Answer:
f(x) = ³/₁₆ (x - 4)² + 7Step-by-step explanation:
The vertex form of the equation of the parabola with vertex (h, k) is:
f(x) = a(x - h)² + k
so the equation of parabola with the vertex (4, 7) is
f(x) = a(x - 4)² + 7
passes through the point (0, 10) means if x=0 then f(x)=10
10 = a(0 - 4)² + 7
10 -7 = a(-4)² + 7 -7
3 = 16a
a = ³/₁₆
Therefore the equation of parabla is:
f(x) = ³/₁₆ (x - 4)² + 7
The value of a boat if depreciating at at a rate of 9% per year. In 2006 the boat was worth $17,800. Find the worth of the boat in 2013.
Answer:
The worth of boat in 2013 will be $9202.6
Step-by-step explanation:
Rate of depreciation = 9% = 0.09
Cost of Boat in 2006 =$ 17,800
Cost of Boat in 2013 = ?
Years = 2013-2006= 7 years
The formula used is: [tex]\mathbf{A=P(1+r)^{t}}[/tex]
Since the value of boat is depreciating the value of r will be r=-0.09
Here P = 17,800 , r=-0.09 and t = 7 years Finding A
[tex]A=P(1+r)^{t}\\A=17,800(1+(-0.09))^7\\A=17,800(0.91)^7\\A=17,800(0.517)\\A=9202.6[/tex]
So, the worth of boat in 2013 will be $9202.6
<
6/11
What is the equation of the line that passes through point (4. 12) and has a y-intercept
of - 2?
Answer:
7x - 2y - 4 = 0
Step-by-step explanation:
from the perpendicular equation formula,
y/a + x/b = 1
x1 = 4
y1 = 12
a = -2
b= ?
Inserting the values into the above formula,
12/-2 + 4/b = 1
-6 + 4/b = 1
4/b = 7
b = 4/7
putting a and b into the original formula,
y/-2 + x/(4/7) = 1
-y/2 + 7x/4 = 1 (×4)
-2y + 7x = 4
7x - 2y - 4 = 0
Therefore, the equation of the line is;
7x - 2y - 4 = 0
Find unit rate for 14 for 2.99
Answer: Okay so let's try to find the amount of money needed to buy 1 lb. Therefore, let's divide the fraction by 14.
Then we'll divide both the numerator and denominator by 14.
÷
Then we simplify and get:
14÷14=1 2.99÷14=.2135 We can round that to .21
The unit rate for each pound would be 1:.21
I don't know if that helped, but yeah. :)
Step-by-step explanation:
A small pool is being drained. There are 1,320 gallons of water remaining in the pool after 2 minutes and 1,040 gallons after 9 minutes.
Answer:
Answer: 35 minutes
Step-by-step explanation:
Step-by-step explanation:
For us to solve the question, we have to calculate the amount of gallons of water that is drained every minute. This will be:
= (1320 - 1040) / (9 - 2)
= 280/7
= 40 gallons per minute
Since we are told that 1,320 gallons of water remain in the pool after 2 minutes. This means that the total water in the pool at the beginning was:
= 1320 gallons + (40 × 2)
= 1320 gallons + 80 gallons
= 1400 gallons
The time taken for the pool to be completely drained will be:
= Total water in pool / Gallons drained per minute
= 1400 / 40
= 35 minutes
Answer:
35 minutes
Step-by-step explanation:
There are 40 gallons drained per minute.
2xy +3y²-6y factor the following expression
Answer:
y(2x+3y-6)
Step-by-step explanation:
2xy+ [tex]3y^{2}[/tex]-6y
Find the H.C.F
2xy= 2×x×y
3y²= 3×y×y
6y= 6×y
H.C.F= y
2xy÷y+ 3y²÷y- 6y÷y
= 2x+ 3y- 6
= y( 2x+ 3y-6)
Solve the inequality.
-1 <-4+ d
A d>3
B d>-3
C d<-3
D d<3
Answer:
A
Step-by-step explanation:
We add 4 on both sides
-1 + 4 < -4 + 4 + d
= 3 < d
Flip it and we get d > 3
The answer is A
what's the simplified expression?
Answer:
6x⁴ + 20x³ - 30x² + 4
Step-by-step explanation:
Collect the like terms
6x⁴ + 18x³ + 2x³ - 36x² + 6x² + 12x - 12x + 4
SImplify expression
6x⁴ + 20x³ - 30x² + 4
Answer:
6x⁴- 18x³-4
i think
Step-by-step explanation:
How many games did he win? Help
30 POINTS!! PLEASE HELP ME! THANK YOU SO MUCH!!
show all steps to solve these problems in the photos
Step-by-step explanation:
Ok so i looked on an app i hope helps(Im not really sure if this is correct)I hope you get it soon!
Please help!!
if you can explain if not that is fine.
Answer:
The graph of y > 3x − 4 has shading above a dashed line. The graphs of the inequalities will intersect.
To celebrate the first day of spring, Lin is putting stickers on some of the 100 lockers along one side of her middle school's hallway. She puts a skateboard sticker on every 4th locker (starting with locker 4), and a kite sticker on every 5th locker (starting with locker 5). Name three lockers that will get both stickers. After Lin makes her way down the hall, will the 30th locker have no stickers, 1 sticker, or 2 stickers? Explain how you know.
Answer:
The 30th sticker will have a sticker. The sticker will be 1 sticker (Kite Sticker) which will be put on the locker by Lin. This is because, following the arithematic progression of the sticker placement:
Locker 5 = Kite sticker
locker 10 = Kite sticker
Locker 15 = Kite sticker
.
.
Locker 30 = Kite sticker
It could be seen that at locker 30, the sticker to be placed by Lin will be Kite sticker
Step-by-step explanation:
A city has an elevation of -752 feet. Which statement describes the city's elevation?
O-752 above sea level
O-752 below sea level
O 752 above sea level
O 752 below sea level
Answer:
The answer is C my good sir
Step-by-step explanation:
An exponential relationship is modeled by y = 31(0.81)x , what is the percent rate of change for this function?
Answer:
19%
Step-by-step explanation:
An exponential relationship is modeled by y = 31(0.81)^x , what is the percent rate of change for this function?
From the above exponential relationship given, we can see that this exponential relationship is an exponential decrease.
Where the formula:
y = a(1 - r)^t
Where a = Initial amount
r = rate of change in percent
t = time in years
y = a(1 - r)^x = y = 31(0.81)^x
1 - r = 0.81
r = 1 - 0.81
r = 0.19
Converting 0.19 × 100
= 19%
When factored completely, which is a factor of 3x3 − 9x2 − 12x?
A.
(x − 3)
B.
(x − 4)
C.
(3x − 1)
D.
(3x − 4)
Answer: I believe it’s D
Step-by-step explanation:
Shiloh and her friends spent the day at an amusement park. In the first hour, they rode two rides. After 2 hours, they had ridden 4 rides. They had ridden 6 rides after 3 hours.
Write a function to represent the arithmetic sequence.
f(n)=
Answer:
The function will be: f(n) = 2n
Step-by-step explanation:
An arithmetic sequence is a sequence where the common difference between consecutive terms is same
The sequence according to given information is:
2,4,6...
Here
a_1 = 2
a_2 = 4
a_3 = 6
the common difference will be:
[tex]d = a_2-a_1 = 4-2 = 2\\d = a_3-a_2 = 6-4 = 2[/tex]
The arithmetic sequence is given by:
[tex]a_n = a_1+(n-1)d[/tex]
Putting the values
[tex]a_n = 2+(n-1)(2)\\a_n = 2+2n-2\\a_n = 2n[/tex]
Hence,
The function will be: f(n) = 2n
Put the following equation of a line into slope-intercept form,
simplifying all fractions.
8x + 2y = -10
Answer:
y=-4x-5
Step-by-step explanation:
Subtract 8x from both sides to get the y variable alone. Then divide both sides by 2 and get y=-4x-5.
Answer:
y=−4x−5 because the guy on top of me said so
Step-by-step explanation:
20 Points
Can anyone help me with these Geometry questions? Will give Brainliest.
Answer:
give brain list first
Step-by-step explanation:
a student is painting a room at a constant rate she is able to paint 2/5 of the room in 1/2 of an hour how long does it take to paint the whole room
Answer:
She is able to paint 2/5's of the room in 1/2 hour. How long does it take to paint the whole room? = 7.5 minutes. Hence, it will take 5*7.5 = 37.5 minutes to paint the entire room.
Answer:
1 1/4 Hours
Step-by-step explanation:
2/5+2/5=4/5
4/5=1 hour
1/2/1/2=1/4
1/5 room in 1/4 hour
1+1/4=1 1/4 hours
Hello :) um Im just trying to learn this question- "Select the division equation that can be used to find the solution to the problem. 4/9 kilogram of baking soda costs $2. How much does 1 kilogram of baking soda cost?"
2 ÷ 4/9= ?
4/9 ÷ 2= ?
2 ÷ 1/9= ?
2 ÷ 2/9= ?
=========================================================
Explanation:
We're told that 4/9 kg of baking soda costs $2
We can form the equation
4/9 kg = 2 dollars
We want to know the cost of 1 kg of baking soda, so we'll need to divide both sides by 4/9 to turn the "4/9 kg" into "1 kg"
Therefore,
4/9 kg = 2 dollars
turns into
1 kg = (2 ÷ 4/9) dollars
We could simplify further, but your teacher has decided not to.
Which of the following expressions is this one equivalent to?
2x? - 15x² + 17x+3
X – 5
x?- 2x+5+
O A.
+2
7
x - 5
2x² - 5x-8 - 37
B.
X-5
2x2 – 25x – 108 - 321
X - 5
D.
2x – 5 –
3
X-5
Answer:
it is D
Step-by-step explanation:
What is an expression for 2 over 3 (4x +9).
Answer:
Step-by-step explanation:
2 / 3 ( 4x + 9 )
Distributive property
2 / 12x + 27
plz help!!
ALEKS math
Answer:
31
Step-by-step explanation:
10-3= 7 so 3+7=10 and 10+7=17 and you just do this to find the answer
PLEASE HELP:( thank youuuu!!
Answer:
A
Sorry I just have to right more to turn it in but good luck with your math work.
The area of a square is 1,521 cm2. Find the length of a side of the square by
prime factorisation method.
Answer:
Isn't it simpler just to take the square root of 1,521?
It's 39
Step-by-step explanation:
Madeline solved the inequality 3x + 7 ≤ 8x - 3 and her solution is x = 2.
Madeline is incorrect. Explain why she is incorrect. *
Answer:
In her answer she has an equality, x=2. Emphasis on equal. However, in the original inequality it's not a equal sign. x=2 is true, just not the complete the answer.
Answer should be x is greater than or equal to 2.
Hopefully that makes sense.
On a sunny day, a 4-foot red kangaroo casts a shadow that is 5 feet long. The shadow of a nearby
eucalyptus tree is 20 feet long. Find the height of the tree?
Answer:
16 feet
Step-by-step explanation:
Set up a proportion where x is the height of the tree:
[tex]\frac{4}{5}[/tex] = [tex]\frac{x}{20}[/tex]
Cross multiply and solve for x:
5x = 80
x = 16
So, the tree is 16 feet tall
Please help I am being timed!
Solve
7k – 8 = 28 + 24k
A. -2 2/17
B. -2
C. -1 5/31
D. 1 3/17
Sorry if this is easy I'm bad at math
Find the length of each side of the triangle determined by the three points P1,P2,P 1,P 2, and P3. P3 State whether the triangle is an isosceles triangle, a right triangle, neither of these, or both. (An isosceles triangle is one in which at least two of the sides are of equal length.) P1=(−1,4);P2=(6,2);P3=(4,−5)P 1=(−1,4);P 2=(6,2);P 3 =(4,−5).
Answer:
IT IS BOTH
Step-by-step explanation:
Given the coordinate of the triangle, P1P2P3, we are to classify the triangle. To do that we need to know the length of each side of the triangle
P1P2, P2P3 and P1P2 using the formula for calculating distance between two coordinates
D = √(x2-x1)²+(y2-y1)²
For P1P2;
P1=(−1,4) P2=(6,2)
P1P2 = √(6-(-1))²+(2-4)²
P1P2 = √7²+2²
P1P2 = √53
For P1P3;
P1=(−1,4) P3=(4,-5)
P1P3 = √(4-(-1))²+(-5-4)²
P1P3 = √5²+9²
P1P3 = √25+81
P1P3 = √106
For P2P3;
P2=(6,2) P3 = (4,-5)
P2P3= √(4-6)²+(-5-2)²
P2P3 = √2²+7²
P2P3 = √53
Since two sides of the triangles are the same, this means that it is an isosceles triangle.
Let's check whether it is right angled by applying Pythagoras theorem
(√53)²+(√53)² = x²
x is the longest side (hypotenuse)
53+53 = x²
106 = x²
x = √106
Since the square of the hypotenuse is equal to the sum of the sum of the square of other two sides, then it is also a RIGHT ANGLED TRIANGLE
The triangles in the picture are congruent by which method
Zion walked 1.7 miles in 1 hour. If he walks at the same rate, how far will he walk in 1.5 hours? Use partial products to find the answer.
Answer:
1 hour = 1.7 miles / 1.5 hours = ? Miles
1.7 × 0.5 = 0.85 + 1.7 = 2.55 Miles
Step-by-step explanation:
1.7 × 0.5 = 0.85 + 1.7 = 2.55 Miles