Answer:
The dimensions of rectangle are 12 m and 4.5 mStep-by-step explanation:
Given that, The length of a rectangle is 3 m more than twice the width, and the area of the rectangle is 54 m²
Let's assume width of rectangle be x m and length be 3 + 2x m respectively. To find the dimensions of the rectangle we will use the formula of Perimeter of rectangle
[tex] \\ { \underline{ \boxed{ \pmb{ \sf{ \purple{Area _{(rectangle)} = Length × width}}}}}} \\ \\ [/tex]
Substituting values in above formula:
[tex] \\ \dashrightarrow \sf \: \: (3 + 2x)(x) = 54 \\[/tex]
[tex]\dashrightarrow \sf \: \: 3x + 2x^2 = 54 \\ [/tex]
[tex]\dashrightarrow \sf \: \: - 54 + 3x + 2x^2 = 0 \\ [/tex]
[tex]\dashrightarrow \sf \: \: 2x^2 + 3x - 54 = 0\\ [/tex]
[tex]\dashrightarrow \sf \: \: 2x^2 + 12x - 9x - 54 = 0\: [/tex]
[tex]\dashrightarrow \sf \: \: 2x(x + 6) -9(x + 6) = 0\\ [/tex]
[tex]\dashrightarrow \sf \: \: (2x -9)(x+6) = 0 \\ [/tex]
[tex]\sf{x=}{\sf{\dfrac{9}{2}}}{\sf{\: or\: -6}} [/tex]
[tex]\dashrightarrow \: \: { \underline{ \boxed{ \pmb{ \sf{\purple{ x = 4.5 }}}}}}[/tex]
Hence,
Length of rectangle = 3 + 2x = 3 + 2(4.5) = 12 mWidth of the rectangle = x = 4.5m[tex] \\ { \underline{ \pmb{ \frak{ \therefore Length \: and \: width \: of \: the \: rectangle \: is \:12 \: m \: and \: 4.5 \: m}}}} \\ [/tex]
Answer:
The dimensions of rectangle are 12 m and 4.5 mStep-by-step explanation:
Given :-
The length of a rectangle is 3 m more than twice the width the area of the rectangle is 54 m²To find :-
Dimensions of rectangleSolution:-
According to the question ,
Let the width of rectangle be x and length of rectangle be 2x+3 m
Area of rectangle :- L×B
L×B = 54m²
(2x+3) * x = 54m²
x = 4.5 m
By putting the value of x , we get
Length :- 2x+3 = 12 m
Width :- 4.5 m
Solve the following equation:
3 x seven tenths
=================================================
Here, we have to multiply fractions.
How to Multiply Fractions?
Here are the steps:-
Turn any whole numbers into fractions (example:- 3 = 3/1)Multiply the numerator of the first fraction times the numerator of the 2nd fraction; same with the denominator.Simplify if necessary.So let's do it.
Step 1:-
[tex]\longmapsto\sf{3=\displaystyle\frac{3}{1}[/tex]
Step 2:-
[tex]\longmapsto\sf{\displaystyle\frac{3}{1} *\frac{7}{10}}[/tex]
[tex]\longmapsto\sf{\displaystyle\frac{21}{10} }[/tex]
We can't simplify this fraction, but there's something else we can do:-
Convert this improper fraction into a mixed numberHere's the answer:-
[tex]\boxed{\sf{2\displaystyle\frac{1}{10} }}[/tex]
=====================================================
note:-Hope everything is clear; if you need any explanation/clarification, kindly let me know, and I will comment and/or edit my answer :)
PLEASE HURRY AND HELP ME WITH THIS !! ILL GIVE BRAINLIEST
Answer:
C. Reflection, translation
Step-by-step explanation:
If we compare Figure A to Figure B, you might notice that they mirror each other. This means that Figure A was reflected. Now, if we take a look at Figure B and Figure C, you should see that both figures are the exact same shape, size, and facing the same direction. The only thing that changed was the location. So, this means that Figure B was translated.
I hope this helps! Have a lovely day!! :)
Gotten two different answers…is it 18 or 55
Answer:
18.2%
Step-by-step explanation:
For this, you want to take the amount of 70 year old men that will die in the next 10 years and divide it by the total amount of men.
The table states "number out of 1,000 men" so this means there are 1000 total men in this study.
So:
182/1000 = 0.182 = 18.2%
the graph of f x shown below resembles the graph of g =x2 but it has been stretched somewhat and shifted which of the following could be the equation of f
The graph of the function g(x) is a quadratic equation
The possible equation of the function f(x) is f(x) = 2(x - 3)^2 + 3
How to determine the possible equation of f(x)?From the question, we have:
g(x) = x^2 --- the equation of the graph
The function f(x) is in the first quadrant.
This means that the function g(x) is shifted right and up.
This is represented as:
f(x) = (x - h)^2 + k
When stretched, the function becomes
f(x) = a(x - h)^2 + k
Where:
a > 0
From the list of given options;
The equation that has the form f(x) = a(x - h)^2 + k is
f(x) = 2(x - 3)^2 + 3
Hence, the possible equation of the function f(x) is f(x) = 2(x - 3)^2 + 3
Read more about function transformation at:
https://brainly.com/question/17586310
In how many ways can first, second, and third prizes be awarded in a contest with 210 contestants?
Answer:
Not entirely sure about this because it was grabbed from someone else
There are 210 ways to win 1st place
There are 209 ways to win 2nd place
There are 208 ways to win 3rd place
Every time an award is won, a spot if taken, therefore one person is eliminated from possibly taking that spot.
Hope that makes sense :)
The total number of ways of contestants can win first, second, and third prizes will be 9,129,120.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
The number of contestants is 210.
The number of ways of contestants who won the first prize will be given as,
⇒ ²¹⁰C₁
⇒ 210
The number of ways of contestants who won the second prize will be given as,
⇒ ²⁰⁹C₁
⇒ 209
The number of ways of contestants who won the third prize will be given as,
⇒ ²⁰⁸C₁
⇒ 208
Then the total number of ways of contestants can win first, second, and third prizes will be
⇒ 210 x 209 x 208
⇒ 9,129,120
The total number of ways of contestants can win first, second, and third prizes will be 9,129,120.
More about the permutation and the combination link is given below.
https://brainly.com/question/11732255
#SPJ2
PU
The data set below represents the different costs of a refrigerator at a local home improvement store.
$777, $498, $619. $379. $895, $1,256, $1,052
b. What is the median of the second half of the data? (third quartile) 379
T
Using the median concept, it is found that the third quartile is of is of $1,052.
What is the median of a data-set?The median of the data-set separates the bottom half from the upper half, that is, it is the 50th percentile.
In this problem, the ordered data-set is:
$379, $498, $619, $777, $895, $1,052, $1,256.
Hence, the median of $777 divides the data-set into two halfs:
The first half is: $379, $498, $619.The second half is: $895, $1,052, $1,256.Hence, the third quartile, which is the median of the second half, is of $1,052.
More can be learned about the median concept at https://brainly.com/question/25215461
99 PTS PLS HELP! Community volunteers helped clean 7 local parks. They each recorded the number of garbage bags they filled and arranged their data from least to greatest. The number of bags filled was 1, 2, 2, 3, 4, 4, and 5. The mean number of garbage bags filled was 3.
What is the MAD (mean absolute deviation) rounded to the nearest tenth?
1.1
1.3
2.3
3.0
Answer: 1.1
Step-by-step explanation:
To find the MAD (mean absolute deviation) we subtract the mean from each data value, and take the absolute value. Then we take the average of all the values. It looks like this:
1 - 3 = -2 -> |-2| = 2
2 - 3 = -1 -> |-1| = 1
2 - 3 = -1 -> |-1| = 1
3 - 3 = 0
4 - 3 = 1
4 - 3 = 1
5 - 3 = 2
-
[tex]\frac{2+1+1+0+1+1+2}{7}[/tex]
[tex]\frac{8}{7}[/tex]
1.14
The mean absolute deviation is about 1.1
After plotting the data where x=the side of a polygon, and f(x) = the area of the polygon, Jack used technology and
determined the appropriate model to approximate the area of the polygon, F(x) = x^2 + 3x + 2. Use the model Jack
created to predict the area of a polygon that has a side length of 3.
10
18
19
020
Answer: 19
Step-by-step explanation:
As per the model created by Jack; f(x) determines the area and x represents length so f(3) = 9+9+1
Therefore, f(3) = 19
Write the equation of a parabola with focus at (1,-4) and a directrix at X=2
Answer:
The equation of a parabola is
[tex]x = \frac{1}{4(f - h)} (y - k) ^{2} + h[/tex]
Step-by-step explanation:
(h,k) is the vertex and (f,k) is the focus.
Thus, f = 1, k = −4.
The distance from the focus to the vertex is equal to the distance from the vertex to the directrix: f - h = h - 2.
Solving the system, we get h = 3/2, k = -4, f = 1.
The standard form is:
[tex]x = - \frac{y ^{2} }{2} - 4y - \frac{13}{2} [/tex]
The general form is:
[tex]2x + {y}^{2} + 8y + 13 = 0[/tex]
The vertex form is:
[tex]x = - \frac{(y + 4) ^{2} }{2} + \frac{3}{2} [/tex]
The axis of symmetry is the line perpendicular to the directrix that passes through the vertex and the focus: y = -4.
The focal length is the distance between the focus and the vertex: 1/2.
The focal parameter is the distance between the focus and the directrix: 1.
The latus rectum is parallel to the directrix and passes through the focus: x = 1.
The length of the latus rectum is four times the distance between the vertex and the focus: 2.
The eccentricity of a parabola is always 1.
The x-intercepts can be found by setting y = 0 in the equation and solving for x.
x-intercept:
[tex]( - \frac{13}{2} \: ,0)[/tex]
The y-intercepts can be found by setting x = 0 in the equation and solving for y.
y-intercepts:
[tex](0, - 4 - \sqrt{3)} [/tex]
[tex](0, - 4 + \sqrt{3)} [/tex]
Aaron has $25 to spend at the carnival. Admission is $4.00 and the ride tickets are $1.25 each. What is the maximum number of ride tickets that Aaron can buy? Write and solve the inequality.
Answer:
25 dollars divided by 1.25 dollars gives a total of 20 tickets Aaron can buy
Moose left a $7.50 tip for his waitress on a $50 restaurant bill. What percent of his bill did he leave as a tip?
Answer:
he left 15 % of his bill as a tip
Step-by-step explanation:
7.5/50 x 100
0.15 x 100
15
Percentage
7.5/50×1000.150(100)15.0%Which number line shows the solution set for l s/2 +4 l <2
Step-by-step explanation:
Hopefully this was helpful!
Determine whether each of these sets is countable or un- countable. For those that are countably infinite, exhibit a one-to-one correspondence between the set of positive integers and that set. a. integers not divisible by 3 b. integers divisible by 5 but not by 7 c. the real numbers with decimal representations con- sisting of all 1s d. the real numbers with decimal representations of all 1s or 9s
Answer:
i do not understand the questions
Step-by-step explanation:
A bag of fruit contains 3 apples, 2 oranges, 1 banana, and 4 pears, Gerald will randomly select two pieces of fruit
one at a time from the bag and not put them back. What is the probability that the first piece of fruit Gerald selects will be a banana and the second piece of fruit will be a pear?
Answer:
2/45
Step-by-step explanation:
The probability that a banana is picked for the first one is:
1/10
because there are 10 fruits and one of them is a banana,
Then, the second piece has to be a pear.
For this we have already picked one fruit out of the bag, which leaves 9 fruits in the bag.
There are 4 pears so the probability of picking a pear second is
4/9
To find the probability of a banana and then a pear, you want to multiply these values together
So:
1/10 x 4/9 = 4/90 = 2/45
So the probability is 2/45
Please help this is due
[tex]\text{Area of equilateral triangle ABC}\\ \\=\dfrac{\sqrt 3}{4} BC^2\\\\=\dfrac{\sqrt 3}4 \cdot 12^2\\\\=\dfrac{144\sqrt 3}{4}\\\\=36\sqrt 3[/tex]
Malcolm draws this map of his neighborhood . Help please and thank you!!!!!
Answer:
Alden, perpendicular, Elm, parallel
Step-by-step explanation:
.......................................
Answer:
what is your question??????
Step-by-step explanation:
A private club grew by 7 members each week for 63 weeks. What was the total change in the club's size? members
Answer:
The answer is 441
Step-by-step explanation:
7 x 63 = 441
Hooray! Poplin Elementary collected 1,224 Box Tops! The 8 volunteer moms will have to tape them to the turn-in sheet. If they share the work equally, how many will each mom need to do?
Fourth Grade
Memory Jogger Week 5 I need helppppp
Answer:
I can help you what you need help with
Step-by-step explanation:
what decimal part of one dollar is two dimes
Answer: Tenths place.
Step-by-step explanation:
0.20
The 2 is part of the tenths place.
Answer:
$0.20
Step-by-step explanation:
1 penny = $0.01
1 nickel = $0.05
1 dime = $0.10
1 quarter = $0.25
Two dimes = $0.20
Or 1/4 of a dollar
Or 0.2 because you don't need to add a 0 at the end of .2 or the $ sign.
Which of the following shows the correct solution steps and solution to 7x- 4 = -182 7x - 4 = -18 71 - 4+4= -18 + 4 72 = -14 A. 72 -14 7 7 = -2 70 – 4= -18 72 - 4+4= -18 + 4 70 = -14 7x - 14 -7 -7 B. = 2
Answer/Step-by-step explanation:
7x- 4 = -182
Step:
Add 4 to both sides
7x - 4 + 4 = -182 + 4
Simplify
7x = -178
Divide both sides by 7
7x/7 = -178/7
Simplify
x = -178/7
Decimal form = -25.4285714286
~lenvy~
Answer:
x = -178/7
Step-by-step explanation:
Given us that:
Which of the following shows the correct solution steps and solution to 7x- 4 = -182
Thus, the steps are:
Adding 4 to both sides
7x - 4 = -182
+4 +4
------------------------
7x = -178
Divide both sides by 7
7x/7 = -178/x
Simplify
x = -178/7
Solution - x = -178/7
[RevyBreeze]
What is the slope of the line with equation y-3=-1/2 (x-2)?
Hello!
This equation is written in Point-Slope Form (y-y₁=m(x-x₁)
Where
y₁=y-coordinate of the point
m=slope
x₁=x-coordinate of the point
In this case, the slope is
[tex]\boxed{\boxed{\bold{\frac{1}{2}}}}[/tex]
Hope everything is clear.
Let me know if you have any questions!
#KeepLearning
:-)
Answer:
C) 1/2
Step-by-step explanation:
woof woof
A library had 6422 music CDs stored on 26 shelves.If the same number of CDs were stored on each shelf how many CDs were stored on each shelf
one shell stores CDs:6422/26
246
can some help me figure this out
Answer:
e
Step-by-step explanation:
e
What is 65% of (102/2)
Answer:
33.15
Step-by-step explanation:
102/2 = 51
65% of 51 = 33.15
Answer:
65% of (102/2) is 33.15
Step-by-step explanation:
I used a calculator and got this answer, it is correct. Have a nice day :)
if the length of a rectangle is 3 times of its breadth and perimeter is 96cm find the length and breadth of rectangle
Solve (images attached) can u check if correct
Answer:
Yes it's correct
Step-by-step explanation:
90 + 40 = 130
180 - 130 = 50
Choose an appropriate metric unit for the mass of bowling ball
A)
kilogram
B)
milligram
C)
meter
D)
gram
Answer:
i think that the correct answer would A
Step-by-step explanation:
hope this helps
PLEASE HELP I WILL GIVE BRAINLIEST
Step-by-step explanation:
37×2=74
360-74 = 286
286 ÷ 2=143
Of course, if AD and BC , and also BA and CD are even.