The figure shows a graph of the function fx in the coordinate plane. f2 is greater than g2.
As the graph of function f(x) is a parabola, so that the equation of function f(x) is:
f(x) = [tex]ax^2+bx+c[/tex]
As it can be seen in thee figure, the graph of function f(x) cross points (0;8) ;(-2; 0) and (4;0)
=> f(0) = 8; f(-2) = 0; f(4) = 0
We have:
f(x=0) = a x 0 + b x 0 + c = 8 => c = 8
We have:
+) 4a -2b + 8 = 0 => 2 x (4a -2b + 8) = 8a - 4b + 16 = 0 (1)
+) 16a + 4b + 8 = 0 (2)
We take (2) minus (1)
=> (16a + 4b + 8) - (8a - 4b + 16) = 0
=> 8a - 8 = 0 => a = 1
Replace a = 1 into (1)
=> 8 x 1 - 4b + 16 = 0 => b = 6
f (2) = 2^2 + 6 x 2 + 8 = 24
g (2) = 3 -2 + 2 = 3
Thus, f(2) is greater than g(2).
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on a line graph, time is usally represented by which of the following?
Time is usually represented by the x axis
a train laves los angles at 2pm, heading north at 50mph. If the next train leaves 3 hours later and heads north at 60 mph, at what time will the second train catch up with the first?
Answer:
8 am
Step-by-step explanation:
First train has a 50 m/hr x 3 hr = 150 mile head start
Second train is going 60 - 50 = 10 m/hr faster and will close this 150 mile distance
in 15 hours to catch the first train
2pm + 3 hours + 15 hours = 8 am
In 8-card poker,each player is dealt 8 card(go figure) from a standard deck of 52 cards. How many different hands can be dealt.
The number of unique 8-card hands to be dealt are752,538,150.
How to solveThe number of different 8-card hands that can be dealt from a standard 52-card deck is given by the combination formula:
[tex]C(n, k) = n! / [(n-k)! * k!][/tex]
C(52, 8) = 52! / [(52-8)! * 8!] = 52! / [44! * 8!]
Evaluating this will give the total number of different 8-card poker hands that can be dealt from a standard deck.
Using these calculations, you would find the number of unique 8-card hands to be 752,538,150.
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Which function is represented by this graph?
Answer:
its A
Step-by-step explanation:
Which of the following is Playfair's axiom?
A. A straight line segment can be drawn between any two points.
B. A circle can be drawn with any center and radius.
C. Through a given point not on a given line, there is exactly one line
parallel to the given line.
D. All right angles are equal to one another.
Answer:
C. Through a given point not on a given line, there is exactly one line parallel to the given line.
Step-by-step explanation:
hope i helped
Answer:
Look down
Step-by-step explanation:
Thanks for reaching out for assistance! Based on the context you provided, it seems like the correct answer is C. Playfair's axiom states that there is exactly one line parallel to a given line that can be drawn through a point not on it. I hope this helps! Let me know if there's anything else I can do for you.
What value of x satisfies the equation −1.5x−2.7=20.1+4.5x
To solve for x in the equation −1.5x−2.7=20.1+4.5x, we need to isolate x on one side of the equation. We can do this by adding 1.5x to both sides of the equation and adding 2.7 to both sides of the equation, which gives us:
-1.5x - 2.7 + 1.5x = 20.1 + 4.5x + 1.5x
Simplifying the left side of the equation and combining like terms on the right side of the equation gives us:
-2.7 = 6x + 20.1
Subtracting 20.1 from both sides of the equation gives us:
-22.8 = 6x
Dividing both sides of the equation by 6 gives us:
x = -3.8
Therefore, the value of x that satisfies the equation is -3.8.
Apple juice costs $2.50 for 128 ounces. What is the price per ounce?
Answer: $0.0195
Step-by-step explanation: To find the price per ounce of apple juice, we need to divide the total cost by the number of ounces.
Price per ounce = Total cost / Number of ounces
Here, the total cost is $2.50 and the number of ounces is 128.
Price per ounce = $2.50 / 128 ounces
Price per ounce = $0.0195
Therefore, the price per ounce of apple juice is $0.0195, which is approximately 2 cents per ounce.
Answer: $0.0195 per ounce
Step-by-step explanation:
We will create a proportion to help us solve this question.
➜ To do this, we will set two fractions equal to each other with the dollar amount in the numerator and the ounce amount in the denominator.
[tex]\displaystyle \frac{\$2.50}{128\;ounces} =\frac{\$x}{1\;ounce}[/tex]
Cross-multiply:
128x = $2.50
Divide both sides of the equation by x:
x = $0.0195 per ounce
Use the figure below to answer the following questions.
Complete the statement: triangle AGC~triangle ___?
Complete the statement: triangle CDE~triangle ___?
What is m
What is m
What is BC?
What is DE?
Were the above figure is given, the complete sentence with regard to the triangles are
ΔAGC ~ ΔCDF
ΔCDE ~ ΔCAB
And, the length of BC is, 51
The length of DE is, 132.7
How is this so?We have to given that;
⇒ CF = 32
Hence, We get;
tan 24 = CF / DF
0.44 = 32 / DF
DF = 72.7
Thus, ΔAGC ≈ ΔCDF
Here, We have;
⇒ ΔCDE ≈ ΔCAB
In triangle BCG;
BC² = 24² + 45²
BC² = 576 + 2025
BC² = 2601
BC = 51
In triangle CEF;
⇒ EC² = CF² + EF²
⇒ 68² = 32² + EF²
⇒ 4624 = 1024 + EF²
⇒ EF² = 4624 - 1024
⇒ EF² = 3600
⇒ EF = 60
Thus, We get;
DE = DF + EF
DE = 72.7 + 60
DE = 132.7
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I thought I understood how to get the answer, but I got the second question wrong so I don't know what to do. Can anyone explain to me how to do it? I also am dyslexic and have a hard time rounding numbers. So, I dont think I understood how to round to the nearest dollar.
Answer:
$223,787
Step-by-step explanation:
r = 0.02
C = 191,000
t = 8
S = 191,000 (1 + 0.02)⁸
Follow order of operations (PEMDAS).
S = 191,000 (1.02)⁸
S = 191,000 (1.171659381)
S = 223,786.9
(We want to round to the nearest dollar, which is the ones place, so ignore all digits after the tenths place.)
Rounding, S = 223,787
What is the place value of 2 in 369.425
Step-by-step explanation:
do it yourself what do you do while teacher is teaching
do it yourself what do you do while teacher is teaching
A
0
5
4
3
2
+
2
D'
02
A
C
02.5
B
3
D
A
Determine the scale factor used to create the image.
4
9
10
11
B
12
The scale factor used to create the image is given as follows:
k = 1/4.
What is a dilation?A dilation can be defined as a transformation that multiplies the distance between every point in an object and a fixed point, called the center of dilation, by a constant factor called the scale factor.
The equivalent segment lengths for the original figure and the image are given as follows:
Original: AB = 12 - 4 = 8 units.Image: A'B' = 3 - 1 = 2 units.Hence the scale factor used to create the image is given as follows:
k = 2/8
k = 1/4.
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PLs anwser these long problems one at a time!:
(U can number them like : number 1, number 2....)
The equations are solved to get
2/5 * (1 1/4 * x - 3 1/3) - 1 1/3 x here x = 1 3/5
2 1/8 x + 3/4 x + 1/6 - 7/12 x + 5 2/3 here x = 2 6/11
0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8 here x = 1.2
How to simplify the expressions1.
2/5 * (1 1/4 * x - 3 1/3) - 1 1/3 * x
opening the parenthesis and converting to improper fraction
1/2 x - 4/3 - 4/3 x
-5/6 x - 4/3
-5/6 x = 4/3
x = 8/5
x = 1 3/5
2.
2 1/8 x + 3/4 x + 1/6 - 7/12 x + 5 2/3
adding like terms
55/24 x + 35/6 = 0
55/24 x = - 35/6
x = 28/11
x = 2 6/11
3.
0.5(x + 1.6) + 1.4(3x + 2.4) = 9.8
removing the parentheses:
0.5x + 0.8 + 4.2x + 3.36 = 9.8
4.7x + 4.16 = 9.8
4.7x = 5.64
x = 1.2
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During a three days period, the stock of money, inc, gained 6 points, lost 10 points, and gained 2 points. What was the total change in points for the three days?
A = 2 points
B = 4 points
C = -6 points
D = -2 points
this is graph of y=-1/2x+10. use the graph to show the equal intervals of x vaules have equaldifferences of y values.
In the graph, differential is 4 or (p+k)-p = k as well as difference is -2 when y = 7 or y = 5, respectively.
A graph comprises a visual representation and diagram that displays facts or values in an organised manner in mathematics. The points of a graph are widely used to depict the connections between various objects. A. The difference between y = 7 or y = 5 is 4 and -2, respectively B. 4 is the difference, so (p+k)-p = k C. It differs by -2 D. Part C depends on 'k' rather than 'p,' not 'p'.
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Stefan wants to buy a toy car at the
store. The price is p dollars. He also
has to pay a 6% tax.
Write an expression to represent
how much Stefan will pay in total for
the toy car.
calculus pls help guys
Calculus a broad subject that covers many topics such as derivatives, integrals, limits, and functions.
Calculus is a branch of mathematics that focuses on the study of change and motion. It provides a framework for understanding and analyzing quantities that vary continuously. The two main branches of calculus are differential calculus and integral calculus.
Differential calculus deals with the concept of derivatives. A derivative measures how a function changes as its input (usually denoted as x) changes. Geometrically, the derivative represents the slope of a function at a particular point. It can also be interpreted as the instantaneous rate of change of a function at a given point. Derivatives have various applications, such as determining the maximum or minimum values of functions, analyzing the behavior of functions, and solving optimization problems.
Integral calculus, on the other hand, focuses on the concept of integrals. An integral is a mathematical operation that measures the accumulation of quantities or the area under a curve. It essentially reverses the process of differentiation. Integrals can be used to compute the total change or accumulation of a quantity over a given interval, find the area of irregular shapes, and solve problems involving rates of change.
Calculus plays a fundamental role in many scientific and engineering disciplines. It is used extensively in physics, engineering, economics, computer science, and many other fields to model and solve real-world problems involving continuous change. The study of calculus also forms the basis for higher-level mathematics such as differential equations, vector calculus, and multivariable calculus.
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what is the range of the function f(x)=x^2+2x+4
Answer: -3 to -infinity
Step-by-step explanation:
If 10 +30 +90+...=2657200, what is the value of n?
The number of terms n of the geometric progression is n = 12
Given data ,
Let the geometric progression be represented as A
Now , the value of A is
10 + 30 + 90 + .... = 2657200
And , let the number of terms be n
common ratio r = 30 / 10 = 3
where sum of first n terms of a GP is Sₙ = a(rⁿ-1) / ( r - 1 )
On simplifying , we get
2657200 = 10 ( 3ⁿ - 1 ) / ( 2 )
Divide by 5 on both sides , we get
3ⁿ - 1 = 5,31,440
Adding 1 on both sides , we get
3ⁿ = 5,31,441
Taking log on both sides , we get
n = 12
Hence , the number of terms of GP is n = 12
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choose the greatest number you can mutiply by 30 you can get close to but not go over 150
Answer:
If it can be exactly 150, then 50.
there’s not exactly enough info for me to solve.
please helppp!!!!!!!!!!!!!!!!!!!
The inequality in slope - intercept form is,
⇒ y ≤ x + 5
We have to given that;
The graph of the inequality is shown in image.
Let two points on the line is,
⇒ (- 5, 0) and (0, 5)
Hence, The equation of line is,
⇒ y - 0 = (5 - 0) / (0 + 5) (x + 5)
⇒ y = x + 5
Thus, The inequality in slope - intercept form is,
⇒ y ≤ x + 5
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The values of x and y are proportional. proportionality (k) and find the missing values. 2. UX x 6 15 9 y 42 200 d. X 14 y 21 6 15 3 7 8 Determine the constant of proportionality
Step-by-step explanation:
To determine the constant of proportionality (k) in a proportional relationship, we need to compare corresponding values of x and y and calculate the ratio between them.
Let's examine the given values:
2. UX: x 6 15 9 y 42 200
To find the constant of proportionality (k), we can take any pair of corresponding values and calculate their ratio. Let's choose the first pair: (6, 42).
k = y / x
k = 42 / 6
k = 7
So, the constant of proportionality (k) is 7.
Now, let's find the missing values for the second set of values:
d. X: 14 y: 21 6 15 3 7 8
Since we know the constant of proportionality is 7, we can calculate the missing values of y by multiplying each corresponding x value by 7.
Missing values for y:
- For x = 21, y = 21 * 7 = 147
- For x = 6, y = 6 * 7 = 42
- For x = 15, y = 15 * 7 = 105
- For x = 3, y = 3 * 7 = 21
- For x = 7, y = 7 * 7 = 49
- For x = 8, y = 8 * 7 = 56
Therefore, the missing values of y are: 147, 42, 105, 21, 49, and 56.
A secretary listed the frequency of calls by a patient to a doctor's office during a year, and the data is displayed in the histogram.
Which of the following best describes the spread and distribution of the data?
1. The data is skewed to the higher values because many patients call the doctor several times a day when they are sick.
2. The data is skewed to the lower values because many patients only call the doctor once or twice a year when they are sick.
3. The data is bimodal with a narrow spread because many patients call the doctor several times a day when they are sick.
4. The data is normal and has a wide spread because many patients only call the doctor once or twice a year when they are sick.
Answer:
2.
Step-by-step explanation:
The data is skewed towards 1-25. From this we can conclude that patients only call the doctor once or twice when they are sick.
A city is now 70,000. The population is decreasing, 14 years ago the population was 93,000. Use Pert to find r
The value of r which is the decay rate is calculated as: -0.0203
How to solve Growth or decay functions?The equation for "continual" growth (or decay) is given by the expression:
[tex]A = Pe^{rt}[/tex]
where:
A is the ending amount,
P is the beginning amount (principal, in the case of money)
r is the growth or decay rate (expressed as a decimal),
t is the time (in whatever unit was used on the growth/decay rate).
We are given that:
A = 70000
P = 93000
t = 14
Thus:
70000 = 93000 * [tex]e^{14r}[/tex]
70/93 = * [tex]e^{14r}[/tex]
14 r = In (70/93)
14r = -0.2841
r = -0.0203
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2.30 1.99 sales tax 8%
Answer:
$2.48 and $2.15, respectively
Step-by-step explanation:
2.30 * 1.08 = 2.48
1.99 * 1.08 = 2.15
A higher credit score reduces your fixed costs because you ____.
A. will pay lower interest rates
B. can have more credit cards
C. are able to carry more debt
D. can reduce the amount you need to borrow
A higher credit score reduces your fixed costs because you will pay lower interest rates. That is option A.
What is a higher credit score?A higher credit score is one of the factors that are being considered by banks or lenders before one is being viewed as being legible to borrow money.
This is soo because a higher credit score will reduce the lending interest rates of the individual because it shows such will pay back the borrowed money as soon as possible.
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Which method is best to display the data?
The method of bar chart is appropriate for representation.
According to the given data,
The most effective way to present the data is in a bar chart.
An effective visual representation of categorical data that shows the frequency or count of each category is a bar chart.
The length of each bar would reflect the frequency or count of each score, and the categories would be the test results in this instance.
It would be a simple and unambiguous approach to compare the various test results.
These are the three key characteristics of bar graphs:
The bar graph makes it simple to compare various sets of data among various groups.
The relationship is depicted using two axes, with the discrete values on one axis and the categories on the other.
The graph displays the key alterations in the data over time.
Hence,
Bar chart method should be used.
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For the line that passes through the points A(5, 8, -2) and B(-1, 3, 5), find:
a. a vector equation.
b. parametric equations.
c. Symmetric equations
The symmetric equations for the line are:
(36x + 40y - 28z - 100) / 0 = (x-5) / -6 = (y-8) / -5 = (z+2) / 7
To find the parametric equations for the line passing through A(5, 8, -2) and B(-1, 3, 5), we can use the vector equation:
r = A + t(B-A)
where r is the position vector of any point on the line, t is a scalar parameter, and A and B are the given points. Substituting the values, we get:
r = (5, 8, -2) + t((-1)-5, 3-8, 5-(-2))
r = (5, 8, -2) + t(-6, -5, 7)
The parametric equations for the line are:
x = 5 - 6t
y = 8 - 5t
z = -2 + 7t
To find the symmetric equations, we can use the fact that any point on the line is equidistant from points A and B. Thus, the distance from a point (x, y, z) to A must be the same as the distance from the same point to B. Using the distance formula, we get:
√[(x-5)² + (y-8)² + (z+2)²] = √[(x+1)² + (y-3)² + (z-5)²]
Squaring both sides and simplifying, we get:
36x + 40y - 28z - 100 = 0
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Use the formula A = bh to find the area, in square meters, of the parallelogram below.
9
12 m
m²
18m
The Parallelogram area is 96 square meters.
We have,
The area of a parallelogram is given by the formula A = bh, where b is the length of the base and h is the height.
In this case,
The base of the parallelogram is the length of one of its parallel sides, which is 12 m.
The height of the parallelogram is given as 8 m.
Therefore, the area of the parallelogram is:
A = bh
A = 12 m x 8 m
A = 96 square meters
Thus,
The Parallelogram area is 96 square meters.
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discuss four contributing factors tha may lead to learners abusing the rights of others at school
please help with this
The solution of the function is as follows:
f(3) = 16
h(0) = -4
h(g(x)) = 3x + 5
g(y) = y + 3
f(x) - h(x) = x² - x + 5
How to solve function?A function relates input and output. In other words, a function is an expression that defines a relationship between one variable (the independent variable) and another variable(dependent variable).
Therefore, let's solve the function as follows:
f(x) = x² + 2x + 1
g(x) = x + 3
h(x) = 3x - 4
Therefore,
f(3) = (3)² + 2(3) + 1 = 9 + 6 + 1 = 16
h(0) = 3(0) - 4 = -4
h(g(x)) = 3(x + 3) - 4 = 3x + 9 - 4 = 3x + 5
g(y) = y + 3
f(x) - h(x) = x² + 2x + 1 - (3x - 4) = x² + 2x + 1 - 3x + 4 = x² - x + 5
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