Answer: = 4 m
There is a negative sign before number 16. It means the butterfly moved in a backward direction. =4 m, from the Initial position
Evaluate the expression, given functions f , and g :
f(x) =7x−4
g(x) =11−x2
3f(1)−4g(−2)=
Number
The value of the function 3f(1)−4g(−2) is -19.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that f(x) =7x−4 and g(x) =11−x². The value of the expression 3f(1)−4g(−2) will be calculated as,
3f(1) = 3 x ( 7 - 4 ) = 9
4g(−2) = 4 x [ 11 - (-2)² ] = 4 x -7 = -28
Substitute the values and solve,
E = 3f(1)−4g(−2)
E = 9 - 28
E = -19
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Three pizzas are being split amongst friends. Everyone will get 1/4 of a pizza. How many friends can eat pizza?
Answer:
12 friends can eat pizza
Step-by-step explanation:
if there are 4 slices in each pizza and there are 3 pizzas and 1 slice per person then 12 people will get 1 slice
4x3=12
Determine the sales of ice cream when the temperature is 20 degrees.
At 0 degree celsius of temperature, Sales will be $-159.474 which is meaningless to interpret.
what is slope ?The slope-intercept form of an equation is used to represent each time the equation of a line is stated as y = mx + b. The line's slope is represented by the m. A straight line's slope is a measure of how steep it is. The gradient is another name for it. The slope equations. The ratio of a line's "change in y" to its "change in x" is known as the slope. You can get the slope of a line by dividing the distance between two points (x1,y1) and (x2,y2) by the distance between the two locations.
From the given information,
By using calculator,
A. Putting Temperature=20 in the given regression equation,
Predicted sales= 442.284
B. Slope=$ 30.0879
If temperature increases by 1 degree celsius then Sales increases by $30.0879, on average.
C. y-intercept= -159.474
At 0 degree celsius of temperature, Sales will be $-159.474 which is meaningless to interpret.
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DUE SOON!!! PLEASE HELP!!
Need help with, both questions 3 and 4, been stuck on these for sometime now, and highly confused.
please explain and show how you came about the answers so I can know for next time.
Many thanks!!
questions are pictured below!
When they worked together, they finished the car in 12 minutes, but it took the second person 28 minutes to do it.
what is unitary method ?The unit technique is a strategy for addressing issues that entails first figuring out the value of a single unit, then multiplying that value to figure out the needed value. Simply put, the unit technique is used to extract a single unit value from a multiple that is supplied. This procedure could follow a regular procedure. a single nation. anything has a distinct identity.
given
A standard shared labor equation can be employed because time varies inversely with the number of persons (i.e., the more people, the less time).
Let the finished task equal 1 and let a = the amount of time needed by the other person alone.
Each person will contribute a portion of the work, and the two fractions together equal one.
When the denominators are removed by multiplying through by 21a,
the answer is 12a + 21(12) = 21a 252
= 21a - 12a 252 = 9a a = 252/9 a
When they worked together, they finished the car in 12 minutes, but it took the second person 28 minutes to do it.
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I’ll give brainiest need a answer asap
Use the given information to find
m∠A.
m∠D=121°
m∠A= (2x)°
m∠B=(x+40)°
M
Answer:
m∠A = 38/3
Step-by-step explanation:
Sum of 3 angles of a triangle = 180°
m∠D + m∠A + m∠B = 180°
Substituting values given for each angle
121 + 2x + (x + 40) = 180
121 + 3x + 40 = 180
3x + 161 = 180
3x = 180-161 = 19
x = 19/3
m∠A = 2x = 38/3
change the mixed fraction 6 5/8 to a percent
It can change be 6 5/8 as a percentage is 662.5%.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
To change a mixed fraction to a percent, you first need to convert the fractional part (in this case, 5/8) to a decimal. To do this, divide the numerator (5) by the denominator (8). In this case, 5/8 simplifies to 0.625.
Next, add the whole number (6) to the decimal from step 1 (0.625) to get 6.625.
Finally, multiply this sum by 100 and add the percent sign %, so 6.625 * 100 = 662.5%
So, 6 5/8 as a percent is 662.5%.
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Jimmy is going to the store to buy candles. Small candles cost $3.50, and large candles cost $5.00. He needs to buy at least 20 candles, and he cannot spend more than $80. Let x represent the number of small candles and y represent the number of large candles.
The inequalities that can be used to represent the situation are:
3.50x + 5y ≤ $80x + y ≥ 20.What are inequalities?Inequalities are mathematical statements showing that two or more mathematical expressions are unequal.
With inequalities, two or more values are compared to show that they are not equivalent.
Inequalities can be represented as follows:
≤: "less than or equal to"<: "less than"≠: "not equal to">: "greater than"≥: "greater than or equal to."The cost of small candles per unit = $3.50
The cost of large candles per unit = $5.00
The number of small candles = x
The number of large candles = y
The number of candles Jimmy needs to buy ≥ 20
The total amount Jimmy can spend on the candles ≤ $80
Inequalities:3.50x + 5y ≤ $80
x + y ≥ 20
Thus, with these inequalities, the total cost of small and large candles must not exceed $80 and the number can be 20 or more.
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Question Completion:Show the two inequalities representing the situation.
Is 3 to 5.9 to 15 equivalent
Answer:
Yes, they are equivalent---------------------------------
Given ratios:
3/5 and 9/15Simplify the second ratio by dividing both parts by 3:
9/3 = 3 and 15/3 = 5The ratio becomes:
3/5We get same ratios so they are equivalent.
The owners of an aquarium have recently built a new tank that can hold up to 110fish. The owners wish to fill it with orange fish and blue fish. The orange fish aresmaller, so they want at least 20 more orange fish than blue fish. Which of thefollowing graphs represents the possible number of orange fish, k, and blue fish, j,that they can put in the tank?
The following graph will represents the possible number of orange fish, k, and blue fish, that they can put in the tank.
Here we have given that owners of an aquarium have recently built a new tank that can hold up to 110 fish.
And here we also know that owners wish to fill it with orange fish and blue fish. The orange fish are smaller, so they want at least 20 more orange fish than blue fish.
Let us consider that x refers the orange fish and y refers the blue fish.
Then the total number of fish in the tank is written as,
=> x + y = 110
Here we have the condition that at least 20 more orange fish than blue fish.
Then the inequality for the situation is written as.
=> x > 20
So, when we plot these on the graph then we get the graph like the following.
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On his first three tests, Luis had a score of 75,96, and 93. What must he score on the fourth test to have an average score of exactly 90 for all four test
Luis must score 96 the fourth test to have an average score of exactly 90 for all four test.
What is Statistics?Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data.
Given that Luis had a score of 75,96, and 93.
We have to find the fourth test to have an average score of exactly 90 for all four test
Let the score of fourth test be x.
75+96+93+x/4=90
264+x=360
Subtract 264 on both sides
x=360-264
x=96
Hence, he must score 96 the fourth test to have an average score of exactly 90 for all four test.
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Option # 2
Predicting when Old Faithful will spurt next can be done by timing the previous eruption.
If an eruption lasts t minutes, the next eruption will occur in approximately 12.5t + 33 minutes.
If a 4-minute eruption begins at 11:32 a.m., at what time would you expect the next eruption to occur? HINT: Think about what time the eruption that begins at 11:32 would end.
Make sure you include your work to demonstrate how you found your answer!
Predicting when Old Faithful will spurt next can be done by timing the previous eruption. the next eruption is expected to occur at 12:59. p.m
What is an eruption?Generally, The eruption that begins at 11:32 a.m. will end at 11:36 a.m.
So, the next eruption will occur approximately 12.5t + 33 minutes after 11:36 a.m., which is 12.5 * 4 + 33 minutes after 11:36 a.m., or 83 minutes after 11:36 a.m.
Therefore, the next eruption is expected to occur at 12:59. p.m. (11:36 a.m. + 57 minutes).
To calculate this, you would first add the minutes (83) to the number of minutes in the starting time (36). This sum, 119, is greater than 60, so you need to carry over 1 hour from the minutes to the hours.
This leaves 19 minutes, which is less than 60, so the result is 12:19. However, you also need to add 1 hour to the starting time to account for the carried over hour, giving you a final result of 12:59.
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The thickness (in millimeters) of the coating applied to hard drives is one characteristic that determines the usefulness of the product. When no unusual circumstances are present, the thickness has a normal distribution with a mean of 2 mm and a standard deviation of 0.04 mm. Suppose that the process will be monitored by selecting a random sample of 25 drives from each shift's production and determining the mean coating thickness for the sample.
A. Describe the sampling distribution of for a random sample of size 25.
The distribution of x is normal with mean 2 mm and standard deviation (Need to find standard Deviation) mm.
B.
When no unusual circumstances are present, we expect x to be within 3 x of 2 mm, the desired value. An x value farther from 2 mm than 3 x is interpreted as an indication of a problem that needs attention. Calculate 2 ± 3 x.
2 − 3 x = mm
2 + 3 x = mm
C.
Referring to part (b), what is the probability that a sample mean will be outside
2 ± 3 x just by chance (that is, when there are no unusual circumstances)? (Round your answer to four decimal places.)
A. The distribution of x is normal with mean 2 mm and standard deviation 0.008 mm.
B. The bounds are given as follows:
Lower bound: 1.976 mm.Upper bound: 2.024 mm.C. The probability that the sample mean is outside the interval 2 ± 3 x is given as follows: 0.003 = 0.3%.
How to obtain the probability using the normal distribution?The z-score of a measure X of a variable that has mean symbolized by [tex]\mu[/tex] and standard deviation symbolized by [tex]\sigma[/tex] is obtained by the rule presented as follows:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
The z-score represents how many standard deviations the measure X is above or below the mean of the distribution, depending if the obtained z-score is positive or negative.Using the z-score table, the p-value associated with the calculated z-score is found, and it represents the percentile of the measure X in the distribution.By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].The mean and the standard deviation for the population are given as follows:
[tex]\mu = 2, \sigma = 0.04[/tex]
Hence, for a sample of 25, the standard error is given as follows:
s = 0.04 / square root(25) = 0.008 mm.
The interval for item b is within three standard errors of the mean, hence:
2 − 3 x = 2 - 3 x 0.008 mm = 1.976 mm.2 + 3 x = 2 + 3 x 0.008 mm = 2.024 mm.The Empirical Rule states that 99.7% of the measures are within three standard errors of the mean, hence the probability that the sample mean is outside the interval 2 ± 3 x is given as follows: 0.003 = 0.3%.
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what property is (2•x)•5=2•(x•5)
Answer:
Associative Property
(2•x)•5=2•(x•5)
this equation represents the Associative Property.
hope that helps...
Answer:cDADVFBDGFZDGSHHDBHDG
Step-by-step explanation:
6. George is learning about mosaics in art class. His teacher passes out small square tiles and
encourages the students to cut up the tiles in various angles. George's first cut tile looks like
this:
B
b. Solve for m.
c. What is the measure of angle MLE?
(% m)
L
Write an equation relating angle MLE with angle ELB.
d. What is the measure of angle ELB?
2(m+5)*
M
The value of m is 32, the measure of the angle ∠ MLE is 16° and the measure of ∠ ELB is 74°.
What is angle?
An angle is a figure in Euclidean geometry made up of two rays that share a common terminal and are referred to as the angle's sides and vertices, respectively. Angles created by two rays are in the plane where the rays are located. The meeting of two planes also creates angles.
Given:
The measure of ∠ MLE = 1 / 2 m, ∠ ELB = 2 (m + 5)
Calculate the value of m as shown below,
∠ MLE + ∠ ELB = 90 (As given on figure)
1 / 2 m + 2 (m + 5) = 90
1 / 2 m + 2 m + 10 = 90
m + 4 m + 20 = 180
5 m = 180 - 20
m = 160 / 5
m = 32
Hence, ∠ MLE = 32 / 2 = 16°, and ∠ ELB = 2 (32 + 5) = 74°
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The complete question is attached below.
Sort the cards to list all the Properties of Parallelograms.
These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.
What exactly is circumcenter?the triangle's circle's center. It is the point where the "perpendicular bisectors," or lines parallel to the centre of both sides, cross.
The intersection of any two perpendicular bisectors of any two triangle sides is known as the circumcenter of a triangle ABC.
The equation y=1 is the perpendicular bisector of sides B(3,0) and C(3,2). Because AB's midpoint is at 3,1 and its slope is unknown. The perpendicular bisector has zero slope. The equation for such a line is y=y1.
The equation for the perpendicular bisector of A(0,0) and B is also x=1.5 (3,0). The reason is that AB has a midpoint of zero slope and (1.5,0). The perpendicular bisector's slope won't be clearly defined. The equation for such a line is x=x1.
These two perpendicular bisectors will meet at (1, 5, 1). These are the coordinates of the triangle's circumcenter.
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A person is running down the staircase. He is in a rush, so he may jump over some steps. If the staircase is 12 steps (including the top one, where he begins, and the last one, where he ends), in how many ways can he reach the bottom step in 5 jumps? What if there are no restrictions on the number of jumps? [Hint: keep
track of the steps he steps on. . .]
The number of ways that he can reach the bottom step in 5 jumps will be 792.
What are permutation and combination?A permutation is an act of correctly arranging things or pieces. Combinations are a method of taking stuff or pieces from an assortment of items or sets in which the order of the items is irrelevant.
Running down the stairway is someone. He could hop over some steps since he is in a hurry. When a staircase has 12 steps (including the top one, where he begins, and the last one, where he ends).
The number of ways will be given as,
¹²C₅ = (12!) / [(12 - 5)! x 5!]
¹²C₅ = (12 x 11 x 10 x 9 x 8 x 7!) / [7! x 5 x 4 x 3 x 2 x 1]
¹²C₅ = 11 x 9 x 8
¹²C₅ = 792
The number of ways that he can reach the bottom step in 5 jumps will be 792.
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10) After hearing that the children were dreaming of sugar plums in "The Night
Before Christmas," Cindy Lou wonders just how much time the kids were dreaming
during their slumber. If the children were asleep from 7.5 to 10 hours, and 25% of
their sleep includes dreams, how much time was spent dreaming of sugar plums?
Write a compound inequality for this situation and solve. Show your answer on a
graph too
Answer:
First, let's find the total amount of time the children spent asleep: 10 hours - 7.5 hours = <<10-7.5=2.5>>2.5 hours
Then, let's find the amount of time the children spent dreaming by multiplying the total amount of time they spent asleep by 25%: 2.5 hours * 25% = <<2.525.01=.625>>.625 hours
We can represent this situation with the compound inequality: .625 hours <= x <= 2.5 hours
To graph this inequality, we can plot a point at 2.5 on the number line and shade in the region to the left of it. Then, we can plot a point at .625 on the number line and shade in the region to the right of it. The solution to the inequality is the region where both shaded regions overlap.
[asy]
unitsize(1 cm);
draw((-2,0)--(4,0));
draw((0,-1)--(0,1));
draw((-.2,0)--(0,.2)--(.2,0)--(0,-.2)--cycle);
draw((2.5,-1)--(2.5,1),dashed);
draw((.625,-1)--(.625,1),dashed);
label("$x$",(4,0),SE);
fill((-2,0)--(-2,1)--(2.5,1)--(2.5,0)--cycle,gray(.7));
fill((2.5,0)--(2.5,1)--(4,1)--(4,0)--cycle,gray(.7));
[/asy]
Step-by-step explanation:
Karima made `9` pairs of earrings in `6` hours. How long will it take Karima to make `12` pairs of earrings?
Answer:
8 hours
Step-by-step explanation:
9 pair of earrings in 6 hours
=> 9 : 6 = 1,5 pair of earrings in 1 hour
12 : 1,5 = 8 hours
Karima can make 12 pair of earrings in 8 hours.
What are proportions?Proportion, in general, is referred to as a part, share, or number considered in comparative relation to a whole. Proportion definition says that when two ratios are equivalent, they are in proportion. It is an equation or statement used to depict that two ratios or fractions are equal.
Given that, Karima made 9 pairs of earrings in 6 hours.
Let the number of hours it took to make 12 pair of earrings be x.
Now, the proportion is
9/6 =12/x
9x=72
x=8
Therefore, Karima can make 12 pair of earrings in 8 hours.
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Can someone help me find the solution for X? Please leave an explanation for me so I can do questions like this by myself!
Also, can you leave an equation that solves for x..?
The value of angle x in the straight line is 41 degrees.
How to find the angle x?The sum of angles on a straight line is 180 degrees. In other words, angles on a straight line add up to 180°. Angles on a straight line relate to the sum of angles that can be arranged together so that they form a straight line.
Therefore, let's find the angles x.
Using sum of angles on a straight line,
x + 139 = 180
subtract 139 from both sides of the equation
x + 139 - 139 = 180 - 139
Hence,
x = 41 degrees
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Question 9 (1 point)
What is the cost of leaving on your 150 watt LCD TV while you go for
a 45 minute walk outside (at a cost of 16 cents per kilowatt hour)?
1.8 cents
21 cènts
542 cents
57-cent
HELP PLEASE GIVING BRIANLESS
Black and very dark greys are difficult for LCDs to produce. They consequently typically have lower contrast than CRTs and have less colour saturation for low intensity hues.
How many watts does a LCD TV use per hour?The majority of TVs on the market range in wattage from 80 to 400. This figure is determined by the TV's size (32 inches, 44 inches, 56 inches, etc.) and kind (CRT, LCD, LED, QLED, Plasma and so on).Multiply the appliance's power rating (watts) by the number of hours it is used for, then divide the result by 1000 to get the kWh for that particular item.No, flat-screen TVs normally do not consume a lot of electricity. Compared to other appliances and devices, they only use a modest amount of energy. Your heating and cooling systems consume a vastly greater amount of electricity than your television. In low-light and dark settings, not recommended for use.To learn more about typically refer to:
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pls help with geometry (see picture)
The line QS represents nothing from the given options, option D is correct.
What is a triangle?A triangle is a polygon with three vertices and three sides. The angles of the triangle are formed by the connection of the three sides end to end at a point. The triangle's three angles add up to 180 degrees in total.
Given a ΔTQR
a line from Q intersects at TR at point S and divides angle Q to 30° and 34°,
The line QS is not a median, because a median divides the side into two equal halves, and the figure does not show that ST is equal to SR.
The line QS is not an attitude because the figure has not specified the angle of S in line TR, if given that the ∠QSR = ∠QST = 90° then QS will be called altitude.
The line QS is also not an angle bisector because an angle bisector divides the angle into two equal parts but the given angles are not equal.
Hence option D is correct.
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Which pairs of polygons are congruent? A. pairs 1, 2, and 3
B. pairs 1, 2, 3, and 4
C. pairs 2 and 3
D.pairs 1 and 3
The Pair 1 and Pair 3 polygons are congruent. Therefore, the correct option is D.
What is a Congruent Polygon?The definition of a congruent polygon is a polygon that is the same shape, has the same length of sides, and has the same interior angles as the polygon it is being compared to. Congruent shapes must all be the same type of shape in order to fulfill the requirement.
Pair 1:
Here, the shapes are same and have same length.
So, the polygons are congruent.
Pair 2:
Here, the shapes are same but they have different lengths
So, the polygons are not congruent.
Pair 3:
Here, the shapes are same and have same length.
So, the polygons are congruent.
Pair 4:
Here, the shapes are same but they have different lengths
So, the polygons are not congruent.
Therefore, option D is the correct answer.
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I already know the answer but the worksheet doesn't give an explanation. that is the only thing I need.
======================================================
Explanation:
Let,
x = measure of angle CAP = measure of angle PABy = measure of angle CBP = measure of angle PBAThese equations are valid because segment AP bisects the angle CAB, i.e. it splits it into two equal pieces. Similarly, segment BP bisects angle ABC.
Then we can say,
x+x = 2x = measure of angle CABy+y = 2y = measure of angle CBALet's focus on triangle CAB. The three interior angles add to 180 degrees. This is true of any triangle.
(angleCAB)+(angleCBA)+(angleACB) = 180
(2x) + (2y) + (44) = 180
2x+2y+44 = 180
2(x+y+22) = 180
x+y+22 = 180/2
x+y+22 = 90
x+y = 90-22
x+y = 68
Normally we would try to isolate one variable, but I'll stop here. We'll use this later in the next section.
--------------------
Now focus your attention on triangle PAB.
The three interior angles add to 180.
(anglePAB)+(angleABP)+(angleAPB) = 180
(x)+(y)+(z) = 180
x+y+z = 180
(x+y)+z = 180
68+z = 180 .... replace "x+y" with 68
z = 180-68
z = 112 degrees is the measure of angle APB.
By what percentage is the highest price city more expensive than the lowest price city for the cost of retail space (to the nearest whole percentage
The required percentage is 65% of the highest price city more expensive than the lowest price city for the cost of retail space.
What is the percentage?The percentage is defined as a ratio expressed as a fraction of 100.
The highest price city for the cost of retail space is Berlin with an average cost per square foot of retail space of 469.
The lowest price city for the cost of retail space is Paris with an average cost per square foot of retail space of 284.
The difference is 469 - 284 = 185
Hence, the required percentage is :
⇒ 185/ 284 x 100%
⇒ 65%
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select the solution of the inequality y>-3x+2
The shaded region shows the possible set of solutions.
What is inequality? Differentiate between equation and expression?inequality : An inequality is used to make unequal comparisons between two expressions or numbers.
expression : A mathematical expression is made up of terms (constants and variables) separated by mathematical operators.
equation : A mathematical equation is used to equate two expressions.
Given is the inequality as -
y > -3x + 2
The inequality is -
y > -3x + 2
Refer to the graph attached. It shows the possible set of solutions under the shaded region.
Therefore, the shaded region shows the possible set of solutions.
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Calculate the area of a triangle with the given properties?
Answer:
82 m²
Step-by-step explanation:
You want the area of the triangle with sides b = 13 m, c = 17 m, and the angle between them, A = 48°.
AreaThe relevant formula for the area is ...
Area = 1/2(bc)sin(A)
Area = 1/2(13 m)(17 m)sin(48°) ≈ 82.1175 m²
The area of the triangle is about 82 square meters.
Abby Baked 124 cookies. While they were cooling she stepped outside. She saw a group of children run into the kitchen and run back with cookies in his hands. When she returned to the kitchen she found only 7 cookies left on the cooling racks. If each child took the same number of cookies and the number of children who took cookies was more than 10 and fewer than 30, how many were in the group?
The number of children in the group based on the information is 13.
How to calculate the number?Total number of cookies Abby baked = 124
Number of cookies remaining after children left the kitchen = 7
Number of cookies taken by the group of children = 124 - 7 = 117
Given that 117 cookies were equally shared by the children.
Let the number of children be x.
Number of children was more than 10 and less than 30
10 < x < 30
x will always be an integer.
Let a number of cookies each child took be c.
The prime factorization of 117 is 3*3*13.
As 117 = x * c
117, when written as the product of 2 numbers, that is x*c form, will be as given below:
1*117, 3*39, 9*13, 13*9, 39*3, 117*1
Given that 10 < x < 30. Therefore, we can only take 13 * 9 as the required x * c form.
x = 13 and c = 9
Number of children in the group is 13.
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What is the product of (-4)(23)(-7)?
644
189
-133
-157
Answer:
its (-644) because 4 multiplication 23 and multiplication 7 is 644 and a minus will be written
Answer:644
Step-by-step explanation:
i got it right
y = x²
y - 6x + 5 = 0
The values of the x are, x = 5, x = 1.
What is solving an equation?
The fundamental guidelines and procedures to simplify any algebraic expression are as follows:
By multiplying factors, remove any grouping symbols like brackets and parentheses.
If the terms contain exponents, use the exponent rule to eliminate grouping.
Add or subtract like terms to combine them.
Add the constants together.
Consider, the given equation
y = x² ..(1)
y - 6x + 5 = 0 ..(2)
Replace y = x² in second equation.
x² - 6x + 5 = 0
x² - 5x - x + 5 = 0
x(x - 5) - 1(x - 5) = 0
(x - 5)(x - 1) = 0
⇒ (x - 5) = 0, (x - 1) = 0
x = 5, x = 1
Hence, the values of the x are, x = 5, x = 1.
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Which of the following is an equivalent form of the function f above in which the mininum value of f
appears as a constant or coefficient?
A) f(x) = x2-24
B) f(x) = x2+2x-24
C) f(x) = (x-1)2 -24
D) f(x) = (x-1)2 -25
Based on the function, an equivalent form of the function f above in which the minimum value of f appears as a constant or coefficient is f(x) = (x+1)^2 -25. (Option D)
The function is f(x) = (x + 6)(x – 4). Solving the function
f(x) = (x + 6)(x – 4)
= x (x – 4) + 6(x – 4)
= x^2 – 4x + 6x – 24
= x^2 + 2x – 24
= x^2 + 2x + 1– 25
= (x + 1)^2 – 25
When x = -1, the value of f(x) = (-1 + 1)^2 – 25 = -25
Hence, the equation for which the minimum value of f appears as a constant or coefficient is (x + 1)^2 – 25.
Note: The question is incomplete. The complete question probably is f(x) = (x + 6)(x – 4). Which of the following is an equivalent form of the function f above in which the minimum value of f appears as a constant or coefficient? A) f(x) = x^2-24 B) f(x) = x^2+2x-24 C) f(x) = (x-1)^2 -21 D) f(x) = (x+1)^2 -25
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