Answer:
[tex]x\geq 7\\[/tex]
[tex]x[/tex] ∈ [tex][7,[/tex] ∞ [tex])[/tex]
Step-by-step explanation:
In this problem, one is given the following function,
[tex]f(x)=(x-7)^2[/tex]
The problem asks one to find the interval for which the function is one-to-one and non-decreasing.
A one-to-one function is when every element in the range corresponds to every element in the range. Moreover, no element in the range will correspond to more than one element in the domain. In essence, every input pairs to only one output, and every output pairs to only one input. In a quadratic equation (an equation with a term to the second degree (exponent of (2)), half of the graph will form a one-to-one function. This is because when one has the full graph, for every output there are two inputs. However, with half of the graph, there is only one input for every output. Therefore, a function with a domain of all values less than the (x-coordinate) of the vertex will form a one-to-one function. The same conclusion can be drawn for any value greater than the (x-coordinate) of the vertex.
The given function is in vertex form. This means that one can find the vertex using the given information. The general format for the vertex form of a quadratic equation is as follows,
[tex]y=k(x-h)^2+k[/tex]
Where vertex is the following,
[tex](h,k)[/tex]
Applying this logic here, one can state that the vertex of the given equation ([tex]f(x)=(x-7)^2[/tex]) is as follows,
[tex](7, 0)[/tex]
Since the coefficient of this equation is positive (no coefficient means that it is (1)) outside of it, one can conclude that the graph of the equation is increasing after the (x) value of (7). Therefore, the function is one-to-one and increasing on the interval ([tex]x\geq 7\\[/tex]).
1.the ratio if the weight of an object on mars to its weight in earth is 9 to 25.If a person weighs 160pouns on earth,how much would the person weigh on mars?
Answer:
57.6 Pounds
Step-by-step explanation:
Weight on Earth = 160 pound
Weight on Mars = (9/25)*160 pound
= 57.6 pounds
Factorise 5x + 10=
ᴘʟᴀʏɪɴɢ: Who Asked (Feat: Nobody did ) ───────────⚪────── ◄◄⠀▐▐⠀►:/:⠀───○
Answer:
5(x+2)
Step-by-step explanation:
5x + 10=
Factor out 5
5(x+2)
Answer:
[tex]5(x + 2)[/tex]
Step-by-step explanation:
Get 5 out
[tex]5x + 10 \\ 5(x + 2)[/tex]
For what values of x is the expression below defined?
VX + 4 = V1- x
Answer:
A
Step-by-step explanation:
A square root must be positive or equal to 0
x + 4 ≥ 0
x ≥ -4
1-x > 0
-x > - 1
x < 1
If we unite the two solutions, we have
-4 ≤ x < 1
Line p passes through points (5,-4) and (2,7). What is the slope of a line that is perpendicular to line p
Answer:
3/11
Step-by-step explanation:
First find the slope of the line
m = (y2-y1)/(x2-x1)
= ( 7 - -4)/(2 - 5)
= (7+4)/(2-5)
=11/ -3
We want a line that is perpendicular, so it is the negative reciprocal
-1 / ( -11/3)
+3/11
A line that is perpendicular will have a slope that is 3/11
Can someone please help me ?
Answer:
(x-2),(x-1),(x), and(x+1)
Step-by-step explanation:
In this scenario, we are given nothing about the polynomial except its graph. We can start in problems like these by looking at when y=0 and going from there.
In this graph, we can see that y=0 when x=2, 1, 0, and -1. Looking at our options, for y to be 0, there must be a factor where, when we plug x=2 in, y=0. The only option here is (x-2). Similarly, for x=1, we have (x-1), for x=0, we have x, and for x=-1, we have (x+1). The polynomial has 3 turning points, so the polynomial must be of degree 4 or higher.
So far, we have (x-2)(x-1)(x)(x+1). Plugging this in to a graphing calculator, we can see that this fits. To check if x²+2 and x²+1 would work here, it would require guess and check with values/graphing calculators, seeing if they fit. For example, when x=1.5, y is greater than -1 on the graph and our function. However, if we multiplied that by x²+1 or x²+2. when x=1.5, y would balloon downward, and the graph wouldn't fit
i will mark the brainliest 100 points
Answer:
4 squared is 16 so 16 times 3.14= 50.24
Step-by-step explanation:
Answer:
4^2 = 16
16 x 3.14 = 50.24 in2
Step-by-step explanation:
Formula of area of a circle:
π x r^2(radius being squared)
To make it more easier:
3.14 or 22/7 x radius^2
Some keywords:
Radius: Half of your diameter or given radius
Radius Squared: Your radius squared, your radius to the power of 2.
Pi: 3.14 or 22/7 depending on what they tell you to use for pi
Which systems of equations Intersect at point A in this graph?
a sum of marbles is shared in the ratio of 4 to 1 the smaller share is 24 marbles what was the total number of marbles shared
Answer:120
Step-by-step explanation: If the smaller number of the ratio is 24 that means the 1 is multiplied by 24 to reach the smaller share of 24. We then multiply 24 with 4 to get the number 96. Lastly you add 96 with 24 to get the total number of marbles
Questlon 18 of 25
Joanne and Betty have a combined age of 41 years. If Joanne is 17 years old,
how old is Betty?
Answer here
SUBMIT
Answer:
24
Step-by-step explanation:
betty age = 41 - 17
= 24
Convert the following equation to slope-intercept form to graph: 7x-y =_3
Answer:
y intercepts are (0,3), x intercepts are (0.43, 0)
Step-by-step explanation:
I think that's correct I'm not to sure.
Marcus is rewriting a polynomial by combining like terms. Which terms does he still need to combine to finish rewriting the polynomial?
Help me plz I’m too slow for this
Answer:
160 units²
Step-by-step explanation:
Surface area of the square pyramid = a² + 2al
Where,
a = side length of the square = 8
l = slant height of the triangular face = 6
Plug in the values
Surface area of the square pyramid = 8² + 2*8*6
= 64 + 96
= 160 units²
solve for system of equations -x+2y=8, x-2y=-8
Answer:
0.. everything just cancels out
Alright, everyone. I'm betting in a lot amount of points and I really need someone to help me out here. It would bring lots and lots of weight off my shoulders.
Answer:
See Below.
Step-by-step explanation:
Part 1)
Since the coral structure has an initial volume of 1,200 cubic centimers, a = 1200.
Since it doubles every year, we can let b = 2.
Hence, our equation is:
[tex]y=1200(2)^t[/tex]
Where t is the time in years since the coral was measured.
Part 2)
Evaluate each value:
[tex]y(5)=1200(2)^5=38,400\text{ cm}^3[/tex]
When t = 5, or after five years, the volume of the coral structure is 38,400 cubic centimeters.
[tex]y(1)=1200(2)^1=2,400\text{ cm}^3[/tex]
When t = 1, or after one year, the volume of the coral structure is 2,400 cubic centimeters.
[tex]y(0)=1200(2)^0=1, 200\text{ cm}^3[/tex]
When t = 0, or during the initial year, the volume of the coral structure is 1,200 cubic centimeters.
And:
[tex]\displaystyle y(-1)=1200(2)^{-1}=\frac{1200}{2}=600\text{ cm}^3[/tex]
[tex]\displaystyle y(-2)=1200(2)^{-2}=\frac{1200}{4}=300\text{ cm}^3[/tex]
Part 3)
In this case, since positive values of t indicates the time in years since the coral was starting to be measured, negative values of t indicates the time in years before the coral was starting to be measured.
We acquired that y = 300 when t = -2. So, this means that two years before the coral was starting to be measured, the volume of the coral was 300 cubic centimeters.
Part 4)
We can set y = 37.5 and solve for t. Hence:
[tex]\displaystyle 37.5=1200(2)^t[/tex]
Divide both sides by 1200:
[tex]\displaystyle \frac{37.5}{1200}=\frac{375}{12000}=\frac{1}{32}=2^t[/tex]
Notice that:
[tex]\displaystyle \frac{1}{32}=\frac{1}{2^5}=2^{-5}=2^t[/tex]
Same bases must have the same exponents. Hence:
[tex]t=-5[/tex]
So, five years before the coral was being measured, the volume of the coral was 37.5 cubic centimeters.
Since the initial volume was 1,200 and it grows each year, it can only be 37.5 before the initial year, so our answer makes sense.
You randomly draw a marble from a bag of marbles that contains 888 blue marbles, 555 green marbles, and 888 red marbles.
Answer:
whats the question?
Step-by-step explanation:
Solve for x 11^x/11^3=11^2 PPEASE I HAVE AN F
Find the volume of the rectangular pyramid below.
Answer:
315 yd cubed
Step-by-step explanation:
To find the volume of the pyramid, we first need to consult the equation below. Thebase is for the rectangular portion, then after multiplied by the height it is divided by 3 to get the pyramid.
[tex]\frac{1}{3} (B * H )[/tex]
To get the base, we multiply the length by the width.
21 * 9 = 189
189 * 5 = 945
945 divided by 3 = 315
Answer:
Let's find the base area:
21 x 9 = 189
Now let's multiply the base area by the height:
189 x 5 = 945
Now let's divide by 3( x 1/3 ):
945 divided by 3(x 1/3) = 315 yd^3 is your answer
Step-by-step explanation:
Formula area of a rectangular Pyramid(just like any other pyramid):
BH x 1/3
To find base we multiply length by width just using the basic formula of finding area of a rectangle.
Then we multiply our base area by our height.
One we've done that we now divide by 3(multiplying by 1/3)
Your shop employs seven people. Today two people are sick. What fraction represents the employees who are sick
Answer:
2/7 of represents employees who are sick
Step-by-step explanation:
Question:
What fraction represents the employees who are sick
Total People = 7
sick people =2
numerator/denominator
2/7
Help please. Forthefunction f(x)=x(x+3)(x−1)
Answer:
x-intercepts= (-3,0) , (1,0) and y-intercepts= (0,-3)
For the graph part it would be graphed and shaped like a U.
Step-by-step explanation:
Hope this helps :)
Evaluate the following expression.
2^0
Answer:
1
Step-by-step explanation:
2^0
Any number raised to the zero power is 1
Help please . Help . Thank you
Answer:
Total weight = 111.6 lbs
Step-by-step explanation:
Given the following data;
Length = 1 feet
Width = 9.5 feet
Height = 13.5 feet
Mass of contents = 0.87 pounds per cubic foot
To find the weight of the contents in the container;
First of all, we would determine the volume of the rectangular prism;
Volume = length * width * height
Volume = 1 * 9.5 * 13.5
Volume = 128.25 cubic feet
Next, we find the overall weight;
Total weight = volume * mass of contents
Total weight = 128.25 * 0.87
Total weight = 111.6 lbs
Check all of the correct names for the object pictured below.
Answer:
VU,UV, and probably VU just pick 3 answers cause there is 6 questions in all but i hope these answers help u have a nice day too.
Step-by-step explanation:
The lines shown below are parallel. If the green line has a slope of -3/7, what is
the slope of the red line?
A. -3/7
B. 7/3
C. -7/3
D. 3/7
। Find the H.C. F. of :
x2+ 2xy+y and 3ax+3ay
Answer:
Factorizing 4x2 - 9y2, we get
(2x)2 - (3y)2, by using the identities of a2 - b2.
= (2x + 3y) (2x - 3y)
Step-by-step explanation:
f(x) = 3x + 4 is y =
Which sequences are geometric?
Check all that apply.
Answer:
3, 12, 48, 192, ...
3, 15, 75, 375, ...
2, 10, 50, 250, ...
After a nice dinner, Benji decides to leave a 20% tip. The total bill comes to $24.25. About how much should he leave for the tip?
Answer:
it will be 4.85 dollars he left
The manager of a new supermarket wished to estimate the likely expenditure of his customers. A sample of till slips from a similar supermarket describing the weekly amount spent by 500 randomly selected customers was collected and analysed. This expenditure was found to be approximately normally distributed with a mean of $50 and a standard deviation of $15.
Find the probability that any shopper selected at random spends more than $80 per week?
Find the percentage of shoppers who are expected to spend between $30 and 80 per week?
Answer:
0.0228 = 2.28% probability that any shopper selected at random spends more than $80 per week.
88.54% of shoppers are expected to spend between $30 and 80 per week.
Step-by-step explanation:
Normal Probability Distribution
Problems of normal distributions can be solved using the z-score formula.
In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
Normally distributed with a mean of $50 and a standard deviation of $15.
This means that [tex]\mu = 50, \sigma = 15[/tex]
Find the probability that any shopper selected at random spends more than $80 per week?
This is 1 subtracted by the p-value of Z when X = 80. So
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 50}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
1 - 0.9772 = 0.0228
0.0228 = 2.28% probability that any shopper selected at random spends more than $80 per week.
Find the percentage of shoppers who are expected to spend between $30 and 80 per week?
The proportion is the p-value of Z when X = 80 subtracted by the p-value of Z when X = 30.
X = 80
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{80 - 50}{15}[/tex]
[tex]Z = 2[/tex]
[tex]Z = 2[/tex] has a p-value of 0.9772
X = 30
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{30 - 50}{15}[/tex]
[tex]Z = -1.33[/tex]
[tex]Z = -1.33[/tex] has a p-value of 0.0918
0.9772 - 0.0918 = 0.8854
0.8854*100% = 88.54%
88.54% of shoppers are expected to spend between $30 and 80 per week.
Hopefully the photo posted...
The teacher of a statistics class records the heights (in inches) of his students and draws a box-and-whisker plot to look over the data collected. This box-and-whisker plot shows theresult. (a) What is the median height? (b) What is the range of heights?
Answer:
a) Median Height = 66 inches
b) Range of Heights = 18 inches
Step-by-step explanation:
a) The median in a box-and-whisker plot is the second quartile, located between the first and third quartiles indicated by the dashed line. Therefore, the median height is 66 inches.
b) The range in a box-and-whisker plot uses the same process of finding the range of a set of data. You find the difference between the maximum and the minimum values of the data. Therefore, the range of heights is 77 - 59 = 18 inches.
Solve for x in the diagram below
Answer:
26.67
Step-by-step explanation:
