Answer:
[tex]\huge\boxed{\text{Axis of Symmetry: } y = 2}[/tex]
[tex]\huge\boxed{\text{Vertex: } (-3, 2)}[/tex]
The parabola opens to the right (horizontally)Step-by-step explanation:
We need to note a few basic rules about focuses and directrix’s of a parabola.
1. The directrix never touches the parabola, however it is perpendicular to the axis of symmetry
2. The focus never touches the parabola, however it lies on the axis of symmetry of the parabola
3. The directrix is always the same distance away from the vertex as the focus
If we know that the focus of the parabola is (0, 2) and the directrix lies on x=-6. that means these points are 6 units apart as we can assume the line x = -6 crosses the point (-6, 2), making these points 6 units apart (since |-6 - 0| = 6)
These are 6 points apart horizontally, via the x-axis, meaning that this is a horizontally facing parabola, and it opens to the right. We know it can’t open to the left because then the directrix (x = -6) would touch the parabola and then it wouldn’t be a directrix!
The vertex of the parabola will be the same distance away from the focus and the directrix. Since these are 6 units apart, that means the focus will lie [tex]6 \div 2 = 3[/tex] units away from either one.
Halfway between 0 and -6 is -3, so we know the vertex lies on x-coordinate -3. We also know that the focus is on y-value 2, meaning that the vertex will also be on y = 2, since the focus is always on the axis of symmetry.
So our vertex is at [tex](-3, 2)[/tex].
We know that this is a horizontally facing parabola, meaning that our axis of symmetry is going to lay on a y coordinate. The axis of symmetry always contains the vertex, so that means that we can just take the y value of the vertex and use that as the axis of symmetry. The vertex lies at y value 2, meaning that the axis of symmetry is [tex]y=2[/tex]
In conclusion
The vertex is at [tex](-3, 2)[/tex] The axis of symmetry is at [tex]y=2[/tex] The parabola opens to the right (horizontally)Hope this helped!
A tutor work with 3 students. The oldest student is 6 years oldder then the middle student, and the youngest student is 3 years younger than the middle student. The sum of the ages of the students is 30. How many years old is the youngest student
Answer:
9 years old.
Step-by-step explanation:
Since the ages of all of these students are being represented in relation to the middle student's age then we can create formulas for each student and then apply them to the formula for the sum of their ages and solve for the middle child's age (M) like so... (oldest child's age is represented by variable O and youngest child's age is represented by variable Y)
O = M + 6
Y = M - 3
30 = (M+6) + M + (M-3) ... combine like terms
30 = 3M + 3 ... subtract 3 from both sides
27 = 3M ... divide both sides by 3
9 = M
Now we know that the middle child is 9 years old.
help no good at maths
If –y + 2x^2 – x = -5y^3 then find dy / dx in terms of x and y.
Answer:
dy/dx = [tex]\frac{4x-1}{1-15y^{2} }[/tex]
Step-by-step explanation:
-y + 2x²- x = -5y³
2x² - x = y - 5y³
4x - 1 = dy/dx - 15y².dy/dx
dy/dx(1 - 15y²) = 4x - 1
dy/dx = [tex]\frac{4x-1}{1-15y^{2} }[/tex]
What is the absolute value of -250?
Answer:
250
Step-by-step explanation:
Pretty much every time it asks for the abasloute value it just asks how much to get the zero on the number line. It will ALWAYS be positive. For example -5 will be 5 to get to zero on the numberline. Same thing with a positive 5.
Charlie graphs the equation y= –12x+2 .
Select all statements about Charlie's graph that are true.
The graph is a straight line.
The line does not pass through the origin.
The line passes through the point (0, –2) .
The slope of the line is 12 .
The y-intercept of the line is 2.
Answer:
The graph is a straight line.
The line does not pass through the origin.
The y-intercept of the line is 2.
Step-by-step explanation:
I know that it's a straight line because the equation is written in this format; y=mx+b (this is a linear equation meaning that it must be a straight line). In that equation, m is our slope and b is our y-intercept with this information. I know that the y-intercept is 2 since this equation is this y= –12x+2 (the 2 replaced the b which is our y-intercept). The line does not pass through the origin because its y-intercept is 2 which means it's impossible for the line to pass through the origin. (I hope this makes sense)
Hope this helped you
a spinner with 10 equally sized slices has 2 red slices, 4 blue slices, and yellow slices. The dial is spun and stops on a slice at random. What is the probability that the dial stops on a red slice.
(Write your answer as a fraction in simplest form).
Since there are 10 total slices and 2 are red the probability of the dial stopping on a red slice is 2/10. But in simplest form 1/5.
The probability that the dial stops on a red slice is 1/5 or 20%.
What is Probability?The ratio of good outcomes to all possible outcomes of an event is known as the probability. The number of positive results for an experiment with 'n' outcomes can be represented by the symbol x. The probability of an occurrence may be calculated using the following formula.
Probability(Event) = Positive Results/Total Results = x/n
In order to better grasp probability, let's look at a straightforward example. Let's say we need to forecast if it will rain or not. Either "Yes" or "No" is the appropriate response to this query.
Given:
number of total slices = 10
Red slices = 2
Blue slices= 4
Yellow slices= 10- 6 = 4
Now, probability that the dial stops on a red slice
=2/10
=1/5
=1/5 x 100
=20%
Hence, the probability that the dial stops on a red slice is 1/5 or 20%..
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Need help will mark brainliest
Answer:
x=18
Step-by-step explanation:
Add up all the angles and then equal them to 180
6x+3x+x=180 Simplify!
10x=180
x=18
WILL MARK BRAINLEST, PLEASE HELP !!!
Answer:
rate of change = first derivative= g'(x)=-2x+6
plug -3 to 5 into that g'(x) equation, it will be your answer
Step-by-step explanation:
9514 1404 393
Answer:
4
Step-by-step explanation:
The average rate of change of f(x) on the interval [a, b] is computed from ...
m = (f(b) -f(a))/(b -a)
On the interval [-3, 5] the average rate of change is ...
m = (f(5) -f(3))/(5 -(-3)) = ((-5^2 +6·5 +12) -(-(-3)^2 +6(-3) +12))/8
= (-25 +30 +12 +9 +18 -12)/8 = 32/8
m = 4
The average rate of change on the interval is 4.
__
Alternate solution
The first derivative of the function is ...
f'(x) = -2x +6
The average rate of change of a parabolic function on an interval is the rated of change at the midpoint of the interval. Here, the midpoint is x=(5+(-3))/2 = 1, so the average rate of change is ...
f'(1) = -2(1) +6 = 4
3. Formulate 900 lbs of a 35% CP ration using Soybean Meal (46% CP) and Oats (12% CP). How many pounds of soybean meal will be used? How many pounds of oats will be used?
Answer:
The amount of Soyabean = 608.82 pounds.
The amount of Oats = 900-608.82 = 291.18 pounds.
Step-by-step explanation:
Given that the Soybean Meal has 46% CP and Oats has 12% CP.
The total amount of ration is 900 lbs of 35% CP.
Let x pounds of Soyabean has been used, so,
the amount of Oats = 900-x lbs.
The CP amount in 900 lbs mixture will be equal to the sum of CP amounts in x lbs Soyabean and 900-x lbs Oats, i.e
35% of 900 = 46% of x + 12% of (900-x)
[tex]\Rightarrow \frac{35}{100}\times 900=\frac{46}{100}\times x+\frac{12}{100}\times (900-x)[/tex]
[tex]\Rightarrow 35\times 900 = 46x + 12\times 900 - 12 x[/tex]
[tex]\Rightarrow 34x= 900(35-12)[/tex]
[tex]\Rightarrow x = (900\times 23)/34[/tex]
[tex]\Rightarrow x = 608.82[/tex] lbs.
So, the amount of Soyabean = 608.82 pounds.
The amount of Oats = 900-608.82 = 291.18 pounds.
find x (11x-1) (20x-3) 151
Answer:
x=5 I think
Step-by-step explanation:
just search it up online
What value of x makes the equation true?
6x+8=3x-19
A. x = 3
B. x = -3
C. x = -9
D. x = -11/3
Correct answer will get brainiest!
Answer:
C
Step-by-step explanation:
Given
6x + 8 = 3x - 19 ( subtract 3x from both sides )
3x + 8 = - 19 ( subtract 8 from both sides )
3x = - 27 ( divide both sides by 3 )
x = - 9 → C
Graham has enough fencing to enclose a rectangular garden with a perimeter of 140 feet. If the width of his garden is 20 feet less than the length, what is the width of the garden?
Answer:
Width = 25 feet
Step-by-step explanation:
Perimeter of a rectangle = 2L + 2W
W = L - 20
P = 140
Hence,
140 = 2L + 2(L - 20)
140 = 2L + 2L - 40
Collect like terms
140 + 40 = 4L
180 = 4L
L = 180/40
L = 45 feet
Length = 45 feet
Width = L - 20 feet
=( 45 - 20) feet
= 25 feet
If a = -9 and b = 4, what is the value of a + b ?
A. -5
B. 5
C. -13
D. 13
Answer:
A. -5
Step-by-step explanation:
-9 + 4 = -5
hope this helps
Nathan writes an essay with a total of 583 words. Every line of his essay has 11 words.
How many lines long is Nathan's essay?
Answer:
53 lines
Step-by-step explanation:
You would divide 583 by 11, and that would get you your final answer of 53 lines.
Answer:
53 lines
Step-by-step explanation:
11 words → 1 line
583 words → (1/11 x 583) lines = 53 lines
can someone convert that to point slope form and tell me the steps?
Sumiko and Jandella ran the bleachers together today at Poly High School. Sumiko runs these same bleachers every 6 days and Jandella runs them every 16 days. The soonest they will see each other again is in days.
Answer:
48 days
Step-by-step explanation:
Given that :
Sumiko runs bleachers every 6 days
Jandella runs bleachera every 16 days
The soonest they will see each other again is in days can be obtained by getting the lowest common multiple of 6 and 16
Multiples of
6 : 6, 12, 18, 24, 30, 36, 42, 48, 54,...
16 : 16, 32, 48, 64,...
Lowest common multiple of 6 and 16 = 48
Hence, the soonest they'll see each other again is in 48 days
Please answer these questions for 8th Grade Algebra! First-person to answer will be marked as brainiest! Worth lots of points!
1. x<=20
2. k<0
3. d<-3
4. m<=11
5. a>=3
6. 6<-5
This should help
A new one-year membership at RecPlex costs $160. A registration fee of $28 is paid up front, and the rest is paid monthly. How much do new members pay each month? Write an equation for this..
Answer:
The first month new members have to pay 188 dollars for the membership.
The equation is 160x+28=y
x stands for the number of months and y stands for the total cost.
For the first month (membership starts) the total cost is 188$. For the second month the total money paid would be 348$. For the third month the total money paid would be 508$. And so on you can use the equation to solve for more months. Just substitute x for the number of months you are solving for.
can you writ the answe in a sheet on paper
Step-by-step explanation:
Make t the subject of the formula (5÷ t) -2 = s
__________________________________________________________
all the questions is on my page there is more 4
Joe had a balance of $34 on his credit card. He bought a sandwich and charged $40 on his credit card. 1a.) Write an equation that represents this scenario.
Answer:
Kindly check explanation
Step-by-step explanation:
Given that:
Credit card balance = $34
Amount of sandwich purchased = $40
The cost of sandwich purchased us added to the Initial credit card balance as the balance in a credit card is amount owed.
Hence it could be interpreted as though Joe has made purchases which amounts to $34 with his card before purchasing sandwich that costs $40
Hence; new card balance :
(Intial card balance + cost of sandwich)
$34 + $40 = $74
Guys plz help me answer this question!!!
Awnser:
1/2 as m, and -3 as b
Step-by-step explanation:
To find the equation of any line, you use the formula: mx+b=y, where m is the slope, y is the y coordinate, b is the y intercept, and x is the x coordinate. However, it only asks for b and m.
You'll need to first find 2 points.
I chose: (6,0) and (0,-3).
The formula to find the slope is: y2-y1/x2-x1.
0-(-3)/6-0
0+3/6
3/6
1/2
Now we need to find the y intercept. However, the graph already tells you what it is. The y intercept always has to have 0 as x.
So the awnser is 1/2 as m, and -3 as b.
If 4(r + 2) – 13 = 11, what is the value of r?
What is 2/5 + + 2/5 + 2/5
(2/5 times 3)
Ty
Answer:
6/5 or 1 1/5
Step-by-step explanation:
2/5 + 2/5 + 2/5 = 6/5 or 1 1/5
This is the same as multiplying 3 x 2/5 = 6/5 or 1 1/5
Answer:
6/5 or 1 1/5
Step-by-step explanation:
2/5 + 2/5 + 2/5 = 6/5 or 1 1/5
This is the same as multiplying 3 x 2/5 = 6/5 or 1 1/5
Step-by-step explanation:
Mai earns $7 per hour mowing her neighbors' lawns. She also earned $14 for hauling away bags of recyclables for some neighbors.
Answer:
Step-by-step explanation:
7x + 14 = 8.4x
14 = 1.4x
x = 10 hours
Each works 10 hours. Their total is 84 dollars each.
Mr. Johnson has a piece of pipe 5 1/3 feet long. He decides to cut it into 3 equal pieces to use in making a railing for his porch. How long should he cut each piece?
HURRY!!! WILL GIVE ALOT OF POINT AND BRAINLIEST
Answer:
1.78
Step-by-step explanation:
7 is repeating but i rounded to the tenths its this. also, i just divided it by three because he cuts into three parts.
PLZZ HELP!!!!
1. Find the value of x and y.
2. In an A-figure house, the two congruent sides extend from the ground to form a 34° angle at the peek. What angle does each side form with the ground?
Problem 4
Note the markings at the top indicate that angle y represents half the angle BAC. In other words, we need 2 copies of angle y to make up angle BAC.
So we know that angle BAC = 2y
Due to the fact that triangle ABC is isosceles, we know that base angles B and C are congruent to 47.
Focusing on triangle ABC we have
A = 2yB = 47C = 47So,
A+B+C = 180 .... for any triangle, the angles always add to 180
2y+47+47 = 180
2y+94 = 180
2y = 180-94
2y = 86
y = 86/2
y = 43
Turn your attention to triangle ABD.
Here we have
angle A = y = 43angle B = 47angle D = xWe'll use the same idea as above, that all angles add to 180, to get...
A+B+D = 180
y+47+x = 180
43+47+x = 180
x+90 = 180
x = 180-90
x = 90
Answer: D) x = 90, y = 43===================================================
Problem 5
Let x be the angle formed by the diagonal sides and the horizontal ground. This is considered the base angle because this triangle is isosceles.
We have two base angles x and the third angle up top is 34
x+x+34 = 180
2x+34 = 180
2x = 180-34
2x = 146
x = 146/2
x = 73
Answer: C) 73Perform the indicated operation 9 15/22 -3 2/11
Answer:
6 1/2
Step-by-step explanation:
Answer:6 1/2
Step-by-step explanation: do the math search it up
Shopping spree. Greg is shopping in a large urban depart-
ment store with many floors. He enters the store on the
middle floor from a skyway, and he goes directly to the
credit department. After making sure his credit is good, he
goes up three floors to the housewares department. Then
he goes down five floors to the sporting goods department.
Next, he goes up six floors to the media department. Finally,
he
goes
down ten floors to the main entrance to the store on
the first floor at ground level and leaves to go to another store.
How many floors does this department store have if it has no
basement?
Answer:
12 floors
Step-by-step explanation:
middle +3 floors= +3 .
+3 - 5 = -2.
-2 + 6= +4.
+4 - 10 = 6 x 2 = answer 12
to clarify the plus or minus mean how many floors he is above or below the middle floor
What is the equation of the exponential function that passes through (0,10) and (3,80) ?
A. y= 80(20)^x
B. y=10(2)^2
C. y=2x+10
D. y=3x+8
Answer: B
Step-by-step explanation:
a pickup truck travels 45 Mi on 2 and 1/3 gallons of gas how far did it travel on 1 gallon of gas
The pickup truck travels 19[tex]\frac{2}{7}[/tex] Miles in gallon.
What is Unit rate?A unit rate means a rate for one of something.
Given that a pickup truck travels 45 miles on 2[tex]\frac{1}{3}[/tex] gallons of gas,
Since there are 45 miles in 7/3 gallons
So, 45*3/7 in one gallon = 19[tex]\frac{2}{7}[/tex] Miles in one gallon
Hence, The pickup truck travels 19[tex]\frac{2}{7}[/tex] Miles in gallon.
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Find the rate of change
(Pls help!)
Answer: 11.5
Step-by-step explanation:
It’s delta y over delta x so you would take any two combination of coordinates and subtract and divide. I used 57.50-23 over 5-2... this gets you 34.5 over 3. This is also equal to 11.5 :)