Given the points (0, 5), (1, 7), and (-2, -5), find the equation of the quadratic polynomial that contains
these points. Show your work.
Answers
Answer:
y=-x²+3x+5.
Step-by-step explanation:
1) the common view of the quadratic function is y=ax²+bx+c, where a, b and c - numbers;
2) according to the equation above, it needed to substitute the given coordinates and to make up the system of the equations:
point (0;5): c=5;
poit(1;7): a+b+5=7 ('c' is already known, 5);
point(-2;-5): 4a-2b+5=-5 (c=5);
3) to solve the system:
[tex]\left \{ {{a+b+5=7} \atop {4a-2b+5=-5}} \right. \ = > \ \left \{ {{a=-1} \atop {b=3}} \right.[/tex]
4) finally, if a=-1, b=3 and c=5, then
y=-x²+3x+5.
Related Questions
Tanvi received a large box of chocolates for Valentine's Day, and about 30% of the chocolates have a
caramel filling. Tanvi took out 2 to eat for dessert. How likely is it that at least 1 has a caramel filling?
Tanvi simulates the situation by creating a spinner with 3 white sections and 7 red sections. She spins
the spinner 2 times. Each time the spinner lands on a white section, it represents a chocolate with a
caramel filling. Tanvi records the results by writing "W" when it lands on a white section and "R" when it lands on a red
section. Here are the results of 20 trials:
RR RR RR RW RR
WR
RR
WR
RR
RW
RR
WR RR
RW RR
RW
I RW RR RR
WR
Based on Tanvi's results, what is the probability that at least 1 of the chocolates has a caramel filling?
Answers
Answer:
45%
Step-by-step explanation:
In Tanvi's simulation, landing on a white section represents a chocolate with a caramel filling. Tanvi records 20 trials, and the spinner lands on at least 1 white section in 9 of them. So, the probability that at least 1 of the chocolates has a caramel filling is
9
20
Convert
9
20
to a percent. Write an equivalent fraction with 100 as the denominator.
9
20
=
95
205
=
45
100
Based on Tanvi's results, the probability that at least 1 of the chocolates has a caramel filling is 45%.
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
You have read 4 of the books shown. Which choice shows 2 ways of writing the fraction of these books that you read?
Answers
So it can be shown as:
[tex]\sf \dfrac{read \ books}{total \ books \ in \ list}[/tex]
[tex]\hookrightarrow \sf \dfrac{4}{12}[/tex]
on simplifying
[tex]\hookrightarrow \sf \dfrac{1}{3}[/tex]
So, option 1 is correct.
First one
Let's find
Total read books=4Total books=12fraction:-
4/12Cancel by 4
1/3Hence verified
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.A coin is biased to display heads 75% of the time. it is tossed 20 times, and the outcomes are recorded. the most improbable simulation for this coin is heads.
Answers
A percentage is a way to describe a part of a whole. The most improbable simulation for this coin is heads are 9.
What are Percentages?A percentage is a way to describe a part of a whole. such as the fraction ¼ can be described as 0.25 which is equal to 25%.
To convert a fraction to a percentage, convert the fraction to decimal form and then multiply by 100 with the '%' symbol.
The most improbable simulation for this coin for heads is the frequency of heads coming up out of 20 which is far from the estimated frequency. Since out of these 20 times 75% of the times the head will come up. Therefore, the number of times the head will come up can be written as,
[tex]75\%\ of\ 20\\\\= \dfrac{75}{100} \times 20\\\\= 15[/tex]
Now it is estimated that at least 15 times out of 20, the head will come up. Thus, the most improbable simulation for this coin is heads are 9.
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Answer:
A coin is biased to display heads 75% of the time. It is tossed 20 times, and the outcomes are recorded. The most improbable simulation for this coin is
9 heads.
Step-by-step explanation:
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]
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 are the missing measures for E and J???
Are the triangles similar? Yes or no?
Answers
Answer:
No
Step-by-step explanation:
To tell whether two triangles are similar or not, we can compare their side lengths or angle measures
in this case, only angle measure are given so will compare those:
m<F = m<I but this is not enough, we need to compare other angles as well
m<H is not equal to m<G
The sum of interior angles in a triangle is equal to 180
so the measure of angle J
100+55+J = 180
J = 25
The measure of angle E
100+35+E = 180
E = 45
Now, neither of these angles are equal to each other so we can conclude that these triangles are not similar.
Someone, please help me! I will give Brainliest!
Identify the key features of the parabola, 8(y + 4) = (x + 1)2:
Axis of Symmetry:
Vertex:
Focus:
Directrix:
Answers
Answer:
Step-by-step explanation:
8(y+4)=2(x+1)
divide by 8 y+4=1/4x+1/4 subtract 4 y=1/4x - 3 3/4 multiply by 4 y=1/4(x-15)
Answers:
Equation in standard form: [tex]y = \frac{1}{8}(x+1)^{2} -4[/tex]
Axis of Symmetry: x = -1
Vertex: (-1, -4)
Focus: (-1, -2)
Directrix: y = -6
Step-by-step explanation:
First, let's clean up some of the mess with the equation that we have been given in this question and put it in standard form so that we can find the features we've been asked to give.
Our initial equation is: [tex]8(y+4)=(x+1)^{2}[/tex]
In order to put our equation in standard form, we must isolate y, so that it is in terms of y.
First, we need to divide both sides by 8. When we do this, we get [tex]y+4=\frac{(x+1)^{2} }{8}[/tex] or [tex]y+4=\frac{1}{8}(x+1)^{2}[/tex]. Then we need to subtract 4 from both sides to get: [tex]y = \frac{1}{8}(x+1)^{2} -4[/tex].
Now, we can start to find the features of the parabola. Remember, the standard form of equations involving parabolas is [tex]y=a(x-h)+k[/tex] where [tex]a =\frac{1}{4p}[/tex].
The axis of symmetry is at [tex]x=h[/tex], in this case [tex]h=-1[/tex] so the axis of symmetry is [tex]x=-1[/tex].
The vertex is located at [tex](h, k)[/tex]. As we previously stated [tex]h=-1[/tex], but additionally, [tex]k=-4[/tex] making the vertex located at [tex](-1,-4)[/tex].
The focus is located at [tex](h, k+p)[/tex] and the directrix is located at [tex]y=k-p[/tex]. For this, we need to find p which we can find with the equation [tex]a =\frac{1}{4p}[/tex]. Substituting the value of “a” into the equation, we get [tex]\frac{1}{8} = \frac{1}{4p}[/tex]. We can cross-multiply to get the equation [tex]4p=8[/tex]. Dividing by 4 on both sides, we get [tex]p=2[/tex]. Now we can find the focus and directrix.
The focus is located at [tex](-1, [-4+2])[/tex] or [tex](-1,-2)[/tex] and the directrix is represented by the equation [tex]y=(-4-2)[/tex] or [tex]y=-6[/tex].
Hopefully this answered your question this time, and with this, I hope you are able to solve it without help the next time
what is the probability of pulling a red card out o a deck of cards
Answers
Answer:
26/52 or 1/2
Step-by-step explanation:
there's 52 cards in a deck 26 of them are red 26 of them are black
two events A and B, are independent P(A)=0.3 P(A and B)=0.24 what is P(B)
Answers
Answer: 0.8
Step-by-step explanation: where the events are independent you multiply p(A) by p(B)
Please help!! Will mark brainlyest.
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.
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Answer:
D ) y = 5^x + 2
Step-by-step explanation:
Here ya go ladies and gentlemen
(1,-5) is on the graph of f(x), find the corresponding point for the function f(x)-1
Answers
Answer:
(5,-1)
Step-by-step explanation:
rotate the point
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]
Alexandra and Stephanie are sisters, and they're saving their money to buy a used car. Together they have more than $2,500, and Alexandra has $700 more than Stephanie. How much money does Stephanie have?
Answers
Answer:
Stephanie has more than $900
Step-by-step explanation:
Represent the unknowns: a for Alexandra and s for Stephanie.
Then a + s > $2,500, and a = s + $700.
Substituting the latter into the former equation, we get:
(s + $700) + s > $2,500, or
2s > $1800
Then s > $900; Stephanie has more than $900.
help im stuck on this question
Answers
Answer:
The answer is C. The frequency is 15 more than expected.
Step-by-step explanation:
A dice has 1-6. There are 3 odd numbers and 3 even numbers. So a 50% chance of landing an even number. Since you rolled 30 times and got 18 even then more than half of 30 times.
PLEASE I REALLY NEED SOMEONE TO ANSWER THIS FOR ME. IF SOMEONE CONTINUES TO ANSWER MY QUESTIONS ILL KEEP UPPING THE POINTS>
Answers
Answer:
WHAT NEEDS TO BE ANSWERED?????
Step-by-step explanation:
I CAN MAYBE HELP!!!
Answer:
Which DId you forgot to link it?
Step-by-step explanation:
What is the mean of the set of data?
25.2, 26.4, 28.7, 25.5
Answers
Check the picture below.
Mr. Blue's first year salary is $30,000 and it doubles each year. What is the explicit rule for the sequence in simplified form?
Question 3 options:
an = 30,000(2)n
an = 29,500(2)n−1
an = 30,000(2)n−1
an = 30,000(0. 5)n+1
Answers
Answer:
an = 30000 * 2^(n-1)
Step-by-step explanation:
The explicit rule of Mr. Blue 's salary
is an = 30000 * 2^(n-1)
How to determine the explicit
How to determine the explicitformula?
Mr. Blue's salary is a geometric sequence
with the following parameters:
First term, a1 = 30000
Rate, r = 2
The explicit rule is calculated as:
an = a1* r^(n-1)
This gives
an = 30000 * 2^(n-1)
A scientist wants to estimate the number of lions living in a region.
On Thursday, he locates and tags some lions. I
On Friday he returns and locates 10 less lions than he had on Thursday.
He notices that 4 of the lions are tagged
The scientist works out an estimate for the total number of lions living in the
region.
He notices that the number of lions that he had caught on Thursday, was a
fifth of the total number of lions.
How many lions live in the region?
Answers
The number of the lions that live in the region investigated by the considered scientist is 80.
How to form mathematical expression from the given description?You can represent the unknown amounts by the use of variables. Follow whatever the description is and convert it one by one mathematically. For example if it is asked to increase some item by 4 , then you can add 4 in that item to increase it by 4. If something is for example, doubled, then you can multiply that thing by 2 and so on methods can be used to convert description to mathematical expressions.
For this case, we're specified that:
He locates and tags lions on ThursdayOn friday, he locates 10 less lions than he had on Friday.He notices (on friday) that 4 of the lions are tagged.The number of lions caught on thursday was a fifth of the total number of lions.Let we take:
x = number of lions the scientist located and tagged on thursday.
Then, we get:
x - 10 = number of lions the scientist located (and assumingly found that they're tagged) on friday,
4 = number of lions he found tagged on friday.
That means, x -10 is same number as 4
or, we get:
[tex]x - 10 = 4\\\text{Adding 10 on both the sides}\\\\x = 14[/tex]
That means, on thursday, the scientist located and tagged 14 lions.
Now, suppose that the region had 'y' number of lions,
Then, as per the data in the question,
one-fifth of y = number of lions located by scientist on thursday
or, we get:
[tex]\dfrac{y}{5} = x\\\\\dfrac{y}{5} = 14\\\\\text{Multiplying 5 on both the sides}\\\\y = 80[/tex]
Thus, the number of lions that live in the region considered is 80
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The total number of lines is 70.
We have given that,
A scientist wants to estimate the number of lions living in a region.
On Thursday, he locates and tags some lions.
On Friday he returns and locates 10 less lions than he had on Thursday.
He notices that 4 of the lions are tagged
The scientist works out an estimate for the total number of lions living in the region.
we have to determine the no of lines in the length.
on Thursday no.of lines=x
on friday=(x-10)=4
x-10=4
add like terms
What is the like terms?Like terms are terms whose variables and their exponents such as the 2 in x^2 are the same.
x=10+4
x=14
No.of total lions =5th of (no. of tagged on Thursday.)
=5(14)
=70
Therefore the total number of lines is 70.
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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
A bike wheel has a 16-inch diameter. Approximately how far will the wheel travel in three rotations? Use 3.14
for π
Answers
Answer:
151 inches
Step-by-step explanation:
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]
Colter rides his dirt bike 8800 yards in 3 days how many miles did he ride?
Answers
Answer:
5 miles
Step-by-step explanation:
Step 1: Convert yards to miles
[tex]1760\ yards = 1\ mile[/tex]
[tex]8800\ yards * \frac{1\ mile}{1760\ yards}[/tex]
[tex]5\ miles[/tex]
Answer: 5 miles
HELP ME PLEASE WORTH 25 points
Answers
Answer:
A. 8
Step-by-step explanation:
When finding the radius of a circle given area we have to remember the following formulas
[tex]A=\pi *r^{2}[/tex] and [tex]r^2=\frac{A}{\pi }[/tex] or [tex]r=\sqrt{\frac{A}{\pi } }[/tex]
So using either [tex]r^2=\frac{A}{\pi }[/tex] or [tex]r=\sqrt{\frac{A}{\pi } }[/tex] we fill out the following
[tex]r^2=\frac{64\pi }{\pi }[/tex] [tex]r=\sqrt{\frac{64\pi }{\pi } }[/tex] both would equal 8
The image below explains how we get 8
The perimeter of a square notepad is 124 centimeters. How long is each side?
Answers
Answer:
31 Centimeters
Step-by-step explanation:
Since a square has 4 equal sides, each side will be the same in measurement. Therefore, we take our total (124 centimeters) and divide it into 4.
124 / 4 = 31
Please help and match the following.
Answers
Answer:
-4x^3 is a monomial
2x + 3 is a binomial
5x^2 + 2x - 10 is a trinomial
Step-by-step explanation:
Monomial equations have one term, biomials have two terms, and trinomial have three.
Answer:
-4x^3 is Monomial
2x + 3 is binomial
5x^2 + 2x - 10 is trinomial
Step-by-step explanation:
Monomial means one term
Binomial is 2 terms
Trinomial is 3 terms
Hope this helps!
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:
A system of equations has no solution. if y = 8x 7 is one of the equations, which could be the other equation? 2y = 16x 14 y = 8x – 7 y = –8x 7 2y = −16x − 14
Answers
A system of equations has no solution. if y = 8x+ 7 is one of the equations, The other equation will be y = 8x - 7.
What is the system of two equations?A set of two linear equations with two variables is called a system of linear equations. They create a system of linear equations when evaluated collectively.
The first equation is given as:
y = 8x + 7
The equations in the system would have different constant values if the system of equations had no solution.
y=8x+b
Where:
b is a variable that is not equal to 7.
The equation whose standard form is y=ax+b has no solution. Only equation 2 satisfies the generalized form.
Hence.if y = 8x+ 7 is one of the equations, The other equation will be y = 8x - 7.
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Answer:
B
Step-by-step explanation:
A system of equations has no solution. If y = 8x + 7 is one of the equations, which could be the other equation?
2y = 16x +14
y = 8x – 7
y = –8x + 7
2y = −16x − 14