Answer:
F(x) = 3·x² vertex (0, 0) axis x = 0 x-int (0, 0) y-int (0, 0) min minimum value (0, 0) domain (x ∈ R) range (f(x) ∈ R+)
Step-by-step explanation:
The given function is f(x) = 3·x²
The given parabola in vertex form y = a(x - h)² + k
Where;
(h, k) = The vertex
By comparison, we have;
h = 0
k - 0
Therefore;
1) The vertex = (0, 0)
2) The axis of symmetry = The line x = 0
3) The x-intercept = The vertex = (0, 0)
4) The y-intercept = The vertex = (0, 0)
5) The minimum value = The vertex = (0, 0)
6) The domain = All real numbers (x ∈ R)
7) The range = All positive real numbers including 0 (f(x) ∈ R+)
A young couple purchases their first new home in 2011 for $95,000. They sell it to move into a bigger home in 2018 for $105,000. First, we will develop an exponential model for the value of the home. The model will have the form
Given:
The value of home in 2011 is $95,000.
The value of home in 2018 is $105,000.
To find:
The exponential model for the value of the home.
Solution:
The general exponential model is
[tex]y=ab^x[/tex] ...(i)
where, a is initial value and b is growth factor.
Let 2011 is initial year and x be the number of years after 2011.
So, initial value of home is 95,000, i.e., a=95,000.
Put a=95000 in (i).
[tex]y=95000b^x[/tex] ...(ii)
The value of home in 2018 is $105,000. It means the value of y is 105000 at x=7.
[tex]105000=95000b^7[/tex]
[tex]\dfrac{105000}{95000}=b^7[/tex]
[tex]\dfrac{21}{19}=b^7[/tex]
Taking 7th root on both sides, we get
[tex]\left(\dfrac{21}{19}\right)^{\frac{1}{7}}=b[/tex]
Put [tex]b=\left(\dfrac{21}{19}\right)^{\frac{1}{7}}[/tex] in (ii).
[tex]y=95000\left(\left(\dfrac{21}{19}\right)^{\frac{1}{7}}\right)^x[/tex]
[tex]y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}[/tex]
Therefore, the required exponential model for the value of home is [tex]y=95000\left(\dfrac{21}{19}\right)^{\frac{x}{7}}[/tex], where x is the number of years after 2011.
The equation of the graphed line is x+2y=5. What is the x-intercept of the graph?
Answer:the x intercept is 5
Step-by-step explanation:
I bet I will mark you as a brainiest if u get this right
To make porridge, Goldilocks mixes together 3 bags of oats with 1 bag containing 20% wheat bran and 80% oats. All the bags have the same volume. What percentage of the volume of Goldilocks' porridge mixture is wheat bran?
5%
6%
20%
26%
60%
15%
8%
Answer:
6%
Step-by-step explanation:
This is an honest guess just because you are not given the content of 2 out of the 3 bags. When starting at 100 percent of the makeup of the porridge you can then divide that by 3 to get the content of 1 bag. You will get around 33 then you find what 20% of 33 is which is closest to either 6 percent.
given the equation 9x+3Y=7 which equation is perpendicular to an equation with a y intercept of 12
I love you. You are worth it.
Answer:
Thanks
Step-by-step explanation:
what is the answer to 66x10?
Answer:
660
Step-by-step explanation:
66x10
=660.
So the answer is 660
John completed 24 math problems in 6 minutes. How many does he complete per minute
Answer:
it would take him a minute to complete 4 problems
Answer:
4 problems per minute.
Step-by-step explanation:
Divide 24 by 6 and you would get 4.
Check: 6 x 4 = 24
6, 12, 18, 24
Hope this helps!
~Jerc~
Oak Street intersects with Mill Avenue. The traffic light on Oak Street follows a cycle. It is green for 35 seconds, yellow for 5 seconds, and red for 20 seconds. As you travel along Oak and approach the intersection, what is the probability that the first color you see is red? Write the probability as a simplified fraction. Incorrect feedback has been removed from the screen. Fill in the blank text field 1
Answer:
1/3
Step-by-step explanation:
20/60 simplified is 1/3
20 for the red light
60 all of them added
Question 2 (1 point)
(03.01 LC)
What is the length of leg y of the right triangle? (1 point)
a- 2
b- 8
c- 12
d- 35
Answer:
my guys its 12 so its c
Step-by-step explanation:
i did the test
Answer:
12
Step-by-step explanation:
what does -4(2x+9) equal
Answer:
-8x-36
Step-by-step explanation:
-4(2x+9)
distribute: -4(2x+9)= -8x-36
Find A. Round to the nearest tenth:
Answer:
24.0
SinA = sinB
a b
Sin150 = Sin12
a 10
cross multiplication:
Sin(150) x 10
Sin(12)
5
sin 12 = 24.0
I hope I got it correct
Answer:
Step-by-step explanation:
[tex]\frac{10}{sn12}[/tex] = [tex]\frac{a}{sin150}[/tex]
a = [tex]\frac{10sin150}{sin12}[/tex] ≈ 24.0
The current exchange rate for the mexican peso to the us dollar is 3 to.if a tourist dinner bill was 15 pesos,what is the amount in the us dollar
Answer:
5
Step-by-step explanation:
3x=15
x=15/3
x=5
there are 12 inches in a foot how many square inches are in 1 1/2 feet
Answer:
144.
The reason is because 1 ft = 12 in, (1 ft)2 = (12 in)2 = 144 in2.
13-715x=130x
show work plzz
Answer:
Solving equation [tex]13-715x=130x[/tex] we get [tex]x= \frac{1}{65}[/tex]
Step-by-step explanation:
We need to solve the equation [tex]13-715x=130x[/tex]
Combining like terms and solving
[tex]13-715x=130x\\Adding \ 715x \ on \ both \ sides:\\13-715x+715x=130x+715x\\13=845x\\Divide \ both \ sides \ by \ 845\\\frac{13}{845}=\frac{845x}{845}\\=>x= \frac{1}{65}[/tex]
So, solving equation [tex]13-715x=130x[/tex] we get [tex]x= \frac{1}{65}[/tex]
Solve the equation. If exact roots cannot be found, state the consecutive integers between which the roots are located.
x = -3 and 1
x = -2
No real roots.
x = 3 and -1
Answer:
No real roots.
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDASAlgebra I
Standard Form: ax² + bx + c = 0Quadratic Formula: [tex]x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]Algebra II
Imaginary Roots: √-1 = iStep-by-step explanation:
Step 1: Define
-3x² + 2x = 1
Step 2: Rewrite in Standard Form
Subtract 1 on both sides: -3x² + 2x - 1 = 0Step 3: Define
a = -3
b = 2
c = -1
Step 4: Find roots
Substitute in variables: [tex]x=\frac{-2\pm\sqrt{2^2-4(-3)(-1)} }{2(-3)}[/tex]Exponents: [tex]x=\frac{-2\pm\sqrt{4-4(-3)(-1)} }{2(-3)}[/tex]Multiply: [tex]x=\frac{-2\pm\sqrt{4-12} }{-6}[/tex]Subtract: [tex]x=\frac{-2\pm\sqrt{-8} }{-6}[/tex]Here we see that we cannot take the square root of a negative number. We will get no real roots and only imaginary ones.
. David drives 40 miles in one hour. How many miles does he drive in 1.5 hours?
Answer:
60 miles in 1.5 hours
Step-by-step explanation:
40 miles times 1 hour = 40 mph
40(1.5)= 60 mph
Answer:
60 miles on 1.5 hours
Step-by-step explanation:
Just do 40*1.5
Ricardo bought 3 pounds of gummy bears for $7.77. What is price per pound for the gummy bears?
Answer:
2.59
Step-by-step explanation:
Jace is working two summer jobs, making $18 per hour lifeguarding and
making $10 per hour washing cars. In a given week, he can work a maximum
of 13 total hours and must earn no less than $170. If x represents the number
of hours lifeguarding and y represents the number of hours washing cars,
write and solve a system of inequalities graphically and determine one
possible solution.
Answer:
One possible solution is Jace spends 5 hours lifeguarding and 8 hours washing cars
Step-by-step explanation:
The parameters of the two summer jobs Jace is working are;
The amount Jace makes for Lifeguarding = $18 per hour
The amount Jace makes for washing cars = $10 per hour
The number of hours he can work a week ≤ 13 hours
The amount he must earn in a ≥ $170
Whereby we have;
x = The number of hours Jace spends lifeguarding
y = The number of hours Jace spends washing cars
The system of inequalities are;
x × 18 + y × 10 ≥ 170
x + y ≤ 13
Making y the subject of the formula of both inequalities gives;
For the first inequality, we have;
x × 18 + y × 10 ≥ 170
10·y ≥ 170 - 18·x
y ≥ 170/10 - 18/10·x
y ≥ 17 - 1.8·x
For the second inequality, we have;
x + y ≤ 13
y ≤ 13 - x
Graphing both inequalities is drawn using Microsoft Excel
Equating both inequalities, given in relation to the y-values, the point where the two lines representing both inequalities meet is given as follows;
17 - 1.8·x = 13 - x
17 - 13 = 1.8·x - x
4 = 0.8·x
x = 4/0.8 = 5
y ≤ 13 - x gives;
y ≤ 13 - 5
y ≤ 8
Given that both relationships are either ≤ or ≥, we have the point where both inequalities meet is one possible solution
Therefore;
One possible solution is x = 5 hours, y = 8 hours
The number of hours Jace spends lifeguarding = x = 5 hours
The number of hours Jace spends washing cars = y = 8 hours.
What are the solutions to the equation w/2w-3= 4/w
Answer:
w=2 , w=6 are the zeroes of the expression
Explanation:
We have been given the expression
after cross multiplication of the given expression so as to simplify it we will get
Solution to the given equation is w=2,w=6
Therefore these are the solutions of the given expression.
Is the value of the expression greater than 1, equal to 1, or less than 1?
(12/64)^0
Answer:
The value of the expression [tex](12/64)^{0}[/tex] is equal to 1
Step-by-step explanation:
You can get this answer two ways:
1. Simply plug in [tex](12/64)^{0}[/tex] into your calculator exactly as it appears. You will get one, so therefore, the expression is equal to 1.
2. If you know your exponent rules, you'll know that anything to the power of 0 equals 1, so no matter the value in the parentheses, the answer will be equal to 1.
Hope this helps!
The ratio of women to men at a college is 9 to 8. If there are 5,644 students in the school, how many more women are there than men?
A) 332
B) 2988
C) 2656
D) 705
Answer:
332
Step-by-step explanation:
Since there is a ratio of 9:8 (women to men), the total should be 17. So even if there were 81 women and 72 men, the total ratio should still be 17. (In simplifiest form.)
So, 5,644 divided by 17=332
Since 9 is 1 more than 8, there are 332 more women than men.
Hope this made sense! I wasn't sure how to explain this.
Answer:
332
Step-by-step explanation:
can someone help me please, its geometry
Answer:
2n
Step-by-step explanation:
Pythagoras [tex]a^{2} + b^{2} = c^{2}[/tex]
2 squared plus 2 squared = 8 but you need to find out the root of 8,
square root of 8 is a surd, so answer in that
Answer:
4n
Step-by-step explanation:
a^2+b^2=c^2
2n^2+2n^2=c^2
4n^2=c^2
sqrt 4n^2=sqrt c^2
4n=c
What do static electricity and current electricity have in common.
Answer: Static electricity is uncontrolled electrons passing from one body to another in sudden, momentary movements, while current electricity is when the electrons are controlled by moving along a path together.
HAVE A BLESSED DAY!!!!
Choose the graph that has a slope of 1/3 and a y-intercept of 1.
Answer:
d
Step-by-step explanation:
The slope is positive which makes the graph increase
Answer:
Step-by-step explanation:
(c). The slope is [tex]-\frac{1}{3}[/tex] and y-intercept is 1
(d). The slope is 2 and y-intercept is 1
-- I assume, that the answer on given task ( Choose the graph that has a slope of 1/3 and a y-intercept of 1. ) is (a) or (b) --
There were 27 meeting rooms reserved for a workshop. Each room contained 134 chairs. How many total chairs were reserved for the workshop?
Answer: 3,618
Step-by-step explanation: You multiply 27 and 134 which equals 3,618.
Answer:
There were 3,618 chairs reserved for the workshop.
Step-by-step explanation:
134 chairs per 27 rooms
134*27 = 3,618
Given m|n, find the value of x.
(8x+6) (9x-30)
Step-by-step explanation:
(8x+6) (9x-30)
=72x²-240x+54x-180
=72x²-186-180
Answer:
(8x+6) (9x-30)
=72x²-240x+54x-180
=72x²-186-180
Step-by-step explanation:
3
EACH STUDENT BELOW MADE AN ERROR IN THEIR WORK WHEN SOLVING THEIR
EQUATION. USE THE TYPING TOOL TO ANSWER THE QUESTIONS IN EACH WHITE BOX.
CULLEN
SERAPHINA
JASPER
-6n + 22 = -4n + 14
- 10n + 22 - 14
-10n = -8
8.4y - 6.8 - -3.2y + 16.4
11.6y - 6.8 - 16.4
11.6y = 23.2
y = 11.6
26 - 32 - - +32
26 - 32 = 32
n - 0.8
b-8
VARIABLES ON BOTH SIDES
DESCRIBE CULLEN'S MISTAKE
DESCRIBE SERAPHINA'S MISTAKE:
DESCRIBE JASPER'S MISTAKE:
WHAT IS THE CORRECT SOLUTION?
WHAT IS THE CORRECT SOLUTION?
WHAT IS THE CORRECT SOLUTION?
More the detto, 2019
Answer:
1) -6·n - (-4·n) = -10·n (The double negative should change to positive + sign here)
-6·n - (-4·n) = -6·n + 4·n = -2·n
The correct solution is;
n = 4
2) y = 23.2 - 11.6 = 11.6, y = 11.6 (Seraphina's mistake is that subtraction was done rather than the division as shown here)
The correct solution is;
y = 2
Step-by-step explanation:
The given parameters are
-6·n + 22 = -4·n + 14
22 - 14= 6·n - 4·n = 2·n
8 = 2·n
n = 8/2 = 4
Cullen's mistake is as follows;
-6·n + 22 = -4·n + 14
-6·n - (-4·n) = -22 + 14
-6·n + 4·n = -22 + 14 (The double negative should change to positive + sign here)
-2·n = -8
n = -8/(-2) = 4
n = 4
2) 8.4·y - 6.8 = -3.2·y + 16.4
8.4·y - (-3.2·y) = -(- 6.8) + 16.4
11.6·y = 23.2 → y = 23.2 - 11.6 = 11.6, y = 11.6 (Seraphina's mistake is that subtraction was done rather than the division as shown here)
y = 23.2/11.6 = 2
y = 2
3) The last equation has parts missing
Answer:
the answer is y=3.88894
Step-by-step explanation:
What is the range of: 21, 35, 17, 27, 32, 12 and 30
Answer:
Please mark as brainliest!!
Step-by-step explanation:
range = maximum value -minimum value
35-12=23
The numerator of a rational number is 7 less than the denominator .If the denominator is increased by 9 and the numerator by 2, we again get the same rational number. Find the Number
Answer:
5/3
Step-by-step explanation:
Let
Denominator = x
Numerator = x - 7
New
Denominator = x + 9
Numerator = x - 7 + 2
= x - 5
x / x-7 = x -5 / x + 9
Cross product
x * x + 9 = x-7 * x-5
x² + 9x = x²- 5x - 7x + 35
x² + 9x - x² + 5x + 7x - 35 = 0
21x = 35
divide both sides by 21
x = 35 / 21
= 5 / 3
x = 5/3
The rational number is 5/3
In a certain country, the true probability of a baby being a girl is 0.479. A mound the next four randomly selected births in the country, what is the probability that at least one of them is a boy ? Round to 3 decimal places as needed
Answer:
0.947
Step-by-step explanation:
We are told that the true probability of a baby being a girl is 0.479.
This means that probability of a baby being a boy is;
p = 1 - 0.479
p = 0.521
Now,using binomial probability distribution formula we can solve this problem.
P(X=x) = C(n, x) × p^(x) × (1 - p)^(n - x)
We are told that a mound the next four randomly selected births in the country, what is the probability that at least one of them is a boy.
This is;
P(X ≥ 1) = P(1) + P(2) + P(3) + P(4)
P(1) = C(4, 1) × 0.521^(1) × (1 - 0.521)^(4 - 1)
P(1) = 0.229
P(2) = C(4, 2) × 0.521^(2) × (1 - 0.521)^(4 - 2)
P(2) = 0.3737
P(3) = C(4, 3) × 0.521^(3) × (1 - 0.521)^(4 - 3)
P(3) = 0.27096
P(4) = C(4, 4) × 0.521^(4) × (1 - 0.521)^(4 - 4)
P(4) = 0.0737
Thus;
P(X ≥ 1) = 0.229 + 0.3737 + 0.27096 + 0.0737
P(X ≥ 1) = 0.94736
P(X ≥ 1) ≈ 0.947