Given:
The given function is:
[tex]f(x)=-(x-2)^2+9[/tex]
To find:
The transformations, intercepts and the vertex.
Solution:
The vertex form of a parabola is:
[tex]y=a(x-h)^2+k[/tex] ...(i)
Where, a is a constant and (h,k) is vertex.
If a<0, then the graph of parent quadratic function [tex]y=x^2[/tex] reflect across the x-axis.
If h<0, then the graph of parent function shifts h units left and if h>0, then the graph of parent function shifts h units right.
If k<0, then the graph of parent function shifts k units down and if k>0, then the graph of parent function shifts k units up.
We have,
[tex]f(x)=-(x-2)^2+9[/tex] ...(ii)
On comparing (i) and (ii), we get
[tex]a=-1,h=2,k=9[/tex]
So, the graph of the parent function reflected across the x-axis, and shifts 2 units right and 9 units up.
Putting x=0 in (ii), we get
[tex]f(0)=-(0-2)^2+9[/tex]
[tex]f(0)=-4+9[/tex]
[tex]f(0)=5[/tex]
The y-intercept is 5.
Putting f(x)=0 in (ii), we get
[tex]0=-(x-2)^2+9[/tex]
[tex](x-2)^2=9[/tex]
Taking square root on both sides, we get
[tex](x-2)=\pm \sqrt{9}[/tex]
[tex]x=\pm 3+2[/tex]
[tex]x=3+2\text{ and }x=-3+2[/tex]
[tex]x=5\text{ and }x=-1[/tex]
Therefore, the x-intercepts are -1 and 5.
The values of h and k are 2 and 9 respectively and (h,k) is the vertex of the parabola.
Therefore, the vertex of the parabola is (2,9).
14) In golf, a birdie means you score (-1) and a bogey means you score (+1), in relation to par. What
would your score be if, after eight holes, you had five birdies and three bogeys?
Answer:
-2
Step-by-step explanation:
Answer:
-2 the other person is also definitely right.
Justin takes his cat to be groomed. The fee to groom the cat is $65 plus 5.75% tax. Is $70 enough to pay for the service?
Answer:
Yes, it is
Step-by-step explanation:
You have to multiply 65 times .0575 to get the amount of money the TAX ALONE will be and you get 3.7375 which rounds up to $3.74 in taxes. Then you add it to the fee to groom the cat and you get $68.74
60 people were asked if they prefer to go on holiday in Britain or in spain
What is the equation of the line through (2, –4) and (0, 4)?A.y = 4x – 4B.y = 4x + 4C.y = –4x + 4D.y = –4x – 4SUBMITarrow_backPREVIOUS
Answer:
C
Step-by-step explanation:
I did this by graphing the points on paper and then forming an equation from there. Another way is to do to slope equation. The slope equation is: [tex]m = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}[/tex], so you would just fill it in here. (4+4) (I did PLUS since subtracting a negative is adding a postive number). This equals 8. (0-2) is -2, so 8/-2 is -4x. For the y-intercept, it is already shown in the equation. This is 4 because if x is 0, then that is the y-intercept. So: y=-4x+4.
"Factor 3x^2+3x-6" "Answer: 3(x-1)(x+2)
Note: I have the answer, but I want the steps so I can do the rest of the problems.
Answer:
Step-by-step explanation:
3x²+3x-6
=3(x²+x-2)
=3(x²+2x-x-2)
=3[x(x+2)-1(x+2)]
=3(x+2)(x-1)
Answer:
3(x - 1)(x + 2)
Step-by-step explanation:
Factor 3x^2 + 3x - 6
Step 1: Factor out a common factor from all terms if possible.
All terms have a common factor of 3. We start by factoring out the 3.
3x^2 + 3x - 6 =
= 3(x^2 + x - 2)
Step 2: We now need to deal with factoring x^2 + x - 2.
It is a trinomial of the form x^2 + ax + b, where the coefficient of x^2 is 1. To factor it, we need 2 numbers whose product is b and whose sum is a. In our case, we have x^2 + x - 2. We need two numbers whose product is -2 and whose sum is 1.
Pairs of numbers with product -2:
-2 and 1 since -2 * 1 = -2
-1 and 2 since -1 * 2 = -2
Now we add the two numbers in each line above.
-2 + 1 = -1 The sum is -1, but we need a sum of 1, so this is not it.
-1 + 2 = 1 Here we do get the sum of 1 that we need, so this pair of numbers is what we need.
The two numbers we need for factoring are -1 and 2.
Now we start the next step.
The factored trinomial will have this form.
= 3(x )(x )
All we need to do now is place each of the numbers in one of the blanks.
= 3(x - 1)(x + 2)
Answer: 3(x - 1)(x + 2)
WILL GIVE BRAINLIEST IMMEDIATELY!!!!!!!
What is the minimum number of degrees that the figure shown below can be rotated so that it maps itself?
A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 360 degrees
IF YOU PUT RANDOM NONSENSE ANSWERS OR A LINK I WILL REPORT YOU AND EMAIL BRAINLY.
Answer:
45 degrees
Step-by-step explanation:
Each triangle in the figure is at a 45 degree angle to the next one, telling us that if you rotate the entire thing by 45 degrees, it will flip.
Answer:
B. 45 degrees
Step-by-step explanation:
The questions is asking us to find the minimun degrees needed to rotate the shape so that it maps itslef, which is just basically asking us to roate the shape so that it looks the same as it is now. That means that we need to rotate the shape so that another one of those traingles is pointing up. There are 8 of those traingle, and there is 360 degrees in a circle. So divide 360 degrees by 8, and we find that there is 45 degrees inbetween each of the triangles. So if we rotate it by 45 degrees the next traingle will be pointing up and the shape will have mapped itself.
The circle below has center Z. Suppose that m XY = 122°. Find the following.
Answer:
m∠XZY = 122°
m∠XWY = 61°
Step-by-step explanation:
From the picture attached,
A circle has been given with center as Z.
∠XZY is a central angles subtended by the arc XY,
Therefore, measure of angle XZY will be equal to measure of ∠XZY.
m(∠XZY) = m(arc XY) = 122°
By another property of the circle,
"Inscribed angle measures the half of the central angle intercepted by the same arc."
Therefore, m∠XWY = [tex]\frac{1}{2}(\angle XZY)[/tex]
= [tex]\frac{1}{2}(122)[/tex]
= 61°
Can someone help me pls
A..
NOT YOU COMMENTING ON POST JUST TO GET POINTS....
Answer:
A.) nine tenths 9/10
Step-by-step explanation:
So if you pronounce 0.9 as it's supposed to be in word form, it's nine tenths, or 9/10
hope this helps:)
Please help! Will mark brainliest!
Ella spins two spinners that are each divided into five sections labeled 1-5. How many different combinations can she spin?
Each spinner has 5 numbers, the total combinations would be 5 x 5 = 25 combinations,
The answer is 25
can you please help me thank you and please write it out
Answer:
≈ 29°
Step-by-step explanation:
Using calculator
[tex]cos^{-1}[/tex] [tex]\frac{7}{8}[/tex] ≈ 29° ( to the nearest degree )
Which decimals are less than the one shown in this diagram?
Answer:
0.20
Step-by-step explanation:
Since the rest of the choices are greater then 22
(-7,-5) lies in which of the following quadrants [ ]
a) Q1 b) Q2 C) Q3 d) Q4
Answer:
C) Q3
Step-by-step explanation:
Starting from the origin, go along the x-axis in a negative direction (left) and along the y-axis in a negative direction (down).
plss help i’ll give brainliest thank you!
Answer:
I think the answer would be point P , first one . ♡
i need help and please write the answer out
Answer:
Dang it I need a picture. Is it any way you can type it out please?
Step-by-step explanation:
Ill answer it when u edit and type it and i duplicated this tab so it doesnt say that max ppl have answered
Answer:
≈ 83°
Step-by-step explanation:
Using a calculator
[tex]cos^{-1}[/tex] (0.12 ) ≈ 83° ( to the nearest degree )
13 p
Roxanna invested $10,000 in an account that earns 8.5% interest that is
compounded monthly. Determine the amount of money in the account in
15 years. (Lesson 7-10b)
Answer:
$35,100
Step-by-step explanation:
Given data
Principal=$10000
Rate= 8.5%
Time = 15 years = 180 months
The expression for monthly compounded interest is
A=P(1+r/12)^t
substitute
A=10000(1+0.085/12)^180
A=10000(1+0.007)^180
A=10000(1.007)^180
A=10000*3.51
A=$35,100
Hence the balance is $35,100
para envasar 600kg de mole en pasta una productora de alimentos utiliza 140 envases ¿cuantos envases se necesitará para 950kg de mole?
Answer:
link respuesta - https://answer-helper.com/mathematics/question21964709
Step-by-step explanation:
Please add a picture explaining how to do this! Ty!!
I really need help with this
Answer:
I don't have a grid with me but look at it this way. if you look at the first set of points look at where they are starting. and. then look at the second set of points. see if the points plotted bend over the x axis or the y axis:)
one ticket costs $8. if you have $56, how many tickets can you buy?
please show work if it’s possible!!:)
Answer:
7
Step-by-step explanation:
because 56 divided by 8 = 7
or 7 x 8 = 56
hope this helps?
if its right can i have brainlist?
:')?
Answer:
You can buy 7 tickets
Step-by-step explanation:
56 devided by 8 is 7
Abigail tosses a coin of a bridge into the stream below. The distance in feet, the coin is above the water is modeled by the equation y=-16x^2+96 +112 , where x represents time in seconds.
answer choices -
7 feet
112 feet
120 feet
256 feet
Sam went to the store to buy some supplies for school. He bought a binder that cost $6.50 and packages of filler paper that cost $1.25 each. If Sam spent a total of $11.50, how many packages of filler paper did he buy? LET p = the number of packages of filler paper
Answer:
4 packages
Step-by-step explanation:
Hi,
1.25x + 6.50 = 11.50
1.25x = 5
x = 4
He bought 4 packages.
I hope this helps :)
Mark rides his bike from his house to the closest edge of the park, across the length of the park, and then back home. The distance from his house to the closest edge of the park is 0.9 km and the distance from the far side of the park to his house is 1.6 km. The map shows the path Mark took on his bike. If ∠B = 85° on the map, then use the law of cosines to determine the length of the park in kilometers.
Answer:
The length of the park is approximately 1.77 kilometers
Step-by-step explanation:
The law of cosines is most appropriate when the measures of two sides and the included angle formed n=by the path of motion is known
The given parameters of the question are;
The distance from Mark's house to the edge of the park, a = 0.9 km
The distance from the far side of the park to Mark's house, c = 1.6 km
Whereby the included angle between lines, 'a' and 'c' is the ∠B = 85°, by cosine rule, we have;
b² = a² + c² - 2·a·c·cos(B)
Where;
b = The length of the park in kilometers
By plugging in the known values of 'a', 'b', and 'c', we get;
b² = 0.9² + 1.6² - 2 × 0.9 × 1.6 × cos(85°) ≈ 3.11899146089
∴ b = √(3.11899146089) ≈ 1.76606666377
Therefore, the length of the park, b ≈ 1.77 km.
find the surface area (will give brainliest)
Answer:
336 ft^2
Step-by-step explanation:
All you have to do is find the area of each face, and add them up.
Firstly lets starts with the identical triangles.
There are two of them, and the area of a triangle is b*h/2
So the area is 6*8/2 , which is 24, and since their are two of them, we add another 24, and we get 48 so far.
Since all the other sides are rectangles, we can just multiply the given lengths and add them up.
So, we have
12x10, which is 120,
12x8, which is 96, and
12x6, which is 72.
Now add all of them up.
48+120+96+72 which is 336
Your answer is 336 ft^2
plz hurry! answer asap!!
The box of a box-and-whisker plot shows:
Check all that are true.
a). Q3
b). Q2
c). The end points of the data set
d). The median of the data set
e). Q1
Answer:
kjvdfvnfjv
Step-by-step explanation:rjfnu4fburbf
Answer:
A, D, E
Step-by-step explanation:
Combine like terms y+4+5(y+8)
Answer:
8y+9
Step-by-step explanation:
Answer:
6y + 44
Step-by-step explanation:
y + 4 + 5(y + 8)
y + 4 + 5y + 40
6y + 44
Find the measure of the exterior angle. *
What is the product of (2p + 7)(3p2 + 4p – 3)?
A.6p3 + 29p2 – 34p + 21
B.6p3 + 29p2 – 22p + 21
C.6p3 + 29p2 + 22p – 21
D.6p3 + 29p2 + 34p – 21
Answer:
C
Step-by-step explanation:
6p3 + 8p2 - 6p + 21p2 +28p -21
6p3 + 29p2 + 22p - 21
I need help with this question asap!
Answer:
c is equivalent to the expression
Step-by-step explanation:
i hope this helps :)
plz help thank u so much.
Answer:
Q.1 area of triangle =1/2×base×height
area oftriangle=1/2×21 feet×16 feet
area of triangle =168feet²
Q.2 A=1/2×base×height
Q.3 area of triangle =1/2× base×height
35feet² =1/2×10feet× h
35 feet² =5 feet×h
35feet²/5 feet = h
7feet = h
Q.4 area of triangle =1/2×base×height
area of triangle =1/2×32×22
area of triangle =352 feet²
[tex] 25x { }^{2} + (5x - 3)(2x + 7) - 9[/tex]
Step-by-step explanation:
[tex]5x - 3 \times 7x + 10[/tex]
Answer:
35x² + 29x - 30
Step-by-step explanation:
Given
25x² + (5x - 3)(2x + 7) - 9 ← expand factors using FOIL
= 25x² + 10x² + 29x - 21 - 9 ← collect like terms
= 35x² + 29x - 30