The equation of the quadratic function is (b) C(t) = (t - 4)²
How to determine the equation of the quadratic function?From the question, we have the table of values that can be used in our computation:
A quadratic equation is represented as
f(x) = a(x - h)² + k
Where
Vertex = (h, k)
From the graph, we have the vertex to be
(h, k) = (4, 0)
Substitute (h, k) = (4, 0) in f(x) = a(x - h)² + k
So, we have
f(x) = a(x - 4)²
Also, from the graph, we have the point (2, 4)
This means that
a(2 - 4)² = 4
So, we have
4a = 4
Divide both sides by 4
a = 1
Substitute a = 1 in f(x) = a(x - 4)²
f(x) = (x - 4)²
Rewrite as C(t)
C(t) = (t - 4)²
Hence, the equation is C(t) = (t - 4)²
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its C(t) = (x − 4)2
use desmos graphing its very helpful
Which ordered
pair is on the line
y = -5x + 2?
Answer:
(0,2)
(1,-3)
(2,-8)
|x-6|=11 solve this equation
Answer:
x = -5 or x = 17
Step-by-step explanation:
The absolute value is the number's distance from 0.
So, we need to write two equations.
x - 6 = 11
x - 6 = -11.
Next, we need to add 6 to both sides of each equations.
11 + 6 = 17
-11 + 6 = -5
So, x = 17 and x = -5.
Answer: It could be -5 or 17
Step-by-step explanation: So, it can be both, but as I see it would most likely be 17 because I see you put x-6 as an absolute value. so, to find the value of x, we could do 11 + 6 (Inverse operations), so 11 + 6 = 17. If it was NOT the absolute value of x-6, we could find it to be -5, by subtracting -6 from 11, to get -5. I hope this helps you understand now, if any questions please comment down below.
gsuppose that grade point averages of undergraduate students at one university have a bell-shaped distribution with a mean of 2.56 and a standard deviation of 0.45. using the empirical rule, what percentage of the students have grade point averages that are greater than 1.66? please do not round your answer.
The percentage of students with GPAs greater than 1.66 is 88.22%.
To answer this question, we need to use the empirical rule, which states that 68% of the data is within one standard deviation of the mean. To calculate the percentage of students with GPAs greater than 1.66, we need to subtract the percentage of students with GPAs less than 1.66 from 100%.
The percentage of students with GPAs less than 1.66 can be calculated by subtracting 1.66 from the mean of 2.56, then dividing by the standard deviation of 0.45. This gives us 2.11 standard deviations below the mean, which corresponds to a percentile of 11.78%.
Therefore, the percentage of students with GPAs greater than 1.66 is 100% - 11.78% = 88.22%.
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Can somebody please help me because I don’t understand
Answer: x = 64
Step-by-step explanation:
5/8x = 40
We divided by 5/8 from both sides
40/1 divided by 5/8 is the same as
40/1 times 8/5 = 320/ 5 = 64
x= 64
Solve the system of equations by substitution.
Answer:
x = -6
y = -18
Step-by-step explanation:
6x -2y = 0
x - y = 12
Times the second equation by -2!
6x -2y = 0
-2x + 2y = -24
Now add them together and solve for x first!
4x = -24
x = -6
Now put -6 back in the equation and solve for y
6(-6) -2y = 0
-36 - 2y = 0
-2y = 36
y = -18
So, x= -6
y= -18
A new patio is in the shape of a square. On a scale drawing, the vertices of the patio's coordinates are (10, 8. 5), (10, 1. 5), (3 ,1. 5 ), and (3, 8. 5). How long is each side of the patio?.
As per the given coordinates, the length of each side is 7
The term coordinate in math refers the pair of numbers that describe the position of a point on a coordinate plane by using the horizontal and vertical distances from the two reference axes.
Here we have given that the new patio is in the shape of a square. On a scale drawing, the vertices of the patio's coordinates are (10, 8. 5), (10, 1. 5), (3 ,1. 5 ), and (3, 8. 5).
And we need to find the length of each side of the patio.
While we have given the following points in the given question
=> (10, 8. 5), (10, 1. 5), (3 ,1. 5 ), and (3, 8. 5).
And then we have to plot these values on the graph.
For that we have to label the graph first and then we have to point put the coordinates on the graph.
=> After pointing the values, we have to label the graph with the corresponding coordinates.
Therefore, the resulting graph is look like the following one.
While we looking into the resulting graph, we get the length as 7.
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Rahul is deciding between two parking garages. Garage A charges an initial fee of $12 to park plus $4 per hour. Garage B charges an initial fee of $6 to park plus $5 per hour. Let AA represent the amount Garage A would charge if Rahul parks for tt hours, and let BB represent the amount Garage B would charge if Rahul parks for tt hours. Write an equation for each situation, in terms of t,t, and determine which garage would be cheaper if Rahul needs to park for 10 hours.
Answer:
1. AA = 4t + 12
2. BB = 5t + 6
3. Garage A would be cheaper to park for 10 hours.
Step-by-step explanation:
1. Garage A's situation is linear, meaning that there is a constant rate of change, or slope.
A linear function in slope-intercept form is: [tex]y = mx + b[/tex], where m is the rate of change, and b is the y-intercept, or the initial value.
Find m and b:m = 4 because that is the cost per hour, which is additive and constantb = 12 because it is the initial cost Rahul has to pay∴ AA = 4x + 122. Garage B's situation is linear, meaning that there is a constant rate of change, or slope.
A linear function in slope-intercept form is: [tex]y = mx + b[/tex], where m is the rate of change, and b is the y-intercept, or the initial value.
Find m and b:m = 5 because that is the cost per hour, which is additive and constantb = 6 because it is the initial cost Rahul has to pay∴ AA = 5x + 63. To find how much it will cost Rahul to park in Garages A and B for 10 hours, substitute 10 into t, which is the number of hours. Then, determine which cost is lower.
Garage A for 10 hours:AA = 4t + 12AA = 4(10) + 12AA = 40 + 12∴ AA = $52Garage B for 10 hours:BB = 5t + 6BB = 5(10) + 6BB = 50 + 6∴ BB = $56$52 < $56, so Garage A is cheaper for 10 hours.
Bonnie makes $12.40/hr and works as a server. on tuesday she worked for 6 hours and twenty minutes and made $110 in tips. how much did she make in total and what is her hourly wage?
Answer: 188.53$ in total.
$31.42 as hourly wage .
Step-by-step explanation:
Wage1 for 6hours = $12.4 * 6
Wage2 for 20minutes = $12.4 / 3
Since an Hour has three 20 minutes in it , so hourly wage $12.4 is divided by 3 to get the wage for a 20minute work.
Wage3 as Tips = $110
Total Wages for Tuesday = Wage1 + Wage2 + Wage3
= $188.53
New hourly Wage = $188.53 / 6 = $31.42
How would you write the equation with a slope of 3/5 and a y-intercept of 5?
The equation of the line that has a slope of 3/5 and a y-intercept of 5 will be y = (3/5)x + 5.
What is a linear equation?A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.
The linear equation is given as,
y = mx + c
Where m is the slope of the line and c is the y-intercept of the line.
The slope of the line is 3/5 and the y-intercept of the line is 5. Then the equation of the line is given as,
y = (3/5) x + 5
The equation of the line that has a slope of 3/5 and a y-intercept of 5 will be y = (3/5)x + 5.
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What are the 3 methods for finding the inverse of a function?
(1) In general, switching the coordinates x and y is how an inverse is calculated.
(2) The function is a one-to-one function and the inverse is also a function if a horizontal line crosses the original function in a single place.
(3) We can find the inverse in algebra by replacing f(x) by y and then solve for x.
In general, switching the coordinates x and y is how an inverse is calculated. Although not strictly a function, this freshly constructed inverse is a relation.
To ensure that the initial function's inverse will be a function, the major purpose must be a one-to-one function. When every second element matches the first value, a function is said to be a one-to-one function.
To determine whether a function is a one-to-one function, use the horizontal line test. The function is a one-to-one function and the inverse is also a function if a horizontal line crosses the original function in a single place.
When a function's formula has been provided to you, follow these steps to discover its inverse:
(1) Change "f(x)" to "y".
(2) Make an effort to resolve the x= equation.
(3) Switch the xs and ys.
(3) Change y to "f1(x)"
We can find the inverse in algebra by replacing f(x) by y and then solve for x.
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a local bank needs information concerning the savings account balances of its customers. a random sample of 15 accounts was checked. the mean balance was $686.75 with a standard deviation of $256.20. find a 98% confidence interval for the true mean. assume that the account balances are normally distributed. round to the nearest cent.
Answer:
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Practice & Problem Solving
Identify the domain and range
{(2, 1), (4, 2), (6, 3), (8, 4), (10,5)}
Answer:
It has a constant order in the problem
X (Domain): 2 up every time Y goes up 1
Y (Range): 1 up every time X goes up 2
This is constant and will NOT be broken factor
What do the positive and negative signs mean in limits?
Positive and negative signs in limits indicate whether the limit is approaching from the positive side or the negative side. If a amount is approaching from the positive side, the sign is positive; if it is approaching from the negative side, the sign is negative.
When taking the amount of a function, the positive and negative signs indicate the direction in which the limit is approaching. A positive sign means the limit is approaching from the positive side of the function’s domain, while a negative sign indicates the limit is approaching from the negative side. For example, if a limit is written as[tex]$\lim\limits_{x \to 3^+} f(x)$,[/tex]this means the limit is approaching from the positive side of the domain, when x is approaching 3. Similarly, if the limit is written as [tex]$\lim\limits_{x \to 3^-} f(x)$[/tex] this means the limit is approaching from the negative side of the domain, when x is approaching 3. Thus, the positive and negative signs in limits indicate the direction the limit is approaching from.
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find the area and perimeter of an equilateral triangle whose equal side is 6cm
Answer:
Area = 9√3 cm²
Perimeter = 18 cm
Step-by-step explanation:
Area of equilateral triangle ABC =
(√3/4) × 6²
= (√3/4) × 36
= 9√3 inches2
ABC is an equilateral triangle with side = 6 cm
Perimeter of an equilateral triangle = AB+BC+CA
Perimeter of an equilateral triangle = 6+6+6
Perimeter of an equilateral triangle = 18 cm
30 points! are the volumes the same? if not which one is greater?
Answer:
i round off to two decimals
LEFT:(solve for radius)circumference = 2ñr
11 = 2(3.14)r
11 = 6.28r
r = 0.57 inches
(solve for volume)
volume = ñr²h
volume = (3.14)(0.57²)(8.5)
volume = (3.14)(0.33)(8.5)
volume = 8.81 inches³
RIGHT:(solve for radius)circumference = 2ñr
8.5 = 2(3.14)r
8.5 = 6.28r
r = 0.74 inches
(solve for volume)
Volume - ñr²h
Volume = (3.14)(0.74²)(11)
Volume = (3.14)(0.55)(11)
Volume = 18 inches
Therefore, the right side cylinder is greater than the left cylinder.
i round off to two decimals
Step-by-step explanation:
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Answer: Adult: $20 Child: $9
Step-by-step explanation:
20 + 20 + 20 = 60
9 + 9 + 9 + 9 = 36
60 + 36 =96
Select the reason that best supports Statement 6 in the given proof.
Answer:
B. Distributive Property
Step-by-step explanation:
The equation for the distributive property is
ab+ac = a(b+c)
We, see it similar to statement 6, so it is the correct answer
How can you determine if the left end behavior of a polynomial function is rising or falling?
To determine if the left end behavior of a polynomial function is rising or falling, you can look at the sign of the leading coefficient of the polynomial. If the coefficient is positive, the left end behavior is rising, and if the coefficient is negative, the left end behavior is falling.
The left end behavior of a polynomial function can be determined by looking at the sign of the leading coefficient. The leading coefficient is the coefficient of the highest degree term in the polynomial. If the leading coefficient is positive, then the left end behavior of the function is rising, because a positive coefficient will cause the function to increase in value as x increases. On the other hand, if the leading coefficient is negative, then the left end behavior of the function is falling, since a negative coefficient will cause the function to decrease in value as x increases. Knowing the sign of the leading coefficient is therefore a quick and easy way to determine whether a polynomial function is rising or falling on its left end.
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A cylinder has a volume of 45 cubic units and a radius of 3 units. What is its height?
Answer:
h = 1.59 (1.6 rounded)
Step-by-step explanation:
A cylinder has a volume of 45 cubic units and a radius of 3 units. What is its height?
A cylinder's volume is π r² h
we use the inverse formula
h=V/πr²
h = 45/π3²
h = 45/3.14 × 9
h = 45 : 28.26
h = 1.59 (1.6 rounded)
eight more than five times a number is twenty thirds. find the number.
Answer:
Step-by-step explanation:Charmaine wanted to study how the area of a rectangle changes with the length if its width is fixed. She computed the areas of several rectangles that have the same width and different lengths. She then plotted the results and connected them with a line, as shown below. The graph shows the area (in ) versus the length (in ).
Find the range and the domain of the function shown.
Answer the questions about the work below:
3x − 8 ≤5x + 6
3x ≤5x −2
−2x ≤−2
Are there any errors in the above work so far? Response area
The correct final answer is:
Answer:
Yes, there is an error in the third step of the solution. The correct result of the third step should be -2x ≤ 8, not -2x ≤ -2. The error occurred because the incorrect value was subtracted from both sides of the inequality
Step-by-step explanation:
The final answer for the inequality 3x − 8 ≤5x + 6 is x ≥ -7, and the third step is wrong, the right answer is -14 ≤ 2x.
What is inequality?An inequality is a relation that compares two numbers or other mathematical expressions in an unequal way. It is most frequently used to compare the sizes of two numbers on the number line.
Given:
3x − 8 ≤ 5x + 6
Add 8 on both sides of the inequality as shown below,
3x − 8 + 8 ≤ 5x + 6 + 8
3x ≤ 5x + 14
Subtract -3x from both sides as shown below,
3x - 3x ≤ 5x + 14 - 3x
0 ≤ 2x + 14
Subtract 14 from both sides as shown below,
0 - 14 ≤ 2x + 14 - 14
-14 ≤ 2x
Divide both sides by 2 as shown below,
-14 / 2 ≤ 2x / 2
-7 ≤ x
or x ≥ -7
Thus, the final answer is x ≥ -7.
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if B=t+10 and A=3t^2-2 find an expression that equals 2B−3A in standard form.
The expression that equals 2B−3A in standard form is - 9t² + 2t + 14
How to determine the expression that equals 2B−3A in standard form.From the question, we have the following parameters that can be used in our computation:
B = t + 10
Also, we have
A = 3t² - 2
The expression that equals 2B−3A is calculated as
Expression = 2B - 3A
Substitute the known values in the above equation, so, we have the following representation
Expression = 2 * (t + 10) - 3 *(3t² - 2)
So, we have
Expression = 2t + 20 - 9t² - 6
Evaluate the like terms
Expression = - 9t² + 2t + 14
Hence, the expression = - 9t² + 2t + 14
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if a rep works eight hours per day and the average length of a call is 30 minutes and the average travel time is 30 minutes and the rep works 250 days per year, then what is the total annual number of calls the rep can make?
Applying basic unitary method and time conversion, The answer is 3750 calls annually.
What is Unitary method?The unitary approach involves calculating the value of a single unit, from which we can calculate the values of the necessary number of units.
Why do we use unitary method?The unitary technique is used practically all the time, from problems involving speed, distance, and time to issues with estimating material costs. The technique is applied to determining a product's pricing. It is used to determine how long it takes a person or vehicle to travel a certain distance in an hour.
average length of call= 30 minutes
average travel time=30 minutes
annual working days=250
per day works 8 hours.
call hour in work = 8*60 - 30 = 450minutes.
number of calls made in those hours= 450/30=15 calls daily.
total annual number of calls= 250 * 15 = 3750
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What are the 4 functions of a roots?
Four main functions of the roots of the plant is given by:
1. Anchorage
2. Absorption of water and minerals
4. Prevention of the soil erosion.
5. Transportation of food from the soil.
Four function of the roots of any terrestrial plants:
Anchorage of the plant :Due to anchorage of the plant root fix in the soil and help in growing the aerial shoot system part of the any tree or plant.
Absorption of water and minerals: It helps to absorb water and minerals from the soil to the roots of the plants .
Prevention of the Soil Erosion : Due to root of the plant soil gets binds to the roots of the plants and does not or in very less quantity get eroded by water or wind.
Transport : Roots of the plants helps to transport food , salt , mineral , and water which given or present in the soil to the shoot or leaves and flowers , fruit of the plant.
Therefore, the four functions of the roots are:
1.Anchorage of the plant
2. Absorption of water and minerals
3. Prevention of the soil erosion
5. Transportation of food.
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6. A recipe requires 2 cups of sugar. If Mrs.
Marina is going to make one half of the recipe,
then how much sugar does she need?
Answer:
Step-by-step explanation: 2 cups of sugar divided by 1/2 equals
*can use calculator and type 2 divided by 1 or 2 times 0.5
Ans. One cup of sugar
Answer:
1
Step-by-step explanation:
the recipe requires to cousin sugar if we are only about to Megha of the recipe we should multiply 2 by 0.5
2x0.5
=1
How do you describe the graph of x is equal to 2?
The graph of x = 2 is a vertical line parallel to y-axis. Also, the slope of x = 2 is undefined and there is no y-intercept.
In this question we need to describe the graph of x is equal to 2.
To draw the graph of x = 2, firstwe find some coordinates of the points.
Consider the points (2, 1), (2, 0), (2, -1)
[As the x coordinate is fixed, we can take any value of y coordinate]
The graph of x = 2 is as shown below.
The graph of x = 2 is a straight vertical line, which is parallel to y-axis.
There is no y-intercept to the graph of x = 2.
Also the slope of line x = 2 is undefined.
Therefore, the graph of x = 2 is a straight line with Slope = Undefined
and no y-intercept.
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How many cans of paint are needed to cover an area of 2000?
The number of cans required to paint an area of 2000 square units is equal to 5 cans.
As given in the question,
Total area to be painted is equal to 2000 square units.
Area covered by one can of paint is equal to 400 square units
400 square units = 1 can of paint
⇒ 1 square units = ( 1 / 400 ) cans of paint
⇒ 2000 square units = ( 2000 / 400 ) cans of paint
⇒ 2000 square units = 5 cans of paint
Therefore, the number of cans required to paint an area of 2000 square units using given can is equal to 5 cans.
The above question is incomplete, the complete question is:
How many cans of paint are needed to cover an area of 2000 square units if one can of paint covers in area 400 square units?
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Are all equilateral triangles congruent Why?
No, All equilateral triangles need not to be always congruent with one another .
Justification of answer:
The reason is that although an equilateral triangle's angles are all 60 degrees, their corresponding sides are not necessarily the same .
Properties of an equilateral triangles:1. All 3 side of an equilateral triangles have same length .
2. All 3 angles of an equilateral triangles have same measure.
3. Each angles of an equilateral triangles is 60 degree .
4. Area of equilateral triangles = [tex]\frac{\sqrt{3} }{4} *a^2[/tex]
5 . Perimeter of an equilateral triangles = 3*a
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When two parallel lines cut by a transversal What do you called the four angle formed inside the parallel lines?
When two parallel lines are cut by a transversal, the four angles formed inside the parallel lines are called interior angles.
Interior angles are the angles formed between the two lines and the transversal that lie within the region bounded by the parallel lines. There are always four interior angles formed when two parallel lines are cut by a transversal. These angles are equal in measure and are supplementary to the corresponding exterior angles. In other words, the sum of an interior angle and its corresponding exterior angle is equal to 180 degrees. Understanding the properties of interior angles is important in geometry, as they can be used to prove the parallelism of lines.
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A realtor leases 180 apartments in a building with 200 apartments. What fraction of the apartments, in tenths, is occupied?
The fraction of the occupied apartments is 9/10.
What is a fraction?In mathematics, a fraction is a symbol for a rational number.
Let a and b be two numbers, then their fraction can be represented as a/b.
Given that,
Total apartments in the building = 200.
Also,
The number of apartments leased by realtor = 180
The fraction of the apartments which is occupied by realtor
= number of apartments leased /Total apartments
= 180 / 200
= 18 / 20
= 9 / 10
The required fraction is 9/10, implies that from each 10 apartments, 9 apartments are occupied.
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