Answer:
I. Length, L = 11 cm
II. Width, W = 6 cm
Step-by-step explanation:
Let the length of the rectangle be L.
Let the width of the rectangle be W.
Given the following data;
Area of rectangle = 66 cm²
Translating the word problem into an algebraic expression, we have;
L = 2W - 1 .....equation 1
We know that the area of a rectangle is given by the formula;
A = L * W
Substituting
66 = L * W ....equation 2
Substituting eqn 1 into eqn 2, we have;
66 = (2W - 1) * W
66 = 2W² - W
2W² - W - 66 = 0
Note: the standard form of a quadratic equation is ax² + bx + c = 0
a = 2, b = -1 and c = -66
Solving the quadratic equation using the quadratic formula;
The quadratic equation formula is;
[tex] x = \frac {-b \; \pm \sqrt {b^{2} - 4ac}}{2a} [/tex]
Substituting into the equation, we have;
[tex] x = \frac {-(-1) \; \pm \sqrt {1^{2} - 4*2*(-66)}}{2*2} [/tex]
[tex] x = \frac {1 \pm \sqrt {1 - (-528)}}{4} [/tex]
[tex] x = \frac {1 \pm \sqrt {1 + 528}}{4} [/tex]
[tex] x = \frac {1 \pm \sqrt {529}}{4} [/tex]
[tex] x = \frac {1 \pm 23}{4} [/tex]
[tex] x_{1} = \frac {1 + 23}{4} [/tex]
[tex] x_{1} = \frac {24}{4} [/tex]
x1 = 6
We do not need the negative value of x, so we proceed.
Therefore, Width, W = x1 = 6 cm
Next, we find the length L;
From eqn 1;
L = 2W - 1
L = 2(6) - 1
L = 12 - 1
L = 11 cm
Genny is arranging flowers in vases for every 1 rose shes uses 6 tuilps .How many tulips would she use for every 5 roses
Answer:
30
Step-by-step explanation:
Ah okay, so this is a simple proportion.
If 1 rose = 6 tulips, then you just multiply however many roses you have by 6. So in your case, 5 x 6 = 30. So in short, for every 5 roses Genny uses, she will use 30 tulips.
Answer:
30 tulips
Step-by-step explanation:
This question gives us the amount of tulips for one rose.
Let us make 1 rose as r and a tulip is t. Now write an equation for the tulips.
Tulip = 6r
If we have 5r:
5r = 6t x 5
Solve!
5r = 30t
5 roses = 30 tulips
Hope this helps :)
A construction worker drops a wrench from a height of 484 feel the function
h =
16x
+ 484 gives the height h of the wrench after a seconds When does the wrench hit the ground?
The wrench hits the ground blank
seconds after it is dropped
Answer:
30.25 seconds
Step-by-step explanation:
If you want to find the time at which the wrench hits the ground, you must recognize that the height of the wrench is 0 feet. If h represents the height, then 0 can be plugged in for h. The equation is now 0=16x+484. You then must subtract 484 from both sides, giving you -484=16x. You then divide both sides by 16 to give you x by itself. -484/16=-30.25. Because this is dealing with time and negative time does not exist, the negative sign on the 30.25 can be neglected.
14. The current of a river is given by the
vector (4, 2). Find the direction of the
vector to the nearest degree.
please helpppp
Answer:
27 Degree
Step-by-step explanation:
First Draw the graph (If you want)
Tan is what we have to use because TAN = Opposite / Adjacent
TanA=2/4
TanA=1/2
TanA=0.5
Tan^-1 x (0.5)
<A= 26.565...
ROUND TO THE NEAREST DEGREE = 27 Degrees
Is 40/1000 and 40% an equivalent pair
Answer:
No
Step-by-step explanation:
40/1000 is 4%
Answer:
no, it would be equivalent if it was 4%
Step-by-step explanation:
Please help me ASAP!!!!
Answer:
<
Step-by-step explanation:
The answer to the question is x < y
Looking at the diagram again, we see that the sides opposite both x and y are equal. And since they both share a line together, this means that two sides are equal in both triangles. Isosceles is the name of the triangle with two sides equal. Since both triangles have two sides equal, this means that x and y are the only sides that are not equal.
Again, looking at the diagram, we are given an angle to be 95°. Which means that, if the triangle of y has an angle of 95, then the corresponding angle in x will be less than 95. This fact also makes x as a side, to be less than y.
to understand more https://brainly.com/question/9872652
22. Write a polynomial in simplest form
to express the shaded area in terms of .
9x2
7x
Answer:
The area of the shaded portion is;
A= π (81x^4 - 49x^2)
Step-by-step explanation:
Looking at the given figure, the area of the shaded part is simply the area of the bigger circle minus the area of the smaller circle
The bigger circle has a radius of 9x^2
The smaller circle has a radius of 7x
The radius is the distance from the center to any part of the circumference
The area of a circle can be calculated using the formula;
A = pi * r^2
For the bigger circle, we have;
A = pi * (9x^2)^2
A = pi * 81x^4
for the smaller circle, we have;
A = pi * (7x)^2
A = pi * 49x^2
So the area of the shaded portion will be;
A= π (81x^4 - 49x^2)
What is the equation of the line that passes through (4, 3) and (-4, -1)?
y = 2 x + 7
y = + 1
2 x + 1
y = + 7
Answer:
Step-by-step explanation:
First find the slope of the line
(4 , 3) ; x₁ = 4 ; y₁ = 3
(-4,-1) ; x₂ = -4 ; y₂ = -1
slope [tex]= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\\\\[/tex]
[tex]=\frac{-1-3}{-4-4}\\\\=\frac{-4}{-8}\\\\=\frac{1}{2}[/tex]
m = 1/2 , and take any one point (4 , 3)
y -y1 = m(x - x1)
[tex]y - 3 = \frac{1}{2}(x - 4)\\\\y -3 = \frac{1}{2}x-4*\frac{1}{2}\\\\y - 3 =\frac{1}{2}x - 2\\\\y = \frac{1}{2}x - 2 + 3\\\\y =\frac{1}{2}x + 1[/tex]
Write an expression that is equivalent to 6(7 x - x)
Answer:
Step-by-step explanation:
Assuming that you meant 6(7x - x), we get: 6(6x) = 36x
It costs $32 for 4 pounds of steak. How much would it cost for a half pound of steak?
Answer:
$4
Step-by-step explanation:
32/4 = $8 per pound
so 1/2 pound = 1/2 x 8 = $4
What is v68 in simplest radical form? Enter your answer in the box.
Answer:
The square root of 68 is 2 √ 17 in the simplest radical form.
Step-by-step explanation:
It cannot be simplified further. √ 17 is an irrational number, therefore, the square root of 68 is an irrational number.
❗️❗️❗️
In the center of town, there is a square park with side length of 30 ft. If a person walks from
one corner of the park to the opposite corner, how far does the person walk? Round to the
nearest foot
021A
042 ft
O 52 ft
O 60 ft
The answer to this is 42ft.
The answers to the complete quick check is
1. d 14
2. a 30, 60, 90
3. b 22 sqrt 2
4. b 42 ft
5. c 30 sqrt 3
miss Nikita age -27 year taxable income is 582000 pay how many income tax on taxable income
Answer:
joi n pls goo gle me. et csz-dftv-vwz joi n pls any one
Use Synthetic substitution to find f(3) and f(-4) for f(x)=x^4-8x-11
f(3)=
f(-4)=
please give working for better understanding
Answer:
46 and 277
Step-by-step explanation:
Given
f(x) = [tex]x^{4}[/tex] - 8x - 11 ← substitute x = 3, x = - 4 into f(x)
f(3) = [tex]3^{4}[/tex] - 8(3) - 11 = 81 - 24 - 11 = 81 - 35 = 46
f(- 4) = [tex](-4)^{4}[/tex] - 8(- 4) - 11 = 256 + 32 - 11 = 288 - 11 = 277
Audrey measures the distance around the lid of her aquarium. The picture
shows the shape of the lid. If the perimeter of the lid is 56 inches, what is the
missing side length?
Explain why the exponents cannot be added in the product 12^3 x
11^3.
Answer:
see explanation
Step-by-step explanation:
The exponents can only be added if the bases are the same
Here one base is 12 and the other is 11
So the rule of addition is not applicable.
Answer:
Because the bases (12 and 11) are different.
Step-by-step explanation:
You can only add exponents when the bases are the same.
What point on the parabola y=3-x^2 is closest to the point (3,3)?
Giving brainlist to whoever answers
Answer:
240 in^3
Step-by-step explanation:
1) remember that a laundry detergent box has a shape of a rectangle parallelepiped
2) find the volume with this formula:
V = base x width x height
V = 12 x 8 x 2.5 = 240 in^3
A parallelogram has one angle that measures 5°. What are the measures of the other three angles in the parallelogram?
Step-by-step explanation:
hope this help the other angles are 5 degrees, 175degrees and 175 degrees
Answer:
jwbeeivrievtidtvidvtirvtjrvtitthtirht
8 elephants plus 4 elephants equal
Can you help me please? I'll mark brainiest
Answer: I’m pretty sure the answer is d
Step-by-step explanation:
HELPPP ME PLEASEeeeeee
Answer:
4.116 × 10^8 = 411,600,000
Step-by-step explanation:
i just put it in the calculator dont get mad at me
On a recent survey, 60% of those surveyed indicated that they preferred walking to running.
If 540 people were surveyed, how many preferred walking to running?
*Remember: change your % to a decimal and multiply by the other number
A 480 people
B 425 people
C 324 people
D) 32 people
Answer:
324 people, C
Step-by-step explanation:
You first make 60 percent a decimal by moving the deciaml point up two digits, which makjes the number .60. Then, multiply 540 x .60 which gets your 324.
A flower takes 8 minutes to grow 5.2 inches. How many inches will the flower grow in 17 minutes?
The time it takes to travel to a destination varies inversely with the average speed. It takes two hours when the average speed is 40mph. If the average speed changes to 80mph, what is the new travel time?
Answer:
4 hours
Step-by-step explanation:
is 40 is two hours then 80 must be 4 hours
Glenda paid $23 for 6 books.What is the rate that Glenda paid for each book?
Answer:
$[tex]3.83[/tex]
Step-by-step explanation:
[tex]23[/tex] divided by [tex]6=3.83333333333.....[/tex]
We round to nearest cent. [tex]3.83[/tex]
identify the vertex of the parabola
2.) Find the volume of the prism. V=Bh*
1 point
4 cm
B= 176 cm?
A. 704 cubic cm
B. 180 cubic cm
O D. 408 cubic cm
Please find the answer ASAP! Thanks!
Answer:
704cm³
Step-by-step explanation:
v=bh
v=176*4
v=704
I WILL DIE IF NO ONE HELP ME PLEASE HELP IM SOOOO SADDDD!!!!in the opposite figure the unit of length is the centimeter
(the points O K and P are collinear )
(the points O B and A are collinear)
(KB) and (PA) are parallel
OK=X,OP=Y
KB=5
KP=6
and PA=8
CALCULATE THE LENGTH OP
Answer:
OP = 16Step-by-step explanation:
Parallel lines cut the transversals into proportional segments.ΔAPO ~ ΔBKO by SASRatio of corresponding sides are same in similar figures:
(x + 6)/x = 8/58x = 5(x + 6)8x = 5x + 303x = 30x = 10Find OP:
OP = x + 6 = 10 + 6 = 16Find the area of the circle.
Answer:
have of 18 is 9
9^2 is 81
81 x 3.14(pi) = 254.34
Formula of area of a circle:
half of diameter or given radius squared
Times
3.14(pi) or whatever you use for pi.
25 7/5 tons = ib ......
Answer:
c. 51,400
Step-by-step explanation:
25 x 2,000=50,000
2,000 x .7= 1,400
50,000+1,400=51,400
Answer:
c
Step-by-step explanation:
