The required steps are explained below to convert the quadratic function into a perfect square.
What is the parabola?It's the locus of a moving point that keeps the same distance between a stationary point and a specified line. The focus is a non-movable point, while the directrix is a non-movable line.
Let the quadratic function be y = ax² + bx + c.
The first step is to take common the coefficient of x². We have
[tex]\rm y = a \left (x^2 + \dfrac{b}{a}x \right) + c[/tex]
Add and subtract the half of the square the coefficient of x,
[tex]\rm y = a \left (x^2 + \dfrac{b}{a}x + \dfrac{b^2}{4a^2} \right) - a \times \dfrac{b^2}{4a^2} + c[/tex]
Then we have
[tex]\rm y = a \left (x + \dfrac{b}{a} \right)^2 - \dfrac{b^2}{4a} + c[/tex]
These are the required step to get the perfect square of the quadratic function.
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Find arc QT.
Answers are:
A.71
B.23
C.46
D.142
Answer:
d)142º
Step-by-step explanation:
[tex]\widehat{AB}=2\times71\º=142\º[/tex]
I would like help :)
Answer:
diameter - B
central angle - E
radius - A
tangent - D
minor arc - F
chord - C
Determine if the sequence is arithmetic. If it is, find the common difference.
1) 35, 32, 29, 26, ...
2) -3, -23, -43, -63, ...
Answer:
1) yes--common difference is 3.
Jeremy finished 3/5 of his homework what percent of homework did he finish
Answer:
60%
Step-by-step explanation:
Percent means per hundred. Change to "per hundred"
3/5 = 6/10 = 60/100
3/5 is 60%
OR
Divide 3/5 means 3÷5...
3÷5 = .6
Change decimal to percent by multiplying by 100.
.6 × 100 = 60
60%
Answer:
60%
Step-by-step explanation:
well if they only finished 3/5 it’s going to be
60/100 = 60%
Find the length of the third side. If necessary, round to the nearest tenth.
Work out the circumference of this circle.
Take to be 3.142 and write down all the digits given by your calculator,
13 cm
diameter= 13 cm
to find:the circumference of the given circle.
solution:[tex]c = \pi \: d[/tex]
[tex]c = 3.142 \times \: d[/tex]
[tex]c = 3.142 \times 13[/tex]
[tex]c = 40.846 \: cm[/tex]
hence, the circumference of the given circle is 40.846 cm
First, we'll have to change the diameter to radius by dividing the diameter by 2.
[tex]\large\boxed{Formula: r= \frac{d}{2}}[/tex]
So we'll have to divide 13 by 2.
Substitute the values according to the formula.
[tex]r= \frac{13}{2}[/tex]
[tex]\bold{6.5 \: cm}[/tex]
Now, we can find the circumference.
[tex]\large\boxed{C= 2\pi{r}}[/tex]
Substitute the values according to the formula.
[tex]C= 2\times\pi\times6.5[/tex]
Calculate value:
[tex]\large\boxed{C= 40.8407045 \: cm}[/tex]
Therefore, the circumference of the given circle is 40.8407045 centimeters.
which of the following numbers ae divisible by 3?
a. 534
b.2176
c.59742
d.45846
which of the following numbers are divisible by 4?
a.9698
b.98746
c.5620
d.56208
Answer:
1. A
2. C
Step-by-step explanation:
1. A
2. C
Gabriella is playing a board game. The
probability that Gabriella will lose a turn on
her next turn is 0%. Which word or phrase
describes the probability that Gabriella will
lose a turn?
Answer:
Impossible.
Step-by-step explanation:
I learned that you can use the word impossible during one of my math classes, so I chose the word impossible since she cannot lose a turn on her next turn.
A rectangular swimming pool has a length of 50 meters, a width of 25 meters, and a depth of 2 meters. How much paint would be needed to cover the sides and bottom of the pool?
Answer:
2500m³
Step-by-step explanation:
A = length x width x height
50m x 25m x 2 m
=2500m³
Please help!!! Will give brainliest
Answer:
y ≥ 14
Step-by-step explanation:
Add 27 to both sides to get:
y ≥ 14
Therefore the answer is y ≥ 14.
What is the angle of evaluation of the top of a tree 8m high from a point on the ground 9.2m away from the foot of the tree
Answer: 40.69°
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The DePeppo children, Ann, Debbie, Damian, and Adam created a contest to test their athletic abilities and physical strength. They threw objects into the air to see who was the best.
These four equations depict the travel of the objects they threw.
y1=−16x2+62x+10
y2=−16x2+75x
y3=−16x2+38x+60
y4=−16x2+20x+10
1 The youngest launched his object from atop the playset.
2 Ann climbed a tall tree to launch her object.
3 Damian’s object went the highest.
4 Debbie’s object was in the air the shortest amount of time.
5 The arrow was shot by the oldest.
6 The golf ball went 87 feet into the air.
7 Ann shot her arrow higher than the tennis and bowling balls.
8 The bowling ball reached its maximum height just under 1 second.
9 Damian’s ball was in the air twice as long as the 2nd oldest sibling.
10 The object of the youngest brother was in the air for more than 4 seconds.
Answer:
y1: Ann
y2: Damian
y3: Adam
y4: Debbi
Step-by-step explanation:
Please help with my math
[tex]7 \times {10}^{ - 3} [/tex]
Hopefully you got what I meant, this is easy.
Help please i only have 5 mins left on my test please answer this
P(Head, Diamond AND Head, Heart) = ?
Using it's concept, it is found that the desired probability is given by:
P(Head, Diamond AND Head, Heart) = 1/64.
What is a probability?A probability is given by the number of desired outcomes divided by the number of total outcomes.
In this problem, each outcome is equally as likely, having a 1/8 probability, and they are independent.
Then:
P(Head, Diamond AND Head, Heart) = 1/8 x 1/8 = 1/64.
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whats the median 19 19 20 21 2324 25 26 27 29 33
Answer:
The median is also known as the middle of the data set when it has already been sorted. So the first thing that we need to do is make sure that our data set is fully sorted.
[tex]19, 19, 20, 21, 23, 24, 25, 26, 27, 29, 33[/tex]
Now that we have our data set sorted, we can located the middle. Since this data set has 11 numbers that means number 6 is going to be our median. Counting from the left we get that our median is 24.
Hope this helps! Let me know if you have any questions
Answer: The answer is 24.
Step-by-step explanation: To find the median, you put all your data in order from least to greatest, which would look like:
19, 19, 20, 21, 23, 24, 25, 26, 27, 29, 33
Then, cross out the numbers from front to back until you find your middle number.
19, 19, 20, 21, 23, 24, 25, 26, 27, 29, 33
This leaves 24 left, which is the answer!
If the couple purchase the house and make all their payments, what is their total cost of the house?
$256,000
$443,504
$513,765
$328,650
Answer:
1,514,919
Step-by-step explanation:
I just used a calculator cuz in 6th you can use one but here's the answer
Answer:
If the couple purchases a house and they made all their payments, their total cost of the house would be $1,541,919.
Explanation:
$256,000
$443,504
$513,765
$328,650 +
------------------
$1,541,919
Instructions: find the marked angle in the triangle diagrams and explain how you figured it out.
(Image below) Also giving brainlyest to the person with a good explanation
Answer: 84 degrees
Step-by-step explanation:
this triangle is an isosceles triangle meaning two sides are of equal length ( the two sides in this case being the ones marked with the two lines // and // ) and that also means the triangle will have two equal angles (48 and 48) how do we know that? The triangle looks like this essentially: (see image below) where angle a = to angle b
a triangles angles added up always =180 degrees
Since we proved angle a is equal to angle b, we should be able to also subtract them from 180 to find angle c. 48+48=96
and simply subtract 96 from 180 to get 84 degrees.
therefore the angle is 84 degrees
Chase goes to a restaurant and the subtotal on the
bill was a dollars. A tax of 7% is applied to the bill.
Chase decides to leave a tip of 15% on the entire bill
(including the tax). Write an expression in terms of x
that represents the total amount that Chase paid.
For items 6-8
Write IMPOSSIBLE, UNLIKELY, AS LIKELY AS UNLIKELY, LIKELY and CERTAIN to describe each of the following statements.
6. ___________ The sun will rise tomorrow. (CAPSLOCK ALL LETTERS)
Answer: ________________
7. __________ Bats are birds. (CAPSLOCK ALL LETTERS)
Answer: __________________
8._________ The weather forecast says there is 50% chance of rain today, (CAPSLOCK ALL LETTERS
Answer: _________________
NONSENSE REPORT
convert 0.29 to a percentage
Answer:
0.29 as a percentage is the same as 29%
Step-by-step explanation:
it’s going to be 29% because you just pretend that there isn’t a 0. In front of the 29 and you have 29%.
The decimal number 0.29 is equivalent to 29% when expressed as a percentage.
Given decimal is 0.29.
To convert a decimal number to a percentage, multiply it by 100 and add the percentage symbol (%).
In this case, to convert 0.29 to a percentage
= 0.29 x 100
= 29
Therefore, 0.29 is equivalent to 29% as a percentage.
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4 1/3
What is the value of this equation?
Answer:
4.33
Step-by-step explanation:
1/3=0.33 recuring
4 just eqauls 4
so you add 0.3 recuring to 4
and depending on significant figures it wants you round it ill assume it wants 3 and go 4.33
Using half angle identities, find an EXACT expression for sin(7π/12).
Answer:
±[tex]\frac{1+\sqrt{3} }{2\sqrt{2} }[/tex]
Step-by-step explanation:
We can rewrite [tex]sin(\frac{7\pi }{12} )[/tex] as [tex]sin(\frac{7\pi }{6} (\frac{1}{2} ))[/tex]. The half-angle identity for sin tells us that [tex]sin(\frac{x}{2} ) = \sqrt{\frac{1 - cos(x)}{2} }[/tex] (plus or minus). Now, we can plug in [tex]\frac{7\pi }{6}[/tex] for x. When we do that, we get [tex]\sqrt{\frac{1 - (-\frac{\sqrt{3}}{2}) }{2} }[/tex] = ± [tex]\frac{1+\sqrt{3} }{2\sqrt{2} }[/tex].
Hope this helped! :)
Drag each tile to the correct box.
The composite figures below are made of right prisms.
Answer: Figure 1, Figure 2, Figure 3
Step-by-step explanation:
Blue figure Volume:
[tex](2 *5^{3} ) + (15*5*5) = 625feet^{3}[/tex]
Pink figure volume:
[tex](5^{3})+(5*5*17.5) + (12.5*2.5*5) = 718.75 feet^{3}[/tex]
Green figure volume:
[tex](4*12.5*11) + (2*9*11) = 748 feet^{3}[/tex]
does anyone know this answer?
the question says that the samples included 100 people each, so it's just 100 multiplied by the amount of samples:
7×100=700
Answer: It looks like the answer is 50. But i would go over it with a calculator.
Step-by-step explanation:
.To help him start a business, Cameron took out a $10,000 loan from a bank. The loan has an annual interest rate of 5%. What expectation should Cameron have?
Answer:
[tex]A = 10,000(1.05t)[/tex] where t is in years
Step-by-step explanation:
I'm going to assume that the expectation that Cameron has is the amount of money after t years.
We can use the simple interest formula [tex]A = P(1+rt)[/tex] where A is the final amount, P is the principal, r is the rate, and t is time.
We can plug in 10,000 for P and 0.05 for r, giving us
[tex]A = 10,000(1.05t)[/tex]
2. What is the solution of matrix equation
[2 7
1 4] x=[2 5]
Answer:
(d) X = [-27, 8]
Step-by-step explanation:
The solution to the matrix equation can be found by left-multiplying both sides of the equation by the inverse of the coefficient matrix.
AX = B . . . . given
X = A⁻¹B
__
[tex]X=\left[\begin{array}{cc}2&7\\1&4\end{array}\right]^{-1}\left[\begin{array}{c}2\\5\end{array}\right] =\left[\begin{array}{cc}4&-7\\-1&2\end{array}\right]\left[\begin{array}{c}2\\5\end{array}\right] \\\\X=\left[\begin{array}{c}-27\\8\end{array}\right][/tex]
_____
Additional comment
A calculator or spreadsheet can help with this. The solution can also be found by row-reducing the augmented matrix.
Complete the table by giving the length and area for each
width. (The width is the side perpendicular to the building.)
width (feet) length (feet)
area (square feet)
10
30
40
W
of the play area
The values of length are 100, 60, and 40 feet respectively, area of the rectangle 1000 square feet, 1800 square feet, and 1600 square feet respectively.
What is the area of the rectangle?It is defined as the area occupied by the rectangle in two-dimensional planner geometry.
The area of a rectangle can be calculated using the following formula:
Rectangle area = length x width
We know the perimeter of the rectangle = 2(w+l)
The sum of w+w+l = 120 (given)
2w + l = 120
From the above equation, we can calculate the l of the rectangle:
We have w = 10 feet
l = 100 feet
Area = 10×100 = 1000 square feet
When w = 30
l = 60 feet
Area = 60×30 = 1800 square feet
When w = 40
l = 40 feet
Area = 40×40 = 1600 square feet
Thus, the values of length are 100, 60, and 40 feet respectively, area of the rectangle 1000 square feet, 1800 square feet, and 1600 square feet respectively.
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PLEASE HELP FAST, I'LL MARK YOU AS BRAINLIST
Marcus walks halfway around a square gym with an area of 90,000m². How far did he walk
I need an answer for this:
stirring a hot cup of tea causes a metal spoon to get warm which statement best explains why the spoon gets warm?
Answer:
here we go
Step-by-step explanation:
Stirring a cup of hot tea causes a metal spoon to get warm. Which statement best explains why the spoon gets warm? Heat energy transfers from the hot tea to the spoon.
Answer:
The molecules at the end of the spoon, in turn, collide with the molecules in the adjacent, cooler part, passing the kinetic energy on. This continues through the spoon until the handle molecules are also heated.Step-by-step explanation:
Stay safe, stay healthy and blessed.Have a good day !Thank you
Find the measure of each side of a square
that has an area of 225 square centimeters.