The equation of the parabola, in vertex-form, is given as follows:
y = -(x - 6)² + 6.
What is the equation of a parabola given it’s vertex?The equation of a quadratic function, of vertex (h,k), is given by the rule presented as follows:
y = a(x - h)² + k
In which the parameters of the equation are given as follows:
h is the x-coordinate of the vertex.k is the y-coordinate of the vertex.a is the leading coefficient.The axis of symmetry is at x = 6, hence:
h = 6.
The maximum height if of 6, hence:
k = 6.
Thus:
y = a(x - 6)² + 6.
The parabola passes through the point (7,5), meaning that when x = 7, y = 5, and thus the leading coefficient a is obtained as follows:
5 = a(7 - 6)² + 6.
a = -1.
Hence the parabola is defined as follows:
y = -(x - 6)² + 6.
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A local salesman receives a base salary of $925 monthly. He also receives a commission of 8% on all sales over $1250. How much would he have to sell in a month if he needed to have a monthly income of $2900?
He would need to sell $
to reach his needed monthly income needs.
The salesman needs to sell $25937.5 to reach his needed monthly income needs.
What is commission?Commission, also known as sales commission, is a payment given to employees based on the sales they make.
Given that, A local salesman receives a base salary of $925 monthly. He also receives a commission of 8% on all sales over $1250.
Monthly salary = fixed part + commission part
The fixed salary is $925.
The commission part is 8% on all sales over $1250
Let x = amount of sales, and x must be greater than $1250.
Then, the amount of sales over $1250 is x - 1250.
He earns 8% on that amount, so the commission part is 8%(x - 1250),
or 0.08(x - 1250).
Monthly salary = fixed part + commission part
Monthly salary = 925 + 0.08(x - 1250)
925 + 0.08(x - 1250) = 2900
0.08x = 2075
x = 25937.5
Therefore, he needs to sell $25937.5.
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Find the perimeter of the image below: (4 points)
37 units
38 units
39 units
40 units
38, 39, 40, 37, 38, and so forth. The perimeter of the supplied figure must be determined. = 38.97 units. As a result, 38.97 units make up the perimeter.
How do you find the perimeter?The circumference of a shape is known as its perimeter. The lengths of all four sides must be added in order to get a rectangle's or square's perimeter.
The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:
d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)^{2} }[/tex]
There are points that correspond to each vertex in the polygon:
P (-2,11)
T (8, 7)
S (1, 7)
R (2, 0)
Q (-4,5)
So, using the distance formula and the vertex positions of side PT, we can determine its length: The total length of all a polygon's sides is its perimeter. The polygon's sides are PT, TS, SR, RQ, and QP. We apply the distance formula to get a side's length:
d =[tex]\sqrt{(x2-x1)^{2}+(y2-y1)\x^{2} }[/tex] ≤ b r/≥ d=[tex]\sqrt{(8-(-2)^{2})+(7-11)^{2} }[/tex] ≤b r/≥
d=[tex]\sqrt{116}[/tex]
There are points that correspond to each vertex in the polygon:
P (-2,11)
T (8, 7)
S (1, 7)
R (2, 0)
Q (-4,5)
So, using the distance formula and the vertex positions of side PT, we can determine its length:
P = (-2, 11)
T = (8, 7)
The length of PT is [tex]\sqrt{116}[/tex]
The other 4 sides are handled in the same way, and the results are as follows:
TS = [tex]\sqrt{49}[/tex]
SR = [tex]\sqrt{50}[/tex]
RQ = [tex]\sqrt{61}[/tex]
QP = [tex]\sqrt{40}[/tex]
You may calculate the perimeter by adding all the sides:[tex]\sqrt{116}[/tex]+[tex]\sqrt{49}[/tex]+[tex]\sqrt{50}[/tex]+[tex]\sqrt{61}[/tex]+[tex]\sqrt{40}[/tex] = 38.97
The solution is 39 units if you round off.
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Please help me with this
Answer:
A represents f(x) and B represents g(x)
Step-by-step explanation:
choose a value for x, substitute , say x = 1 into both f(x) and g(x) , then check the values obtained on the graph.
f(x) = 100 × [tex](\frac{3}{5}) ^{1}[/tex] = 100 × [tex]\frac{3}{5}[/tex] = 20 × 3 = 60
thus (1, 60 ) is a point on the graph of f(x)
the point (1, 60 ) is on graph A
g(x) = 100 × [tex](\frac{2}{5}) ^{1}[/tex] = 100 × [tex]\frac{2}{5}[/tex] = 20 × 2 = 40
thus (1, 40 ) is a point on the graph of g(x)
the point (1, 40 ) is on graph B
"Customers of CC Car Wash visit the station at a constant rate (you can ignore any effects of variability) of 40 customers per day. Of these customers, 40 percent buy Package 1, 15 percent buy Package 2, 15 percent buy Package 3, and 30 percent buy Package 4. The mix does not change over the course of the day. The store operates 12 hours a day."
According to the information, we can infer that the number of customers that buy package 1 is 16 customers.
How to calculate how many customers buy package 1?To calculate how many customers buy package 1 we have to identify some important information such as:
Total customers: 40 customers.Percent that buy package 1: 40%To calculate this value, we have to divide 40 in 100, and then we have to multiply the result by 40.
40 / 100 = 0.40.4 * 40 = 16According to previous information, the number of customers that buy package 1 is 16 customers. So, 24 customers buy package 2, 3 or 4. If we have to identify exactly how many buy an specific package we have to make the same procedure. For example package 3.
40 / 100 = 0.4
0.4 * 15 = 6
So, 6 customers buy package 3.
Note: This question is incomplete because there is some information missing. Here is the complete information:
TASK
Calculate how many customers buy package 1.
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5) Is the sequence geometric?
a) 100, 25, 6.25, 1.5625,....
b) 3, -8, -19, -30,...
The sequence of 100, 25, 6.25, 1.5625 is geometric.
What is meant by geometric?The Geometric Mean (GM) in mathematics is the average value or mean that, by calculating the product of the values of the set of numbers, denotes the central tendency of the numbers.
In essence, we multiply the numbers together and calculate their n[tex]th[/tex]root, where n is the total number of data values.
A succession of shapes are used to create geometric patterns.
Because the pattern is governed by a rule, patterns created from shapes are comparable to patterns created from numbers.
The dimensions, perimeter, area, surface area, volume, etc. of geometric shapes are determined using geometry formulas.
Mathematics' branch of geometry examines the connections between points, lines, angles, surfaces, solids' measurements, and qualities.
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In 2018, the population of Sydney was 5.48 million.
This was 22% of the total population of Australia.
Work out the total population of Australia in 2018
Give your answer correct to 3 significant figures.
The population of Australia in 2018 was 24.909 million.
Given: The population of Sydney in 2018 = 5.48 million
This population of Sydney is equal to 22 % of the total population of Australia.
To find: Total population of Australia
Solution:
According to the Question,
Total population of Australia * 22% = total population of Sydney
Total population of Australia * 22/100 = 5.48 million
= 5.48 million * 100/22
= 24.909 million (approx.)
Hence, the population of Australia in 2018 was 24.909 million.
The total population of Australia in 2018 was 24.90 million.
What is percentage?A percent is a dimensionless number, meaning that it has no units of measurement, since it represents a part of whatever whole is being measured.
Given that, the population of Sydney was 5.48 million, which was 22% of the total population of Australia.
We need to find the total population of Australia.
Let the total population of Australia be y.
Therefore,
y × 22% = 5.48
y = 5.48 × 100/22
y = 24.90
Hence, the total population of Australia in 2018 was 24.90 million.
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If a1=3 and an=-2an-1 then find the whole value of a 5
Answer:
a₅ = 48
Step-by-step explanation:
using the recursive rule [tex]a_{n}[/tex] = - 2[tex]a_{n-1}[/tex] and a₁ = 3 , then
a₂ = - 2a₁ = - 2(3) = - 6
a₃ = - 2a₂ = - 2(- 6) = 12
a₄ = - 2a₃ = - 2(12) = - 24
a₅ = - 2a₄ = - 2(- 24) = 48
Please help with geometry question!!!
Answer:
x = 14EG = 9Step-by-step explanation:
You want the missing length EG and the corresponding value of x in isosceles triangle DEF with midline GH of length 6 parallel to base DF of length 12.
MidlineThe length of segment GH is half the length of segment DF (6/12 = 1/2), so we know that corresponding sides EG and ED have the same ratio:
EG/ED = 1/2
2EG = ED . . . . . . . . . . . . multiply by 2·ED
2(x -5) = (x-5)+9 . . . . . . substitute given values
2x -10 = x +4 . . . . . . . . simplify
x = 14 . . . . . . . . . . . . . add 10-x
Then the length of EG is ...
EG = 14 -5 = 9
Please help me solve this i'm not sure what else to do
The equation of the line in point-slope form is obtained as y = -2x + 4.
What is the point-slope form?
Point-slope is the general form of a linear equation which is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
The line passes through point (x1,y1) = (0,4)
The slope of the line is m = -2.
The formula for point-slope form of equation is -
y-y1=m(x-x1)
Substituting the values in the equation -
y - 4 = -2(x - 0)
y - 4 = -2x
y = -2x + 4
Therefore, the equation is obtained as y = -2x + 4.
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5, Infigure 4.48 • vertical cliff IS Hom high and is absor ved from about which is from from the foot of the cliff calculate the angle of elevation of the top of the cliff from boak ?
Therefore , the solution of the given problem of elevation comes out to be
X = 21.23°.
What is the elevation and depression angle?When it is between the horizontal line and the line of sight, the angle of elevation is formed. The angle that forms when the line of sight is above the horizontal line is referred to as the angle of elevation. The line of sight, however, is to the horizontal line downward in the angle of depression.
Here,
Given : tan X = P/ B
tan X = 68 / 175
X = tan⁻¹ (68 /175)
X = 21.23
Therefore , the solution of the given problem of elevation comes out to be
X = 21.23°.
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The area of a rectangular room is 750 square feet. The width of the room is 5 feet less than the length of the room. Which equations can be used to solve for y, the length of the room? Select three options. y(y + 5) = 750 y2 – 5y = 750 750 – y(y – 5) = 0 y(y – 5) + 750 = 0 (y + 25)(y – 30) = 0
10. When cycling 2.4km to the beach, the wheels on Sue's bike
rotated 1255 times. Find the diameter of the wheels.
Therefore , the solution of the given problem of circle comes out to be
the diameter is 62 cm.
A circle is what?A circle is created in the plane by each point that is a specific distance from another point (center). Thus, it is a curve made up of points that are separated from one another by a defined distance in the plane. Additionally, it is rotationally symmetrical about the center at every angle. Every pair of endpoints in a circle's closed, two-dimensional plane are evenly spaced apart from the "center." A circular symmetry line is made by drawing a line through the circle. Additionally, it is rotationally equal about the center at every angle.
Here,
Given : Sue covered 2.4 km distance and
bike wheel rotated 1225 times.
Thus,
To find the value of diameter of the wheel
=>2400=2πr*1225
=> 2400/2 = πr*1225
=> 1200 = πr*1225
=>r=31
Diameter = 2*31 = 62cm
Therefore , the solution of the given problem of circle comes out to be
the diameter is 62 cm.
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HELP PLS
Factor the trinomal or stage that the trinomal is prime
The correct answer is x² - 7x - 18 = (x - 9)(x + 2)
Inso ice cream machines make a total of 320 gallons in a certain amount of time.
Working together for the same length of time, how many gallons of ice cream can 4
machines make?
The gallons of ice cream 4 machines can make is 650 gallons.
How to find the number of gallons of ice cream 4 machine can make?Two ice cream machines make a total of 320 gallons in a certain amount of time.
Working together for the same length of time, the number of gallons of ice creams 4 machine can make can be calculated as follows:
Therefore,
If 2 ice cream machine = 320 gallons
4 ice cream machine = ?
cross multiply
Hence,
gallons of ice cream made by 4 machines = 320 × 4 / 2
gallons of ice cream made by 4 machines = 1280 / 2\
Therefore,
gallons of ice cream made by 4 machines = 640 gallons
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Write a rule to represent a function for the set of ordered pairs.
Answer:
y = 4[tex]x^{2}[/tex]
Step-by-step explanation:
Your inputs (x's): are -1,0,1,2,3,4 if you plug them into the equation, you get the matching outputs given in the order pairs
input -1 (x value)
y = [tex]4x^{2}[/tex]
y = 4[tex](-1)^{2}[/tex]
y = 4(1)
y = 4
(-1,4)
input 0 (x)
y = [tex]4x^{2}[/tex]
y = [tex]4(0)^{2}[/tex]
y 4(0)
y = 0
(0,0)
input 1 (x)
y = [tex]4x^{2}[/tex]
y = [tex]4(1)^{2}[/tex]
y = 4(1)
y = 4
(1,4)
input 2 (x)
y = [tex]4x^{2}[/tex]
y = [tex]4(2)^{2}[/tex]
y = 4(4)
y = 16
(2,16)
input 3 (x)
y = [tex]4x^{2}[/tex]
y = [tex]4(3)^{2}[/tex]
y = 4(9)
y = 36
(3, 36)
input 4 (x)
y = [tex]4x^{2}[/tex]
y = [tex]4(4)^{2}[/tex]
y = 4(16)
y = 64
(4,64)
1.5 (-2)^(n-1) > -6000
Find n (n is integer)
Answer:
что там а? я даже не знаю hehe
I can’t figure out this problem please help me
Answer:
95 6/7
Step-by-step explanation:
The perimeter can be found by adding the length and width together and then multiplying the sum by 2.
Perimeter = 2(L + W)
Where L is the length and W is the width.
So, using the given measurements:
Perimeter = 2(33 5/7+ 14 3/14) = 94 26/14
94 26/14 -> 95 12/14 -> 95 6/7
Answer:
The perimeter is [tex]95\frac{6}{7}[/tex] inches.
Step-by-step explanation:
The formula for the perimeter of a rectangle is
[tex]P=2L+2W[/tex]
We are given the length and the width. Lets evaluate the perimeter.
First lets convert the length and width to an improper fraction.
Length: [tex]33\frac{5}{7}[/tex]
To write 33 as a fraction with a common denominator, multiply by [tex]\frac{7}{7}[/tex]. Then simplify.
[tex]\frac{33*7}{7} +\frac{5}{7}[/tex]
[tex]\frac{231}{7} +\frac{5}{7}[/tex]
[tex]\frac{231+5}{7}[/tex]
[tex]\frac{236}{7}[/tex]
Width:
To write 14 as a fraction with a common denominator, multiply by [tex]\frac{14}{14}[/tex]. Then simplify.
[tex]\frac{14*14}{14} +\frac{3}{14}[/tex]
[tex]\frac{196}{14} +\frac{3}{14}[/tex]
[tex]\frac{196+3}{14}[/tex]
[tex]\frac{199}{14}[/tex]
Lets enter the 2 fractions into the perimeter equation.
[tex]P=(2*\frac{236}{7} )+(2*\frac{199}{14} )[/tex]
Simplify each term.
[tex]P=\frac{2*236}{7} +2*\frac{199}{14}[/tex]
[tex]P=\frac{472}{7} +2*\frac{199}{14}[/tex]
Factor 2 out of 14.
[tex]P=\frac{472}{7} +2*\frac{199}{2(7)}[/tex]
Cancel the common factor of 2.
[tex]P=\frac{472}{7} +\frac{199}{7}[/tex]
Combine the numerators over the common denominator.
[tex]P=\frac{472+199}{7}[/tex]
[tex]P=\frac{671}{7}[/tex]
[tex]P=95\frac{6}{7}[/tex]
Make sure to show working
Hope it helps. If you have any query, feel free to ask.
hello , please help !
Answer:
4,7
Step-by-step explanation:
4,7
I need a so please don,t get it wrong
Answer: 48 square inches
Step-by-step explanation:
To find the area of an irregular shape, we first break the shape into common shapes. Then we find the area of each shape and add them. For example, if an irregular polygon is made up of a square and a triangle, then: Area of irregular polygon = Area of Square + Area of Triangle.
area of triangle L x W = 6x4=24
area of rectangle LxW =6x4=24
24+24=48
The
term-to-term rule for a sequence is given as u_n+1=u_n+2
a) Explain in words what this means.
b)Given that u, = -4, list the first five terms of the sequence.
Answer:
- 8, - 6, - 4, - 2, 0
Step-by-step explanation:
the term- to- term rule
[tex]u_{n+1}[/tex] = [tex]u_{n}[/tex] + 2
means that to find a term in the sequence you add 2 to the previous term.
given u₃ = - 4 , then
u₄ = u₃ + 2 = - 4 + 2 = - 2
u₅ = u₄ + 2 = - 2 + 2 = 0
to find the first 2 terms, rearrange the rule as
[tex]u_{n+1}[/tex] = [tex]u_{n}[/tex] + 2 ( subtract 2 from both sides )
[tex]u_{n+1}[/tex] - 2 = [tex]u_{n}[/tex] , that is
[tex]u_{n}[/tex] = [tex]u_{n+1}[/tex] - 2
this allows for a term to be found by subtracting 2 from the next term, so
a₂ = a₃ - 2 = - 4 - 2 = - 6
a₁ = a₂ - 2 = - 6 - 2 = - 8
the first 5 terms are then : - 8, - 6, - 4, - 2, 0
A,B,C,E,F et G sont du plan Simplifier l’écriture de chacun des sommes 1)AB+CE+BC+EF 2) AB+DE+AB+EG 3) AB-BC-AB+BE 4) AB+DE+CD+AD+BC+ED
please helppp!!! im confused
In the equation for the exponential function, f ( x ) = P ( 1 + r ) ^ x, how do we find r (rate of change) algebraically?
Answer:
[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]
Step-by-step explanation:
Given exponential function:
[tex]f(x)=P(1+r)^x[/tex]
Replace f(x) with y:
[tex]y=P(1+r)^x[/tex]
Divide both sides by P:
[tex]\dfrac{y}{P}=(1+r)^x[/tex]
Take natural logs of both sides:
[tex]\ln \left(\dfrac{y}{P}\right)=\ln (1+r)^x[/tex]
[tex]\textsf{Apply the power law}: \quad \ln x^n=n \ln x[/tex]
[tex]\ln \left(\dfrac{y}{P}\right)=x \ln (1+r)[/tex]
Divide both sides by x:
[tex]\dfrac{1}{x}\ln \left(\dfrac{y}{P}\right)=\ln (1+r)[/tex]
[tex]\textsf{Apply the power law}: \quad n \ln x=\ln x^n[/tex]
[tex]\ln \left(\dfrac{y}{P}\right)^{\frac{1}{x}}=\ln (1+r)[/tex]
Raise both sides to power of e:
[tex]\large\text{$e^{\ln \left(\frac{y}{P}\right)^{\frac{1}{x}}}=e^{\ln (1+r)}$}[/tex]
[tex]\textsf{Apply the power law}: \quad e^{\ln x}=x[/tex]
[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}=1+r[/tex]
Subtract 1 from both sides:
[tex]\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1=r[/tex]
Therefore, the equation to find r is:
[tex]r=\left(\dfrac{y}{P}\right)^{\frac{1}{x}}-1[/tex]
How would you solve questions 25a+b?
Answer:
(a) See attachment.
(b) 12:23
Step-by-step explanation:
Part (a)A bearing is the angle (in degrees) measured clockwise from north.
To mark the position of J on the given map:
Measure an angle of 36° clockwise from K and draw a line.Measure an angle of 284° clockwise from L and draw a line.The location of J is the point of intersection of the two lines.(See attachment).
Part (b)Given:
Distance between K and L = 9600 mSpeed Kendra walks from K to L = 4.5 km/hConvert 9600 meters into kilometers by dividing by 1000:
⇒ 9600 m = 9600 ÷ 1000 = 9.6 km
[tex]\boxed{\sf Speed=\dfrac{Distance}{Time}}[/tex]
Therefore:
[tex]\sf Time=\dfrac{Distance}{Speed}[/tex]
Substitute the given distance and speed into the formula to calculate the time it took Kendra to walk from K to L:
[tex]\implies \sf Time=\dfrac{9.6\;km}{4.5\;km/h}=2.133333...\;hours[/tex]
Convert 2.133333.. into a mixed number:
[tex]\implies \sf 2.133333...=2\frac{2}{15}\;hours[/tex]
To find the number of minutes in 2/15ths of an hour, multiply 2/15 by 60:
[tex]\implies \sf \dfrac{2}{15} \times 60=\dfrac{120}{15}=8\;minutes[/tex]
Therefore, it took Kendra 2 hours and 8 minutes to walk from K to L.
If Kendra left at 10:15:
[tex]\implies \sf 10:15 + 2\;hours = 12:15[/tex]
[tex]\implies \sf 12:15 + 8\;minutes=12:23[/tex]
Therefore, Kendra arrived at L at 12:23.
Jason likes to play video games. His parents allow him to play for 20 min plus 10
min for each half hour he does chores or studies. He can never play for more
than 90 min/day.
The function f(x)=20+10x models the number of minutes per day Jason could
play where x represents the number of half hour increments he has done chores
or studied.
What is the practical range of the function?
A. all multiples of 10 greater than or equal to 20 and less than or equal to 90
B. all integers
C. all real numbers greater than or equal to 20
D. all real numbers
Answer:all integers
Step-by-step explanation:
the correct is all integers
There is 25 pounds of dog food in a bag. There are approximately 2.2 kilograms in 1 pound. PLEASE HELP ME !! THANK YOU SMM!!
Which statement is true?
A. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 55/22.
B. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
C. There is approximately 55 kilograms of dog food in the bag, because 1/2.2 = 25/11.36
D. There is approximately 11.36 kilograms of dog food in the bag, because 1/2.2 = 11.36/25
Using multiplication operation, the TRUE statement about the number of kilograms of dog food in the bag is A. There are approximately 55 kilograms of dog food in the bag, because 1/2.2 = 55/25.
How is the number determined?The number of kilograms of dog food in the bag is determined using the multiplication operation.
The multiplication operation is one of the basic mathematical operations, including addition, subtraction, and division.
The multiplication operation involves multiplying the multiplicand by the multiplier to get a result called the product after the equal sign.
The pounds of dog food in a bag = 25 pounds
Approximately 2.2 kilograms = 1 pound
The number of kilograms = 25 x 2.2
= 55 pounds
Thus, Option A is correct since 1/2.2 equals 55/25, based on the multiplication operation.
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These points are linear. Find the slope.
to get the slope of any straight line, we simply need two points off of it, let's use those in the picture below.
[tex](\stackrel{x_1}{-4}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{2}-\underset{x_1}{(-4)}}} \implies \cfrac{8 }{2 +4} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4 }{ 3 }[/tex]
Why is the denominator of each fraction 12?
Pls help me
12 is the denominator because it represents the total number of times Nicanor selects a diving ring from the bag
Explaination:
Nicanor randomly selects a ring from the bag a total of 12 times. 3 times he selects a red ring, 4 times a yellow one, and 5 times a blue one.
When he selects a red ring, he selects it 3 times out of the 12 times total, which is represented as the fraction 3/12.
When he selects a yellow ring, he selects it 4 times out of the 12 times total, which is represented as the fraction 4/12.
When he selects a blue ring, he selects it 5 times out of the 12 times total, which is represented as the fraction 5/12.
Hope this helps you!
devin has a ribbin that is 2 ft long. he cuts it into peices, s shown in the model
The model shows that there are 10 pieces that are each 0. 2 ft long.
How to find the number of pieces ?From the given model, we see that Devin cut the ribbon in equal proportions. The number of proportions can be found by summing the different sections on the ribbon.
This number comes to 10 sections which means that Devin cut the ribbon into 10 pieces.
The length of each of these pieces is:
= Length of entire ribbon / Number of pieces
= 2 / 10
= 0. 2 ft long
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