Answer:
- 6
Step-by-step explanation:
The average rate of change of f(x) in the closed interval [ a, b ] is
[tex]\frac{f(b)-f(a)}{b-a}[/tex]
here [ a, b ] = [ - 7, - 1 ]
f(b) = f(- 1) = (- 1)² + 2(- 1) - 8 = 1 - 2 - 8 = - 9
f(a) = f(- 7) = (- 7)² + 2(- 7) - 8 = 49 - 14 - 8 = 27
Hence
average rate of change = [tex]\frac{-9-27}{-1-(-7)}[/tex] = [tex]\frac{-36}{6}[/tex] = - 6
Which is the simplified form of x^-12
For this case we must simplify the following expression:
[tex]x ^ {12}[/tex]
By definition of power properties we have to:
[tex]a ^ {- 1} = \frac {1} {a ^ 1} = \frac {1} {a}[/tex]
Then we can rewrite the expression as:
[tex]x ^ {- 12} = \frac {1} {x ^ {12}}[/tex]
ANswer:
[tex]x ^ {- 12} = \frac {1} {x ^ {12}}[/tex]
Answer:
[tex]\frac{1}{x^{12}}[/tex]
Step-by-step explanation:
The given expression is [tex]x^{-12}[/tex]
We never leave the final expression having a negative exponent.
So, we must change this negative exponent to a positive exponent.
In order to do that, we use the below property of exponent:-
[tex]x^{-m}=\frac{1}{x^m}[/tex]
Here m = 12
Therefore, by using this property, we get
[tex]x^{-12}\\\\=\frac{1}{x^{12}}[/tex]
Thus, the simplified form is
[tex]\frac{1}{x^{12}}[/tex]
choose the standard form of the equation of the circle with radius 5 √ 3 centered at( -6, 2) please help
Answer:
(x + 6)² + (y - 2)² = 75
Step-by-step explanation:
The equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k) are the coordinates of the centre and r is the radius
here (h, k) = (- 6, 2) and r = 5[tex]\sqrt{3}[/tex], hence
(x - (- 6))² + (y - 2)² = (5[tex]\sqrt{3}[/tex] )², that is
(x + 6)² + (y - 2)² = 75
what is the radius of a circle with a 30 degree angle and a 12.7 yd
Answer:
15
Step-by-step explanation:
30 divided by 2 to find a radius. that equals 15.
The answer to that is 15!
Suppose that f(x)=x^2 and g(x)=2/5x^2. How does the graph of g(x) compare with the graph of f(x)?
Answer: The graph of g(x) is the graph of f(x) compresed vertically.
Step-by-step explanation:
Given the parent function [tex]f(x)^2[/tex], there are some transformations rules:
If [tex]f(x)=a(x^2)[/tex] when [tex]a>1[/tex], then it is stretched vertically.
If [tex]f(x)=a(x^2)[/tex] when [tex]0<a<1[/tex], then it is compresed vertically.
If [tex]f(x)=(ax)^2[/tex] when [tex]0<a<1[/tex], then it is stretched horizontally.
If [tex]f(x)=(ax)^2[/tex] when [tex]a>1[/tex], then it is compresed horizontally.
In this case for [tex]g(x)=\frac{2}{5}x^2[/tex], it has the form [tex]f(x)=a(x^2)[/tex] and [tex]0<a<1[/tex], then the graph of g(x) is the graph of f(x) compresed vertically.
The graphs of the functions f(x) = x^2 and g(x) = 2/5x^2 both represent parabolas, with g(x) being vertically compressed by a factor of 2/5 compared to f(x), which makes the g(x) graph appear narrower and less steep than the f(x) graph.
Explanation:The functions f(x) = x2 and g(x) = 2/5x2 both represent parabolas, which are U-shaped curves on a graph. The significant difference between these two functions is their scaling, or how they stretch or compress vertically. The function f(x) = x2 has no scaling factor, which means it represents a standard square function with a one-to-one ratio. On the other hand, the function g(x) = 2/5x2 has a scaling factor of 2/5, meaning the graph of g(x) compared to f(x), will be vertically compressed by a factor of 2/5. This means the heights on the graph of g(x) are 2/5 times the corresponding heights on the graph of f(x). Therefore, the g(x) graph will appear narrower and less steep than the f(x) graph.
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What can you tell about the mean of each distribution?
Answer:
there is a SMALL DIFFERENCE in the mean number of stray cats placed in homes by a new leash on life animal clinic each week and the mean number of stray cats placed in homes by no ruff stuff animal each week
Step-by-step explanation:
i got it right lol
There is a small difference in the mean number of stray cats placed in homes.
We have given the mean of each distribution
What is the mean?
The mean is the mathematical average of a set of two or more numbers that can be computed with the arithmetic mean method or the geometric mean method.
Therefore we can say that,
There is a small difference in the mean number of stray cats placed in homes by a new leash on life animal clinic each week and the mean number of stray cats placed in homes by no ruff stuff animal each week.
Therefore there is a small difference in the mean of each distribution.
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Which of the following is equivalent to 5x+2/x = -12/x-1
A) 6x - 1 = -12x
B) - 12(5x + 2) = x(x-1)
C) - 12(x - 1) = x(5x + 2)
D) (5x + 2) (x - 1) = -12
Answer:
[tex] \frac{5x + 2}{x} = \frac{ - 12}{x - 1} [/tex]
[tex]equivalent \: to \\ \: (5x + 2)(x - 1) = - 12x[/tex]
For this case we must find an expression equivalent to:
[tex]\frac {5x+2} {x} = \frac {-12} {x-1}[/tex]
We multiply both sides of the equation by "x":
[tex]5x+2 = \frac {-12x} {x-1}[/tex]
We multiply both sides of the equation by "x-1":[tex](5x+2) (x-1) = - 12x[/tex]
ANswer:[tex](5x+2) (x-1) = - 12x[/tex]
Match each expression with an equivalent expression.
Question 4 options:
6x−4y
6−4x
6x−4x
6x−4
1. 2x
2. 2(3x−2)
3. 2(3−2x)
4. 2(3x−2y)
Answer:
[tex]6x-4y[/tex] → 4. [tex]2(3x-2y)[/tex]
[tex]6-4x[/tex] → 3. [tex]2(3-2x)[/tex]
[tex]6x-4x[/tex] → 1. [tex]2x[/tex]
[tex]6x-4[/tex] → 2. [tex]2(3x-2)[/tex]
Step-by-step explanation:
You need to:
Factor out 2 from [tex]6x-4y[/tex], then you get the equivalent expression:
[tex]=2(3x-2y)[/tex] this matches with OPTION 4
Factor out 2 from [tex]6-4y[/tex], then you get the equivalent expression:
[tex]=2(3-2x)[/tex] this matches with OPTION 3
Make the subtraction for [tex]6x-4x[/tex], then you get the equivalent expression:
[tex]=2x[/tex] this matches with OPTION 1
Factor out 2 from [tex]6x-4[/tex], then you get the equivalent expression:
[tex]=2(3x-2)[/tex] this matches with OPTION 2
Answer:
6x-4y=2(3x-2y),
6-4x=2(3-2x),
6x-4x=2x,
6x-4=2(3x-2)
Step-by-step explanation:
We have been given 4 expressions
6x−4y, 6−4x, 6x−4x, 6x−4
Now we need to simplify or factor so that we can match each expression with an equivalent expression.
6x-4y=2(3x-2y)
6-4x=2(3-2x)
6x-4x=2x
6x-4=2(3x-2)
Now we can easily see that right side is unique for each of the given expression which can be easily matched with given choices.
what is an equation of the line that is perpendicular to y-3=4(x+2) and passes through the point (-5, 7)
Answer: [tex]y-7=-\frac{1}{4}(x+5)[/tex]
Step-by-step explanation:
The equation of the line in Point-Slope form is:
[tex]y-y_1=m(x-x_1)[/tex]
Where "m" is the slope and ([tex]x_1,y_1[/tex]) is a point on the line.
You can identify that in the equation of the line [tex]y-3=4(x+2)[/tex], the slope is:
[tex]m=4[/tex]
By definition, the slopes of perpendicular lines are negative reciprocals. Then, the slope of the other line is:
[tex]m=-\frac{1}{4}[/tex]
Finally, knowing that this line passes through the point (-5, 7),you can substitute this point and the slope into the equation [tex]y-y_1=m(x-x_1)[/tex] to get the equation of this line:
[tex]y-7=-\frac{1}{4}(x-(-5))[/tex]
[tex]y-7=-\frac{1}{4}(x+5)[/tex]
volume of this prism
The volume is (area of cross-section) x (length) .
-- The cross-section is a triangle. The area of a triangle is
Area = (1/2) (base) (height) .
In this one, the base is 9/4 m and the height is 3-1/3 m .
Area = (1/2) (9/4 m) (3-1/3 m)
Area = (1/2) (9/4) (10/3)
Area = 90/24 m² .
-- Volume = (area of cross-section) x (length)
Volume = (90/24 m²) x (7-1/3 m)
Volume = (90/24) x (22/3) m³
Volume = (1,980 / 72) m³
Volume = 27.5 m³
40 POINTS!!
Q: Evaluate. 9^2+2x4−5
A.21
B.75
C.84
D.327
No false answers, no spamming to get points, no saying "Why don't you just try"
The answer is C 84. Your welcome
A doctor estimates that a particular patient is losing bone density at a rate of 3% annually. The patient currently has a bone density of 1,500 kg/mg3. The doctor writes an exponential function to represent the situation. Which values should the doctor use for a and b in a function written in the form f(x) = abx, where f(x) represents the bone density after x years?
Answer:
it is 1500 and .97 on
Step-by-step explanation:
Answer:
a = 1500 (initial Bone density)
b = 0.97 (remaining percentage every year)
x = x (years)
Step-by-step explanation:
The question already sets x as the "years" variable, and the function must be expressed:
[tex]f(x) = a*b^x[/tex]
Then we can set a as the initial bone density: 1,500 kg/mg3
and b as the remaining percentage after each year: 100% - 3% = 97%
In decimal notation: 97% is equivalent to 0.97
The x exponent of b represents the succesive density reduction each year.
For example, replacing for values for the first 5 years we obtain the following results:
(Note: results are limited and rounded to two decimals)
[tex]f(x) = 1500*0.97^1 = 1455[/tex]
[tex]f(x) = 1500*0.97^2 = 1411.35[/tex]
[tex]f(x) = 1500*0.97^3 = 1369,01[/tex]
[tex]f(x) = 1500*0.97^4 = 1327,94[/tex]
[tex]f(x) = 1500*0.97^5 = 1288,10[/tex]
PLEASE HELP ME ILL GIVE YOU POINTS
Answer: I think the answer is the second box.
Step-by-step explanation: It says 20 males have watched the show. I hope I helped you. If I am wrong, tell me in a polite way. :D
Hello there! The answer is the second chart, or B.
To find the answer, look at the parts of the question.
Let's start in the beginning. Note how it says "Of the 80 participants, 30 were male and 50 were female". This means that, looking at the options, in the "total" row, there should be a value for "30" by male, "50" by female and 80 at the bottom. This means that it cannot be A since this option says that there were 80 females and 80 males and 160 total, or C since it says there are 80 males and 55 females with a total of 135.
Next, it says that 45 have watched the show and 35 have not. If you look at the options left B and D, the only one the has these numbers for have and have not watched is B, making this the correct answer.
I hope this helps and have a great rest of your day! :)
Which algebraic expression is equivalent to the expression below? 2(9x+11)+3
A: 18x + 28
B: 18x + 25
C: 9x + 17
D: 11x + 22
Answer:
B: 18x + 25
Step-by-step explanation:
2(9x+11)+3
Distribute the 2
2*9x + 2*11 +3
18x +22 +3
Combine like terms
18x +25
Work out the value of a and b in the identity.
3ax + 6 - 4(x + b)= 11x + 14
Answer:
a=5, b=-2
Step-by-step explanation:
If you simplify the equation, you get:
3ax +6 -4x -4b - 11x - 14 = 0 =>
3ax - 15x -4b -8 = 0
group together x's and constants:
(3a-15)x -8 -4b = 0
To make this 0 for all x, we have to find an a such that 3a-15 = 0 and b such that -8-4b = 0. this leads to a=5, b=-2
You are standing 16 ft. from the center of a circular swimming pool. The distance from you to a point of tangency is 25 ft. What is the approximate DIAMETER of the pool?
Check the picture below.
recall the diameter is twice as long as the radius, thus d = 2r = 38.42 or rounded up to 38.
help fast I am not sure about this question.
Use the following data and graph the best-fit quadratic curve. What is a good approximation for the value of c?
1 ) 2
2) 3
3) 1
4) -2
Answer:
3
Step-by-step explanation:
Graphing the best-fit quadratic curve for the data-set can be done using Ms. Excel Application.
The first basic step is to enter the data into any two adjacent columns of the excel workbook. Highlight the two columns where the values have been entered, click on the insert tab and then select the x,y scatter-plot feature. This will create an x,y scatter-plot for the data.
Next, click on the Add Chart Element feature and add a polynomial trend-line of order 2 which is basically a quadratic curve. Finally, check the display equation on chart box. This step will plot the quadratic curve as well as give the equation of the best-fit quadratic curve.
The attachment below shows the best-fit quadratic curve to the data-set and its corresponding equation.
A good approximation for the value of c from the equation is thus 3. This is simply the y-intercept of the curve. 3.21 is closer to 3.
I need help with this question
3rd one for the answer all the other ones are wrong. It shifted down
ANSWER
[tex]y = \sqrt[3]{x + 4} - 1[/tex]
EXPLANATION
The given function is
[tex]y = \sqrt[3]{x} [/tex]
The transformation
[tex]y = \sqrt[3]{x + k} - c[/tex]
shifts the graph of the base function k units left and c units down.
Since the graph is shifted 4 units left, k= 4
Also, the graph is shifted 1 unit down.
This implies that c=1
The new equation is
[tex]y = \sqrt[3]{x + 4} - 1[/tex]
The last option is correct.
In the cordinate plane what is the length of the line segment that connects points at (0, -1) and (-7, -2) ? Enter your answer in the box. Round to the nearest hundredth.
Answer:
≈ 7.07
Step-by-step explanation:
Calculate the length using the distance formula
d = √ (x₂ - x₁ )² + (y₂ - y₁ )²
with (x₁, y₁ ) = (0, - 1) and (x₂, y₂ ) = (- 7, - 2)
d = [tex]\sqrt{(-7-0)^2+(-2+1)^2}[/tex]
= [tex]\sqrt{(-7)^2+(-1)^2}[/tex]
= [tex]\sqrt{49+1}[/tex] = [tex]\sqrt{50}[/tex] ≈ 7.07
(16+5i) + (6-7i)
How do I solve this?
Answer:
[tex]\large\boxed{(16+5i)+(6-7i)=22-2i}[/tex]
Step-by-step explanation:
[tex](16+5i)+(6-7i)=16+5i+6+7i\qquad\text{combine like terms}\\\\=(16+6)+(5i-7i)=22-2i[/tex]
Answer:
22-2i
Explanation:
16+6=22
5i-7i=-2i
Convert 192 cups to gallons. Enter your answers in the boxes. There are cups in 1 gallon. Therefore, 192 cups is equal to gallons.
The answer is 12 because there are 16 cups in 1 gallon. 192/16 is 12! Hope this helps! :)
Answer:
Convert 192 cups to gallons. Enter your answers in the boxes. There are (16) cups in 1 gallon. Therefore, 192 cups is equal to (12) gallons.
What is the measure of angle b? Enter your answer as a number only
Answer:
The measure of angle B is [tex]132\°[/tex]
Step-by-step explanation:
step 1
Find the value of x
we know that
In an inscribed quadrilateral, opposite angles are supplementary
so
[tex]x\°+(2x+36)\°=180\°[/tex]
[tex]3x=180\°-36\°[/tex]
[tex]3x=144\°[/tex]
[tex]x=48\°[/tex]
step 2
Find the measure of angle B
[tex]B=(2x+36)\°[/tex]
[tex]B=(2(48)+36)\°=132\°[/tex]
Find the equation of the line passing through the points (6,2)(10,6)
Slope-intercept form: y= mx + b (m is the slope, b is the y-intercept or the y value when x = 0 ---> (0, y))
To find the slope, use the slope formula and plug in 2 points:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
(x₁ , y₁) = (5, 2)
(x₂ , y₂) = (10, 6)
[tex]m=\frac{6-2}{10-5} =\frac{4}{5}[/tex]
[tex]y=\frac{4}{5}x+b[/tex] To find b, plug in a point into the equation (5, 2)
[tex]2=\frac{4}{5}(5)+b[/tex]
2 = 4 + b
-2 = b
[tex]y=\frac{4}{5}x -2[/tex]
Answer:
y = 4/5x -2
Step-by-step explanation:
equation of a line passing through two points is given by
y - y₁ = m (x - x₁), where m = (y₂ - y₁) / (x₂ - x₁)
y₂ = 6, y₁ = 2
x₂ = 10, x₁ =5
m = (6-2)/(10-5)
m = 4/5
y - 2 = 4/5 (x - 5)
multiply both sides by 5
5(y -2) = 4(x - 5)
5y -10 = 4x -20
5y = 4x -20 +10
5y = 4x -10
divide through by 5
y =4/5x -2
Which statement below is ALWAYS TRUE?
(A) Complementary angles are both acute angles.
(B) Any two acute angles are complementary angles.
(C) Supplementary and Complementary angles are always adjacent angles.
(D) Supplementary angles are both obtuse angles
The statement that is always true is that supplementary and complementary angles are always adjacent angles.
Explanation:The statement that is ALWAYS TRUE is (C) Supplementary and Complementary angles are always adjacent angles. Supplementary angles are two angles that add up to 180 degrees, while complementary angles are two angles that add up to 90 degrees. Adjacent angles are two angles that have a common vertex and a common side between them. So, it is always true that supplementary and complementary angles are adjacent angles because they share a common side.
In how many different, distinguishable orders can the letters of the word mathematics be arranged?
A)39,916,800
B)4,989,600
C)6,652,800
Answer:
B)4,989,600
Step-by-step explanation:
The letters of 'MATHEMATICS' contains 11 letters.
The following letters repeats twice, TT,MM,AA.
When we talk of distinguishable wasy, we are referring to arrangement without repetition.
Therefore the letters of "MATHEMATICS" can be arranged in [tex]\frac{11!}{2!2!2!}=4,989,600[/tex] distinguishable ways.
The correct answer is B.
please help me asap!!!!!
Answer:
y=0.5x+3
Step-by-step explanation:
Can someone help me?
Answer:
C
Step-by-step explanation:
Since you are basically interested in what the graph looks like, there is no need to go beyond a good graphing program like Desmos. The graph is provided below.
Red: y = -1/2 x + 4
Blue:2y + x = -8
Since both of them have the same slope, they never meet.
The correct answer is C: No solution
what is the simplest form of Q40
Answer:
-10√5 + 30
Step-by-step explanation:
This is a product of two monomials, so we would kind of like FOIL this.
F - Multiply the first terms in each set of parentheses FARTHEST TO THE LEFT.
O - Multiply the first term in the first set of parentheses FARTHEST TO THE LEFT by the last term in the second set of parentheses FARTHEST TO THE RIGHT.
I - Multiply the last term in the first set of parentheses FARTHEST TO THE RIGHT by the first term in the second set of parentheses FARTHEST TO THE LEFT.
L - Multiply the last terms in each set of parentheses FARTHEST TO THE RIGHT.
Doing this will give 5 - 10√5 + 25. Combine like-terms to end up with -10√5 + 30 [or 30 - 10√5].
I am joyous to assist you anytime.
Angle C is an inscribed angle of circle P.
Angle C measures (20x - 5)º and arc AB
measures (30x + 30)". Find the measure of
arc AB
100 degrees
50 degrees
75 degrees
150 degreea
Answer:
150°
Step-by-step explanation:
(30x+30)=2(20x-5)
x=4
AB=30×4+30=150
Answer:
150°
Step-by-step explanation:
The angle at the centre subtended by arc AB is twice the inscribed angle, that is
30x + 30 = 2(20x - 5) ← distribute
30x + 30 = 40x - 10 ( subtract 40x from both sides )
- 10x + 30 = - 10 ( subtract 30 from both sides )
- 10x = - 40 ( divide both sides by - 10 )
x = 4
Hence
arc AB = (30 × 4) + 30 = 120 + 30 = 150°
The measurement of one angle of a right triangle is 34º.
What is the measurement of the third angle?
Enter your answer in the box.
A triangle's angles always add up to a total 180º, and a right triangle always has an angle equal to 90º.
90º + 34º + xº = 180º
124º + xº = 180º
xº = 56º
In a class there are 15 students. 8 of them like playing soccer , 6 of them like swimming , and 2 like both and swimming and playing soccer. How many students do not like either playing soccer or swimming?
Answer: 1
Step-by-step explanation:
8 likes playing soccer
6 likes swimming
2 likes both
So in other words, because the 2 students likes swimming and playing soccer, they must be coming from the combined number of students (8+6=14) leaving only 1 who doesn't like to play either swimming/soccer.
There are 3 students who do not like either playing soccer or swimming and it can be determined by using set operation.
Given that,
In a class, there are 15 students. 8 of them like playing soccer, 6 of them like swimming, and 2 like both and swimming and playing soccer.
We have to determine,
How many students do not like either playing soccer or swimming?
According to the question,
Let x be the number of students who do not like either playing soccer or swimming.
Total number of students = n(U) = 15
Number of students who like playing soccer = n(A) = 8
Number of students who like swimming = n(B) = 6
Then,
The number of students like both = 2
Number of students who like swimming = Total number of students who like swimming - number of students like both
Number of students who like swimming = 6 -2 = 4
And Number of students who like playing soccer = Total number of students who like playing soccer - number of students like both
Number of students who like swimming = 8 -2 = 6
Therefore,
The total number of students = Number of students who like swimming + Number of students who like swimming + Number of students who do not like either playing soccer or swimming.
[tex]\rm 15 = (8-2) + (6-2) + x +2\\\\15 = 6+4+x+2\\\\15 = 12+x\\\\x = 15-12\\\\x=3[/tex]
Hence, there are 3 students who do not like either playing soccer or swimming.
To know more about Sets click the link given below.
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