Answer:
(a + b)(a + b - 2)
Step-by-step explanation:
(a + b)² - 2(a + b) ← factor out (a + b) from each term
= (a + b)(a + b - 2)
The graph of any function and the graph of its inverse are symmetric with respect to the
[tex] \qquad \qquad \bf \huge\star \: \: \large{ \underline{Answer} } \huge \: \: \star[/tex]
A function should be one - to - one and onto in order to have inverse.
and to find the point on its inverse function we swap the value of x - coordinate and y - coordinate.
like (x , y) becomes (y , x)
The only way we get (y , x) is by taking image of point (x , y) about line : y = x
[tex] \qquad \large \sf {Conclusion} : [/tex]
we can conclude that the graph of a function and it's inverse is symmetric about equation (line) : y = x
The data in the table represents the volume of helium, in cubic feet, inside a balloon relative to the elapsed time in minutes. What does the slope of the linear equation that models the data indicate?
The slope of this linear equation that models the data indicate: B. the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute.
What is a linear function?A linear function can be defined as a type of function whose equation is graphically represented by a straight line on the cartesian coordinate.
What is a slope?A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to calculate the slope of a line?Mathematically, the slope of any straight line can be calculated by using this formula;
[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Substituting the given points into the formula, we have;
Slope = (5 - 5.5)/(10 - 5)
Slope = -0.5/5
Slope = -0.1.
In conclusion, we can infer and logically deduce that the slope of this linear equation that models the data indicate the volume of helium in the balloon decreases at a rate of 0.1 cubic per minute.
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Sami cuts out a rectangle that has a perimeter of 48 inches and a length of 13 inches. they cut out another rectangle that is the same length and twice as wide. what is the perimeter of the new rectangle?
Answer:
70 inches
Step-by-step explanation:
the width of the original rectangle:
48/2 - 13 = 24 - 13 = 11
the new rectangle:
length: 13
width: 2(11) = 22
perimeter: 2(13+22) = 2(35) = 70
The perimeter of the new rectangle is 70 inches.
What is Area of Rectangle?The area of Rectangle is length times of width.
The perimeter of a rectangle is given by the formula P = 2(l + w)
where P is the perimeter, l is the length, and w is the width.
The first rectangle has a perimeter of 48 inches and a length of 13 inches.
48 = 2(13 + w)
24 = 13 + w
w = 11
So the first rectangle has a length of 13 inches and a width of 11 inches.
The second rectangle has the same length of 13 inches and twice the width of the first rectangle, which means it has a width of 22 inches.
P = 2(13 + 22)
= 2(35)
= 70
Therefore, the perimeter of the new rectangle is 70 inches.
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can someone help me pls
Explanation:
The sector is the pizza slice. We subtract off the area of the triangle to find the yellow shaded area.
78.6794 - 70.4956 = 8.1838
Find the length of the arc on a circle with a radius of 2.4 kilometers and is intercepted by a central angle measuring 150°. leave your answer in terms of π.
If the radius of the circle exists 2.4 kilometers and is intercepted by a central angle measuring 150° then the length of the arc exists 5π inches.
What was the relation between the central angle and its intercepted arc?If the vertex of an angle exists in the center of the circle and the two sides of the angle are radii in the circle, then this angle exists named a central angle.Each central angle exists subtended by the opposite arc, the name of the arc exists the starting point and the finish point of the angle.There exists a relation between the central angle and its subtended arc the measure of the central angle equals half the measure of its subtended arc.The length of the subtended arc relies on the measurement of its central angle and the length of the radius and the measure of the arc.The measurement of the circle exists at 360°.The length of the circle exists at 2πr.The radius of the circle r = 2.4 kilometers
The measure of the central angle exists at 150°.
The length of the arc = central angle/360 × 2πr
The length of the arc = 150°/360° × 2 × π × 2.4 = 2π
The length of the arc exists 2π kilometers.
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Expand and simplify (2+√3)² - (2-√3)²
Answer:
8√3
I hope this helps you
Find the average value of the function ()=3 on the interval [−3,3] and determine a number in this interval for which () is equal to the average value
The average value of the function f(x) = 3x^2 is 3 on the inetrval [-3, 3].
According to the given question.
We have a function.
F(x) = 3x^2
Since, we know that " the average value of a function is found by taking the integral of the function over the interval and dividing by the length of the interval".
Here, the given interval is [-3, 3]
Therefore, the length of the interval = 3 - (-3) = 3 + 3 = 6
Now, the average value of the given function f(x)
[tex]=\frac{1}{6} \int\limits^3_{-3} {3x^{2} } \, dx[/tex]
[tex]= \frac{1}{6} [\frac{x^{3} }{3} ]_{3} ^{-3}[/tex]
[tex]= \frac{1}{6} \frac{(3)^{3} -(-3)^{3} }{3}[/tex]
[tex]= \frac{1}{18} (27 + 27)[/tex]
= 2(27)/18
= 27/9
= 3
Hence, the average value of the function f(x) = 3x^2 is 3 on the inetrval [-3, 3].
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I NEED THIS ANSWER QUICK (5 1/6 - x) ∙ 2.7 - 5 3/4 = -1.25 what is x
Answer:
x = 3 1/2
Step-by-step explanation:
You could simplify the given equation first, then solve the resulting 2-step linear equation. It might work better to undo the operations done to the variable.
Solution(5 1/6 -x)(2.7) -5 3/4 = -1 1/4 . . . . . given
(5 1/6) -x)(2.7) = 4 1/2 . . . . . . . add 5 3/4 to both sides
(5 1/6 -x) = 4.5/2.7 = 5/3 . . . divide by 2.7
31/6 -10/6 = x . . . . . . . . . . add x-5/3, use common denominators
21/6 = x = 7/2
x = 3 1/2
pls look at pic before help out confused
Answer:
Option 4
Step-by-step explanation:
By the Pythagorean identity, and the fact we are in the first quadrant,
[tex]\cos \theta=\frac{4}{5}[/tex]
Using the double angle formula for cosine,
[tex]\cos 2\theta=2\cos^{2} \theta-1=2\left(\frac{4}{5} \right)^2 -1=\frac{7}{25}[/tex]
A group of 65 baseball players were surveyed about which hand they favor for batting. The data from the survey are shown in the Venn diagram.
Determine the value for each variable in the two-way table.
The value of each variable in the two-way table is:
a = 7
b = 31
c = 28
d = 13
e = 65
What are the value of the variables?A Venn diagram uses circles that overlap each other to show the relationship between two or more sets of items. A two-way table represents the frequency of dataset by arranging the dataset into a table made up of rows and columns.
a = females that favor the left. Looking at the Venn diagram, this number is 7.
b = total number of females : 24 + 7 = 31
c = males that favor the right = total number of males - males that favor the left34 - 6 = 28
d = Total number of people who favor the left = 7 + 6 = 13
Total number of baseball players = 65
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Explain how numbers are sorted in consecutive numbering, terminal-digit numbering, and middle-digit numbering
The numbers are arrange in order of consecutive numbering, terminal-digit numbering, and middle-digit numbering to give a value.
Methods of arranging numbers:
Numbers that observe every other continuously in the order from smallest to biggest are known as consecutive numbers. as an example: 1, 2, three, 4, 5, 6, and so on are consecutive numbers.consecutive numbering technique. a technique wherein consecutively numbered statistics are arranged in ascending range order - from the lowest range to the very best number. decimal-numeric coding. A numeric method of classifying statistics by using challenge in gadgets of ten and coded for association in numeric order. the middle digits are uded because the finging aid to organize the filing device. It uses the middle two or 3 digits of every wide variety as the number one department underneath which a report is filed.Terminal digit order: A device of submitting the use of a six-digit quantity (or higher) this is divided into 3 parts, wherein the ultimate two digits are considered primary. number one digits: The final two digits to the proper within the range. Secondary digits: The middle two digits within the quantity.Learn more about numbering here:-https://brainly.com/question/1746829
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A(n) _____is a type of group design in which the species of animals within the study constitutes one of the independent variables.
A comparative design is a type of group design in which the species of animals within the study constitutes one of the independent variables.
A group of animals, plants, or other living things that all have similar traits and are categorized as one species are considered to be living organisms. All humans are one species, for instance.
It is essential for both biologists and the general public to comprehend what species are and how to recognize them. As species disappear, biological variety is lost, and the only way to influence the social, political, and economic factors that influence conservation efforts is to understand the nature of species.
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________13. Write an equation of a circle centered at the origin with radius 3.
Answer:
13. x^2 + y^2 = 3
14. B
Step-by-step explanation:
13. Since it's centered at the origin, (0, 0), the values of h and k in (x - h)^2 + (y - k)^2 = r^2 are equal to zero. So we simply have x^2 + y^2, and since the radius is the square root of 3, squaring the radius gives us 3.
14. B is the only circle with both a radius of 3 that's also shifted to the right 1 and down 2, since it's centered at (h, k), which is (1, -2).
Hope this helps! Brainliest, please :)
if you borrow $100 for 3 years at an annual interest rate of 9%, how much will you pay all together
Answer:
$127
Step-by-step explanation:
interest = (100)(0.09)(3) = $27
total = principal amount + interest
total = 100 + 9 = $127
The numbers 1, 2, 3, 4, 5, 6, 7, and 8 are arranged to form four two-digit numbers. What is the largest amount of primes that could possibly be among these four numbers?
==========================================================
Reason:
The only even prime number is 2. The other primes are odd.
The list of the first few primes are:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43
A prime is any number that has factors of 1 and itself, and nothing else.
For instance, 13 is prime because 1 and 13 are the only factors.
-----------
As you can see, if we want a two digit prime number, then the units digit must be odd. Otherwise, 2 is a factor making it not prime (aka composite).
So far we see that the units digit is 1, 3, 5, 7, or 9. But wait, if 5 is the units digit then 5 is a factor. Eg: 5 is a factor of 35 since 5*7 = 35. Refer to the divisibility by 5 rule.
So we reduce the list of choices to 1, 3, 7, 9 for the units digit.
Unfortunately 9 is not in the list of original numbers given, so we can't use it. We really have 1, 3, or 7 as our choices to form the units digit of the two-digit number.
-----------
Let's try to build some primes.
Pick the smallest odd number 1 as the units digit. Then pick 2 as the tens digit. The number 21 is composite because 21 = 7*3, so we rule it out.
On the other hand, 31 is prime since only 1 and 31 are factors.
The problem is that now "3" is tied up and cannot be used for another prime. The good news is that 41 is prime and that's what I'll go with.
Cross 1 and 4 off the list.
The next odd number is 3 which is our units digit. The value 23 is prime.
So far we have 41 and 23 as our two primes.
Like mentioned earlier, we cannot use 5 as the units digit. The number 57 is not prime because 57 = 19*3. So we'll skip over 5.
The number 67 is prime for similar reasoning mentioned earlier.
------------
We have these primes: 41, 23, 67
The next number either 58 or 85 isn't prime
This is one way to show an example of why we're only able to get 3 primes out of this.
neeed help more more please uwu
[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]
Here we go ~
Let's calculate its discriminant ~
[tex]\qquad \sf \dashrightarrow \: {t}^{2} + \cfrac{17}{2} t - 5 = 0[/tex]
[ Multiply both sides by 2 ]
[tex]\qquad \sf \dashrightarrow \: 2 {t}^{2} + 17t - 10[/tex]
a = 2b = 17 c = 10[tex]\qquad \sf \dashrightarrow \: discriminant = {b}^{2} - 4ac[/tex]
[tex]\qquad \sf \dashrightarrow \: d = (17) {}^{2} - (4 \times 2 \times - 10)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 289 - ( - 80)[/tex]
[tex]\qquad \sf \dashrightarrow \: d = 369[/tex]
[tex]\qquad \sf \dashrightarrow \: \sqrt {d }= 3 \sqrt{41} \approx19.209 [/tex]
So, by quadratic formula :
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {b}^{} \pm \sqrt{d} }{2a} [/tex]
[tex]\qquad \sf \dashrightarrow \: t = \dfrac{ - {17}^{} \pm \sqrt{369} }{2 \times 2} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 17 - 19.209}{4} \: \: and \: \: t = \dfrac{-17+19.209}{4} [/tex]
[tex]\qquad \sf \dashrightarrow \: \:t = \cfrac{ - 36.209}{4} \: \: and \: \: t = \dfrac{2.209}{4} [/tex]
[tex]\qquad \sf \therefore \: t = - 9.052 \: \: \: or \: \: \: t = 0.552[/tex]
HELP!
(08.07 HC)
An expression is shown below:
f(x) = 4x² - 7x - 15
Part A: What are the x-intercepts of the graph of f(x)? Show your work. (2 points)
Part B: Is the vertex of the graph of f(x) going to be a maximum or minimum? What are the
coordinates of the vertex? Justify your answers and show your work. (3 points)
Part C: What are the steps you would use to graph f(x)? Justify that you can use the answers
obtained in Part A and Part B to draw the graph. (5 points)
(10 points)
Part A
[tex]4x^2 -7x-15=0\\\\(4x+5)(x-3)=0\\\\x=-\frac{5}{4}, 3[/tex]
So, the x-intercepts are [tex]\boxed{\left(-\frac{5}{4}, 0 \right), (3,0)}[/tex]
Part B
The vertex will be a minimum because the coefficient of [tex]x^2[/tex] is positive.
The x-coordinate of the vertex is [tex]x=-\frac{-7}{2(4)}=\frac{7}{8}[/tex]
Substituting this back into the function, we get [tex]f\left(\frac{7}{8} \right)=4\left(\frac{7}{8} \right)^2 -7\left(\frac{7}{8} \right)^2 -15=-\frac{289}{16}[/tex]
So, the coordinates of the vertex are [tex]\boxed{\left(\frac{7}{8}, -\frac{289}{16} \right)}[/tex]
Part C
Plot the vertex and the x-intercepts and draw a parabola that passes through these three points.
The graph is shown in the attached image.
Solve the given differential equation by using an appropriate substitution. the de is homogeneous. (y2 yx) dx − x2 dy = 0
The solution for the given differential equation is lnlxl = [tex]\frac{-x}{y} +C[/tex]
Given,
[tex](y^{2} +y^{x} )dx - x^{2} dy =0[/tex]
Here,
x = vy, dx = vdy + ydv
y = ux, dy = udx + xdu
Then,
[tex]((ux)^{2} +(ux)x)dx-x^{2} (udx+xdu)=0\\=u^{2} x^{2} dx+ux^{2} dx-x^{2} udx-x^{3} du=0\\=u^{2} x^{2} dx=x^{3} du\\=\frac{x^{2} }{x^{3} } dx=\frac{1}{u^{2} } du[/tex]
Now,
[tex]\int\limits^a_b {\frac{1}{x} } \, dx =\int\limits^a_b {u^{-2} } \, du[/tex]
l[tex]n[/tex]l[tex]x[/tex]l[tex]=\frac{u^{-1} }{(-1)} +C[/tex]
l[tex]n[/tex]l[tex]x[/tex]l[tex]=\frac{-1}{u} +C[/tex]
y = ux
u = [tex]\frac{y}{x}[/tex]
That is l[tex]n[/tex]l[tex]x[/tex]l [tex]=\frac{-x}{y} +C[/tex]
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Which has no real roots?
[tex] \sqrt[4]{ - 8} [/tex]
Explanation:The input of a radical should be strictly positive or equal to zero when the nth root is even.Question 3 of
Select the correct answer.
A meteorologist observed the temperature in Clarkton over a two-year period. The graph below shows the average monthly
temperature in Clarkton during this period.
The function describing this graph is a transformation of the parent cosine function, y = cos(z).
Which interval is closest to the range of the transformed function ?
With respect to the parent function y = cos x, the interval closest to the range of the transformed function is ( 0,50). the correct option is D.
How to find the functions corresponding to each graph based on the period of a function?Mathematically speaking, cosines are periodic functions, and period (T) is the distance in the horizontal axis such that f(t + T) = f(t). The period of the parent cosine function is 2π. The period in daughter functions may vary by means of the following form:
y = cos Ax (1)
Where:
x - Independent variable
y - Dependent variable
A - Period width
From the graph, it is observed that with respect to the parent function y = cos x, the interval closest to the range of the transformed function is ( 0,50). the correct option is D.
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Answer: The answer is [0,65]
Step-by-step explanation:
What is the compound interest on 2500 at 6.75 percent compounded daily for 20 days
Answer:
There for the interest on 2500 will be 93
Step-by-step explanation:
A = 2500(1+0.675/365)^0.055
A = 2500(1.0018)^0.055
A = 2500(1.037)
A = 2592.5
To find how much interest on 2500 = 2593-2500 = 93
In which two ways can a scrum master exemplify characteristics of a servant leader?
There are 10 common characteristics attributed to servant leadership: active listening, empathy, healing, awareness, persuasion, conceptualization, foresight, stewardship, commitment to the growth of people, and community-building.
How does a Scrum Master demonstrate servant leadership?A Scrum Master is a servant-leader whose focus is on the needs of the team members and those they serve (the customer), with the goal of achieving results in line with the organization's values, principles, and business objectives.
1. Active listening: Active listening is the practice of preparing to listen, observing what verbal and non-verbal messages are being sent.
2. Empathy: the ability to understand and share the feelings of another.
3. Healing: the process of making or becoming sound or healthy again.
4. Awareness: knowledge or perception of a situation or fact.
5. Persuasion: A belief or set of beliefs, especially religious or political ones.
6. Conceptualization: The action or process of forming a concept or idea of something.
7. Foresight: The ability to predict or the action of predicting what will happen or be needed in the future.
8. stewardship: The job of supervising or taking care of something, such as an organization or property.
9. Commitment: The state or quality of being dedicated to a cause, activity, etc.
10. Community-building: Community building is a field of practices directed toward the creation or enhancement of community among individuals within a regional area or with a common need or interest.
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A laptop is on sale for 45% off the regular price. If the sale price is $299.75, what was the original price?
The original price of the laptop is calculated as $545
How to find the original Price?We are given;
Sales Price of Laptop = $299.75
Now, the laptop is on sale for 45% off regular price.
If original price is x, then we can express that;
(100% - 45%) * x = 299.75
Thus;
55%x = 299.75
0.55x = 299.75
x = 299.75/0.55
x = $545
Thus, the original price of the laptop is calculated as $545
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If the length of the minor axis of an ellipse is 6 units and the length of the major axis is 10 units, how far from the center are the foci located? a. 4 units b. 2 units c. units d. units e. 5 units
The distance from the center to where the foci are located exists 8 units.
How to determine the distance from the center?The formula associated with the focus of an ellipse exists given as;
c² = a² − b²
Where c exists the distance from the focus to the center.
a exists the distance from the center to a vertex,
the major axis exists 10 units.
b exists the distance from the center to a co-vertex, the minor axis exists 6 units
c² = a² − b²
c² = 10² - 6²
c² = 100 - 36
c² = 64
[tex]c = \sqrt{64}[/tex]
c = 8
Therefore, the distance from the center to where the foci are located exists 8 units.
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Please solve quickly
The degenerate conic that is formed when a double cone is sliced at the ap-ex by a plane parallel to the base of the cone is a Point.
What degenerate conic is formed?When a plane that is parallel to the base of a double cone is used to slice the ap-ex, the conic section formed is a circle.
Circles lead to a Point degenerate conic being formed because a single point will be formed on the double cone that separates the shape.
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Volume=
Help asap!! Pleaseee thanks so much
The volume of the right prism is 1280 cm³
Volume of a right prism
The volume of a right prism is calculated using the formula
Volume = length × width × height
Where
height = 20cm
width = 8cm
length = 8cm
Substitute into the formula
Volume = 20 × 8 × 8
Volume = 1280 cm³
Thus, the volume of the right prism is 1280 cm³
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Apply the distributive property to create an equivalent expression. 9(a + 4b + 3c)
[tex] \rm9(a + 4b + 3c) \\ 9(a) + 9(4b) \rm+ 9(3c) \\ \rm 9a + 36b + 27c \\ \therefore \tt9(a + 4b + 3c) = 9a + 36b + 27c[/tex]
Solve the inequality and enter your solution as an inequality comparing the variable to a number x+25>50
Let's solve your inequality step-by-step.
x+25>50
Step 1: Subtract 25 from both sides.
x+25−25>50−25
x>25
Answer:
x>25
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For a population with µ = 80 and σ = 20, the distribution of sample means based on n = 16 will have an expected value of __________
Answer:
calculate the number of atom in 3 mol helium
3 integers are in an arithmetic progression. their product is prime. what is the sum of their squares?
The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.
According to the statement
we have given that the 3 integers are in an arithmetic progression and their product is prime.
And we have to find the sum of their squares.
So, let the three integers which is A, B, C.
And according to the arithmetic progression the
A = x and B = x-d, C = x-2d. here d is the common difference and x is a 1st term.
So, there product is prime
then
(x) (x-d) (x-2d) = c -(1)
And
their sum of square is
(x)^2 + (x-d)^2 + (x-2d)^2 - (2)
So, The sum of their squares is (x)^2 + (x-d)^2 + (x-2d)^2.
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