Answer:
The value of f(0)=1
Step-by-step explanation:
We are given that
[tex]f(x)=k[/tex]
[tex]y=f(x)[/tex]
(6,1) and (8,1) lies on the graph of y=f(x)
We have to find the value of f(0).
[tex]f(6)=1[/tex]
[tex]f(8)=1[/tex]
[tex]f(x)=k[/tex]
By comparing ,we get
k=1
Therefore, [tex]y=f(x)=1[/tex]
Now, substitute x=0
[tex]f(0)=1[/tex]
Hence, the value of f(0)=1
will give BRAINLIEST ! plz help
Triangle ABC has A (-3, 6), B (2, 1), and C (9, 5) at its vertices.
The length of side AB is
A. (50)^1/2
B. (65)^1/2
C. (105)^1/2
D. (145)^1/2
units.
The length of side BC is
(one of the above options)
units.
The length of side AC is
(one of the above options)
units.
A. 55.21
B. 85.16
C. 105.26
D. 114.11
Answer:
AB= A. (50)^1/2
BC= B. (65)^1/2
AC= D. (145)^1/2
<ABC≈ 105
HELP PLEASE 50 points !!! Given a polynomial function describe the effects on the Y intercept, region where the graph is increasing and decreasing in the end behavior when the following changes are made make sure to account for even and odd functions
When f(x) becomes -f(x)+ 2
When f(x) becomes f(x+3)
Even function:
A function is said to be even if its graph is symmetric with respect to the , that is:
Odd function:
A function is said to be odd if its graph is symmetric with respect to the origin, that is:
So let's analyze each question for each type of functions using examples of polynomial functions. Thus:
FOR EVEN FUNCTIONS:
1. When becomes
1.1 Effects on the y-intercept
We need to find out the effects on the y-intercept when shifting the function into:
We know that the graph intersects the y-axis when , therefore:
So:
So the y-intercept of is one unit less than the y-intercept of
1.2. Effects on the regions where the graph is increasing and decreasing
Given that you are shifting the graph downward on the y-axis, there is no any effect on the intervals of the domain. The function increases and decreases in the same intervals of
1.3 The end behavior when the following changes are made.
The function is shifted one unit downward, so each point of has the same x-coordinate but the output is one unit less than the output of . Thus, each point will be sketched as:
FOR ODD FUNCTIONS:
2. When becomes
2.1 Effects on the y-intercept
In this case happens the same as in the previous case. The new y-intercept is one unit less. So the graph is shifted one unit downward again.
An example is shown in Figure 1. The graph in blue is the function:
and the function in red is:
So you can see that:
2.2. Effects on the regions where the graph is increasing and decreasing
The effects are the same just as in the previous case. So the new function increases and decreases in the same intervals of
In Figure 1 you can see that both functions increase at:
and decrease at:
2.3 The end behavior when the following changes are made.
It happens the same, the output is one unit less than the output of . So, you can write the points just as they were written before.
So you can realize this concept by taking a point with the same x-coordinate of both graphs in Figure 1.
FOR EVEN FUNCTIONS:
3. When becomes
3.1 Effects on the y-intercept
We need to find out the effects on the y-intercept when shifting the function into:
As we know, the graph intersects the y-axis when , therefore:
And:
So the new y-intercept is the negative of the previous intercept shifted one unit upward.
3.2. Effects on the regions where the graph is increasing and decreasing
In the intervals when the function increases, the function decreases. On the other hand, in the intervals when the function decreases, the function increases.
3.3 The end behavior when the following changes are made.
Each point of the function has the same x-coordinate just as the function and the y-coordinate is the negative of the previous coordinate shifted one unit upward, that is:
FOR ODD FUNCTIONS:
4. When becomes
4.1 Effects on the y-intercept
In this case happens the same as in the previous case. The new y-intercept is the negative of the previous intercept shifted one unit upward.
4.2. Effects on the regions where the graph is increasing and decreasing
In this case it happens the same. So in the intervals when the function increases, the function decreases. On the other hand, in the intervals when the function decreases, the function increases.
4.3 The end behavior when the following changes are made.
Similarly, each point of the function has the same x-coordinate just as the function and the y-coordinate is the negative of the previous coordinate shifted one unit upward.
Which polynomial function has a leading coefficient of 3 and roots 4, I, and 2, all with multiplicity 1? Of(x) = 3(x + 4)(x - 1)(x - 2) O f(x) = (x - 3)(x + 4)(x - 1)(x - 2) f(x) = (x - 3)(x + 4)(x - 1)(x + 1)(x - 2) O f(x) = 3(x + 4)(x - 1)(x + 1)(x - 2) N
Note: There must be -4 instead of 4 otherwise all options are incorrect.
Given:
A polynomial function has a leading coefficient of 3 and roots -4, 1, and 2, all with multiplicity 1.
To find:
The polynomial function.
Solution:
The general polynomial function is defined as:
[tex]P(x)=a(x-c_1)^{m_1}(x-c_2)^{m_2}...(x-c_n)^{m_n}[/tex]
Where, a is the leading coefficient, [tex]c_1,c_2,...,c_n[/tex] are the zeros with multiplicity [tex]m_1,m_2,...,m_n[/tex] respectively.
It is given that a polynomial function has a leading coefficient of 3 and roots 4, 1, and 2, all with multiplicity 1. So, the polynomial function is defined as:
[tex]P(x)=3(x-(-4))^1(x-1)^1(x-2)^1[/tex]
[tex]P(x)=3(x+4)(x-1)(x-2)[/tex]
Therefore, the correct option is A.
find the discriminantof the quadratic equation root 2 X square + 7 x + 5 root 2
[tex]\displaystyle\ 2x^2+7x+5\sqrt{2} =0 \\\\\boxed{D=7^2-4\cdot2\cdot 5\sqrt{2} =49-40\sqrt{2} }[/tex]
Match the measures of each angle
Find the volume of this cylinder. Use 3 for .
V = 7r2h
14 cm
2
V = T[?]?
28 cm
Hint: Plug in the value of the
radius for r. The radius is shown
directly in the diagram.
Step-by-step explanation:
V = πr²h
V = 3 × 14² × 28
v = 16464cm³
Find the Value of x.
Answer:
x = 91
Step-by-step explanation:
Opposite angles of an inscribed quadrilateral are supplementary.
x + 89 = 180
x = 91
Help me with this problem
Answer:
Angle A is F Angle A = 57. 52+71=123. 180-123=57
number of ways you can wear 10 outfits to school each day in a 5 day week
Answer:
1 day=10outfits
5days=10outfits×5
=50outfits
Step-by-step explanation:
hope this is helpful
Based on the calculation, you can wear the 10 outfits in 50 different ways throughout the week.
How to calculate the number of waysTo calculate the number of ways you can wear 10 outfits to school each day in a 5-day week, you need to consider the total number of outfits across all days. Since there are 10 outfits and 5 days, the total number of outfit combinations can be calculated by multiplying the number of outfits per day by the number of days:
10 outfits/day × 5 days = 50 outfit combinations
Therefore, you can wear the 10 outfits in 50 different ways throughout the week.
Learn more about permutations
https://brainly.com/question/4658834
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hello can you help me with this?
Answer:
x = 25.5
Step-by-step explanation:
suppose RS and MQ are parallel the sum of angle MRS and RMN would be 180 degrees
2x + x + x 78 = 180 add like terms then subtract 78 from both sides
4x = 102 divide both sides by 4
x = 25.5
Find the y-intercept of the line: 9x + 3y = -18
(0,-6)
(0,6)
(-2,0)
(3,9)
Answer:
(0,-6)
Step-by-step explanation:
9x + 3y = -18
Solve for y to get equation in slope intercept form
( y = mx + b )
9x + 3y = -18
Subtract 9x from both sides
9x - 9x + 3y = -18 - 9x
3y = -9x - 18
Divide both sides by 3
3y/3 = y
-9x - 18 / 3 = -3x - 6
We're left with y = -3x - 6
The equation is now in y intercept form
y = mx + b where b = y intercept
-6 takes the spot of b therefore the y intercept would be at (0,-6)
A(3,4) and B(-3,2) are pointd on a coordinate plane. find the coordinate of a points C on the x axis such that AC=BC
Answer:
Step-by-step explanation:
Here's the game plan. In order to find a point on the x-axis that makes AC = BC, we need to find the midpoint of AB and the slope of AB. From there, we can find the equation of the line that is perpendicular to AB so we can then fit a 0 in for y and solve for x. This final coordinate will be the answer you're looking for. First and foremost, the midpoint of AB:
and
Now for the slope of AB:
and
So if the slope of AB is 1/3, then the slope of a line perpendicular to that line is -3. What we are finding now is the equation of the line perpendicular to AB and going through (0, 3):
and filling in:
y - 3 = -3(x - 0) and
y - 3 = -3x + 0 and
y - 3 = -3x so
y = -3x + 3. Filling in a 0 for y will give us the coordinate we want for the x-intercept (the point where this line goes through the x-axis):
0 = -3x + 3 and
-3 = -3x so
x = 1
The coordinate on the x-axis such that AC = BC is (1, 0)
help asap please ----------------
Answer:
-1 Not in domain
0 In domain
1 In domain
Step-by-step explanation:
The domain for the square root function is all positive numbers including (0). The domain is the set of real numbers which when substituted into the function will produce a real result. While one can substitute a negative number into the square root function and get a result, however, the result will be imaginary. Therefore, the domain for the square root function is all positive numbers. It can simply be expressed with the following inequality:
[tex]x\geq0[/tex]
Therefore, one can state the following about the given numbers. Evaluate if the number is greater than or equal to zero, if it is, then it is a part of the domain;
-1 => less than zero; Not in domain
0 => equal to zero; In domain
1 => greater than zero: In domain
PLEASE HELP ASAP!!!!
Use the graph of ƒ to find x if ƒ(x) = 2.
x = –0.5
x = –8
(–∞, –0.5)
x = 0.5
Answer:
[tex]{ \tt{f(x) = 2}} \\ when \: y = 2 \\ { \bf{x = - 0.5}}[/tex]
the first 4 questions
Answer:
(3)(4)(4)(2)Step-by-step explanation:
1.
7 > 0.7 > 0.07 > 0.007
2.
5h - 15hg
taking 5h common
5h (1 - 3g)
3.
5(2x- 1) = 35
dividing both sides by 5
2x - 1 = 7
2x = 7 + 1
2x = 8
x = 4
4.
if x is an odd number x + 2 will also be odd.
for example
11 is an odd number
on adding 2 we get 13 which is also an odd number.
There are 24 students in a class. Three new students join the class. Work out the percentage change in the number of students in the class.
Answer:
12.5% increase
Step-by-step explanation:
To find the percentage increase ( students joined)
Take the new number minus the original amount
There are 27 students in the class after 3 joined
27 - 24 = 3
Divide by the original amount
3/24 = 1/8 = .125 = 12.5%
Answer:
12.5%
Step-by-step explanation:
Intial number = 27
Final number = 24 + 3 = 27
Percentage change :-
% change = 3/24 × 100 % change = 100/8 % Change = 25/2 % change = 12.5 %Neeeeed helpppppppppp
Answer:
The answer is x = -3.
Step-by-step explanation:
To solve for (x), start by realizing that line segment IJ and line segment JK sum up to line segment IK, which equals 5. These line segments can then be turned into an equation, and the equation will look like [tex]7+x+2x+7=5[/tex].
Next, begin to solve the equation by combining like terms, which will look like [tex]3x+14=5[/tex]. Then, subtract 14 from both sides of the equation, which will look like [tex]3x=-9[/tex], and divide both sides by 3 and simplify, which will look like [tex]x=-3[/tex]. The final answer is x = -3.
identify the unit rate shown in the graph
Choices:
A. 1/3 mile per hour
B. 3 hours per mile
C. 3 miles per hour
D. 4 miles per hour
The answer is C or 3 miles per hour
how is it 3?:
there is a point at 6 and another at 3 all we do is 6 - 3 = 3
Find the surface area or volume of each rectangular prism. (Show work pls)
Answer:
496 in.²
346 mm²
880 in.²
168 cm³
960 m³
420 yd³
Step-by-step explanation:
SA = 2(wl + hl + hw)
SA = 2 · (8 · 16 + 5 · 16 + 5 · 8)
SA = 496
SA = 2(wl + hl + hw)
SA = 2 · (5 · 13 + 6 · 13 + 6 · 5)
SA = 346
SA = 2(wl + hl + hw)
SA = 2 · (4 · 20 + 15 · 20 + 15 · 4)
SA = 880
V = whl
V = 4 · 7 · 6
V = 168
V = whl
V = 10 · 8 · 12
V = 960
V = whl
V = 14 · 3 · 10
V = 420
prime factor of 8 and prime factor of 12
Answer:
2
Step-by-step explanation:
a prime factor is a factor that is a prime number
a prime number is a number that will have a fraction in the quotient if it's divided by any number other than itself
2 is the only prime factor shared between 8 and 12
Find the domain and range for each of the relations described by the sets of
ordered pairs below.
4. (-1, 2), (2, 51), (1,3), (8, 22), (9,51)
Domain:
Range:
Answers:
Domain = {-1, 2, 1, 8, 9}
Range = {2, 51, 3, 22}
==================================
Explanation:
The domain is the set of allowed inputs of a function. So it's the set of possible x values. We simply list the x coordinates of each point to form the domain.
The range is the set of possible y values or y outputs. So we simply list the y coordinates of the points. We toss out any duplicates. Since order doesn't matter in a set, we can have the values listed any way we want.
Side notes:
This is a function since we don't have any repeated x values between any of the points. This graph passes the vertical line test.This function is not one-to-one because we have y = 51 correspond to multiple x values (x = 2 and x = 9 simultaneously). This graph fails the horizontal line test.$975, and there is 7 percent sales tax on the purchase.
How much is the sales tax?
Answer:
$68.25
Step-by-step explanation:
To get the sales tax, you must notice that the sales tax is 7% of 975.
That is equal to:
975 × 0.07
0.07 is equal to 7%, or [tex]\frac{7}{100}[/tex].
The answer to the equation is 68.25.
Can like someone help me I'm lost-
Answer:
the first graph
Answer:
1st option
Step-by-step explanation:
If the rate of change is constant, then it's always a straight line, so the 1st option, and if you see the graph, you'll see the line is going down at a rate of 1/4, so the slope is 1/4. So the answer to your question will be the 1st option.
Answered by GAUTHMATH
The following figures are not drawn to scale but AB and CD are straight lines. Find x.
Answer:
x=60
Step-by-step explanation:
solve, 180-(90+x) = 180-(30+2x)
Can someone help me with this math homework please!
Answer:
well I'm not gonna explain it but
#1 is C or the 3rd one (DOMIAN)
#2 is B or the second one (RANGE)
Answer:
DOMAIN OF THE FUNCTION :-
all real numbers
RANGE :-
all real numbers greater than or equal to - 2
as we the graph's vertex is at -2 so basically -2 is the lowest value of the function.
Find the measure of the missing angle using the triangle angle sum theorm.
3x-4y=-24
Identify the x- and y-intercept of the graph of each question
Answer:
x = -8 and y = 6
Step-by-step explanation:
3x - 4y = -24
Solve for y - intercept
3x - 4y = -24
To find y intercept , substitute x = 0
3 × 0 - 4y = -24
Any expression multiplied by 0 equals 0.
0 - 4y = -24
-4y = -24
Divide both sides by -4
-4y / -4 = -24/-4
y = 6
Similarly, Solve for x-intercept
3x - 4y = -24
To find x- intercept , susbtitute y = 0
3x - 4 × 0 = -24
Any expression multiplied by 0 equals 0.
3x - 0 = -24
3x = -24
Divide both sides by 3
3x / 3 = -24 / 3
x = -8
Therefore, y = 6 and x = -8
can someone help please ? i’ve completed a and got (x-3)(x+1) but cant figure out b. thank u :)
Answer:
the answer is probably complicated but this is POSSIBLY similar to your problem
Step-by-step explanation:
x^2 - 1x - 3x + 3
x^2 - 4x + 3
Please help! will give brainly
Answer:
5/6
Step-by-step explanation:
first form numerator you will multiply by π it means 3.14 multiply 11
the answer equals 34.54 ..and then you will use √ it means square root....so the answer is 5
the annwer is
5/6
Answer:
Step-by-step explanation:
[tex]\frac{11\pi }{6}[/tex] = 11 × [tex]\frac{\pi }{6}[/tex] = (12 - 1) × [tex]\frac{\pi }{6}[/tex]
The terminal point located in IV quarter ⇒ x-coordinate is positive and y-coordinate is negative.
(x, y) = ( [tex]\frac{\sqrt{3} }{2}[/tex] , - [tex]\frac{1}{2}[/tex] )
(05.06 LC)The net of an isosceles triangular prism is shown. What is the surface area, in square units, of the triangular prism?
Three rectangles are shown, one below the other. The middle rectangle has a width of 6 units, and, along each width, is a triangle with a height of 4 units. The length of the lowermost rectangle is 8 units and its width is 5 units.
104 units²
132 units²
152 units²
168 units²
Answer:
C. 152 units²Step-by-step explanation:
Total surface area is the area of the net.
The rectangles have area:
8*(5 + 6 + 5) = 128 units²The triangles have area:
2*(1/2*6*4) = 24 units²Total area is:
128 + 24 = 152 units²Correct choice is C
Answer:
C. 152 square units
Step-by-step explanation:
I'll do the rectangles first because they are the easiest.
8(5)=40. There are 2 of those rectangles, so multiply by 2: 80.
6(8)=48. Add that to 80, you get 128.
The two triangles actually make a rectangle, so to save work, just multiply the base by the height: 6(4). You get 24.
Add them all up, and you get 152.
Hope this helps!
