Answer:
Step-by-step explanation:
Parabola's equation is
y
=
1
16
(
x
−
7
)
2
+
1
and vertex is
(
7
,
1
)
.
Explanation:
Parabola is locus of a point which moves so that its distance from a given point calld focus and a given line ccalled directrix is always constant.
Let the point be
(
x
,
y
)
. Here focus is
(
7
,
5
)
and distance from focus is
√
(
x
−
7
)
2
+
(
y
−
5
)
2
. Its distance from directrix
y
=
−
3
i.e.
y
+
3
=
0
is
|
y
+
3
|
.
Hence equaion of parabola is
(
x
−
7
)
2
+
(
y
−
5
)
2
)
=
|
y
+
3
|
2
or
x
2
−
14
x
+
49
+
y
2
−
10
y
+
25
=
y
2
+
6
y
+
9
or
x
2
−
14
x
+
65
=
16
y
i.e.
y
=
1
16
(
x
2
−
14
x
+
49
−
49
)
+
65
16
or
y
=
1
16
(
x
−
7
)
2
+
65
−
49
16
or
y
=
1
16
(
x
−
7
)
2
+
1
Hence parabola's equation is
y
=
1
16
(
x
−
7
)
2
+
1
and vertex is
(
7
,
1
)
.
graph{(1/16(x-7)^2+1-y)((x-7)^2+(y-1)^2-0.15)((x-7)^2+(y-5)^2-0.15)(y+3)=0 [-12.08, 27.92, -7.36, 12.64]}
Find the product: a) (5 – 2h) (3 + h) b)4p ^2 q ^2 (p ^2 – q ^2)
Answer:
A.) -8h
Step-by-step explanation:
a.) . (5 – 2h) (3 + h)
a.) (5 – 2h) (3 + h)
(5+3) (h-2h)
8(-h)
-8h
two shapes that represent the cross-sections
Answer:
it's the square and the rectangle
1)There are whole numbers that are not integers.
true or false
2)All rational numbers are whole numbers.
true or false
3)All integers are whole numbers.
true or false
4)All integers are rational numbers.
true or false
Answer:
1).false 2). false 3).true 4). true
Step-by-step explanation:
1).All whole numbers are integers, so s...” That's right! All whole numbers are integers, so since 0 is a whole number, 0 is also an integer.
3).. Integers include all whole numbers and their negative counter part e.g. … -4, -3, -2, -1, 0,1, 2, 3, 4,… Where a and b are both integers. is a rational number but not an integer. 4). All integers are rational number. Since we can rewrite an integer into a fractional form by diving it by 1. For example, 4=41 4 = 4 1 . But not all rational numbers are integer.
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]
1) \: \: \: \: False[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]
2) \: \: \: \: False[/tex]
[tex]Exam)\frac{1}{2} \: \: is \: \: rational \: \: but \: \: it \: \: is \: \: not \: integer \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]
3) \: \: \: False[/tex]
[tex]Exam)- 1 \: \: is \: \: integer \: \: but \: \: it \: \: is \: \: not \: \: whole \: \: number \\ [/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
[tex]4) \: \: \: \: True[/tex]
♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️♥️
Heather sells cosmetics for a local company. During her first month of employment her sales were $60. During her second month her sales were $300. What was Heather’s percent of increase in sales? (Remember to move your decimal two places or multiply by 100 to make a decimal a percent!)
Answer:
80%
Step-by-step explanation:
300/3=100
60/3=20
100-20=80
Order the numbers from least to greatest.
-0.5, 3, -3, 1.2
The order of the numbers from least to greatest is (blank)
Answer:
The order of the numbers from least to greatest is -3, -0.5, 1.2, 3.
Answer:
-3, -0.5, 1.2, 3
30+ points need it asap! :) pls show work.
Write a polynomial function f of least degree with the following zeros: 3, 4 + i
Answer:
[tex]f(x)=(x-3)(x^2-8x+17)[/tex]
Or:
[tex]f(x)=x^3-11x^2+41x-51[/tex]
Step-by-step explanation:
To find our factors, we can work backwards.
We know that 3 is a zero. This means that:
[tex]x=3[/tex]
Subtract 3 from both sides:
[tex](x-3)=0[/tex]
So, (x-3) is one of our factors.
We also know that (4+i) is a zero. So:
[tex]x=4+i[/tex]
First, let’s isolate the imaginary. So, subtract 4 from both sides:
[tex](x-4)=i[/tex]
Now, let’s square both sides:
[tex](x-4)^2=(i)^2[/tex]
Expand the left. Evaluate the right:
[tex](x^2-8x+16)=-1[/tex]
Add 1 to both sides. So, our factor is:
[tex](x^2-8x+17)=0[/tex]
Hence, our polynomial function is:
[tex]f(x)=(x-3)(x^2-8x+17)[/tex]
This is also the least degree since we did the most minimum we can do to solve backwards.
Further Notes:
If we want to convert this to standard form, we can distribute:
[tex]f(x)=(x^3-8x^2+17x)+(-3x^2+24x-51)[/tex]
Combining like terms will yield:
[tex]f(x)=x^3-11x^2+41x-51[/tex]
Marissa substracted a negative number from a positive number. Her result was negative. Is that reasonable? Explain.
Answer: It is not reasonable.
Step-by-step explanation: when subtracting a negative number from a positive number the answer is always going to be positive because two negatives make a plus. For example 3-(-5). The two negatives cancel each other out, so it’s 3+5=8
What is the binary number for 17
Answer:
♡ hi there! madeline here. ♡
- your answer is 10001
also, since I answered first, can I get the brainliest?
thank you, have a great day sandra!
✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧･ﾟ: *✧･ﾟ:･ﾟ✧*:･ﾟ✧
Step-by-step explanation:
travels only on Saturdays and Sundays and has miles this month. Travels every weekday and has miles this month. If they each travel about the same number of miles each day, who travels more miles per day for this month?
Complete question :
William travels only on Saturdays and Sundays and has flown 400 miles this month. Jason travels every weekday and has flown 500 miles this month. Who travels more miles per day for this month
Answer:
WILLIAMS ; 50 miles per day
Step-by-step explanation:
Given that :
Williams travel times = Saturdays and Sundays
Total distance traveled = 400 miles
Jason travel times = Every weekday
Total distance traveled = 500 miles
Number of weeks in a month = 4
Hence, saturdays and Sundays = 4 * 2 = 8 days
Weekdays = 5 * 4 = 20 days
Miles traveled per day:
Williams :
Total distance / number of days
= 400 miles / 8 days
= 50 miles per day
Jason :
Total distance / number of days
= 500 miles / 20 days
= 25 miles per day
50 > 25
Hence, Williams travel more miles per day than Jason
can someone help with these two problems?
Answer:
a and b
Step-by-step explanation:
just trust =) ive done this before
Answer: The first one i think is C and the second one is B
Plssss help 30 point!!!
A survey of 100 parks showed the following.
37 had camping.
28 had camping and hiking trails.
69 had hiking trails. 33 had hiking trails and biking paths.
58 had biking paths. 15 had hiking trails, biking paths and camping.
22 had camping and biking paths.
Answer:
A) 2
B)109
c) 4
d)71
I'm a hundred percent sure
Step-by-step explanation:
Draw the Venn diagram
A train to New York city leaves a station every 7 minutes. Another train to Boston leaves the station every 6 minutes. Suppose it is 6:30 am right now. At what time will both trains leave the station together?
Answer:
7:12 a.m
Step-by-step explanation:
Given that:
Train to New York city leaves station every 7 minutes
Train to Boston leaves station every 6 minutes
Current time = 6:30 a.m
Time both will leave station together is obtained by finding the least common multiple of 6 and 7
Multiples of ;
6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60,...
7 = 7, 14, 21, 28, 35, 42, 49, 56, 63, 70,...
The least common multiple of 6 and 7 is 42.
Hence, both trains will leave the station together after 42 minutes ;
Current time + 42 minutes
6:30 a.m+ 42 minutes = 7:12 a.m
Simplify the following.
a) 3x*y * 2xy
Simplify the expression.
6x^2y^2
Given the expression below, write an equivalent expression that does not contain parentheses.
Answer:
-2x - 12 - 2
Step-by-step explanation:
Apply the distributed property: -2x - 12 - 2I hope this helps!
Use the given information to write the equation of the parabola.
Vertex: [tex](0,0)[/tex]
Focus: [tex](0,-\dfrac{1}{2})[/tex]
Answer:
x² = -2y
Step-by-step explanation:
The focus is p away from the vertex, and so is the directrix.
To find the equation of the parabola, we must first determine if the parabola is horizontal or vertical.
Horizontal parabola [Standard form]: (y – k)² = 4p(x – h)Vertical parabola [Standard form]: (x – h)² = 4p(y – k)If the parabola is vertical, the directrix, and focus will have the same x value but different y value compared to the vertex (h, k). You can also tell if the directrix in in the form y = k – p, and if the focus is in the form (h, k + p).
Likewise, if the parabola is horizontal, the directrix, and focus will have the same y value but different x value compared to the vertex (h,k) . You can also tell if the directrix is in the form x = h – p, and if the focus is in the form (h + p, k).
For this problem, given that the vertex is at the origin (0,0), and that the focus is at the point (0, -½).
You can tell that the x value is the same for the vertex, and focus so this must be a vertical parabola. Because this is a vertical parabola, we can use the form mentioned as earlier (x – h)² = 4p(y – k).
If h = 0, and k = 0, the p value must be the difference between the k of the vertex, and the k of the focus: -½ - 0 → -½.
Now we can just plug in our known information to derive the equation!
h = 0, k = 0, p = -½ → (x - h)² = 4p(y - k) →
(x - 0)² = 4(-½)(y - 0) → x² = -2(y - 0) →
x² = -2y.
Also p = 1/4a, if you are wondering.
So because this is a vertical parabola, x² = -2y is generally the same as y = -1/2x² in standard quadratic form. I just like to think of the horizontal parabola as an inverse quadratic because it is like reflecting over the line y = x.
Answer:
[tex]\boxed {\boxed {\sf x^2=-2y}}[/tex]
Step-by-step explanation:
First, plot the two points. We can see the focus is below the vertex. The result will be a vertical parabola. Since the parabola must contain the focus, it will have to open downward.
From this information, we know that the following equation must be used:
[tex](x-h)^2=-4p(y-k)[/tex]
where (h,k) is the vertex and p is the distance from the focus to the vertex.
Next, find p, the distance between the focus and vertex. We can use the distance formula.
[tex]d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
The vertex is (0,0) and the focus is (0, -1/2). Therefore:
[tex]x_1=0\\y_1=0\\x_2=0\\y_2= -1/2[/tex]
[tex]d=\sqrt{(0-0)^2+(0--1/2)^2}[/tex]
[tex]d=\sqrt{(0)^2+(0+1/2)^2}[/tex]
[tex]d=\sqrt{0+(1/2)^2}[/tex]
[tex]d=\sqrt{0+1/4}[/tex]
[tex]d=\sqrt{1/4}[/tex]
[tex]d=1/2[/tex]
Now we know the distance and vertex. We can plug the values into the equation.
d=1/2 and (h,k)= (0,0)
[tex](x-0)^2=-4(1/2)(y-0)[/tex]
[tex](x)^2=-2(y)[/tex]
[tex]x^2=-2y[/tex]
The equation of the parabola is x²= -2y
A freight train traveling along a certain route uses 12 units of fuel per mile plus an additional 2.2 units of fuel per mile for each railcar on the train. Let N represent the number of railcars on the train. What is an expression for f(N), the total number of units of fuel used per mile? find f(12). How many railcars does the train have if f(N)=34?
Answer:
[tex]38.4\ \text{units of fuel/mile}[/tex]
10
Step-by-step explanation:
Let [tex]N[/tex] represent the number of rail cars on the train
Each rail car adds 2.2 units of fuel per mile.
Fixed fuel consumption is 12 units of fuel per mile
The function of fuel consumption per mile is
[tex]f(N)=12+2.2 N[/tex]
when
[tex]N=12[/tex]
[tex]f(12)=12+2.2\times 12\\\Rightarrow f(12)=38.4\ \text{units/mile}[/tex]
[tex]\boldsymbol{f(12)=38.4\ \text{units/mile}}[/tex]
[tex]f(N)=34\\\Rightarrow 12+2.2N=34\\\Rightarrow N=\dfrac{34-12}{2.2}\\\Rightarrow N=10[/tex]
So, the number of rail cars when [tex]f(N)=34[/tex] is 10.
Marco is 6 feet 3 inches tall. There are 2.54 centimeters in 1 inch. What is Marco's height in centimeters?
Answer:
192 cm
Step-by-step explanation:
Answer:
Step-by-step explanation:
First, let's convert 6 feet 3 inches to just inches. Because there are 12 inches in 1 foot, we can say that there are 72 inches in 6 feet. Combined with the other 3 inches, we can say that Marco is a 75 inches tall.
Now, we can multiply the number of inches we found by 2.54 to get Marco's height in centimeters. This gives us 190.5 cm.
Can somebody help me? Will mark brainliest!
Find the measure of angles 1,2 and 3
Answer:
1-75 2-105 3-35
Step-by-step explanation:
1- 180-75-30=75
2- 180-75=105
3- 180-105-40=35
How do you find the slope of the table below
due soon will give brainalist no fake answers!!
Answer:
90gr strawberry jelly
6 sponge fingers
315ml custard
135gr tinned fruit
Step-by-step explanation:
120/4 = 30 * 3 = 90
8/4 = 2 * 3 = 6
420/4 = 105 * 3 = 315
180/4 = 45 * 3 = 135
Your comment will be deleted along with your account BlueDragon123r5 You are working on finding x in the diagram above. You come up with the equation: 9y + 7 = 2y + 98. Your friend who has just started Algebra is blown away and doesn't understand how you came up with the equation. Explain to your friend how you found the equation and how to solve it.
Answer
I know how to solve it just don't know how to explain how you came up with the equation
Step-by-step explanation:
To solve 9y+7=2y+98 you add 9y+2y and you get 11y and then you add 7+98 and get 105 then you put 11y=105 divide both ides by 11 y= 9.54
2m² +2m- 24=0
Alguien me podría ayudar a decirme gracias .
Answer:
Required Answer:-[tex]{:}\longrightarrow[/tex][tex]\sf 2m^2+2m-24=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 2m^2-6m+4m-24=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 2m (m-6)+4 (m-6)=0[/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf (2m+4)(m-6)=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf (2m+4)=0{\quad}or\: (m-6)=0 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf 2m=-4=0 {\quad}or\: m=6 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf m={\dfrac {4}{-2}}{\quad}or\: m=6 [/tex]
[tex]{:}\longrightarrow[/tex][tex]\sf m=-2 {\quad} or\:m=6 [/tex]
[tex]\therefore[/tex][tex]{\underline{\boxed{\bf m=-2,6}}}[/tex]
In a survey of 2,200 people who owned a certain type of car, 880 said they would buy that type of car again. What percent of the people surveyed were satisfied with the car?
*blank*% of the people surveyed were satisfied with the car.
Answer:
40%
Step-by-step explanation:
Given parameters:
Number of people surveyed = 2200
Number of people who said they would buy the car again = 880
Unknown:
The percentage of people satisfied with the car = ?
Solution:
The percentage of people satisfied with the car purchase can be determined using the expression below:
Percentage of people satisfied = [tex]\frac{Number of people who said they would buy the car again}{Number of people surveyed} x 100[/tex]
Percentage of people satisfied = [tex]\frac{880}{2200}[/tex] x 100 = 40%
Esmeralda works in the snack bar at the movie theater. She serves popcorn in two sizes, small and giant. The dimensions of the small box of popcorn are similar to the dimensions of the giant box of popcorn.
What is x when the width of the small box is 4 inches? Round your answer to the nearest tenth.
Answer:
Step-by-step explanation:
6.7
When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream after t minutes is given by C(t) = 0.08t − 0.0004t2, where 0 ≤ t ≤ 240 and the concentration is measured in mg/L.
Answer:
4mg/L
Step-by-step explanation:
Here is the complete question;
When a certain drug is taken orally, the concentration of the drug in the patient's bloodstream after t minutes is given by
C(t) = 0.08t − 0.0004t2, where 0 ≤ t ≤ 240 and the concentration is measured in mg/L. When is the maximum serum concentration reached?
Given the concentration of the drug in the patient's bloodstream after t minutes modeled by the equation;
C(t) = 0.08t − 0.0004t^2
The maximum serum concentration is reached at when d(C(t))/dt = 0
d(C(t))/dt = 0.08-2(0.0004)t
d(C(t))/dt = 0.08-0.0008t
since d(C(t))/dt = 0
0 = 0.08-0.0008t
get the value of t
-0.08 = -0.0008t
t = 0.08/0.0008
t = 100secs
Get the maximum serum concentration reached by substituting t = 100s into the equation as shown;
C(t) = 0.08t − 0.0004t^2
C(100) = 0.08(100) − 0.0004(100)^2
C(t) = 8-0.0004(10000)
C(t) = 8-4
C(t) = 4mg/L
Hence the maximum serum concentration reached is 4mg/L
how would you solve p-11=-14
Answer:
Step-by-step explanation:
all you would need to do is add 11 to both sides, and then you would get your answer.
Mandy divided a 5-pound bag of oranges into 12 equal piles. Which rational number represents the weight of the oranges in each pile? 1/5 5/12 2 1/6 2 2/5
Answer:
5/12
Step-by-step explanation:
Total pound of oranges = 5
Number of piles = 12
Weight of the oranges in each pile = Total pound of oranges / Number of piles
= 5 / 12
The rational number which represents the weight of the oranges in each pile is 5/12
A rectangle is 9 centimeters long and 5 centimeters wide. What is the diameter?
Answer:
A rectangle doesn't has a diameter
________________________________
But if you are asking about perimeter.
Step-by-step explanation:
Perimeter = 2(l + b)
l = 9cm
b = 5cm
Perimeter = 2(l + b)
= 2(9 + 5)
= 18 + 10
= 28cm
Lance's bowling score was 28 pins more than Jim's score. Lance's bowling score was 205. (a) Write an equation to determine Jim's score (j), (b) What was Jim’s score?
yt is anser 4325
Step-by-step explanation:
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