Answer:
[tex]y = (x - 7)^{2} + 7[/tex].
Step-by-step explanation:
Let [tex]a[/tex], [tex]h[/tex], and [tex]k[/tex] be constants, and let [tex]a \ne 0[/tex]. The equation [tex]y = a\, (x - h)^{2} + k[/tex] represents a parabola in a plane with vertex at [tex](h,\, k)[/tex].
For example, for [tex]y = -(x + 7)^{2} + 7 = -(x - (-7))^{2} + 7[/tex], [tex]a = (-1)[/tex], [tex]h = (-7)[/tex], and [tex]k = 7[/tex].
A parabola is entirely above the [tex]x[/tex]-axis only if this parabola opens upwards, with the vertex [tex](h,\, k)[/tex] above the [tex]x\![/tex]-axis.
The parabola opens upwards if and only if the leading coefficient is positive: [tex]a > 0[/tex].
For the vertex [tex](h,\, k)[/tex] to be above the [tex]x[/tex]-axis, the [tex]y[/tex]-coordinate of that point, [tex]k[/tex], must be strictly positive. Thus, [tex]k > 0[/tex].
Among the choices:
[tex]y = -(x + 7)^{2} + 7[/tex] does not meet the requirements. Since [tex]a = (-1)[/tex], this parabola would open downwards, not upwards as required.[tex]y = (x - 7)^{2} - 7[/tex] does not meet the requirements. Since [tex]k = (-7)[/tex] and is negative, the vertex of this parabola would be below the [tex]x[/tex]-axis.[tex]y = (x - 7)^{2} + 7[/tex] meet both requirements: [tex]a = 1[/tex] and [tex]k = 7[/tex].[tex]y = (x - 7)^{2}[/tex] (for which [tex]k = 0[/tex]) would touch the [tex]x[/tex]-axis at its vertex.Answer:
its c
Step-by-step explanation:
What is the number of x-intercepts of the graph of the function f ( x ) = 25 x 2 + 4 ?
Answer:
0.
Step-by-step explanation:
For x-intercepts:
25x^2 + 4 = 0
x^2 = -4/15
There are no real square roots of a negative value, so there are no x-intercepts.
What is the total amount of screen that Alice will need for her habitat?
Give an exact answer (do not round).
Answer:
SA = 3.04 m²
Step-by-step explanation:
→ Find: Surface Area (SA)
SOLUTION:
→ SA = 2(1x0.8) + 2(0.4x0.8) + 2(1x0.4)
→ SA = 1.6 + 0.64 + 0.8
↓
SA = 3.04 m²
Let f(x)=12x^5-36x^4-6x^3 and g(x)=6x^2. Find f(x) over g(x)
Answer:
GCF = 6{x}^{3}6x
step 1. 6{x}^{3}(\frac{12{x}^{5}}{6{x}^{3}}+\frac{-36{x}^{4}}{6{x}^{3}}+\frac{-6{x}^{3}}{6{x}^{3}})
step 2. 6x3x6x3x12x5+6x3−36+4-6x3=3,888-32
step 3. 3,888-32=3,856
Step-by-step explanation:
your answer is 3,856 hope this helps
For the first 6% of Bianca's salary, her employer matches 100% of her 401(k)
contributions, and from 6% to 12%, Bianca's employer matches 50% of her
401(k) contributions. Bianca's salary is $50,000, and last year, she contributed
$6000 to her 401(k) plan. What was her employer's contribution to the
401(k)?
Answer:
4500
Step-by-step explanation:
Type the correct answer in the box. Use numerals instead of words.
A toy ball has a surface area of 7,543 square millimeters.
What is the radius of the toy ball to the nearest tenth of a millimeter?
The radius is millimeters.
Answer:
The answer is 7,540 to the nearest tenth. If I'm wrong put it in the comments olease
The radius of the toy ball is 24.5 millimeter (to nearest tenth)
What is the surface area of a sphere ?Let, r be the radius of the sphere.
Then the surface area of the sphere = [tex]4\pi r^{2}[/tex] sq. unit
How to find the radius of the toy ball?The structure of the toy ball is sphere.
Given, Surface area of the toy ball = 7543 square millimeter
Let, the radius be r millimeter
∴ [tex]4\pi r^{2}[/tex] = 7543
⇒ [tex]r^{2}[/tex] = [tex]\frac{7543}{4*3.14}[/tex] , where [tex]\pi[/tex] = 3.14
⇒ [tex]r^{2}[/tex] = [tex]\frac{7543}{12.56}[/tex]
⇒ [tex]r^{2}[/tex] = 600.56
⇒ r = [tex]\sqrt{600.56}[/tex]
⇒ r = 24.5 (approx)
Radius = 24.5 millimeter (to nearest tenth)
Learn more about Surface area of sphere here :
https://brainly.com/question/27311622
#SPJ2
Which expression is equivalent to 312 • 79?
Answer:
Step-by-step explanation:
Describe the length and width of a rectangle that has the same area as the one below, but a different perimeter.
the area of both rectangles is 34yd²
hope it really helps...!!!
A group consists of 10 kids and 2 adults. On a hike, they must form a line with an adult at the front and an adult at the back. How many ways are there to form the line
Answer:
1
Step-by-step explanation:
One adult at the front ~ ten students in a line ~ Second adult
PLEASE HELP! MATH QUESTION
Answer:
the midline is at f(x)=0
it takes the ball 2 s to complete a cycle
QUESTION 1 of 10: If you pay a total of $400 for your social media campaign, and you agreed to pay $0.20 per click, how many clicks did you
get?
a) 80
b) 160
c) 1,200
d) 2,000
Answer:
d. 2,000
Step-by-step explanation:
400 (total) / 0.20 (per click) = 2,000
Solve for m. 2 = m /3 − 2
Answer:
12
Step-by-step explanation:
Add 2 to both sides, giving 4 = m/3Multiply both sides by 3, giving 12 = mThe tables represent two linear functions in a system. A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 0, 2. The second column, y, has the entries, 26, 18, 10, 2. A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 0, 2. The second column, y, has the entries, 14, 8, 2, negative 4. What is the solution to this system? (1, 0) (1, 6) (8, 26) (8, –22) tables represent two linear functions in a system. A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 0, 2. The second column, y, has the entries, 26, 18, 10, 2. A 2 column table with 5 rows. The first column, x, has the entries, negative 4, negative 2, 0, 2. The second column, y, has the entries, 14, 8, 2, negative 4. What is the solution to this system? (1, 0) (1, 6) (8, 26) (8, –22) is deciding which of two gyms to join. Each gym charges a monthly rate plus a one-time membership fee. Lian correctly wrote and solved a system of linear equations by substitution to compare the costs of the memberships. In her work, she substituted an expression for one variable and solved for the other. This resulted in the equation 75 = 75. What can Lian conclude? One gym charges $75 per month. Each gym charges $75 per month. Both gyms charge the same monthly rate and the same membership fee. Both gyms charge the same monthly rate, but not the same membership fee.
Answer:
We want to solve a system of linear equations, we will get that the solutionis (8, -22)A system of equations is a group of equations that we must solve simultaneously. Here we have two lines defined by tables:line 1:x y-4 26-2 180 102 2line 2:x y-4 14-2 80 22 -4Remember that a line is written as:y = a*x + bWhere a is the slope and b is the y-intercept.We know that if a line passes through the points (x₁, y₁) and (x₂, y₂), then the slope can be computed as:With this we can find the slope of the first line, using any pair of the given points, I will use (0, 10) and (2, 2)And we know that the line passes through (0, 10), then the y-intercept is equal to 10.y = -4*x + 10For line 2 we can use the points (0, 2) and (2, - 4), so we get:And the y-intercept is y = 2, then the line is:y = -3*x + 2Now we must solve:-4*x + 10 = -3*x + 210 - 2 = 4x - 3x8 = xNow we evaluate x = 8 in any of the two lines:y = -3*8 + 2 = -22Then the solution of the system is (8, -22)
how would you change these equaions to y=mx+b form?
7x + 9y = 1
14x + 18y = 2
Answer:y=-7/9x+1/9 and y= -7/9x + 1/9
Step-by-step explanation:
Glven: AABC with altitude h shown in the diagram. The altitude is perpendicular to BC.
Prove: Area of AABC = 1/2ab sin(C)
By the definition of the (sine ratio, area of triangle, or perimeter of triangle) , the area of ABC is 1/2 ah, then, sin (C)h/b bye the definition of the sine ratio. Using the (division property, multiplication property, substitution property,) bsin(C) = H. Lastly A= 1/2absin(C) by the (simplification, division property, multiplication property, substitution property)
Answer:
Area of triangle
Multiplication property of equality
Substitution property of equality
Step-by-step explanation:
Hope this helps
So, it is proven that the area of triangle ABC is [tex]\frac{1}{2} * a*b*SinC[/tex].
What is a triangle?A triangle is a 2D shape having three sides and the sum of all angles is 180°.
We have,
A ΔABC,
And,
AB = c
BC = a
CA = b
H = Altitude of the triangle,
Now,
Area of triangle [tex]=\frac{1}{2} * Base *Altitude[/tex]
i.e.
Area of triangle ABC [tex]=\frac{1}{2} * a*h[/tex] .....(i)
Now,
Using trigonometric ratios,
[tex]Sin C = \frac{Perpendicular}{Hypotenuse}[/tex]
i.e.
[tex]Sin C = \frac{h}{b}[/tex]
We get,
h = b * SinC
Now,
putting this value in equation (i),
We get,
Area of triangle ABC [tex]=\frac{1}{2} * a*b*SinC[/tex]
So,
It is proved that area of triangle ABC [tex]=\frac{1}{2} * a*b*SinC[/tex] ,
Hence, we can say that it is proven that the area of triangle ABC is [tex]\frac{1}{2} * a*b*SinC[/tex], using trigonometric ratios and the triangle's area formula.
To know more about triangles click here
https://brainly.com/question/2272632
#SPJ2
A hen weighs 2.7 kg. After laying an egg her weight is reduced by 1%. How much does she
weigh now?
2.673 is the asnwer to your quesstion.
Brainly patrol, this is a real answer. Stop it.
you roll a six-sided die. find the probability of the event described. explain your reasoning: you roll a number less than three
If the walls of a square room require 480 ft^2 of paint and the floor to ceiling height is 10
ft, what are the dimensions of the room?
After find the area of one side, we proceeded to find the length and with as
Length = 10.95 feet width = 10.95 feet
Mensuration of ShapesGiven Data
Height of the Room = 10 feetArea of 4 sides of the room = 480 ft^2If the area of 4 side = 480 ft^2
Area of 1 side will be = x
Cross multiply we have
x = 480/4
x = 120 ft^2
Let us find the length and width of the room
x = √120
x = 10.95 feet
hence Length = 10.95 feet
width = 10.95 feet
Height = 10 feet
Learn more about area of shapes here:
https://brainly.com/question/2607596
18) 2(NH4)3PO4
# of
molecules:
# of
elements:
Name of element:
# of atoms:
Total # of atoms:
The #2 is a
(coefficient or subscript)
Answer:
3(14+4)+28+64 = 54+92 = 146 gm/mol
Step-by-step explanation:
Name of elements : 1) Nitrogen
2) hydrogen
3) phosphorus
4) oxygen
If two number cubes are rolled what is the probability of rolling two numbers with a sum less than or equal to 10
Answer:
[tex]p = \frac{11}{12}[/tex]
Step-by-step explanation:
If we roll two number cubes we can summarize the results in the following table (Check table in the attachment)
According to table of sum we roll two numbers with a sum less than or equal to 10 in 33 cases out of a total of 36 result
Then
The probability of rolling two numbers with a sum less than or equal to 10 is: 33/36 = 11/12
Find the measure of the missing angles.
147°
b =
c =
Step-by-step explanation:
b = 147° ( vertically opposite angle )
c + 147 ° = 180° ( supplementary angle )
c = 180° - 147°
c= 33°...
Answer:
Step-by-step explanation:
b = 147° {Vertically opposite angles are congruent}
Linear pair: A linear pair is a pair of adjacent angles whose non-common arms form a line ( opposite rays)
c + 147 = 180 {Linear pair}
c = 180 - 147
c = 33°
the sum of 2 thousands, 11 hundreds, 8 tens 2 ones=
Answer:
answer is 3182
Step-by-step explanation:
hdjsiabehdk
PLEASE PLEASE PLEASE HELP ME WITH THIS QUICK QUESTION!!
Answer: the y intercept is 4 and there is no x intercept
Step-by-step explanation: the intercept is where on the line it connects, on the y line, it touches 4 and it doesnt touch the x line
20 points!! Will give brainilisest. ASAP!!
Answer:
Measure the border between the black lines and the distance between the two places. Then calculate the difference.
Step-by-step explanation:
EX: Let’s say distance is 10 inches distance and 7 inches distance between cities.
7/10–> 7x36/10x36
252/360
And then simplify!
Complete the statement about taxes on dividends. Dividends that are (nonqualified or qualified) are taxed the same as short-term capital gains, which is (equal to, higher than, lower than) the investor's marginal tax rate
Dividends that are nonqualified are taxed the same as short-term capital gains, which is lower than the investor's marginal tax rate.
What is Marginal tax rate?This is defined as the amount of additional tax paid for every additional dollar earned as income.
The additional amount calculated therefore makes nonqualified dividends to have a lower value than it.
Read more about Marginal tax rate here https://brainly.com/question/14435010
#SPJ1
Answer: dividends that are NONQUALIFIED are taxed the same as short-term capital gains, which is EQUAL TO the investors marginal tax
Step-by-step explanation:
How do I solve this ?
come get a prize brainlest
Answer: 70 - 79
hope this helps! :)
Please Help! will give brainlest!
Step-by-step explanation:
sin²zeta + cos²zeta = 1 .....1
sin²zeta - 5coszeta - 5 = 0 .....2
.......1 - .......2
cos²zeta + 5coszeta = 1
I only know just this ....
Entercept word problems
arn
r
2. the water in nate's swimming pool is
currently 72 inches deep. however, nate
noticed a hole in the liner that is causing
water to leak out of the pool. the depth of
the water is decreasing at a rate of 2 inches
per hour. which equation relates the depth
(d) of the water in inches after h hours?
Which of the relations given by the following sets of ordered pairs is a function?
(8,1),(-4,1),(3,5),(0,4),(-1,2)
{(-5,-4),(-4,-3),(-3,-2),(-4,-5),{(-2,-1)}}
((2,4),(2,6),(2,8),(2,10),(2,12)]
({(0,3),(-6,8),(-3,5),(0,-3),(7,11)})
Answer:
Number 1
Step-by-step explanation:
Functions have to have no repeating x-intercepts.
Tyrone randomly drew pieces of paper numbered 10 through 50 out of a bowl. After he drew each piece of paper, he recorded the number, returned the piece of paper to the bowl, and then drew the next piece of paper. His results are recorded in the stem-and-leaf plot below.
1 1 1 2 3 4 4 5 7 8
2 0 1 2 2 2 3 4 6 8 9
3 0 0 1 2 3 4 5 5 6 7 9 9
4 3 4 4 5 6 7 8 8 9
Key: 1 6 represents 16
Based on the information in the stem-and-leaf plot, what is the experimental probability that a piece of paper randomly drawn from the bowl will have the number 35 written on it?
A.
B.
C.
D.
Answer:
the answer is D, 1/20
Step-by-step explanation:
i got it wrong the first time but just look at the correct answer choice
The experimental probability is 1/20 that a piece of paper randomly drawn from the bowl will have the number 35 written on it.
What is the stem-and-leaf diagram?A stem-and-leaf diagram is a quantitative assessment of a collection of data in which the data values are divided into a "stem" (the first digit of the number) and a "leaf" (the remainder of the number) (the last digit of the number).
As per the given stem-and-leaf plot, the required solution would be as:
First, determine the total number of pieces of paper pulled from the bowl by totaling the entries in the stem-and-leaf plot.
The stem-and-leaf layout has 40 numbers, with two of them being 35.
As a result, two of the forty pieces of paper drawn had the number 35 scrawled on them.
So, the experimental probability of the piece of paper having 35 on it is :
2/40 = 1/20.
To learn more about the stem-and-leaf diagram click here:
https://brainly.com/question/8450114
#SPJ2