Answer:
(h, k )
Step-by-step explanation:
given the standard form of an absolute function
f(x) = a| x - h | + k , then
vertex = (h, k )
The standard form of an absolute value function is f(x) = a|x - h| + k, where (h,k) is the vertex of the absolute value function.
The correct option is (h,k).
What is a function?The term "function" refers to a relationship between a set of inputs and outputs. Just one output is connected to each input in a function, which connects inputs in that manner. Every function has a domain, co-domain, and range.
In general, the standard form of an absolute value function is given as:
f(x) = a |x - h| + k
where:
a is a non-negative constant that determines the shape and direction of the V-shaped graph of the absolute value function
h is the horizontal shift of the graph of the function from the origin (if h > 0, the graph shifts to the right; if h < 0, the graph shifts to the left)
k is the vertical shift of the graph of the function from the origin (if k > 0, the graph shifts up; if k < 0, the graph shifts down)
The vertex of the absolute value function is the point where the graph changes direction, that is, the point where the graph changes from sloping downwards to sloping upwards or vice versa.
Since the vertex is the point of the absolute value function where the graph changes direction, it lies at the center of the V-shaped graph. Thus, the vertex is located at the point (h,k).
Therefore, in the standard form f(x) = a |x - h| + k, (h,k) represents the coordinates of the vertex of the absolute value function.
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What is the answer? Thank you in advance
Coordinates are numerical lengths or angles that uniquely identify locations on two-dimension. The missing coordinates are coordinates 3 and 4.
What is the best way to understand the Cartesian coordinate plane?A Cartesian coordinate plane is a two-dimensional plane with infinite dimensions. On an endless 2d plane, any two-dimensional figure may be drawn. A location is assigned to each point on a Cartesian plane.
It is the perpendicular distance between that point and the horizontal and vertical axes, which are commonly referred to as the x-axis and y-axis.
Location is then written as (a,b), where 'a' is the point's shortest distance from the y-axis, 'b' is the point's shortest distance from the x-axis, and 'c' is the point's shortest distance from the x-axis.
Coordinates are numerical lengths or angles that uniquely identify locations on two-dimensional (2D) surfaces or in three-dimensional (3D) space ( 3D ).
Mathematics, scientists, and engineers frequently employ a variety of coordinate systems.
Hence the missing coordinates are coordinates 3 and 4.
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6543549 ² × 4³ ÷8
it also states to simplify to the simplest form
The simplification form of the provided expression 6543549 ² × 4³ ÷8 is 3.4254×10¹⁴
What is an arithmetic operation?It is defined as the operation in which we do the addition of numbers, subtraction, multiplication, and division. It has a basic four operators that is +, -, ×, and ÷.
We have a mathematical expression:
= 6543549² × 4³ ÷ 8
Using BODMAS
= 6543549² × 8
= 3.4254×10¹⁴
Thus, the simplification form of the provided expression 6543549 ² × 4³ ÷8 is 3.4254×10¹⁴
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Can someone explain how I do this?
Answer:
oh soooooooooooooooo sorry
Step-by-step explanation:
sorry
Answer:
12.5N
Step-by-step explanation:
See attached image.
If a(x) = 3x + 1 and (x)= x-4, what is the domain of (boa)(x)?
I am assuming you meant to write b(x) = x-4.
[tex](b \circ a)(x)=b(a(x))=b(3x+1)=(3x+1)-4=\boxed{3x-3}[/tex]
Since this is a linear function, the domain is all real numbers.
Work out the area of this triangle
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
baseline and height must be at a right angle with each other.
so, in our case
6 × 11 / 2 = 3 × 11 = 33 cm²
Answer:
Area = 33 cm²
Step-by-step explanation:
[tex]\textsf{Area of a triangle}=\sf \dfrac{1}{2}bh[/tex]
where:
b is the baseh is the height (perpendicular to the base)If we turn the triangle counterclockwise, so that the side that measures 6 cm is the base, we will see that the length that measures 11 cm is the height of the triangle (see attached).
Therefore:
b = 6 cmh = 11 cmSubstitute the found values into the formula and solve for A:
[tex]\implies \sf A=\dfrac{1}{2}(6)(11)[/tex]
[tex]\implies \sf A=\dfrac{1}{2}(66)[/tex]
[tex]\implies \sf A=33[/tex]
Therefore, the area of the triangle is 33 cm²
The subject of the formula below is y.
y=X+p-q
Rearrange the formula to make x the subject.
Answer:
x=y-p+q
Step-by-step explanation:
y=x+p-q
x=y-p+q
When planning road development, the road commission estimates the future population using the function represented in the table, where x is the time in years and f(x) is the total population.
What is the significance of 160,000 in the function?
the maximum population of the city
the expected population in 5 years
the initial population at the time of the estimation
the amount of increase in the population in 5 years
The significance of 160,000 in the function is the initial population at the time of the estimation.
The correct option is (C)
What is data?A collection of facts, such as numbers, words, measurements, observations or even just descriptions of things.
Given:
As per the table attached below:
F(x) signify the total population when the time was x hour.
So, 160,000 in the function signifies that the population at starting i.e., initial point.
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i need this for sparx hwk
can someone please help mee i need the right answers please(30 points and i will give brainliest!!!)
Step-by-step explanation:
Funtion-A:Given:
[tex]y = {x}^{2} - x - 6[/tex]
To find the x-intercepts set y to 0 and solve for x which is done below:
⇒x²-x-6=0⇒(x-3)(x+2)=0X=3 and -2Therefore x-intercepts:(3,0),(-2,0)
To figure out the y-intercept , substitute 0 for x and simplify
⇒y=0²-0-6⇒y=-6Hence, The y-intercept is (0,-6)
The vertex (0.5,-6.25)(skipped the steps as you've already figured it out)
Function-B:Likewise A:
X-intercepts:
⇒-x²+x+6=0⇒x²-x-6=0⇒x=3 and -2Therefore,x-intercepts:(3,0),(-2,0)
Y-intercept:
⇒y=-0²+0+6
⇒y=6
Therefore, y-intercept (0,6)
The vertex:(0.5,6.25)
Inspection of the Parabolas:The difference between the two parabolas is that The blue parabola is the result of reflection over x-axis of the red one.
Answer:
a.
The x-intercepts are 3 and -2
The y-intercept is -6
The vertex is (1/2 , -25/4)
b.
The two parabola are symmetric across the x-axis
Step-by-step explanation:
x² - x - 6
[tex]=x^{2}-2\times \frac{x}{2} +\frac{1}{4} -\frac{1}{4}-6[/tex]
[tex]=(x-\frac{1}{2} )^{2} -(\frac{1}{4}+6)[/tex]
[tex]=(x-\frac{1}{2} )^{2} -\frac{25}{4}[/tex]
The x-intercepts :
(x-1/2)² = 25/4
Then
x - 1/2 = 5/2 or x - 1/2 = -5/2
Then
x = 3 or x = -2
The y-intercepts :
We get the y-intercept by replacing x by 0 in the trinomial :
0² - 0 - 6 = -6
b.
we notice that :
-x² + x + 6 = -(x² - x - 6)
Then
-x² + x + 6
[tex]=-(x-\frac{1}{2} )^{2} +\frac{25}{4}[/tex]
The x-intercepts :
[tex]-(x-\frac{1}{2} )^{2} +\frac{25}{4}=0[/tex]
⇔ (x-1/2)² = 25/4
Then
x - 1/2 = 5/2 or x - 1/2 = -5/2
Then
x = 3 or x = -2
The y-intercepts :
We get the y-intercept by replacing x by 0 in the trinomial :
0² + 0 + 6 = 6
What is 2*4*6.5*24.5
Answer:
1274
it is 1274
Step-by-step explanation:
mark as brainlest for the answer thankyou
4 2/3 ÷ 2 1/3 ? what is the quotient?
Answer: 42/21 or 2
Step-by-step explanation:
you first convert them to improper fractions, which is 14/3 and 7/3. Then, you multiply the reciprocal and get 14/3x3/7, and get 42/21. Simplify, and you get 2.
A dilation maps (9, 12) to (3, 4). Find the coordinates of the point (8, 4) under the same dilation
Assuming the dilation is centered at the origin, the scale factor is 1/3.
This means the coordinates of the point (8,4) are [tex]\boxed{\left(\frac{8}{3}, \frac{4}{3} \right)}[/tex]
How many complex roots does the equation 0=3x5−x4−5x2+1 have?
The given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.
What is a polynomial?A polynomial is defined as a mathematical expression that has a minimum of two terms containing variables or numbers. A polynomial can have more than one term.
The given polynomial equation below is:
0 = 3x⁵ − x⁴ − 5x² + 1
3x⁵ − x⁴ − 5x² + 1 = 0
The given polynomial equation is a polynomial of degree 5.
The simplest method is to solve it graphically using a graphing program.
Clearly, the polynomial equation is a degree 5 equation, hence it has a maximum of 5 roots.
We may now locate the roots of the equation using the graph.
Since there are 3 real roots, the remaining are two complexes, so there are 2 complex roots
Hence, the given polynomial equation 3x⁵ − x⁴ − 5x² + 1 = 0 has two complex roots.
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Shapes F and G are similar
Shape F has a perimeter of 180mm and an area of 2196mm².
Shape G has a perimeter of 300mm
Work out the area of shape G.
Give your answer to 1.d.p if decimal
Shape F has a perimeter of 180mm and an area of 2196mm² is similar to shape G with perimeter 300mm then area of shape is 6100mm².
As given,
Shapes F and G are similar
Perimeter of shape F=180mm
Area of shape F=2196mm²
Perimeter of shape G=300mm
Let xmm²be the area of shape G
Square of ratio of perimeter of similar shape =Ratio of area of similar shape
⇒(180 /300)² =(2196/x)
⇒9/25=2196/x
⇒x=(2196×25)/9
⇒x=6100mm²
Therefore, shape F has a perimeter of 180mm and an area of 2196mm² is similar to shape G with perimeter 300mm then area of shape is 6100mm².
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Write the equation 0.10x + 0.25y = 16 so that the number of quarters y is a function of the number of dimes x. Describe the domain and range of the function and explain how you determined the domain and range.
Pls solve with working out. Ok thanks
Answer:
AB and CD have the same midpoint, therefore they bisect each other.
Step-by-step explanation:
Find the midpoint of AB. Then, find the midpoint of CD. They are the same. The segments bisect each other. See image.
Part A
? Question
Enter the correct answer in the box.
Recall that the width is x + 15, and the length is 49 less than 2 times the width. Write a simplified expression for the
length of the garage in terms of x.
(101 0² +
An expression is defined as a set of numbers, variables, and mathematical operations. A simplified expression for the length of the garage in terms of x is 2x-19.
What is an Expression?In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.
Given the width is x + 15, and the length is 49 less than 2 times the width. Therefore, a simplified expression for the length of the garage in terms of x is,
Length = 2(x+15) - 49 = 2x + 30 - 49 = 2x-19
Hence, a simplified expression for the length of the garage in terms of x is 2x-19.
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Which of the following is a geometric sequence? A. 1, 1, 2, 3, 5, ... B. 2, 4, 6, 8, ... C. 7, 4, 1, -2, ... D. 1, ½, ¼, ⅛
if point (4, 5) is on the graph of a function, which equation must be true?
f(5)=4
f(5,4)=9
f(4)=5
f(5,4)=1
Answer:
f(4) = 5
Step-by-step explanation:
The notation used for a point is (x,y). The first number is the x and the second number is the y.
In function notation, you have f(x) = y.
The input number, x, is in the parenthesis beside the f. The output, y is all by itself on the other side of the equal sign.
For the point (4,5), 4 is the x so it goes by the f. 5 is the y so it goes by itself on the other side of the equal sign.
f(4) = 5
The solution is : f(4) = 5, the equation must be true.
What is equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.
here, we have,
The notation used for a point is (x,y).
The first number is the x and the second number is the y.
In function notation, you have f(x) = y.
The input number, x, is in the parenthesis beside the f. The output, y is all by itself on the other side of the equal sign.
For the point (4,5), 4 is the x so it goes by the f.
5 is the y so it goes by itself on the other side of the equal sign.
f(4) = 5
Hence, The solution is : f(4) = 5, the equation must be true.
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PLEASE HELP!!!!!
Estimate the solution to the system of equations.
y=4x−2
y=x+3
(Choice A)
x= 2/3
y= 4 2/3
(Choice B)
x= 1 2/3
y=3 2/3
(Choice C)
x= 1 2/3
y=4 2/3
(Choice D)
x=2/3
y= 3 2/3
The value of the variable x and y will be 1 2/3 and 4 2/3. Then the correct option is C.
What is the solution of the equation?The solution of the equation means the value of the unknown or variable.
The equations are given below.
y = 4x − 2 ...1
y = x + 3 ...2
Subtract equation 1 from 2, then we have
0 = 3x – 5
3x = 5
x = 5/3
x = 1 2/3
Then the value of y will be
y = 5/3 + 3
y = 14 / 3
y = 4 2/3
Then the correct option is C.
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Which ordered pair is not a solution of the linear equation shown?
1
y=-x
2
OA) (2, 1)
B) (1.-—-)
1,
2
OC) (4,8)
OD) (-2,-1)
Answer:
C : (4,8)
Step-by-step explanation:
The equation y = (1/2) x
Or, 2y = x ==> x = 2y
means that, for any value of x, the y value must be one-half that value or, in other words, for any value of y, x must be twice the value of y
A, B and D will satisfy the above equation if you plug in values of x and y given
In C we have x = 4 and y =8 so x = y/2 NOT 2y
I need answer as fast as possible please.
Step-by-step explanation:
a=110. x,55
y=180-(x+75)=50
w,75
b,110
x,40
y,30
What is the difference between the answers when numbers are switched in a subtraction?
please help me(20 points will give brainliest!!!)
Answer:
A. Vertex is ( -1, 16)
B. Do they mean y-intercept for vertical intercept? That is (0,14)
C. X-intercepts are
(-3.838, 0) and (1.828, 0)
Step-by-step explanation:
plug the equation into desmos. It will graph and give you the info.
To find y-int, plug in 0 for x. This gives you the point 0, 14.
You can also use the quadratic equation to find the x-intercepts.
Answer:
see explanation
Step-by-step explanation:
A
given a parabola in standard form
f(x) = ax² + bx + c ( a ≠ 0 ) , then the x- coordinate of the vertex is
x = - [tex]\frac{b}{2a}[/tex]
f(x) = - 2x² - 4x + 14 ← is in standard form
with a = - 2, b = - 4 , then
x = - [tex]\frac{-4}{-4}[/tex] = - 1
substitute x = - 1 into f(x) for corresponding y- coordinate
f(- 1) = - 2(- 1)² - 4(- 1) + 14 = - 2 + 4 + 14 = 16
vertex = (- 1, 16 )
B
to find the y- intercept let x = 0
f(0) = - 2(0)² - 4(0) + 14 = 0 - 0 + 14
y- intercept = (0, 14 )
C
to find the x- intercepts let f(x) = 0 , that is
- 2x² - 4x + 14 = 0 ( divide through by - 2 )
x² + 2x - 7 = 0 ( add 7 to both sides )
x² + 2x = 7
using the method of completing the square
add ( half the coefficient of the x- term )² to both sides
x² + 2(1)x + 1 = 7 + 1
(x + 1)² = 8 ( take square root of both sides )
x + 1 = ± [tex]\sqrt{8}[/tex] ( subtract 1 from both sides )
x = - 1 ± [tex]\sqrt{8}[/tex]
then
x = - 1 - [tex]\sqrt{8}[/tex] ≈ - 3.83 ( to 2 dec. places )
x = - 1 + [tex]\sqrt{8}[/tex] ≈ 1.83 ( to 2 dec. places )
that is x- intercepts are (- 3.83, 0 ) , (1.83, 0 )
Mike has 63 toys. 18 of them are new and 12 are his favorites, while 4 are new and favorites. Mike is giving away all the toys that are neither new nor favorites. How many toys does mike GIVE AWAY. ASAP ASAP
please help me with this problem!
Answer:
The choice A ;
[tex] \frac{1}{ {7}^{8} } [/tex]
Step-by-step explanation:
[tex] \frac{ {7}^{ - 6} }{ {7}^{2} } = \frac{ {7}^{ - 6 - 2} }{1} = {7}^{ - 8} = \frac{1}{ {7}^{8} } \\ \\ \\ or. \: \frac{ {7}^{ - 6} }{ {7}^{2} } = \frac{1}{ {7}^{ 2 + 6} } = \frac{1}{ {7}^{8} } [/tex]
Hii!
Answer:
Step-by-step explanation:
Use the rule of exponents.
If we divide two numbers with the same bases, we subtract the exponents.
7^-6/7^2=7^-6-2=7^-8
Now, if we have a negative exponent, we flip over the number.
7^-8=1/7^8
Great job!
—
Hope that this helped.
Sahil chooses a number, divides it by 8 , adds 8 to the answer. Then multiples the answer with 8 . He obtains the result as 952 . The number he chooses in the beginning was
I'M IN LOVE WITH A FAIRYTALE
EVEN THOUGH IT HURTS
CAUSE I DON'T CARE IF I LOOSE MY MIND
I'M ALREADY CURSED
Answer:
888
Step-by-step explanation:
let the number be n then divide by 8 , that is [tex]\frac{n}{8}[/tex]
now add 8 to this
[tex]\frac{n}{8}[/tex] + 8 and finally multiply this by 8 and equate to 952
8([tex]\frac{n}{8}[/tex] + 8) = 952 ( divide both sides by 8 )
[tex]\frac{n}{8}[/tex] + 8 = 119 ( subtract 8 from both sides )
[tex]\frac{n}{8}[/tex] = 111 ( multiply both sides by 8 to clear the fraction )
n = 888
the number chosen was 888
Luis is going to an amusement park. The price of admission into the park is $20, and once he is inside the park, he will have to pay $4 for every ride he rides on. How much money would Luis have to pay in total if he goes on 6 rides? How much would he have to pay if he goes on r rides?
Cost with 6 rides:
Cost with r rides: need answers fast
Using a linear function, it is found that the costs are given as follows:
With 6 rides: $24.With r rides: C(r) = 20 + 4r.What is a linear function?A linear function is modeled by:
y = mx + b
In which:
m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.Considering the price of admission and the price per ride, the y-intercept is of 20 and the slope is of 4, the cost for r rides is given by:
C(r) = 20 + 4r.
Hence, for 6 rides, the cost is given by:
C(6) = 20 + 4 x 6 = $44.
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Required school supplies include 6 spiral notebooks and 2 binders. If the notebooks cost 90 cents and the binders cost $4.77, how much will you spend?
A. $22.85
B. $14.94
C. $15
D. $30
Answer:
Hey, You don't need to buy supplies. Just use your at home!
Step-by-step explanation:
Brainlest?
Answer: Algebra: 3 sub. spiral notebook, pencil pouch to hold colored pencils and ... Algebra 2: 2 or 3 subject spiral notebook (can use folder instead of binder).
Step-by-step explanation:
What is the probability of drawing a red card, replacing it, and then drawing an odd card?
4 red 5 blue 6 red 7 blue 8 blue
Answer:
4
Step-by-step explanation:
5
