Answers
i)
length of rectangle : x + 5ii)
breadth of rectangle : x - 3iii)
area of rectangle = length * breadth105 = (x + 5)(x - 3)105 = x² + 2x - 15 x² + 2x - 15 - 105 = 0 x² + 2x - 15 - 105 = 0 x² + 2x - 120 = 0iv)
x² + 2x - 120 = 0x² + 12x -10x - 120 = 0x( x + 12) -10 (x +12) = 0(x-10)(x+12)x = 10, -12With x = -12, Not applicable so x will be 10
Length → x + 5 → 10 + 5 → 15
Breath → x -3 → 10 - 3 → 7
Therefore,
Length : 15 cm
Breadth : 7 cm
Answer:
Given:
The length of the rectangular shaped lamina is 5 cm more than the length of the square shaped lamina.The breadth of the rectangular shaped lamina is 3 cm less than the length of the square shaped lamina.x = side length of squarei) Length of rectangular shaped lamina = (x + 5) cm
ii) Breadth of rectangular shaped lamina = (x - 3) cm
ii) Area of a rectangle = length × breadth
⇒ area of rectangular shaped lamina = (x + 5)(x - 3) cm²
Given:
area of rectangular shaped lamina = 105 cm²⇒ (x + 5)(x - 3) = 105
Expand:
⇒ x² - 3x + 5x - 15 = 105
Combine like terms:
⇒ x² + 2x - 15 = 105
Subtract 105 from both sides:
⇒ x² + 2x - 120 = 0
iv) Solve x² + 2x - 120 = 0
Rewrite:
⇒ x² + 12x - 10x - 120 = 0
Break into groups:
⇒ (x² + 12x) - (10x + 120) = 0
Factorize the parentheses:
⇒ x(x + 12) - 10(x + 12) = 0
Factor out common term:
⇒ (x - 10)(x + 12) = 0
Therefore,
x - 10 = 0 ⇒ x = 10
x + 12 = 0 ⇒ x = -12
As length is positive, x = 10 only
Therefore,
Length of rectangular shaped lamina = 15 cm
Breadth of rectangular shaped lamina = 7 cm
Related Questions
Determine if true:
1y+8y+10y=20y
Answers
Answer:
False
Step-by-step explanation:
1+8=9
9+10=19
1y+8y=9y
9y+10y=19y
19y=20y
The equations dont match.
Hence, the equation is false.
Answer:
False.
Step-by-step explanation:
1+8+10 is 19. 19 is not equal to 20.
A cab ride from your home to the airport cost $23.47. If you want to tip the cab driver close to 10 percent of the fare, how much should you tip?
Answers
Answer:
$2.35
Step-by-step explanation:
Multiply $23.47 by 10%
what is the distance between the points C(2,-3) and d(10,-3)
Answers
What is the surface area of a cone that has a radius of 5 units and a
height of 10 units? Use 3.14 for i and round your answer to the
nearest whole number.
Answers
Answer:
254 units^2
I took the test and got it correct.
The surface area of a cone that has a radius of 5 units and a
height of 10 units is 508.06 square units.
What is surface area?Surface area is the total area of the exposed surfaces of a three-dimensional object. It is the sum of all the areas of the exposed faces of the object, including any curved surfaces. The formula to find the surface area of a cone is A=πr(r+√(h²+r²)).
Given that, radius of a cone is 5 units and the height of a cone is 10 units.
Surface area = 3.14×10(5+√(10²+5²)
= 508.06 square units
Therefore, the surface area of a cone that has a radius of 5 units and a
height of 10 units is 508.06 square units.
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Is there any outliers? Explanation needed, if yes. If no, then I don’t need one. Thank you!
Answers
Answer:
No there are not any outliers
Salma operates a ramen restaurant. Historically, half of customers order pork ramen, and the other half of customers are split evenly between chicken and vegetarian ramen. Salma modified the chicken and vegetarian recipes, and she wonders if customers' ordering habits will change. Here are results from a sample of 323232 orders after launching the new recipes along with a chi-square goodness-of-fit test:
Type of ramen Pork Chicken Vegetarian
Historical distribution 50% 25% 25%
Observed 15 4 13
Expected 16 8 8
Components 0.06 2 3.13
x^2 = 5.19, gl = 2
Valor p=0.075
What type of ramen contributed the most to the test statistic?
a. Pork ramen
b. Chicken remen
c. Vegetarian ramen
Answers
The type of ramen that contributed the most to the test statistic is C. Vegetarian ramen.
What is test statistic?It should be noted that test statistic simply means a method in statistics that's is used to decide whether a data supports a hypothesis.
In this case, the type of ramen that contributed the most to the test statistic is the vegetarian ramen based on the percentage allocated. There's also sufficient evidence to conclude that rte proportion changed.
Learn more about test statistic on:
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Answer: Vegetarian ramen
Step-by-step explanation:
Whats the answer for 12.3 x 1.2 =
Answers
14.76
12.3
*
1.2. =14.76
Answer:
14.76
Step-by-step explanation:
12.3 x 1.2=
12.3
x 1.2
--------
24.6
+123.0
---------
14.76
Kindly help me to solve.
Answers
Answer:
statement : ABCD is a parellogram reason: given
need help with math problem if do 5 star and brain point
Answers
Answer:
1. 7
2. 6
3. 35
Step-by-step explanation:
1. 35:60 = 7:12
2. ratio is 60:10 so 6:1 so 6
3. total number is 175.
ratio would be 175 :35 so 35:5
You play basketball at your school’s indoor stadium. You have two payment options. Option A is to buy a membership card for $20 and pay $2 each time you go to the gym, t. Option B is to pay $4 each time you go. After how many trips to the gym will the costs be the same?
The costs are the same after
trips to the gym.
Answers
Answer:
10 times
Step-by-step explanation:
Let x be the amount of times you go to the gym
Option A would be 20+2x
Option B would be 4x
now the question is after how many trips would the cost be the same?
20+2x=4x
Solve the equation so
20=4x-2x
20=2x
X=10
It would take 10 times for the cost to be the same for both options
how many times can 64 go into 865?
Answers
Answer: 12 times
Identify the percent of change as an increase or a decrease. 9 points to 4 points
Answers
Answer:
Decrease of 55.6%
Step-by-step explanation:
Because it clearly decreased,
9 - 4 / 9
5 / 9
55.6% decrease
A house is on an 80,000 square foot lot. About how many acres is the lot?
Answers
Answer:
There
Step-by-step explanation:
mark me brainliest!!
Answer:
1.836 acres
Step-by-step explanation:
Help pls help me with homework
Answers
Marcia wants to get a new car stereo. She researches the cost with a variety of local car stereo installers and places her findings in a stem-and-leaf plot
Answers
Answer:
I didn't understand properly, but if your question is what the median is, then it's $115.
Step-by-step explanation:
Don't have one sorry,
Examine the two boxes.
Box A
Box B
How much greater is the surface area of Box A than Box B?
Answers
Answer:
Box A is greater than Box B by 34.
Step-by-step explanation:
First, you need to start with finding the surface area of every individual side on Box A we have side A, B, and C. After finding the individual area for each side, double each area because there is two of each side. This is the the same method you apply to Box B.
Then subtract the surface area of Box B from Box A.
The number of paintings Jurnee can make varies directly with the amount of time she spends making the paintings. She can make two paintings in 1/4 week. How many paintings can Jurnee make in three weeks?
Answers
Answer:
24 is the answer
Step-by-step explanation:
1/4x4=2 per 1/2 week she can make 4
1/2x4=8 per week
and 8x3=24 so 24 per week
I hope this helped :)
In quadrilateral ABCD, AB ||CD which additional peice of information is needed to determine that ABCD is a parallelogram
Answers
Answer:
BC||AD
Step-by-step explanation:
A parallelogram is said to be parallelogram iff it's opposite pairs of sides are parallel to each other.
Since one pair is parallel (given)
then another pair needs to be parallel.
Hence BC||AD
(b) The pizzeria sold 85 pizzas yesterday. Suppose the number of pizzas sold today was 60. Determine the percent increase or decrease in the pizzas sold, rounded to the nearest hundredth. Show your work.
_____________ % (Increase or decrease?)
PLEASE SHOW WORK thank you :D
Answers
Answer:
The difference is 21.21%
work shown below
Step-by-step explanation:
I'm going to first find the difference between both.
85-60=25
Now, we have to find 25% of 85
We don't have to use the formula, we can do this in our brain, like this -
We can see that 25% of 80 = 20, since 25 = 1/4, and 1/4 of 80 = 20, then, there is the 5 part left, how do we find that??? well, 25% of 5 = 1.25, since 1.25x5=5,
So hence, our answer is 21.25
Hi! 29.4118 (decrease) is your answer. My work's below!
- - - - - - - - - - - - - - - - - - - -
Here's a formula for percentages I've used...
(Old # - New # ) /Old # x 100
- - - - - - - - - - - - - - - - - - - -
In this case, the old number is 85, and the new number (today's pizza number) is 60.
(85 - 60) / 85 x 100 =
(85 - 60 = 25)
25 / 85 = 0.29411764705
0.29411764705 x 100 = 29.411764705
Now, round it to the nearest hundredth.
29.4118 (decrease)
- - - - - - - - - - - - - - - - - - - -
Good luck! :)
~pinetree
mathematics help ...
no links
Answers
Answer:
Ok ------------------
Maya has 760 carrots. 27% of them went rotten. What number of the carrots ARE'NT rotten?
Answers
Answer:
About 554 carrots aren't rotten.
Step-by-step explanation:
100% - 27% = 73%
73% = 0.73
760 x 0.73 = 554.80
Answer:
205.2 carrots went rotten
Step-by-step explanation:
27% of 760 = 205.2
I hope I'm not too late and that this helps!
If it does, please give me brainliest :)
Paul, Shawn and Tim have a box of marbles. Paul has 1/5 of the marbles. Shawn has 3/8 of the remainder and Tim has has the rest of the marbles. Tim has 84 marbles more than Paul. How many marbles are in the box?
Answers
Answer:
374 marbles
Step-by-step explanation:
Paul (P) has 1/5 this was given
Shawn (S) has 3/8 this was given
That means Tim (T) must have 17/40 because 1/5 + 3/8 = 23/40 and 1- 23/40 = 17/40
Those are the fractional amounts each boy has. We can set up an equation based on the information in the problem to get the total number of marbles (M). Tim has 84 marbles more than Paul. Thus, Tim has a greater number of marbles. 84 more, to be exact. Our equation would then look like this:
P+84=T
Because we have three unknowns, we need three equations. Thus, we need two more, but we can get them from our fractions at the top.
We need to have a question where we find the total number of marbles.
We know that Paul has 1/5 of the marbles. We can use M to represent the total number of marbles.
P = (1/5)M
T= (17/40)M
We had this from before: P+84=T
If we substitute into the equation:
(1/5)M + 84 = (17/40)M
Now there is only one variable in the equation and we can solve for M.
For M, I got 1120/3 which simplifies to 373 and 1/3, since there cannot be 1/3 of a marble, we can round to 374. There are three hundred, seventy-four marbles in the box.
If you want to check the answer, you can put (1120/3) back in for M in the third equation and you will see that each side is equivalent.
Solve for all missing sides and angles.
Answers
Answer:
Step-by-step explanation:
Sum of interior angles in a triangle is 180degree.
<B + 15degree + 45degree = 180degree
<B = 180 - 45 - 15 = 120 degree
By sine rule,
sin<B / AC = sin<C / AB = sin <A / BC
sin120degree / 200 = sin15degree / AB = sin45degree / BC
AB = 200*sin15degree/sin120degree
= 59.77
BC = 200*sin45degree/sin120degree
= 163.30
Find the s.....................
Answers
Answer:
AC = 8
Step-by-step explanation:
Area of kits is half the product of diagonals
[tex]Area\; of \;kite = \frac{d_1d_2}{2}\\\\36 = \frac{AC*BD}{2} \\\\36 = \frac{AC(6+3)}{2} \\\\36*2 =9AC[/tex]
AC = 72/9
AC = 8
What is the volume of a cube whose edge measures 21 centimeters each
Answers
Question :-
What is the Volume of a Cube, whose Edge measures 21 cm each .Answer :-
Volume of the Cube is 9261 cm³ .[tex] \rule {180pt} {2pt} [/tex]
Given :-
Edge of the Cube = 21 cmTo Find :-
Volume of the Cube = ?Solution :-
As per the provided information in the given question, we have been given that the Edge of the Cube is 21 cm . And, we have been asked to calculate the Volume of the Cube .
For calculating the Volume , we will use the Formula :-
Volume of Cube = ( edge )³Therefore , by Substituting the given values in the above Formula :-
⇒ Volume = ( edge )³
⇒ Volume = ( 21 )³
⇒ Volume = 21 × 21 × 21
⇒ Volume = 441 × 21
⇒ Volume = 9261
Hence :-
Volume = 9261 cm³ .[tex] \underline {\rule {180pt} {4pt}} [/tex]
HELPPP PLS SHOW WORK
Answers
Answer:
61
Step-by-step explanation:
1. let the unknown be x
2. using theorem of Pythagoras that states the hypotenuse will be equal to the sum of the other two sides we can determine that 75=14+X
3. this implies that X=75-14
4. therefore X= 61
Out of 3500 students of a school, only 36% passed. How many students failed?
Answers
Answer:
2240
Step-by-step explanation:
If 36% out of 100% passed, then
100% - 36% = 64% failed
64% of 3500 = 0.64 × 3500 = 2240
Explanation: using the percentage, move the decimal back two spaces.
36 >>> 3.6 >>> 0.36
Now multiply 0.36 times 3500 to find out how many students PASSED. You get 3500 x 0.36 = 1260.
Finally, to find out how many FAILED, subtract how many PASSED (1260) from the total (3500) to get 3500 - 1260 = 2240
It takes 5 minutes for an individual to shower. Of each person showers twice per day, approximately how long does each person spend showering in a year?
Answers
Answer:
c
Step-by-step explanation:
Beejjj
Each person spends 2.53 days showering in a year.
What is algebra?Algebra is a study of mathematical expressions, in which numbers and quantities are represented in formulas and equations by letters and other universal symbols.
Given that,
Time taken by one person to shower = 5 minutes.
Also, one person take shower 2 times in a day.
Total time taken to shower twice per day = 5 x 2 = 10 minutes.
Since, in one year total number of days = 365.
Time taken to shower in 365 days = 365 x 10 = 3650 minutes.
In one day total number of minutes = 24 x 60 = 1440 minutes.
Total days = 3650 / 1440 = 2.534722 days = 2.53
Person showers for 2.53 days in a year.
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6. One side of a rhombus is 14 inches long, and one diagonal of the rhombus is 15 inches
long. What is the area, in square inches, of the rhombus?
Answers
Answer:
3.31
Step-by-step explanation:
14ª1 is 718th 15/10 is equal to 15 and 10 tenths
Prove triangle congruence by SSS and SAS
Answers
Answer:
Step-by-step explanation: