Answer:
[tex]\displaystyle f(x) = -(x-4)^2 + 6[/tex]
Step-by-step explanation:
A given quadratic has its vertex at (4, 6) and the point (1, -3). We want to write the equation in vertex form of the quadratic.
Recall that vertex form is given by:
[tex]\displaystyle f(x) = a(x-h) ^2 + k[/tex]
Where (h, k) is the vertex and a is the leading coefficient.
Since our vertex is at (4, 6), h = 4 and k = 6:
[tex]\displaystyle f(x) = a(x - 4)^2 + 6[/tex]
To determine the leading coefficient, since we are given that (1, -3) is a point on the parabola, when x = 1, y = -3. Substitute and solve for a:
[tex]\displaystyle \begin{aligned} (-3) & = a((1)-4)^2 + 6 \\ \\ -3 & = a(-3)^2 + 6 \\ \\ 9a & = -9 \\ \\ a & = -1 \end{aligned}[/tex]
Hence, the leading coefficient a is -1.
Then our equation in vertex form is:
[tex]\displaystyle f(x) = -(x-4)^2 + 6[/tex]
Do you think school is good or bad why? (Use your own opinion) I just wanna see your guys opinions
Answer:
its good because it can help u with ur future it is bad because it is early in the morning and u go there tired
Step-by-step explanation:
Answer:
Good and bad
Step-by-step explanation:
Part of it is good since its actually getting me to my dream job. Bad because it causes a lot of stress (for me anyway).
Am I doing this right I’m trying to help my little brother with his math homework but I don’t remember how to do this and he wants me to use the “cake method” (LCM stands for least common multiple)
Answer:
The least common multiple is 30. Hope that helps!!
Step-by-step explanation:
please help me on this
Answer:
[tex] {36}^{ - \frac{1}{2} } \\ = \frac{1}{ {36}^{ \frac{1}{2} } } \\ = \frac{1}{ \sqrt{36} } \\ = \frac{1}{6} \\ {64}^{ \frac{1}{3} } \\ = {(4 \times 4 \times 4)}^{ \frac{1}{3} } \\ = { {4}}^{ {3}^{ \frac{1}{3} } } \\ = 4 \\ thank \: you[/tex]
how man times can 2 go intp 9
Answer:
4 times
Step-by-step explanation:
It goes in because 2+2+2+2=8 so you cant add 2 again or else it will go over so there for the answer is 4 times.
If f(x)=(x-3)^2, find f(-4)
f(-4) = 49.
49
Step-by-step explanation:
f(x) = (x - 3)²
f(-4) = (-4 - 3)²
f(-4) = (-7)²
f(-4) = 49
Is point (90, 68) on line j? Explain how you know
Can someone do 1-4 for me please i will give brainiest
Answer:
Step-by-step explanation:
f(4)=5
f(-1)=0
f(0)=1
F(2)=3
24x - 10 = -12x + 40, What would be the coefficient of x if the variables were moved to the left side of the equation?
Answer:
25/18
Step-by-step explanation:
24x - 10 = -12x + 40
<=> 24x + 12x = 40 + 10
<=> 36x = 50
<=> x = 50/36
<=> x= 25/18
What is the area of the polygon?
please, someone, help me with this. Im giving brainliest!
Answer:
2x-10=14
2x=10+14
2x=24
x=24/2
x=12.
i guess it cant have infinite solutions.........
false.
May I please receive help?
9514 1404 393
Answer:
parallel: y = -7x -44perpendicular: y = 1/7x -8/7Step-by-step explanation:
The given equation is in slope-intercept form:
y = mx +b . . . . . . line with slope m and y-intercept b
For the purpose of this question, you need to recognize that the line with equation ...
y = -7x +8
has a slope (x-coefficient) of -7.
The parallel line will have the same slope (x-coefficient).
The perpendicular line will have a slope that is the opposite reciprocal of this:
m = -1/(-7) = 1/7
Each line will have a y-intercept (b) that makes the line go through the given point. The y-intercept can be found by solving the slope-intercept equation for b:
b = y - mx . . . . . . where (x, y) is the point you want the line to go through
__
parallel line:
b = -2 -(-7)(-6) = -2 -42 = -44
The equation of the parallel line is y = -7x -44.
__
perpendicular line:
b = -2 -(1/7)(-6) = -14/7 +6/7 = -8/7
The equation of the perpendicular line is y = 1/7x -8/7.
(x + 2)(x + 3)(x + 4) can be written in the form x + ax² + bx + c
where a, b and care positive integers.
Work out the values of a, b and c.
Answer:
[tex]a=9, b=26, c=24[/tex]
Step-by-step explanation:
Let's expand the expression bit by bit.
[tex](x+2)(x+3)=(x)(x)+(x)(3)+(2)(x)+(2)(3)=x^2+5x+6[/tex] by FOIL.
We have that [tex](x^2+5x+6)(x+4)=x(x^2+5x+6)+4(x^2+5x+6)=x^3+5x^2+6x+4x^2+20x+24=x^3+9x^2+26x+24[/tex].
So, the answer is [tex]\boxed{a=9, b=26, c=24}[/tex]
A cubic polynomial is a type of polynomial with the degree of 3 i.e. the highest exponent of the variable is 3.
The general form of a cubic polynomial is written as p(x): ax³ + bx² + cx + d, a ≠ 0, where a, b, and c are coefficients and d is the constant with all of them being real numbers.
Given:
(x + 2)(x + 3)(x + 4)
Now, Multiplying the monomial
= (x² + 2x + 3x+ 6 ) ( x+4)
= (x² + 5x+ 6 ) ( x+4)
= x³ + 4x² + 5x² + 20x + 6x+ 24
= x³ + 9x² + 26x+ 24
Now, Comparing it with the standard form of cubic Polynomial
ax³ + bx² + cx + d
So, a= 1, b= 9, c= 26 and d= 24.
Learn more about cubic Polynomial here:
https://brainly.com/question/28081769
#SPJ2
please someone help me with this. Giving brainliest!!
Step-by-step explanation:
option A is correct
we will add 5 to both the sides
→ 1/8x - 5 = 3
→ 1/8x = 8
than we will multiply 8 to both the sides
→ x = 8×8 = 64.
hope this answer helps you dear...take care abd may u have a great day ahead...and ur test/exam/assignment also go well!
3 The diagram shows parallel lines a and b cut by
transversals cand d.
If mzi = 115° and m_8 = 105°, what is the measure of
each of the following angles?
56
87
4/3
9 10
13/14
b
Answer: mz5=
t
12 11
16/15
mZ11 =
m2 16 =
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Grade 8 Lesson 9 Understand Angle Relationships
hol narconnel anly Thic rochure ovires on 6/30/2003
Answer:get the government ewual
Step-by-step explanation:
You have to get the government equal
choosw thw graph that represents the following function :
y=2+4
graph a linear equation with a function table
please help me i will mark as brainlyst
Answer:
do you mean y=2+4x?
if it is, it would be the top one.
Find the equation of a line that is perpendicular to the line x=-9 and contains the point (-8,1)
Step-by-step explanation:
the line x = -9 had only one valid x value (-9), but then all values for y between -infinity and +infinity are valid.
does this sound familiar ?
it should, because the y-axis is the same type of line.
it is x = 0.
so, x = -9 is simply parallel to the y-axis.
and any line perpendicular to it (crosses the original line in a right angle = 90 degrees) is then parallel to the x-axis.
there the situation is upside-down: there is only one valid y value, and all values between -infinity and +infinity are valid x values.
since the specified point on that line has y = 1, it means that the whole line is
y = 1
What is the equation of this line?
A. y = -3x + 1
B. y = -3x - 1
C. y = 3x + 1
D. y = 3x - 1
Please help me find the value of x
Answer:
60 degree angle
Step-by-step explanation:
If both of thise angles make 180 then you can divide 180 by 3. this give you 60. you would divide by t3 because 2 of the 3 parts go to the 2x angle. 2x means it is double your welcome
solve the inequality 3x-5<10
Answer:
answer is 5
Step-by-step explanation:
am 100% sure lol
Answer:
x < 5
Step-by-step explanation:
3x - 5 < 10
[make x the subject of the formula]
3x < 10 + 5
3x < 15
[divide both sides of the equation by 3]
3x / 3 < 15 / 3
x < 15 / 3
x < 5
Which expeession can be simplified as 1/n¹⁸ ?
(n²)⁹
[tex]( {n}^{ - 9}) ^{ - 2} [/tex]
[tex](n^{ - 6}) ^{ - 3} [/tex]
[tex](n^{ - 3}) ^{6} [/tex]
Step-by-step explanation:
the last one is the correct answer
[tex] \frac{1}{ {n}^{18} } \\ = {n}^{ - 18} \\ = {n}^{( - 3 \times 6)} \\ = ( {n}^{ - 3} ) ^{6} [/tex]
Answer:[tex]( {n}^{ - 3} ) ^{6} [/tex]
the weekly average cost of hiring a caravan in wales is £250
in July the average cost increases to £800
calculate the percentage increase
give your answer in 2 signifcant figures
9514 1404 393
Answer:
220%
Step-by-step explanation:
The percentage change is computed by ...
% change = ((new value)/(old value) -1) × 100%
= (800/250 -1) × 100% = (3.2 -1) × 100%
= 220%
The increase was 220%.
helpp pls no random or wrong answers!
Answer:
a) 2/5, b) 2.5Step-by-step explanation:
a)
[tex](4/25)^{1/2} = \sqrt{4/25} = 2/5[/tex]b)
[tex](4/25)^{-1/2}=(25/4)^{1/2}=\sqrt{25/4} =5/2=2.5[/tex]Step-by-step explanation:
please mark me as brainlest
Could someone help me
Answer:
A: the answer is 10
B: the answer is 0.03
Step-by-step explanation:
Answer:
a is 10
b is 0.03
hope this helps
What is the value of
( - ) x 43 - ?
A. 6
16
B. 10
C. 35
D. 40
evaluate the series 2 + 4 + 8 + 16 + 32 + 64
Which graph represents a function.
Answer:
one on bottom rght
Step-by-step explanation:
what percent of 500is 120
Answer:
24%
Step-by-step explanation:
Hope this helps :)
Answer:
24% of 500 is 120...........
How would you write 43—% asa decima
Answer:
if it's -43% it's -0.43. If it's 43% it's 0.43
Step-by-step explanation:
please someone help me. Im giving brainliest ! Correct answers only :)
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The Correct choice is : D
Here's the solution :
[tex] \sqrt{528} = 22.978250[/tex][tex] \sqrt{528} \approx23[/tex]Which three cards have an equal value
Answer:
the bottom 3 the bottom left one equals 1.33 altogether and if you count the second one it's also 1.33 or 133 blocks coloured and the last one is also 1.33