The x-intercept of the line whose equation is 2x - 3y = 6 is
Answer:
(3,0)
Step-by-step explanation:
What transformations change the graph of (f)x to the graph of g(x)?
f(x) = x² ; g(x) = (x + 7)² + 9
The graph of g(x) is obtained by the combination of shifting the graph of f(x) to the left 7 units and upward 9 units.
Further explanationTransformation of a graph: changing the shape and location of a graph.
We already know there are four types of transformation geometry: translation (or shifting), reflection, rotation, and dilation (or stretching).
The transformation that we will discuss is shifting horizontally or vertically.Translation (or shifting): moving a graph on an analytic plane without changing its shape.Vertical shift: moving a graph upwards or downwards without changing its shape.Horizontal shift: moving a graph to the left or right downwards without changing its shape.In general, given the graph of y = f(x) and k > 0, we obtain the graph of:
[tex]\boxed{ \ y = f(x) + k \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] upward k units.[tex]\boxed{ \ y = f(x) - k \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] downward k units.Furthermore in general, given the graph of y = f(x) and h > 0, we obtain the graph of:
[tex]\boxed{ \ y = f(x + h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the left h units.[tex]\boxed{ \ y = f(x - h) \ }[/tex] by shifting the graph of [tex]\boxed{ \ y = f(x) \ }[/tex] to the right h units.,The combination of vertical and horizontal shifts is as follows:
[tex]\boxed{\boxed{ \ y = f(x \pm h) \pm k \ }}[/tex]
The plus or minus sign follows the direction of the shift, i.e., up-down or left-right
Given: [tex]\boxed{ \ f(x) = x^2 \ becomes \ g(x) = (x + 7)^2 + 9 \ }[/tex]
We set h = +7 and k = +9.
In the graph, additionally note the shift of points from (0, 0) to (-7, 9).
Conclusion
The graph of g(x) is drawn by the combination of shifting the graph of f(x) to the left 7 units and upward 9 units.
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The graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex] axis and then shifted [tex]9[/tex] units towards the positive direction of [tex]y-[/tex] axis.
Further explanation:
The functions are given as follows:
[tex]\fbox{\begin\\\ \begin{aligned}f(x)&=x^{2}\\g(x)&=(x+7)^{2}+9\end{aligned}\\\end{minispace}}[/tex]
The objective is to determine the transformation or the way in which the graph of the function [tex]g(x)[/tex] is obtained from the graph of the function [tex]f(x)[/tex].
Concept used:
Shifting of graphs:
Shifting is a rigid translation because it does not change the size and shape of the curve. Shifting is used to move the curve vertically or horizontally without any change in shape and size of the curve.
The function [tex]y=f(x+a)[/tex] and [tex]y=f(x-a)[/tex] is a shift of the curve [tex]y=f(x)[/tex] horizontally towards negative and positive direction of [tex]x-[/tex]axis respectively.
The function [tex]y=f(x)+a[/tex] and [tex]y=f(x)-a[/tex] is a shift of the curve [tex]y=f(x)[/tex] vertically towards positive and negative direction of [tex]y-[/tex]axis respectively.
Step1: Draw the graph of the function [tex]f(x)=x^{2}[/tex].
Figure 1 (attached in the end) represents the graph of the function [tex]f(x)=x^{2}[/tex]. From figure 1 it is observed that the curve of the function [tex]f(x)=x^{2}[/tex] is a parabola with origin as the vertex and mounted upwards.
Step 2: Obtain the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] from the graph of the function [tex]f(x)=x2[/tex].
The function [tex]g'(x)=(x+7)^{2}[/tex] is of the form [tex]y=f(x+a)[/tex].
So, as per the concept of shifting of the graphs the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex]axis.
Figure 2 (attached in the end) represents the graph of the function [tex]g'(x)=(x+7)^{2}[/tex].
In figure 2 the dotted line represents the curve of [tex]f(x)=x^{2}[/tex] and the bold line represents the curve of [tex]g'(x)=(x+7)^{2}[/tex].
Step3: Obtain the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] from the graph of the function [tex]g'(x)=(x+7)^{2}[/tex].
The function [tex]g(x)=(x+7)^{2}+9[/tex] is of the form [tex]y=f(x)+a[/tex].
So, as per the concept of shifting of graph the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]g'(x)=(x+7)^{2}[/tex] when each point on the curve of [tex]g'(x)=(x+7)^{2}[/tex] is shifted [tex]9[/tex] units towards upwards or the positive direction of [tex]y-[/tex]axis.
Figure 3 (attached in the end) represents the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex].
In figure 3 the dotted line represents the curve of [tex]g'(x)=(x+7)^{2}[/tex] and the bold line represents the curve of [tex]g(x)=(x+7)^{2}+9[/tex].
From the above explanation it is concluded that the graph of the function [tex]g(x)=(x+7)^{2}+9[/tex] is obtained from the graph of the function [tex]f(x)=x^{2}[/tex] when each point on the curve of [tex]f(x)=x^{2}[/tex] is shifted [tex]7[/tex] units towards the negative direction of [tex]x-[/tex] axis and then shifted [tex]9[/tex] units towards the positive direction of [tex]y-[/tex] axis.
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Answer details:
Grade: High school
Subject: Mathematics
Chapter: Graphing
Keywords: Graph, curve, function, parabola, quadratic, f(x)=x2, g(x)=(x+7)2+9, shifting, translation, scaling, shifting of graph, scaling of graph, horizontal, vertical, coordinate, horizontal shift, vertical shift.
In an isometric transformation, the preimage and image must not __________.
A.
change size
B.
rotate
C.
preserve angle measures
D.
reflect across the -axis
Find the values of x and y for which the lines are parallel.
a)x = 47, y = 79
b)x = 58, y = 57
c)x = 79, y = 49
d)x = 79, y = 47
Final answer:
Lines represented by equations in the form x = a constant are vertical lines and are parallel to each other. The correct answer indicating parallel lines is (d) x = 79, y = 47.
Explanation:
To determine which pair of values for x and y indicates that the lines described are parallel, we need to understand that for two lines to be parallel, they must have the same slope. For standard linear equations in the form y = mx + b, where m is the slope, lines with the same m value are parallel. However, when the equation is given in the form x = a constant, as is the case for options (a) and (c), it denotes a vertical line, which does not have a slope in the traditional sense but is parallel to other vertical lines.
Given the information, lines described by equations x = 47 and x = 79 would be parallel since they both represent vertical lines. Therefore, the correct answer is (d) x = 79, y = 47.
Find sin2A if sinA=1/4 and 0<=A<=(pi/2)
write an expression that represents the area of a square with side length 6xy^2 (for any square with side length s, A=s^2=s.s.)
The amount of milk sold each day by a grocery store varies according to the Normal distribution with mean 130 gallons and standard deviation 12 gallons. On a randomly selected day, the probability that the store sells at least 154 gallons is
A. .0228.
B. .1587.
C. .8413.
D. .9772.
To find the probability that the store sells at least 154 gallons of milk on a randomly selected day, we need to standardize the value and use a standard normal distribution table or calculator.
Explanation:To find the probability that the store sells at least 154 gallons of milk on a randomly selected day, we need to find the area under the Normal distribution curve to the right of 154.
First, we need to standardize the value of 154 using the formula Z = (X - mean) / standard deviation, where X is the value we want to standardize, mean is the mean of the distribution, and standard deviation is the standard deviation of the distribution. Using the given values, we have Z = (154 - 130) / 12 = 2.
Next, we can use a standard normal distribution table or a calculator to find the cumulative probability associated with a z-score of 2. The probability that a standard normal random variable is greater than 2 is approximately 0.0228.
Therefore, the probability that the store sells at least 154 gallons of milk on a randomly selected day is approximately 0.0228, or option A.
A geneticist is studying a population of fruit flies. Of the 1278 flies, 467 are wingless and 446 have red eyes. There are 210 flies that are wingless whose eyes are not red. What is the approximate probability that a fly is wingless or has red eyes?
0.49
0.51
0.71
0.88
The approximate probability that a fly is wingless or has red eyes is 0.49.
A geneticist is studying a population of fruit flies. Of the 1278 flies, 467 are wingless and 446 have red eyes.
What is the probability?Probability means possibility. It is a branch of mathematics that deals with the occurrence of a random event. The value is expressed from zero to one.
There are 210 flies that are wingless and whose eyes are not red.
We have determined the approximate probability that a fly is wingless or has red eyes.
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Which conditional and its converse form a true biconditional?
A) If x>0, then lxl >0
B) If x=3, then x2^2=9
C) If x^2 =4, Then x=2
D) If x=19, then 2x-3=35
Answer: D) If x=19, then 2x-3=35
Step-by-step explanation:
A) If x > 0, then lxl >0,
L.H.S. x > 0,
R.H.S. lxl >0 ⇒ ± x > 0
⇒ L.H.S. ≠ R.H.S.
B) If x = 3 then [tex]x^2 = 9[/tex]
L.H.S. x = 3,
R.H.S. [tex]x^2 = 9[/tex] ⇒ x = ± 3
⇒ L.H.S. ≠ R.H.S.
C) If [tex]x^2 =4[/tex], Then x=2
L.H.S. [tex]x^2 =4[/tex] ⇒ x = ± 2,
R.H.S. x = 2,
L.H.S. ≠ R.H.S.
D) If x=19, then 2x-3=35
L.H.S. x = 19,
R.H.S. 2x-3=35 ⇒ 2x = 38 ⇒ x = 19
⇒ L.H.S. = R.H.S.
⇒ Option D is correct.
A coffee supply store waits until the orders for its special blend reach 100 pounds before making up a batch. Columbian coffee selling for $8.85 a pound is blended with Brazilian coffee selling for $3.85 a pound to make a product that sells for $6.55 a pound. How much of each type of coffee should be used to make the blend that will fill the orders?
how do you write 19/15 as a mixed number
By definition of fraction of the numbers, The mixed form of the fraction 19/15 is,
⇒ 19/15 = 1 4/15
What is mean by Division method?Division method is used to distributing a group of things or numbers into equal parts. And, Division is just opposite of multiplications.
For example, dividing 20 by 2 means splitting 20 into 2 equal groups of 10.
We have to given that;
The fraction of the number in fraction form is,
⇒ 19/15
Now,
We can simplify the fraction to change into mixed number as;
⇒ 19/15
⇒ 15 ) 19 ( 1
- 15
-----
04
---------
Thus, We get;
The fraction is written as;
⇒ 19 / 15
⇒ 1 4/15
Therefore, We get;
By definition of fraction of the numbers, The mixed form of the fraction 19/15 is,
⇒ 19/15 = 1 4/15
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how do you evaluate log2 1/64
In the table, the relation (x, y) is not a function if the missing value of x is
Answer:
In the table, the relation (x, y) is not a function if the missing value of x is
Step-by-step explanation:
In the tab
le, the relation (x, y) is not a function if the missing value of x is
The water level in a lake was 12 inches below normal at the beginning of march. The water level decreased 2 1/4 inches in march and increased by 1 5/8 inches april. What was the water level compared to normal at the end of april? Explain how you solved his question
The water level in the lake was 12 inches below normal at the beginning of March, decreased by 2 1/4 inches in March, and then increased by 1 5/8 inches in April. By the end of April, the water level was 12 5/8 inches below the normal level.
Explanation:The student is asking about the changes in water level over the course of two months and wishes to compare the final water level with the normal water level at the end of April. To solve this, we need to perform a series of arithmetic operations with mixed numbers.
The water level was 12 inches below normal at the beginning of March. In March, it decreased by 2 1/4 inches; therefore, we add 2 1/4 inches to the negative deviation (because going further below normal). By the end of March, the water level is 12 + 2 1/4 = 14 1/4 inches below normal.
In April, the water level increased by 1 5/8 inches. We now subtract this value from 14 1/4 inches to find the new level: 14 1/4 - 1 5/8 = 12 5/8 inches below normal. Thus, at the end of April, the lake's water level is still below the normal level.
The water level in the lake ended up being -12 5/8 inches below normal at the end of April. This was calculated by subtracting the March decrease and adding the April increase to the initial level.
The water level in a lake was 12 inches below normal at the beginning of March. After a decrease of 2 1/4 inches in March and an increase of 1 5/8 inches in April, we need to calculate the final water level compared to normal at the end of April.
Step-by-Step Explanation:
Start with the initial level: -12 inches (below normal).
Decrease by March's change: -12 - 2 1/4 = -14 1/4 inches.
Increase by April's change: -14 1/4 + 1 5/8 = -12 5/8 inches.
Therefore, the water level was -12 5/8 inches below normal at the end of April.
Graph the solution on a number line
x<2
Graph is included!
Find the value of x. Round the answer to the nearest tenth, if needed. A. 4.8 B. 5.1 C. 8.2 D. 9.5
which improper fraction that is equivalent to the mixed number 6 4/7
A carpenter makes chairs with slats that run across the chair as shown. each chair uses 7 slats. he needs to make 24 chairs.how many slats must he make?
A jewelry store marks its merchandise up by 80%. If the wholesale price of a bracelet is $55, what will the store charge for the retail price?
A.) $63
B.) $75
C.) $99
D.) $110
The retail price of the bracelet is $99. Therefore, option C is the correct answer.
Given that, a jewelry store marks its merchandise up by 80%.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
The wholesale price of a bracelet is $55.
Let the retail price of the bracelet be x.
Here, x=55+80% of 55
=55+0.8×55
=55+44
=$99
The retail price of the bracelet is $99. Therefore, option C is the correct answer.
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Find the values of x and y that satisfy the equation. 3x+6i=27+yi
The values that satisfy the equation 3x + 6i = 27 + yi are x = 9 and y = 6, which are found by equating real and imaginary parts separately.
To find the values of x and y that satisfy the equation 3x + 6i = 27 + yi, we must equate the real parts and the imaginary parts separately. The real part of the equation gives us x, and the imaginary part gives us y.
From the real part, we have:
3x = 27
x = 27 / 3
x = 9
From the imaginary part, we have:
6i = yi
y = 6
Therefore, the values x = 9 and y = 6 satisfy the given equation.
Ari has a total of 22 coins consisting of pennies and nickels. The total value of the coins is $0.54.
How many of each type of coin does Ari have?
Answer:
Let n = the number of nickels that Ari has.
Let p = the number of pennies that Ari has.
The total number of coins she has is 22.
n + p = 22
We have our first equation... But we another one to solve this.
Each penny is going to be $0.01 and a nickel is work $0.05.
And the total is $0.54
Our second equation. 0.05n + 0.01p = 0.54
n + p = 22
0.05n + 0.01p = 0.54
Multiply the top by -0.05
-0.05n - 0.05p = -1.1
0.05n + 0.01p = 0.54
The n terms cancel out.
-0.04p = -0.56
p = 14
Step-by-step explanation:
What isthe answer to 3/5 ❌ 20
On average 113,204 aluminum cans are recycled in a minute. Approximately how many cans will be recycled in 16 days? (Express your answer in scientific notation.)
a.
2.61x10^9 cans
b.
4.35x10^7 aluminum cans
c.
1.09x10^8 aluminum cans
d.
1.63x10^8 aluminum can
Answer:
the answer is A
Step-by-step explanation:
Final answer:
The answer is approximately 2.61x10⁹ cans recycled in 16 days, which is option (a).
Explanation:
The student is asking about a mathematical estimation of how many aluminum cans are recycled over a 16-day period, given an average rate of recycling per minute.
To find the answer, we'll first calculate the number of minutes in 16 days:
16 days × 24 hours/day × 60 minutes/hour = 23,040 minutes.
Now, we multiply this by the average number of cans recycled per minute:
23,040 minutes × 113,204 cans/minute = 2.61x10⁹ cans.
Expressing this value in scientific notation gives us:
About 2.61x10⁹ aluminum cans recycled in 16 days, which corresponds to option (a) in the multiple-choice provided by the student.
Alex buys 24 apples and when he opens it 6 apples are bad whats the perecentage of the bad apples
A coupon offers $1.00 off the 16-ounce size. which size is better buy then
Answer:first u have to multiply 1 .00 by 16 then
which is bigger, half of 30 or one third of 75
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How many pints is 4 liters?
a. 0.21
b. 8.4
c. 0.84
d. 4
What is 70℅ written as decimal
Answer: .70 or .7
Step-by-step explanation: To write a percent as a decimal, we simply move the decimal point 2 places to the left so 70% can be written as the decimal .70 or just .7. Both of these answers would work just fine.
information is given about a polynomial f(x) whose coefficients are real numbers. Find the remaining zeros of f
Degree 4; zeros: i, 14+i
what are the remaining zeros of f
The remaining zeros of the given degree 4 polynomial f(x) with known zeros i and 14+i are -i and 14-i.
In Mathematics, particularly in studying polynomials, if a polynomial has real coefficients, then complex zeros always occur in conjugate pairs.
That is, if a+bi is a zero, then its conjugate, a-bi is also a zero.
Given that f(x) is a polynomial of degree 4 with zeros i and 14+i, then its conjugate zeros are -i and 14-i. Therefore, the four zeros of the polynomial f(x) are i, -i, 14+i and 14-i.
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express in simplest form with a prime number base
2^t*8