the graph of f(x)=x is shown on the coordinate plane. function g is a transformation of f as shown below. g(x)=f(x-5) graph function g on the same coordinate plane.
Answers
The graph of function g(x) = f(x - 5) on the same coordinate plane as f(x) = x is obtained by shifting f(x) five units to the right.
To graph the function g(x) = f(x - 5) on the same coordinate plane as f(x) = x, we need to apply the transformation to each point on the graph of f(x).
Let's start by understanding the function f(x) = x. This is a simple linear function where the value of y (or f(x)) is equal to the value of x. It passes through the origin (0, 0) and has a slope of 1, meaning that for every increase of 1 in x, y also increases by 1.
Now, let's consider the transformation g(x) = f(x - 5). This transformation involves shifting the graph of f(x) to the right by 5 units. This means that every point (x, y) on the graph of f(x) will be shifted horizontally by 5 units to the right to obtain the corresponding point on the graph of g(x).
To graph g(x), we can apply this transformation to a few key points on the graph of f(x). Let's choose some x-values and find their corresponding y-values for both f(x) and g(x).
For f(x) = x:
When x = 0, y = 0
When x = 1, y = 1
When x = 2, y = 2
Now, to obtain the corresponding points for g(x), we need to subtract 5 from each x-value:
For g(x) = f(x - 5):
When x = 0, x - 5 = -5, y = -5
When x = 1, x - 5 = -4, y = -4
When x = 2, x - 5 = -3, y = -3
Now, let's plot these points on the coordinate plane and connect them to visualize the graph of g(x):
The graph of f(x) = x:
The graph of g(x) = f(x - 5):
As you can see, the graph of g(x) = f(x - 5) is a shifted version of the graph of f(x) = x. It has the same slope of 1, but all the points are shifted horizontally to the right by 5 units. The point (0, 0) on the graph of f(x) becomes (-5, -5) on the graph of g(x), and so on.
This transformation is useful for shifting functions horizontally, allowing us to study how changes in the input affect the output.
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Related Questions
Evaluate (-9)+9
please
Answers
The answer for this question is 0
Kyle found the product of two rational expressions and identified the excluded values of the expression. However, he made a mistake in his work and included an extra number in his list of excluded values. His work is shown below.
Select the step where Kyle made his first mistake. Then select the number that should not be included in the list of excluded values.
Answers
Answer:
Step-by-step explanation:
Mistake in step 3 the (2x+1) and the (x-1) both cancel out but the other binomials (x + 3) and (x - 3) are different so don't cancel out.
Step 3 should be 3(x-3) / 4(x+3)
3 should not be an excluded value.
Enter the equation of the circle described below.
Center (5,2), radius = 3
Answers
Answer:
(x - 5)² + (y - 2)² = 9
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r the radius
Here (h, k ) = (5, 2 ) and r = 3 , then
(x - 5)² + (y - 2)² = 3² , that is
(x - 5)² + (y - 2)² = 9
George
makes $5 per autograph, (a), and $8 per hour working as an actor (c) at a local theater. He needs $730 for rent. Select an appropriate inequality
below that would show how much he needs from each source of income to have enough for rent.
Answers
This inequality states that Max needs to make at least $730, which is the amount of his rent, from the combination of his earnings from autographs and earnings from working at the theater.
Let's use the variables "a" and "c" to represent the number of autographs and hours worked as an actor, respectively. The amount of money Max makes from autographs is $5a and the amount of money he makes from working at the theater is $8c. To have enough money to pay for rent, his total earnings must be at least $730.
Therefore, the appropriate inequality is:
5a + 8c ≥ 730
what is number?
In mathematics, a number is a mathematical object used to count, measure, and label. There are different types of numbers, including natural numbers, integers, rational numbers, irrational numbers, real numbers, and complex numbers. Natural numbers are the counting numbers (1, 2, 3, 4, 5, ...), while integers include the counting numbers and their negative counterparts (-1, -2, -3, -4, -5, ...). Rational numbers are numbers that can be expressed as a fraction of two integers, and irrational numbers cannot be expressed as a fraction of two integers. Real numbers include both rational and irrational numbers, while complex numbers are numbers that can be written in the form a + bi, where a and b are real numbers, and i is the imaginary unit, equal to the square root of -1.
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Your family's car can hold 20 gallons of gas. If you use .5 gallons of gas a day, how many gallons do you use in 10 days
Answers
find the volume of the largest rectangular box with edges parallel to the axes that can be inscribed in the ellipsoid(x^2/4) + (y^2/64) + (z^2/49) = 1Hint: By symmetry, you can restrict your attention to the first octant (where x,y,z=0), and assume your volume has the form V=8xyz. Then arguing by symmetry, you need only look for points which achieve the maximum which lie in the first octant.What is the maximum volume?
Answers
The volume of the rectangular box is given by using the Lagrangian multiplier theorem is 172.435 cubic units.
It states that any local maxima or any local minima of the function are calculated under the equality constraints.
The equation of ellipsoid is given as,
\(\frac{x^2}{4} +\frac{y^2}{64} +\frac{z^2}{49} =1\)
Let the edges of the required rectangular box be x, y, and z.
Then, the volume of the box in the first quadrant is V = xyz
Then we have,
\(\phi(x,y,z) = \frac{x^2}{4} +\frac{y^2}{64} +\frac{z^2}{49} -1\)
By the Lagrange multiplier,
\((V_x,V_y,V_z) = \lambda (\phi_x, \phi_y,\phi_z)\\\\(yz,xz,xy)=\lambda(\frac{2x}{4},\frac{2y}{64},\frac{2z}{49} )\\\\xyz = \lambda\frac{x^2}{2},xyz =\lambda\frac{y^2}{32} ,xyz=\lambda\frac{2z^2}{49} \\\\x^2 = 2k, y^2=32k,z^2=49k/2\)
Solving for k we have the value of k as k = 2/3.
Put k=2/3 in equation 2, we have
x² = 2*2/3 , y² = 32*2/3, z² = 49/2*2/3
x =±2/√3 , y= ±8/√3 , z = ±7/√3
Then the volume of the rectangular box will be
Volume = \(\frac{2}{\sqrt{3} } \frac{8}{\sqrt{3} } \frac{7}{\sqrt{3} }\)
Volume = 172.435 cubic units.
Therefore, the value of volume of the rectangular box is 172.435 cubic units.
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Evaluate the expression if b=3 and c=1/3.
3c / (2b²)
Answers
After evaluation we get the above expression 1/18
What is mathematical expression?It is the mathematical statement that expresses the method of a mathematical operation in a symbolic way. An expression is developed based on two or more terms along with operator. The terms are variables and numbers. In a word, an expression is either combination of numbers, operators or numbers, variables, operators.
How to evaluate the above expression?we are given an expression
3c/ (2b²)
the value of b and c are also given, b= 3 and c = 1/3
The expression is written in fractional form that has 2 numbers and 2 variables. The number are 2 and 3, variables are c and b
The numerator 3c and the denominator 2b²
if we put the value of b and c
(3×1/3) / (2×9) =1/18
hence the result 1/18
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The cost of 4 pounds of chocolate is $18.24. What is the constant
of proportionality that relates the cost in dollars, y, to the number
of pounds, x?
a. $18.24
b. $4.56
c. 4
d. Not Here
Help plss
Answers
Solve a = b - 4/ c for b.
Answers
Answer:
ac + 4 = b
Step-by-step explanation:
Step 1: Write equation
a = (b - 4)/c
Step 2: Multiply both sides by c
ac = b - 4
Step 3: Add 4 on both sides
ac + 4 = b
Answer:
b=a + 4/c
Step-by-step explanation:
Simplify both sides of the occasion.
The point ( ¯ 2 , 6 ) is plotted on a coordinate plane. Which statements are true? Select the two statements that are true. A. The reflection point across the y-axis is ( 2 , 6 ) . B. The reflection point across the y-axis is ( 2 , ¯ 6 ) . C. The reflection point across the y-axis is ( ¯ 2 , ¯ 6 ) . D. The reflection point across the x-axis is ( 2 , 6 ) . E. The reflection point across the x-axis is ( 2 , ¯ 6 ) . F. The reflection point across the x-axis is ( ¯ 2 , ¯ 6 ) .
Answers
Answer:The two true statements are:
A. The reflection point across the y-axis is (2, 6).
D. The reflection point across the x-axis is (¯2, ¯6).
Step-by-step explanation:
Answer:
The two true statements are:
A. The reflection point across the y-axis is (2, 6).
D. The reflection point across the x-axis is (¯2, ¯6).
Step-by-step explanation:
A function can only have one transformation
happen to it.
True
False
Answers
Answer:
False
Step-by-step explanation:
You can transform a function many times
:)
can someone post the back of the paper on Quiz 3-1 Parallel Lines, Transversals, and Special Angle Pairs
Answers
The following statements are true:
Segment DEF is parallel to ABC
The line segment AB is parallel to DE
Line FC is parallel to AD
the line that is skewed to DE is BC
What is geometry?One of the first areas of mathematics is geometry, along with arithmetic. It is concerned with spatial characteristics like the separation, shape, size, and relative placement of objects.
The given diagram is a triangular prism. From the diagram, some of the sides are parallel to each other (that is facing each other directly)
Some of the lines are also parallel to each other. From the given diagram, the sides that are parallel to each other are;
DEF is parallel to ABC
CADF is parallel to CBEF
For the lines, the lines that are parallel to each other are:
AD is parallel to BE
AB is parallel to DE
FC is parallel to AD
Skew lines are straight lines that do not intersect and are not in the same plane. Hence the line that is skewed to DE is BC
The missing image is attached with the answer below.
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A square and a rectangle have diagonals of 52 cm. The rectangle has a side of 20 cm. Which polygon has the largest area? Which polygon has greater perimeter? Explain.
Answers
The polygon with greater area is the square and that with greater perimeter is the rectangle, this is so because the length of sides of the square differ from that of the rectangle
How to determine the parametersFrom the information given, we have that:
Diagonal of rectangle and square is 52cmSide of the rectangle is 20cmFormula for perimeter of a rectangle
Perimeter = \(2l + 2 \sqrt{d^2 - l^2}\)
Perimeter = 2( 20) + 2 \(\sqrt{52^2 - 20^2}\)
Perimeter = 40 + 2 ( 48)
Perimeter = 136 cm
Perimeter of a square = 2 √2d
Perimeter = 2 √ 2(52)
Perimeter = 2√104
Perimeter = 20. 3 cm
Area of square = 1/2 diagonal square
Area = 1/ 2 × 52²
Area = 1352 cm²
Area of rectangle = \(l\sqrt{d^2 - l^2}\)
Area = 20 \(\sqrt{52^2 - 20^2}\)
Area = 20 × 48
Area = 960cm²
Thus, the polygon with greater area is the square and that with greater perimeter is the rectangle, this is so because the length of sides of the square differ from that of the rectangle
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pls help!!
solve for y :
m=n/y
Answers
Answer:
\(ym = n \\ y = n \div m\)
The results of a paired-difference test are shown below to the right. d = 5.6
a. Construct and interpret a 99% confidence interval estimate for the paired difference Sd =0.25 in mean values.
b. Construct and interpret a 90% confidence interval estimate for the paired difference n=16 in mean values_ (Round to two decimal places as needed:) Choose the correct answer below:
OA This interval will contain the true population mean 90% of the time_
OB. There is a 90% chance that the true population mean is contained in the interval.
Oc: If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean: 0
D. Approximately 90% of the differences will be contained in the interval.
Answers
If many random samples of this size were taken and intervals constructed, 90% of them would contain the true population mean. In repeated sampling, about 90% of the constructed confidence intervals will capture the true population mean difference. The correct answer is C.
When we construct a confidence interval, it is important to understand its interpretation. In this case, the correct answer (Oc) states that if we were to take many random samples of the same size and construct confidence intervals for each sample, approximately 90% of these intervals would contain the true population mean difference.
This interpretation is based on the concept of sampling variability. Due to random sampling, different samples from the same population will yield slightly different sample means.
The confidence interval accounts for this variability by providing a range of values within which we can reasonably expect the true population mean difference to fall a certain percentage of the time.
In the given scenario, when constructing a 90% confidence interval for the paired difference, it means that 90% of the intervals we construct from repeated samples will successfully capture the true population mean difference, while 10% of the intervals may not contain the true value.
It's important to note that this interpretation does not imply a probability or chance for an individual interval to capture the true population mean. Once the interval is constructed, it either does or does not contain the true value. The confidence level refers to the long-term behavior of the intervals when repeated sampling is considered.
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Lame Example Furniture Company makes two products for its adoring public: chairs (C)and tables (T). Each chair requires 5 hours of labor (L) and 4 linear feet of rich mahogany (M), and each table requires 3 hours of labor and 20 linear feet of rich mahogany. The company has 240 labor hours available this week, and the warehouse has 700 linear feet of rich mahogany available. Profit for each chair is $150 and for each table is $750. At the optimal solution, how many tables should be produced? What is the maximum profit?
Answers
Maximize: Profit = 150C + 750T
Subject to:
5C + 3T ≤ 240 (Labor constraint)
4C + 20T ≤ 700 (Material constraint)
C ≥ 0
T ≥ 0
To determine the optimal production quantity of tables and the maximum profit, we can set up a linear programming problem based on the given information.
Let's define the decision variables:
Let C represent the number of chairs produced.
Let T represent the number of tables produced.
Objective function:
The objective is to maximize profit. The profit for each chair is $150, and the profit for each table is $750. Therefore, the objective function can be expressed as:
Profit = 150C + 750T
Constraints:
Labor constraint: The total labor hours available is 240, and each chair requires 5 hours, while each table requires 3 hours. So the labor constraint can be represented as:
5C + 3T ≤ 240
Material constraint: The warehouse has 700 linear feet of rich mahogany available, and each chair requires 4 linear feet, while each table requires 20 linear feet. Therefore, the material constraint can be expressed as:
4C + 20T ≤ 700
Non-negativity constraint: Since we cannot produce a negative quantity of chairs or tables, both C and T should be greater than or equal to zero:
C ≥ 0
T ≥ 0
Now, we can solve the linear programming problem to find the optimal solution:
Maximize: Profit = 150C + 750T
Subject to:
5C + 3T ≤ 240 (Labor constraint)
4C + 20T ≤ 700 (Material constraint)
C ≥ 0
T ≥ 0
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Complete the two column proof.
Answers
The two-column table to prove ∠ABC ≅ ∠DBE using the angle addition postulate is presented as follows;
Statements \({}\) Reasons
1. ∠ABD is a right angle \({}\) 1. Given
∠CBE is a right angle
2. ∠ABD are complementary \({}\) 2. Definition of complementary angles
3. ∠CBE are complementary \({}\) 3. Definition of complementary angles
4. ∠ABC ≅ ∠DBE \({}\) 4. Congruent complements theorem
What is the angle addition postulate?The angle addition postulate states that the when two angles are placed side by side such that they share a common ray, the measure of the angle formed by the two angles is the sum of the measure of the individual angles.
∠ABD = ∠ABC + ∠CBD (angle addition postulate)
∠ABD = 90° (definition of right angle)
∠ABC + ∠CBD = 90° (substitution property of equality)
∠ABC and ∠CBD are complementary (definition of complementary)
Similarly
∠CBE = ∠CBD + ∠DBE (angle addition postulate)
∠CBE = 90° (definition of right angle)
∠CBD + ∠DBE = 90° (substitution property of equality)
∠CBD and ∠DBE are complementary (definition of complementary)
∠ABC is a complementary angle to ∠CBD and ∠DBE is a complementary angle to ∠CBD
Therefore;
∠ABC is congruent to ∠DBE (congruent complements theorem)
∠ABC ≅ ∠DBEThe congruent complement theorem states if an angle ∠A is a complement to an angle ∠C and if an angle ∠B is also a complement of angle ∠C then ∠A is congruent to ∠B.
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IMAGINE HAVING A HEADACHE BC YOUR TEACHERS PILEEE SOOO MUCH WORK ON YOU, AND ALL YOU WANNA DO IS JUST SLEEEPPPPPPP
Answers
Answer:
relatable
Step-by-step explanation:
Answer:
couldnt be me
Step-by-step explanation:
and whatchu mean imagine ITS HERE
Estimate the value of the integral from negative 2 to 4 of x cubed, dx by using the Trapezoidal Rule with n = 3. (5 points)
252
128
63
72
Answers
Answer:
Good luck on your test guys, Did a lil digging for this one
Step-by-step explanation:
solve this please. i need an answer
Answers
What type of triangle can u form with 4.5cm,6cm, and 8.5cm
Answers
scalene triangle
hope it helps...
Answer:
down below - hope this helped :)
Step-by-step explanation:
you can make a scalene traingle with these mesurements
since none of the sides are equal :)
Standardized tests for certain subjects, given to high school students, are scored on a scale of 1 to 5. Let X represent the score on a randomly selected exam. The distribution of scores for one subject’s standardized test is given in the table.
A 2-column table with 5 rows. Column 1 is labeled score with entries 1, 2, 3, 4, 5. Column 2 is labeled Probability with entries 0.18, 0.20, 0.26, 0.21, 0.15.
What is the probability of earning a score of 3 or higher?
0.26
0.36
0.62
0.66
Answers
Answer:
C. 0.62
Step-by-step explanation:
probability of earning a score of 3 or higher means the probability we are trying to find includes 3,4,5 so we just add these together to get the probability of 3 and above
3 = 0.26
4= 0.21
5= 0.15
0.26+0.21+0.15= 0.62
Is the triangle sum theorem true on the surface sphere? Explain why or why not.
Answers
Answer: No, the triangle sum theorem is not true for a sphere surface.
Explanation:
Consider 3 cities A,B,C at the following locations
A is somewhere on the equatorB is at the north poleC is also on the equator such that the curved distance from A to B is exactly 1/4 of the earth's circumferenceThe placement of C is important because this then allows angle ABC to be 90 degrees. Angles BAC and BCA are also 90 degrees each because B is directly north of both A and C (all northerly roads lead to the north pole at point B). This bizarre triangle has all three angles of 90 degrees. The angles here sum to 90+90+90 = 270 degrees.
No, the triangle sum theorem is not true on the surface sphere.
What is the triangle sum theorem?The triangle sum theorem states that, the sum of the three interior angles of any triangle is always 180°.
Given that, is the triangle sum theorem true on the surface sphere or not, so in relation to Euclid's geometry,
A statement that is equivalent to the parallel postulate is that there exists a triangle whose angles add up to 180°. Since spherical geometry violates the parallel postulate, there exists no such triangle on the surface of a sphere. The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere's surface that is enclosed by the triangle. For any positive value of f, this exceeds 180°.
Hence, there exists no such triangle on the surface of a sphere.
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Choose the set of equivalent fractions that correctly uses the LCD for these fractions: 2/3 and 1/6
O 8/12 and 2/12
O 4/6 and 1/6
O 12/18 and 3/18
O None of these are correct
Answers
2/3 is equivalent to 4/6 (multiply the numerator and denominator by 2)
1/6 is equivalent to 1/6 (multiply the numerator and denominator by 1)
Therefore, the set of equivalent fractions that correctly uses the LCD for 2/3 and 1/6 is 4/6 and 1/6.
So, the answer is 4/6 and 1/6.
solve: 3(p - 1) = 3p + 2
Answers
Answer: solve for p or solve for the inequality of p??
What's the greatest common factor of 18 and 27
Answers
Answer:
9
Step-by-step explanation:
Just ask. :)
Hope this helps you. :)
327 ÷ 8 please help me im d.u.m.b
Answers
In a recent election, 63% of all registered voters participated in voting. In a survey of 275 retired voters, 162 participated in voting. Which is higher, the population proportion who participated or the sample proportion from this survey?
Answers
The population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
To determine whether the population proportion who participated in voting or the sample proportion from the survey is higher, we need to compare the percentages.
The population proportion who participated in voting is given as 63% of all registered voters.
This means that out of every 100 registered voters, 63 participated in voting.
In the survey of retired voters, 162 out of 275 participants voted. To calculate the sample proportion, we divide the number of retired voters who participated (162) by the total number of retired voters in the sample (275) and multiply by 100 to get a percentage.
Sample proportion = (162 / 275) \(\times\) 100 ≈ 58.91%, .
Comparing the population proportion (63%) with the sample proportion (58.91%), we can see that the population proportion who participated in voting (63%) is higher than the sample proportion from this survey (58.91%).
Therefore, based on the given data, the population proportion who participated in voting is higher than the sample proportion from this survey.
It's important to note that the sample proportion is an estimate based on the surveyed retired voters and may not perfectly represent the entire population of registered voters.
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−9x+5y=45 slope intercept form
Answers
Answer:
5y=9x+45
Y=9/5x+9
Step-by-step explanation:
Find the distance between points P(8, 2) and Q(3, 8) to the nearest tenth.
Answers
\(~~~~~~~~~~~~\textit{distance between 2 points} \\\\ P(\stackrel{x_1}{8}~,~\stackrel{y_1}{2})\qquad Q(\stackrel{x_2}{3}~,~\stackrel{y_2}{8})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ PQ=\sqrt{(~~3 - 8~~)^2 + (~~8 - 2~~)^2} \implies PQ=\sqrt{( -5 )^2 + ( 6 )^2} \\\\\\ PQ=\sqrt{ 25 + 36 } \implies PQ=\sqrt{ 61 }\implies PQ\approx 7.8\)