Find the dimensions of a rectangle whose width is 8 miles less than its length and whose area is 105 square miles
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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Which operation should you perform last in the expression 12 × 4^2?
Answer:
Multiplication
Step-by-step explanation:
Follow GEMDAS or PEMDAS. I would recommend GEMDAS. GEMDAS stands for Grouping symbols, exponents, multiply, divide, addition, subtraction. GO form the order G to S
How do we Round with any numbers, (on a number line) ?
Answer:
round it to the nearest 10th?
Step-by-step explanation:
that's what I do at least.
Answer: Round up or down.
Step-by-step explanation: When you round up, look at the number to the right of the number you wanna round. If it’s less than 5, you round down, if it’s more than 5, you round up. On a number line, for ex. Let’s say you wanna round 550 to hundreds, 600 or 500, 600 would be the answer because 550 is more closer to 600 by default.
Two sides of an obtuse triangle measure 9 inches and 14 inches. The length of the longest side is unknown. What is the smallest possible whole-number length of the unknown side?
Answer:
17 inches.
Step-by-step explanation:
Answer:
answer is 17 inches
Step-by-step explanation:
A helicopter is flying from Hong Kong to Jakarta. The latitude of Jakarta is -6.20°, and its longitude is 106.80°. The latitude of Hong Kong is 22.27°, and its longitude is 114.15°. What is the helicopter’s net change in latitude and longitude as it travels from Hong Kong to Jakarta?
A. -28.47° latitude and 7.35° longitude
B. -28.47° latitude and -7.35° longitude
C. 28.47° latitude and -7.35° longitude
D. 38.34° latitude and 220.95° longitude
E. -38.34° latitude and 220.95° longitude
Answer:
I think the answer is A
Step-by-step explanation:
Because you add both latitude (22.27+ -6.20) = -28.47 because a negative plus a positive equals a a negative then you add the longitude (114.15 -106.80) = 7.35 so the answer would be
-28.47 latitude and 7.35 longitude.
the answer would be C.)28.47 lat -7.35 long
What is 300 million divided by 1 thousand?
Answer:
the answer is three hundred thousand
Plz help asap In 4 years, Harry’s age will be the same as Jim’s age is now. In 2 years, Jim will be twice as old as Harry will be. Find their ages now.
Answer:
Harry is 2, Jim is 6
Step-by-step explanation:
The first statement tells us they are 4 years part. Then you need to find two numbers that are 4 apart and that has one that is half the other, like 4 and 8. Finally, subtract two because this will happen in two years and you need their ages now.
Sorry if this was confusing.
4|m−n| if m=−7 and n=2 i really need to know what this is asap please
Answer:
36
Step-by-step explanation:
Plug in -7 as m and 2 as n into the expression:
4 | m - n |
4 | -7 -2 |
Solve:
4 | -9 |
4(9)
= 36
60 point question!...........
Answer:
dhsfhb
Step-by-step explanation:
top secret
Answer:
Have a good day, dont see a picture?
Step-by-step explanation:
Find the indicated values, where gt) = 12 - and Ax) = 1 + X.
g(f(2) + 3)
a. 1
b. 3
c. 30
d. -1
Please select the best answer from the choices provided
ΟΑ
B
OD
Answer:
c
Step-by-step explanation:
Ms. D bought 18 bagels for $1.35 each and 2 containers of cream cheese for $3.45 each. Write and evaluate ONE expression to find the total cost of the food.
Answer:
(18+2)x($1.35+$3.45)= $96
Could I please have BRAINLIEST.
solve for x 7x½+2=0
Answer:
here's your answer
hope this helped you
please mark as the brainliest (ㆁωㆁ)
Answer: 7/2x + 2
Step-by-step explanation:
Help please, will mark you as brainliest!!
Need help on both..
Answer:
the answer is c for the second one and the first one is A
the sum of 12 and the quantity 8 times a number k is equal to 48
Answer:
12 + (8k) = 48
k= 9/2
Step-by-step explanation:
x2 can be combined with X?
Answer:
Your first instinct might be to go ahead and add the x terms together, BUT this would be a bad thing to do! You cannot combine the x2 and 2x, because the first term has an exponent (2) and the second one does not have an exponent; therefore, you cannot add them together!
Step-by-step explanation:
Answer:
Not sure if you mean multiplying or adding by "combine". But generally the rule of thumb with exponents is when you are adding and they are not like terms, you cannot combine the two terms together. So in other words, they would be left as x²+x. However, when you are multiplying you can add the exponents together. So, it will be like this: x²·x = x³
HELP I HAVE TO SUBMIT IN 1 HOUR
Answer:
Step-by-step explanation:
Volume = Base * height
V=2(7 1/3)
V=44/3 OR 14 2/3 Or 14.666
help!
what is the answer to this problem?
Answer:
D
Step-by-step explanation:
Because 12 is greater than -5 and when you divide a postive and a negative you get a negative number. And negative numbers are less than 0 .
At 6 am, the temperature was 73 degrees Fahrenheit. By noon, then temperature had rose 8 degrees. At 4 pm, the temperature was 5 degrees warmer than it was at noon. By 9 pm, the temperature had dropped 16 degrees. What was the temperature at 9 pm?
Answer:
70 degrees Fahrenheit
Answer:
70
Step-by-step explanation:
We started at 73 degrees and the temperature rose by 8 degrees so 73 + 8 = 81. At 4 pm, the temperature rose again by 5 degrees so 81 + 5 = 86. By 9 pm, the temperature dropped 16 degrees so 86 - 16 = 70, Therefore, the temperature at 9 pm was 70 degrees.
Solve the inequality and graph the solution set for 2(3r − 10) ≤ 3r − 5
Answer:
r≤5
Step-by-step explanation:
Steps are in the photo. Hope this helps.
Which angles could you add to 1 to make a supplementary angle. Please helppp
solve for p in the literal equation 8p+5r=q
Write the expression as a square of a monomial. 4/9b^6
Answer:
Step-by-step explanation:
It just so happens that all the numbers and variables in that expression are perfect squares. 4 has a square root of 2; 9 has a square root of 3; and b^6 has a square root of b^3. Putting that altogether into one simplified expression that we can square is:
[tex](\frac{2}{3}b^3)^2[/tex]
The expression as a square of a monomial (4/9b⁶) is (2²/3²b³)²
What is a polynomial?A polynomial is an algebraic expression.
A polynomial of degree n in variable x can be written as,
a₀xⁿ + a₁xⁿ⁻¹ + a₂xⁿ⁻² +...+ aₙ.
A monomial is a polynomial that has only one term.
Given, a monomial (4/9b⁶).
To write this monomial in terms of as a square of a monomial we'll factor out the power of 2 from each f the constants and variables contained in the monomial which is,
= (2²/3²b³)²
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PLEASEEE HELP
1. Andrea ran and biked for a total of 32 mi in 4 hours. Her average running speed was 5 mph and her average biking speed was 13 mph.
Let x = total hours Andrea ran.
Let y = total hours Andrea biked.
Use substitution to solve for x and y. Show your work. Check your solution.
(a) How many hours did Andrea run?
(b) How many hours did she bike?
Answer:
Ran: 2.5hr
Biked: 1.5hr
Step-by-step explanation:
x = total hrs ran
y = total hrs biked
4 = total hours ran + biked
soo.....
x + y = 4hr
then you can convert that for solving y or x
Ex. x = 4-y or y = 4-x
Then just plug in either x or y
EQUATION: 5x + 13y = 32
Dont plug in both x or y at the same time. Pick one and solve
Study the dot patterns in parts (a) and (b) below. Assume that each pattern continues to increase by the same number of dots and in the same locations for each figure.
For each pattern, sketch the 4th and 5th figures. Then predict how many dots will be in the 100th figure.
Answer:
east-56 a=+b 2squared
Step-by-step explanation:
give me the answer now
Answer:
what is the Question
Step-by-step explanation:
100 POINTS!! ASAP - Pls Show all WORK
Answer:
x ≈ 28.7 ft
Step-by-step explanation:
Step 1: Define variables
Height (vertical leg of triangle) = 2 ft
∅ = 4°
We are trying to find the length of the hypotenuse x
Step 2: Use trig
sin∅ = opposite over hypotenuse
sin4° = 2/x
Step 3: Solve for x
xsin4° = 2
x = 2/sin4°
x = 28.6712
x ≈ 28.7 ft
Answer:
the Length of ramp is 28.7 feet.
Step-by-step explanation:
see attached image for clarity
give:
height (h) of clinic = 2 feet
angle of ramp = 4°
find:
Length (L) of ramp
using the formula : sin(Ф) = height (h)
Length of ramp (hypothenuse)
plugin values into the formula:
sin (4) = 2
L
L = 2
sin(4)
L = 28.7 feet
therefore,
the Length of ramp is 28.7 feet.
kx-fy=cx+p for x ????????????
Move all terms to the left side and set equal to zero. Then set each factor equal to zero.
x=[tex]\frac{p + fy}{K - c}[/tex]
Which THREE storage devices are non-volatile? Non-volatile devices can store data regardless of whether they are powered on or not.
thumb drive
RAM
hard disk
ROM
Answer: Thumb drive, ROM, Hard-disk
Step-by-step explanation:
Find
-/16. (4 points)
a
-4
ob
4
Ос
+4
Od
-8
Answer:
4i
Step-by-step explanation:
I hope its not too complicated
[tex]\sqrt{-16} \\\\\mathrm{Apply\:radical\:rule}:\quad \sqrt{-a}=\sqrt{-1}\sqrt{a}\\\\\sqrt{-16}=\sqrt{-1}\sqrt{16}\\\\\mathrm{Apply\:imaginary\:number\:rule}:\quad \sqrt{-1}=i\\\\=\sqrt{16}i\\\\\sqrt{16}=4\\\\=4i[/tex]
Given: Lines a and b are parallel and line c is a transversal. Prove: 2 is supplementary to 8 What is the missing reason in the proof? Statement Reason 1. a || b, is a transv 1. given 2. ∠6 ≅ ∠2 2. ? 3. m∠6 = m∠2 3. def. of congruent 4. ∠6 is supp. to ∠8 4. def. of linear pair 5. ∠2 is supp. to ∠8 5. congruent supplements theorem corresponding angles theorem alternate interior angles theorem vertical angles theorem alternate exterior angles theorem
Answer:
vertical angles theorem
Step-by-step explanation:
Just took the test
Answer:
A. corresponding angles theorem
Step-by-step explanation: