Answers
Step-by-step explanation:
[tex]area \: of \: rectangle = length \times \: width[/tex]
Given
[tex]l = 2w - 3[/tex]
using this
[tex]area = l \times w = (2w - 3)(w) = 27[/tex]
[tex]2 {w}^{2} - 3w = 27[/tex]
[tex]2 {w}^{2} - 3w - 27 = 0[/tex]
[tex]2 {w}^{2} - 9w + 6w - 27 = 0[/tex]
[tex]2w(w - 4.5) + 6(w - 4.5) = 0[/tex]
[tex](2w + 6)(w - 4.5) = 0[/tex]
[tex]w = - 3 \: \: or \: \: w= 4.5[/tex]
Since size cannot be negative therefore
[tex]w = 4.5cm[/tex]
[tex]l = 2w - 3 = 9 - 3 = 6[/tex]
Hence length of the rectangle=6m
width of the rectangle=4.5m
Answer:
Let length and breadth of rectangle be x metres and y metres respectively.
xy = 27 ---- eqn 1
x = 2y-3 ---- eqn 2
Sub eqn 2 into eqn 1:
(2y-3) × y = 27
2y² - 3y = 27
2y² - 3y - 27 = 0
(y+3)(2y-9) = 0
y+3=0 or 2y-9=0
y=-3 (rejected) 2y=9
y=4.5
Sub y=4.4 into eqn 2:
x = 2(4.5) - 3
= 6
Hence,
length of rectangle = x metres
= 6m
breadth of rectangle = y metres
= 4.5m
Related Questions
VERY EASY ITS FOR MY COUSIN AND I CANT FIGURE IT OUT NEITHER CAN SHE
A construction team builds a brick wall in 2 weeks. At the end of the
first week, the wall is 3.6 meters high. During the second week, the
team makes the wall 2.25 meters higher. The final height of the wall is
1.3 times the originally planned height.
How tall was the wall originally going to be?
Answers
Answer:
4.5 meters high
Step-by-step explanation:
3.6 + 2.25 = 5.85. 5.85 divided by 1.3 is 4.5.
4. Mindy has two secret numbers. Her numbers are prime numbers and they are between the
numbers 18 and 25. List Mindy's two numbers.
19, 25
18, 25
24, 25
19, 23
Answers
Answer:
19 23
Step-by-step explanation:
19 and 23 are the only primes in her range
Select all the statements that are true. Explain your reasoning
4−2(3+7)=4−2⋅3−2⋅7
4−2(3+7)=4+−2⋅3+−2⋅7
4−2(3+7)=4−2⋅3+2⋅7
4−2(3+7)=4−(2⋅3+2⋅7)
Answers
Answer:
First and second are both true.
Third and fourth are not true.
Step-by-step explanation:
4−2(3+7)=4−2⋅3−2⋅7
4−2(3+7)= 4 - 2(3+7) [ -2*3 - 2*7 : the -2 can be removed from -2*3-2*7 to make -2(3 + 7); communative] This results in 4-2(3+7), the same on the left side
4−2(3+7)=4+−2⋅3+−2⋅7
The (4+-2*3+-2*7) can be written as (4-2*3-2*7) to simplify the "-+" to simply "-". That can be written as 4 - 2(3+7), the same as on the left side.
4−2(3+7)=4−2⋅3+2⋅7
The right side, 4-2*3+2*7, can be written as 4-2(3-7), which is NOT the same as on the left.4−2(3+7)=4−(2⋅3+2⋅7)
The right side can be written as 4-2(3-7), which is not the same as on the left side.Imani earned $48 in interest after two years on an account that paid 8% simple interest annually. Use the formula I = Prt to find Imaríi's principal balance.
$30.00
$76.80
$300.00
$768.00
Answers
Answer:
I=$48
t=2 years
r=8%
Principal=(I×100)/(t×r)
($48×100)/(2×8)
$4800/16
$300
What is the similarity statement that goes with the image, sorry I couldn't find the symbols.
white up pointing triangle S T R tilde white up pointing triangle S Q R
white up pointing triangle S T R tilde white up pointing triangle T Q R
white up pointing triangle S T R tilde white up pointing triangle R T Q
white up pointing triangle S T R tilde white up pointing triangle R S T
Answers
Answer: Option (3)
Step-by-step explanation:
What’s The Answer Of This? Please Answer ASAP
Answers
Answer:
c) 80⁰
isosceles triangle, two sides and angels are equal.
Step-by-step explanation:
180⁰= full triangle
80⁰+20⁰=100⁰
180-100=80⁰
A spinner with 8 equally sized slices has 8 yellow slices. The dial spun and stops on a slice at random. What is the probability that the dial stops on a yellow slice? Write your answer as a fraction in the simplest form.
Answers
The range of which function is (2, infinity)? y = 2x y = 2(5x) y = 5x 2 y = 5x 2
Answers
The function which has range (2, infinity) from the provided function is y = 5ˣ +2. Option 4 is correct.
What is range of function?Range of a function is the set of all the possible output values which are valid for that function.
The function whose range is (2, ∞) has to be find out.
The first function given in the problem is,
[tex]y=2^x[/tex]
This function has the periodic function with period of logarithmic function and the range of this function is all the real number. This is not the correct option.
The second function given in the problem is,
[tex]y=2(5)^x[/tex]
This function has the periodic function with period of logarithmic function and the range of this function is all the real number. This is not the correct option.
The fourth function given in the problem is,
[tex]y=(5)^x+2[/tex]
This function is translated 5 units up to the function 5ˣ which has the range (0,∞).
Thus, the range of this function is (2, ∞).
Hence, the function which has range (2, infinity) from the provided function is y = 5ˣ +2. Option 4 is correct.
Learn more about range of the function here;
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Answer:
D ) y = 5^x + 2
Step-by-step explanation:
Here ya go ladies and gentlemen
A standard deck of playing cards is shuffled and three people each choose a card. Find the probability that the first two cards chosen are diamonds and the third card is black if the cards are chosen without replacement.
Answers
Answer:
don't worry about this question
Need help 10 points
Answers
Answer:
The answer is B :)
Step-by-step explanation:
The closed dot means less than or equal to. That is why b is correct :)
Have an amazing day!!
Please rate and mark brainliest!!
Answer:
no a, is the answer not b. salamat po
If secθ = -6.743, find the two values of θ
between 0° and 360°. Round your answers to one
decimal place.
Answers
Answer:
Θ ≈ 98.5° , 261.5°
Step-by-step explanation:
using the identity
cosΘ = [tex]\frac{1}{sec0}[/tex] , then
cosΘ = [tex]\frac{1}{-6.743}[/tex] ≈ - 0.1483
since cosΘ < 0 then Θ is in 2nd and 3rd quadrants
Θ = [tex]cos^{-1}[/tex] (- 0.1483) ≈ 98.5° ← in 2nd quadrant
related acute angle = 180° - 98.5° = 81.5° , then
Θ = 180° + 81.5° = 261.5° ← in 3rd quadrant
using the completing square method, what are the zeros of the quadratic function f(x) = 2x2 -3?
Answers
[tex]~~~~~2x^2 -3 =0\\\\\implies 2x^2 = 3\\\\\implies x^2 =\dfrac 32\\\\\implies x = \pm\sqrt{\dfrac 32 }[/tex]
Cooper gave out a survey to some students in his school about their favorite color. Students could choose between red and blue. 129 of those surveyed said their favorite color was red. 57% of the students surveyed said their favorite color was blue. How many students were surveyed in total?
Answers
Using proportions, it is found that since 43% of the total amount is 129, 300 students were surveyed in total.
What is a proportion?A proportion is a fraction of a total amount.
In this problem, since 57% of the students surveyed said their favorite color was blue, hence 100 - 57 = 43% said it was red, and this amount is of 129 students, hence:
0.43n = 129
n = 129/0.43.
n = 300.
300 students were surveyed in total.
More can be learned about proportions at https://brainly.com/question/27396612
A right rectangular prism has a square base, with sides that are each 2 meters in length. The height of the prism is 34 meters. Find the volume of the prism in cubic meters
Answers
Answer:
136m
Step-by-step explanation:
The formula for the volume of a rectangular prism is V = L · W · H
We can take the given values and multiply them to find our answer.
L = 2
W = 2
H = 34
2x2x34 = 136
The volume of the rectangular prism will be 136 cubic meters.
What is a rectangular prism?A rectangular prism is a solid three-dimensional shape with six faces and rectangular bases. A rectangular prism is also a cuboid. A cuboid and a rectangular prism have the same cross-section.
Given that a right rectangular prism has a square base, with sides that are each 2 meters in length. The height of the prism is 34 meters.
The formula for the volume of a rectangular prism is V = L · W · H
We can take the given values and multiply them to find our answer.
L = 2
W = 2
H = 34
The volume of the prism will be calculated as,
V = 2x2x34
V = 136 cubic meters
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Veronica painted 6 doghouses. She used 5 quarts of paint. If she used the same amount of paint for each doghouse, how many quarts of paint did she use on each doghouse?
Answers:
A 1/5
B 5/6
C 1/6
D 6/5
Answers
Answer:
A. 1/5
Step-by-step explanation:
First, you do 6 and divide it by 5. 6 divided by 5 is 1/2. 1/5 times 6 equals 1/2.
help me out and please provide steps
Answers
Answer:
3(x+2)/(2(x+4))
Step-by-step explanation:
A compound fraction is simplified by rewriting it as a simple fraction, and reducing it to lowest terms by cancelling common factors from numerator and denominator. The division of one fraction by another is accomplished in the usual way: multiply the numerator by the inverse of the denominator.
__
[tex]\dfrac{\left(\dfrac{6x^2-24}{x^2+7x+12}\right)}{\left(\dfrac{4x^2-4x-8}{x^2+4x+3}\right)}=\left(\dfrac{6x^2-24}{x^2+7x+12}\right)\times\left(\dfrac{x^2+4x+3}{4x^2-4x-8}\right)\\\\=\dfrac{6(x-2)(x+2)}{(x+3)(x+4)}\times\dfrac{(x+1)(x+3)}{4(x-2)(x+1)}=\dfrac{3(x-2)(x+1)(x+2)(x+3)}{2(x-2)(x+1)(x+3)(x+4)}\\\\=\boxed{\dfrac{3(x+2)}{2(x+4)}}[/tex]
what is 0.24x2.412 step by step
Answers
Answer:
0.57888
Step-by-step explanation:
0.24
2.412
----------
0.57888
Hope I helped
Which term is defined as two intersecting lines that form four right angles in a plane?.
Answers
Answer:
Perpendicular.
Step-by-step explanation:
Two lines that come together and form 4 angles are known as perpendicular lines.
The radius and center of circle C are shown. Use 3.14 for pi . Round to the nearest tenth.
Answers
Answer:
See below
Step-by-step explanation:
Circumference = pi * d = 18 pi inches
Area = pi r^2 = pi * 9^2 = 81 pi in^2
Can you tell us what the missing number is in this sequence? 7,10,15,22, ?, 42
Answers
so it would be counting up from 3,5,7…
in this case 22 + 9 is 31
answer = 31
Answer:
31
the difference between the numbers is the number, plus 2, so for example, the difference between 7 and 10 is 3, add two and you have 5, and ten plus 5 equals 15. Using this formula, we have 5+2=7, which is 15+7=22. For the missing number, we have 7 (the last number used) +2=9, so, 22+9=31.
Step-by-step explanation:
im kinda bad at explaining things, but i really hoped this helped :)
find the inverse of the function
Answers
If h⁻¹(x) is the inverse of h(x), then by definition of inverse function,
h(h⁻¹(x)) = x
Given that h(x) = 6∛(2x + 5) - 1, we have
h(h⁻¹(x)) = 6∛(2 h⁻¹(x) + 5) - 1 = x
Solve for h⁻¹(x) :
6∛(2 h⁻¹(x) + 5) - 1 = x
6∛(2 h⁻¹(x) + 5) = x + 1
∛(2 h⁻¹(x) + 5) = (x + 1)/6
[∛(2 h⁻¹(x) + 5)]³ = [(x + 1)/6]³
2 h⁻¹(x) + 5 = (x + 1)³/216
2 h⁻¹(x) = (x + 1)³/216 - 5
h⁻¹(x) = (x + 1)³/432 - 5/2
If the area of this rectangle is 55 square units, what is the perimeter. Help asap
Answers
Answer:
32 unit is your correct answer
Answer:
Step-by-step explanation:
the answer is 32
What is the additive inverse of the polynomial –9xy2 6x2y – 5x3? –9xy2 – 6x2y 5x3 –9xy2 – 6x2y – 5x3 9xy2 6x2y 5x3 9xy2 – 6x2y 5x3
Answers
The additive inverse of the given polynomial is
-f(x,y)=-9xy^2+6x^2y-5x^3
You have the polynomial f(x,y)=-9xy^2+6x^2y-5x^3.
What is the additive inverse of a polynomial?Additive inverse means changing the sign of the number and adding it to the original number to get an answer equal to 0.
The additive inverse of a polynomial f(x,y) is a polynomial that makes zero when it is added to polynomial f(x,y).
So additive inverse of polynomial f(x,y) will be -f(x,y).
Thus, the additive inverse will be
-f(x,y)=-9xy^2+6x^2y-5x^3
To learn more about the additive inverse visit:
https://brainly.com/question/1548537
Answer:
D
Step-by-step explanation:
Nicholas is 12 years old and he has collected 459 trading cards. Phillip is 14 years old and he has collected 721 trading cards. How many more cards does Phillip have than Nicholas?
Phillip has _____
more cards than Nicholas.
Answers
Answer: Phillip has 262 more cards than Nicholas
Step-by-step explanation:
Since we are looking for how many more cards Phillip has compared to Nicholas we can subtract Nicholas' amount from Phillip's amount to see how much more he has.
721-459=262
Taking a simple difference, we can see that Phillip has _262_
more cards than Nicholas.
How many more cards does Phillip have than Nicholas?To find this, we need to take the difference between the number of cards that Philip has and the number of cards that Nicholas has, so we just need to solve a subtraction:
Phillip's cards - Nicholas' cards
Where:
Phillip's cards = 721
Nicholas' cards = 459
Then the difference is:
721 - 459 = 262
So we can see that Phillip has 262 more cards than Nicholas.
Learn more about differences at.
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Isabelle runs a restaurant that offers a children's menu. This past week, 20 children ate at her restaurant, and 8 of them ordered grilled cheese. What is the probability that a randomly selected child eating in Isabelle's restaurant this past week ordered grilled cheese?
Write your answer as a fraction or whole number
Answers
What is trigonometry and where is it used?
Answers
Answer:
Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures. Trigonometry developed from a need to compute angles and distances in such fields as astronomy, mapmaking, surveying, and artillery range finding.
What is the mean of the set of data?
25.2, 26.4, 28.7, 25.5
Answers
Check the picture below.
solve 7^x-2 =30.
Type the correct answer in the box. Round your answer to three decimal places.
X=
Answers
Answer:
x = 3.748
Step-by-step explanation:
this problem requires logs
[tex]log_{7} 30 = x-2[/tex]
x = 2 + log_7 (30) or 3.7479
daniel is going to melt some wax and pour it into a mold shaped like the cone shown below
which is the closest volume to the cone
A.75in^3
B.226in^3
C.151in^3
D.301in^3
Answers
Answer:
A. 75 in³
Step-by-step explanation:
[tex]volume = \frac{1}{3} \times \pi \: {r}^{2} \: h = \frac{1}{3} \times \pi \times { 3}^{2} \times 8 = 75.4[/tex]
Please help!! Will mark brainlyest.