The solution to the two functions f(x) = 3ˣ and g(x) = -x + 4 is, 1
What are functions?Function is a relation between a set of inputs and a set of outputs which are permissible. In a function, for particular values of x we will get only a single image in y. It is denoted by f(x).
Vertical line test:-
Whenever we want to check whether a given expression is a function or not we can apply a vertical line test, in this test we check for a single image of x , we are getting a single image or more.
If we get more images then it will not be a function.
For example, let us take, y² = 4ax
y = ±√4ax
For single value of x we get two values of y
Hence, it will not be a function.
Given that,
The number of visitors increases exponentially as the temperature increases, and this situation can be expressed by the function
f(x) = 3ˣ
The number of people who leave the park early depending on the change in temperature, and it can be expressed by the function,
g(x) = −x + 4
the solution of both the graphs = ?
the intersection of the two curves of graphs of the functions is the solution,
Basically, it represent that,
both function have same value for particular value of x,
So,
when both functions have same value that will be our solution,
f(x) = 3ˣ
g(x) = −x + 4
it is shown in the graph, both functions are intersecting each other at x = 1
f(1) = 3
g(1) = −1 + 4 = 3
Hence, the solution for the equations is 1
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A rectangular field is four times as long as it is wide. If the perimeter of the field is 560 yards, what are the field’s dimensions?
Answer:
Width=56 yards
length=224 yards
Step-by-step explanation:
let:
Width=x
length= x*4= 4x
perimeter = 2*x + 2*4x
working
[tex](x \times 2) + (4x \times 2) = 560[/tex]
[tex]2x + 8x = 560[/tex]
[tex]10x = 560[/tex]
[tex] \frac{10x}{10} = \frac{560}{10} [/tex]
[tex]x = 56[/tex]
[tex]4x = 56 \times 4 = 224[/tex]
width =56 yards
length = 224 yards
Which, if any, of the following equations are quadratic equations? How do you know?
x2=10
6x2+2=80
4x3-6=25
2(x+4)2=65
(5x-2)=3x4
Answer:
(5x-2)=3x4
Step-by-step explanation:
add that's in the () first
Answer: .
Step-by-step explanation:
Clothing Online An online clothing company sells custom sweatshirts. The company charges $2.50 for shipping plus $6.50 for each sweatshirt. Write a linear function rule that models the total cost y (in dollars) for any number of sweatshirts x.
Use pencil and paper. Describe how the linear function rule would change if the shipping charge applied to each sweatshirt.
When there is a single shipping charge, the linear function rule is y =_____
The linear function for the cost is:
f(x) = 6.5*x + 2.5
How to write the linear function?A general linear function is something like:
y = a*x + b
Where a is the slope and b is the y-intercept.
Here we know that there is a fixec charge of $2.50 plus $6.50 for each sweatshirt, then if you buy x of these, the cost will be modeled by the linear function below:
f(x) = 6.5*x + 2.5
The slope is the cost of each item and the y-intercept is the fixed cost.
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what is x-5>-12 solve for x
Answer:
x>-7
Step-by-step explanation:
x-5>-12
x>5-12
x>-7
x > -7.
Step-by-step explanation:1. Write the expression.[tex]x-5 > -12[/tex]
2. Add "5" ob both sides of the equation.[tex]x-5+5 > -12+5\\ \\x > -7[/tex]
3. Verify your answer.If x >-7 is the correct answer, then substituting x by "-7" in the inequation should make the inequation return the same value on both sides of the inequality symbol (>).
Substituting:
[tex](-7)-5 > -12\\ \\-12 > -12[/tex]
That's correct! x > -7 is the correct answer.
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Question 5 For the pair of functions, find the indicated sum, difference, product, or quotient. f(x) = 2-9x, g(x) = -5x² + 9 Find (f + g)(x).
The correct answer is (f + g)(x)= -5x²-9x+11.
What is function?Function, in mathematics, an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable.
here, we have,
you have two functions f(x) and g(x) the sum of them f(x) + g(x) is represented as (f + g)(x)
then if our functions are f(x) =2-9x,
and g(x) = -5x² + 9
then (f + g)(x)
= f(x) + g(x)
= -5x²-9x+11
Hence, The correct answer is -5x²-9x+11.
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eighty-four percent of products come off the line ready to ship to distributors. your quality control department selects 12 products randomly from the line each hour. let x represent the number of these products that are within specifications. looking at the binomial distribution, if x is less than , the outcome would be considered unusual, and the production line should be repaired. group of answer choices fewer than 7 fewer than 6 fewer than 9 fewer than 8
If 84% of products come off the line ready to ship to distributors, then the probability of a product being within specifications is 0.84.
Since we are selecting 12 products randomly from the line each hour, the number of products within specifications (x) follows a binomial distribution with parameters n = 12 and p = 0.84.
Using a binomial cumulative distribution function (CDF), we can calculate the probability that x is less than a certain value. For example, if x is less than 7, the probability of this outcome would be considered unusual and the production line should be repaired.
So, the answer is "fewer than 7".
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find the values of the sine, cosine, and tangent of the angle a . you may assume angle c is a right triangle.
For the given triangle find the exact value for cos(A) will be 5/13.
The sine is the side that faces away from the angle being examined.
The sine of the angle under consideration is called the cosine.
or the hypotenuse divides the opposite side to get the sine.
or the hypotenuse divides the adjacent side by the cosine.
Cosine is adjacent/hypotenuse, so keep that in mind. The values provided for this triangle can be plugged in.
Cos(A) = 5/13.
Avoid using a decimal response because rounding would be required and you wouldn't be providing an accurate figure. 5/13 as your response.
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The complete question
For the given triangle find the exact value for cos(A) assume angle C is a right angle
Use this table to find all the missing expense values.
Expenses Budget Percent of Budget
Utilities
5%
Labor
15%
Supplies
30%
Rent $2,400 40%
Advertising
10%
TOTAL
100%
The missing expense values are given as follows:
Utilities: $300.Labor: $900.Supplies: $1800.Advertising: $600. Total: $6000.How to obtain the missing expenses?The missing expenses are obtained applying the proportions in the context of this problem.
The rent expense of $2,400 is 40% of the total expenses, hence the total expenses are given as follows:
0.4x = 2400
x = 2400/0.4
x = $6000.
The utilities expenses are 5% of that, hence:
0.05 x 6000 = $300.
The labor expenses are 15% of the total, hence:
0.15 x 6000 = $900.
The supplies expenses are 30% of the total, hence:
0.3 x 6000 = $1800.
The advertising expenses are 10% of the total, hence:
0.1 x 6000 = $600.
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A+b+c=90 and 12a+10b+6c=870 solve for a,b, and c
Answer:
Step-by-step explanation:
You can solve for a, b, and c by using a system of linear equations.
Starting with the first equation:
a + b + c = 90
You can isolate a by subtracting b and c:
a = 90 - b - c
Next, substitute the expression for a into the second equation:
12(90 - b - c) + 10b + 6c = 870
Expanding the equation:
1080 - 12b - 12c + 10b + 6c = 870
Combining like terms:
1070 - 2b + -6c = 870
Adding 2b and 6c to both sides:
1070 = 870 + 2b + 6c
Subtracting 870 from both sides:
200 = 2b + 6c
Dividing both sides by 2:
100 = b + 3c
Finally, subtracting 3c from both sides:
100 - 3c = b
To find c, substitute the expressions for a and b back into the first equation:
a + b + c = 90
90 - b - c + b + c = 90
90 - c = 90
-c = 0
Therefore, c = 0.
To find b, substitute c = 0 into the expression for b:
100 - 3c = b
100 = b
Therefore, b = 100.
Finally, to find a, substitute b = 100 and c = 0 into the expression for a:
a = 90 - b - c
a = 90 - 100 - 0
a = -10
Note that negative values for a, b, and c are possible, but not necessarily meaningful for this specific problem or context.
The solution is:
a = -10
b = 100
c = 0
to study this, you have sleep-deprived subjects (such as parents of newborn babies or night-shift workers) record the number of minutes they sleep each night and take a series of motor performance assessments, with 1 minute being the smallest unit on the scale. suppose the first subject sleeps 250 minutes. determine the real limits of 250.
the real limits are; Lower Real Limits = 249.5 and Upper Real Limits = 250.5
Given the data in the question;
1 minute being the smallest unit on the scale
so we say; 1/2 which 0.5 minutes which we will use to calculate pur real limits time;
given that; the first subject sleeps 250 minutes
so
Lower Real Limits will be;
Lower Real Limits will = 250 - 0.5 = 249.5
Also our Upper Real Limits will be;
Upper Real Limits = 250 + 0.5 = 250.5
Therefore; the real limits are;
Lower Real Limits = 249.5
Upper Real Limits = 250.5
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Please help me I’m begging you I’m so confused
Isosceles triangles have two equal angles. The two equal angles are the bottom left and bottom right.
X = 28
Y = 152
See picture for explanation
- Jeron
The table gives the volume of cylinders where the height is a function of the radius of the base. Given radius, r, the height can be modeled with the function h(r), the base area of the of the cylinder with the function B(r), and the volume of the cylinder with the function V(r).
The volume of the cylinder will be 138.2 inches³
How to calculate the volumeFrom the information, the shape has a height 3 in more than 4 times the radius of the cylinder's base.
The volume of a cylinder is equal to V = πr²h
where
r is the radius of the base
h is the height
In the problem, h = 3 + 4r
r = 2 inches
To calculate h, h = 3 + 4 × 2
h = 11 inches
The volume of a cylinder is equal to:
v = πr²h
v = π × 2² × 11
v = 44π inches³
V = 138.2 inches³
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Write a function rule for the volume of the cylinder shown at the right with a height 3 in more than 4 times the radius of the cylinder's base. What is the volume of the cylinder when it has a radius of 2 in?
Determine the equation of the parabola of this graph.
taking a looksie at the picture above, we can see the parabola has zeros/solutions at x = -2 and x = 1, we can also see that it passes through (0 , 2) as well, so
[tex]\begin{cases} x = -2 &\implies x +2=0\\ x = 1 &\implies x -1=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a( x +2 )( x -1 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that} \begin{cases} x=0\\ y=2 \end{cases} \\\\\\ a ( 0 +2 )( 0 -1 ) = 2\implies -2a=2\implies a=\cfrac{2}{-2}\implies \boxed{a=-1} \\\\[-0.35em] ~\dotfill\\\\ -(x+2)(x-1)=y\implies -(x^2+x-2)=y\implies {\Large \begin{array}{llll} -x^2-x+2=y \end{array}}[/tex]
Check the picture below.
Which of the following is a solution to this inequality?
y less than two thirds times x plus 2
(0, 3)
(−3, 1)
(3, 5)
(1, 2)
The point that is a solution if the inequality:
y < (2/3)*x + 2
is (1, 2).
Which one is a solution of the inequality?Here we want to find a solution for the inequality below:
y < (2/3)*x + 2
To check if an ordered pair is a solution, then we need to replace the values of the ordered point and check if the inequality is true.
If we try with the first point we will get:
3 < (2/3)*0 + 2
3 < 2
That is false.
The correct option is (1, 2)
2 < (2/3)*1 + 2
2 < 8/3
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Dan plays basketball on his high school team. During
the last game Dan scored 18 points, while for the
season he averages 20 points per game. What percent
of Dan's average did he score during this game?
The percent of Dan's average did he score during this game is 11.11%
What percent of Dan's average did he score during this game?Dan's score in the high school basketball team during last game= 18 points
Dan's score in the high school basketball team during this season = 20 points
Percent of Dan's score during this game = (20 - 18) / 18 × 100
= 2/18 × 100
= 11.11%
In conclusion, Dan scored an average percentage of 11.11% during this game.
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. the creators of spss statistics have combined ratio and interval variables into one category that they refer to as
Numeric Variables, as they are referred to by the creators of SPSS Statistics, are a combination of ratio and interval variables.
Numeric Variables are a type of data used in statistical analysis, and are a combination of both ratio and interval variables. Ratio variables are those that can be measured, counted, and compared, and include ratios and differences between values. Interval variables are those that measure an amount, such as temperature, but are not able to be compared in terms of ratios or differences. The creators of SPSS Statistics refer to these combined variables as Numeric Variables. Numeric Variables can be used to measure and compare data, as well as to create graphs and charts. They are particularly useful in understanding the relationships between different sets of data.
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the united states of of representatives has 35 more members than four times the number of members in the unites states senate. define a variable and write an expression to represent the number of members in the house of representatives. Then find the number of members in the house of representatives, if there 100 members in the senate.
There are 435 members in the House of Representatives.
What is the algebraic expression?Algebraic expressions are mathematical statements with a minimum of two terms containing variables or numbers.
Let's call the number of members in the Senate "s".
The expression for the number of members in the House of Representatives is "h".
According to the problem, there are 35 more members in the House than four times the number of members in the Senate, so the expression for the number of members in the House is:
h = 4s + 35
If there are 100 members in the Senate, then we can substitute this value into the expression:
h = 4 × 100 + 35
h = 435
So, there are 435 members in the House of Representatives.
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How much water should be added to 14mL of 9% alcohol solution to reduce the concentration to 7%? We should add mL.
The water that should be added to 14mL of 9% alcohol solution to reduce the concentration to 7% is 4ml.
How much more water must be added to reduce a concentration?Here; In this problem we have a concentration problem, represented by the volume of the solvent divided by the volume of the entire solution. The initial and final concentrations of the solutions are presented in the following formulas;
Given;
14mL of 9% alcohol solution.
Initial concentration;
9/ 100 = x / 14
x = 63/50
Final concentration;
7 / 100 = x / (14 + y)
(14 + y)=x*100/7
y=18-14
y=4
Therefore, water must be added to reduce the concentration will be 4ml.
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Write by which rule you know the triangles are congruent, or write CNBD (Cannot Be Determined). Segments and angles are congruent only if marked congruent. FAD congruent to FED by
The congruency rule that shows us that ΔBLK ≅ ΔACK by; SAS Congruency Postulate
How to determine the Congruency Theorem?The image showing the triangles tell us that;
∠BKL ≅ ∠CKA by opposite angles theorem
Likewise we see that BL is parallel to AC and as such;
∠BLK ≅ ∠ACK by alternate angles theorem
Similarly, we will also see that;
∠LBK ≅ ∠CAK by alternate angles theorem
Finally, we see that BL ≅ CA and as such we can conclude that ΔBLK is congruent to ΔACK by SAS Congruence Postulate
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Danielle is working on practice problems and must translate the verbal expression "4 less than twice a number" in to an algebraic expression. Write the algebraic expression that Danielle should write. Type your expression with no spaces.
The translation of the verbal expression "4 less than twice a number" in to an algebraic expression is 2n - 4.
What is an expression?One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.
Given:
Danielle is working on practice problems and must translate the verbal expression "4 less than twice a number" in to an algebraic expression.
Let the number is n.
The phrase can be expressed as,
2n - 4.
Therefore, the expression is 2n - 4.
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is 5/11 closer to 0,1/2,1
Based on the given task content; 5/11 is closer to 1/2.
How to solve fractions?A fraction is a number which has a numerator and a denominator. A numerator refers to the upper or top value while a denominator refers to the lower or bottom value of a fraction.
5/11
= 0.454545454545454
Approximately,
= 0.5
1/2 = 0.5
Hence, 1/2 is closer to 5/11
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i have a fair coin and a two-headed coin. i choose one of the two coins randomly with equal probability and flip it. given that the flip was heads, what is the probability that i flipped the two-headed coin? enter your answer using four decimal places.
With equal probability and flip it, given that the flip was heads, the probability that I flipped the two-headed coin is: 0.6667
Let's call the event of flipping the fair coin "F" and the event of flipping the two-headed coin "T".
The probability of flipping heads given that we flipped the fair coin is 1/2, so P(heads | F) = 1/2.
The probability of flipping heads given that we flipped the two-headed coin is 1, so P(heads | T) = 1.
The probability of flipping the fair coin is 1/2 and the probability of flipping the two-headed coin is 1/2, so P(F) = P(T) = 1/2.
Using Bayes' Theorem, we can find the probability that we flipped the two-headed coin given that the flip was heads:
P(T | heads) = (P(heads | T) * P(T)) / (P(heads | T) * P(T) + P(heads | F) * P(F))Plugging in the values, we get:
P(T | heads) = (1 * 1/2) / (1 * 1/2 + 1/2 * 1/2) = 2/3So the probability that we flipped the two-headed coin given that the flip was heads is 2/3, or approximately 0.6667.
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The table shows the number of students graduating from a university in selected years. Use a calculator to write a cubic model for the number of graduates in a given year since 1990. Then use the model to estimate the number of graduates in 2001.
P(x) ≈ 27.13x3 − 473.44x2 + 2829.33x − 4381.69
The estimated the number of graduates in 2001 is 5,565.
P(x) ≈ −473.44x2 + 2829.33x − 4381.69
The estimated the number of graduates in 2001 is 4,133.
P(x) ≈ 473.44x2 − 2829.33x + 4381.69
The estimated the number of graduates in 2001 is 3,535.
P(x) ≈ −27.13x3 + 473.44x2 − 2829.33x + 4381.69
The estimated the number of graduates in 2001 is 2,504.
The cubic regression equation is y = 27.13x^3 - 473.44x^2 + 2829.33x - 4381.69 and the estimated the number of graduates in 2001 is 5565
How to determine the cubic regression equationFrom the question, we have the following parameters that can be used in our computation:
See attachment
Using a graphing calculator, we have the following summary:
a = -4381.6892b = 2829.3314c = -473.4406d = 27.1349Standard Error of Regression: 81.5267Coefficient of determination R²: 0.9978The model from the above summary is
y = 27.1349x^3 - 473.4406x^2 + 2829.3314x - 4381.6892
Approximate
y = 27.13x^3 - 473.44x^2 + 2829.33x - 4381.69
In the year 2001, we have
x = 11
So, we have
y = 27.13 * 11^3 - 473.44 * 11^2 + 2829.33 * 11 - 4381.69
Evaluate
y = 5565
The estimated the number of graduates in 2001 is 5565
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(-1,4), slope =-2
Write the point slope form of the equation of the line through the given point with the given slope. Then, rewrite the equation into slope intercept form.
The point slope form of the equation of the line through the given point with the given slope is y - 4 = -2(x + 1).
The equation in slope intercept form is y = -2x + 2.
What is the point-slope form?Mathematically, the point-slope form of a straight line can be calculated by using this mathematical expression:
y - y₁ = m(x - x₁)
Where:
m represents the slope.x and y are the points.At data point (-1, 4), a linear equation of this line can be calculated in point-slope form as follows:
y - y₁ = m(x - x₁)
y - 4 = -2(x - (-1))
y - 4 = -2(x + 1)
Next, we would rewrite the equation in slope-intercept form as follows;
y - 4 = -2(x + 1)
y = -2x - 2 + 4
y = -2x + 2
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I need help with the 2 questions. What is the mean age of the employees to the nearest year?
What is the median age of the employees?
the distribution of the number of siblings for students at a large high school is skewed to the right with mean 1.8 siblings and standard deviation 0.7 sibling. a random sample of 100 students from the high school will be selected, and the mean number of siblings in the sample will be calculated.
The mean number of siblings for the sample of 100 students is likely to be close to 1.8 siblings, with a standard deviation of 0.7/√100 = 0.07 siblings.
A skewed distribution is one in which the data deviates from the normal distribution and has a longer tail on one side. In the case of the number of siblings, the distribution is skewed to the right, meaning that there are more students with higher numbers of siblings. The mean of 1.8 siblings and standard deviation of 0.7 sibling indicate the average and spread of the number of siblings in the entire student population of the high school. When a random sample of 100 students is selected, the mean number of siblings in the sample will be calculated. This mean will provide an estimate of the mean of the population, but there is still a chance of sampling error.
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Find a formula for the piecewise function where the taxable income is the input, and the tax is the output using the table.
PLEASE HELP I AM REALLY STRUGGLING WITH THIS
I have added a photo of the table.
The piecewise function of the tax expressed below
How to determine the piecewise functionFrom the question, we have the following parameters that can be used in our computation:
The table of values
To determine the piecewise function, we make use of the following variables:
x = taxable income
f(x) = tax
Using the above and the table of values as guides, we have the following:
f(x) = 0.1x, 0 ≤ x ≤ 9700
f(x) = 970 + 0.12(x - 970), 9701 ≤ x ≤ 39475
f(x) = 4543 + 0.22(x - 39475), 39476 ≤ x ≤ 84200
f(x) = 14382.5 + 0.24(x - 84200), 84201 ≤ x ≤ 160725
f(x) = 32748.5 + 0.32(x - 160725), 160726 ≤ x ≤ 204100
f(x) = 46628.5 + 0.35(x - 204100), 204101 ≤ x ≤ 510300
f(x) = 153798.5 + 0.37(x - 510300), x > 510300
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the bearing of point B from point A is 237 find the bearing from A to B
The bearing from point point A to point B is given as follows:
57º.
How to obtain the bearing between the two points?From the text in this problem, the bearing from point B to point A is given as follows:
237º.
To obtain the inverse bearing, that is, the bearing from point A to point B, we must subtract the bearing from point B to point A given in this problem by 180º, as follows:
237 - 180 = 57º.
Hence the bearing from point point A to point B is of 57º.
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Need to write an equation
A survey stopped men and women at random to ask them where they purchased
groceries, at a local grocery store or online. Results are shown in the table below, but
some values are missing. Fill in the missing values.
Answer:
1. Women
Store
66-34= 32
Online
13
Total
32+13= 45
2. Men
Total
34+9=43
3. Total
online
13+9=22
total
66+22= 88