Answer:
vertex = (5, - 1 )
Step-by-step explanation:
The focus and directrix are equidistant from the vertex
Since the equation of directrix is y = - 3 then the parabola is vertical,
The distance between the focus and directrix is
| 1 - (- 3) | = | 4 | = 2
Thus the vertex is 2 units below the focus
vertex = (5, 1 - 2 ) = (5, - 1 )
A parabola has focus (5, 1) then the vertex of the parabola will be (5, -1).
What is a Parabola?A location on the curve that is equally spaced from both a fixed location and a fixed line is referred to as a parabola. The parabola's focus requires and fixed line are referred to as its foci and directrix, respectively.
As per the given information in the question,
The focus and directrix are equidistant from the vertex then,
The parabola is vertical because the directrix's equation is y = - 3; hence, the focus and directrix are separated by:
|1 - (-3)| = |4| = 2
The vertex is therefore 2 units below the focus.
vertex = (5, 1 - 2) = (5, -1)
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NEED HELP ASAP
NEED TO FIND THE MEAN
Answer:
mean=2.6
Step-by-step explanation:
1+3+4+4+1=13
13 divided by 5=2.6
Answer:mean= 2.6=13/5
Step-by-step explanation:
mean=sum of all values/number of values
so,
mean=(1+3+4+4+1)/5
mean=13/5=2.6
which of the following lengths cannot be the lengths of a triangle? 4,6,9 a.) 3,4,2 b.) 2,2,3 c.) 1,1,2 d.)
Answer:
D. 1, 1, 2
Step-by-step explanation:
A triangles sides have to have the two smallest side's sum add up to be greater than the largest number. In D, 1+1 = 2, and 2 is the largest number, since 2 is not greater than 2, It cannot be a triangle.
Which statement about the quadratic equation below is true?
2x2 - 15x + 18 = 0
Answer:
x=3/2 or x=6
Step-by-step explanation:
2x2−15x+18=0
Step 1: Factor left side of equation.
2x^2-12x-3x+18=0
taking common factors
2x(x-6)-3(x-6)=0
(2x−3)(x−6)=0
Step 2: Set factors equal to 0.
2x−3=0 or x−6=0
x=3/2 or x=6
The length of a rectangle is 2/3 units. The width is 5/6 units. What is the area of the rectangle?
Answer: The length is 0
Step-by-step explanation:
Answer: 5/9
Decimal form: 0.555.......
Step-by-step explanation:
Area = length • width
The ratio of the cost of a ticket to the number of tickets is 15:1. If the Cox family spent $45 on
tickets, how many tickets did they buy?
They bought 3 tickets! Hope this helps :) ✨
hehehdhdhdhdhdhshshshhs
bghvfdddddcvbnmjkliuytrftfgvvvvv nbv nbv hjgfdc
Step-by-step explanation:
hgfdcvbnmkloiuytredfxghgcfxchgjnjngjggjjjjjttttttttttttttttrrrrrtkkkkkkkkkkddddddddddddddddddddddddddddddddddujhhhhhhhhgfnmmmmmmmmmhhurtghbfnvbmgjkuttdggggggggggggggggggggggggggggggggggggggggggggggggggggf
Determine the value of y for y=x-2
Answer:
y=7, -3, 3, -9, 1 (in the empty boxes from left to right)
Step-by-step explanation:
Since y=x-2, all you have to do is take an x value from the top box and subtract 2 from that number to find the value of y.
Give the diagram below find the value of x HELP PLEASEEEEEE IM BAD AT MATH
Answer:
44
Step-by-step explanation:
sum of two interior angle is equal to the exterior angle
: . 14 +30 = 44
Find the volume of the
rectangular prism.
2 cm
8 cm
5 cm
V = [?] cm3
The volume of a rectangular prism is 80 cm³.
The dimensions of a rectangular prism are length=8 cm, breadth=5 cm and height=2 cm.
What is the formula to find the volume of a rectangular prism?The formula to find the volume of a rectangular prism is l×b×h.
Now, the volume of a rectangular prism=8×5×2=80 cm³.
Therefore, the volume of a rectangular prism is 80 cm³.
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(TUTORS HELP ME I BEG YOU!! ILL GIVE BRAINLY AND ITS A MULTIPLE CHOICE, I WILL ALSO SEND PICS PLSSS)
Answer:
2)
Step-by-step explanation:
plug in a random number for x i used 2. So y=2^x+14x-3 which equals 29 and 1)=253 2)=29 3)=207 4)=35
Simplify the expression
(3x4 + 9x3 – 7x + 15) + (-6X4 – 8x2 + 5x – 3)
Answer:
If the numbers next to the "x" are "carroted" ( ^ ) then the answer is
-3x^4 + 9x^3 -8x^2 -2x +12
Step-by-step explanation:
Basically, you just add the like terms together.
Please someone help me
2x^2 + 14x + 12 = 0
x^2 + 7x + 6 = 0
( x + 1 )( x + 6 ) = 0 ==》 x = - 1 Or x = - 6
The ratio of lime juice to soy sauce in a salad dressing is 5:4. The total of bath ingredients is 27 tablespoons. How many tablespoons of each ingredient are used?
Answer:
There would be 15 tablespoons of lime juice and 12 tablespoons of soy sauce.
Lucy purchase a swimsuit and a towel. The towel represent 30% of the total cost. If she spent $15.00 on the towel, then what was her purchase total
Answer:
$50
Step-by-step explanation:
Given data
Let the total purchase be x
Hence 30% of x is $15
Let us find the value of x
30/100*x= 15
0.3*x=15
0.3x=15
x= 15/0.3
x= $50
Hence the purchase is $50
Answer:
$50 is the total
Step-by-step explanation:
30% over 100% = 15 over x
then you cross multiply and get:
30x = 1500
you then divide both sides by 30
30 and 30 cross out
1500 ÷ 30 = $50
find the value of x
−9(10+x)=−243
Answer:
x = 17
I think this is the value for x
The drama club is selling tickets to their play to raise money for the show's expenses. Each student ticket sells for $5.50 and each adult ticket sells for $10. The auditorium can hold at most 140 people. The drama club must make no less than $1100 from ticket sales to cover the show's costs. If
xrepresents the number of student tickets sold and
y represents the number of adult tickets sold, write and solve a system of inequalities graphically and determine one possible solution.
Answer:
x=66 y=74
Step-by-step explanation:
5.5x + 10y = 1100
x + y = 140
---
y = 140 - x
---
5.5x + 10(140-x) = 1100
5.5x + 1400 - 10x = 1100
-4.5x = -300
x = 66.67
---
x = 66
y = 74
= $1103
Isabelle rides her bike to school. The graph shows her speed at different times during her ride.
Select the word that describes Isabelle’s speed during the indicated interval.
Time Interval Speed
0 to 2 minutes
3 to 4 minutes
6 to 8 minutes
9 to 11 minutes
Answer:
0 to 2 minutes - Accelerating
3 to 4 minutes - Constant
6 to 8 minutes - Decelerating
9 to 11 minutes Accelerating
hope i have helped u
Step-by-step explanation:
Jason jumped off a cliff into the ocean in Acapulco while vacationing with some friends. His height as a function of time could be modeled by the function h ( t ) = − 16 t 2 + 16 t + 480 h(t)=−16t 2 +16t+480, where t is the time in seconds and h is the height in feet. What is the maximum height that Jason reaches?
Answer:
484feet
Step-by-step explanation:
If the height as a function of time could be modeled by the function h(t)=−16t^2 +16t+480, where t is the time in seconds and h is the height in feet.
The maximum height of Jason occurs when dh/dt = 0 (velocity is zero)
dh/dt = -32t + 16
0 = -32t + 16
32t = 16
t = 16/32
t = 1/2
t = 0.5secs
Get the maximum height
Recall that h(t)=−16t^2 +16t+480
Substitute t = 0.5
h(0.5)=−16(0.5)^2 +16(0.5)+480
h(0.5) = -4 + 8 + 480
h(0.5) = 4 + 480
h(0.5) = 484
Hence the maximum height reached by Jason is 484feet
The maximum height that Jason reaches is h = 484 feet and it will be reached at t = 0.5 sec.
How to find the maximum of a polynomial function?Let the function be denoted by [tex]y = f(x)[/tex]
If it is twice differentiable, then, firstly, we differentiate it with respect to x and equate with 0 to find the critical values.
Let the obtained critical values be [tex]x_1, x_2, ... x_n[/tex]
The second derivative of that function is then evaluated on those critical values.
The [tex]i^{th}[/tex] critical value has got the maximum if [tex]f''(x_i) < 0[/tex]
That means, if at [tex]x = x_i[/tex] , we get
[tex]f'(x-i) = 0\\and\\f''(x_i) < 0[/tex]
Then that point is where function will have maximum.
If [tex]f''(x_i) > 0[/tex], then the point where the function will have minimum
If value of second rate at point [tex]x_i[/tex] is 0, then we go for third rate of function and check the same facts so on for upper rate(if they exist).
For the given case, we're given the height function as:
[tex]h(t) = - 16t^2 + 16t + 480[/tex]
The function is infinitely differentiable as its polynomial(by a theorem).
Its first and second rate with respect to 't', we get;
[tex]h(t) = - 16t^2 + 16t + 480\\h'(t) = -32t + 16\\h''(t) = -32 < 0[/tex]
Thus, all critical points will be maximum points.
The critical points are evaluated by [tex]h'(t) = 0[/tex]
They are calculated as:
[tex]h'(t) = 0\\-32t + 16 = 0\\t = 0.5 \: \rm sec[/tex]
The height at t = 0.5 s is evaluated as:
[tex]h(0.5) = - 16(0.5)^2 + 16(0.5) + 480 = 484 \: \rm feet[/tex]
Thus, at time 0.5, the height function will be at its maximum value(484 feet). That means, the height of Jason will be maximum when time will be 0.5 seconds from initial time.
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solve for x. does anyone know how to do these so i could do them myself
Eric's cell phone service costs $40.00 a month for unlimited calls. He also pays $0.02 for each text message he sends Which equation represents the total costin dollars, for a month when Eric sends text messages?
Answer:
the answer is d
Marco's family is renting a cabin by the lake. The cost is $40 per day plus a one-time cleaning fee of $60. How many whole days can the family stay, if they have budgeted a maximum of $275 for the cabin? What is the variable for this situation?
Answer:
Step-by-step explanation:
Cost per day = 40
Cleaning fee = 60
Budget = 275
Total cost for one day = 100
The family can stay two whole days
The frequency,f kilohertz of a radio wave is inversely proportional to its wavelength, Ym. The frequency of a radio wave that has a wavelength of 3000m is 100 kHz. Find (i) The frequency of a radio wave that has a length of 500m (ii) The wavelength of a radio wave that has a frequency of 800kHz
Step-by-step explanation:
The frequency of a radio wave that has a wavelength of 3000m is 100 kHz
(a) Wavelength = 500 m
We know that,
[tex]f=\dfrac{c}{\lambda}\\\\f=\dfrac{3\times 10^8}{500}\\\\f=600\ kHz[/tex]
(b) Frequency, f = 800 kHz
[tex]\lambda=\dfrac{c}{f}\\\\\lambda=\dfrac{3\times 10^8}{800\times 10^3}\\\\\lambda=375\ m[/tex]
Hence, this is the required solution.
Ileana buys a large circular pizza that is divided into eight equal slices. She measures along the outer edge of the crust from one piece and finds it to be 512 inches. What is the diameter of the pizza to the nearest inch? A.4 in. B.7 in. C.8 in. D.14 in.
Answer:
14 inches
Step-by-step explanation:
She measures along the outer edge of the crust from one piece and finds it to be 5.5 inches.
We need to find the diameter of the pizza. A pizza is divided into 8 equal parts.
The circumference of one part = [tex]\dfrac{2\pi r}{8}=\dfrac{\pi r}{4}[/tex]
So,
[tex]\dfrac{\pi r}{4}=5.5\\\\2r=D=14\ inch[/tex]
So, the diameter of the pizza is 14 inches.
Is someone’s opinion a statistical question???? Pls help
Answer:
NO
Step-by-step explanation:
A statistical question is a question that can be answered by collecting data that vary. For example, “How old am I?” is not a statistical question, but “How old are the students in my school?” is a statistical question.
Rewrite without absolute value for the given conditions: y =|x −3|+|x +2|−|x −5|, if x >5
9514 1404 393
Answer:
y = x + 4
Step-by-step explanation:
For x > 5, the expressions in each absolute value argument are all positive, so we can simply remove the bars and sum the terms.
y = x - 3 + x + 2 - x + 5
y = x +4
Martin recorded the low temperatures at his house for one week. The temperatures are shown below -7, -3, four, one, -2, -8, seven approximately what was the average low temperature for the week?
Identify the terms, like terms, coefficients, and constants in 7-5y+2+1
Answer:
coefficient is 5y
constants are 7,2,1
no like terms
The Garcia family drives 3/4 of the distance to their. grandparents house in 3/4 hour. How many hours will it take to drive to their grandparents house at the same rate? A-9/16 B-1. C- 1 7/9
Answer:
B
Step-by-step explanation:
what is the number of distinguishable permutations of the letters in the word, POTATO
Answer:
720
Step-by-step explanation:
Potato has 6 letters
6!/2!×2!
6×5×4×3×2/2×2
In a bag, there are 16 marbles: 4 green, 2 yellow, 9 orange, and 1 blue. What is the probability of randomly choosing a green marble?
Answer: 4/16 or 1/4 (simplified)
Answer:
1/4
Step-by-step explanation:
put # of green over total # of marbles in bag
4/16 and simplify by dividing both by 4
1/4
