The value of k is -1 of tangent over the parabola.
Equation of a line: y = (2 + x - k) ÷ 2, in line form of y = mx + c.
Equation of the parabola: x² = (y - 6x - 3) ÷ 2
Given,
y = (x ÷ 2) + (1) - (k ÷ 2)
where, m = 1 ÷ 2 and c = (1 - k) ÷ 2
For parabola equation in parabola form,
y = 2x² + 6x - 3
y = 2(x² + 3x - n) - 3
n = (b ÷ 2)²
n = (6 ÷ 2)²
n = 9
y = 2(x² + 3x - 9 + 9) - 3
y = 2(x² + 3x + 9) - 9 - 3
y = 2(x² + 3x + 9) - 12
y = 2(x + 3)² - 12, Hence the parabola equation is in vertex form.
Now, comparing the above vertex form with the parabola equation,
x² = 4ay
(x + 3)² = (y ÷ 2) + 6
where a = 1 ÷ 2
Now using the condition of tangency c = a ÷ m
c = (1 - k) ÷ 2
m = 1 ÷ 2
a = 1 ÷ 2
(1 - k) ÷ 2 = (1 ÷ 2) ÷ (1 ÷ 2)
1 - k = 2
k = -1
Therefore, the value of k is -1.
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write an equation of the line in slope intercept format (-3,3) (0,-1)
write an equation of the line in slope intercept format (-3,3) (0,-1)
the equation of the line is
y=mx+b
so
step 1
Find the slope
m=(-1-3)/(0+3)
m=-4/3
step 2
Find the equation
we have
m=-4/3
b=-1 ----> is given
substitute
y=-(4/3)x-1a town's population has been growing linearly. in 2003, the population was 59000, and the population has been growing by 1700 people each year. write an equation for the population x years after 2003.
Answer:
The population after x years will be P = 29000 + 700x
Let the population after the years be represented by P
Population of the town in 2003 = 29000
Annual increase in growth = 700
Then, the population after x years will be:
P = 29000 + 700(x)
P = 29000 + 700x
Therefore, the population will be P = 29000 + 700x.
Find the sum of 1\5 And 7\10. The expression Written in equivalent form with Common denominator is.... The sum is.....
The Solution:
Given the fractions below:
[tex]\frac{1}{5}\text{ and }\frac{7}{10}[/tex]We are asked to find the sum of the above two fractions.
[tex]\frac{1}{5}+\frac{7}{10}[/tex]The Lowest Common Multiple (LCM) of 5 and 10 is 10
[tex]\frac{2+7}{10}=\frac{9}{10}[/tex]Thus, the correct answer is
[tex]\frac{9}{10}[/tex]Please help I beg of y’all
Answer:
I think its 180
Step-by-step explanation:
Multiple gaming tournaments can be played online. In these games, players can compete with players from any part of the world. Step-by-step-explanation (Simple linear equation)
In a tournament,200 points are awarded for a win, and 20points are deducted for a loss.
Chetan participated in the tournament.
He won two more matches than the number of matches he lost.
He scored 1120 points.
How many matches did he play?
B. 8
A. 6
D. 14
C. 10
if a tank holds 2000 gallons of water, andthe water can drain from the tank in 40 min-utes, then torricelli’s law gives the volumevof water remaining in the tank aftertminutesasv
V'(t) = -250(1-(1/40)t)
If we know the time, we can plug in the value for "t" in the above derivative and find how much water drained for the given point of t.
Given:
V =2000( 1- (1/40)t)^2 , where 0≤t≤40.
Here we have to find the derivative with respect to "t"
We have to use the chain rule to find the derivative.
V'(t) = 2 (2000)(1- (1/40)t)d/dt(1- (1/40)t)
V'(t) = 2(2000)(1-(1/40)t(-1/40)
When we simplify the above, we get
V'(t) = -250(1-(1/40)t)
If we know the time, we can plug in the value for "t" and find how much water drained for the given point of t.
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Bessie added 1 2/3 cups of fertilizer to each bag of topsoil. She used 7 5/8 bags of topsoil. Bessie used 12 17/24 cups of fertilizer altogether. True or False?
Answer: false
Step-by-step explanation:
Use 1/4 cup per square foot
At 11:59 a.m you change the time on your phone to 11:00 a.m. Is the assignment still missing or no?
Answer:
its still missing
Step-by-step explanation:
U changed it for yourself, not other peoples
Answer: it will say “assigned” but it wouldn’t come up like that for your teacher. I’ve tried it before and it doesn’t work
Step-by-step explanation:
Solve for f(-2).
f(x) = 2x - 4
f(-2) = [?]
Answer:
f(-2) = -8
Step-by-step explanation:
GivensWe are given a function:
[tex]f(x)=2x-4[/tex]
We are told to find f(-2).
SolveFirst, substitute -2 as x in f(x):
[tex]f(x) = 2x-4\\\\f(-2) = 2x-4[/tex]
Then, substitute -2 as x in the equation itself:
[tex]f(-2) = 2(-2) - 4[/tex]
Then, simplify by multiplying 2(-2):
[tex]f(-2) = 2(-2) - 4\\\\f(-2) = -4 - 4[/tex]
Finally, simplify by performing the final arithmetic:
[tex]f(-2) = -4 - 4\\\\f(-2) = -8[/tex]
Final AnswerTherefore, f(-2) = -8.
6,095 divided by
Two answers
Answer: Last Digit Method: If the last digit in 6095 is 0, 2, 4, 6, or 8, then 6095 is divisible by 2. The last digit in 6095 is 5, thus 6095 is not divisible by 2.
Step-by-step explanation:
find the perimeter of the regular hexagon
9 ft. 2 in.
please help asap thank u so much
Answer:660 in
Step-by-step explanation: Just add 6 sides, 9 ft= 108 in, + 2 in = 110, 110x6 = 660
Which property of multiplication is shown?
1 · t = t
Carlita had -$15 in her checking account. She earned $87.99 from her job and decided to pay her phone bill for $47.82. After paying her phone bill, how much money is left in her account? Responses
Carlita has $25.17 in her checking account.
A deposit account held at a bank or other financial institution is known as a transaction account.
It is also referred to at credit unions as a share draught account, checking account, chequing account, current account, and demand deposit account. It is accessible frequently and instantly to both the account holder and any other users they may name. The account owner can access it "on demand." It is possible to gain access using a variety of techniques, including cash withdrawals, debit card use, cheques, and electronic transfers. Economically speaking, the funds in a transaction account are regarded as liquid funds. They are treated as currency in the context of accounting.The amount of money in her checking account = -$ 15
She earned $87.99
Now money in her checking account = -15+87.99 = $ 72.99
She paid her phone bill worth $47.82
money in her checking account = $ ( 72.99 - 47.82 ) = $25.17
Therefore she has $25.17 in her checking account.
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shirt sold at buyer for $7.00 each.
buyer sells shirt for $10.50, what is
his gain?
Answer:
His gain is 3.50$ which is also 50% of 7
Step-by-step explanation:
for next time so you dont gotta waste points all you have to do is go 10.50 -7.00 =3.50 and then just ask go ogle if you are able what percentage is 3.50 of 7.00 because 7.00$ is what he had to pay for so he is making a 50% gain
7(u + 2) = 42 solve for u simplify your answer as much as possible
Answer:
7(u+2)=42
7u+14=42
-14 -14
7u=28
u=4
Pre- Calculus
log(x^5)=3
Answer:
x ≈ 3.9810717
Step-by-step explanation:
according to a study by the centers for disease control and prevention, about 33% of u.s. births are caesarean deliveries. suppose seven expectant mothers are randomly selected. what is the probability that at least one of the expectant mothers will have a caesarean delivery?
The probability that at least one of the expectant mothers will have a cesarean delivery is 0.9394.
What is probability?Probability is the likelihood that something will happen. Based on the information, about 33% of u.s. births are cesarean deliveries.
The number (n) is also given as 7.
p = 33% = 0.33
n! / (n – r)!
N is the number of things you are choosing from,
r is the number of items.
P(x:n,p) = ⁿCˣ x pˣ(1-p)ⁿ⁻ˣ
n is the number of trials (occurrences)
X is the number of successful trials
p is probability of success in a single trial
ⁿCₓ is the combination of n and x
Therefore, the probability will be:
= 1 - P(no mother will have a Caesarean section)
= 1 - P(X = 0)
= 1 - ⁷C₀ (0.33)^0(0.67)^7
= 1 - 0.0606
= 0.9394
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find w, given that the line joining a(3,4) to b(w,-5) is perpendicular to a line with slope -2/3
Answer:
w is -3
Step-by-step explanation:
A line with a perpendicular slope with have a slope that is the negative inverse of the reference line. If the reference line is -(2/3), the perpendicular line will have a slope of (3/2).
The line formed by ab: y = (3/2)x + b
We have one given point on line ab with one coordinate known, (3,4), so let's use it to find b:
y = (3/2)x + b
4 = (3/2)*3 + b for (3,4)
4 = (9/2) + b
b = 4 - (9/2)
b = - 0.5
The equation is y = (3/2)x - 0.5
The slope of (3/2) is equal to the Rise/Run of two points on the line: (3,4) and (w,-5):
Rise = (4 - (-5)) = 9
Run = (3 - w)
Slope = 9/(3-w)
(3/2) = 9/(3-w)
(3/2)(3-w) = 9
(9/2) - (3/2)w = 9
9 - 3w = 18
-3w = 9
w = -3
Point b is (-3, -5)
See attached graph.
Supposed Justins graph had an empty circle at 12. Write the inequality represented by this graph.
the inequality is
x> 12
all real numbers greater than 12
interval (12, infinite)
The stopwatch shows the time Mike took to complete a puzzle.
Round this time to 1 d.p.
36.98sec
Answer:
37.0seconds
Step-by-step explanation:
when you round you take the second number (8) and find out if it is higher or lower than 5. When it is higher you round up.
But, since the next number is 9 you have to continue to round up the next number which is 6.
Hope this is helpful!
State whether the Law of Detachment, the Law of Syllogism, or the Law of the
Contrapositive was used to draw the conclusion from the given statements. If it's an
invalid conclusion, write invalid.
If you are at least 25 years old, then you can rent a car.
Anna is 28 years old.
Therefore Anna can rent a car.
Law of Detachment
Law of Syllogism
Law of Contrapositive
Invalid Conclusion
This is an invalid statement. The law of syllogism is what was used to draw the conclusion in the statement here.
What is the law of syllogism?This is the law that is used in logic in the form of
If a , then b . If b , then c . Then we can derive a third true statement: (3) If a , then c.The law of Syllogism can be interpreted as if a person is at least at the age of 25 then they rae able to rent a car. Now given that Anna has fulfilled this condition because she is at the age of 28, then she would be able to rent a car.
Therefore the second option ios correct
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What is this number in standard form?
(3×100)+(1×110)+(4×11,000)
pls help tysm
The number (3×100)+(1×110)+(4×11,000) in standard form will be 4.4410 × 10⁴
How to calculate the value?It should be noted that standard form simply means a way of presenting numbers as a mathematical expression.
The number given is illustrated as:
= (3×100)+(1×110)+(4×11,000)
= 300 + 110 + 44000
= 44410
This will be expressed in standard form as:
= 4410
= 4.4410 × 10⁴
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Graph the line that represents each linear equation does anyone know a 2d version I can see instead of words to explain it?
The graph of the first linear equation:
y = x + 3
Can be seen in the image at the end.
How to graph the linear equation?Let's graph the first line, which is:
y = x + 3.
To graph it, we need to find two points on the line, to find these, we can evaluate the linear equation in two values of x.
Using x = 0 we get:
y = 0 + 3
y = 3
So we have the point (0, 3).
Using x = 1, we get:
y = 1 + 3
y = 4
So we have the point (1, 4)
Now we can graph these two points on the same coordinate axis and connect them with a line. Like in the example below.
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Is this a function if so explain if not explain
Answer:
Not a function
Step-by-step explanation:
It is not a function because it doesn't pass the vertical line test.
3 to the power of -3 =1/3
Answer: -27
Step-by-step explanation: -3 raised to the power of 3 is written (-3) 3 = -27. Note that in this case the answer is the same for both -3 3 and (-3) 3 however they are still calculated differently. -3 3 = -1 * 3 * 3 * 3 = (-3) 3 = -3 * -3 * -3 = -27. For 0 raised to the 0 power the answer is 1 however this is considered a definition and not an actual calculation.
Mr musa since the servant to the market to buy orange is 15 naira the servants have eaten three oranges on the way ,mr musa a 25 cover orange more than the market price. taking x to be number of oranges mr musa received ,form an equation in x and find x .
Mr musa since the servant to the market to buy orange is 15 naira the servants have eaten three oranges on the way ,mr musa a 25 cover orange more than the market price. Hence 12 be number of oranges mr musa received.
What is Equation?Two or more expressions with an equal sign is called as equation.
Let market price be M
(M+0.25)x=15
Oranges brought=15M
Servent ate 15M-3=x
15M=x+3
Divide both sides by 15.
M=(x+3)/15
((x+3)/15+1/4)x=15
Calculate the LCM and solve
(4x+12+15)x/60=15
Apply cross multiplication
4x²+27x=900
4x²+27x-900=0
By solving it we get x=12
Hence 12 be number of oranges mr musa received.
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A plane flew 216 miles from Bristol airport to Leeds Bradford airport. It had an average speed of 162mph and arrived at 18:15. Work out what time the plane left Bristol airport. Give your answer using the 24 hour clock.
The plane left Bristol airport at 16:55.
This is a problem from time and distance. We can solve this problem by following a few steps.
We have to know the relation between time, speed, and distance. The relation is denoted as,
t = s/v; t is denoted as time interval, v is denoted as velocity or speed in this case and s is denoted as displacement or distance.
We have to find the time. Here velocity is 162 mph and the total distance between Bristol airport to Leeds Bradford airport is 216 miles.
t = 216 miles/ 162 mph = 1.33 hour = 80 minutes.
Therefore the plane left Bristol airport is, ( 18 hours 15 minutes - 80 minutes) = 16 hour 55 minutes = 16:55
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For #26-30, use the diagram at the right. Name the lines
that are parallel for the two given angles. Then classify the
angles.
I need this answered please
Carmen invested her saving in fund B as $11,000.
What is termed as the investment?Investing entails allocating capital (money) to tasks or projects that are anticipated to generate a profit over time.The type of return generated is determined by the project or asset; for example, real estate can generate both rents as well as capital gains; numerous stocks pay semiannual dividends; and bonds typically pay regular interest.For the given question;
Let 'x' be the amount invested by Carmen in fund B.
The, the amount invested in fund A is x - 5000.
The profit on fund A is 2% = 2%(x - 5000).
the profit on fund B is 5% = 5%(x).
Then, the total profit is $670.
The equation will be .
2%(x - 5000) + 5%(x) = 670
2(x - 5000)/100 + 5(x)/100 = 670
2x - 10,000 + 5x = 67,000.
Further simplifying.
7x = 67,000 + 10,000
7x = 77,0000
x = 11,000
Thus, amount invested in fund B is $11,000.
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sofia and manuel are purchasing a home. they wish to save money for 15 years and purchase a house that has a value of $180,000 with cash. if they deposit money into an account paying 5% interest, compounded monthly, how much do they need to deposit each month in order to make the purchase?
We will have the following:
We will have that the value at the end will be $180 000.
The number of periods will be 15*12 = 180.
The interest per month is 0.05/12 = 0.0042
Now:
[tex]A=\frac{P((1+i)^n-1)}{i}_{}[/tex]Here "A" is the value at the end, "P" will be the monthly payments, "i" the monthly interest rate and "n" the number of periods. So:
[tex]180000=\frac{P((1+0.0042)^{180}-1)}{0.0042}\Rightarrow P=\frac{180000\cdot0.0042}{((1+0.0042)^{180}-1)}[/tex][tex]\Rightarrow P=671.1819761\ldots\Rightarrow P\approx671.2[/tex]So, they will need to deposit approximately $671.2 each month.