The equation of parabola in vertex form is y=-3(x+2)^2+6
What is parabola and equation of parabola in vertex form?
Parabola is equation of a curve, such that a point on the curve is equidistant from a fixed point, and a fixed line. The fixed point is called the focus of the parabola, and the fixed line is called the directrix of the parabola.
The equation of parabola in vertex form is
y=a(x-h)^2+k
Given the vertex (-2,6) and (-1,3)
h=-2 and k=6
y=a〖(x+2)〗^2+6
To find the value of a at vertex (-1,3)
Put y = 3 and x = -1
3=a(-1+2)^2+6
3=a+6
a=-3
The equation of parabola is given by y=-3(x+2)^2+6
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identify the y-intercept: 6 - 2y = -6
We know that the equation of a line is given by
y = mx + b, where m and b are numbers:
m is the slope of the line and b is the y intercept.
In this case we have the equation:
6 - 2y = - 6
We clear y so we can identify m and b
6 - 2y = -6
6 = -6 + 2y
6 + 6 = 2y
12 = 2y
12/2 = y
6 = y
In this case
y = 6
Then m=0 and b = 6
Then, the y-intercept is b =6the number of students in the school went from 1028 down to 755 what is the percent decrease?
Step-by-step explanation:
100% = 1028
1% = 100%/100 = 1028/100 = 10.28
the decrease was
1028 - 755 = 273
these 273 were how many % ?
as many % as how often 1% fits into 273 :
273 / 10.28 = 26.55642023... %
this was a 26.55642023...% decrease.
PLease help it’s due tomorrow morning
Explain the step that is used to solve the equation
-x = -16
Answer:x=16
Step-by-step explanation:
just divide both sides by negative 1
Which expression can be used to find the total number of squares below?
6 × 7
7 × 5
6 × 1
7 + 5
6 + 1
An expression which can be used to find the total number of squares below (see attachment) is: B. 7 × 5
What is an expression?An expression can be defined as a mathematical equation which is used to show the relationship existing between two or more variables and numerical quantities.
In this exercise, you're required to determine the total number of squares that are shown in the image attached below. By critically observing the image, we can reasonably and logically deduce that there are five (5) categories of squares and each of them comprises seven (7) squares.
Therefore, the total number of squares can be calculated by using this expression:
Total number of squares = 7 × 5
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What is a hour and how manyyyy
Answer:
An hour is a unit of time.
Step-by-step explanation:
An hour is a period of 60 minutes.
1 hour = 60 minutes.
Answer:
an hour is the si unit of time
1 hour = 60 minutes
1 minutes = 60 seconds
pls mark as brainliest
Step-by-step explanation:
Write an equivalent expression for -3(7+5g)
Answer:
-3(12g)
Step-by-step explanation:
Because if we simplify the 7+5g to 12g because 7+5=12.
Therefore,
-3(7+5g)= -3(12g)
Part B If m=18, what must be the value of n for the equation to have infinitely many solutions? Explain your answer
The equation have infinitely many solution when n is equal to -15.41.
What is linear equation?A linear equation in one variable is an equation which has a maximum of one variable of order 1. It is of the form ax + b = 0, where x is the variable. This equation has only one solution.
Given equation is;
24( mx + n ) = 3x + 17
where; m and n are real numbers.
Part 1. If m = 14 and n = 13 then
Putting the value of m and n in the equation we get;
= 24( 14.x + 13 ) = 3x + 17
= 336x + 312 = 3x + 17
= 336x - 3x = 17- 312
= 333x = -295
x = 0.886
Hence, x = 0.886 the equation having one solution .
part 2. if m = 18 then to find n .
put m = 18 in the given equation;
= 24(18.(0.886) + n ) = 3(0.886) + 17
= 24(15.94) + 24n = 2.658 + 17
= 382.56 + 24n = 19.658
= 24n = 19.658 - 382.56
n = -15.41
Hence, The equation have infinitely many solution when n is equal to -15.41.
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The complete question is;
PART A: Rosie writes the equation 24(mx+n)=3x+17, where m and n are real numbers.
If m=14 and n=13, does the equation have one solution, infinitely many solutions, or no solutions? Explain your answer.
Please help me!!!!!!!!!
Answer:
m∠TQS = 137°
m∠RQS = 43°
Step-by-step explanation:
It is given that ∠RQT is a straight angle
That means that this angle is 180° and RQT is a straight line
Therefore m∠TQS + m∠RQS = m∠RQT = 180°
Given
m∠TQS = (6x + 20)° and m∠RQS = (2x + 40)°
adding the two angles together will imply
(6x + 20)° + (2x + 40)° = 180°
=> 6x + 20 + 2x + 4 = 180
=> 6x + 2x + 20 + 4 = 180
=> 8x + 24 = 180
=> 8x = 180 - 24= 156
=> x = 156/8 = 19.5
Substitute for x in the angle expressions
m∠TQS = 6x + 20 = 6(19.5) + 20 = 117 + 20 = 137°
m∠RQS 2x + 4 = 2(19.5) + 4 = 39 + 4 = 43°
(or we could subtract m∠TQS from 180 to get 180 - 137 = 43°)
Check if they add up to 180°
137° + 43° is indeed 180°
Julia owns a food truck that sells tacos and burritos. She only has enough supplies to make 67 tacos or burritos. She sells each taco for $3.75 and each burrito for $6. Julia must sell no less than $330 worth of tacos and burritos each day. If 42 burritos were sold, determine all possible values for the number of tacos that Julia must sell in order to meet the requirements. Your answer should be a comma separated list of values. If there are no possible solutions, submit an empty answer.
Julia must sell 21 tacos to meet the requirement .
Given: Price of each taco = $ 3.75
Price of each burrito = $ 6
Total amount of money she needs to earn = $ 330
Also the number of burritos sold= 42.
So the total amount earned on selling these burritos= 42× 6 = $ 252
And as it is given that total money she needs to earn is $ 330 .
so required money= $ 330- $ 252
=$ 78
Thus the total number of tacos she needs to sell = 78/ price of 1 taco
= 78/ 3.75
= 20.8 ≈ 21
Thus Julia must sell 21 tacos to meet the requirement .
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Given three points of a quadratic function, find the equation of the function: (-1, -3), (0, -4), (2, 6)
A) f(x)=2x^2+2x−4f
B) f(x)=x^2+2x−4f
C) f(x)=x^2+x−4f
D) f(x)=2x^2+x−4f
The quadratic function has an equation of f(x) = 2x²+ x - 4
How to determine the equation of the functionFrom the question, the ordered pairs are given as
(-1, -3), (0, -4), (2, 6)
A quadratic function is represented as
f(x) = ax²+ bx + c
Using the point (0, -4), we have
a(0)²+ b(0) + c = -4
So, we have
c = -4
This gives
f(x) = ax²+ bx - 4
Using the point (-1, -3), we have
a(-1)²+ b(-1) - 4 = -3
So, we have
a - b = 1
Using the point (2, 6), we have
a(2)²+ b(2) - 4 = 6
So, we have
4a+ 2b = 10
So, we have
a - b = 1
This gives
a = b + 1
Substitute a= b + 1 in 4a+ 2b = 10
4(b + 1) + 2b = 10
This gives
4b + 4 + 2b = 10
Evaluate
6b = 6
Divide
b = 1
So, we have
a = 1 + 1
a = 2
So, we have
f(x) = 2x²+ x - 4
Hence, the equation is f(x) = 2x²+ x - 4
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15. what are the coordinates of point u, point v, and point w
Answer:
is there a picture because this can't be solved without a picture
PLEASE HELP!!!! 40 POINTS
solve for y. 49-y=6y
Answer:
y = 7
eight grade math comes back to haunt me
Solve the given system of equations.S =t =-6s+ 3t = - 45-s-5t= -2
1. Solve s in the second equation:
[tex]\begin{gathered} -s-5t=-2 \\ -s=-2+5t \\ s=-(-2+5t) \\ s=2-5t \end{gathered}[/tex]2. Substitute the s in the first equation by the value you get in the previous step:
[tex]-6(2-5t)+3t=-45[/tex]3. Solve t:
[tex]\begin{gathered} -12+30t+3t=-45 \\ -12+33t=-45 \\ 33t=-45+12 \\ 33t=-33 \\ t=\frac{-33}{33} \\ \\ t=-1 \end{gathered}[/tex]4. Use the value of t to solve s:
[tex]\begin{gathered} s=2-5t \\ s=2-5(-1) \\ s=2+5 \\ s=7 \end{gathered}[/tex]Then, the solution of the given system of equations is s=7t= -1Given P(A) = 0.6, P(B) = 0.42 and P(B|A) = 0.63, find the value ofP(An B), rounding to the nearest thousandth, if necessary
Here, we are given;
P(A)=0.6
P(B)=0.42
P(B/A)=0.63
We have to find;
[tex]P(A\cap B)[/tex]Now,
[tex]P(\frac{B}{A})=\frac{P(A\cap B)}{P(A)}[/tex]This is the formula for finding conditional probability.
From here,we can see that we have values of P(B/A) and P(A) and we can easily find P(Aand B) from here.
Since P(A)>0 so we can use this formula.
Therefore,
[tex]\begin{gathered} P(A\cap B)=P(A)\times P(\frac{B}{A}) \\ P(A\cap B)=0.6\times0.63 \\ P(A\cap B)=0.378 \end{gathered}[/tex]76,300,000 in scientific notation
Answer:
7.63 x 10⁷
Step-by-step explanation:
To convert to scientific notation you have to move the decimal place to where there is only one number in front of it. In this cause the number in front is 7. You have to maintain the same number of significant figures which in this case was 3 then multiply by 10 to the exponent of how many times you moved the decimal place.
Answer:
=76.3×10⁶
Step-by-step explanation:
=76,300,000÷1,000,000
=76.3×10⁶
A hiker walked 15 miles from 8:00 a.m. to noon. He walked an additional 18 miles from 1:00 p.m. to 7:00 p.m.
What is his average rate for the entire walk, in miles per hour?
The average rate for the entire walk of hiker is 3.75 miles per hour by the concept of average speed.
What is average speed?The instantaneous speed is the upper limit of the average speed as the duration of the time interval approaches zero. An object's average speed during a certain period of time is equal to its distance traveled over that period divided by its duration. Speed and velocity are distinct concepts.
The whole distance traveled divided by the total time results in the average rate for the entire walk, expressed in miles per hour.
Given that:
Distance A = 12.8 miles
Distance B = 17.2 miles
Total distance = Distance A + Distance B
Total distance= 12.8 + 17.2
Total distance= 30 miles
Time A = 9:00 a.m. to noon = 3 hours
Time B = 1:00 p.m. to 6:00 p.m. = 5 hours
Total time = Time A + Time B
Total time= 3 + 5
Total time= 8 hours
Average rate = Total distance/Total time
Average rate= 30 miles/8 hours
Average rate= 3.75 miles per hour
Therefore, the average rate for the entire walk of hiker is 3.75 miles per hour.
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Multiply. Write your answer as a fraction in simplest form.
If 2x² + 7x + 10 = p(x+q)² +r for all values of x, find the values of p and q
If the coordinates of the vertex of a parabola are known [tex]V(p,k)[/tex], the equation for that parabola can be written by the following formula;7
[tex]y=a.(x-p)^2+k[/tex]Now let's find the vertex of the given equation.
[tex]V(p)=\frac{-b}{2a}=\frac{-7}{4} =p[/tex][tex]V(k)=f(p)=2(\frac{-7}{4} )^2+7(\frac{-7}{4} )+10=\frac{31}{8} =k[/tex]We've found our vertex.
[tex]V(p,k)=(\frac{-7}{4} ,\frac{31}{8} )[/tex]Let's substitute the unknowns in the formula I've given.
[tex]p(x+q)^2+r=p(x+\frac{7}{4} )^2+\frac{31}{8}[/tex]Let's expand the expression and find the coefficient p.
[tex]px^2+\frac{7px}{2}+\frac{49p}{16}+\frac{31}{8} =2x^2+7x+10[/tex][tex]p=2[/tex]Finally;
[tex]q=\frac{7}{4}[/tex]
[tex]p=2[/tex]
What is the minimum additional information would you need in order to be able to state that the triangles are congruent by AAS?
The minimum additional information needed in order to be able to state that the triangles are congruent by AAS is . Option A
[tex]\angle A B C=\angle A D C[/tex]
This is further explained below.
What is the congruent angle?Generally, The triangles are said to be congruent if they satisfy the AAS (Angle-Angle-Side) condition, which states that if two angles and a non-included side in one triangle are congruent to two angles and the equivalent non-included side in another triangle, then the triangles are congruent.
In conclusion, The following pieces of knowledge are the bare minimum that is required in order to be able to make the assertion that the triangles are congruent according to AAS:
[tex]\angle A B C=\angle A D C[/tex]
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7x - 7; x = 4................
Answer:
21
Step-by-step explanation:
7x - 7
=> substituting x = 4
=> 7(4) - 7
=> 28 - 7
=> 21
which situation is best modeled by an exponential distribution? tafadzwa runs between 10 and 16 laps every day. his times get slower as he gets tired, but his daily average is 48.2 s per lap. what is the probability that his mean lap time tomorrow will be less than 45 s? suppose that meteors large enough to cause mass extinction strike the earth at regular, although exceedingly large, intervals. what is the probability that a large meteor strike will cause a mass extinction event within the next 1000 years? on a dark desert highway, drivers fall asleep and run off the road randomly. what is the probability that a driver will run off the road in one particular 10-mile stretch of this highway? suppose that people call in sick randomly and independently of one another at a business called acme anvil supply. on average, one person calls in sick per week. what is the probability that no one will call in sick next week? suppose that 0.76% of tires are defective, and defective tires occur independently of one another. what is the probability that no more than three of the next 100 tires are defective?
The situation that is best represented by an exponential distribution is given by the following option:
Tafadzwa runs between 10 and 16 laps every day. his times get slower as he gets tired, but his daily average is 48.2 s per lap. what is the probability that his mean lap time tomorrow will be less than 45 s?.
Exponential distributionThe exponential probability distribution, with mean m, is described by the following mass function:
[tex]f(x) = \mu e^{-\mu x}[/tex]
In which [tex]\mu = \frac{1}{m}[/tex] is the decay parameter.
From this, we get that the exponential distribution is used when we want to study the time between events in a distribution, and only the first option in this problem gives it.
As for the other options, the distributions are as follows:
Meteor: Poisson distribution or binomial distribution, mean in a given time, we want to find the probability of a number.Drivers asleep in the highway: Poisson or binomial, also number of events in an interval.People calling in sick: Binomial distribution.Defective tires: Binomial distribution.More can be learned about the exponential distribution at https://brainly.com/question/16371214
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Circle the two subtraction problems that have a difference of 10.2.
The problems with a difference of 10.2 are:
16.29 - 6.09 = 10.236.1 - 25.9 = 10.2We are given some subtraction problems for which we need to find the ones with a difference of 10.2.
The problems are:
12.05 - 2.03
16.29 - 6.09
36.1 - 25.9
22.09 - 21.07
10.82 - 9.8
We find the difference for each of them one-by-one after subtraction.
12.05 - 2.03 = 10.0216.29 - 6.09 = 10.236.1 - 25.9 = 10.222.09 - 21.07 = 1.0210.82 - 9.8 = 1.02The question is incomplete. Find the complete question below:
Circle the two subtraction problems that have a difference of 10.2.
12.05 - 2.03
16.29 - 6.09
36.1 - 25.9
22.09 - 21.07
10.82 - 9.8
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Vă rog mult de tot
√ ( 2√2-3 ) ² + |2√2 + 5|-|-2,5 |
Answer: 4√2-0.5
Step-by-step explanation:
[tex]\sqrt{(2\sqrt{2}-3)^2 } +|2\sqrt{2}+5|-|-2.5|=\\\\|2\sqrt{2}-3|+(2\sqrt{2}+5)-(2.5 )=\\\\2\sqrt{2}-3+2\sqrt{2}+5-2.5 =\\\\4\sqrt{2} -0.5[/tex]
4. You take a $4,500 loan to pay for trip
to the Amazon rainforest to photograph
wild animals. If the loan's interest rate is
8% for 1 year, what is the interest for the
first payment?
A $12.58
C $30.00
B $26.00
D $80.99
The interest for the first payment is $30.00
How to find interest?Interest is how much is paid for the use of money.
Therefore, you take a $4,500 loan to pay for trip to the Amazon rainforest to photograph wild animals.
The loan's interest rate is 8% for 1 year.
Therefore, the interest for the first payment can be calculated as follows:
Interest for the first payment = 8% of 4500 × 1 / 12
Interest for the first payment = 8 / 100 × 4500 × 1 / 12
Interest for the first payment = 8 × 45 × 1 / 12
Interest for the first payment = 360 / 12
Interest for the first payment = $30
Therefore,
interest = $30
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Solve the equation for C
R-C=P
PLEASE HELP SOON!!
Q.1 What is the expression written in simplified radical form? 6 sqrt 27 + 11 sqrt 75
Q.2 53√5 x (-103√50)
Q.3 Which expressions simplify to a rational answer?
Select each correct answer.
1/4 + 1/2
sqrt3 + 4
sqrt4 + 7
2 x sqrt9
7 x sqrt6
4x2sqrt3
3. 7 x (1/3)
7 x sqrt81
Step-by-step explanation:
Q.1
6×sqrt(27) + 11×sqrt(75) =
= 6×sqrt(3×9) + 11×sqrt(3×25) =
= 3×6×sqrt(3) + 5×11×sqrt(3) =
= 18×sqrt(3) + 55×sqrt(3) = 73×sqrt(3)
Q.2
53×sqrt(5) × (-103×sqrt(50)) =
= 53×-103 × sqrt(5)×sqrt(50) =
= -5459 × sqrt(5×50) = -5459 × sqrt(250) =
= -5459 × sqrt(10×25) = -5459 × 5×sqrt(10) =
= -27,295 × sqrt(10)
Q.3
1/4 + 1/2 rational (as both terms are rational)
sqrt3 + 4 irrational (as sqrt(3) is not rational)
sqrt4 + 7 rational (sqrt(4) = 2, 2+7 = 9)
2 x sqrt9 rational (sqrt(9) = 3, 2×3 = 6)
7 x sqrt6 irrational (sqrt(6) is not rational)
4x2sqrt3 irrational (sqrt(3) is not rational)
3. 7 x (1/3) rational (all terms are rational)
7 x sqrt81 rational (sqrt(81) = 9, 7×9 = 63)
6- 1/3x=-1 what is x
Answer:
x=21
Step-by-step explanation:
6-1/3x=-1
-6 -6
-1/3x=-7
__ __
-1/3 -1/3
x=21
Hello!
Let's solve:
[tex]\text{Copy down the equation}\\6-\dfrac{x}{3}=-1 \\\\\text{Move 'x/3' to the right side and '-1 to the other side}\\6+1=\dfrac{x}{3}\\ 7=\dfrac{x}{3} \\\\\text{Multiply 3 to both sides}\\7*3=3*\frac{x}{3} \\x = 21[/tex]
Answer: x = 21
Hope that helps!
The value of y varies directly with x. If y = 8, when x = 4, what is y when x = 48?
Answer:
96
Step-by-step explanation:
If Y is directly proportional (or in this case varies directly) then whatever you do to one value you do to the other.
So in this case, when Y = 8 and X = 4 that means that Y is double of X (cause 8 is double 4).
So when X = 48 all you need to do is double X which will give you 96.
Dale has $100 in a saving account that earns 5% annually, the interest earned is a simple interest. How much will he earn in 3 years? pleasee help asap tyty
The earned amount by Dale in 3 years is: 15 dollars.
How to calculate the amount?
To calculate the annually amount based on the principal money is by using simple interest method. This interest was given by the bank. And it is calculated by multiplying the principal amount, rate and time and divided by 100.
According to the question, the given amount parameters for the simple interest calculation is as follows:
Principal amount: $100
Rate of interest: 5%
Time(years): 3 years
Using standard simple interest formula, we get:
S.I. = (P x R x T)/100
S.I. = (100 x 5 x 3)/100 = 15 dollars
Hence, the earned amount by Dale in 3 years is: 15 dollars
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don’t know what to do
A power function has the formula f(x) = kxⁿ,
A power function is a function that has a single term that is the product of a real number, a coefficient, and a variable raised to a fixed real value. (A coefficient is a value that increases an exponent by a variable.)
A power function has the formula f(x) = kxⁿ, where k and n are both real numbers. You can change the appearance of a power function's graph by changing the values of k and n. As a result, in this graph, n is greater than zero.The Power function produces an integer that has been raised to a particular power. Power is an alternative for the exponent operator in a mathematical equation (^). The Power function only takes two arguments: number and power. Number must be a numeric value that is either a hardcoded constant or a cell reference.Monomial functions:
Linear: y=3x+5
Quadratic: y = x²
Constant: y = 6
Cubic: y = x³+5
Quartic : y = x⁴
Quantic : y = x⁵
Therefore the function with a power function is given by y = k xⁿ
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