For the given function, identify the x- and y-intercepts if any, the vertex, the axis of symmetry, and the maximum or minimum value. f(x)=−x2+25 A) There are no x-intercepts. The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is y=0. The maximum value of the function is 25. B) The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is x=0. The maximum value of the function is 25. C) The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,−25). The vertex is (0,−25). The axis of symmetry is x=0. The minimum value of the function is −25. D) The x-intercepts are (−25,0) and (25,0). The y-intercept is (0,5). The vertex is (0,5). The axis of symmetry is x=0. The maximum value of the function is 5.
Answers
Answer:
B) The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is x=0. The maximum value of the function is 25.
Step-by-step explanation:
Given that the function is:
[tex]y=f(x)=-x^2+25[/tex]
It is quadratic equation, therefore we can observe that it is a parabola.
The coefficient of [tex]x^{2}[/tex] is negative, therefore it opens downwards.
That means it will have a maximum value.
This maximum value is at the vertex and where x = 0.
Also, vertex is at x intercept.
x intercept is the value of x where we have y = 0 and
y intercept is the value of y where we have x = 0
So, let us put y = 0 first.
[tex]0=-x^2+25\\ \Rightarrow x^{2} =25\\\Rightarrow x =5, -5[/tex]
Therefore x intercepts are at (5, 0) and (-5, 0)
Now, let us put x = 0,
[tex]y=0+25\\\Rightarrow y =25[/tex]
Therefore y intercept is at (0, 25).
It is the point of maximum value (which is 25) and vertex of parabola as explained above.
Kindly refer to the attached image for the graph of given function.
Therefore, correct option is:
B) The x-intercepts are (−5,0) and (5,0). The y-intercept is (0,25). The vertex is (0,25). The axis of symmetry is x=0. The maximum value of the function is 25.
Answer:
Vertex = (3,–4), y-intercept = (0,5), x-intercepts = (1,0) and (5,0), axis of symmetry is x = 3
Step-by-step explanation:
Related Questions
Determine the equation of the line shown in the graph: 3O POINTS PLS HELP ASAP! graph of a vertical line with an x intercept of negative 1 y = −1 y = 0 x = −1 x = 0
Answers
Answer:
[tex]\boxed{x = -1}[/tex]
Step-by-step explanation:
Hey there!
Well a vertical line means it starts with x =,
Whereas a horizontal line starts as y =.
So if the x intercept is at -1 then the equation is x= -1.
Hope this helps :)
Answer:
x = -1
Step-by-step explanation:
A total solar eclipse in 2003 lasted minutes and was viewed from the southern hemisphere. The next total solar eclipse in 2005 lasted minutes and was viewed from the northern hemisphere. How much longer was the 2003 solar eclipse?
Answers
For the 2003 solar eclipse, it lasted 217 seconds (3 minutes, 37 seconds).
Evaluate ƒ(x ) = x 2 + 1 for ƒ(-1). A. 0 B. undefined C. 2
Answers
Answer:
2
Step-by-step explanation:
f(-1)=(-1)²+1=1+1=2
How to do this question plz answer my question
Answers
Answer:
510,064,471,910,000 m² or 5.1 x 10^14 m²
Step-by-step explanation:
4πr²
if the diameter is 12742, then the radius is 6371
4π(6371)²
510,064,471.91 km²
510,064,471,910,000 m²
Answer:
510064471909788 m²
Step-by-step explanation:
diameter=12742 so the radius r=12742/2=6371=6371*1000=6371000
A=4πr²
A=4π(6371000)²
A=162358564000000π =510064471909788 m²
5 times the sum of the digits of a two digit number is 9 less than the number formed by reversing its digits. If 4 times the value of the digit at ones place is equal to the half of the place value of the digit at tens place, find out the number.
Answers
Answer:
5 times the sum of the digits of the number is 9 less than the number formed by reversing digits. → x = (5y - 9)/4 -- equation (1). Case - 2 : And, 4 times the value of the digits at ones place is equal to half the place value of digit at tens place (10x/2).
A full case of soda contains 24 bottles. Tom filled a partially empty case by putting in seven bottles. How many bottles were in the case before he filled it?
Answers
Answer:
17 bottles
Step-by-step explanation:
full case: 24
he added 7 bottles to fill a case
24-7=17
What is the area, in square meters, of the shaded part of the rectangle below?
6 m
14 m
13 m
Answers
Answer:
130 meters squared
Step-by-step explanation:
14-6=8
8*13/2=52
14*13=182
182-52=130 meters
Answer:
130 square metres
Step-by-step explanation:
The shaded area is a trapezium.
Therefore, the rule for its area is base1+base2/2xh
base1=6
base2=14
height = 13
Therefore, 6+14/2 x 13
= 130
Hope that helped!!! k
Ms. Malle owns a restaurant. Typically 3/20 of the customer’s order fish, while 7/20 of the customer’s order poultry. What fraction of her customers order either fish or poultry?
Answers
Find x round to the nearest tenth
Answers
Answer:
[tex] X = 70.5 [/tex]
Step-by-step explanation:
The law of Cosine given can be written in another form to make the Cos(C) the subject of the formula. Which is: [tex] cos(C) = \frac{a^2 + b^2 - c^2}{2ab} [/tex]
Where,
a = 20 ft
b = 18 ft
c = 22 ft
C = X
[tex] cos(X) = \frac{20^2 + 18^2 - 22^2}{2*20*18} [/tex]
[tex] cos(X) = \frac{400 + 324 - 484}{720} [/tex]
[tex] cos(X) = \frac{240}{720} [/tex]
[tex] cos(X) = 0.3333 [/tex]
[tex] X = cos{-1}(0.3333) [/tex]
[tex] X = 70.5 [/tex]
Which of the following is a rational number?
square root of 22, square root of 23, square root of 24, square root of 25
square root of 22
square root of 23
square root of 24
square root of 25
Answers
Answer:
square root of 25 because it equals 5
Step-by-step explanation:
Because the square root of the other they don’t replete or terminate.
square root of 22 is 4.6904157...
square root of 23 is 4.7958315...
square root of 24 is 4.8989794...
square root of 25 is 5
You buy six T-bone steaks that cost $15.99 per pound. The weight that is listed on the package is 5.77 pounds. The scale that weighed the package is accurate to within 1 32 pound. How much per kilogram might you be undercharged or overcharged? (Round to the nearest cent.)
Answers
Answer:
Amount per kilogram, undercharged or overcharged is 0.50
Step-by-step explanation:
Given:
cost of T-bone steaks per pound = $ 15.99
weight listed on package = 5.77 lb
Accuracy of the scale = 1/32 lb
To find:
Amount undercharged or overcharged
Solution:
Let x represent the weight of the package.
Then compute the error in the weight
| x - 5.77 | < 1 / 32
This makes an absolute value inequality
If an inequality is given in the form | x | < a then solution is in the form:
–a < x < a.
If an inequality is in the form | x | > a, then solution splits in the form:
x < –a or x > a.
compute the amount undercharged or overcharged:
First multiply the above inequality by cost of T-bone steaks per pound
15.99 |x - 5.77| < 15.99 (1 / 32)
15.99 |x - 5.77| < 15.99(0.03125)
15.99 |x - 5.77| < 0.4996875
15.99 |x - 5.77| < 0.50
Hence the amount undercharged or overcharged is $0.50
Find f(−1) given that f(x)=x3+2x2+3x+4.
A. 10
B. -2
C. 2
D. -10
Answers
Answer:
The answer is option C
Step-by-step explanation:
f(x) = x³ + 2x² + 3x + 4
To find f(-1) substitute the value of x that's
- 1 into f(x)
That's
[tex]f( - 1) = ({ - 1})^{3} + 2 ({ - 1})^{2} + 3( - 1) + 4 \\ = - 1 + 2(1) - 3 + 4 \\ = - 1 + 2 - 3 + 4 \\ = 1 - 3 + 4[/tex]We have the final answer as
[tex]f( - 1) = 2[/tex]Hope this helps you
How many solutions does the system of equations have?
2x + 3y = 6
y=-2/3x-1
Α. Ο
B. 1
C. 2
D. infinite
(Doesn’t give me a graph or anything hurry please)
Answers
Answer:
0
Step-by-step explanation:
0.017 and 10, please retype the steps you use to set up the problem and type your steps to solve .
Answers
Answer:
0.17
Step-by-step explanation:
0.017 times 10 will equal to 0.17 as you will need to move the decimal point forward by one
u need help ASP .
f(x)=1-3X and g (x)=x+4 calculate gf(-2)
Answers
Answer:
gf (-2) = 11
Step-by-step explanation:
[tex]f(x) = 1 - 3x \\ g(x) = x + 4 \\ gf( - 2) = ..[/tex]
[tex]gf = .. \\ g(1 - 3x) \\ = 1 - 3x + 4 \\ = - 3x + 5 \\ gf = - 3x + 5[/tex]
[tex]gf( - 2) = - 3( - 2) + 5 \\ = 6 + 5 = 11[/tex]
Can i please get some quick help?
Answers
Answer:
the inverse is the third choice
A line 8cm Long is measured as 8.04cm. what is the percentage error?
Answers
Answer:
0.04%
Step-by-step explanation:
8.04-8.00
0.4/100
0.04%
Whats the answer? For all of them
Answers
Answer:
cow = 4
pig = 5
chicken = 9
horse = 3
horse + chicken - pig =7
Y = A system of equations. Y equals StartFraction one-half EndFraction x minus 6. X equals negative 4.X – 6 x = –4 What is the solution to the system of equations?
Answers
Answer:
[tex]x = -4, y =-8[/tex] is the solution to the system of equations.
Step-by-step explanation:
Given the system of equations as:
[tex]y= \dfrac{1}{2}x-6[/tex]
and
[tex]x =-4[/tex]
To find:
The solution to the system of equations = ?
Solution:
Here, we are given two equations and two variables i.e. [tex]x[/tex] and [tex]y[/tex].
So, we can solve the system of equations for the values of [tex]x[/tex] and [tex]y[/tex].
Let us first consider the 2nd equation.
[tex]x =-4[/tex] we already have the value of [tex]x[/tex].
Now, let us put the value of [tex]x[/tex] in the 1st equation to find the value of [tex]y[/tex].
[tex]y= \dfrac{1}{2}x-6[/tex]
[tex]\Rightarrow y= \dfrac{1}{2}\times (-4)-6\\\Rightarrow y= -\dfrac{1}{2}\times 4-6\\\Rightarrow y= -2-6\\\Rightarrow \bold{y =-8}[/tex]
So, the solution to the system of equations is:
[tex]x = -4, y =-8[/tex]
What is the equation for the axis of symmetry of a parabola?
Answers
Answer:
The graph of the parabola is represented by the quadratic function
y = a( x - p )2 + q which has an axis of symmetry represented by the equation of the vertical line x = p.
Step-by-step explanation:
Answer:
x=-b/2a
Step-by-step explanation:
Please help Show that the inverse of a linear function y=mx+b, where m≠0 and x≠b, is also a linear function
Answers
Let f(x) = mx+b. Also, let g(x) be the inverse of f(x)
To find the inverse, we start with y = mx+b and swap x and y. From there, we solve for y like so
y = mx+b
x = my + b
x-b = my
my = x-b
y = (x-b)/m ... note m is in the denominator, so m cannot be 0
y = (x/m) - (b/m)
y = (1/m)x - (b/m)
g(x) = (1/m)x - (b/m)
This new equation is linear because it is in the form (slope)x+(y intercept)
The new slope is 1/m and the new y intercept is -b/m
So this proves that the inverse g(x) is linear when f(x) is linear.
The inverse function is:
[tex]y = \frac{x}{m} - \frac{b}{m}[/tex]
Since [tex]m \neq 0[/tex] and [tex]x \neq b[/tex], it is a linear function with slope [tex]\frac{1}{m}[/tex] and intercept [tex]-\frac{b}{m}[/tex].
---------------------------------
A linear function is given by:[tex]y = mx + b[/tex]
In which:
m is the slope and b is the y-intercept.To find the inverse function, we exchange x and y in the original function, and then isolate y. Thus:[tex]x = my + b[/tex]
[tex]my = x - b[/tex]
[tex]y = \frac{x}{m} - \frac{b}{m}[/tex]
Since [tex]m \neq 0[/tex] and [tex]x \neq b[/tex], it is a linear function with slope [tex]\frac{1}{m}[/tex] and intercept [tex]-\frac{b}{m}[/tex].
A similar problem is given at https://brainly.com/question/18594541
Make a square measuring 5ft x 5ft. Count the number of people that can comfortably fit into the square. Find the ratio of the number of people in the square to the area of the square. What does this ratio mean?
Answers
Answer:
25 Ft
Step-by-step explanation:
you multiply it's so the square root is 25 ft
The length of a rectangle is 3cm longer than its width.If the perimeter of the rectangle is 54cm,find its length in cm.
Answers
Answer:
length = 15 cm
Width = 12 cm
Step-by-step explanation:
Let width = w cm
Length = w + 3
Perimeter of rectangle = 54 cm
2 * (length + width) = 54
2 * (w+3 + w) = 54 {Add like terms}
2 *(2w + 3) = 54
2*2w + 2 * 3 = 54
4w + 6 = 54
Subtract 6 form both sides
4w = 54 - 6
4w = 48
Divide both sides by 4
w = 48/4
w = 12 cm
Length = 12 + 3= 15 cm
Answer:
Length = 15cm
Step-by-step explanation:
let width be x
length = x+3
Perimeter = 2(l + b)
Perimeter = 54cm
equating:
2(x + x + 3) = 54
2(2x +3) = 54
4x + 6 = 54
4x = 54 - 6
4x = 48
x = 48/4 = 12
width = x = 12cm
length = x +3 = 12 + 3 = 15cm
I'm trying to find 1, 2, & 3 but idk how? Sry if it's sideways I'm new
Answers
Answer:
Step-by-step explanation:
m∠1+∠2=180
2x+40+2y+40=180
2x+2y=180-80
2x+2y=100
x+y=50
x=50-y
m∠1=m∠3
2x+40=x+2y
2x-x=2y-40
x=2y-40
2y-40=50-y
2y+y=50+40
3y=90
y=30
x=50-y=50-30=20
m∠1=2x+40=2×20+40=80°
m∠2=2y+40=2×30+40=60+40=100°
m∠3=x+2y=20+2×30=80°
-7 - p= p +3
How do you do this
Answers
Answer:
-5 = p
Step-by-step explanation:
-7 - p= p +3
Add p to each side
-7 - p+p= p+p +3
-7 = 2p+3
Subtract 3 from each side
-7-3 = 2p+3-3
-10 = 2p
Divide each side by 2
-10/2 = 2p/2
-5 = p
Identify the rule for each pattern.
Pattern A: 0,3,6,9, 12, 15, 18,...
Pattern B: 0, 12, 24, 36, 48, 60, 72,...
*
Your answer
This is a required question
After the zeros, how is each number in the Pattern B related to the
corresponding number in Pattern A?
Your answer
Answers
Answer:
ar some point pattern A will have the same numbers as pattern B as it moves along like if you add 3 for 2 more times in pattern A it will have 24 and so on..
Find the GCF of the terms of the polynomial.
Answers
====================================================
Explanation:
The GCF of the coefficients {6, -42, 14} is 2 as it is the largest factor found in each of the three values.
----------
For the variable portions, we can
write z^5 as z^3*z^2write z^4 as z^3*z^1write z^3 as z^3*1Each time we see z^3 show up, so this is the largest common factor among the three variable terms.
----------
The two results we got were 2 and z^3
Putting the two results together, we end up with the overall GCF of 2z^3
find the area of the 1/4 circle when the radius is 8
Answers
Answer:
Method 1 (using the area of a whole circle and dividing by 4)
First work out the area of the whole circle by substituting the radius of 8cm into the formula for the area of the circle:
A = π ×r²
= π ×8²
= 64π (leave the answer as an exact solution as this need to be divided by 4).
So all you need to do now is divide the answer by 4:
Area of a quadrant = 64π ÷4 = 16π = 50.3 cm² to 3 significant figures.
Method 2 (using ¼ πr²)
Substitute r = 8 directly into the formula A = ¼ πr².
A = ¼ πr².
A = ¼ × π × 8².
A = 50.3 cm²
As you can see it gives exactly the same answer as method 1.
Answer:
64pi / 4 = 16pi, or 50.27
Step-by-step explanation:
We use the area formula:
π * r^2 = Area
Substitute in 8 for r to get 64pi
Then all you have to do is divide 64pi by 4 to find a quarter of the area of the circle, which is 16pi. Or if you want rounded to nearest tenth, 50.27
please help :) Which sentence is true? A. 9.46 times 10 to the 12 power > 4.0 times 10 to the 13 power B. 9.46 times 10 to the 12 power < 4.0 times 10 to the 13 power
Answers
Answer:
B
Step-by-step explanation:
The problem is simple because they use powers of 10. When something is multiplied by a power of ten, it is essentially moving the decimal point over for every power.
9.46x10^12= 9460000000000
4.0x10^13= 40000000000000
Although 4 itself is less than 9.46, since is is being multiplied by 10^13, it will be one decimal place bigger.
An account pays 8% per year simple interest paid a new one, the amount in the account is $850. How much is the account in year 6?
Answers
Answer:
1258
Step-by-step explanation:
SI = (P x R x T) / 100
SI = Simple Interest
P = Principal
R = Rate
T = Time
SI = (850 x 8 x 6)/100
=> SI = 85 x 8 x 6 /10
=> SI = 680 x 6 /10
=> SI = 68 x 6
=> SI = 408
The total amount after 6 years = Principal + Simple Interest
=> Total Amount = 850 + 408
=> Total Amount = 1258
After 6 years, the amount in account is 1258.