Answer:
The length of the rectangle is of 9 units.
Step-by-step explanation:
Solving a quadratic equation:
Given a second order polynomial expressed by the following equation:
[tex]ax^{2} + bx + c, a\neq0[/tex].
This polynomial has roots [tex]x_{1}, x_{2}[/tex] such that [tex]ax^{2} + bx + c = a(x - x_{1})*(x - x_{2})[/tex], given by the following formulas:
[tex]x_{1} = \frac{-b + \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]x_{2} = \frac{-b - \sqrt{\bigtriangleup}}{2*a}[/tex]
[tex]\bigtriangleup = b^{2} - 4ac[/tex]
Area of a rectangle:
A rectangle has width [tex]w[/tex] and length [tex]l[/tex]. The area is the multiplication of these measures, that is:
[tex]A = wl[/tex]
The length of a rectangle is the sum of the width and one.
This means that [tex]l = w+1[/tex], or [tex]w = l - 1[/tex]
The area direct angle 72 units. What’s the length, in units, of the rectangle
We want to find the length. So
[tex]wl = 72[/tex]
[tex](l-1)l = 72[/tex]
[tex]l^2 - l - 72 = 0[/tex]
Quadratic equation with [tex]a = 1, b = -1, c = -72[/tex]. So
[tex]\bigtriangleup = (-1)^{2} - 4(1)(-72) = 289[/tex]
[tex]l_{1} = \frac{-(-1) + \sqrt{289}}{2*(1)} = 9[/tex]
[tex]l_{2} = \frac{-(-1) - \sqrt{289}}{2*(1)} = -8[/tex]
Since the length is a positive measure, the length of the rectangle is of 9 units.
In the coordinate plane, which of the following functions dilates by a factor of 3
about the point (9, 6)?
A. (, ) = (3 + 9, 3 +6)
B. (, ) = (3( + 9), 3( + 6))
C. (, ) = (9+ 3( − 9), 6 + 3( −6))
D. (, ) = (9+ 3(9− ), 6+ 3(6 − ))
Answer: the answer is D
Step-by-step explanation:I had that question on a quiz
The points after dilation is (27, 18).
What is Dilation?Resizing an item uses a transition called dilation. Dilation is used to enlarge or contract the items. The result of this transformation is an image with the same shape as the original.
Enlargements are dilations that result in a larger image. Reduction is the name for a dilatation that shrinks the image. The initial figure is stretched or contracted by a dilatation.
Given:
Scale Factor= 3
Points (9, 6).
If the coordinates is dilated by factor 3.
Then, (9, 6).
= (9(3), 6(3)).
= (27, 18)
Hence, the points after dilation is (27, 18).
Learn more about dilation here:
https://brainly.com/question/13176891
#SPJ2
Raul is considering three different
Answer:
WHAT?!
Step-by-step explanation:
3/4(x + 3) = 9
How do I solve this
Answer:
x = 10
Step-by-step explanation:
so first distribute the 3/4 to everything on the inside
3/4x + 1 1/2 = 9
now subtract 1 1/2 on both sides
3/4x = 7 1/2
Now divide both sides by 3/4
x = 7 1/2 divided by 3/4
x = 15/2 divided by 3/4
x = 15/2 times 4/3
x = 5/1 times 2/1
x = 10
13 out of 25 people agreed to help at a charity event. What percentage is
this?
21 out of 40 children arrived on time. What percentage were late? *
Find the percentage
A French test is out of 48 marks.
Simone scores 30 marks.
What is Simone's score as a percentage?
Answer:
Hi! The correct answer is 3.25, 7.6 and 0.3!
Step-by-step explanation:
A shop sells floor tiles at Rs 48 per square meter. A
building contractor employees
machine that polishes
the tiles that damages 10% of the total number of
tiles which cannot be used
any
more. Calculate the
amount that need to be paid by contractor to tile
Shop owner, if the hall is of a square shape and
has a perimeter of 400m
a.Rs 400.000
b.Rs 600 000
c. 528000 d.365000
Answer:
c. 528000
Step-by-step explanation:
The computation of the amount that need to be paid is shown below:
Let us assume the side of the square shaped hall be X meter s
So,
Perimeter = 4X
Now
4X = 400
X = 100m
Now
Area of the hall = 100 × 100 = 10000 sq. meter.
And,
The cost on total tiles is
= 10,000 × 48 = Rs. 480000
But, there is 10% damage has occurred that involved in the cost
So,
Total cost is
= Rs 480,000 + 10% of 480,000
= 480,000 + 48,000
= Rs. 5,28,000
A rectangular bathroom floor is covered with square tiles that are 1 LaTeX: \frac{1}{2}1 2 feet by 1 LaTeX: \frac{1}{2}1 2 feet. The length of the bathroom floor is 10 LaTeX: \frac{1}{2}1 2 feet and the width is 6 LaTeX: \frac{1}{2}1 2 feet. a) How many tiles does it take to cover the length of the floor?
Answer:
273 tiles
Step-by-step explanation:
Given
Square tile
[tex]Side=\frac{1}{2} ft[/tex]
Bathroom floor
[tex]Length = 10\frac{1}{2}ft[/tex]
[tex]Width = 6\frac{1}{2}ft[/tex]
Required
Determine the number of tiles to cover the floor
First, we calculate the area of the floor:
[tex]A_{floor} = Length * Width[/tex]
[tex]A_{floor} = 10\frac{1}{2} * 6\frac{1}{2}[/tex]
Convert to decimals
[tex]A_{floor} = 10.5 * 6.5[/tex]
[tex]A_{floor} = 68.25ft^2[/tex]
Next, we calculate the area of the square tile:
[tex]A_{tile} = Side * Side[/tex]
[tex]A_{tile} = \frac{1}{2} * \frac{1}{2}[/tex]
Convert to decimal
[tex]A_{tile} = 0.5 * 0.5[/tex]
[tex]A_{tile} = 0.25ft^2[/tex]
The number of tiles is then calculated as:
[tex]Tiles = \frac{A_{floor}}{A_{tile}}[/tex]
[tex]Tiles = \frac{68.25ft^2}{0.25ft^2}[/tex]
[tex]Tiles = \frac{68.25}{0.25}[/tex]
[tex]Tiles = 273[/tex]
Hello! Please answer this question with all of the info it is asked for. Please be sure to include all of your work and share any of your thoughts you had when solving. Please do not answer unless you know the answer. Thanks! Good Luck!
A football is kicked straight up into the air from 3 feet above the ground with an initial velocity of 208 ft/s. The function that models the ball's height is: h(t) = -16t^2 + 208t + 3.
a) Find how long it takes for the football to reach its maximum height.
b) Determine how long the football was in the air (approximately). Why might this not quite be accurate?
c) Determine the maximum height of the football.
Answer:
a) 6.5 secondsb) 13 secondsc) 679 ftStep-by-step explanation:
Given function:
h(t) = -16t^2 + 208t + 3a) Maximum height is the vertex. The ball reaches the maximum after:
h = -208/2(-16) = 6.5 secondsb) Time the ball was in the air:
-16t^2 + 208t + 3 = 0Solving we get approximately t = 13 seconds
c) Maximum height is at vertex, we found t above:
h(6.5) = -16(6.5)^2 + 208*6.5 + 3 = 679 ftA delivery person uses a service elevator to bring boxes of books up to an office. The delivery person weighs 160 lbs and each box of books weighs 50 lbs. The maximum capacity of the elevator is 1000 lbs. How many boxes of books can the delivery person bring up at one time? Note: The delivery person cannot bring up a partial/fraction of a box.
Answer:
16 boxes
Step-by-step explanation:
160+50x=1000
Solve for the x and you'll get 16.8. Now, because you can't have a fraction of a box, and you can't go over the limit, the answer is 16 boxes.
(How to solve for x:
Get x by itself by subtracting 160 to both sides.
50x=1000-160
50x=840
Divide both sides by 50.
x=16.8)
The sides of a rectangle are 2x + 3 and 14. What are 2 expressions that represent the area of the rectangle?
Answer:
28x+42
14(2x+3)
Step-by-step explanation:
Area of a rectangle is lenght times width
A = L * W
So
14(2x+3)
28x+42
I GIVEEEEE BRAINLILST
Answer:
113
Step-by-step explanation:
The area is π[tex]r^{2}[/tex], and pi is about 3. r is d/2 which is 12/2=6.
6^2 is 36 and 36*3 = 108. 113 is the closest, so that is the best estimate.
hellpp please 20 points for that
Answer:
a) 12cm
b) 360cm²
c) 2160cm cubed
Step-by-step explanation:
a)
you would use Pythagoras theorem for A
so half of 18 is 9
15² - 9² = 144
the square root of 144 is 12
the height is 12cm
b)
18 x 20 = 360cm²
c)
csa x L
csa = b x h divide by 2
18 x 12 = 216cm²/2 = 108cm²
108xm² x 20cm = 2160cm cubed
Nelson did 105 sit-ups in 3 minutes.
What is the unit rate?
Answer:
The answer is 35
Step-by-step explanation:
What percent is equivalent to 24/50 24% 48% 50% 52%
Answer:
48%
Step-by-step explanation:
(24/50)2
= 48/100
= 48%
What are the solutions to the absolute value inequality |x − 70| ≤ 3?
Remember, the inequality can be written as −3 ≤ x − 70 ≤ 3
or as x − 70 ≤ 3 and x − 70 ≥ −3.
Answer:
67 ≤ x ≤ 73
Step-by-step explanation:
The absolute value of a real number x is the non negative value of x. Therefore the absolute value of x (|x|) = x for x ≥ 0 and -x for x < 0.
An expression |x - a| = b signifies that x - a = b or -(x - a) = b
Given that |x − 70| ≤ 3, hence:
|x − 70| ≤ 3
x - 70 ≤ 3 or -(x - 70) ≤ 3
x ≤ 3 + 70 or x - 70 ≥ -3
x ≤ 73 or x ≥ -3 + 70
x ≤ 73 or x ≥ 67
67 ≤ x ≤ 73
Hence the solution of |x − 70| ≤ 3 is 67 ≤ x ≤ 73
PLEASE HELP ME THANK YOU ILL MARK BRAINLESS
Answer: y=4/3x-8
Step-by-step explanation:
Find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s radius r 35 kilometers arc length s 85
Answer:
Step-by-step explanation:
s=rtheta
s/r=theta
11.5/25=theta
theta=.46
I need help please ASAP
Solve the following equation for X. X=
-2x – 3.2 – 15 = 20
Answer:
x = -7
Step-by-step explanation:
-2x - 3x = -5x
so then its -5x - 15
you then add 15 to both sides which gives you -5x = 35
divide -5 from each side to get the answer
-7 = x
Step-by-step explanation:
-2x - 3x -15 = 20
-5x = 20 + 15
-5x = 35
x = 35/-5
x = -7
Reflect (-3, -3) over the y-axis.
Then translate the result to the left 2 units.
What are the coordinates of the final point?
Answer: (1,-3)
Step-by-step explanation:
Several members of a running club would like to survey the rest of the members to determine which 5K races the club should enter. They decide to use a random number table to sample 10 of the 78 members. Which of the following correctly labels the population?
A.) 0–78
B.) 1–78
C.) 00–78
D.) 01–78
Answer:
D
Step-by-step explanation: edge 2021
I need help I’m so confused
Answer:
5.60 ganeyryjfj3ym5uhwrbeyny3nte y
hi can you tell me whether a appeal must be filed within 6 months of a claim determination. its medical billing chapter 18
Answer: Decisions and Determinations -If a Medicare appeal request does not result in a dismissal, adjudication of ... dismissal by providing an explanation for the late filing to the MAC within 6 months of the dismissal of the.
Step-by-step explanation:g brain
What is the slope of a line parallel to y=2x + 3
Answer:
2
Step-by-step explanation:
The slope of the line with equation y=2x+3 is 2 . So, any line parallel to y=2x+3 has the same slope 2 .
Hello!
Parallel lines have the same slope. So if one line has a slope of 2, the line parallel to it has a slope of 2 as well.
Therefore, the slope is 2. Hope it helps.
If you have any questions, feel free to ask.
~A forlorn teen
[tex]MagicalNature[/tex]
The melting/freezing point of mercury is –39ºC. A scientist put liquid mercury into a freezer that is kept at a constant temperature of –35ºC. Will the liquid mercury freeze?
Answer:
The mercury will not freeze because the freezer is warmer than the freezing point of mercury.
Step-by-step explanation:
A "freezing point" is a point that allows a liquid to solidify. This is lower than the melting point (of course). However, specific liquids freeze at varying freezing points.
For example, the freezing point of water is 0°C while the freezing point of Mercury is -39°C. This means that water will only freeze once it reaches a temperature of 0°C or lower than this. Same goes for Mercury–it needs to reach the temperature of -39°C or lower in order to freeze.
One of the vertices of △PQR is P(2, −1). The midpoint of PQ is M(3, 0). The midpoint of QR is N(5, 3). Show that MN || PR and MN = 1/2 PR.
The coordinates of Q are:
The coordinates of R are:
The slope of MN is:
The slope of PR is:
The line segments are (select)
MN =
PR =
Answer:
See the proof below
Step-by-step explanation:
Given the following coordinates
P(2, −1)
Midpoint of PQ M(3, 0)
We can get the coordinate point Q using the midpoint formula;
M(X,Y) = (x1+x2/2, y1+y2/2)
X = x1+x2/2
3 = 2+x2/2
6 = 2+x2
x2 = 6-2
x2 = 4
Y = y1+y2/2
0 = -1+y2/2
0 = -1 + y2
y2 = 0+1
y2 = 1
Hence the coordinate of Q is (4, 1)
Next is to get the coordinate of R
Given the midpoint of QR to be N(5, 3)
(5,3) = (4+x2/2, 1+y2/2)
5 = 4+x2/2
10 = 4+x2
x2 = 10-4
x2 = 6
1+y2/2 = 3
1+y2 = 6
y2 = 6-1
y2 = 5
Hence the coordinate of R is (6,5)
Given the coordinates M(3, 0) and N(5, 3)
Slope is expressed as:
m = y2-y1/x2-x1
m = 3-0/5-3
m = 3/2
Slope of MN = 3/2
Get the slope of PR
Given the coordinates P(2, −1) and R (6,5)
Slope of PR = 5-(-1)/6-2
Slope of PR = 5+1/4
Slope of PR = 6/4 = 3/2
Since the slope of MN is equal to that of PR, hence MN is parallel to PR i.e MN || PR
To show that MN = 1/2PR, we will have to take the distance between M and N and also P and R first as shown:
For MN with coordinates M(3, 0) and N(5, 3)
MN = √(x2-x1)²+(y2-y1)²
MN = √(5-3)²+(3-0)²
MN = √2²+3²
MN = √13
Get the length of PR where P(2, −1) and R (6,5)
PR = √(6-2)²+(5+1)²
PR = √4²+6²
PR = √16+36
PR = √52
PR = √4*13
PR = √4*√13
PR = 2√13
Since MN = √13
PR = 2MN
Divide both sides by 2
PR/2 = 2MN/2
PR/2 = MN
Hence MN = 1/2 PR (Proved!)
Rahul drives his car and travels 10Km in 12mins. What is the distance covered by him in 1 hour?
Pls answer quick I have an exam tomm I need answer for this question
First helpful answer will be marked as brainliest
Regards,
Me
Answer:
50
Step-by-step explanation:
first of all thimk about how many 12s there is in 60 (which is 1hr=60) and thats 5, so multiply 5 by 10 because in each 12 mins its 10 km which gives you 50 as the answer
Abby is trying to pay off her debt. She owes $422 to her bank. In may she paid $76, but had to borrow an additional $135. In June she paid $45 and borrowed $110. The bank also charged her $58 in interest. How much did she owe at the end of June.
Extra points
Answer: 624
Step by Step Explanation: Subtract 422 with 76, add 135, subtract 45, add 110, and lastly add 58.
Subtract 422 with 76, 422-76=366.
Add 366 with 135, answer will be 501.
Subtract 501 with 45 since she paid $45. 501-45=456.
Add 456 with 110 and that would be 566.
For the last step add 58 to find the answer and you would get 624.
Final Result: 624.
Did I do this right math functions need fast
Answer:
The rate of change of Function A is less than the rate of change of function B.
Other than that, everything else you put is correct.
Step-by-step explanation:
None.
Answer:
Option A, B and D are correct options.
Step-by-step explanation:
First we will find rate of change of function A and function B
Rate of Change of Function A
The formula used to calculate rate of change is: [tex]Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}[/tex]
We have x_1=1, y_1=5, x_2=2, y_2=7
Putting values in formula and finding rate of change
[tex]Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\\Rate\:of\:Change=\frac{7-5}{2-1}\\Rate\:of\:Change=\frac{2}{1}\\Rate\:of\:Change=2[/tex]
So, Rate of change of Function A = 2
Now, finding y-intercept.
y-intercept is found by putting x =0
Looking at the function, we can write the equation: y=2x+3
Now, put x =0
y=2(0)+3
y=3
So, when x =0, y=3
So, y-intercept is 3 for function A.
Rate of Change of Function A
The formula used to calculate rate of change is: [tex]Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}[/tex]
We have x_1=1, y_1=1, x_2=2, y_2=4
Putting values in formula and finding rate of change
[tex]Rate\:of\:Change=\frac{y_2-y_1}{x_2-x_1}\\Rate\:of\:Change=\frac{4-1}{2-1}\\Rate\:of\:Change=\frac{3}{1}\\Rate\:of\:Change=3[/tex]
So, Rate of change of Function B = 3
Now, finding y-intercept.
y-intercept is found by putting x =0
Looking at the graph, when x=0, y is -2
So, y-intercept is -2 for function B.
We get following answers:
Rate of change of Function A = 2
Rate of change of Function B = 3
y-intercept is 3 for function A.
y-intercept is -2 for function B.
So, The correct options are:
The rate of change of function A and B are positive
The rate of change of function A is less than the rate of change of function B. (Because 2 is less than 3)
The y-intercept of function A is positive, while y-intercept of function B is negative.
So, Option A, B and D are correct options.
turn -2x+4y=0 into slope-intercept form
Simplify
2g + 4h + 4i -8g + 3h - 4i
Answer:
-6g + 7h
Step-by-step explanation: