Answers
So given the vertex is at (-1, 7), this means that b = -1 and c = 7:
y = a(x + 1)^2 + 7
Then we substitute a point from the graph (aside from the vertex). The easiest is the y-intercept of (0, 5):
5 = a(1)^2 + 7
a = -2
Therefore the equation is: y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5
The equation for the parabola graphed below is [tex]y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5[/tex]
A parabola's general equation is: y = a(x - b)2 + c
Given that the vertex is located at (-1, 7), this means that b = -1 and c = 7:
y = a(x + 1)^2 + 7
Then, instead of the vertex, we replace a point from the graph. The y-intercept of (0, 5) is the simplest:
5 = a(1)^2 + 7
a = -2
As a result, the equation is as follows: [tex]y = -2(x + 1)^2 + 7 = -2x^2 - 4x + 5[/tex]
Related Questions
Please answer this and thank you
If DF=78, DE=5x-9, and EF=2x+10, find EF.
Answers
5x - 9 + 2x + 10 = 78
7x+ 1 = 78
7x = 77
x = 77/7 = 11
EF = 2x + 10
EF = 2*11 + 10
EF = 22 + 10
EF = 32
Question
If DF = 78, DE = 5x-9, and EF = 2x+10, find EF.Answer
EF = 32
What is the value of x? The figure shows 2 right triangles, triangle K L J with right angle J and triangle L J M with right angle M. The measure of angle L K J is 30 degrees. The measure of angle L J M is 45 degrees. The length of side K L is 8 square root 2. The length of side L M is x. Enter your answer in the box.
Answers
In triangle KLJ, the hypotenuse is 8 square roots of 2. The side opposite the 30 degree angle is half of that amount. Therefore, it is only 4 square roots of 2.
That side is also the hypotenuse in the 45 45 90 triangle. To find the leg, we simply divide by the square root of 2. We will end of with legs that are 4.
Identify the 35th term of an arithmetic sequence where a1 = -7 and a18 = 95. (2 points)
Question 1 options:
1) 203
2) 197
3) 168
4) 163,
Answers
Answer: 197
Step-by-step explanation: I took the test :)))
what is: 2/3 X 5/6 X 14 =
this is so that i can help a 5th grader. and i am horrible at fractions. please show work and or explain how to do it. so that i can show her how to do it as well.,
Answers
Which is the graph of f(x)= square root of x
Answers
For this case what you must do is build a table with the values that the function takes when inserting a value of x.
We have then:
x f (x)
1 1
4 2
16 4
25 5
36 6
When you get a sufficient number of points, graph each orderly and see the behavior of the graph.
Answer:
The graph looks like in the attached image.
Water is flowing into a 50-gallon bathtub at a rate of 2.3 gallons per minute (gpm). To the nearest minute, how long will it take to completely fill the bathtub?
A. 48 minutes
B. 22 minutes
C. 26 minutes
D. 115 minutes
Answers
Mark raises guppies in an aquarium. He finds out that guppies reproduce very rapidly, and the number quadruples every month. He starts out with only 2 guppies, and the function y equals 2 times 4 to the x models the number of guppies he will have after x months. Which graph represents this function?
Answers
y = 2 * (4) ^ x
The graph of the function is shown for two different intervals:
A small interval of -1.5 to 0.5
A larger interval of -6.5 to 6.5.
In both intervals the exponential growth of the function is demonstrated.
Answer:
See attached image.
Calculate the difference 12.0875 – 7.50 using significant digits.
A. 4.5
B. 4.587
C. 4.59
D. 4.6
Answers
C. 4.59
Step-by-step explanation:Significant digits are digits expressing precision of a measurement. Non-zero digits are always significant but zeroes can be either included or ignored. For instance, zeroes that comes before other digits aren't significant. For example 0.058 has two significant digits. In this exercise, we have two numbers:
12.0875
7.50
The number 12.0875 has five significant digits while 7.50 has three significant digits. If we add or subtract two numbers, the least number of decimal places (that isn't the same as significant digits) in any of the two numbers must be the same as the number of decimal places in the result. Hence, for 12.0875 we have four decimal places and for 7.50 we have two decimal places. Therefore, the result must have two decimal places:
12.0875 - 7.50 = 4.59
This is a word problem where you have to create an equation and a solution to.
"Michaela and Aleah play on the same basketball team. In one game Michaela scored one fifth of the team's points and Aleah scored one tenth's of the teams points. Together they scored a total of 42 points. How many points did the team score?"
(I might find an equation for it, but I doubt it so if anyone is good with creating equations for word problems please help me!!)
-matty
Answers
.. Michaela scored s/5 . . . . . one fifth of the team's points
.. Aleah scored s/10 . . . . . . . one tenth o the team's points
These scores together are (s/5 +s/10) and that amount is 42 points.
.. s/5 +s/10 = 42
.. s(2/10 +1/10) = 42 . . . . . factor out s
.. s(3/10) = 42 . . . . . . . . . . form the sum of the numbers in parentheses
.. s = 42*10/3 = 140 . . . . . multiply by the inverse of the coefficient of s
The team scored 140 points.
______
Michaela scored 140/5 = 28 points; Aleah scored 140/10 = 14 points.
To solve this word problem, set up the equation (1/5) x + (1/10) x = 42 and solve for x. The team scored 140 points.
Explanation:To solve this word problem, we can start by letting the total number of points scored by the team be represented by 'x'. Since Michaela scored one-fifth of the team's points, her score can be represented as (1/5)x. Similarly, Aleah's score can be represented as (1/10)x. Together, their scores add up to 42 points, so we can set up the equation:
(1/5)x + (1/10)x = 42
To simplify the equation, we can find a common denominator of 10:
(2/10) x + (1/10) x = 42
Combining like terms, we get:
(3/10) x = 42
To isolate x, we can multiply both sides of the equation by 10/3:
x = 42 * (10/3)
Simplifying further, we get:
x = 140
Therefore, the team scored 140 points.
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I need help with this question
Answers
.. A = (1/2)*b*h
.. Aside = (1/2)*(6 cm)*(5 cm) = 15 cm^2
The area of the triangular base is
.. Abase = ((√3)/4)*s^2 = (√3)/4*(6 cm)^2 = 9√3 cm^2
The total surface area is the base area plus the area of the three sides.
.. Atotal = Abase + 3*Aside
.. = 9√3 cm^2 +3*15 cm^2
.. = (45 +9√3) cm^2
.. ≈ 60.6 cm^2
Actually, there's an error in the picture. The height of the side should be 4, and the length of the edge should be 5. Making that adjustment, the total area is 51.6 cm^2.
It is hard to tell what is intended. Not all answers are showing, so we can't "reverse-engineer" the problem from the answers.
What are the coordinates for this graph!
Answers
Your friend wants to borrow $1,137.45 from you to pay off a credit card that charges a 14.7% APR. You agree to the loan but require your friend to pay you interest of 3.6% APR on the loan and your friend agrees.
Your friend pays you $200.00 at the end of the first month. How much goes toward the principal?
Answers
Let's start by calculating the interest on the first month. 1137.45 * (0.036/12) = 1137.45 * 0.003 = 3.41235
So at the end of the 1st month, the amount owed will be 1137.45 + 3.41 = 1140.86
And after the 200 payment is done, the new balance will be:
1140.86 - 200 = 940.86
Meaning that the principle reduced is: 1137.45 - 940.86 = 196.59
We could have also gotten the amount going towards the principle by subtracting the interest from the paying like: 200 - 3.41 = 196.59
The amount that goes into the principal when friend pays you $200.00 at the end of the first month is $296.56.
How to calculate the amount?The first interest will be:
= 1137.45 × (0.036/12)
= 3.41
The amount owed at the month end will be:
= 1137.45 + 3.41
= 1140.86
The new balance after 200 payment will be:
= 1140.86 - 200
= 940.86
Therefore, the reduction in principal will be:
= 1137.45 - 940.86
= 196.59
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(40 POINTS!)
What is the center of the circle that has a diameter whose endpoints are (-3, -5) and (-11, -7)
A. (-8, -1)
B. (-7, -6)
C. (-4, -6)
Answers
The center of any circle is the midpoint of the diameter.
Let's use the midpoint formula to find the midpoint of the diameter.
The midpoint of a line segments with endpoints [tex](x_1, y_2)[/tex] and [tex](x_2, y_2)[/tex] will have a midpoint of [tex]( \dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2})[/tex]
Midpoint of the diameter:
[tex]( \dfrac{-3-11}{2}, \dfrac{-5-7}{2})[/tex]
[tex]=(-7, -6)[/tex]
Your answer is B. Hope this helps!
Solve the system by substitution.
x - 2y = 4
2x - 6y = 8
Answers
2.) 2x - 6y = 8, Add 6y to both sides, then divide both sides by 2. --> answer is, X = 3y + 4
To solve this system with substitution, we need to set x equal to [its value] and plug it into the second equation.
x = 2y + 4
2(2y + 4) - 6y = 8
4y + 8 - 6y = 8
-2y + 8 = 8
-2y = 0
y = 0
Now, we plug y into the equation and solve for x.
x = 4
Hope this helps!
pls help me with this one question
Answers
This should m=be the answer, but i am 51.1111%sure
Expand the logarithmic expression.
log5(7)a^5
A. log57 • 5log5a
B. log57 + 5log5a
C. 7log5a^5
D. log57 – 5log5a
Answers
B. log5(7)+5log5(a)
The explanation of the problem is shown below:
1. You have the following expression given in the problem above:
log5(7)(a^5)
2. To expand it, you must use the logaritms properties, as following:
log5(7)(a^5)
log5(7)+log5(a^5)
log5(7)+5log5(a)
3. Therefore, as you can see, the answer is the option B.
Answer: is b. log57 + 5log5a
HURRY!!! PLEASE
Which equation represents a direct variation?
y = 2x
y = x + 4
y =1/2x
y = 3/x
Answers
Answer:
A. [tex]y=2x[/tex]
Step-by-step explanation:
We are asked to find the equation that represents a direct variation.
We know that a direct variation is in form [tex]y=kx[/tex], where y is directly proportional to x and k is constant of variation.
Upon looking at our given choices, we can see that equation [tex]y=2x[/tex] represents direct variation, where [tex]k=2[/tex].
Therefore, option A is the correct choice.
a factory worker can make 14 products in 45 minutes. what is the worker's unit rate?
Answers
unit rate = (14 products)/(45 minutes) = 0.311 products/minute
Since there are 60 minutes in an hour, if you want the unit rate in products per hour, just multiply what we got above by 60.
unit rate = 18.667 products/hour
divide 14 by 45.0 = 3.2 r 30
hope this helps
Determine how many, what type, and find the roots for f(x) = x4 + 21x2 − 100.
Answers
Answer:
Step-by-step explanation:
We will make a substitution to make our work easier (when we get there). We also need to know that
[tex]i^2=-1[/tex]
We will use that as another substitution. First, let's make the job of factoring a bit easier. Here's the first substitution. We will let
[tex]x^4=u^2[/tex]
Therefore,
[tex]x^2=u[/tex]
Now we will write the polynomial in terms of u instead of x:
[tex]f(x)=u^2+21u-100[/tex]
Solve for the values of u by setting the polynomial equal to 0 and factoring. When you factor, you will get:
[tex](u+25)(u-4)[/tex]
But don't forget that
[tex]x^2=u[/tex]
so we have to put those back in now:
[tex](x^2+25)(x^2-4)=0[/tex]
By the Zero Product Property, either
[tex]x^2+25=0[/tex] or
[tex]x^2-4=0[/tex]
We will factor the first term. Solving for x-squared gives us:
[tex]x^2=-25[/tex] and
x = ±√-25
which simplifies down to
x = ±√-1 × 25
we can sub in an i-squared for the -1:
x = ±√[tex]i^2*25[/tex]
The square root of i-squared is "i" and the square root of 25 is 5, so
x = ±5i
The next one is a bit easier. If
[tex]x^2=4[/tex], then
x = ±2
You can see you have 4 solutions. But you knew that already, since this is a 4th degree polynomial. The types of solutions are: 2 real, 2 imaginary
The population of wild horses on a wildlife refuge decreased from 110 to 99 in a year. If this trend were to continue, what exponential equation could be used to predict the horse population in the future?
y = 110(1.1)^x
y = 99(0.9)^x
y = 99(1.1)^x
y = 110(0.9)^x,
Answers
The exponential equation for this situation is y = 110(0.9) ^x. This is because 110 is the principal or the initial number of horses and y is the resultant population after a certain number of years X with a rate of 0.9. Note that the rate is less than 1 which means that the population is decreasing as time goes by.
Answer:
The person is right.
Step-by-step explanation:
Look at his profile.
It takes Susan 3 hours to fix 2 broken cars and it takes Joseph 4 hours to fix 3 broken cars. If they work together how long will it take them to fix 17 broken cars?
Answers
Susan = 2 car / 3 hr
= 2/3
Joe = 3 car / 4 hr
= 3/4
add the rates to get the new combined rate as 17 cars in "t" hours.
2/3 + 3/4 = 17/t
Need common denominator
2/3(4/4) + 3/4(3/3) = 17/t
8/12 + 9/12 = 17/t
17/12 = 17/t
see that "t" is 12 hours
Susan and Joseph can fix 17 broken cars together in 12 hours.
Explanation:To calculate the time it takes for Susan and Joseph to fix 17 broken cars together, we can calculate their individual rates of work.
Susan takes 3 hours to fix 2 cars, so her rate is 2/3 cars per hour.
Joseph takes 4 hours to fix 3 cars, so his rate is 3/4 cars per hour.
When they work together, their rates are additive. So their combined rate is (2/3 + 3/4) cars per hour. This is equal to (8/12 + 9/12) cars per hour, which simplifies to 17/12 cars per hour.
To find the time it takes to fix 17 cars, we can divide the number of cars by the combined rate: 17 cars / (17/12 cars per hour) = 12 hours.
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emily is converting 9 feet per hour into inches per minute. which conversion factor should she use
Answers
[tex] = 9 \dfrac{ft}{hr} \times \dfrac{12~in \times hr}{60~ft \times min} [/tex]
[tex] = 9 \dfrac{ft}{hr} \times \dfrac{1~in \times hr}{5~ft \times min} [/tex]
The conversion factor is 1/5.
A person invested $7,200 in an account growing rate allowing money to double every 8 years. How much money would be in the account after 19 years, to the nearest dollar?
Answers
After 19 years, the final amount is $29,936.93, to the nearest dollar.
What is the formula for exponential growth?The formula for exponential growth:
[tex]final amount = initial amount * (rate)^(number of time periods)[/tex]
In this case, the initial amount is $7,200, the rate is 2 (since the money doubles every 8 years), and the number of time periods is 19/8=2.375 (since 19 years is 2.375 times the 8-year doubling period). Plugging these values into the formula, we get:
final amount = $7,200 * 2^2.375
The final amount is $29,936.93, to the nearest dollar.
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2. Solve 10^6x = 93. Round to the nearest ten-thousandth. (1 point)
11.8109
1.0986
13.3801
0.3281
3. Use a graphing calculator. Solve 5.5^3x = 805 by graphing. Round to the nearest hundredth. (1 point)
2.91
3.92
1.31
0.97,
Answers
3. 1.31
2. 10^(6x) = 93
For this problem, using a calculator makes it quite simple. What you want is the power that you can raise 10 to that gives you 93. That value is the logarithm of 93 to base 10. So
10^(6x) = 93
log(10^(6x)) = log(93)
6x = 1.968482949
x = 0.328080491
x = 0.3281
3. This problem is both trickier and easier than the previous. All you need to do is plot the function on your calculator and look for the answer that's nearest which is 1.31, you could also get a more precise answer by calculating the logarithm to base 5.5 of 805. You won't find such a logarithm function on your calculator, but that isn't a major problem since you can easily convert a logarithm from any base to any other base by simply dividing by the logarithm of the desired base. So:
5.5^(3x) = 805
log(5.5^(3x)) = log(805)
log(5.5^(3x))/log(5.5) = log(805)/log(5.5)
log to base 5.5 of 5.5^(3x) = log(805)/log(5.5)
3x = 2.90579588/0.740362689
3x = 3.92482755
x = 1.30827585
x = 1.31
1. B
2. D
3. C
4. A
5. B
ESKETIT
how would you do this problem
Answers
so you would set up the problem to find x as:
5x-19=2x+14
+19 +19
____________
5x=2x+33
-2 -2
_____________
3/3x=33/3
____________
x=11
Just pug in x to the equations to solve the rest
Simplify: 8x + 4 - 5
Answers
8x + 4 - 5
8x - 1
Calculate the sum or difference.
Keep the sign of the number with the larger absolute value and subtract the smaller absolute value from the larger.
- ( 5 - 4 )
Subtract the numbers.
-1
8x - 1
The formula v =sqrt 64h can be used to find the velocity, v, in feet per second, of an object that has fallen h feet. Find the velocity of an object that has fallen 75 feet. Round to the nearest tenth.,
Answers
Think it’s b not sure though
Answers
A1 = 30.25pi cm ^ 2
We now look for the area of the triangle, which by definition is:
A2 = (1/2) * (b) * (h)
Where,
b: base
h: height
Substituting the values:
A2 = (1/2) * (11) * (11)
A2 = 60.5 cm ^ 2
The area of the shaded region will be given by the subtraction of both areas:
A1-A2 = (30.25pi - 60.5) cm ^ 2
Answer:
A1-A2 = (30.25pi - 60.5) cm ^ 2
option 3
Simplify each expression. Use positive exponents.
m^3 n^-6 p^0
Answers
1/n^6 is the second one
1 is the third answer
The following sequence is an arithmetic sequence what comes next ? 7,___,17
Answers
Since this is an arithmetic sequence, you can conclude that the addition to the number is constant.
Let x = the number asked
k = constant number added to the sequence
7 + k = x
x + k = 17
Solve the system of equation:
7 + k + k = 17
7 + 2k = 17
2k = 10
k = 5
Therefore, the missing number is 12 (7 + 5).