Answer:
[tex] \rm \displaystyle g(a) = \sqrt{1 + {a}^{2} } \xrightarrow{ \rm Domain}a \in \mathbb{R}[/tex]
[tex] \rm\displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1} \xrightarrow{ \rm Domain}x \in \mathbb{R} / \{0, - 1 \}[/tex]
Step-by-step explanation:
Question-1:we want to figure out the domain of the following function:
[tex] \displaystyle g(a) = \sqrt{1 + {a}^{2} } [/tex]
remember that, the domain of an even root function are all values of x for which the redicand is positive or 0 that is being said the domain of the function g(a) belong to [tex]\mathbb{R}[/tex] . another way to think about it, the domain of square root function f(x) belong to x≥0. In this case we have square variable in the redical so when we input a negative number, it yields a positive number with that said the domain of the function g(a) belong to all the real numbers.Thus,
[tex] \rm \displaystyle g(a) = \sqrt{1 + {a}^{2} } \xrightarrow{ \rm Domain}a \in \mathbb{R}[/tex]
Question-2:we'd like to find the domain of the following function:
[tex] \displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1}[/tex]
in order to do so we need to simplify it further,so simplify addition in order to do so the first step is to figure out the LCM of the denominator i.e x(x+1) ⇒ x²+x, secondly divide the denominator of every fraction by the LCM and multiply the result by the numerator of very fraction ,then finally add them therefore,
[tex] \displaystyle f(x)=\frac{2x + 2+4x}{ {x}^{2} + x } \\ \displaystyle \boxed{\frac{6x + 2}{ {x}^{2} + x }} [/tex]
we know that the domain of a rational function are all the values of x for which the denominator is different than 0.
the denominator of the function would be 0 when x=0 and -1 thus,
[tex] \rm\displaystyle f(x)=\frac{2}{x} + \frac{4}{x+1} \xrightarrow{ \rm Domain}x \in \mathbb{R} / \{0, - 1 \}[/tex]
and we're done!
Problem 2
Find the area of each shaded region. Show or explain your reasoning.
A
2 cm
B
2 cm
2cm
6 cm
5 cm
3 cm
6 cm
8 cm
C С
D
15 cm
8 cm
8 cm
15 cm
9 cm
6 cm
10 cm
Step-by-step explanation:
A
this is the combination of a 4×6 rectangle and a 2×2 square. nothing is excluded.
so, the area is
(6-2)×6 + 2×2 = 4×6 + 4 = 24 + 4 = 28 cm²
B
this is the area of the large 8×5 rectangle minus the area of the small 2×3 rectangle.
so the area is
8×5 - 3×2 = 40 - 6 = 34 cm²
C
Basically the same thing as for B. large rectangle minus smaller rectangle.
so, the area is
15×10 - 9×6 = 150 - 54 = 96 cm²
D
the area of a triangle is
baseline × height / 2
or baseline here is 2×8, and the height is 5
so we get the area
2×8 × 5 / 2 = 8×5 = 40 cm²
RACE A city hosts a race annually. They decide to place a
camera halfway between the start and finish lines. If A
represents the starting line and Z represents the finish line,
find the coordinate of the midpoint.
Answer:
M
Step-by-step explanation:
M is in the middle of the alphabet, so it would be the midpoint of A-Z if they were placed on a coordinate plane.
How do Curves A and B compare to each other with respect to f and f ′?
The answer cannot be determined.
f: Curve B, f ′: Curve A
f: Curve A, f ′: Curve B
Neither Curve A nor Curve B are derivatives of each other.
It's likely that curve A is f and curve B is f '.
The points where curve B crosses the horizontal axis correspond to the extrema of curve A at around 0 and 0.45, and the extremum of curve B corresponds to the inflection point of curve A at around 0.2. These observations are consistent with the first and second derivative tests.
Is the product of a rational number and an irrational number always irrational?
Answer:
The product of any rational number and any irrational number will always be an irrational number.
Step-by-step explanation:
A triangle has a perimeter of 75 inches. Find the length of three sides
if one side is 15 inches larger than the smallest side, and the third
side is twice the smallest
9514 1404 393
Answer:
15 in, 30 in, 30 in
Step-by-step explanation:
Let x represent the length of the smallest side. Then the other two sides are (x+15) and (2x). The perimeter is the sum of the side lengths:
x +(x +15) +2x = 75
4x = 60
x = 15 . . . . . . . . . . . shortest side
(x+15) = 30 . . . . . . second side
(2x) = 30 . . . . . . . third side
The shortest side is 15 inches, the second side is 30 inches, and the third side is 30 inches.
Need help for this question. ASAP
Answer:
Data set A1, 2, 2, 2, 3, 4, 5Mean = (1 + 2*3 + 3 + 4 + 5)/7 = 2.71Mode = 2Median = 2Mean > median ⇒ Skewed rightData set B1, 2, 3, 4, 4, 4, 5, 6, 7Mean = (1 + 2 + 3 + 4*3 + 5 + 6 + 7)/9 = 4Mode = 4Median = 4Mean = median ⇒ SymmetricalData set C1, 1, 2, 2, 3, 3, 4, 4Mean = (1*2 + 2*2 + 3*2 + 4*2)/8 = 2.5Mode = noneMedian = (2+3)/2 = 2.5Mean = median ⇒ UniformData set D1, 2, 3, 4, 5, 5, 5, 6Mean = (1 + 2 + 3 + 4 + 5*3 + 6)/8 = 3.875Mode = 5Median = (4+5)/2 = 4.5Mean < Median ⇒ Skewed leftUnit 1.1.E.01 State the value of the CONSTANT TERM. y=x2−4
Answer:
-4
Step-by-step explanation:
Should be lah, cuz the others like y and x2 are variables
7. What's the perimeter of a rectangle with length 12 m and width 5 m?
A. 60 m
B. 49 m
C. 34 m
D. 17 m
Answer:
Option(c) 34m
Step-by-step explanation:
Perimeter of a rectangle = 2(length + breadth)
length = 12m
breadth/width = 5m
Perimeter = 2(12 + 5)
= 2(17)
= 34m
Answer:
34
you just add, 12+5+12+5 to get 34
a rectangle has points at 4, 2, 6, 2, 4, 7, and 6, 7 what is the perimeter of the square
Answer:
Perimeter=14
Step-by-step explanation:
SEE THE IMAGE FOR SOLUTION
HOPE IT HELPS
HAVE A GREAT DAY
Solve the below:
4x+3y=7 3x-2y=9
10. Which statement is NOT true about rational numbers?
F The sum of two rational numbers is also a rational number
G 0is not a rational number.
H The product of two rational numbers is also a rational number.
J The opposite of a rational number is also a rational number.
Answer:
The rational numbers are the numbers can be expressed in the form of
r = p/qLet's see the answer choices:
F The sum of two rational numbers is also a rational number
This is TRUEG 0 is not a rational number.
This is FALSE as 0 can be expressed in the form of r= p/q, where p = 0H The product of two rational numbers is also a rational number.
This is TRUEJ The opposite of a rational number is also a rational number.
This is TRUEAnswer:
Answer :-
F. The sum of two ration number is a rational number.
TrueEg - 1/2 + (-1)/3
3 - 2/3 = 1/3
G. 0 is not a rational number
False. Because 0 can't be represented as p/q form.
H. The product of two rational numbers is also a rational number.
True.
Eg - 1/2 × 3/4 = 3/8
J.The opposite of a rational number is also a rational number.
True. Eg - 1/2 and 2/1
Evaluate81−−√4????? HELP
Answer:
3 to the power of 4 is 81
Step-by-step explanation:
solve for r
A= 3r(to the 2 power) i couldn’t make it a small two
Answer:
r = [tex]\sqrt{\frac{a}{3}}[/tex]
Step-by-step explanation:
1. A = 3r²
(Divide 3 by both sides)
2. A/3 = r²
(Square root both sides)
√A/3 = r
On solving for 'r' we get - r = [tex]\sqrt{\frac{A}{3} }[/tex].
We have the following expression -
[tex]$A=3r^{2}[/tex]
We have to solve for r.
Solve for x : [tex]$x^{2} = 9[/tex]On solving, we get -
x = [tex]$\pm\sqrt{9}[/tex]
x = [tex]$\pm3[/tex]
According to the question, we have -
[tex]$A=3r^{2}[/tex]
[tex]$r^{2} = \frac{A}{3}[/tex]
r = [tex]\pm\sqrt{\frac{A}{3} }[/tex]
Since, the area cannot be negative, therefore -
r = [tex]\sqrt{\frac{A}{3} }[/tex]
Hence, on solving for 'r' we get - r = [tex]\sqrt{\frac{A}{3} }[/tex].
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Calculate the derivative using implicit differentiation:
∂w /∂z,x^(5)w+w^7+wz^2+8yz=0
∂w/ ∂z= ?
Step-by-step explanation:
Given: [tex]x^5w + w^7 + wz^2 + 8yz = 0[/tex]
Taking the partial derivative of the above equation with respect to z, we get
[tex]x^5\dfrac{\partial{w}}{\partial{z}} + 7w^6\dfrac{\partial{w}}{\partial{z}} + z^2\dfrac{\partial{w}}{\partial{z}} + 2z + 8y =0[/tex]
Collecting all terms containing [tex]\frac{\partial{w}}{\partial{z}},[/tex] we get
[tex](x^5 + 7w^6 + z^2)\dfrac{\partial{w}}{\partial{z}} = -2(z + 4y)[/tex]
Then
[tex]\dfrac{\partial{w}}{\partial{z}} = \dfrac{-2(z + 4y)}{x^5 + 7w^6 + z^2}[/tex]
The derivative using implicit differentiation can be calculated and after rearranging the terms.
What is implicit differentiation?Implicit differentiation is the technique in which the derivative of y with respect to x using implicit differentiation without having to solve the supplied equation for y.
We have:
[tex]\rm x^5w+w^7+wz^2+8yz=0[/tex]
We have to find the:
= ∂w/ ∂z
[tex]\rm \dfrac{\partial }{\partial z}[\rm x^5w+w^7+wz^2+8yz=0][/tex]
[tex]\rm x^5\dfrac{\partial w}{\partial z} +7w^6\dfrac{\partial w}{\partial z}+z^2\dfrac{\partial w}{\partial z}+2z+8y=0[/tex]
After rearranging the terms:
[tex]\rm (x^5 +7w^6+z^2)\dfrac{\partial w}{\partial z}= -2(z+4y)[/tex]
[tex]\rm \dfrac{\partial w}{\partial z}= \dfrac{-2(z+4y)}{x^5 +7w^6+z^2}[/tex]
Thus, the derivative using implicit differentiation can be calculated and after rearranging the terms.
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Help me then get brainlest
Hi ;-)
This angle is
obtuseAnswer:
This is an obtuse angle
Step-by-step explanation:
Anything over 90 degrees is obtuse
a ball is drawn randomly from a jar 8 red balls, 12 white balls and 13 yellow balls. find the probability of drawing a white ball
After writing a $400 check to pay a bill, a student had a balance of $550 in his account. How much did he have in the account before he wrote the check?
a) Let x= his balance before writing the check. Write the equation you would use to solve this problem.
Answer:
x=950
Step-by-step explanation:
550+400=x
Determine whether (a) x = -1 or (b) x = 2 is a solution to this equation
Answer: (a) x = -1
Step-by-step explanation:
Given
-2 (x - 1) = 1 - 3x
Expand parentheses and apply the distributive property
(-2) · x - (-2) · 1 = 1 - 3x
-2x + 2 = 1 - 3x
Add 3x on both sides
-2x + 2 + 3x = 1 - 3x + 3x
x + 2 = 1
Subtract 2 on both sides
x + 2 = 1 - 2
[tex]\boxed{x=-1}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
3cm and 7cm
please help me find the area and the perimeter of the above figures using the formular
Its must be a rectangle
Length=3cmBreadth=7cmPerimeter:-
[tex]\\ \sf\longmapsto 2(L+B)[/tex]
[tex]\\ \sf\longmapsto 2(3+7)[/tex]
[tex]\\ \sf\longmapsto 2(10)[/tex]
[tex]\\ \sf\longmapsto 20cm[/tex]
Area:-
[tex]\\ \sf\longmapsto Length\times Breadth[/tex]
[tex]\\ \sf\longmapsto 3(7)[/tex]
[tex]\\ \sf\longmapsto 21cm^2[/tex]
Answer:
Length=3cm
breadth=7cm
Area(A)=?
we know that,
Area of rectangle (A)=l*b
=3cm*7cm
= 21cm^2
Now,
Perimeter (P)= 2(l+b)
=2(3cm+7cm)
=2*10cm
=20cm Ans.
Identify which of the twelve basic functions listed below fit the description given.
y = x, y = x2, y = x3, y = , y = , y = ex, y = , y = ln x, y = sin x, y = cos x, y = int (x), y = 1/1+e-x
The two functions with infinitely many zeros
Try this option:
only periodical functions have many zeros, that is why y=sinx and y=cosx are the correct answer.
The functions y = x and y = x³ have infinitely many zeros. These functions pass through the origin and have a unique property that allows them to intersect the x-axis an infinite number of times.
The two functions with infinitely many zeros from the given list of twelve basic functions are y = x and y = x³
The function y = x has infinitely many zeros because any value of x that equals zero will result in y also being zero.
In other words, for every x value of 0, the corresponding y value is also 0.
This makes the function pass through the origin (0, 0) and have an infinite number of zeros.
2. The function y = x³ also has infinitely many zeros because the cube of any real number is zero if and only if the number itself is zero.
This means that for every x value of 0, the corresponding y value is also 0. Hence, the function y = x³ passes through the origin (0, 0) and has an infinite number of zeros.
In summary, the functions y = x and y = x³ have infinitely many zeros. These functions pass through the origin and have a unique property that allows them to intersect the x-axis an infinite number of times.
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Consider the points below. P(â1, 4, 1), Q(0, 6, 2), R(4, 3, â1)
a. Find a nonzero vector orthogonal to the plane through the points P, Q, and R.
b. Find the area of the triangle PQR.
Answer:
B. Find the area of the triangle PQR.
The sum of twice a number and three
Answer:
i dont get what youre asking
Step-by-step explanation:
Answer:
2n + 3
Step-by-step explanation:
n = number
Sum of twice a number (2n) and (3)
-> 2n + 3
How many days are there in j weeks
Answer:
ummm is that a thing
Step-by-step explanation:
3/6, 1/12, 3/6, 3/60 determine the lcd by division of prime number
Answer:
LCD = 60
BRAINLIEST, PLEASE!
Step-by-step explanation:
All of the denominator numbers are multiples of 60, and since 60 is also equal to the largest denominator number, it's the LCD.
help me for 50 points
Answer:
I hope it helped U
stay safe stay happy
Answer:
Step-by-step explanation:
In △PQR, sinQ=25, sinR=13, and q=6. Find the side length r.
Can someone please help
Answer:
r = 5
Step-by-step explanation:
the sine rules formula :
sin Q/q = sin R/r
=> r = q× sin R / sin Q
= 6× ⅓ / (2/5)
= 2 /(2/5)
= 2× 5/2
= 5
The measure of side length "r" if sinQ=2/5, sinR=1/3, and q=6 is 5
Application of sine rule.According to the rule, the ratio of the sides to the opposite angles is a constant. Mathematically:
p/sinP = q/sinQ = r/sinR
Given the following parameters
sinQ=2/5, sinR=1/3, and q=6.
6/(2/5) = r/(1/3)
30/2 = 3r
15 = 3r
r = 5
Hence the measure of side length "r" if sinQ=2/5, sinR=1/3, and q=6 is 5
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find x
14.5, -8, -4.5, x; The mean is 9.5.
Answer:
x = 36
Step-by-step explanation:
multiply 4 and 9.5 to get the total amount.
38 = 14.5 + (-8) + (-4.5) + x; hence x is 36.
Answer: x=36
Step-by-step explanation:
To solve this question, we first want to know what mean is. Mean is the same as the average. You take the sum and divide it by the amount. Since we know there are 4 numbers and the mean, we can easily find the value of x.
[tex]\frac{14.5-8-4.5+x}{4} =9.5[/tex] [multiply both sides by 4]
[tex]14.5-8-4.5+x=38[/tex] [combine like terms]
[tex]2+x=38[/tex] [subtract both sides by 2]
[tex]x=36[/tex]
Now, we know that x=36.
Write an
equation that passes through the origin with a rate of change equal to 1
Answer:
y = x
Step-by-step explanation:
Rate of change is also known as the gradient of a curve and denoted as "m".
If the rate of change is equal to one then "m" is equal to 1
In the general equation of a straight line:
y = mx + c
this would look like:
y = 1x
If it passes through the origin it intercepts the y-axis at 0 so c = 0
y = x + 0
or
y = x
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7th grade math plz help
Answer:
The total weight of Luigi's inventory if he collects 27 socks is 39.91 grams.
Step-by-step explanation:
Here is how you solve this problem:
1. Replace the variable for 27.
i = [tex]\frac{4}{3} 27 + 3\frac{2}{2}[/tex]
2. To make the equation easier, let's transform this fraction and mixed number into decimals.
4/3 = 4 ÷ 3 = 1.33
3 2/2 = 8/2 = 8 ÷ 2 = 4
3. Now, let's rewrite this equation.
i = 1.33 x 27 + 4
4. It's time to solve the equation.
i = 35.91 + 4
i = 39.91
Therefore, the total weight of Luigi's inventory if he collects 27 socks is 39.91 grams.
Which of the following statements are true? Select all that apply. A. 1,000 is both a perfect square and a perfect cube. B. 27 is a perfect cube. C. 6 is neither a perfect square nor a perfect cube. D. 9 is a perfect cube. E. 36 is a perfect square.
Answer:
C
E
Step-by-step explanation: