Answer:
D; 5pi/3 units
Step-by-step explanation:
Here, we want to find the period of the function;
y = 3/2 cot (3/5x) + 5
By definition, the period of a function is the interval between two matching points in the function.
Let’s say it is the distance between two peaks, crests, etc on a function.
To find the value of the period. We shall standardize the function.
What this means is that we shall be writing the function in the standard form.
The standard form is as follows;
f(x) = A trig(Bx -C) + D
Where trig refers to the accompanying trigonometric function in question.
Comparing this standard form with our question, we can see that;
A is 3/2
B is 3/5
C is 0
D is 5
Now for cot and tan functions, we shall need to divide pi by the absolute value of B
Thus we have; pi divided by 3/5 which gives 5pi/3 units
Answer:
D. 5pi/3, period is the distance between the repetition of a function.
Step-by-step explanation:
Eight years ago, twice Manuel's age was 36. What is Manuel's age now? Pls hell
Answer:
Hey there!
Eight years ago, Manuel's age was 36/2, or 18.
Now, his age is 18+8, or 26 years old.
So, he is 26 years old now.
Hope this helps :)
Represent 1/3 and 5/2 on the same number line.
Step-by-step explanation:
1/3 and 5/2 can be shown as:
1/3= 3/6 5/2= 15/6points with 1/6 interval on the number line:
0, 1/6, 2/6, 3/6, 4/6, ..., 15/6
04
Apples cost £a and bananas cost £b. Which is a correct expression for how 1 point
much 4 apples and 5 bananas cost? *
4a + 5b
4a 5b
9ab
4 + 5
Simplify fully
Answer:
4a+5b
Step-by-step explanation:
Given:
Apple=£a
Banana=£b
Quantity of Apple=4
Quantity of banana=5
Find the cost of 4 apples and 5 bananas
Total cost=PaQa+PbQb
Where,
Pa=price of Apple
Qa=quantity of Apple
Pb=price of banana
Qb=quantity of banana
Total cost=PaQa+PbQb
=4*a+5*b
=4a+5b
Which function increases at the fastest rate between x = 0 and x = 8? A 2-column table with 5 rows titled Linear Function with the equation f of x = 2 x + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 6, 10, 14, 18. A 2-column table with 5 rows titled Exponential Function with the equation f of x = 2 Superscript x Baseline + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 3, 6, 18, 66, 258. A 2-column table with 5 rows titled Quadratic Function with the equation f of x = 2 x squared + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 10, 34, 74, 130. A 2-column table with 5 rows titled Linear Function with the equation f of x = 3 x + 2. The first column is labeled x with entries 0, 2, 4, 6, 8. The second column is labeled f of x with entries 2, 8, 14, 20, 26.
Answer:
The correct option is;
Exponential function 2ˣ + 2
x = 0, 2, 4, 6, 8
f(x) = 3, 6, 18, 66, 258
Step-by-step explanation:
The given functions are;
f(x) = 2x + 2
x = 0, 2, 4, 6, 8
f(x) = 2, 6, 10, 14, 18
f(x) = 2ˣ + 2
x = 0, 2, 4, 6, 8
f(x) = 3, 6, 18, 66, 258
f(x) = 2·x² + 2
x = 0, 2, 4, 6, 8
f(x) = 2, 10, 34, 74, 130
f(x) = 3·x + 2
x = 0, 2, 4, 6, 8
f(x) = 2, 8, 14, 20, 26
By comparison, the function that increases at the fastest rate between x = 0 and x = 8 is Exponential function 2ˣ + 2
Answer: The answer is B on edg
Step-by-step explanation:
Type the correct answer in each box, If necessary, use / for the fraction bar(s).
1
-1
The point on the number line shows the opposite of
or the opposite of the opposite of
Reset
Next
Answer: -1/1
Step-by-step explanation: The fraction, -1/1 or just -1, passes through the transactional point through the slope of the line, y=3x+5.
Find all pairs $(x,y)$ of real numbers such that $x + y = 10$ and $x^2 + y^2 = 56$. For example, to enter the solutions $(2,4)$ and $(-3,9)$, you would enter "(2,4),(-3,9)" (without the quotation marks).
Answer:
(3.26795, 6.73205)
(6.73205, 3.26795)
Step-by-step explanation:
Easiest and fastest way to get your solutions is to graph the systems of equations and analyze the graph for where they intersect.
The defect length of a corrosion defect in a pressurized steel pipe is normally distributed with mean value 30 mm and standard deviation 7.8 mm [suggested in the article "Reliability Evaluation of Corroding Pipelines Considering Multiple Failure Modes and Time-Dependent Internal Pressure" (J. of Infrastructure Systems, 2011: 216–224)].
What values separate the largest 80% from the smallest 20% of the defect length distribution.
Answer:
[tex]z=-0.842<\frac{a-30}{7.8}[/tex]
And if we solve for a we got
[tex]a=30 -0.842*7.8=23.432[/tex]
So the value of height that separates the bottom 20% of data from the top 80% is 23.432.
Step-by-step explanation:
Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(30,7.8)[/tex]
Where [tex]\mu=30[/tex] and [tex]\sigma=7.8[/tex]
For this part we want to find a value a, such that we satisfy this condition:
[tex]P(X>a)=0.80[/tex] (a)
[tex]P(X<a)=0.20[/tex] (b)
As we can see on the figure attached the z value that satisfy the condition with 0.20 of the area on the left and 0.80 of the area on the right it's z=-0.842
If we use condition (b) from previous we have this:
[tex]P(X<a)=P(\frac{X-\mu}{\sigma}<\frac{a-\mu}{\sigma})=0.20[/tex]
[tex]P(z<\frac{a-\mu}{\sigma})=0.20[/tex]
But we know which value of z satisfy the previous equation so then we can do this:
[tex]z=-0.842<\frac{a-30}{7.8}[/tex]
And if we solve for a we got
[tex]a=30 -0.842*7.8=23.432[/tex]
So the value of height that separates the bottom 20% of data from the top 80% is 23.432.
Write the following in ascending order a)4/10,49/100,357/10,1/1001 plz fast ,correct and plzz with explanation
Answer:
1/1001 < 4/10 < 49/100 < 357/10
Step-by-step explanation:
4/10 => 0.4
49/100 => 0.49
357/10 => 35.7
1/1001 => 0.0009
Ascending order is from smallest to the greatest.
Answer:
1/1001, 4/10, 49/100, 357/10
Step-by-step explanation:
Convert the fractions to decimals.
4/10 = 0.4
49/100 = 0.49
357/10 = 35.7
1/1001 = 0.0009
Arrange in ascending order.
0.0009, 0.4, 0.49, 35.7
Change back to fractions.
Simplify 2(x - 3) + 7(x + 2)
Answer:
9x + 8.
Step-by-step explanation:
2(x - 3) + 7(x + 2)
= 2x - 6 + 7x + 14
= 2x + 7x - 6 + 14
= 9x + 8.
Hope this helps!
Mario writes the equation (x+y ) 2 = z 2 +4( 1 2 xy) (x+y)2=z2+4(12xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.
Answer:
For the drop down menu:
i) x + y
ii) z²
iii) ½ xy
The complete question related to this found on brainly (ID:16485977) is stated below:
Mario writes the equation (x+y)² = z² +4( 1/2 xy) to begin a proof of the Pythagorean theorem. Use the drop-down menus to explain why this is a true equation.
_____finds the area of the outer square by squaring its side length.
_____finds the area of the outer square by adding the area of the inner square and the four triangles.
These expressions are equal because they both give the areas of outer space.
Find attached the diagram of the question.
Step-by-step explanation:
Pythagoras theorem is a formula that shows the relationship between the sides of a right angled triangle.
Pythagoras theorem
Hypotenuse ² = opposite ² + adjacent ²
From the diagram of the question.
Hypotenuse = z
Opposite = y
Adjacent = x
z² = x² + y²
Area of outer square = area of inner square + 4(area of triangles)
area of inner square = length² = (x+y)²
Expanding area of the outer square:
(x+y)² = (x+y)(x+y) = x²+xy+xy+y²
(x+y)² = x²+y²+2xy
= z² + 2xy
Area of inner square = length² = z²
Area of triangle = ½ base × height
= ½ × x × y = ½ xy
Area of outer square = area of inner square + 4(area of triangles)
(x + y)² = z² + 4(½xy )
Therefore, it is a true equation.
( x + y )² finds the area of the outer square by squaring its side length.
z² + 4( 1/2xy ) finds the area of the outer square by adding the area of the inner square and the four triangles.
These expressions are equal because they both give the areas of outer space.
So for the drop down menu:
i) x + y
ii) z²
iii) ½ xy
Construct the described data set. The entries in the data set cannot all be the same. The median and the mode are the same. What is the definition of median? A. The value that lies in the middle of the data when the data set is ordered. B. The sum of the data entries divided by the number of entries. C. The data entry that occurs with the greatest frequency. D. The data entry that is far removed from the other entries in the data set.
Answer:
Option A
Step-by-step explanation:
The median is the value that lies in the middle of the data when the data set is ordered.
It is also the value that separates the higher half of the dataset from the lower half of the dataset.
Answer:
B
Step-by-step explanation:
A triangle is shown with its exterior angles. The interior angles of the triangle are angles 2, 3, 5. The exterior angle at angle 2 is angle 1. The exterior angle at angle 3 is angle 4. The exterior angle at angle 5 is angle 6.
Which is a true statement about the diagram?
m∠5 + m∠6 = m∠1
m∠3 + m∠4 + m∠5 = 180°
m∠1 + m∠2 = 180°
m∠2 + m∠3 = m∠5
Answer:
m∠1 + m∠2 = 180°
Step-by-step explanation:
An interior angle and its exterior angle are supplementary (they add up to 180°).
I would really appreciate it if you would mark me brainliest!
Have a blessed day!
Answer:
c
Step-by-step explanation:
To create a giant gemstone, sara first made two identical square pyramids that each had a base area of 100 square inches. Then she glued the pyramids' bases together to form the gemstone. The surface area of the gemstone is 520 square inches. What is the value of x? Explain.
Answer:
8 inches.
Step-by-step explanation:
From the statement we have that they first made two identical square pyramids, each with a base area of 100 square inches.
Ab = s ^ 2 = 100
Therefore each side would be:
s = (100) ^ (1/2)
s = 10
So, side of the square base = 10 inches
Then they tell us that they glued the bases of the pyramids together to form the precious stone. The surface area of the gemstone is 520 square inches, so for a single pyramid it would be:
Ap = 520/2 = 260
For an area of the square pyramid we have the following equation:
Ap = 2 * x * s + s ^ 2
Where x is the height of each triangular surface and s is the side of the square base
Replacing we have:
260 = 2 * x * 10 + 10 ^ 2
20 * x + 100 = 260
20 * x = 160
x = 160/20
x = 8
Therefore, the value of x is 8 inches.
A dilation has center (0, 0). Find the image of each point for the given scale factor. A(3,4);D7(A)
Answer:
6,8
Step-by-step explanation:
need this ASAP. pls answer this question
Answer:
this is ur answer so memories
what is the sum of the values of x that are solutions to the equation x^2 - 10x - 22 = 2 ? a. -12 b. -10 c. -2 d. 2 e. 10
Answer:
[tex]x = 2, 12[/tex]
Your correct answer is D, since I don't see a -12.
Step 1: Subtracting 2 from both sides
Since we have to find the value of x, we have to factor the equation. To do so, we first have to subtract the two from both sides of the equation so all the values are on one side of the equation.
[tex]x^2-10x-22(-2)=2(-2)\\x^2-10x-24=0[/tex]
Step 2: Factoring the equation
Part 1
After subtracting 2 from both sides of the equation, we have to factor the polynomial to be able to get it into two sets of parentheses, so in order to do that, we will ignore the equal sign and the 0 for now. We are now left with:
[tex]x^2-10x-24\\[/tex]
First, we find the multiples of the first term, [tex]x^2\\[/tex], and the last term, -24. Since there is an invisible 1 before the first term, we are basically finding the multiples of [tex]1x^2[/tex], which is [tex]1x[/tex] and [tex]1x[/tex], or x and x. Now we have to find the correct set of numbers for -24. Do do that, we have to make sure that when we multiply the first set of numbers (x, x) with the second set (?, ?) and add them together, then we would get the number in the middle (-10x). So: Two of the most obvious multiples for 24 are 6 and 4, 12 and 2, and 3 and 8. But, this is a negative 24, so we have to work ahead to find out which pair we use first. If we multiply 8 and 3 with x and x, we get 8x and 3x. When we add them together, we do not get 10x, but instead, we get 11x, so it is the wrong pair. If we do the same thing to 6 and 4, we would get 10x, but since 24 is negative, it is not correct because we would need one of the numbers to be negative. In this case, they equal to 10x, but one of the numbers would have to be negative because (if 6 was the negative):
[tex]-6 * 4=-24\\[/tex]
But:
[tex]4-6\neq 10\\[/tex]
So this is not the correct set either. Our last set is 12 and 2, and when we multiply by x (12x and 2x) and we set one of the numbers to be a negative (-12) and subtract them, we get -10x, so, therefore, this is the correct number pair.
[tex]-12*2=-24\\2-12=-10[/tex]
Part 2
With all that done, we now have to factor the numbers. We take the first numbers (x and x), and we place them in front of each of the two parentheses.
[tex](x,?)(x,?)[/tex]
Now, we place -12 and 2 in those places.
[tex](x,-12)(x,2)[/tex]
To find x, we have to plug in the equal sign and 0 from the beginning.
[tex](x,-12)(x,2)=0[/tex]
Since they both have to equal to 0, then that means there would be two different answers because, for example: 12 - 12 = 0, but 12 - 2 ≠ 0.
To find both solutions, we treat the numbers in each of the parentheses as its own equation, and we solve it from there.
x - 12 = 0
12 - 12 = 0
x - 2 = 0
2 - 2 = 0
12 and 2 are our solutions! Hope this helps :)
Answer:
12 and 2
Step-by-step explanation:
factor the euqation x^2-10x-22=2 and you get (x,-12)(x,2)=0 and when you solve that you get 12 and 2
I need some help on this
Answer: The answer is B
Step-by-step explanation:
Answer:
Option B is correct
Step-by-step explanation:
cos (3pi/4) = -cos(pi - 3pi/4) = -cos(pi/4) = -sqrt(2)/2
=> Option B is correct
Two points A (-2, 9) and B (4, 8) lie on a line l.Find the distance between points A and B.
Answer:
[tex]\sqrt{37}[/tex]
Step-by-step explanation:
Calculate the distance d using the distance formula
d = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = A(- 2, 9) and (x₂, y₂ ) = B(4, 8)
d = [tex]\sqrt{(4+2)^2+(8-9)^1}[/tex]
= [tex]\sqrt{6^2+(-1)^2}[/tex]
= [tex]\sqrt{36+1}[/tex]
= [tex]\sqrt{37}[/tex] ≈ 6.1 ( to 1 dec. place )
Help help help please I need help fast
The answer would be x =7/5 because you would need to multiply everything by two. Then you would add 4+3 and you would end up with 5x = 7. After that, you need to divided both answers by five
Please Mark brainliest
Answer:
The answer is x=7/5
Step-by-step explanation:
because you have to multiply everything by 2 the add 4+3 and you end up with 5x=7 then divide both sides by 5
A cup holder in a car contains 19 quarters, 39 dimes, some number of nickels, and 58 pennies. If all the coins in the cup holder equal $10.08, then how many nickels are in the cup holder?
Answer:
17 nickels
Step-by-step explanation:
To be able to find the answer, you can say that the sum of the value of each coin multiply for its quantity is equal to 10.08, which you can express as follows:
quarters= 0.25
dimes= 0.10
nickels= 0.05
pennies= 0.01
(0.25*19)+(0.10*39)+(0.05*x)+(0.01*58)=10.08, where
x= the quantity of nickels
Now, you can solve for x:
4.75+3.9+0.05x+0.58=10.08
0.05x=10.08-4.75-3.9-0.58
0.05x=0.85
x=0.85/0.05
x=17
According to this, the answer is that there are 17 nickels in the cup holder.
The equation of a circle is given below. ( x + 7 ) 2 + ( y + 8 ) 2 = 4 9 (x+7) 2 +(y+8) 2 = 9 4 left parenthesis, x, plus, 7, right parenthesis, squared, plus, left parenthesis, y, plus, 8, right parenthesis, squared, equals, start fraction, 4, divided by, 9, end fraction What is its center? ( (left parenthesis , ,comma ) )right parenthesis What is its radius? If necessary, round your answer to two decimal places. units
Answer:
The center is (-7,-8) and the radius is sqrt (2/3)
Step-by-step explanation:
( x + 7 )^ 2 + ( y + 8 ) ^2 = 4 /6
The equation of a circle can be written as
(x-h)^2 + (y-k)^2 = r^2 where (h,k) is the center and r is the radius
Rewriting
( x - -7 )^ 2 + ( y - -8 )^ 2 = (sqrt(2/3)^2
The center is (-7,-8) and the radius is sqrt (2/3)
Answer:
center: (-7,-8) radius: 2/3
Step-by-step explanation:
i got this from wegnerkolmp2741o. thank you wegnerkolmp2741o!!!!!
also got this correct on khan academy
I need an asnwer Tutor and the answer to this question
Answer:
[tex] \dfrac{1}{a^6} [/tex]
Step-by-step explanation:
[tex] a^{-6}x^0 = [/tex]
[tex] = \dfrac{1}{a^6} \times 1 [/tex]
[tex] = \dfrac{1}{a^6} [/tex]
The sum of the interior angles of a polygon is 9x². If x is 3 greater than the number of side of the polygon, how many sides does the polygon have?
Answer:
17
Step-by-step explanation:
This is a very neat problem -- for teachers.
Let the number of sides = y
The sum of the interior angles is 180*(y - 2)
We are told that this sum equals 9x^2
So far the equation is
(y - 2)*180 = 9x^2 Divide both sides by 9
(y - 2)*20 = x^2 Remove the brackets on the left.
20*y - 40 = x^2
We need another fact. We get that from the statement that x is three greater than the number of sides (y). Therefore y = x - 3
20*(x - 3) - 40 = x^2
20x - 60 - 40 = x^2 Combine like terms on the left
20x - 100 = x^2 Bring the left side to the right side.
0 = x^2 - 20x + 100 You have a quadratic.
a = 1
b = - 20
c = 100
When you solve the quadratic equation, you get
x = 20
Therefore the number of sides is 17.
Which equation could be used to find the length of the hypotenuse?
А
С
5 cm
С
B
8 cm
Answer:
The first option (5^2 + 8^2 = c^2).
Step-by-step explanation:
According to the Pythagorean Theorem, a^2 + b^2 = c^2.
If a is 5 cm, and b is 8 cm, you would have the following equation...
5^2 + 8^2 = c^2.
That matches with the first option.
Hope this helps!
The sum of two numbers is 26. The sum of their squares is a minimum. Find the numbers.
Answer:
The numbers at 13 and 13
Step-by-step explanation:
The two numbers in question are equal, and if their sum is 26, then they must be 13 and 13.
The two numbers are (13, 13).
Given that,
The sum of the two numbers is 26.
And the sum of their square is minimum.
We have to determine,
The two numbers are.
According to the question,
Let, the first number be x,
and the second number be y.
The sum of the two numbers is 26.
[tex]x + y = 26[/tex]
And The sum of their squares is a minimum.
[tex]x^2 + y^2 = h[/tex]
Solving both the equation,
[tex]x + y = 26\\\\x = 26-y[/tex]
Substitute the value of x in equation 2,
[tex]x^2 + y^2 = h\\\\(y-26)^2 + y^2 = h \\\\y^2 + 676 -52y + y^2 = h\\\\2y^2 -52y + (676-h) = 0[/tex]
Then, The vertex of the parabola is,
[tex]\dfrac{-b}{2a} = \dfrac{-(-52)}{2(2)} = \dfrac{52}{4} = 13[/tex]
The minimum value of the parabola is 13, which is also the sum of squares.
Therefore, The two number is x = 13 and y =13.
To know more about Parabola click the link given below.
https://brainly.com/question/4074088
write a function that represents the situation: A population of 210,000 increases by 12.5% each year
Answer
y= 12.5x + 210,000
Step-by-step explanation:
This is a linear function because it is increasing constantly by 12.5 percent so it will me written as y=mx+b
The value of function that represents the situation is,
⇒ P = 210,000 (1.125)ⁿ
Where, n is number of years.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
We have to given that;
The situation is,
⇒ A population of 210,000 increases by 12.5% each year.
Now, Let number of years = n
Hence, The value of function that represents the situation is,
⇒ P = 210,000 (1 + 12.5%)ⁿ
⇒ P = 210,000 (1 + 0.125)ⁿ
⇒ P = 210,000 (1.125)ⁿ
Learn more about the mathematical expression visit:
brainly.com/question/1859113
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The ratio of boys to girls in a group is 5:3. If there are 24 more boys than girls, work out how many girls there are
Answer:
36
Step-by-step explanation:
Let's call the # of boys and girls 5x and 3x respectively. We can write:
5x = 3x + 24
2x = 24
x = 12 so the # of girls = 12 * 3 = 36
Answer:
36 girlssolution,
Let the number of girls be X
Number of boys be 'x+24'
Now,
[tex] \frac{x + 24}{x} = \frac{5}{3} \\ or \: 3(x + 24) = 5x \\ or \: 3x + 72 = 5x \\ or \: 3x - 5x = - 72 \\ or \: - 2x = - 72 \\ or \: x = \frac{ - 72}{ - 2} \\ x = 36[/tex]
hope this helps..
Good luck on your assignment..
13. Gayle is getting ready for her first day of school. She has 7 new dresses to choose from and 4
new pairs of shoes. How many different outcomes are possible for Gayle to wear one dress and
one pair of shoes?
Answer:
49
Step-by-step explanation:
7 times 4 equals 49.
Pls can someone help it’s due tmrz
Answer:
Step-by-step explanation:
In a quadrilateral all the angles equal to 360 degrees
ADC= 136+90+62=288.
360-288=72
A straight line is equal to 180 degrees
CDE= 180-72=108
x=108
Answer:
the value of x is 62 degrees.
Step-by-step explanation:
we know that corresponding angles are equal, so the value of x is 62 degrees as x is an corresponding angle of 62°
Rewrite the expression in the form k x z^n .
Answer:
(squareroot2^2) times 27 (1/2)
Step-by-step explanation:
Answer:3z^2/9
Step-by-step explanation: