Given:
The length of a rectangle is 3 cm less than its width.
The area of the rectangle is 270 cm².
To find:
The dimensions of the rectangle.
Solution:
Let x be the width of the rectangle. Then,
[tex]\text{Length}=x-3[/tex]
Area of a rectangle is:
[tex]\text{Area}=\text{Length}\times \text{width}[/tex]
[tex]270=(x-3)(x)[/tex]
[tex]270=x^2-3x[/tex]
[tex]0=x^2-3x-270[/tex]
Splitting the middle term, we get
[tex]x^2-18x+15x-270=0[/tex]
[tex]x(x-18)+15(x-18)=0[/tex]
[tex](x-18)(x+15)=0[/tex]
[tex]x=18,-15[/tex]
Width of the rectangle cannot be negative. So, the only value of x is 18.
[tex]Width=18[/tex]
[tex]Length=18-3[/tex]
[tex]Length=15[/tex]
Therefore, the length of the rectangle is 15 cm and the width of the rectangle is 18 cm.
Mr. Rockwell's class is holding a canned food drive for charity. Kim collected 10 more cans than Stephanie. Natasha collected twice as many cans as Kim. If they collected 130 cans altogether, how many cans did Kim collect?
Answer:
35 cans
Step-by-step explanation:
big brain
A cylinder has a radius of 4 inches and a height of 5 inches. If the radius of the cylinder is tripled and the height remains the same to create a new cylinder, what will be the difference in the surface areas of the two cylinders? Answer in terms of Pi.
Answer:
336π in²Step-by-step explanation:
Cylinder 1
r₁= 4 inh = 5 inCylinder 2
r₂ = 3*4 = 12 inh = 5 inSurface area of cylinders:
S = 2πr(r + h)S₁ = 2π*4*(4 + 5) = 72π in²S₂ = 2π*12*(12 + 5) = 408π in²The difference is:
S₂ - S₁ = 408π - 72π = 336π in²A cylinder has a radius of 4 inches and a height of 5 inches. If the radius of the cylinder is tripled and the height remains the same to create a new cylinder, what will be the difference in the surface areas of the two cylinders ? Answer in terms of Pi.
Answer:-Given:-A cylinder has a radius of 4 inches and a height of 5 inches.
To Find:-If the radius of the cylinder is tripled and the height remains the same to create a new cylinder, what will be the difference in the surface areas of the two cylinders ?
Solution:-Let in case of 1st cylinder,[tex] \bullet [/tex] Radius [tex] (r_1) [/tex] is 4 inches
[tex] \bullet [/tex] Height is 5 inches
And in case of 2nd cylinder,[tex] \bullet [/tex] Radius [tex] (r_2) [/tex] is 3 × 4 = 12 inches [as in the question it is given that the radius of the cylinder is tripled]
[tex] \bullet [/tex] Height is 5 inches
Now,
Surface area [tex] (s_1) [/tex] of 1st cylinder
is 2πr(r + h) = 2π × 4(4 + 5)
= 8π(9)
= 72π sq inches
Surface area [tex] (s_2) [/tex] of 2nd cylinder
is 2πr(r + h) = 2π × 12(12 + 5)
= 24π(17)
= 408π sq inches
[tex] \therefore [/tex] The difference in the surface areas of the two cylinders is = [tex] (s_2 \: - \: s_1) [/tex] = (408π - 72π) = 336π sq inches
The difference in the surface areas of the two cylinders is 336π sq inches. [Answer]If you read 340 pages in 45 minutes how many pages do read in 1 minute
Answer:
7 5/9
Step-by-step explanation:
340/45 = 7 5/9
Answer:
7.6 pages
Step-by-step explanation:
Okie, so this is a standard unit rate problem, so what you're going to do is divide the number of whatever, in this case, pages, by the time, so:
340 ÷ 45 = 7.6 (rounded)
So you read 7.5 pages per minute
(which is pretty impressive if it's a chapter book)
hope this helps:)
visitors spend 1/3 of their time waiting in line for rides. Of the santos family spends 53/4 hours at the park how long do they wait in line
Answer: 1 11/12 hours
Step-by-step explanation:
Since visitors spend 1/3 of their time waiting in line for rides and the Santos family spends 5¾hours at the park.
The tune spent waiting in line will be calculated by multiplying ⅓ by 5¾. This will be:
= ⅓ × 5¾
= ⅓ × 23/4
= 23/12
= 1 11/12 hours
Therefore, they'll wait in the park for 1 11/12 hours
5/6 + 7/9
help me pls
helpppp plsssssssssssssssssssss quick
Identify the slope and the y-intercept of the following equation 1/2x - 1 = y
b =
m =
uto: Which is the “first point” given, the slope or the y-intercept ?
Answer:
see below
Step-by-step explanation:
Our equation is y = 1/2x - 1. This mirrors our standard linear parent function of y = mx + b.
m is the slope and b is the y-intercept.
From this, we can see that
m = 1/2
and
b = -1.
The first point given is the y-intercept because with y-intercepts, we know the coordinates right away. A y-intercept's coordinates will always have an x-value of 0. This allows it to lie on the y-axis, hence the name. Our y-value of the coordinates is given with the b value of the equation. Therefore, by simply looking at the end of the equation, we know our first point.
Hope this helps!
i need help with 6 and 7! please help asap!! and explain why
Answer: I would say 6 its a function and 7 its not because in number seven the x value repeats so it can't be a function and number 6 the x-value its not the same
Step-by-step explanation: When the x-value repeats its not a function if the y-value repeats it doesn't matter
SOMEBODY PLEASE HELP!!!!
Answer:
A the first one.
Step-by-step explanation:
Please solve this quadratic equation:
3^2x -9 =0
Answer:
[tex] {3}^{2} x - 9 = 0 \\ 9x = 9 \\ x = 1[/tex]
find the area 10ft 2 1/2
Answer:
if your trying to find the area of 10ft and 2 1/2 all you gotta do is turn the 2 1/2 in a decimal and multiply it by 10 which is 25
Step-by-step explanation:
please...............
Answer: A and D
Step-by-step explanation:
An urban planner wants to create a city block. The city block will be 50 feet by 75 feet. What will the dimensions of his scale drawing be if the drawing has a scale factor of 1 cm = 12.5 ft?
Answer:
The dimensions of his scale drawing = 4 cm by 6 cm
Step-by-step explanation:
An urban planner wants to create a city block. The city block will be 50 feet by 75 feet. What will the dimensions of his scale drawing be if the drawing has a scale factor of 1 cm = 12.5 ft?
From the above question
12.5 ft = 1 cm
Hence
For 50 feet
12.5 feet = 1 cm
50 feet = x
Cross Multiply
12.5 × x = 50
x = 50/12.5
x = 4 cm
For 75 feet
12.5 feet = 1 cm
75 feet = x
Cross Multiply
12.5 × x = 75
x = 75/12.5
x = 6 cm
The dimensions of his scale drawing = 4 cm by 6 cm
please help me with this math problem, the question is on the picture that i attached, ill mark brainliest if the answer is correct. NO links!
PLease help with this
Answer:
huh
Step-by-step explanation:
NO SCAMMERS!!!! I WILL REPORT! MAX POINTS!!!!! ARCS & ANGLES NEED TO KNOW HOW TO DO IT. ANSWERS ALSO VERY MUCH APPRECIEATED !!!FRESHMAN CLASS GEOMETRY!!!
Answer:
[i] 12x + 5 = 1/2(83 +95)
12x + 5 = 89
12x = 84
x = 7.
[ii] 9x + 7 = 1/2(198 + 7x - 8)
18x + 14 = 198 + 7x - 8
11x = 176
x = 16.
[iii] 15x - 8 = 1/2(16x +1 + 5x + 19)
30x16 21x + 20
9x = 36
x = 4.
[iv] 20x - 4 = 360 - 2 × 72
20x = 220
x=220/20=11°
[v] 13x - 1 = 2(6x + 11)
13x - 1 = 12x + 22
x = 23.
[vi] 46 = 1/2(21x-5-x-23)
20x2892
20x = 120
x = 6.
[vii] 6x - 21 = 1/2(13x - 3-3x - 11)
12x - 4210x - 14
2x = 28
x = 14.
[viii] 2x + 1 = 1/2(9x − 14 − 4x + 7)
4x + 2 = 5x - 7
x = 9.
[ix] 9x - 4 = 180 - 76
9x - 4 = 104
9x = 108
x = 12.
Please help, Does this graph show a constant or variable rate of change?
Answer:
constant
Step-by-step explanation:
Answer:
pretty sure it's a variable change
Step-by-step explanation:
The value is decreasing by a different number each time, in the same interval
y = -5x+1
y = 3x – 2
Is (3.8) a solution of the system?
Answer: No, 3.8 is not a solution.
Step-by-step explanation:
Set -5x+1 equal to 3x-2
-5x+1=3x-2 subtract 3x making it -8x+1=-2 subtract one from both sides and get -8x=-3 divide by -8 and get -3/-8 which equals in decimal form 0.375
Check it
plug in 0.375 for X
-5(0.375)+1= -0.875
3(0.375)-2 = -0.875
It checks out ^_^
What is a simpler form of (3x-4)(x+2)?
Answer: 3x^2+2x-8
Step-by-step explanation:
Answer:
3xto the power of 2+2x -8
For Anya's birthday her father gave out colorful birthday hats that were cone shaped. Anya was very happy that day. The opening of the bottom of the hat was 5 cm and the height of the cone was 7 cm. Anya fills her hat with candy. What is the approximate volume, in cm^ ^ 3 , of candy?
please help meeee please
Isaac has a points card for a movie theater. He receives 45 rewards points just for signing up. He earns 11.5 points for each visit to the movie theater. He needs 160 points for a free movie ticket.
Answer: 10 visit
Step-by-step explanation:
Given
45 Points earned by signing up
11.5 points earned for each visit to the theatre
160 points are needed for a movie ticket
Suppose, after x visit he gets enough points to buy a movie ticket
[tex]\therefore 160=45+11.5x\\\Rightarrow 115=11.5x\\\Rightarrow x=10[/tex]
So, after 10th visit, he earns a movie ticket
The sum of two numbers is 12 and there diffrence is 8 find the 2 numbers
Answer:
10 and 2
Step-by-step explanation:
a + b = 12
a - b = 8
let 'a' = 8 + b
substitute:
8 + b + b = 12
2b + 8 = 12
2b = 4
b = 2
a must be 10 then
What is the y-intercept of a line whose equation is y = -3x - 4
Answer:
(0, -4)
Step-by-step explanation:
To find the y-intercept, set x equal to zero:
y = -3(0) - 4, or y = -4, or (0, -4)
Answer: (0,4)
Step-by-step explanation:
Which of the following statements about a rhombus is not true?
A rhombus is a parallelogram.
A rhombus has two sets of parallel sides.
A rhombus has four sides of equal length.
A rhombus has four right angles.
Answer:
„A rhombus has four right anglesv” → is not true.Step-by-step explanation:
This is a parallelogram. It is a quadrilateral with two pairs of parallel sides. Here, the opposite angles are alternate, that is, they have togheter 180°.
Rhombus
This is a rhombus. It is a quadrilateral whose four sides all have the same length. Here, the diagonals of a rhombus intersect at equal angles.
A rhombus has opposite angles equal and the figure formed by joining the midpoints of the sides of a rhombus is a rectangle, and vice versa. It has an inscribed circle.
Good luck:)
convert each of these fractions so that they share the lowest common denominator 3/4 4/5 and 5/6
The lowest common denominator is 120.
Convert 3/4: 90/120
Convert 4/5: 96/120
Convert 5/6: 100/120
DO NOT SEND ME PDFS!!!
For the three-part question that follows, provide your answer to each question in the given workspace. Identify each part with a coordinating response. Be sure to clearly label each part of your response as Part A, Part B, and Part C.
Part A: A homeowner wants to purchase new carpet for his rectangular living room, which is 8 feet wide and 12 feet long. What is the area of the carpet needed to completely cover the floor of the living room? Choose the correct answer.
A. 40 feet
B. 40 square feet
C. 96 square feet
D. 96 feet
Part B: Bianca wants to wrap a gift for her sister. The gift is in a box with a length of 10 inches, height of 2 inches, and depth of 3 inches. What is the minimum amount of wrapping paper Bianca needs to completely cover the box?
Part C: Greg had a rectangular vegetable garden that was 4 feet wide by 5 feet long. He increased the length of his garden by 2 feet and doubled the width. How many square feet larger is the area of his new garden compared to the area of his old garden? In a short paragraph, explain your answer in your own words.
A man's salary is increased by $925 to $1036. Find the percentage increase. What would have been his new salary if the increase had been 16%
Answer:
See the solutions below
Step-by-step explanation:
Initial Salary= $925
Final salary= $1036
% increase= Change/initial *100
substitute
% increase= 1036-925/925 *100
% increase=111/925 *100
% increase=0.12 *100
% increase=12%
2. Let us find 16% of $925
=16/100*925
=0.16*925
=$148
Hence the salary would have been
=148+925
=$1073
Penny is going to fly her plane to her sister's house, which is 544.32 miles away. Penny's airplane flies at an average speed of 672 miles per hour. How long does it take Penny to fly to her sister's house?
Answer:
0.81 hour
Step-by-step explanation:
Given data
Distance= 544.32 miles
Speed= 672 miles per hour.
We know that
Speed= distance/time
Substitute
672= 544.32/time
cross multiply
time*672= 544.32
time= 544.32/672
time= 0.81 hour
A sphere has a volume of approximately 24,416.64 cubic inches (using 3.14 for ).
The diameter of the sphere is ___ inches.
Answer:
diameter = 36 in.
Step-by-step explanation:
V = 4π r^3/3
24416.64 = (4(3.14) r^3)/3
73249.92 = 12.56 r^3
r^3 = 5832
r = cube root of 5832 = 18
diameter = 36 in.
