Type the correct answer in the box.
Consider the table below.
х у
-3 0.5
-2
1
-1 2.5
0
5
18.5
Complete the standard form equation representing the quadratic relationship displayed above, where a, b, and care constants.
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Answer:
Step-by-step explanation:
Use the standard form equation along with 3 of the coordinates from the table. I used (-1, 2.5), (0, 5), and (1, 8.5). Begin always with the coordinate where you have a 0:
[tex]5=a(0)^2+b(0)+c[/tex] and we get immediately that c = 5. We can use that value as move forward with the next coordinate pair.
[tex]8.5=a(1)^2+b(1)+5[/tex] and
8.5 = a + b + 5 and
3.5 = a + b Hold that thought while we come up with the second equation for this system.
[tex]2.5=a(-1)^2+b(-1)+5[/tex] and
2.5 = a - b + 5 and
-2.5 = a - b Now solve this system using the method of eliination:
a + b = 3.5
+ a - b = -2.5
so
2a = 1 and a = 1/2 Now we can plug that in and solve for b:
a + b = 3.5 becomes
1/2 + b = 3.5 so
b = 3 and the equation is
[tex]y=\frac{1}{2}x^2+3x+5[/tex]
Related Questions
classify the expression by both degree and terms 2x4 - x +5
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Answer:
x=3
Step-by-step explanation:
Find the volume of this sphere.
Use 3 for T.
Answers
Help help help help
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\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}
Answers
Answer:
[tex]= \frac{2x-3\sqrt{x} }{x-1}[/tex]
Step-by-step explanation:
Given the expression
[tex]\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}[/tex]
Expand
[tex]\frac{(\sqrt{x} +1)^{2} +(\sqrt{x} -1)^{2} )}{(\sqrt{x} +1)(\sqrt{x} -1)} -\frac{3\sqrt{x} +1}{x-1}\\= \frac{x+2\sqrt{x}+1+(x-2\sqrt{x} +1) }{x-1}- \frac{3\sqrt{x} +1}{x-1}\\= \frac{2x+1}{x-1} - \frac{3\sqrt{x} +1}{x-1}\\= \frac{2x+1-(3\sqrt{x} +1)}{x-1}\\= \frac{2x-3\sqrt{x} +1-1}{x-1}\\= \frac{2x-3\sqrt{x} }{x-1}[/tex]
This gives the simplified form
pls ans this
its urgent
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Solve for x in these two similar triangles
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The standard form of a quadratic function is given below. Select ALL
statements which MUST be true about its graph.
f (x) = ax? + bx + c
A. The y-intercept of the graph is at (0,c).
B. The graph has an x-intercept at (c,0).
C. When "a" is positive, the graph opens up.
D. The graph always has two distinct x-intercepts,
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Answer:
A; C.
Step-by-step explanation:
B. not correct: the graph can have no interception; one interception or two interception;
D. not correct: the graph can have no interception; one interception or two interception.
What is the value of the 9 in the number 0.09432
Answers
Answer:
hundredths
Step-by-step explanation:
Numbers after the decimal start with
tenth
hundredth
The sum of the first eight terms in a Geometric Series is 19680 and the sum of the first four terms is 240. A) Find the first term. B) Find the common ratio. C) Justify your answers by showing steps that demonstrates your answers generate S8=19680 and S4=240.
Answers
Answer:
First Term = 6
Common Ratio = 3
Step-by-step explanation:
According to the Question,
Given, The sum of the first eight terms in a Geometric Series is 19680 and the sum of the first four terms is 240 .Thus, [tex]S_{8} = 19680[/tex] & [tex]S_{4} = 240[/tex] .
The Sum of n-term of Geometric Mean is [tex]S_{n} = \frac{a(r^{n-1)} }{r-1}[/tex] Where, r>1 , a=First term of G.P & r=common Ratio .Now, on solving [tex]\frac{S_{8} }{S_{4} }[/tex] we get,
[tex]\frac{19680}{240} = \frac{\frac{a(r^{8-1)} }{r-1}}{\frac{a(r^{4-1)} }{r-1}}[/tex]
[tex]82 = \frac{r^{8}-1 }{r^{4}-1 }[/tex]
[tex]82r^{4}-82 = r^{8}-1\\r^{8}-82r^{4}+81 = 0\\r^{8}-81r^{4}-r^{4}+81 = 0\\(r^{4}-81)( r^{4}-1) =0[/tex](r=1 is not possible so neglect [tex]( r^{4}-1) =0[/tex] )
So, r=3 Now Put this value in [tex]S_{4} = {\frac{a(r^{4-1)} }{r-1}}[/tex] We get a=6 .
Which of the following are not polynomials? O A. x2 +x+1 O B. X-2 + x + 1 am. x + V3x+1 OD. 3+x+1 E. x + 0x2 + 2x + 2
Answers
Answer:
Option B
Step-by-step explanation:
Look.......Polynomial is something which has more than 3 term..So, as you can see option B has more than three.
(1.3) Sequence A: 4; 7; 10; 13; 16; Sequence B: 5; 10; 20; 40; 80; .......... Sequence C: 2; 5; 10; 17; 26; (1.3.1) Write down the next three numbers in each of given sequences. (3) Sequence A Sequence B: Sequence C: (1.3.2) Write down how you decided what the next number would be in each of the three sequences. (3) Sequence A: Sequence B: Sequence C
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Answer with Step-by -step explanation:
Sequence A;4,7,10,13,16
[tex]a_2-a_1=7-4=3[/tex]
[tex]a_3-a_2=10-7=3[/tex]
The difference between two consecutive terms is equal. Therefore, it forms arithmetic sequence.
Common difference, d=3
a=4
[tex]a_n=a+(n-1)d[/tex]
[tex]a_6=a+5d=4+5\times 3=19[/tex]
[tex]a_7=a+6d=4+6(3)=22[/tex]
[tex]a_8=a+7d=4+7(3)=25[/tex]
Sequence B: 5,10,20,40,80,...
[tex]a_1=5,a_2=10,a_3=20[/tex]
[tex]\frac{a_2}{a_1}=\frac{10}{2}=2[/tex]
[tex]\frac{a_3}{a_2}=\frac{20}{10}=2[/tex]
The ratio of two consecutive terms is equal. Therefore, it forms geometric sequence.
Common ratio, r=2
a=5
[tex]a_n=a r^{n-1}[/tex]
[tex]a_6=ar^5=5(2)^5=160[/tex]
[tex]a_7=ar^6=5(2^6)=320[/tex]
[tex]a_8=ar^7=5(2^7)=640[/tex]
Sequence C:2,5,10,17,26,..
a1=2
[tex]a_2=5=2+3=a_1+3[/tex]
[tex]a_3=10=5+5=a_2+5[/tex]
[tex]a_4=17=10+7=a_3+7[/tex]
[tex]a_5=26=17+9=a_4+9[/tex]
From the following pattern
We can get
[tex]a_6=a_5+11=26+11=37[/tex]
[tex]a_7=a_6+13=37+13=50[/tex]
[tex]a_8=a_7+15=50+15=65[/tex]
In triangle ABC, b = 600, ∠B = 11°, and ∠C = 75°. Find a.
Answers
Answer:
Step-by-step explanation:
We could use the Law of Sines if we only knew what angle A was. It just so happens that by the Triangle Angle-Sum Theorem, angle A is equal to
180 - B - C. Therefore,
angle A = 180 - 11 - 75 so
angle A = 94. And the Law of Sines is
[tex]\frac{sin94}{a}=\frac{sin11}{600}[/tex] and cross multiply to get
600sin94 = asin11 and solve for a:
[tex]a=\frac{600sin94}{sin11}[/tex] gives you that
a = 3136.85
A rectangle measures 15 cm by 10 cm is given, if the length of side is
increased by 20%, find the increase of area in percentage.
Answers
Answer:
20 % increase in Area
Step-by-step explanation:
1. Original Rectangle Area = 150cm ²
2. 20% of 15 is 3
3. Increased length is equal to 18
4. Increased Rectangle Area = 180cm ²
5. Ten percent of 150 = 15.
6. 15x2(ten percent) = 30. Which give us 150+30 equal to 180.
7. 2 ten percent equals 20%
8. Answer is 20%.
Find the measure of each angle indicated. Please help !!
Answers
Answer: 86°
Step-by-step explanation:
You add 28°+58° to get 86
a scalene triangle always equals (adds up to) 180°
So you minus 86° from 180 to get 94° for angle EGF
Then since line EGT is 180° the ? has to add together with 94° to find your answer
94°+?=180°
180°-94°= 86°
Was this equation solved correctly? How do you know?
Subtract three from both sides
Combine like terms
Divide by 4 on both sides
Simplify
19 = 4x + 3
19 - 3 = 4x + 3-3
16 = 4x
16/4 = 4x/4
3 = x
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What's the domain of the graph?
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Step-by-step explanation:
In interval form, the domain of f is (−∞,∞).
1. (x^3 - 9 x^2 + 26 x - 24) ÷ (x - 4)
2. (6 x^3 + x^2 - 26 x - 21) ÷ (3x - 7)
3. 2 x^4 - x^3 + 10 x^2 + 8 x - 6) ÷ (x^2 - x + 6)
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Answer:
1. = x^2 -5x+6
Step-by-step explanation:
2. = 2x^2 +5x+3
3. =2x^2 +(x-1) +((x)/x^2 -x+6)
is 15 over -4 negative
Answers
Answer:
15 is larger than -4
Step-by-step explanation:
Answer:
Yes
Step-by-step explanation:
15 ÷ (-4) = -3.75
When 345 is multiplied by a power of 10 the number of zeros in the product is related to the power of 10. Explain how the number of zeros relates to the power of 10.
Answers
Answer:
The Number of Zeroes In The Results is Always equal To the Powers of 10.
Step-by-step explanation:
Example:-
345*[tex]10^{2}[/tex] = 34500
345*[tex]10^{5}[/tex] = 34500000
345*[tex]10^{7}[/tex] = 3450000000
345*[tex]10^{8}[/tex] = 34500000000
(In the Above examples, There is All The Numbers of Zeroes In The Results is equal To the Powers of 10)
f(x)4x+1 and g(x)=x^2 -5
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Answer:
B. x² + 4x - 4
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to RightAlgebra I
Terms/CoefficientsFunctionsFunction NotationStep-by-step explanation:
Step 1: Define
Identify
f(x) = 4x + 1
g(x) = x² - 5
(f + g)(x) = f(x) + g(x)
Step 2: Find
Substitute in functions: (f + g)(x) = 4x + 1 + x² - 5Combine like terms: (f + g)(x) = x² + 4x - 4Answer:
B
Step-by-step explanation: 6 18 11 18
f(x)=4x+1 and g(x)=x^2 -5
f(x)= 4x+1
g(x)=x^2 -5 just add these two equations
(f+g)(x) = x² + 4x +1 - 5
(f+g)(x) = x² + 4x - 4 B
please give answer of 6 number
Answers
Answer:
[tex]7,500[/tex]
Step-by-step explanation:
Let's solve this problem step-by-step. The library had 1,500 books in 2011. The ratio of books in 2011 and in 2012 is 1:2. Therefore, let the number of books in 2012 be [tex]x[/tex].
We have the following proportion:
[tex]\frac{1}{1,500}=\frac{2}{x},\\x=2\cdot 1,500=3,000[/tex]
Therefore, there were 3,000 books in 2012. The ratio of books in 2012 and in 2013 is 2:5. Let the number of books in 2013 be [tex]y[/tex].
We have:
[tex]\frac{2}{3,000}=\frac{5}{y},\\2y=5\cdot 3,000,\\2y=15,000\\y=\boxed{7,500}[/tex]
Therefore, there were 7,500 books in 2013.
Answer:
7,500 books
Step-by-step explanation:
What is the angle measure ?
Answers
Answer:
140 degrees
Step-by-step explanation:
7. From eye level 5 feet off the ground, a person has to look up at an angle of 35
degrees to see the top of a tree 60 feet away. How tall is the tree.
Answers
Answer:
47.01 ft
Step-by-step explanation:
answer in photo above
Which conversion factor would you use to convert from meters to feet?
Answers
Answer:
To convert a meter measurement to a foot measurement, multiply the length by the conversion ratio. The length in feet is equal to the meters multiplied by 3.28084.
Step-by-step explanation:
the question is on the image
Answers
Answer:
70
Step-by-step explanation:
the fraction 7/10 turns into 70% which means 70 out of 100 tickets were sold.
Answer:
70 tickets sold
Step-by-step explanation:
Multiply the number of tickets by the fraction of tickets sold
100 *7/10
Rewriting
100/10 * 7
10*7
70
Which of the following is the quotient of the rational expressions shown below?
Answers
Answer:
A
Step-by-step explanation:
multiple across
5 * 6 = 30
2x+1 * x = 2x^2 + x
1. Which two points fail the VLT here in this graph?
PLEASE HELP!!!!
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They are on the same vertical line so they fail
Help asappppp hbshhshshhshshsshshshs
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9 on the top as well so 9 x 2 18 3x2 6 3
Mary’s school is selling tickets to a choral performance. On the first day of ticket sales the school sold 4 senior citizen tickets and 2 child tickets for a total of $64. The school took in $204 on the second day by selling 12 senior citizen tickets and 8 child tickets. What is the price of one senior citizen ticket and one child ticket.
Answers
Answer:
$13 - senior
$6 - child
Step-by-step explanation:
set up a system of equations:
s = senior tickets price
c = child tickets price
4s + 2c = 64; you can simplify this by dividing through by 2 to get:
2s + c = 32
12s + 8c = 204; you can simplify this by dividing through by 4 to get:
3s + 2c = 51
we can say that 'c' = 32-2s' and substitute that for 'c' in the second equation:
3s + 2(32-2s) = 51
3s + 64 - 4s = 51
-s = -13
s = 13
now find 'c' by substituting 13 for 's':
2(13) + c = 32
26 + c = 32
c = 6
ONE reason why people loan money from banks.
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Answer:
to use the money when in an emergency