The function f(x) = √3x - 3 could be the one graphed.
From the given information, we can deduce the following about the graph of the square root function:
The graph is a square root function, which means it has the form f(x) = √(ax + b), where a and b are constants.
The graph is shifted horizontally by a certain amount.
The graph is shifted vertically by a certain amount.
Using this information, we can analyze each function option to determine if it matches the graph:
Of(x) = √x - 3: This function is a square root function shifted vertically downward by 3 units. It does not match the given graph, as it is shifted vertically, not horizontally.
Of(x) = √x - 1: This function is a square root function shifted vertically downward by 1 unit. It also does not match the given graph, as it is shifted vertically, not horizontally.
Of(x) = √x + 1: This function is a square root function shifted vertically upward by 1 unit. It does not match the given graph, as it is shifted vertically, not horizontally.
f(x) = √3x - 3: This function is a square root function with a coefficient of 3 in front of x, causing a horizontal compression. It is also shifted vertically downward by 3 units. This function matches the given graph, as it represents a horizontal and vertical shift of the square root function.
Therefore, the function f(x) = √3x - 3 could be the one graphed.
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PLS HELP ME WILL MAKRK BRAINLIEST 1. In the distance, an airplane is taking off. As it ascends during take-off, it makes a slanted line that outs through the rainbow at two points. Create a table of at least four values for the function that includes two points of intersection between the airplane and the rainbow.
2. Analyze the two functions. Answer the following reflection questions in complete sentences
• What is the domain and range of the rainbow? Explain what the domain and range represent. Do all of the values make sense in this situation? Why or why not?
• What are the x- and v-intercepts of the rainbow? Explain what each intercept represents.
• Is the linear function you created with your table positive or negative? Explain.
¡a What are the solutions or solution to the system of equations created? Explain
what it or they represent.
13. Create your own piecewise function with at least two functions. Explain, using complete sentences, the steps for graphing the function. Graph the function by hand or using a graphing software of your choice (remember to submit the graph).
The graph rainbow which is in the shape of a parabola and the selected points indicates that we get;
1. (a) The table can be presented as follows;
x; -10, -4, 2, 8
f(x); 10, 20, 30, 40
2. Domain; [-6, 6], range; [0, 36]
Yes, the values make sense
x-intercepts; (-6, 0), and (6, 0), y-intercepts; (0, 36)Then linear function is positiveThe solution are; (-4, 20), and (2, 30)3. The piecewise function is; f(x) = x² + 15, when 0 ≤ x ≤ 5 and y = x - 1 when 5 < x ≤ ∞
Please find attached the graph of the piecewise function created with MS Excel
What is a parabola?A parabola is the shape of the graph of a quadratic function.
1. (a) The points on the graph of the parabola which are on a straight line are;
(-4, 20), and (2, 30)
The table of values are therefore;
x [tex]{}[/tex] f(x)
-10 [tex]{}[/tex] 10
-4[tex]{}[/tex] 20
2[tex]{}[/tex] 30
8 [tex]{}[/tex] 40
2. The domain is the set of the possible x-values of the data, therefore;
The domain of the rainbow is; [-6, 6]
The range is the set of the possible x-values of the data, therefore;
The range of the rainbow is; [0, 36]
The domain represents the length of the rainbow at ground level
The range represents the height of the rainbow
The values are reasonable, where the axis of symmetry for the rainbow is the y-axis
The x-intercepts are; (-6, 0), and (6, 0), which are the points the rainbow reaches the ground
The y-intercept is the point (0, 36), which is the highest point on the rainbow
The slope of the linear function is; (30 - 20)/(2 - (-4)) = 5/3
The positive slope indicates that the linear function is positive
i(a) The solutions of the system of equation are the point of intersection of the airplane and the rainbow, which are; (-4, 20), and (2, 30)
The point of intersection represents the intersection of the airplane and the rainbow
3. The piece wise function that can be created can be presented as follows;
f(x) = x² + 15 Where; 0 ≤ x ≤ 5
f(x) = x - 1 Where; 5 < x < ∞
Please find attached the graph of the piecewise function created with MS Excel
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How are the two angles related?
The two angles are related in that they are supplementary angles
Supplementary angles would add tuo to 180 degrees according to the angle Theorem.
Adding the two given angles :
52+128 = 180These angles are supplementary
The angles aren't vertical in that , vertical angles should have the same vertex. Complementary angles on the other hand add to 90 degrees. While the angles doesn't share the same side, hence, they aren't adjacent.
Hence, the angles are related as they are supplementary angles .
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. What is the value of the discriminant of 0 = -2x² + 6x+13
The discriminant of the quadratic equation -2x² + 6x + 13 is 140.
To find the discriminant of the quadratic equation 0 = -2x² + 6x + 13, we can use the formula for the discriminant, which is given by Δ = b² - 4ac. The quadratic equation is in the form ax² + bx + c = 0, with coefficients a = -2, b = 6, and c = 13.
Substituting these values into the discriminant formula, we have:
Δ = (6)² - 4(-2)(13)
Δ = 36 - (-104)
Δ = 36 + 104
Δ = 140
The discriminant provides valuable information about the nature of the solutions of a quadratic equation.
It can take on different values, and each value indicates a different scenario:
If the discriminant (Δ) is greater than zero (Δ > 0), then the quadratic equation has two distinct real solutions.
If the discriminant is equal to zero (Δ = 0), then the quadratic equation has a single real solution (a repeated root).
If the discriminant is less than zero (Δ < 0), then the quadratic equation has no real solutions, but rather two complex solutions.
The discriminant is 140 (Δ = 140), which is greater than zero, the quadratic equation -2x² + 6x + 13 has two distinct real solutions.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
A. The area of the triangle is 108 mm².
B. The area of parallelogram is 286√2 in²
How to find the area of each parallelogram of triangle?A. Area of a triangle (A) = 1/2 * Base (b) * Height (h)
We have:
b = 18 mm
h = 12 mm
Thus:
A = 1/2 * 18 * 12
A = 108 mm²
B. The area of parallelogram is given by:
A = b * h
where b is the base and h is the height
We have:
b = 26 in
Using trig.:
sin 45 = h/22
h = 22 * sin 45
h = 11√2 in
Thus,
A = 26 * 11√2
A = 286√2 in²
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help with the question please
100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
A. The volume of the hemisphere with a diameter of 48 yards is approximately 1001.1 cubic yards.
B. The volume of the sphere with a circumference of a great circle approximately equal to 26 meters is approximately 359.4 cubic meters.
A. To find the volume of a hemisphere, we first need to calculate the radius. The diameter is given as 48 yards, so the radius is half of that, which is 24 yards.
The formula for the volume of a hemisphere is (2/3)πr^3, where r is the radius. Plugging in the values:
Volume = (2/3) * π * (24^3)
Volume ≈ 1001.1 cubic yards (rounded to the nearest tenth)
Therefore, the volume of the hemisphere is approximately 1001.1 cubic yards.
B. To find the volume of a sphere, we need to know the radius. Since the circumference of a great circle is given as approximately 26 meters, we can use the formula C = 2πr, where C is the circumference and r is the radius.
We can rearrange the formula to solve for the radius: r = C / (2π). Plugging in the circumference:
r = 26 / (2π)
r ≈ 4.134 meters (rounded to the nearest thousandth)
The formula for the volume of a sphere is (4/3)πr^3. Substituting the radius:
Volume = (4/3) * π * (4.134^3)
Volume ≈ 359.4 cubic meters (rounded to the nearest tenth)
Therefore, the volume of the sphere is approximately 359.4 cubic meters.
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The formula represents the surface area S of a cube with side lengths x. S=6x^2. Solve for x.
The value of x can be found by rearranging the formula S = 6[tex]x^2[/tex] to x = √(S/6).
1. The formula for the surface area of a cube is given as S = 6[tex]x^2[/tex], where S represents the surface area and x represents the side length.
2. To solve for x, we need to isolate it on one side of the equation.
3. Divide both sides of the equation by 6: S/6 = [tex]x^2[/tex].
4. To eliminate the exponent of 2, take the square root of both sides: √(S/6) = x.
5. Therefore, the value of x is given by x = √(S/6).
6. If you have a specific value for S, you can substitute it into the equation to find the corresponding value of x.
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What
is an arithmetic sequence with a common difference of −2?
Answer:
An arithmetic sequence with a common difference of −2 is 20,18,16,14,12..
Step-by-step explanation:
An arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is same. Here, the common difference is -2, which means that each term in the sequence is obtained by subtracting 2 from the previous term.
To find the arithmetic sequence with a common difference of -2, you can start with an first term and then subtract 2 successively to find the subsequent terms.
Let the initial term is 20. Subtracting 2 from 20, we get 18. Subtracting 2 from 18, we get 16. Continuing this pattern, we subtract 2 from each subsequent term to generate the sequence. The arithmetic sequence with a common difference of -2 starting from 20 is
20,18,16,14,12
In this sequence, each term is obtained by subtracting 2 from the previous term, resulting in a common difference of -2.
Mr Mangena invested an amount of R13 890,00 divided in two different schemes, A and B, at the simple
interest rate of 14% per annum and 11% per annum respectively. If the total amount of simple interest earned
in three years is R5 508,00, what was the amount invested in Scheme B?
The amount invested in Scheme B is R6,000.
Let's assume that Mr Mangena invested "x" amount in Scheme A and "y" amount in Scheme B.So, as per the problem, the total amount invested by Mr Mangena in Scheme A and Scheme B is equal to R13,890. Hence,x + y = 13,890This is our first equation.
The second equation is that after 3 years, the total interest that Mr Mangena earned was R5,508. Now, we know that the interest earned is simply the product of principal, rate of interest and time. The rate of interest is given as 12% for Scheme A and 10% for Scheme B. Hence, we can write the following equation:0.12x * 3 + 0.10y * 3 = 5,508This is our second equation.
We have two equations and two variables. We can solve these equations simultaneously to get the values of x and y, and hence, we can find the amount invested in Scheme B.x + y = 13,890 ................... Equation 1 0.12x * 3 + 0.10y * 3 = 5,508 .............. Equation 2 Simplifying Equation 1, we get:x = 13,890 - ySubstituting this value of x in Equation 2, we get:0.12(13,890 - y) * 3 + 0.10y * 3 = 5,508Simplifying this equation, we get:y = R6,000.
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discuss three dramatic techniques that makes the play look back in anger interesting
The three dramatic techniques that make "Look Back in Anger" interesting are social realism, strong language and rhetoric, and character conflict and dynamic relationships.
"Look Back in Anger" by John Osborne is a play known for its compelling portrayal of post-war disillusionment and social critique. Here are three dramatic techniques used in the play that contribute to its enduring interest:
1. Social Realism: Osborne employed social realism, depicting the gritty realities of working-class life, alienation, and societal discontent. This authenticity and portrayal of relatable characters and situations engage the audience emotionally and intellectually.
2. Strong Language and Rhetoric: The play is characterized by sharp, biting dialogue and impassioned monologues. The use of strong language and rhetoric adds intensity, captures the characters' frustrations, and conveys their anger and disillusionment effectively.
3. Character Conflict and Dynamic Relationships: The play revolves around intense conflicts between characters, particularly the central couple, Jimmy and Alison. Their volatile relationship and the clash between Jimmy's anger-fueled rebellion and Alison's desire for a different life create tension and keep the audience engaged.
Overall, these dramatic techniques of social realism, powerful language, and dynamic relationships make "Look Back in Anger" interesting by effectively portraying societal issues, engaging the audience emotionally, and highlighting the complexities of human interactions.
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100 Points! Geometry question. Photo attached. Please show as much work as possible. Thank you!
The trigonometric ratios for this problem are given as follows:
sin(R) = 16/34 = 0.47.cos(R) = 30/34 = 0.88.tan(R) = 16/30 = 0.53.sin(S) = 30/34 = 0.88.cos(S) = 16/34 = 0.47.tan(S) = 30/16 = 1.88.What are the trigonometric ratios?The three trigonometric ratios are the sine, the cosine and the tangent of an angle, and they are obtained according to the formulas presented as follows:
Sine = length of opposite side to the angle/length of hypotenuse of the triangle.Cosine = length of adjacent side to the angle/length of hypotenuse of the triangle.Tangent = length of opposite side to the angle/length of adjacent side to the angle = sine/cosine.The hypotenuse for this problem is of 34, and the sides are given as follows:
r = 16: opposite to R, adjacent to S.s = 30: opposite to S, adjacent to R.Hence the trigonometric ratios are given as follows:
sin(R) = 16/34 = 0.47.cos(R) = 30/34 = 0.88.tan(R) = 16/30 = 0.53.sin(S) = 30/34 = 0.88.cos(S) = 16/34 = 0.47.tan(S) = 30/16 = 1.88.A similar problem, also about trigonometric ratios, is given at brainly.com/question/24349828
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The perimeter of triangle is 22cm if one of side is 9cm, find the other side of the area of a triangle 20.976cm
The other side of the triangle is approximately 4.664 cm.
Let's denote the other side of the triangle as x. We know that the perimeter of the triangle is 22 cm, and one of the sides is 9 cm. The perimeter of a triangle is the sum of the lengths of its three sides. So, we can set up the equation:
9 + x + z = 22
where z represents the remaining side.
Now, we are given that the area of the triangle is 20.976 cm². The area of a triangle can be calculated using the formula:
Area = (1/2) * base * height
Since we know the area and one side (9 cm), we can rearrange the formula to solve for the height (which is the remaining side, z):
z = (2 * Area) / 9
Substituting the given values, we get:
z = (2 * 20.976) / 9
z ≈ 4.664 cm
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100 Points! Geometry question. Photo attached. Only looking for an answer to B. Please show as much work as possible. Thank you!
The measure of the length VT from the diagram is 5.4
Triangular geometry and similarity theoremFrom the given diagram, we can see that the triangle TSR and TUV are similar, hence the correct expressed needed to determine the value of x is given as:
6/x+2 = 14/4x-1
Cross multiply to have
6(4x - 1) = 14(x + 2)
24x - 6 = 14x + 28
24x - 14x = 28 + 6
Simplify to have:
10x = 34
x = 3.4
Determine the measure of VT
VT = x + 2
VT = 3.4 + 2
VT = 5.4
Hence the measure of VT from the diagram is 5.4
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ead the situations below and determine which relationship is not functional.
Situation 1: a cell phone bill to the amount of minutes used
Situation 2: the perimeter of a square to the length of one of the sides of a square
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned
Situation
does not represent a function.
This is because
.
There can be multiple outputs (monthly charges) for a given input (number of credit cards), violating the definition of a function. hence, Situation 3 does not represent a function.
Situation 3: the total amount of money charged monthly on credit cards to the number of credit cards owned does not represent a function.
In a function, each input (or x-value) should have a unique output (or y-value). However, in this situation, the total amount of money charged monthly on credit cards depends on the number of credit cards owned. It is possible to have different credit card numbers but still have the same total amount of money charged monthly.
For example, two people could own different numbers of credit cards but have the same monthly charges.
As a result, the definition of a function can be violated by having many outputs (monthly charges) for a single input (number of credit cards).
Because of this, case 3 does not represent a function.
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Given the attached graph and the equation of the line in the slope intercept form?
The slope, "m," indicates the rate of change of the line, while the y-intercept, "b," represents the value of y when x equals zero.
I apologize, but as a text-based AI model I'm unable to directly view or analyze any attached images or graphs. However, if you provide me with the equation of the line in the slope-intercept form or describe the relevant details from the graph, I can certainly help you with a response within the given word limit.
The slope-intercept form of a linear equation is given by y = mx + b, where "m" represents the slope of the line and "b" represents the y-intercept, the point where the line intersects the y-axis.
Using this equation, you can determine the slope and y-intercept by comparing the given equation with the slope-intercept form.
Once you provide me with the equation or necessary information, I'll be able to assist you further in understanding the line and its characteristics.
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what is the slope of the line that passes through the points (-5, 8) and (-5, 4)
Write your answer in simplest form.
Answer:
undefined
Step-by-step explanation:
To find the slope, we can use the slope formula.
m = ( y2-y1)/(x2-x1)
= ( 4-8)/(-5 - -5)
= (4-8)/(-5+5)
= -4/0
The slope is undefined.
What are the perfect squares up to 100?
Answer:
1,4,9,16,25,36,49,64,81,100
What is the slope of the line graphed below?
m=
P
B. -2
C. 2
(0,-5)
(03.1)
The correct answer is C. 2.
To determine the slope of a line, we need to calculate the change in the y-coordinates divided by the change in the x-coordinates between two points on the line. In this case, we have the points (0, -5) and (3, 1).
The change in the y-coordinates is 1 - (-5) = 6, and the change in the x-coordinates is 3 - 0 = 3.
Therefore, the slope of the line is the ratio of the change in the y-coordinates to the change in the x-coordinates, which is 6/3 = 2.
Hence, the slope of the line graphed is 2.
Therefore, the correct answer is C. 2.
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Which pair of angles are interior angles?
Find y' and then find the slope of the tangent line at (3, 324). Round the slope and y-intercept to 3 decimal
place.
y = (x²+2x+3)²
y =
The tangent line at (3, 324) is
y =….. x+
The equation of the tangent line at (3, 324) is y = 288x - 540.
To find y' (the derivative of y), we can differentiate the given function y = [tex](x^2 + 2x + 3)^2[/tex] using the chain rule.
y' = [tex]2(x^2 + 2x + 3) \times (2x + 2) = 4(x^2 + 2x + 3)(x + 1)[/tex]
Now, to find the slope of the tangent line at (3, 324), we substitute x = 3 into y' and evaluate it:
y' = [tex]4(3^2 + 2(3) + 3)(3 + 1) = 4(9 + 6 + 3)(4) = 4(18)(4) = 288[/tex]
So, the slope of the tangent line at (3, 324) is 288.
To find the y-intercept of the tangent line, we substitute the coordinates (3, 324) and the slope (288) into the point-slope form equation: y - y1 = m(x - x1).
Using (x1, y1) = (3, 324) and m = 288, we have:
y - 324 = 288(x - 3)
y - 324 = 288x - 864
y = 288x - 540
Therefore, the equation of the tangent line at (3, 324) is y = 288x - 540.
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45°
Find X.
X
4√3
45°
X
x = [?]√√]
x = 4√3
-----------------------------
The director of the IRS has been flooded with complaints that people must wait more than 50 minutes
before seeing an IRS representative. To determine the validity of these complaints, the IRS randomly
selects 300 people entering IRS offices across the country and records the times which they must wait
before seeing an IRS representative. The average waiting time for the sample is 52 minutes with a
standard deviation of 4 minutes. Is there overwhelming evidence to support the claim that the wait time
to see an IRS representative is more than 50 minutes at a 0.100
The enough evidence to support the claim that the wait time to see an IRS representative is more than 50 minutes at a 0.100 level of significance.
The null hypothesis is, H0:
µ ≤ 50 minutes.
The alternative hypothesis is,
Ha: µ > 50 minutes.
The significance level is α = 0.100Sample size = 300
Sample mean (x) = 52 minutes
Sample standard deviation (s) = 4 minutes
We have to find whether there is enough evidence to support the claim that the waiting time to see an IRS representative is more than 50 minutes or not.
For that, we perform a one-sample t-test.
The test statistic is given by:
t = (x - µ) / (s/√n)t
= (52 - 50) / (4/√300)t
= 7.905
Critical t-value = t 0.100,299 = 1.646
Since the calculated t-value (7.905) is greater than the critical t-value (1.646), we can reject the null hypothesis.
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The graph of the function f(x)=log6(x) is stretched vertically by a factor of 7, reflected over the x-axis, reflected over the y-axis, and shifted up by 2 units.
Find the equation of the function g(x) described above.
The function g(x) is obtained by stretching the logarithmic function f(x) vertically by 7, reflecting it over the x-axis and y-axis, and shifting it up by 2 units. The equation for g(x) is -7*log₆(-x) + 2.
To find the equation of the function g(x), we can apply a series of transformations step by step. First, we stretch the function vertically by a factor of 7 by multiplying it by 7. This gives us the function g₁(x) = 7*log₆(x).
Next, we reflect the function g₁(x) over the x-axis by multiplying it by -1. This results in the function g₂(x) = -7*log₆(x).
To reflect the function g₂(x) over the y-axis, we replace x with -x, giving us the function g₃(x) = -7*log₆(-x).
Lastly, we shift the function g₃(x) up by 2 units by adding 2 to it. This gives us the final equation for g(x) as g(x) = -7*log₆(-x) + 2.
In summary, the function g(x) is obtained by vertically stretching the logarithmic function f(x) by a factor of 7, reflecting it over the x-axis, reflecting it over the y-axis, and then shifting it up by 2 units.
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Simplify 3 hours: 45 m
The simplification of 3 hours : 45 m is 4 minutes : 1 minutes.
How to simplify ratio?Ratio refers to a number representing a comparison between two named quantities.
3 hours : 45 m
Convert hours to minutes:
1 hour = 60 minutes
3 hours = 180 minutes
3 hours : 45 m = 180 minutes : 45 minutes
= 180/45
= 4 / 1
= 4 : 1
Ultimately, 3 hours : 45 m is 4 minutes ratio 1 minutes.
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3square root 2 divided by 3square root 4 and rationalize the denominator
Answer:
[tex]\frac{\sqrt{2}}{2}[/tex]
Step-by-step explanation:
[tex]\frac{3\sqrt{2}}{3\sqrt{4}}=\frac{\sqrt{2}}{\sqrt{4}}=\frac{\sqrt{2}}{2}[/tex]
Determine which integers in the set S: {−2, −3, −4, −5} will make the inequality 4p − 7 ≥ 9p + 8 true.
PLS HELP ME
The integers in the set s: {-2,-3,-4,-5} will make the inequality 4p-7 [tex]\geq[/tex] 9p+8 true are : -3, -4, -5
Let's solve the inequality first
4p -7 [tex]\geq[/tex] 9p +8
Taking p's on the same side we will get :
-7 - 8 [tex]\geq[/tex] 9p - 4p
-15 [tex]\geq[/tex] 5p
Divide by 5 into both sides
-3 [tex]\geq[/tex] p
i.e. p [tex]\leq[/tex] -3
Therefore p must be less than or equal to -3
From the set, we have the numbers -3,-4,-5 which are less than or equal to -3
Hence the integers -3,-4,-5 will make the inequality 4p-7 [tex]\geq[/tex] 9p+8 true
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Please help me I am stuck
The equation that represents the total cost of purchasing currency is 1.30x + 1.50y = 3200.00.
The equation that represents the relationship between the number of currency A and number of currency B is x = 5y.
x = 2000 and y = 400
There are 2000 of currency A and 400 of currency B
How to determine the number of currency?In order to write a system of linear equations to describe this situation, we would assign variables to the number of currency A and currency B, and then translate the word problem into an algebraic equation as follows:
Let the variable x represent the number of currency A.Let the variable y represent the number of currency B.Since she budgeted $3200.00 for spending money on an upcoming trip and currency A is trading at $1.30 per euro, and currency B is trading at $1.50 per pound, a system of linear equations to describe this situation is given by;
1.30x + 1.50y = 3200.00
x = 5y
1.30(5y) + 1.50y = 3200.00
8y = 3200
y = 3200/8
y = 400
x = 5y
x = 5(400)
x = 2000
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Match each graph with the quadratic function it represents.
f(x) = -2x2 + 12x − 17
f(x) = 2x2 − 12x + 17
f(x) = 2x2 + 12x + 17
f(x) = 2x2 + 12x − 17
f(x) = -2x2 − 12x − 19
Graph shows downward parabola plotted on a coordinate plane. The parabola has vertex at (minus 3, minus 1). The parabola has left slope at (minus 4, minus 3) and right slope at (minus 2, minus 3).
arrowRight
Graph of quadratic functions on a coordinate plane. Upward parabola vertex is at (minus 3, minus 1) in quadrant 3. Left slope at (minus 4, 1) and right slope at (minus 2, 1) in quadrant 2.
arrowRight
Graph shows downward parabola plotted on a coordinate plane. The parabola has vertex at (3, 1). The parabola has left slope at (2, minus 1) and right slope at (4, minus 1).
arrowRight
Graph shows upward parabola plotted in quadrant 1 of a coordinate plane. The parabola has vertex at (3, minus 1). The parabola has left slope at (2, 1) and right slope at (4, 1).
The graph with the upward parabola plotted in quadrant 1 of a coordinate plane, with the vertex at (3, -1), and left and right slopes at (2, 1) and (4, 1), matches the quadratic function f(x) = (x - 3)^2 - 1.T
To match the graph with the quadratic function it represents, we need to analyze the given information about the graph.
The graph shows an upward parabola plotted in quadrant 1 of a coordinate plane. This means that the parabola opens upwards.
The vertex of the parabola is given as (3, -1), which means that the axis of symmetry is a vertical line passing through x = 3, and the vertex is the lowest point on the parabola.
The left slope of the parabola is given as (2, 1), which means that the slope on the left side of the vertex is positive and equal to 1.
The right slope of the parabola is given as (4, 1), which means that the slope on the right side of the vertex is also positive and equal to 1.
Based on this information, we can determine the quadratic function that matches the graph.
The vertex form of a quadratic function is given by f(x) = a(x - h)^2 + k, where (h, k) represents the vertex.
In this case, the vertex is (3, -1), so the equation can be written as f(x) = a(x - 3)^2 - 1.
Since the parabola opens upwards, the coefficient of a must be positive.
The left and right slopes of the parabola are both equal to 1, which means that the coefficient a must be equal to 1.
Therefore, the quadratic function that matches the graph is f(x) = (x - 3)^2 - 1.
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Solve
60 = 9p − 3 + 7p
The solution to the equation 60 = 9p − 3 + 7p is 3.94.
To solve the equation 60 = 9p - 3 + 7p, we need to simplify and combine like terms in order to isolate the variable "p" on one side of the equation.
First, let's combine the "p" terms by adding the coefficients of "p":
60 = 9p + 7p - 3
This simplifies to:
60 = 16p - 3
To isolate the variable "p", we want to get rid of the constant term (-3) on the right side of the equation. We can do this by adding 3 to both sides:
60 + 3 = 16p - 3 + 3
63 = 16p
Now we have the equation 63 = 16p. To solve for "p", we need to get rid of the coefficient 16. We can do this by dividing both sides of the equation by 16:
63/16 = 16p/16
3.9375 = p
Therefore, the solution to the equation is p ≈ 3.9375, or approximately p ≈ 3.94.
In summary, by simplifying and combining like terms, we obtained the equation 63 = 16p. By dividing both sides by 16, we found the value of "p" to be approximately 3.9375.
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En cierto laboratorio se cultiva la cepa de una bacteria, causal de múltiples problemas. Con fin de determinar la rapidez de reproducción de dicha bacteria, esta se coloca en un medio de crecimiento y condiciones favorables. La población existente es de 250 bacterias y se observa que cada hora se duplica la cantidad
The exponential function giving the number of bacteria after x hours is given as follows:
[tex]y = 250(2)^x[/tex]
How to define an exponential function?An exponential function has the definition presented according to the equation as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for this problem are given as follows:
a = 250, b = 2.
Hence the function is given as follows:
[tex]y = 250(2)^x[/tex]
Missing InformationThe problem asks for the exponential function giving the number of bacteria after x hours is given as follows:
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