Answer:
[tex]f(x)=-7(x-3)^2+1[/tex]
Step-by-step explanation:
Vertex form of a quadratic is given by:
[tex]f(x)=a(x-h)^2+k[/tex]
Where (h, k) is the vertex and a is the leading coefficient.
We are given that the vertex is (3, 1). Hence, h = 3 and k = 1. By substitution:
[tex]f(x)=a(x-3)^2+1[/tex]
We are also given a point (2, -6). This means that when x = 2, f(x) = -6. Hence:
[tex]-6=a((2)-3)^2+1[/tex]
Solve for a. Subtract:
[tex]-6=a(-1)^2+1[/tex]
Simplify:
[tex]-6=a+1[/tex]
Therefore:
[tex]a=-7[/tex]
Hence, our quadratic is:
[tex]f(x) = -7 (x-3)^2 + 1[/tex]
Find the unit vector in the direction of the vector <3,-1>
Answer:
Step-by-step explanation:
v=<3,-1>
[tex]||v||=\sqrt{x^{2} +y^{2} } \\\sqrt{(3)^{2}+(-1)^{2} } \\\sqrt{9+1} =\sqrt{10} \\u=\frac{1}{||v||} *v\\u=\frac{1}{\sqrt{10} } *<3,-1>\\u=<\frac{3}{\sqrt{10} } ,-\frac{1}{\sqrt{10} } >\\[/tex]
A park is rectangular with a length of 1/2 miles. If the area of the park is 6/8 square miles, what is its width? Input your answer as a fraction.
giving 40 points! please help soon <33
Step-by-step explanation:
Area of Park = Length * Width
Therefore Width = Area / Length
= (6/8) / (1/2) = (6/8) * (2/1) = 3/2 miles.
Answer:Area of Park = Length * Width
Therefore Width = Area / Length
= (6/8) / (1/2) = (6/8) * (2/1) = 3/2 miles.
Step-by-step explanation:
I need help on thisss —> 8x4=8(2+_)
Answer: 2
Step-by-step explanation:
8x4=32, you have to distribute the 8 into the parentheses so you will have 8x2+8x2 which is 16+16=32
When you add a positive number and negative number how can you tell whether the sun will be positive or negative?
Answer:
Because
Step-by-step explanation:
(+) × (-) = (-)
(-) × (+) = (-)
Explain how to solve X/3 < -2
Please and thank you!
evaluate the expression (-20)-17=
Determine whether each sequence is arithmetic or geometric. Find the next three terms,
81,27,9,3,...
A. arithmetic, 0, -3, -6
O B. geometric, 0, -3, -6
C.
geometric, 1,
1 1
39
<
OD. The sequence is neither geometric nor arithmetic,
Answer:yes
Step-by-step explanation:
Explain which line must be parallel pllleeeaaaasser hurryyyy
Answer:
Lines P and Q
Answer:
parallel lines are lines that are directly next to each other so i think line's
p and q
Step-by-step explanation:
please mark me the brainliest if i am right
Alyssa drive 10 miles in 20 minutes if she drove one hour in total at the same rate how far did she go
Answer:
30 miles
Step-by-step explanation:
60 ÷ 20 = 3
10 × 3 = 30
Find the mean of the ending balance in Teresa’s account for the week.
A 2-column table with 8 rows titled Daily Ending Balance. Column 1 has entries 1, 2, 3, 4, 5, 6, 7, total. Column 2 has entries 320 dollars, 206 dollars, 245 dollars, negative 2 dollars, negative 2 dollars, 18 dollars, 20 dollars, 805 dollars.
Total balance
Number of days
= 805
7
Mean (Average) =
Answer:
$115
Step-by-step explanation:
805 divide it by 7 you get 115 also got right guys trusted me ( >-< )
Answer:
yep! 115$ is correct! :)
Translate the given phrase into an algebraic expression and simplify if possible: the sum of -8 and -9, increased by 23.
Note: Enter only the simplified result.
Step-by-step explanation:
(-8-9)+23
-17+23
6.........
The value of algebraic expression [(-8) + ( -9)] + 23 is 6.
Here,
We have to simplify; the sum of -8 and -9, increased by 23.
And, find an algebraic expression.
What is Algebraic expression?
An algebraic expression in mathematics is an expression which is made up of variables and constants, along with algebraic operations.
Now,
The written expression is, the sum of -8 and -9, increased by 23.
It can be written as,
⇒ [(-8) + ( -9)] + 23
⇒ - 8 - 9 + 23
⇒ - 17 + 23
⇒ 6
Hence, The value of algebraic expression [(-8) + ( -9)] + 23 is 6.
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How many solutions does the system have?
- 2x - 4
y = 3x + 3
Choose 1 answer:
A
Exactly one solution
B
No solutions
С
Infinitely many solutions
1800 yards per hour is the same rate as which of the following?
A. ____ yards per second B. _____ yards per minute
Answer:
a............ you are welcome
Work out the diffeence beteeen 77.5 and 2.27
A tennis racket that cost $79 is now on sale for $83. What is the
percent of change?
Answer:
5.06%
or
5.06329114%
Step-by-step explanation:
The increase if $4.
4/79 = 0.0506329114, which is 5.06%
What is the result of adding these two equations?
-52 - 9y = 3
5.2 - 9y = -2
Answer:
5.7-18y=1
Step-by-step explanation:
52-9y=3
5.2-9y=-2
or,57.2-18y=1
Answer:
-18y = 46.8
Step-by-step explanation:
Adding Left hand side elements together as well as right hand side
Eq1 = equation 1
Eq2 = equation 2
LHS(left hand side of the equation)
RHS(right hand side of the equation)
LHS of Eq1 + LHS of Eq2 = RHS of Eq1 + RHS of Eq2
-52 -9y + 5.2 -9y = 3 - 2
=> -9y -9y - 52 + 5.2 = 1
=> -18y - 46.8 = 1
=> -18y - 46.8 = 0
=> -18y = 46.8
Select the correct answer.
Which statement correctly describes this expression?
1231 +5
ОА.
the sum of the absolute value of three times a number and 5
OB.
5 more than the absolute value of the cube of a number
O c.
the cube of the sum of a number and 5
OD.
the absolute value of three times a number added to 5
Answer:
it should be c sorry if I get it wrong
What is the value of the expression when x = 5? 3x^2 + 14 - 10x
Answer: 39
Step-by-step explanation:
Please help, 5 (y + 2/5) = -13. Y=?
Answer:
y = -3
Step-by-step explanation:
5y + 10/5 = -13 (distribute 5)
5y + 2 = -13 (simplify fraction)
5y = -15 (subtract 2 from both sides)
y = = -3 (divide 5 from both sides)
Checked worked:
5 ([-3] +2/5)
-15 + 10/5
-15 + 2 = -13
y = -3
A cirdie is divided up into 24 equal pieces. What percentage of the total circle area will each piece be? Round to the nearest
percent
A 2%
B. 8%
C 7%
D4%
Answer:
4 %
Step-by-step explanation:
100/24=25/6=4 1/6
What is the value of of x,a,b and c?
Answer:
a= 98 b= 82 c= 98 is the answer .....
The rectangle below has an area of x^2
-114square meters and a length of x+12metters
Given that,
The area of the rectangle, [tex]A=x^2-114[/tex]
Length of the rectangle, [tex]l=x+12\ m[/tex]
To find,
The width of the rectangle.
Solution,
The formula for the area of a rectangle is given by :
A = lb
b is width of the rectangle
[tex]b=\dfrac{A}{l}\\\\b=\dfrac{x^2-114}{x+12}\\\\b=\dfrac{x^2-12^2}{x+12}\\\\b=\dfrac{(x-12)(x+12)}{(x+12)}\\\\=(x-12)\ m[/tex]
So, the width of the rectangle is (x-12) m.
How many solutions does -3x+15=3(5-x) have
Answer:
Infinite solutions
Step-by-step explanation:
So if simplified it would be
-3x+15=15-3x
Which is basically the same thing if arranged
15-3x=15-3x
-3x+15 can also be 15-3x still the same thing as adding 15 to -3x
So since these are equal anything could be used
like try 0
Both get 15
Try 1
Both get 12
Try legit any number
youll get the same results (I would choose 3 positive easy ones, 0,1,2 and 3 negative ones -1,-2,-3)
Find the missing side length
Answer:
7 ft
Step-by-step explanation:
16-9=7
1. How many odd positive integers less than 50 are there?
Answer:
25
Step-by-step explanation:
Evaluate
2^-4/4^0
Write your answer as a fraction in simplest form
Answer:
1/16 or 0.0625
Step-by-step explanation:
Im not sure but this may be the answer
The given fraction in simplest form is 1/16.
What is the fraction?In Mathematics, fractions are represented as a numerical value, which defines a part of a whole. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.
The given fraction is 2⁻⁴/4⁰.
Now, 2⁻⁴/4⁰ =2⁻⁴/4⁰
= 2⁻⁴/1
= 1/2⁴
= 1/16
Therefore, the given fraction in simplest form is 1/16.
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What is the equation, in point-slope form, of the line
that is parallel to the given line and passes through the
point (4, 1)?
Answer:
Step-by-step explanation:
Given:
The line parallel to the given line containing the points (-3,3) and (-2,1).
Also, the parallel line passes through the point (4,1).
We need to determine the equation of the line in slope - intercept form.
Slope:
Since, the two lines are parallel, then their slopes are equal.
Thus, the slope of the parallel line can be determined using the formula,
Substituting the points (-3,3) and (-2,1), we get;
Thus, the slope of the line is
Equation of the line:
The equation of the line can be determined using the formula,
Since, the line passes through the point (4,1), let us substitute the point (4,1) in the above formula, we have;
Thus, the equation of the line is
Hence, y − 1 = −2(x − 4) is the correct answer.
:)
what is the qoutient -3 ÷ 9?
Answer:
0.25
Step-by-step explanation:
What are all values of x for which the function f defined by f(x)=x3+3x2−9x+7 is increasing ?
(A) −3
(B) −1
(C) x<−3 or x>1
(D) x<−1 or x>3
(E) All real numbers.
Answer:
C. [tex]x < -3[/tex] or [tex]x > 1[/tex].
Step-by-step explanation:
Let [tex]f(x) = x^{3}+3\cdot x^{2}-9\cdot x +7[/tex], the first derivate of the function is:
[tex]f'(x) = 3\cdot x^{2}+6\cdot x -9[/tex] (1)
By the Quadratic Formula, we determine the roots of this polynomial:
[tex]x_{1} = 1[/tex], [tex]x_{2} = -3[/tex]
And the factorized form of the polynomial is:
[tex](x-1)\cdot (x+3) > 0[/tex]
By law of Signs, the polynomial is increasing when [tex]x-1 > 0[/tex] and [tex]x +3 > 0[/tex] or [tex]x-1 < 0[/tex] and [tex]x+3 < 0[/tex], which means that:
[tex]x < -3[/tex] or [tex]x > 1[/tex]
Therefore, the right answer is C.
Answer:
The correct option is an option (c).
Given:
The given function is,
[tex]f(x)=x^{3}+3x^{2}-9x+7[/tex]
Computation:
The function is increasing when [tex]f'(x)>0[/tex].
Now, differentiating the given function with respect to [tex]x[/tex] up to first order we get,
[tex]f'(x)=3x^{2}+3(2x)-9(1)+0\\f'(x)=3x^{2}+6x-9\\=3(x^{2}+2x-3)\\=3(x(x+3)-1(x+3))\\=3(x+3)(x-1)[/tex]
So, the sign function is,
Therefore, [tex]f'(x)>0[/tex] when [tex]x\in (-\infty ,-3)\cup (1,\infty )[/tex]
So, [tex]f(x)[/tex] is increasing on [tex]x<-3[/tex] or [tex]x>1[/tex]
Hence, the correct option is an option (c).
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A line passes through the points (4,8) and (2,0). What is its equation in slope-intercept
form?
Answer:
The answer is y = 4x - 8.
Step-by-step explanation:
☆Remember: [tex]m = \frac{y_2 - y_1}{x_2 - x_1} [/tex]
☆Slope-intercept: [tex]y = mx + b[/tex]
---
☆We need to find the slope first. So just plug in according to the slope formula!
[tex]m = \frac{0 - 8}{2 - 4} = \frac{ - 8}{ - 2} = 4[/tex]
---
☆Now we need to find the y-intercept. We are going to plug in the slope and a set of coordinates to find the y-intercept.
[tex]y = mx + b \\ 8 = 4(4) + b \\ 8 = 16 + b \\ \frac{ - 16 = - 16 \: \: \: \: \: \: \: \: \: \: \: \: }{ - 8 = b \: \: \: \: \: \: \: \: \: \: \: \: \: \: } [/tex]
---
☆Now all we need to do is plug in and we are done!
[tex]y = 4x - 8[/tex]
▪Happy To Help <3