(
Solve the equation x-3=23
X=
Answer:
26
Step-by-step explanation:
26 - 3 = 23
hope this helps
Answer:
x = 26
Step-by-step explanation:
x-3=23
Add 3 to each side
x-3+3=23+3
x = 26
Integers are ________ whole numbers. braineist for first person to get it right and hurry im on a time limit 20 points for it also
sometimes whole numbers
Step-by-step explanation:
maybe
please help me guys im lost
Answer:
D. BC ≅ EF
Step-by-step explanation:
ASA means you're trying to show congruence by showing two angles A..A and the segment between them ..S.. are congruent. The figure shows two congruent angles. What remains is to show the segments between are congruent.
__
In ∆ABC, the marked angles are B and C, so the segment between them is BC.
In ∆DEF, the marked angles are E and F, so the segment between them is EF.
These are the segments that need to be shown congruent if you're using ASA.
BC ≅ EF
Solve equation 17=r+10
Answer:
unless I am mistaken r=7
Step-by-step explanation:
you subtract 10 from each side and boom done