Answers
Answer:
The even functions are options 2, 3, and 5
Step-by-step explanation:
Please, see the attached file.
Thanks.
Answer:
Options B, C and E are even functions.
Step-by-step explanation:
If f(x) = f(-x) then function is called to be even.
A). f(x) = ∛8x
f(-x) = ∛8(-x) = (∛8)(∛(-x) = 2∛(-x)
Therefore f(x) ≠ f(-x)
So function is not an even function.
B). [tex]f(x)=log_{9}x^{6}[/tex]
[tex]f(-x)=log_{9}(-x)^{6}[/tex]
[tex]=log_{9}(x)^{6}[/tex]
f(x) = f(-x)
So this function is even.
C). [tex]f(x)=\frac{1}{x^{8}+7x^{7}}[/tex]
[tex]f(-x)=\frac{1}{(-x)^{8}+7(-x)^{6}}[/tex]
= [tex]\frac{1}{x^{8}+7x^{6}}[/tex]
f(x) = f(-x)
Therefore given function is even.
D). f(x) = [tex]e^{x^{8}-x }[/tex]
[tex]f(-x)=e^{(-x)^{8}-(-x)}=e^{x^{8}+x}[/tex]
Therefore f(x) ≠ f(-x)
So the given function is not even.
E). f(x) = |8x| - 3
f(-x) = |8(-x)| - 3
= |8x| - 3
f(x) = f(-x)
Therefore, function is even.
F). [tex]f(-x)= -9(-x)^{10}+5(-x)^{4}-12(-x)[/tex]
[tex]f(-x)= -9(x)^{10}+5(x)^{4}+12(x)[/tex]
f(x) ≠ f(-x)
Therefore the given function is not an even function.
Options B, C and E are even functions.
Related Questions
Nell's mom makes chocolate milk with 30mL of chocolate syrup for every 2 ounces of milk. Nell's dad adds 65 mL of chocolate syrup for every 5 ounces of milk. Whose chocolate milk is more chocolatey?
Answers
Answer:
The more 'chocolatey' chocolate milk is the one prepared by Nell's mom.
Step-by-step explanation:
This problem can be solved by establishing the ratio of chocolate syrup for one ounce of milk in each beverage.
For mom's chocolate milk:
[tex]\frac{30mL}{2ounces} = 15\frac{mL}{ounce}[/tex]
For dad's chocolate milk:
[tex]\frac{65mL}{5ounces} = 13\frac{mL}{ounce}[/tex]
We know that:
15 > 13
So we can conclude that mom's chocolate milk is more 'chocolatey'.
1. Is down below and is the first photo.
2. The graph shows f(x) and its transformation g(x).
Enter the equation for g(x) in the box.
g(x)=
3. What ia the domain and range of the relation shown in the table?
X -12, -8, 0, 1
Y 0, 12, 0, 8
Answers
Answer:
1. [tex]a_{n}=\frac{1}{3} a_{n-1}[/tex] where [tex]a_{1} =27[/tex]
2. [tex]2^{x+1}[/tex]
3. The domain is {-12,-8,0,1}. The range is {0,12,8}.
Step-by-step explanation:
1. The recursive formula is defined as an implicit way of writing the rule of a function or pattern. It is implicit because it uses previous terms to find the next term in the pattern. We multiply, add, subtract or divide a previous term by a constant value or expression to find the next. In this case, 27 becomes 9 through division by 3 or multiplication by 1/3. The pattern continues 9(1/3)=3 and so forth.
2. The function f(x) is an exponential and has a general form of [tex]y=ab^x[/tex]. We know f(x) is [tex]2^x[/tex]. The points of g(x) all changed from f(x) by shifting over to the left. This transformation occurred by [tex]2^{x+1}[/tex].
3. Domain is defined as the set of all x-values. Range is defined as the set of all y-values. The domain is {-12,-8,0,1}. The range is {0,12,8}.
It costs Guido $0.20 to send a text message from his cell phone. He has already spent $4 in text messages this month. If he has a total of $10 that he can spend this month on text messages, write and solve an inequality that will give the greatest number of text messages that he can send. Interpret the solution.
Answers
The greatest number he can spend on is $5 since he has $10 he will have $5 reamining.
What does the fundamental theorem of algebra state about the equation 2x^2−4x+16=0 ?
Answers
Answer:
option B
Step-by-step explanation:
[tex]2x^2-4x+16=0[/tex]
We need to solve this equation using quadratic formula
[tex]x= \frac{-b+-\sqrt{b^2-4ac}}{2a}[/tex]
a=2, b= -4, c=16
Plug in the values in the formula
[tex]x= \frac{-(-4)+-\sqrt{(-4)^2-4(2)(16}}{2(2)}[/tex]
[tex]x= \frac{4+-\sqrt{16-128}}{4}[/tex]
[tex]x= \frac{4+-\sqrt{-112}}{4}[/tex]
Simplify the square root. the value of square root (-1) = 'i'
[tex]x= \frac{4+-4i\sqrt{7}}{4}[/tex]
Now we divide by 4
[tex]x= 1+-i\sqrt{7}[/tex]
So there are two complex roots. since the degree of polynomial is 2
Answer:
B
Step-by-step explanation:
I took the test :)
Joe has 12 cups of soup in a pot. If he puts 1/4 cup of soup into each bowl, how many bowls will be used?
Answers
Answer:
48
Step-by-step explanation:
you need 4 one-fourth cups to make one cup. multiply 12 by 4 and you get 48
By dividing the total amount of soup (12 cups) by the amount of soup per bowl (1/4 cup), we find that Joe can fill 48 bowls.
The student poses a question related to division and unit conversion. To address the student's question, we should calculate how many bowls Joe can fill by dividing the total amount of soup by the amount used for each bowl. Joe has 12 cups of soup and uses 1/4 cup of soup for each bowl. The calculation would be:
Number of bowls = Total cups of soup / Cups of soup per bowl
Number of bowls = 12 cups / 1/4 cup per bowl
Number of bowls = 12 / 0.25
Number of bowls = 48
Therefore, Joe will use 48 bowls to serve the 12 cups of soup, with 1/4 cup of soup in each bowl.
A freight train left Miami and traveled toward the fueling station at an average speed of 60 mph. A passenger train left three hours later and traveled in the same direction but with an average speed of 72 mph. find the number of hours the freight train traveled before the passenger train caught up.
a. 12
b. 15
c. 18
d. 21
Answers
Answer:
The correct option is b. 15
Explanation:
We are given that a freight train travels at an average speed of 60 mph.
Also we are given that the average speed of passenger train is 72 mph.
We are also given that the freight train leaves 3 hours before passenger train. So the number of miles covered by freight train in 3 hours is:
[tex]3 \times 60 = 180[/tex] miles.
Let X be the number of hours it takes the passenger train to catch up the freight train.
Therefore, we have:
[tex]180 + 60 \times X = 72 \times X[/tex]
[tex]72X-60X = 180[/tex]
[tex]12X=180[/tex]
[tex]X=\frac{180}{12}[/tex]
[tex]X=15[/tex]
Therefore, the passenger train will take 15 hours to catch up the freight train.
Answer:
sorry im answering late but the answer is C. 18
Step-by-step explanation:
60 x 18 = 1,080
72 started 3 hours later so that means you subtract 3 from 18 which equals 15 and 72 x 15 = 1,080
ur answer is 18
Graph y=3x^2-12x+13. What is the minimum value of the function?
Answers
Answer:
(2,1)
Step-by-step explanation:
You are only asking that the graph be drawn and that the minimum be stated. You are not asking how the minimum was obtained (by completing the square).
The graph (using Desmos) shows that the min is at (2,1)
Graphing is a mighty powerful tool, wouldn't you say? It tells you the answer before you have to do one bit of algebra.
Please help, i need to turn this in. Thank you in advance :)
(Full explination would be helpful but anything will do)
Answers
Answer:
12x
Step-by-step explanation:
number 1 is 12x bcuz two x plues ten equals 12x although i did it another way i still got it right just letting you no im working on the second one
The outside angle is equal to the sum of the two opposite inside angles.
So you have:
X + 82 = 2X+10
Subtract 1 X from each side:
82 = X+10
Subtract 10 from each side:
x = 72
Now you can calculate the exterior angle by replacing x with 72:
2x+10 = 2(72) +10 = 144+10 = 154
Penelope is making cards for her family members . She completed 9/16 of the cards on Monday and 2/16 on Tuesday . Which fraction of the cards has Penelope completed so far
Answers
The length of a rectangle is twice it’s width. The perimeter is 102 inches. Write an equation and find the length and width
Answers
Answers:
Equation is 2*(2*W+W) = 102
Width is 17
Length is 34
=============================
Explanation:
L = 2*W because the length is twice the width
2*(L+W) = P is the perimeter formula
Replace P with the given perimeter (102). Also replace L with 2*W. Then isolate W
2*(L+W) = P
2*(2*W+W) = 102
2*(3W) = 102
6W = 102
6W/6 = 102/6
W = 17
If the width is W = 17, then the length is
L = 2*W = 2*17 = 34
So the width and length of this rectangle is 17 by 34
---------
Check:
P = 2*(L+W)
P = 2*(34+17)
P = 2*51
P = 102
Answer is confirmed
To find the length and width of a rectangle with given perimeter and lengths as twice of the width, first plug the length into the perimeter formula. Solve the resulting equation for width. Substitute this width into the length formula to get the length.
Explanation:In this problem, we have a rectangle where the length (L) = 2 * width (W). Also, the perimeter of the rectangle (P) = 2L + 2W. The given perimeter is 102 inches.
Since L = 2W, substituting this equation into the formula for perimeter, we get P = (2*2W) + 2W = 102.
This simplifies to 6W = 102, and therefore W = 102 / 6 = 17 inches. Substituting the width back into the equation L = 2W, we find that the length (L) is 2 * 17 = 34 inches.
So, the width is 17 inches and the length is 34 inches.
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Solve for xx. Write the smaller solution first, and the larger solution second. X^2 + 12x + 27 = 0x 2 +12x+27=0
Answers
Answer:
x = -9, -3
Step-by-step explanation:
x^2 + 12x + 27 = 0
We need 2 numbers whose product is + 27 and whose sum is + 12. These are 3 and 9. So the factors are:-
(x + 3)(x + 9) and this = 0
So (x + 3) = 0 or x + 9 = 0
x = -3 , -9
Answer:
-5 and 7
Step-by-step explanation:
we need to find numbers a and b such that a+b=-2 and ab=-35.
a=5 and b=-7 satisfy both conditions, so our equation can be re-written:
(x + 5)(x-7) = 0
According to the zero-product property, we know that
x+5=0 or x-7=0, which means
x=-5x or x=7
Please mark brainliest and thank! Thank you!
Ms.Keller is grading semester projects.In the past two hours, she has graded five projects.At this rate, she will grade _ project in seven hours at a rate of _ project per hour. Fill in the blank
Answers
Final answer:
Ms. Keller will grade 17.5 projects in seven hours at her current rate of 2.5 projects per hour.
Explanation:
The student's question is about determining at what rate Ms. Keller is grading projects and how many projects she will grade in seven hours based on her current pace. Since Ms. Keller has graded five projects in two hours, her grading rate is 5 projects / 2 hours, which simplifies to 2.5 projects per hour. To find out how many projects Ms. Keller will grade in seven hours at this rate, we multiply 2.5 projects/hour by 7 hours, resulting in 17.5 projects.
Therefore, Ms. Keller will grade 17.5 projects in seven hours at a rate of 2.5 projects per hour.
Ther are 330 walnuts in 6 bags if each bag has the same number of walnuts how many walnuts are in 2 bags
Answers
Answer:
110 Walnuts
Step-by-step explanation:
Firstly, there are 6 bags and 330 walnuts. You divide 330 by 6 and you get 55. 330/6. Now, you multiply 55 by 2 and you get your answer. So basically in each bag there are 55 walnuts and if you multiply that by 6 you get 330 again. Hope this helped!
Answer:
110 walnuts
Step-by-step explanation:
330÷6 is 55
55•2 is 110
write a quadratic equation in standard form (with integer coefficients) that has roots: 2 and -5?
Answers
Answer:
y = x^2 +3x-10
Step-by-step explanation:
If we know the roots of a quadratic function, we know that
y = (x -a) (x-b) where a and b are the roots
y = (x-2 ) (x--5)
y = (x-2)(x+5)
We need to foil this out to get this in standard form of ax^2 + bx+c
FOIL (x-2) (x+5)
First x*x: x^2
outer : 5*x = 5x
inner: -2x = -2x
last : -2*5 = -10
Add them up
x^2 +5x-2x-10
x^2 +3x-10
Final answer:
A quadratic equation in standard form with roots 2 and -5 is obtained by multiplying (x - 2)(x + 5), which simplifies to x² + 3x - 10 = 0.
Explanation:
To write a quadratic equation in standard form with integer coefficients that has roots 2 and -5, we use the fact that if α and β are roots of a quadratic equation, the equation can be written as:
ax² + bx + c = 0
Where:
The quadratic equation in standard form using the roots 2 and -5 is given by:
(x - 2)(x + 5) = 0
Expanding this we get:
x² + 5x - 2x - 10
Which simplifies to:
x² + 3x - 10 = 0
Thus, the quadratic equation with integer coefficients and roots 2 and -5 is x² + 3x - 10 = 0.
Find the midpoint M of the line segment joining the points S = (−8, −1) and
T = (−4, −7)
Answers
Answer:
The midpoint is (-6,-4)
Step-by-step explanation:
The formula for the midpoint is
midpoint = (x1+x2)/2, (y1+y2)/2
Substituting what we know
= (-8+-4)/2, (-1+-7)/2
= -12/2, -8/2
= -6, -4
Final answer:
The midpoint M of the line segment joining points S = (-8, -1) and T = (-4, -7) is calculated using the midpoint formula and is found to be M = (-6, -4).
Explanation:
The midpoint M of the line segment joining the points S and T can be found using the midpoint formula. To find the midpoint M between the points S = (-8, -1) and T = (-4, -7), you need to take the average of the x-coordinates and the y-coordinates separately.
The midpoint M's x-coordinate is the average of the x-coordinates of S and T: ((-8 + (-4)) / 2 = -6. Similarly, the midpoint M's y-coordinate is the average of the y-coordinates of S and T: ((-1 + (-7)) / 2 = -4.
Therefore, the midpoint M is located at (-6, -4).
Congruency statements
ΔABC≅ΔDEF
List all pairings of congruent angles & sides for the above congruence statement.
Answers
ΔABC ≅ ΔDEF
I find it easier to see the congruencies if I write them underneath each other:
ABCDEF∠A ≅ ∠D [tex]\overline{AB}[/tex] ≅ [tex]\overline{DE}[/tex]
∠B ≅ ∠E [tex]\overline{BC}[/tex] ≅ [tex]\overline{EF}[/tex]
∠C ≅ ∠F [tex]\overline{AC}[/tex] ≅ [tex]\overline{DF}[/tex]
I need help right away please.
Answers
[tex] {2}^{2} = 4 \\ {3}^{2} = 9 \\ {4}^{2} = 16 \\ {5}^{2} = 25 \\ {6}^{2} = 36 \\ {7}^{2} = 49 \\ {8}^{2} = 64 [/tex]
This represents the values of k^2 from 2 to 8.
Im sure you can C the answer from this.
Jason is selling video games. To earn his monthly bonus, he must sell a minimum of 5 games. He has 30 he can sell. The video games cost $20 each. The function f(x) = 20x can be used to represent this situation. What is the practical range of the function?
All whole numbers from 5 to 30, inclusive.
All whole numbers from 100 to 600, inclusive.
All real numbers.
All multiples of 20 between 100 and 600, inclusive.
Answers
Answer:
Correct choice is B
Step-by-step explanation:
The function [tex]f(x)=20x[/tex] represents the situation, where x is the number of sold video games and f(x) is the total cost of sold games.
Jason must sell a minimum of 5 games, this means that [tex]x\ge 5.[/tex] He has 30 video games he can sell, then [tex]x\le 30.[/tex] Thus, the domain of the function is [tex]5\le x\le 30.[/tex]
The range of the function f(x) is
[tex]20\cdot 5\le f(x)\le 20\cdot 30,\\ \\100\le f(x)\le 600.[/tex]
A rectangular cutting board is 8 inches wide and 10 inches long. What is its area?
Answers
Answer:
18
Step-by-step explanation:
8x10= 18
Area of the rectangular cutting board is 80 square inches.
What is a rectangle?Any figure bounded by 4 sides and opposite sides are equal and all the internal angles are 90° is called rectangle. A rectangle is a parallelogram.Area of the rectangle can be found by multiplying its length with its breadth.How to find what is the area of the given rectangle?According to the problem,
Length of the rectangle is 8 inchesBreadth of the rectangle is 10 inches.∴ Area of the rectangle = (8 x 10) square inches
= 80 square inches
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Help??????????????????
Answers
For this one the answer is -2 so the answer is A.
Which of the following statements best describes the amount of water in the pool?
The answer is A
Hope this helps!
Consider these four data sets. Set A: {32, 12, 24, 46, 18, 22, 14} Set B: {4, 12, 11, 14, 11, 5, 12, 13, 18, 14} Set C: {5, 4, 9, 12, 14, 26, 22, 18} Set D: {1, 1, 1, 2, 2, 3, 3, 4, 5, 6} The sets that show a positive skew are sets . The sets that show a negative skew are sets
Answers
The elements of this set are,
[tex]32,12,24,46,18,22,24[/tex]
We arrange this data set in ascending order to get,
[tex]12,18,22,24,24,32,46[/tex]
The median for this data set is
[tex]median = 24[/tex]
The mean for this data set can be calculated using the formula,
[tex]\bar X = \frac{ \sum x}{n} [/tex]
This implies that,
[tex]\bar X = \frac{ 12 + 18 + 22 + 24 + 24 + 32 + 46}{7} [/tex]
[tex]\bar X = \frac{154}{7} = 22[/tex]
This data set is negatively skewed because the mean is less than the median.
SET B
This set contains the elements,
[tex]4, 12, 11, 14, 11, 5, 12, 13, 18, 14[/tex]
We arrange the elements of this set in ascending order to obtain,
[tex]4,5,11,11,12,12,13,14,14,18[/tex]
The median for this data set is,
[tex]median = \frac{12 + 12}{2} = 12[/tex]
The mean is
[tex] \bar X = \frac{4 + 5 + 11 + 11 + 12 + 12 + 13 + 14 + 14 + 18}{10} [/tex]
.
[tex]\bar X = \frac{114}{10} = 11.4[/tex]
This data set is negatively skewed because the mean I'd less than the median.
SET C
The set C has elements,
[tex]5, 4, 9, 12, 14, 26, 22, 18[/tex]
We arrange this set in ascending order to get,
[tex]4,5,9,12,14,18,22,26[/tex]
The median of this data set is
[tex]median = \frac{12 + 14}{2} = 13[/tex]
The mean of this data set is
[tex]\bar X = \frac{4 + 5 + 9 + 12 + 14 + 18 + 22 + 26}{8} [/tex]
[tex]\bar X = \frac{110}{8} = 13.75[/tex]
This is a positively skewed distribution because the mean is greater than the median
SET D
The elements of this set are
[tex]1, 1, 1, 2, 2, 3, 3, 4, 5, 6[/tex]
The median of this data set is
[tex]median = \frac{2 + 3}{2} = 2.5[/tex]
The mean is
[tex]\bar X= \frac{1 + 1 + 1 + 2 + 2 + 3 + 3 + 4+ 5 + 6}{10} [/tex]
[tex]\bar X= \frac{28}{10} = 2.8[/tex]
This data set is positively skewed because the mean is greater than the median.
Answer:
Step-by-step explanation:
Set A: {32, 12, 24, 46, 18, 22, 14}
Mean =24 : Median =22:
Mean>Median hence positive skewed
Set B: {4, 12, 11, 14, 11, 5, 12, 13, 18, 14}
Mean =11.4 and median = 12
Mean <Median, hence negative skewed
Set C: {5, 4, 9, 12, 14, 26, 22, 18}
Mean=13.75 and median = 13
Mean >Median hence positive skewed
Set D: {1, 1, 1, 2, 2, 3, 3, 4, 5, 6}
Mean =2.8 Median = 2.5
Mean>Median Hence positive skewed
Tim is opening up a bookstore, where he sells both new old books. He charges 11.50 for a new book , and $4.50 for an old book. What was Tim's revenue last month if he sold 15 books and 12 old books
Answers
Answer:
226.50
Step-by-step explanation:
11.50*15=172.5(0)+4.50*12=54.0226.50
Answer:
It’s $226.50
Step-by-step explanation:
PLEASE NEED HELP....I NEED TO FINISH IN ABOUT AN HOUR....PLEASE
Quadrilateral OPQR is inscribed inside a circle as shown below. What is the measure of angle R? You must show all work and calculations to receive credit.
Circle N is shown with an inscribed quadrilateral labeled OPQR. O is labeled 2x degrees. P is labeled y degrees. Q is labeled 2x plus 4 degrees. R is labeled 3y plus 8 degrees.
Answers
Answer: ∠R = 137°
Step-by-step explanation:
The opposite angles of a quadrilateral are supplementary (equal to 180°).
Since ∠P and ∠R are opposite angles, their sum is 180°
∠P + ∠R = 180°
y + 3y + 8 = 180
4y + 8 = 180
4y = 172
y = 43
∠R = 3y + 8
= 3(43) + 8
= 129 + 8
= 137
What is the constant of proportionality for the relationship shown in this table?
x 1 2 3 4
y 4 8 12 16
1/4
4
8
16
Answers
Answer:
The Constant of Proportionality is 4.
Step-by-step explanation:
This is because in the table provided,
4x = y for every situation1 * 4 = 42 * 4 = 83 * 4 = 12and so on...You can find this by dividing y by x.The correct answer to the question is 4.
I did the quiz and got an A on it.
Hope it helps, I'm on K12 OHVA aswell.
Mr.Rice needs to replace the 166.25 ft of edging on the flower beds in his backyard.The edging is sold in lengths of 19 ft each.How many lengths of edging will mr mr.Rice need to purchase?
Answers
Answer: 8.75
Step-by-step explanation: Divide 166.25 by 19
Mr Rice will purchase 8.75 ft of edging
Total length of edging on the flower beds = 166.25 ft Total length of an edging being sold = 19 ft The lengths of edging Mr rice will need to purchase = Y Further Explanationif we derive equation for this question, then we have:
166.25 = 19Y
Y= [tex]\frac{166.25}{19 }[/tex]
Y= 8.75
You can also solve it quickly by following this step:To determine the lengths of edging Mr Rice will need to purchase, the total length of edging on the flower beds (166.25) will be divided by the total length of an edging being sold (19) i.e. 166.25 ÷ 19
= 166.25 ÷ 19
= [tex]\frac{166.25}{19 }[/tex]
= 8.75
Therefore, the total length of edging Mr Rice will need to purchase is 9 ft.
The above mathematical expression is a number problem, and was solved with the aid of division.
The term, division, is a basic arithmetic operation which deals with splitting or dividing two or more numerical values into different equal part.
In this case, it could be observed that the significant numbers that were divided are 166.25 and 19, resulting to 8.75. It is also a function of BODMAS (which is an order of operations).
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Mr.Rice166.25 ft flower beds19 ft eachlengths of edgingbodmasInverse function for f (x) = square root 2x-6
Answers
Answer:
(x^2 +6)/2
or 1/2 x^2 +3
Step-by-step explanation:
f(x)= sqrt(2x-6)
y =sqrt(2x-6)
To find the inverse function, we interchange the x and y and solve for y
x = sqrt(2y-6)
Square each side
x^2 = sqrt(2y-6)^2
x^2 = 2y-6
Add 6 to each to each side
x^2 +6 = 2y-6+6
x^2 +6 = 2y
Divide each side by 2
(x^2 +6)/2 = 2y/2
(x^2 +6)/2 = y
The inverse function is
(x^2 +6)/2
or 1/2 x^2 +3
Two functions f(x) and g(x) are inverses if:
f(g(x)) = x = g(f(x))
The solution is:
[tex]g(x) = \frac{1}{2} x^{2} + 3[/tex]
Now we want to find the inverse function to:
[tex]f(x) = \sqrt{2x - 6}[/tex]
Because this is a square root function, we know that the inverse must be a quadratic function, so let's try with something like:
[tex]g(x) = a*x^2 + c[/tex]
Now we can use the first property to get:
[tex]g(f(x)) = a*f(x)^2 + c = x\\\\ = a*\sqrt{2x - 6}^2 + c = x\\\\= a*(2x - 6) + c = x\\\\2*a*x -6*a + c = x[/tex]
Then we must have:
2*a =1
a = 1/2
And:
-6*a + c = 0
-6*(1/2) + c = 0
-3 + c = 0
c = 4
Then the inverse function is:
[tex]g(x) = \frac{1}{2} x^{2} + 3[/tex]
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Which of the vectors in the graph below is the negative of the vector v?
Answers
Option: C is the correct answer.
C. Vector d
Step-by-step explanation:Vector--
We know that the vector is used to represent a quantity which have both magnitude as well as direction.
The vector is represented in a diagram with the help of a line segment with an arrow.
We know that the negative of a vector reverses the direction of the original vector i.e. it directs to the opposite direction of the original vector.
i.e. both have the same starting point but the direction changes.
Here by looking at the figure we observe that the negative of the vector v is the vector d.
A recipe calls for 1 1/2 cups of sugar. Marley only has 1/4 cup to measure. How many times will Marley ave to fill up measuring cup?
Answers
1 1/2 of sugar with a 1/4 spoon
so it is 1 1/2 ÷ 1/4
1 1/2 is also 3/2
3/2 ÷ 1/4 we could turn 1/4 around and change the ÷ to ×
3/2 × 4
(3×4) ÷ 2
12/2
6
he would fetch it 6 times
Find the exponential function that satisfies the given conditions: Initial value = 33, increasing at a rate of 7% per year (2 points)
Answers
Answer:
[tex]f(x)=33*(1.07)^x[/tex]
Step-by-step explanation:
Let f(x) be our exponential growth function representing growth after x years.
We are asked to find the exponential function that satisfies the given conditions: Initial value = 33, increasing at a rate of 7% per year.
Since an exponential growth function is in form: [tex]y=a*(1+r)^x[/tex], where a= initial value of function and r = growth rate in decimal form.
Given:
a=33
r=7%.
Let us convert our given rate in decimal form.
[tex]7\text{ percent}=\frac{7}{100}=0.07[/tex]
Now let us substitute our given values in exponential function form:
[tex]f(x)=33*(1+0.07)^x[/tex]
[tex]f(x)=33*(1.07)^x[/tex]
Therefore, the exponential function that satisfies our given conditions will be [tex]f(x)=33*(1.07)^x[/tex].
Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. (Hint: Let (x,y) be the unknown endpoint. Apply the midpoint formula, and solve the two equations for x and y.) midpoint (-11,-20) endpoint (-2,-14) The other endpoint is ____
Answers
[tex]\text{The formula of a midpoint:}\\\\\left(\dfrac{x_1+x_2}{2};\ \dfrac{y_1+y_2}{2}\right)[/tex]
[tex]\text{We have}\\\\\text{endpoint}\ (-2,\ -14)\to x_1=-2,\ y_1=-14\\\\\text{midpoint}\ (-11,\ -20)\\\\\text{Therefore we have the equations:}\\\\\dfrac{-2+x_2}{2}=-11\qquad\text{multiply both sides by 2}\\\\-2+x_2=-22\qquad\text{add 2 to both sides}\\\\\boxed{x_2=-20}\\\\\dfrac{-14+y_2}{2}=-20\qquad\text{multiply both sides by 2}\\\\-14+y_2=-40\qquad\text{add 14 to both sides}\\\\\boxed{y_2=-26}\\\\Answer:\ \boxed{(-20,\ -26)}[/tex]
Final answer:
To find the other endpoint of a line segment when given the midpoint and one endpoint, use the formulas x2 = 2xm - x1 and y2 = 2ym - y1. For the given midpoint (-11, -20) and endpoint (-2, -14), the other endpoint is calculated to be (-20, -26).
Explanation:
To find the coordinates of the other endpoint of a segment when the midpoint and one endpoint are known, the midpoint formula can be used in reverse. For a line segment with endpoints (x1, y1) and (x2, y2) and midpoint (xm, ym), the coordinates of the midpoint are found by the formulas xm = (x1 + x2)/2 and ym = (y1 + y2)/2. If one endpoint is known, say (x1, y1) = (-2, -14) and the midpoint is (xm, ym) = (-11, -20), we can find the other endpoint (x2, y2) by rearranging the formulas: x2 = 2xm - x1 and y2 = 2ym - y1.
Calculating the values we get:
x2 = 2(-11) - (-2) = -22 + 2 = -20
y2 = 2(-20) - (-14) = -40 + 14 = -26
Therefore, the coordinates of the other endpoint are (-20, -26).