Answers
Answer:
1, -0.5, -6.25
Step-by-step explanation:
The number in the left box is the leading coefficient. The coefficient of x^2 is 1, so that goes in the first box.
__
The number in the second box is half the coefficient of x, divided by the leading coefficient:
(1/2)(-1)/1 = -1/2
__
The number in the third box (k) is the number required to make the rewritten g(x) match the original g(x). So far, we have ...
g(x) = 1(x -1/2)^2 + k = x^2 -x -6
x^2 -x +1/4 +k = x^2 -x -6 . . . . . expand the square
1/4 +k = -6 . . . . . . . . . . . . . . . . . subtract the x-terms from both sides
k = -6 1/4 . . . . . . . . . . . . . . . . . . subtract 1/4
So, you have ...
[tex]g(x)=\boxed{1}(x+\boxed{-0.5})^2+\boxed{-6.25}[/tex]
Related Questions
double the sum of x and 5
Answers
Answer:
2(x+5) = 2x+10
Step-by-step explanation:
2(x+5)
= 2*x + 2*5
= 2x+10
Solve the system of equations
Y = 4x - 11
Y = x + 13
x = ??????
Y = ??????
Please tell me what Y and X are first..
Answers
arrange the following fraction in ascending order 2/3 1/6 3/5
Answers
Answer:
2/3 3/5 1/6
Step-by-step explanation:
look at the denominators and arrange from least to greater
A wall Of a building is 34 inches wide, 14 inches is concrete, 12 inches is brick, and 8 inches is limestone. what fraction of the wall is brick?
Answers
Step-by-step explanation:
It is given that,
A building is 34 inches wide. Its 14 inches is concrete, 12 inches is brick, and 8 inches is limestone. We need to find the fraction of the wall is brick.
A fraction is in the form of x/y. y is total value and x is a part of y.
Here, 12 inches is brick. So, its fraction is :
[tex]F=\dfrac{12}{34}=\dfrac{6}{17}[/tex]
So, fraction of [tex]\dfrac{6}{17}[/tex] is the wall which is brick.
19. If the polynomial P(x) = 27x^3 + 9x^2 – 3x – 10 is divided by 3x – 2, the remainder will be
options:
A) 1
B) 2
C) 3
D) 0
Answers
Answer:
D) 0
Step-by-step explanation:
Remainder is zero as 10 is fully divisible by 2.
Proof:
27x^3 + 9x^2 – 3x – 10 = (3x -2) (9x^ 2 +9x+5)Correct choice is D) 0
Calculate the total surface area of a rectangular box 10cm long, 8cm wide and 6cm tall.
Answers
Answer:
The answer is
376 cm²Step-by-step explanation:
Since the rectangular box is a cuboid,
Total surface area of a cuboid is given by
2( lw + wh + lh)Where
l is the length
w is the width
h is the height
From the question
l = 10 cm
w = 8cm
h = 6cm
Substitute the values into the above formula
That's
Total surface area of the rectangular box is
2 [ (10)(8) + (8)(6) + (10)(6) ]
2 [ 80 + 48 + 60 ]
2( 188)
We have the final answer as
Total surface area = 376 cm²Hope this helps you
If y varies inversely with x and y=11 when x=3, find the equation that relates x and y.
Answers
Answer:
y = [tex]\frac{33}{x}[/tex]
Step-by-step explanation:
Use the inverse relationship equation, y = [tex]\frac{k}{x}[/tex]
Plug in what we know to solve for k:
11 = [tex]\frac{k}{3}[/tex]
33 = k
Plug 33 in as k to find the equation:
The equation will be y = [tex]\frac{33}{x}[/tex]
Let f(x) = 1/x+2 and g (x) = 1/x-3. Find (f/g) (x). Assume all appropriate restrictions to the domain. help!!!!
Answers
Answer:(f/g)(x)=(1+2x)/(1-3x) where x<>0
Step-by-step explanation:
f(x)= 1/x+2= (1+2x)/x , x<>0
g(x)=1/x-3=(1-3x)/x , x<>0
=>f(x)/g(x)= (1+2x)/(1-3x) , x<>0
A. 3/4=a/36
B.4/9=b/36
Answers
Answer:
A. = 27 B. = 16
Step-by-step explanation:
A. 36/4 = 9 3X9 = 27
B. 36/9 = 4 4X4 =16
How many time is 0.02 contained in 807 or 80
Answers
Answer:
0.02 appears 40,350 times in 807 & 4000 times in 80
Step-by-step explanation:
807/0.02=40,350
80/0.02=4000
Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)Binomial (-x + 3) and trinomial (-2x2 + 5x + 6) are the factors of what polynomial? (Hint: 4 and 2 are factors of 8. Multiply.)
Answers
Answer:
2x^3-11x^2+9x+18
Step-by-step explanation:
By multiplying both the binomial and the trinomial given, we obtain a polynomial which contains both as factors. We notice as well that the given trinomial doesn't have 3 as a root (so there is no multiple root x = 3 in the product we obtain:
[tex](-x+3)\,(-2x^2+5x+6)=2\,x^3-5x^2-6x-6x^2+15x+18=2x^3-11x^2+9x+18[/tex]
Then, this new polynomial
[tex]2x^3-11x^2+9x+18[/tex]
has both given polynomials as factors.
the ratio of Encik Arif's mass to his sons mass is 3:2 . If his son's mass is 42 kg, find Encik Arif's mass.
Answers
Answer:
Encik Arif's mass is 63kgStep-by-step explanation:
Let Encik Arif's mass be x
the ratio of Encik Arif's mass to his son's mass is 3:2
That's
[tex] \frac{3}{2} [/tex]The son's mass is 42, so the ratio of Encik Arif's mass to his son's is
x : 42
That's
[tex] \frac{x}{42} [/tex]Now equate the two fractions
That's
[tex] \frac{3}{2} = \frac{x}{42} [/tex]Cross multiply
3(42) = 2x
126 = 2x
Divide both sides by 2
We have the final answer as
x = 63Hope this helps you
Evaluate the expression when x= -3 X^2+8x-7
Answers
9-24-7
= -22
Your answer is -22.
PLEASE HELP!!!! what is the value of 6n - 2 when n = 3?
A: 7
B: 6
C: 16
D: 12
Answers
Answer: C, 16
Step-by-step explanation:
6n - 2 when n = 3
Replace n with 3
1. 6(3) -2
2. 6(3) =18
3.18-2 = 16
Answer is 16.
Answer: C: 16
Step-by-step explanation: 6*3 =18. 18-2=16
rounds the capacity of a 1.85 liter jug to the tenth
Answers
Answer:
1.9 liters.
Step-by-step explanation:
The hundredths digit is 5 so we add 1 to the tenths digit.
Answer: 1.9 liter
Step-by-step explanation: the tenth is the first digit after the decimal point. Anything greater than it equal to 5 will be rounded up. So 1.85 is rounded up to 1.9
Numbers 2-4 Will choose brainliest
Answers
Answer:
2. 9, 8+9
3. 17-8=9, 17, 8, 9
4. 13-7=6
Step-by-step explanation:
Please help me ?! ❤️❤️
Answers
Answer:
Hey there!
(3,5) is your answer.
Hope this helps :)
Answer:
its (3,5)
hope it helps
(3+4i)+(8+2i) complex number in standard form
Answers
Answer:
(3 + 4i) + (8 + 2i) = 3 + 4i + 8 + 2i
(3 + 4i) + (8 + 2i) = (3 + 8) + (4i + 2i)
(3 + 4i) + (8 + 2i) = 11 + 6i
hope it helps if yes mark me BRAINLIEST!
Tysm!
:)
Answer:
11 + 6i
Step-by-step explanation:
Well, by the looks of it, you're combining like terms. Just add numbers that have the same variable or jut add coefficients:
(3 + 4i) + (8 + 2i)
= 3 + 4i + 8 + 2i
= (3 + 8) + (4i + 2i)
= 11 + 6i
Solve the following:
2x – 7 > 9
a
3> 8
b
x > 1
C
3 < 8
d
x>-1
Answers
Answer: x > 8
2x - 7 > 9
2x > 9+7
2x > 16
2x / 2 > 16 / 2
x > 8
-13+(-4)÷2-3[-{(-3)×(-7)-(3+5)}]
Answers
Explanation:
(-13-4)/2-3[-{(-3) x (-7)-(3+5)}]
= -17/2-3[-{21 - 3 - 5}]
= -17/2-3[-13]
= -17/2-3-13
= -17/-14
= 17/14
Solve -4r + 18= 6 I need this equation
Answers
Answer:
r = 3Step-by-step explanation:
[tex]-4r + 18= 6\\\\\mathrm{Subtract\:}18\mathrm{\:from\:both\:sides}\\\\-4r+18-18=6-18\\\\\mathrm{Simplify}\\\\-4r=-12\\\\\mathrm{Divide\:both\:sides\:by\:}-4\\\\\frac{-4r}{-4}=\frac{-12}{-4}\\\\\mathrm{Simplify}\\\\r=3[/tex]
What are the explicit equation and domain for a geometric sequence with a first term of 5 and a second term of −10? an = 5(−2)n − 1; all integers where n ≥ 1 an = 5(−2)n − 1; all integers where n ≥ 0 an = 5(−15)n − 1; all integers where n ≥ 1 an = 5(−15)n − 1; all integers where n ≥ 0
Answers
Answer:
A
Step-by-step explanation:
The standard form of an explicit formula for a geometric sequence is given by:
[tex]x_n=a(r)^{n-1}[/tex]
Where n is the nth term, a is the initial term, and r is the common ratio.
We are given that the first term is 5. Hence, a = 5.
Also, we are given that the second term is -10. Therefore, the common ratio r is -2, because we multiply the first term by -2 to acquire -10.
Substituting yields:
[tex]x_n=5(-2)^{n-1}, n\geq 1, n\in\mathbb{Z}[/tex]
(Note: Z means the set of all integers. This is required because the term number can only be positive starting from one. For instance, we can't have the 0th term or the 1.5th term.)
In conclusion, the answer is A.
Which expression is the simplest form of...
Answers
Answer:
The answer is option A
Step-by-step explanation:
[tex]( {x}^{ - \frac{4}{7} } )^{7} [/tex]Using the rules of indices
That's
[tex]( { {a}^{x} })^{y} = {a}^{x \times y} [/tex]Simplify the expression
We have
[tex]( { {x}^{ - \frac{4}{7} } })^{7} = {x}^{ - \frac{4}{7} \times 7 } \\ = {x}^{ - 4} [/tex]Again using the rules of indices
That's
[tex] {x}^{ - y} = \frac{1}{ {x}^{y} } [/tex]The final answer is
[tex] \frac{1}{ {x}^{4} } [/tex]Hope this helps you
What is the value of 4 in the number 45?
Answers
Answer:
40
Step-by-step explanation:
The 4 in 45 is 40 because it is in the tens place, 4 times 10= 40. The 5 is 5 becasue it's in the ones place. :)
It's just place value:
Answer:
The first digit i.e. 4 is called the tens' place. Here, there are 4 tens. The last or right digit i.e. 5 is called the ones' place. Therefore, in the number 45 = 4 tens plus 5 ones = 40 + 5 = 45
Tan45degree - 10cos60degree
Answers
Answer:
- 4
Step-by-step explanation:
Tan(45°) - 10 * cos (60°) = - 4
I need help with #66 and #68
Answers
Step-by-step explanation:
66. Δy = -3.4 Δx
Δy/Δx = -3.4
The slope of the line is -3.4. Slope-intercept equation of the line is:
y = -3.4x + b
Plug in the given point to find b:
2 = -3.4(4) + b
b = 15.6
Therefore, the equation is y = -3.4x + 15.6.
Use the equation to find the y coordinates.
[tex]\left[\begin{array}{cc}x&y\\-4&29.2\\4&2\\6&-4.8\\18&-45.6\end{array}\right][/tex]
68. Repeat the same steps as 66.
Δy = -1.7 Δx
Δy/Δx = -1.7
The slope of the line is -1.7. Slope-intercept equation of the line is:
y = -1.7x + b
Plug in the given point to find b:
3 = -1.7(-7) + b
b = -8.9
Therefore, the equation is y = -1.7x − 8.9.
Use the equation to find the x or y coordinates.
[tex]\left[\begin{array}{cc}x&y\\-19&23.4\\-7&3\\-2.412&-4.8\\3.2&-14.34\\9.1&-24.37\end{array}\right][/tex]
A bottle of hot sauce is 3/4 full. Leigh uses 2/9 of the contents of the hot sauce bottle for lunch. How much of a full bottle of hot sauce did Leigh use for lunch?
Answers
Leigh uses [tex]\frac{1}{6}[/tex] of full bottle of hot sauce
What is Unitary method?The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.
Given,
A bottle of hot sauce is 3/4 full.
Leigh uses 2/9 of the contents of the hot sauce bottle for lunch.
Therefore
How much of a full bottle of hot sauce did Leigh use for lunch = [tex](\frac{3}{4}).(\frac{2}{9})[/tex]
= [tex]\frac{1}{6}[/tex]
Hence, Leigh uses [tex]\frac{1}{6}[/tex] of full bottle of hot sauce
Learn more about Unitary method here
https://brainly.com/question/22056199
#SPJ2
Arnold deposited $732.19 in a savings account that earns 2.7% simple interest. What is Arnold's account balance after seven years?
Answers
Answer:
Step-by-step explanation:
$870.57
use equation total = Principal(1 + rate*time)
if you bought a stock last year for $59 and it risen 13% how much is the stock worth now
Answers
Answer:
$ [tex] \underline{ \underline { \sf{ \bold{66.67}}}}[/tex]Step-by-step explanation:
Price of stock bought = $ 59
% rise = 13%
Price of stock rise :
⇒[tex] \sf{13\% \: of \: 59}[/tex]
⇒[tex] \sf{ \frac{13}{100} \times 59}[/tex]
⇒$ [tex] \sf{7.67}[/tex]
New price is 13% more than $ 59
Hence, New price = $ 57 + $ 7.67
= $ 66.67
Hope I helped!
Best regards!!
A line segment (DE) joining the midpoints of two sides of a triangle is
parallel
to the third sid
Answers
Answer:
Given = A △ABC in which D and E are the mid-points of side AB and AC respectively. DE is joined .
To Prove : DE || BC and DE = 1 / 2 BC.
Const. : Produce the line segment DE to F , such that DE = EF. Join FC .
Proof : In △s AED and CEF, we have
AE = CE [∵E is the mid point of AC]
∠AED = ∠CEF[vert. opp.∠s]
and DE = EF [by construction]
∴ △AED ≅ △CEF [by SAS congruence axiom]
⇒ AD = CF ---(i)[c.p.c.t.]
and ∠ADE and ∠CEF ---(ii) [c.p.c.t.]
Now, D is the mid point of AB.
⇒ AD = DB ---(iii)
From (i) and (iii), CF = DB ---(iv)
Also, from (ii)
⇒ AD = || FC [if a pair of alt. int. ∠s are equal then lines are parallel]
⇒ DB || BC ---(v)
From (iv) and (v), we find that DBCF is a quadrilateral such that one pair of opposite sides are equal and parallel.
∴ DBCF is a ||gm
⇒ DF || BC and DF = BC [∵opp side of ||gm are equal and parallel]
Also, DE = EF [by construction]
Hence, DE || BC and DE = 1 / 2 BC