[tex]~~~~~~\textit{vertical parabola vertex form} \\\\ y=a(x- h)^2+ k\qquad \begin{cases} \stackrel{vertex}{(h,k)}\\\\ \stackrel{"a"~is~negative}{o pens~\cap}\qquad \stackrel{"a"~is~positive}{o pens~\cup} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex](\stackrel{h}{-3}~~,~~\stackrel{k}{4})\qquad \implies f(x) = a[x-(-3)]^2+4\implies f(x) = a(x+3)^2+4 \\\\\\ \textit{we know that} \begin{cases} x=0\\ f(x) = -5 \end{cases}\implies -5=a(0+3)^2+4\implies -5=9a+4 \\\\\\ -9=9a\implies \cfrac{-9}{9}=a\implies \boxed{-1=a}~\hfill \blacktriangleright f(x)=-(x+3)^2+4 \blacktriangleleft[/tex]
Zander was given two functions: the one represented by the graph and the function f(x) = (x + 4)2. What can he conclude about the two functions?
They have the same vertex.
They have one x-intercept that is the same.
They have the same y-intercept.
They have the same range.
Answer:
C.They have the same y-intercept.
Step-by-step explanation:
Edge 2021
The conclusion about the two functions is (c) they have the same y-intercept.
What are functions?Functions are used to represent equation, graphs and tables
The equation of the function is given as:
[tex]f(x) = (x + 4)^2[/tex]
Set x = 0, to calculate the y-intercept
[tex]f(0) = (0 + 4)^2[/tex]
Evaluate
[tex]f(0) = 16[/tex]
From the complete question, the graph crosses the y-axis at y = 16
This means that both functions have the same y-intercept
Hence, the true statement about the functions is (c) they have the same y-intercept.
Read more about functions at:
https://brainly.com/question/15602982
What is the first step needed to solve (2/5)x - 6 = -16
Answer:
Add 6 to both sides
Step-by-step explanation:
The (usual) first thing to do when solving any equation is to simplify both sides of the equation. However, since we have nothing to simplify, we move onto the next step that'll be the first step: isolating the variable, x. To do so, we must do the inverse of subtracting 6 (which is adding 6).
plz help I can't get it
Answer:
A) 0.25/0.6 B) 40:96 E) 1/3 / 0.8
Step-by-step explanation:
A)
0.25/0.6 = 1/4÷3/5
=5/12
B)
40:96 = 5:12 You can divide 40 and 96 both by 8 to get 5:12
=5/12
E)
1/3 / 0.8 = 1/3 ÷ 4/5
=5/12
Hope this helps :)
What is the degree of each polynomial?
(x^2 - y)^2 Degree _______
8x^4-5x^7+4c^5 Degree ______
x^2y^3/3+2x^3+8x^3 Degree ______
x^4 +2x^3-6x^4-17 Degree ______
-x^2+7x-4x Degree _____
x^7+y^8+x^7-y^8 Degree_____
Answer:
A- 4
B- 5
C- 8
D- 4
E- 2
F- 7
I'm 99% sure these are right!! I hope this helps :(
Frank had 5/9 acres of land. He planted 2/3 of this land with corn. How many acres did he plant with corn ?
Answer:
22/45
Step-by-step explanation:
i literally just looked it up and that's what it gave me i pretty sure its right
Azad wants to Buy a book he has 25,000 dinars which is 9000 dinars less than she needs does the book cost 34,000 Dinars or 16,000 dinars
Answer: 34,000 Dinars
Step-by-step explanation: As 25,000 + 9000 is 34,000
Does anyone know these answers?
Answer:
A
Step-by-step explanation:
We know the answer to the first question is 3 because GC, FB, HD are parallel to AE, so we can eliminate choices B and C, we know D is incorrect because the answer to the third question is 4
Answer:
A. 3, 3, 4Step-by-step explanation:
Parallel segments to AE are:
BF, CG, DH ⇒ 3Parallel segments to EF:
AB, CD, GH ⇒ 3Segments intersecting with EF under right angle:
AE, EG, BF, GH ⇒ 4Correct choice is A
Bella conducted a scientific experiment. For a certain time, the temperature of a compound rose
3
1
3
3
3
1
degrees in
15
15 minutes. What was the rate, in degrees per hour, that the temperature of the compound rose?
Answer: 13 1/3 degrees per hour
Explanation: 10/3 x 4 = 40/3
40/3 = 13 1/3
Which of the following tables does not represent a function?
Answer:
It's the 3rd option
Step-by-step explanation:
A function cannot have one value of 5 associated to more than one value on y
Find the distance between the points (-15,3) and (-9,8).
Distance:-
[tex]\\ \sf\longmapsto \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
[tex]\\ \sf\longmapsto \sqrt{(-9+15)^2+(8-3)^2}[/tex]
[tex]\\ \sf\longmapsto \sqrt{(6)^2+(5)^2}[/tex]
[tex]\\ \sf\longmapsto \sqrt{36+25}[/tex]
[tex]\\ \sf\longmapsto \sqrt{61}[/tex]
[tex]\\ \sf\longmapsto 7.32units[/tex]
Given info:- Find the distance between the points (-15,3) and (-9,8).
Explanation:-
Distance formulae:
Distance = √{(x₂ - x₁)² + (y₂ - y₁)²}
Let's figure out the distance between two points A = (-15,3) and B = (-9,8).
From those points,
x₁ = -15
x₂ = -9
y₁ = 3
y₂ = 8
Using them in the formula,
Distance btw AB = √[{(-9 - (-15)}² + (8 - 3)²]
= √[(-9 + 15)² + (8 - 3)²]
= √[(6)² + (5)²]
= √[(6*6) + (5*5)]
= √[36 + 25]
= √[61] Units.
Therefore, the distance between A(-25,3) and B(-9,8) is √(61) units.
PLEASE HELP.
Directions: find x so that L || M. state the converse used
Answer:
8. x=6; supplementary consecutive interior angles
10. x = 4; no applicable theorem
Step-by-step explanation:
8.The marked angles are "consecutive interior" angles. When their sum is 180°, the lines l and m will be parallel.
(7x -15) +(24x +9) = 180
31x = 186
x = 6
Consecutive interior angles being supplementary will make the lines parallel.
__
10.The sum of the remote interior angles of a triangle is equal to the exterior angle:
28x = 48 +16x
12x = 48
x = 4
The above relation holds regardless of whether line l is parallel to line m. There is no applicable theorem or converse.
_____
Additional comment
Adding the marking shown in the attachment would make the converse of the alternate interior angles theorem applicable to problem 10.
Can anyone help me with this equation? I need to show the work
Simplify the expression (5-4i) (-3 - 4i) – (10-3i)
Answer:
[tex]-5i-41[/tex]
Step-by-step explanation:
Hi there!
[tex](5-4i) (-3 - 4i) - (10-3i)[/tex]
Open up the parentheses
[tex]= -15-20i+12i+16i^2- 10+3i[/tex]
i² = -1
[tex]= -15-20i+12i-16- 10+3i[/tex]
Combine like terms
[tex]= -5i-41[/tex]
I hope this helps!
What is the y-intercept of the function /(x) = -2/9x + 1/3
Answer:
Step-by-step explanation:
f(x)= -2/9x + 1/3 = -2/9(0) + 1/3 = 0 + 1/3= 1/3
I need to know the answer
Answer:
2 x 6 = 12
6 x 2 = 12
12 ÷ 6 = 2
12 ÷ 2 = 6
Step-by-step explanation:
Solve the inequality for u 20>u+8
Answer:
u < 12
Step-by-step explanation:
20 > u + 8 ( subtract 8 from both sides )
12 > u , then
u < 12
Answer:
See below:
Step-by-step explanation:
Hello! My name is Galaxy and I will be helping you today. I hope you are having a nice day!
We can solve this equation in one step, which is Algebra, I'll start solving the problem now.
Algebra
We can start by simplifying the problem, [tex]20>u+8[/tex], we can subtract by 8 on each side to simplify the equation. I'll explain why afterwards.
[tex]20>u+8\\12>u[/tex]
As you can see we've subtracted by 8 on both sides, the reason this works is because when we do something to one side, we must do it to the other, which keeps the equation balanced.
We can prove this works by picking a random number for [tex]u[/tex] from our simplified version. For this case, lets pick 11.
We can see that if we plug it in to the first unsimplified equation, it works perfectly fine:
[tex]20>11+8?\\20>19[/tex]
We've proven that its correct.
So our final answer is [tex]u<12[/tex].
Cheers!
Write an equation for the line with a slope 3 and Y intercept -2
A. y=-3x -2
B. y= 1/3 x -2
C. y= 3x - 2
with explanation pls
Answer:
C. y=3x-2
Step-by-step explanation:
Well we know the equation: y=mx+b
The slope is m, so m= 3
And the y-intercept is b, so b= (0,-2) or b=-2
Then,
Subsitute everything in:
y= 3x -2
I hope this helped :)
please help me i will give u a thanks
Answer:
1024
Step-by-step explanation:
because its going by 4
PLEASE HELP the information is below
Answer:
yellow: x=6
red: y=4
blue: y=-2
Step-by-step explanation:
Need the answer to this pls
Answer:
b
Step-by-step explanation:
y=-1/4 x -3
show that √20 = 2√5
hence , 2√5 = √20
The radius of a circle is constantly increasing. At a certain moment, the rate of increase of the circumference is the same as the rate of increase of the area. At that moment, what is the area of the circle?
a. 1/pi
b.pi/4
c.4pi
d.pi
e.4/pi
Find two numbers x and y with a sum of 200 and a difference of 82
Answer:
Let x be the bigger number, and y be the smaller number.
[tex]x+y=200[/tex]
[tex]x=200-y[/tex]
Since the difference is 82,
[tex]x-y=82[/tex]
Substitute x in:
[tex](200-y)-y=82[/tex]
[tex]200-2y=82[/tex]
[tex]2y=200-82[/tex]
[tex]2y=118[/tex]
[tex]y=59[/tex]
[tex]x=200-59[/tex]
[tex]x=141[/tex]
Anthony is in a hot air ballon that has taken off and is floating above its launching point. Leroy is standing on the ground, 8 METERS away from the launching point. If Anthony and Leroy are 10 meters apart, how high up is Anthony?
Help help help please good luck be honest
Answer:
A'(-6,4) B'(2,2) C'(-2,-2)
Step-by-step explanation:
The dilation is by 2. This just means you multiply each number by two. FOr example, for point a, multiply -3 by 2 and 2 by 2 to get (-6, 4).
Tarik filled his tank with 11 gallons of
premium gasoline. He paid $38.76. How
much did Tarik pay per gallon?
It is 9 kilometers from Charlie's house to the nearest mailbox. How far is it in meters?
Be sure to include the correct unit in your answer.
Answer:
Step-by-step explanation:
9,000 meters
Chris rented a truck for one day. There was a base fee of $14.99, and there was an additional charge of 75 cents for each mile driven. Chris had to pay
$167.24 when he returned the truck. For how many miles did he drive the truck?
M miles
Answer:
Chris drove the truck 203 miles.
Step-by-step explanation
So, first I subtracted the base free cost of the amount he paid and got $152.25. Then, I divided $152.25/0.75 and got 203. S0, that's how I got the answer. I subtracted the base free because we know he had to pay that initially and then I just divided the rest of the money he had to pay by 0.75 because he was charge 0.75 per mile driven.
Three different maths books are arranged in a line on my table. In how many different orders can these Maths books be arranged.? *
in 5 ways
in 6 ways
in 7 ways
________________________________
that means is it horizontally
vertically
up
down
one by one ?
explain with an example
Answer:
Step-by-step explanation:
Three options for the first position
Two options for the second position
one option for the third position
3•2•1 = 6 ways
their orders could be
1) ABC
2) ACB
3) BAC
4) BCA
5) CAB
6) CBA
Answer:
Would be 6 ways
Step-by-step explanation
3x2=6
Due Tomorrow: answer question 1 with steps
Answer:
the 1 st qn that is no2 c is just down right corner am I right
Step-by-step explanation:
plzzz make me ans as the brainliest ans
Equations
So I’m having trouble with this pls explain step by step
Here’s the question
W+2=12
Pls explain
Answer:
w = 10
Step-by-step explanation:
To find the value of w, you need to isolate w on one side.
You can start by subtracting 2 from both sides. What you do to one side of the equation, you have to do to both.
12 - 2 = 10
So now w is isolated and is equal to 10.
w = 10
You can check your work by replacing w with 10 in the equation.
10 + 2 = 12