PLEASE HELP!! Compare & Contrast how Completing the Square is used to Convert a quadratic function to vertex form with how it is used to Solve a quadratic equation.
Answer:
Step-by-step explanation:
Given a general quadratic formula given as ax²bx+c = 0
To generate the general formula to solve the quadratic equation, we can use the completing the square method as shown;
Step 1:
Bringing c to the other side
ax²+bx = -c
Dividing through by coefficient of x² which is 'a' will give:
x²+(b/a)x = -c/a
- Completing the square at the left hand side of the equation by adding the square of half the coefficient x i.e (b/2a)² and adding it to both sides of the equation we have:
x²+(b/a)x+(b/2a)² = -c/a+(b/2a)²
(x+b/2a)² = -c/a+(b/2a)²
(x+b/2a)² = -c/a + b²/4a²
- Taking the square root of both sides
√(x+b/2a)² = ±√-c/a + b²/√4a²
x+b/2a = ±√(-4ac+b²)/√4a²
x+b/2a =±√b²-4ac/2a
- Taking b/2a to the other side
x = -b/2a±√√b²-4ac/2a
Taking the LCM:
x = {-b±√b²-4ac}/2a
This gives the vertex form with how it is used to Solve a quadratic equation.
Carmela borrows $400 and will pay 5.25% yearly simple interest. How much
more interest will Carmela owe if she borrows the money for 4 years instead.
of 2 years? Show your work.
Answer:
Camels has to pay $42 more as interest
Step-by-step explanation:
We are given that Carmela borrows $400 and will pay 5.25% yearly simple interest.
Principal = $400
Rate of interest = 5.25%
Time = 2 years
Formula :[tex]SI = \frac{P \times T \times R}{100}[/tex]
So, [tex]SI =\frac{400 \times 2 \times 5.25}{100}[/tex]
SI=42
She borrows the money for 4 years instead of 2 years,
So,[tex]SI =\frac{400 \times 4 \times 5.25}{100}[/tex]
SI=84
Difference in interests = 84-42 = 42
Hence Camels has to pay $42 more as interest
Answer:she has to pay 42 dollars more
Step-by-step explanation
scale factor is 6/5 is the dilation an enlargement, reduction or congruence transformation? *
Answer:
Enlargement transformation
Step-by-step explanation:
A dilation is a transformation which produces an image of the same shape as the original, but may/may not be of the same size. A dilation could be an enlargement, reduction or a congruence.
The following rule applies(given the scale factor k)
If k > 1, there is an enlargement. If 0 < k < 1, there is a reduction. If k = 1, there is a congruence.therefore, since k=6/5=1.2>1, there is an enlargement transformation
Final answer:
When the scale factor is 6/5, it indicates that each dimension of the original figure is increased to achieve the new figure's dimensions, marking this transformation as an enlargement because the scale factor is greater than 1.
Explanation:
If a scale factor is 6/5, this means every dimension in the original figure is multiplied by 6/5 to get the dimensions of the new figure. Since the scale factor is greater than 1, each dimension of the original figure is increased to get the dimensions of the new figure. Therefore, this type of dilation is an enlargement, not a reduction or congruence transformation. An enlargement increases the size of an object while keeping its shape the same. In contrast, a reduction would mean the scale factor is less than 1, and a congruence transformation, which includes transformations like translation, rotation, and reflection, does not change the size at all.
Jon’s weight loss for each week of the month is 5 lbs., 2.5 lbs., and 2.5 lbs. He gained 3.5 lbs. the last week. If Jon originally weighed 198 lbs., how much does he weigh now? *
Answer:
191.5 lbs.
Step-by-step explanation:
His weight loss for each week of the month is:
Week 1: 5 lbs. Week 2: 2.5 lbs. Week 3: 2.5 lbs. On the final week he gained 3.5 Ibs.
We know his original weigh was 198 lbs. So subtract 198 from 10 (sum from adding his weight loss). You get 188 lbs. Finally add the amount of pounds he gained on the final week. 188 lbs. + 3.5 lbs. = 191.5 lbs.
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Jon's total weight loss for the month is 10 lbs., but he gained 3.5 lbs. the final week. This makes his total weight change 6.5 lbs. Thus, from his original weight of 198 lbs., his weight after a month is 191.5 lbs.
Explanation:To find out Jon's weight now, we must calculate the total weight change. Jon lost 5 lbs. in the first week, then 2.5 lbs. both in the second and third week. He, however, gained 3.5 lbs. in the last week. Therefore, the total change in weight is calculated as follows:
Weight loss in the first three weeks = 5 lbs. + 2.5 lbs. + 2.5 lbs. = 10 lbs. Total weight change = Weight loss - Weight gain = 10 lbs. - 3.5 lbs. = 6.5 lbs.Jon's weight after the month = Original weight - Total weight change = 198 lbs. - 6.5 lbs. = 191.5 lbs.So, Jon now weighs 191.5 lbs.
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What is the main idea of this passage from the
9/11 Commission Report?
O
The United States had no chance at stopping
the attacks and should not have tried to do
so.
The United States might not have been able
to stop the attacks, but it could have made a
better effort to do so.
Since the plotters were flexible and
resourceful, we cannot know whether any
single step or series of steps would have
defeated them. What we can say with
confidence is that none of the measures
adopted by the U.S. government from 1998 to
2001 disturbed or even delayed the progress
of the al-Qaeda plot. Across the government,
there were failures of imagination, policy,
capabilities, and management.
- The 9/11 Commission Report
2004
The United States tried its best to stop the
attacks, but terrorist groups were too
resourceful to be stopped.
DONE
AnnnnnOno
Answer: B. The United States might not have been able to stop the attacks, but it could have made a better effort to do so.
Step-by-step explanation:
Answer:
b
Step-by-step explanation:
If the perimeter of square ABCD is 92 meters find the value of x
Answer:
23
Step-by-step explanation:
if X is a side
so squares have 4 sides that are the same so 92/4 equals 23
Easy Question
Topic: Volume
Use the other attachment to help u find the formula
Answer:
see below
Step-by-step explanation:
V = l*w*h for the rectangular tank
V = 70* 40*40
=112000 cm^3 = 1mL
The water is 84000
Make this a fraction
84000/112000 = 3/4
The water fills 3/4 of the tank
1-3/4 = 1/4
It is 1/4 from the top
Find the volume of the treasure chest
V = 12*10*8 =960
Tower
V = pi r^2
3.14 * 10^2 *10
=3140
Water + chest + tower
84000+960+3140 =88100
This is less than 112000 so the water will not overflow
Answer:
a) 10 cm
b) Will not overflow
Step-by-step explanation:
8400 = base area × height
84000 = 70 × 40 × h
h = 30
From the top: 40 - 30 = 10cm
b) Capacity of the tank:
70 × 40 × 40
112,000 cm³
Combined volume of the two vessels:
(12 × 10 × 8) + (3.14 × 10² × 10)
960 + 3140
4,100 cm³
4100 = 70 × 40 × rise
rise = 1.464285715 cm
Since 1.464285715 < 10
It will not overflow
A pathway made of slate tiles measures 513 yards long. A tile measuring 2 feet is added to the end of the pathway. What is the total length of the pathway now? 513 ft 1023 ft 18 ft 22 ft
Answer:
The total length of the pathway now is 1,541 ft
Step-by-step explanation:
To calculate the length of the pathway now, what we need to do is to have a consistency in units.
Thus, we need to convert the 513 yards to ft
Mathematically 1 yard = 3 feet
Thus 513 yards will be = 513 * 3 = 1,539 ft
Thus the total length of the pathway now will be 1539 ft + 2 ft = 1541 ft
Answer: the answer is 1 5 3 ft
Step-by-step explanation:
What’s the area of this figure?
Awnser:
14.5 cm
Step-by-step explanation:
1*7=7, 5*3=15/2=7.5
Answer:
14.5 cm^2
Step-by-step explanation:
We can find the area by adding the area of the long rectangle and the triangle
The rectangle is 1 cm by 7 cm
A = 1*7 = 7 cm^2
The triangle is 5 cm by (7-4) =3 cm
A = 1/2 (5*3)
A = 7.5 cm^2
The total area is
7+7.5 = 14.5 cm^2
Identify asymptote of a function y = 2(3)^x+7 – 5
O y=7
O x=7
O y=-5
Ox=-5
The asymptote of the function is y = -5.
What are Vertical and Horizontal Asymptotes?A vertical asymptote of a function is the vertical line x = c such that the function tends to approach to infinity as the value of x approaches a.
Horizontal asymptote is the horizontal line y = d, such that the function approaches this line as the value of x approaches positive or negative infinity.
Given function is,
y = 2 (3)⁽ˣ⁺⁷⁾ - 5.
Horizontal asymptote of an exponential function y = kˣ is the line y = 0.
If the parent function is transformed and becomes something of the form y = akˣ + d, then the horizontal asymptote if the line y = d.
Here, the value instead of d = -5.
So the horizontal asymptote is y = -5.
Hence the correct option is C. y = -5.
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Consider this sphere with a diameter of 5 m.
What can be concluded about the sphere? Check all
that apply,
The sphere has a radius of 10 cm.
The diameter measure is substituted into the
formula to find the volume.
5 m
The radius is half the diameter.
The formula to apply is y=- Bh
The volume of the sphere is two-thirds the volume
of a cylinder with the same radius and height.
9514 1404 393
Answer:
The radius is half the diameter.The volume of the sphere is two-thirds the volume of a cylinder with the same radius and height.Step-by-step explanation:
Regardless of the diameter, the radius is half the diameter. For this sphere, it is 5/2 m = 2.5 m.
__
The height of the sphere is equal to its diameter, so is 2r. The volume of a cylinder with radius r and height 2r is ...
V = πr²h = πr²(2r) = 2πr³
The volume of a sphere with radius r is ...
V = 4/3πr³
Then the ratio of sphere volume to cylinder volume is ...
(4/3πr³)/(2πr³) = (4/3)/2 = 2/3
The sphere volume is 2/3 that of a cylinder with the same radius and height.
HELP MEE ! no guessing
Answer:
3 mph
Step-by-step explanation:
Take the miles and divide by the hours
15 3/4 ÷ 5 1/4
Change to improper fractions
63 /4 ÷ 21 /4
Copy dot flip
63/4 * 4/21
63/21 *4/4
3 *1
3
how many days until 20 november from 19 october
answer: 334 days googled it
HELP HELP HELP PLZZ!!!
Michael has 3 quarters, 2 dimes, and 3 nickels in his pocket. He randomly draws two coins from his pocket, one at a time, and they are both dimes. He says the probability of that occurring is 1/4
because 2 of the 8 coins are dimes. Is he correct? Explain.
Answer:
Yes he is
Step-by-step explanation:
he is saying 1/4 and 2/8 of the coins are dimes 2/8 simplified is 1/4
let me know if this helps
Answer:
The events are dependent. The size of the original sample space is 8. It changes to 7 after the first dime is chosen. The probability of picking the first dime is 2/8. The probability of picking the second dime is 1/7 ,To find the probability of the compound event, multiply the probabilities.
Step-by-step explanation:
What is the value of (-1/2)-4
Answer:
2
Step-by-step explanation:
-1/2 * (- 4)
2 Answer
Don has two jobs for job 1 he earns 7.55 an hour. For job 2 he earns 8.45 an hour last week he worked at the first job for 10 hours and the second job for 15 hours. What were his average earnings per hour
Answer:
for the first job is $75.05 and for the second job is $126.75
The average earning of Don is obtained as 8.09.
How to calculate the average?In order to calculate average, divide the total sum of the data to the total number of data. An average is a standard number for a given data whose value can both be more or less than it.
The total value can be calculated by multiplying the average to the number of data.
The time spent on first job is 10 hours and on second is 15 hours.
Now, the average earning per hour can be calculated as below,
(Earning for first job + Earning for second job) ÷ 25
⇒ (10 × 7.55 + 15 × 8.45) ÷ 25
⇒ 8.09
Hence, the average earnings per hour is given as 8.09.
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I NEED HELP ASAP ITS DUE IN 10 mins PLEASE
ILL MARK YOU AS BRAINLIST
Step-by-step explanation:
Simple
x - 7 = 0
x = 7
x + 8 = 0
x = - 8
Option no 1 is the correct answer
Suppose the system of linear equations has no solution. Which is NOT a possible value of the constant for the second equation?
6x + 9y = 15
2x + 3y = __
A) 5
B) 10
C) 15
D) 20
Answer:
A) 5
Step-by-step explanation:
The coefficients of the second equation are 1/3 of those of the first equation. If the constant of the second equation is also 1/3 of the constant of the first equation, then the equations are dependent, and will have an infinite number of solutions.
The constant must be something other than 1/3·15 = 5 to make the equations inconsistent, having no solutions.
find the median
66, 73, 66, 75, 80
please help!!!
Answer:
median= 73
Step-by-step explanation:
Answer:
73
Step-by-step explanation:
list from lowest to highest.
so
66, 66, 73, 75, 80
Pick the middle, because that is the median.
73
Please help with this problem
Answer:
i dont know
Step-by-step explanation:
French Fries Onion Rings
Hamburger 62 41
Cheeseburger 56 54
Bacon Cheeseburger 41 40
Jack owns a small restaurant called Best Burgers. For one week, he collected sales data on the type of side order served with each type of burger purchased. Jack serves a half pound of french fries with every kind of burger. If Jack sells 180 regular hamburgers how many pounds of french fries will he serve? (round to nearest whole number)
Answer:
170 that is the answer hope it's right
Answer:
answer is 30
Step-by-step explanation:
120/2 60 the weight then since the competitor of that side is fries divide it by 2 and plus i just did it on USA test prep
What is the data point that is the farthest from other data points when the box plot is NOT symmetrical?
A. Median
B. Outliner
C. Greatest Point
need an answer ASAP
Answer: B. Outlier
Step-by-step explanation:
An outlier is an extremely large or extremely small data value in a data set such that it appears far from the other data points when we plot data points on scatter plot or box plot.
Thus, the data point that is the farthest from other data points when the box plot is NOT symmetrical is Outlier.
Its presence affects the value of mean directly. So when a data set have outliers , we prefer Median(Mid value of a data set) as the best measure of central tendency because existence of outliers does not effect Median .
Hence, the correct option is B. Outlier.
what is the five-number summary for this data set? 3, 8, 14, 19, 22, 29, 33, 37, 43, 49
Assume the numbers in each answer choice are listed in this order: min, Q1, median, Q3, max
Answer: 3, 14, 25.5, 37, 49
Step-by-step explanation: Apex said so
A cardboard party favor is shaped like two square pyramids stuck together at their bases.
What is the approximate volume of the party favor?
4.3 in.3
8.7 in.3
12.9 in.3
26.1 in.3
Answer:
B. 8.7 in.3
Step-by-step explanation:
Answer:
I did it on edgen
Step-by-step explanation:
Hope it helps!
Michael is finding the area of parallelogram ABCD. To do
this, he follows the steps in the table.
Step Draw a rectangle around parallelogram ABCD.
To solve the problem using these steps, what are the
dimensions of the rectangle he should draw?
ТУ
С
B
Step Find the area of the rectangle.
2
Step Find the area of the four right triangles created in the
3 corners of the rectangle.
Step Subtract the area of the right triangles from the area
4 of the rectangle.
D
-5-4-3
-1
A
2 units by 4 units
3 units by 2 units
4 units by 4 units
Answer:
It's option C) 4 units by 4 units
Step-by-step explanation:
I hope this helps
The dimensions of the rectangle that Michael should draw are 4 units by 4 units.
What is a rectangle?A rectangle is defined as a four-sided shape with opposite sides that are equal in length and parallel to each other.
A parallelogram is defined as a special type of quadrilateral that has both pairs of opposite sides parallel and equal.
The dimensions of the rectangle that Michael should draw are:
Length = AB = CD = 4 units (horizontal side of the parallelogram)
Width = AD = BC = 4 units (vertical side of the parallelogram)
This creates a rectangle with dimensions of 4 units by 4 units.
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An airplane is preparing to land an airport. It is 34,800 feet above the ground and descending at the rate of 3,000 feet per minute. At the same airport, another airplane is taking off and will ascending at the rate of 2,800 feet per minute. When will the two airplanes be at the same altitude and what will that altitude be?
Answer:
6 mins, and the altitude will be 16,800 ft
Step-by-step explanation:
1st: Subtract 3000 from 34800
2nd: Multiply 2 to 2800
Keep doing this until you get the same altitude for each one.
After 6 minutes, both airplanes will be at an altitude of 16,800 feet. This is found by solving two equations for the descending and ascending planes and determining the time when their altitudes are equal.
Explanation:To determine when two airplanes will be at the same altitude, we can set up an equation where the altitude of the descending airplane equals the altitude of the ascending airplane.
Let t be the time in minutes after the planes have begun their ascent and descent respectively.
The descending airplane starts at 34,800 feet and descends at 3,000 feet per minute. Therefore, its altitude after time t will be:
Altitude of descending plane = 34,800 feet - (3,000 feet/minute × t)
The ascending airplane starts at the ground level and ascends at 2,800 feet per minute. Thus, its altitude after time t will be:
Altitude of ascending plane = 0 feet + (2,800 feet/minute × t)
To find the time when the altitudes are equal:
34,800 feet - (3,000 feet/minute × t) = (2,800 feet/minute × t)
Solving for t, we get:
t = 34,800 feet / (3,000 feet/minute + 2,800 feet/minute)
t = 34,800 feet / 5,800 feet/minute
t = 6 minutes
Now, to find the altitude at which they will be at the same level, we can plug t back into either equation for altitude:
Altitude at 6 minutes = 2,800 feet/minute × 6 minutes
Altitude at 6 minutes = 16,800 feet
Therefore, after 6 minutes, both airplanes will be at an altitude of 16,800 feet.
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The scale of a model train is 1 inch to 14 feet. One of the cars of the model train is 5 inches long. What is the length, in feet, of the actual train car.
Answer:
70 feet
Step-by-step explanation:
1/14=5/x
x=14*5
x=70
Find the slope of the line that passes through (57, -27) and (-19, -34)
Answer:
10.86
Step-by-step explanation:
m = Y2 - Y1 / X2 - X1 = -19 -57 / -34 +27 = -76 / -7 = 10.86
Answer:
y=7/76x-129/4
Step-by-step explanation:
I'm going to assume you want this in slope intercept form.
The equation of a line is equal to y = mx+b
Where m is the slope and b is the y-intercept.
The slope of a line is a measure of how steep the line is.
For lines like these, the slope is always defined as "the change in y over the change in x" or, in equation form:
y2-y1/x2-x1
So what we need now are the two points you gave that the line passes through. Let's call the first point you gave, (57,-27), point #1, so the x and y numbers given will be called x1 and y1, and the second point will be x2 and y2.
So we just plug in the numbers, and find the slope to be 7/76.
What about b(the y-intercept), I can already hear you typing. Well, to do that, you plug in the coordinates of the points given and solve for b.
And there you have it:
y=7/76x-129/4 is the equation of the line.
In a train yard, there are 6 flatcars, 7 boxcars, and 3 livestock cars. A train is made up of 9 cars.
Which would you use to find the number of ways the train could be made up?
Answer:
The answer is A on edge
Step-by-step explanation:
The number of ways the train could be made up are 4,151,347,200.
What is permutation?A permutation of a set is an arrangement of its members into a sequence or linear order, or if the set is already ordered, a rearrangement of its elements.
Now the given cars are 6 flatcars, 7 boxcars, and 3 livestock cars.
So the total number of cars, n = 6 + 7 + 3
= 16
Now, a train is made up of 9 cars,
Therefore, r = 9
Hence the required number of ways the train could be made is nPr
nPr = n!/(n-r)!
nPr = 16!/(16-9)!
nPr = 16!/7!
nPr = 16*15*14*13*12*11*10*9*8
nPr = 4,151,347,200
Hence,the number of ways the train could be made up are 4,151,347,200.
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answer for brainliest
Answer:
The slope of the equation is -3
The y-intercept of the equation is (0,-1)
Step-by-step explanation:
For slope: [tex]\mathrm{For\:a\:line\:equation\:for\:the\:form\:of\:}\mathbf{y=mx+b}\mathrm{,\:the\:slope\:is\:}\mathbf{m}[/tex]
[tex]m=-3[/tex]
For y-intercept: [tex]y\mathrm{-intercept\:is\:the\:point\:on\:the\:graph\:where\:}x=0[/tex]
[tex]\mathrm{Solve\:}\:y=-3\cdot \:0-1:\quad y=-1[/tex]
[tex]\mathrm{Apply\:rule}\:0\cdot \:a=0\\y=-0-1\\\\\mathrm{Subtract\:the\:numbers:}\:-0-1=-1\\y=-1\\[/tex]