Answer:
f(x)=(x-1)^2+3
Step-by-step explanation:
Both equations vertexes equal (1, 3) while the rest do not match.
f(x) = (x - 1)² + 3 function in vertex form is equivalent to f(x) = 4 + x² - 2x.
We can use the technique of completing the square to rewrite the given function f(x) in vertex form.
f(x) = 4 + x² - 2x
f(x) = (x² - 2x) + 4
Adding and subtracting (1) inside the parentheses
f(x) = (x² - 2x + 1) + 4 - 1
f(x) = (x - 1)² + 3
So, the equivalent function in vertex form is f(x) = (x - 1)² + 3.
Therefore, the correct option is f(x) = (x - 1)² + 3.
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Which graph shows the image of ABCD? On a coordinate plane, parallelogram A prime B prime C prime D prime has points (negative 2, 5), (0, 3), (0, negative 1.2), (negative 2, 1). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (negative 2, 5), (negative 2, 1), (0, negative 1), (0, 3). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (5, 2), (3, 0), (negative 1.5, 0), (0.5, 2). On a coordinate plane, parallelogram A prime B prime C prime D prime has points (5, 2), (1, 2), (negative 1.5, 0), (2.8, 0).
A graph which shows the image of ABCD is: A. on a coordinate plane, parallelogram A'B'C'D' has points (-2, 5), (0, 3), (0, -1.2), (-2, 1).
What is a transformation?A transformation refers to the movement of a point on a cartesian coordinate from its original (initial) position to a new location.
In Geometry, there are different types of transformation and these include the following:
DilationReflectionRotationTranslationBased on transformation of parallelogram ABCD, we can infer and logically deduce that a graph which shows the image of ABCD is that on a coordinate plane, with parallelogram A'B'C'D' having points (-2, 5), (0, 3), (0, -1.2), (-2, 1) as shown in the image attached below.
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Diego wants to paint his room purple. He bought one gallon of purple paint that is 30% red paint and 70% blue paint. Diego wants to add more blue to the mix so that the paint mixture is 20% red, 80% blue.
1. How much blue paint should Diego add? Test the following possibilities: 0.2 gallons, 0.3 gallons, 0.4 gallons, 0.5 gallons.
0.2 gallons
0.2 gallons,
0.3 gallons
0.3 gallons,
0.4 gallons
0.4 gallons,
0.5 gallons
0.5 gallons,
BoldItalicUnderlineImage (12 image limit)Increase indentDecrease indentFormula keypadUndoRedoBullet listNumbered list
Edit imageView imageDelete image
2. Write an equation in which x
represents the amount of paint Diego should add.
3. Check that the amount of paint Diego should add is a solution to your equation.
idrk but I hope you have a good day and good luck with ur answer
Natalie charges $1,490 per month to rent each of her three rental houses. natalie must pay $5,850 in maintenance costs per house per year. if all three houses are occupied, how much money will natalie earn over seven years? a. $334,250 b. $252,630 c. $84,210 d. $375,480
The correct option is B.
Natalie charges $1490 in rent for each home Per month.
According to given information:Natalie charges $1490 in rent for each home.
Given that Natalie owns three homes, her monthly rent will be:
= $4470 (3 * 1490) dollars.
The annual income Natalie receives from her three homes is
=($12 * $4470)
= $53680.
Natalie spends $5850 a year on maintenance for each home.
The total amount Natalie spends annually to maintain her three homes is therefore:
=(3 * 5850) dollars, which comes to 17550 dollars.
Then Natalie's annual income would be
= [(53640 - 17550) dollars]
= 36090 dollars.
The total amount Natalie made over the course of seven years was
= ($7 * 36090)
=$252630
The correct option is B.
Natalie charges $1490 in rent for each home Per month.
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Answer:B) $252630
Step-by-step explanation:edge
Tina wrote a check for $35 on Monday. On Tuesday she made of withdrawal of $60 and on
Wednesday she deposited $75. What is the change in Tina's account after the three days?
The change in Tina's account after the three days; Monday, Tuesday and Wednesday is $-25
Deposit and withdrawalDeposit is a sum of money or other asset given as an initial payment, to show good faith, or to reserve something for purchase.
Withdrawal on the other hand, is to extract money from an account.
Check = $35Withdrawal = $60Deposit = $75Change in Tina's account after the three days = - 35 - 60 + 75
= -95 + 75
= $-20
Therefore, the change in Tina's account after the three days; Monday, Tuesday and Wednesday is $-25.
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1. How many quarters are in 12 1/4
2. How many ninths are in 6 1/9
3. How many eighths are in 5 3/4
help math related pleaseee
[tex]c^2 = a^2 + b^2 - 2ab \cos C \\ \\ 55^2 = 24^2 + 40^2 - 2(24)(40)\cos C \\ \\ \cos C=\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \\ \\ C=\cos^{-1} \left(\frac{55^2 - 24^2 - 40^2}{-2(24)(40)} \right) \\ \\ \cos C=-\frac{283}{640} \\ \\ C=\boxed{\arccos \left(\-frac{283}{640} \right)}[/tex]
[tex]C=\boxed{\arccos \left( - \frac{283}{640} \right)}[/tex]
x² + y² if x = 7 and y = 5. What is the solution to this??
Step-by-step explanation:
x = 7
y = 5
[tex] = {x}^{2} + {y}^{2} [/tex]
[tex] = (7 {)}^{2} + (5 {)}^{2} [/tex]
= 7 × 7 + 5 × 5
[tex] = 49 + 25 [/tex]
[tex] = 74[/tex]
Hey there!
x^2 + y^2
= 7^2 + 5^2
= 7 * 7 + 5 * 5
= 49 + 25
= 74
Therefore, your answer should be: 74
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Hazel is measuring two prisms whose bases are squares.
Given the volume V and the base's side length a of the first prism, Hazel uses the formula
h=V/a^2
to compute its height h to be 10 centimeters.
The base of the second prism has the same side length, but has 5 times the volume. What is its height?
The height of the second square base prism is 50 cm.
How to find volume of a square base prism?The volume of the first square base prism is represented as follows:
v = ha²
where
h = heighta = side length of the baseTherefore, the height of the prism is 10 cm.
v = 10a²
Hence, the volume of the initial prism is 5 times the volume. Therefore,
v = 5(10a²)
v = 50a²
Therefore,
50a² = ha²
divide both sides by a²
50a² / a² = ha² / a²
50 = h
h = 50 cm
Therefore, the height of the second square base prism is 50 cm.
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7/3=7:
what will seven over three equals seven divide be
Answer:
3(7/3=7:3)Step-by-step explanation:
7/3=7:
what will seven over three equals seven divide be
7/3 is a division (7:3)
so
your answer is :
3
(7/3=7:3)
help on this math problem!! if there is any work that can be shown it would be great thanks!!!
Answer:
4230.44
Step-by-step explanation:
Simplify 10 times the square root of quantity 3 x end quantity plus 4 times the square root of quantity 3 x end quantity plus 5 times the square root of quantity 3 x end quantity. 9 times the square root of quantity 3 x end quantity 9 times the square root of quantity 6 x end quantity 19 times the square root of quantity 3 x end quantity 19 times the square root of quantity 9 x cubed
The square root of the quantity x plus 7 end quantity minus 1 equals x=2.
What is square root?A number's square root is the factor that can be multiplied by itself to yield that number. Square root of, end square root is the symbol for square root. Finding an integer's square root is the inverse of squaring a number.To find the square root:
√(x + 7) − 1 = x√(x + 7) = x + 1x + 7 = (x + 1)²x + 7 = x² + 2x + 10 = x² + x − 60 = (x + 3) (x − 2)x = -3 or 2Check for extraneous solutions:
√(-3 + 7) − 1 = -3√4 − 1 = -32 − 1 = -31 = -3x ≠ -3√(2 + 7) − 1 = 2√9 − 1 = 23 − 1 = 22 = 2x = 2Therefore, the square root of the quantity x plus 7 end quantity minus 1 equals x = 2.
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The correct question is given below:
The square root of the quantity x plus 7 end quantity minus 1 equals x
The scatter plot shows the number of pumpkins that have been picked on the farm during the month of October:
A scatter plot with points showing an upward trend with points that are moderately spread out from a line of best fit. The y axis is labeled Number of Pumpkins and the x axis is labeled Days in October
Part A: Using computer software, a correlation coefficient of r = 0.51 was calculated. Based on the scatter plot, is that an accurate value for this data? Why or why not? (5 points)
Part B: Instead of comparing the number of pumpkins picked and the day in October, write a scenario that would be a causal relationship for pumpkins picked on the farm. (5 points)
Question 4 (Essay Worth 10 points)
(05.07 HC)
A student is assessing the correlation between the number of hours a plant receives sunlight and the height to which it grows. The table shows the data:
Number of hours of sunlight
(x) 0 1 2 3 4 5 6 7 8 9
Height of plant in cm
(y) 4 7 10 13 16 19 22 25 28 31
Part A: Is there any correlation between the number of hours of sunlight that a plant receives and the height to which it grows? Justify your answer. (4 points)
Part B: Write a function that best fits the data. (3 points)
Part C: What does the slope and y-intercept of the plot indicate about the plant? (3 points)
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FDK121.12
The correlation coefficient of r = 0.51 shows that it's an accurate value for this data.
A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm
There is a correlation between the number of hours of sunlight that a plant receives and the height to which it grows.
The function that best fits the data is y = 3x + 4.
The y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.
What is a Scatter Plot?The association between two variables that are correlated can be shown by a scatter plot which has a trendline along which the data points are located.
A correlation coefficient of r = 0.51 is accurate based on the scatter plot given. If the trendline slopes upwards from the left to the right, it shows a positive correlation and vice versa.
A scenario that would be a causal relationship can be the quantity of fertilizer used vs kg of pumpkins picked on the farm.
There is a direct correlation between the number of hours of sunlight that a plant receives and the height to which it grows. This can be seen through the growth in the plant.
The function is y = 3x + 4
When x = 0, y = 3(0) + 4 = 4.
In conclusion, y-intercept indicates that the plant started at 4cm and the slope shows that with each hour of sunlight, the plant grows 3 inches.
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How do you graph x < 5 on a number line and is the circle open or not? Where's the number line going? Thanks!
The inequality sign < means "less than." If there is a line underneath the inequality sign that means "less than or equal to."
To graph x < 5, we first need to understand what the inequality is saying. In this case, x must be less than 5. So, a number that will make this inequality true will be less than, but not equal to, 5.
Start by putting an open circle on the number 5. An open circle indicates that 5 is not a value that works in this inequality. Then, we know that our values that make this inequality true are less than 5, so we'll draw an arrow from the circle to the left as numbers to the left of 5 are less than it.
Hope this helps!
Write the first five terms of the recursively defined sequence. a1 = 6, ak 1 = 1 3 ak2
The first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
For given question,
We have been given the recursive formula of a sequence.
[tex]a_{k+1}=\frac{1}{3}{a_k}^2[/tex]
Also, the first term of the sequence is,
a1 = 6
Substitute k = 1 in given recursive formula.
⇒ [tex]a_{1+1}=\frac{1}{3}{a_1}^2[/tex]
⇒ a2 = 1/3 (6)²
⇒ a2 = (1/3) × 36
⇒ a2 = 12
Substitute k = 2 in given recursive formula.
⇒ [tex]a_{2+1}=\frac{1}{3}{a_2}^2[/tex]
⇒ a3 = (1/3) × (12)²
⇒ a3 = (1/3) × 144
⇒ a3 = 48
Substitute k = 3 in given recursive formula.
⇒ [tex]a_{3+1}=\frac{1}{3}{a_3}^2[/tex]
⇒ a4 = (1/3) × (48)²
⇒ a4 = (1/3) × 2304
⇒ a4 = 768
Substitute k = 4 in given recursive formula.
⇒ [tex]a_{4+1}=\frac{1}{3}{a_4}^2[/tex]
⇒ a5 = (1/3) × (768)²
⇒ a5 = (1/3) × 589824
⇒ a5 = 196608
Therefore, the first five terms of the recursively defined sequence are 6, 12, 48, 768, 196608
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[tex]2x+5\ \textless \ \frac{x+1}{4}[/tex]
Answer:
x < -19/7
Step-by-step explanation:
Solve for x
2x+5 < (x+1)/4
Multiply each side by 4
4( 2x+5) < (x+1)/4 *4
8x + 20 < x+1
Subtract x from each side
8x+20-x < x+1-x
7x + 20 < 1
Subtract 20 from each side
7x+20-20 < 1-20
7x< -19
Divide by 7
7x/7 < -19/7
x < -19/7
Answer:
[tex] \red{x < \frac{ - 19}{7} }[/tex]
Step-by-step explanation:
[tex]2x + 5 < \frac{x + 1}{4} \\ \text{use \: cross \: muliplication} \\ 4(2x + 5) < x + 1 \\ 8x + 20 < x + 1 \\ 8x - x < - 20 + 1 \\ 7x < - 19 \\ \frac{7x}{7} < \frac{ - 19}{7} \\ x < \frac{ - 19}{7} [/tex]
A basketball player averages 12.5 points per game. There are 24 games in a season. At this rate, how many points would the player score in an entire season?
In the entire season, the basketball player would score
point
Answer:
300 points
Step-by-step explanation:
Since we have a constant rate (12.5 points/game), we can find the number of points by setting up a proportion:
[tex]\frac{12.5}{1}=\frac{x}{24}\\\\x=(12.5*24)=300[/tex]
Airport administrators take a sample of airline baggage and record the number of bags that weigh more than 75 pounds. What are the cases?
In this situation, the cases are the bags or each piece of baggage.
What is a case?In statistics, the word case is used to refer to the individual from which data is collected. For example, in a study about students' performance, the cases are each of the students.
What is the case in this situation?Considering the administrators will need to weight and record each bag, the cases are each piece of baggage.
Note: This question is incomplete; here are the missing options:
A. Number of bags weighing more than 75 pounds.
B. Average weight of the bags.
C. Each piece of baggage.
D. The airport administrators.
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a 3 gallon jug of water cost $11.04. what’s the price per cup?
4|a| + 8 -a, if a = -2
PLEASE HELP!!!!!!!!!!!!!! I'm stuck on this!!
4|a| + 8 - a, if a = -2
What we're doing here is plugging in the given value of a for every instance of a in the expression.
4|-2| + 8 - (-2)
---The absolute value of a number is its distance from 0. -2 is 2 units away from 0, so the absolute value of -2 is 2. And, remember two negatives make a positive!
4(2) + 8 + 2
8 + 8 + 2
16 + 2
18
Hope this helps!
A base- three-digit number is selected at random. What is the probability that the base- representation and the base- representation of are both three-digit numerals
The probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753
How to determine the probability?To calculate the probability that the base-9 representation and the base-11 representation of are both three-digit numerals, we need the following parameters:
The smallest 3-digit base 11 number in base 10The largest 3-digit in base 9 in base 10 with 3 digits The count of base 10 3-digit numbersThe smallest 3-digit base-11 number is 100
When converted to base 10, the equivalent number is 121
The largest 3-digit base-9 number is 888
When converted to base 10, the equivalent number is 728
So, the total number of possibilities is:
Possibilities = 728 - 121 + 1
Possibilities = 608
The count of base 10 3-digit numbers is
Count = 999 - 100 + 1
Count = 900
The required probability is:
P = 608/900
Evaluate
P = 0.6753
Hence, the probability that the base-9 representation and the base-11 representation of are both three-digit numerals is 0.6753
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Complete question
A base-10 three-digit number is selected at random. What is the probability that the base-9 representation and the base-11 representation of are both three-digit numerals
If f(x)=3x, g(x)=x+2 and fog(x)=18, find the value of x.
solve this
Answer: 4
Step-by-step explanation:
f(g(x)) = f(x+2) = 3(x+2) = 18
x + 2 = 6
x = 4
is it true or false! I need help fast thanks!
The answer is True.
On differentiating using product rule,
[tex]\mathsf {\frac{d}{dx}[xe^{x}] = x(e^{x})+e^{x}(1)}[/tex]
[tex]\mathsf {\frac{d}{dx}[xe^{x}] = e^{x}(x + 1)}[/tex]
The general form of product rule :
[tex]\boxed {\frac{d}{dx}(ab) = a(b')+b(a')}[/tex]
Anderson uses the discriminant to correctly find the number of real solutions of the quadratic equation one-halfx2 4x 8 = 0. which explanation could anderson provide?
Anderson could provide 0.5x2 + 4x + 8 = 0 has exactly one real root if the discriminant is 0,
What is quadratic equation?Any equation that can be rewritten in standard form as where x represents an unknown, a, b, and c represent known numbers, and where a 0 is true is a quadratic equation. As there is no ax2 term when a = 0, the equation is linear rather than quadratic.
What is discriminant?A polynomial's discriminant is a quantity that depends on the coefficients and enables for some root attributes to be inferred without actually computing them. It is actually a polynomial function of the original polynomial's coefficients.
According to the given information:0.5x^2 + 4x + 8 = 0
The discriminant is computed utilizing:
d = b^2 - 4ac
Thus, we have:
d = 4^2 - 4 * 0.5 * 8
Evaluate
d = 0
The equation has only one real root since the discriminant is 0,
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From the top of a 6m house, the angle of elvation to the top of a flappole is across the street is 9 degrees. the angle of depression is 22 degrees to the base of the flapole. Redraw the diagram below and label all the angles. How tall is the flagpole? Round naswer to one decimal place.
The height of the flag pole which is described as in the task content is; 8.2m.
What is the height of the flagpole as described from the top of the 6m house?The horizontal distance between the 6m house and the flagpole in discuss can be evaluated by means of the angle of depression and trigonometric identity, tan as follows;
tan 22° = 6/x
x = 6/tan 22 = 14.9m.
Consequently, the horizontal distance from the top of the house to the top of the flagpole is therefore;
tan 9° = y/14.9
y = 14.9 tan 9° = 2.2m
Ultimately, the height of the flagpole is; 6+2.2 = 8.2m.
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Which of the following equations is an example of inverse variation?
Since this is the result of the second function, hence equations I and II are inverse of each other.
Inverse of a function
Inverse of a function is s a function that serves to undo another function. That is, if f(x) produces y, then putting y into the inverse of f produces the output x.
Given the function f(x) = 3x
Find its inverse
Replace with y with x
y = 3x
x =3y
Make y the subject of the formula
3y = x
y = x/3
Since this is the result of the second function, hence equations I and II are inverse of each other.
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Brass is an alloy made by melting and mixing copper and zinc. A metallurgist has two brass
alloys, one that is 65% copper and one that is 90% copper. He would like to combine a
portion of each alloy to produce 500 g of a new alloy that is 75% copper.
Write a system of equations for this problem
Answer:
x +y = 5000.65x +0.95y = 0.75(500)solution: (x, y) = (300, 200)Step-by-step explanation:
A system of equations for the problem can be written using the two given relationships between quantities of brass alloys.
SetupLet x and y represent the quantities in grams of the 65% and 90% alloys used, respectively. There are two relations given in the problem statement.
x + y = 500 . . . . . . quantity of new alloy needed
0.65x +0.90y = 0.75(500) . . . . . quantity of copper in the new alloy
These are the desired system of equations.
SolutionThis problem does not ask for the solution, but it is easily found using substitution for x.
x = 500 -y
0.65(500 -y) +0.90y = 0.75(500)
(0.90 -0.65)y = 500(0.75 -0.65) . . . . . . subtract 0.65(500)
y = 500(0.10/0.25) = 200
x = 500 -200 = 300
300 grams of 65% copper and 200 grams of 90% copper are needed.
A rubber gasket has a circumference of 3.2 cm. when placed in service, it expands by a scale factor of 2. what is the circumference of the gasket when in service?
6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.
What does circumference mean?The boundary length of any circular shape is known as the circumference.
What is scale factor?A scale factor is a quantity multiplier (also known as a scale). The scaling factor for x, for instance, is represented by the letter "C" in the equation y = Cx. The factor would be 5 if y = 5x were the equation.
According to the given data:After scale factor 2 is applied, 6.4 cm must be the gasket's needed circumference.
It includes a rubber gasket with a 3.2 cm circumference. The circumference of the gasket has must be calculated after scaling up by factor 2.
Here,
3.2 cm is the gasket's circumference.
The circumference changed upon scale factor 2 dilatation.
Dilated gasket circumference: 2 * 3.2 = 6.4 cm
As a result, 6.4 cm is the needed circumference of the gasket following dilatation with a scale factor of 2.
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Answer:
6.4cm
Step-by-step explanation:
I Just Took the Test.
Today, Stephen is three times as old as Gautham. Ten years ago Stephen turned 2. How old will Gautham be
in 8 years?
NEED URGENT HELP: A random sample is taken of people who have bought tickets for a concert. In the sample, 21 out of 150 people say they will contribute $5.00 each towards a music scholarship for a local high school students. If 3,500 people bought concert tickets, predict how much will be raised for the scholarship.
Answer:
$2,450
Step-by-step explanation:
21:150 is the ratio of people who will donate $5.
21:150 / 3 = 7:50
7:50 x 2 = 14:100
14:100 = 21:50
14:100 x 35 = 490:3500
490 out of 3500 people will contribute $5.
490 x 5 = $2,450
Determine whether the geometric series is convergent or divergent. if it is convergent, find the sum. (if the quantity diverges, enter diverges. ) 7 − 8 64 7 − 512 49
The sum of the given series is 49 and it converges to infinity.
According to the statement
we have given that a series which is 7, -8, 64/7, 512/49
And we have to find that the series is converges or diverges.
So, For this purpose,
The nth term in the series is 6 multiplied by the (n-1)th power of -8/7:
So,
[tex]a_{1} = 7(\frac{-8}{7} )^{1-1}[/tex]
[tex]a_{2} = -8(\frac{-8}{7} )^{2-1}[/tex]
[tex]a_{3} = \frac{64}{7} (\frac{-8}{7} )^{3-1}[/tex]
And so on then
Sum of the series become to the nth partial sum
[tex]S_{N} = 7(1 +\frac{-8}{7} + ......+ (\frac{-8^(n-2)}{7^(n-2)}) + (\frac{-8^(n-1)}{7^(n-1)}))[/tex]
Multiplying both sides by -8/7 gives
[tex]\frac{-8}{7} S_{N} = 7(\frac{-8}{7} +\frac{-8^{2} }{7^{2}} + ......+ (\frac{-8^(n-1)}{7^(n-1)}) + (\frac{-8^n}{7^n}))[/tex]
and subtracting this from [tex]S_{N}[/tex] gives
[tex]\frac{-1}{7} S_{N} = 7(1-\frac{-8^n}{7^n} )[/tex]
[tex]S_{N} = 49 (-1 + (8/7)^n)[/tex]
Now the sum of the series is 49 and the it converges to infinity.
So, The sum of the given series is 49 and it converges to infinity.
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