Answer:
[tex]\frac{dy}{dx} = \frac{cos(x+y)}{1-cos(x+y)}[/tex]
Step-by-step explanation:
We have the function [tex]y=sin(x+y)[/tex]
We need find the derivative of y with respect to x
Note that the function [tex]y = sin (x + y)[/tex] depends on the variable x and the variable y. Therefore the derivative of y with respect to x will be equal to the derivative of [tex]sin (x + y)[/tex] by the internal derivative of [tex]sin (x + y)[/tex]
[tex]\frac{dy}{dx}= cos(x+y)*\frac{d}{dx}(x+y)[/tex]
[tex]\frac{dy}{dx}= cos(x+y)*(1+\frac{dy}{dx})\\\\\frac{dy}{dx}= cos(x+y)+\frac{dy}{dx}cos(x+y)\\\\\frac{dy}{dx} -\frac{dy}{dx}cos(x+y)=cos(x+y)\\\\\frac{dy}{dx}(1-cos(x+y))=cos(x+y)\\\\\frac{dy}{dx} = \frac{cos(x+y)}{1-cos(x+y)}[/tex]
Answer:
Step-by-step explanation:
Note that y=sin(x+y) is an implicit function; y appears on both sides of the equation, which makes it difficult or impossible to solve for y.
However, our job here is to find the derivative dy/dx.
We apply the derivative operator d/dx to both sides. Here are the results:
dy
---- = cos(x + y)(dx/dx + dy/dx), or
dx Note: dx/dx = 1
dy
---- = cos(x + y)(1 + dy/dx), or = cos(x + y) + cos(x + y)(dy/dx)
dx
We move that cos(x + y)(dy/dx) term to the left side to consolidate dy/dx terms:
dy
---- - cos(x + y)(dy/dx) = cos(x + y)
dx
or:
dy
[ ---- ] [ 1 - cos(x + y) ] = cos(x + y)
dx
Finally, we divide both sides by [ 1 - cos(x + y) ], obtaining the derivative:
dy cos(x + y)
[ ---- ] -------------------------
dx 1 - cos(x + y)
What is the volume of right rectangular prism with a height of 15 feet length of 24 inches and width of 6 feet
Answer:
2,160 [tex]ft^{3}[/tex]
Step-by-step explanation:
The formula is V = lhw
15 x 24 x 6 = V
15 x 24 = 360
360 x 6 = 2,160
2,160[tex]ft^{3}[/tex]
Answer: 180 ft³
Step-by-step explanation:
You can calculate the volume of a right rectangular prism with this formula:
[tex]V=lwh[/tex]
Where "l" is the length and "w" is the width.
You know that the height of that this right rectangular prism is 15 feet, its length is 24 inches and its width is 6 feet.
Then, you need to make the conversion from 24 inches to feet (1 feet=12 inches):
[tex]l=(24in)(\frac{1ft}{12in})= 2ft[/tex]
Then, susbtituting values, you get:
[tex]V=(2ft)(6ft)(15ft)=180ft^3[/tex]
Match The following.
1. dilation
2. domain
3. radicand
4. translation
A.a shift of a graph
B.a stretching or shrinking of a graph
C.the set of input values for which a function is defined
D.the number (expression) inside a radical sign
1. B
2. C
3. D
4. A
Hope this helps!
Answer:
1. B
2. C
3. D
4. AStep-by-step explanation:
PLZZ HELP BASIC ALGEBRA
Solve the equation
8+2z=3(2-z)
Answer:
z = [tex]-\frac{2}{5}[/tex] or - 0.4
Step-by-step explanation:
8+2z = 6 - 3z
2z = 6 - 8 - 3z
2z + 3z = - 2
5z = -2
z = [tex]-\frac{2}{5}[/tex] or - 0.4
the equation of a circle is x^2+y^2+6x-2y-15=0. find the center and radius of the circle.
Answer:
(-3, 1), 5
Step-by-step explanation:
x² + y² + 6x - 2y - 15 = 0
Rearrange:
x² + 6x + y² - 2y = 15
Complete the square:
x² + 6x + 9 + y² - 2y + 1 = 15 + 9 + 1
(x + 3)² + (y - 1)² = 25
Therefore, the center is (-3, 1) and the radius is 5.
The center of the circle is (-3, 1), and the radius is 5.
To find the center and radius of the circle described by the equation[tex]x^2 + y^2 + 6x - 2y - 15 = 0,[/tex] we'll first rewrite the equation in standard form, which has the general form:
[tex](x - h)^2 + (y - k)^2 = r^2[/tex]
Where (h, k) represents the center of the circle, and r represents the radius.
Let's complete the square to rewrite the given equation in standard form:
[tex]x^2 + 6x + y^2 - 2y = 15[/tex]
Now, we'll complete the square for both the x and y terms.
To complete the square for the x terms, we add and subtract [tex](6/2)^2 = 9:x^2 + 6x + 9 + y^2 - 2y = 15 + 9[/tex]
Now, complete the square for the y terms by adding and subtracting (-2/2)^2 = 1:
[tex]x^2 + 6x + 9 + y^2 - 2y + 1 = 15 + 9 + 1[/tex]
Now, we have:
[tex](x^2 + 6x + 9) + (y^2 - 2y + 1) = 25[/tex]
Next, we can rewrite this as two perfect square trinomials:
[tex](x + 3)^2 + (y - 1)^2 = 25[/tex]
Now, the equation is in standard form. Comparing it to the standard form, we can see that:
h = -3 (opposite sign in the equation)
k = 1 (opposite sign in the equation)
[tex]r^2 = 25[/tex] (radius squared)
To find the radius (r), take the square root of 25:
r = √25 = 5.
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find the value of k for which one root of the quadratic equation kx2 14x 8 = 0 is 6 times the other
Answer:
k = 3.
Step-by-step explanation:
If the 2 roots are A and B we have the relations:
AB = 8/k and A+B = -14/k.
We are given that A = 6B so
6B^2 = 8/k
B^2 = 8/6k = 4/3k
B = 2 /√(3k) ......(1)
Now A + B = -14/k so
6B + B = 7B = -14/k
B = -2/k..........(2)
Eliminating B from equations (1) and (2):
2 /√(3k) = -2/k
Cross multiply:
2k = -2√(3k)
Squaring both sides:
4k^2 = 4 * 3k
4k^2 = 12k
k^2 = 3k
k = 3.
To find the value of k, we first define the roots as p and 6p. We then use the properties of the sum and product of roots in a quadratic equation to form two equations. We can solve these equations to get the value of k.
Explanation:The given quadratic equation is kx2 + 14x + 8 = 0. We are looking for the value of k for which one root of the equation is six times the other. Let's denote the roots by p and 6p (since one is 6 times the other).
For a quadratic equation ax2 + bx + c = 0, the sum of the roots is given by -b/a and the product of the roots is c/a. In this case, -b/a or -14/k is equal to the sum of the roots (p + 6p). The product of the roots, c/a or 8/k, is equal to p*6p.
From the sum of the roots equation, we can determine p = -14/7k and by substitifying p in the other equation we can solve for k.
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{(-3, 7.5) , (-2, 10) , (-1, 12.5)} arithmetic or geomatic
Answer:
arithmetic
Step-by-step explanation:
The points fall on a straight line. They won't do that for a geometric sequence.
___
Normally the terms of either sort of sequence are numbered with counting numbers: 1, 2, 3, .... Your x-values are negative, so are obviously not term numbers of a sequence. The differences of x-values are 1, and the differences of y-values are 2.5, so we know the x- and y-values are linearly related. That relationship can be expressed in point-slope form by ...
y = 2.5(x +1) +12.5
which can be simplified to
y = 2.5x +15
__
The arithmetic sequence with first term 17.5 and common difference 2.5 would be described by this same equation.
Convert 32 ounces to pounds
Answer: 2 pounds
Step-by-step explanation: There are 16 ounces in one pound. So when you divide 32 by 16, you get 2. Therefore your answer would be 2 pounds!
For this case we must make a conversion.
We know, by definition, that 1 ounce is equivalent to 0.0625 pounds.
We make a rule of three to determine how many pounds are 32 ounces.
1oz ---------------> 0.0625lb
32oz -------------> x
DOnde "x" represents the number of pounds
[tex]x = \frac {32 * 0.0625} {1}\\x = 2[/tex]
So, 32 ounces equals 2 pounds
Answer:
2 pounds
Find the supplement of the complement of angle a if angle a equals 82
Answer:
172 degrees
Step-by-step explanation:
The complement of an angle, when added to that angle is equal to 90, so do x + 82 = 90
x = 8
The supplement of a an angle when added to that angle is equal to 180 so do
y + 8 = 180
y = 172
Applying the definition of supplementary angles and complementary angles, if angle A is 82 degrees, the supplement of the complement of angle A is: 172 degrees.
Recall:
Angles that are complementary, will sum up to give 90 degrees.Angles that are supplementary, will add up to give 180 degrees.
Given that Angle A equals 82 degrees.
The complement of angle A will be: 90 - 82 = 8 degrees.Thus:
The supplement of 8 degrees will be: 180 - 8 = 172 degrees.
Therefore, applying the definition of supplementary angles and complementary angles, if angle A is 82 degrees, the supplement of the complement of angle A is: 172 degrees.
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What is the y-intercept of the line with a slope of −14 that passes through the point (−2,−92)?
Enter your answer as a number, like this: 42
Or, if your answer is a fraction, such as 314, enter it like this: 3/14
Using the equation of a line as y -y1 = m(x-x1)
Replace m with the given slope and y1 and x1 with the given point:
y - (-92) = -14(x- (-2))
Simpligy:
y + 92 = -14(x +2)
Simplify the right side:
y +92 = -14x -28
Subtract 92 from each side:
y = -14x-120
The y - intercept is -120
Please help me for this homework
Answer:
None
Step-by-step explanation:
Follow me To get The Answer
Answer:
123. [tex]A=lw[/tex], [tex]A=72[/tex]
124. B) 20 square feet
125. C) [tex]\frac{1}{6}[/tex]
126. A) 24 + 12, B) (4*6)+(4*3)
127. 30, 36, 44
Step-by-step explanation:
123. Area = length*width
Substitute '9' for [tex]l[/tex] and '8' for [tex]w[/tex].
[tex]A=(9)(8)[/tex] or [tex]A=(9*8)[/tex]
[tex]9*8=72[/tex], so [tex]A=72[/tex].
124. Using the formula [tex]A=lw[/tex], substitute '5' for [tex]l[/tex] and '4' for [tex]w[/tex].
[tex]A=(5)(4)[/tex] or [tex]A=(5*4)[/tex]
[tex]5*4=20[/tex], so [tex]A=20[/tex].
125. The hexagon was divided into 6 triangles, so each of the triangles is one out of six, one sixth ([tex]\frac{1}{6}[/tex].
126. The lighter rectangle's area is 24 and the darker's is 12 because (4*6) = 24 and (4*3) = 12.
127. For these shapes, I am using the 'subtraction' method (find the area of the shape as if it were a larger rectangle, then subtract the 'blank' spaces).
A(larger rectangle) = [tex]6*7=42[/tex]
A('blank' space) = [tex]3*4=12[/tex]
A(larger rectangle - 'blank' space) = [tex]42-12=30[/tex]
A(larger rectangle) = [tex]8*7=56[/tex]
A('blank' space) = [tex]5*4=20[/tex]
A(larger rectangle - 'blank' space) = [tex]56-20=36[/tex]
A(larger rectangle) = [tex]8*6=48[/tex]
A('blank' space) = [tex]2*1=2[/tex] (there are two of them (both equal), so add them both together) 2 + 2 = 4.
A(larger rectangle - 'blank' space) = [tex]48-4=44[/tex]
Select the correct answer.
Nathan had an infection, and his doctor wanted him to take penicillin. Because Nathan’s father and paternal grandfather were allergic to penicillin, Nathan had a 75% chance of having the same allergy. The doctor performed a skin test to see whether Nathan would react to it. The test is 98% accurate. What is the probability that Nathan is allergic to penicillin and the test predicts it?
Answer:
[tex]P=0.735[/tex]
Step-by-step explanation:
Call A to the event in which Nathan is allergic to penicillin
So
[tex]P (A) = 0.75[/tex]
[tex]P (A') = 1-P (A) = 0.25[/tex]
Call B the event in which the skin test predicts correctly.
So:
[tex]P (B) = 0.98\\P (B ') = 1-P (B) = 0.02[/tex]
We look for the probability that Nathan is allergic to penicillin and the test predicts it.
This is [tex]P (A\ and\ B)[/tex].
[tex]P (A\ and\ B) = P (A)*P (B)\\\\P (A\ and\ B) = 0.75 * 0.98\\\\P (A\ and\ B) = 0.735[/tex]
On a map with a scale of 1 inch= 12 miles, the distance between two cities is 4
inches. What is the actual distance between the two cities?
48 miles. If 1 inch means 12 miles you can multiply both sides by 4 to get "4 inches = 48 miles"
Find the GCF of the monomials: 72x^3 y^2 and 210x^2y^5
For this case we have by definition, that the Greatest Common Factor or GFC, of two or more whole numbers is the largest integer that divides them without leaving a residue.
Now, we look for the factors of 72 and 210:
72: 1,2,3,4,6,8,9,12,16,24,36,72
210: 1,2,3, 5,6,7 ...
Thus, the GFC of both is 6.
Then, the GFC of [tex]72x ^ 3y ^ 2[/tex] and [tex]210x ^ 2y ^ 5[/tex] is given by:
[tex]6x ^ 2y ^ 2[/tex]
ANswer:
[tex]6x ^ 2y ^ 2[/tex]
Subtract (8x-2) -(5x-7)
Answer:
[tex]3x+5[/tex]
Step-by-step explanation:
we have
[tex](8x-2)-(5x-7)[/tex]
step 1
Eliminate the parenthesis
[tex](8x-2)-(5x-7)=8x-2-5x+7[/tex]
step 2
Groupe terms that contain the same variable
[tex]8x-5x-2+7[/tex]
step 3
Combine like terms
[tex]3x+5[/tex]
The simplified expression of (8x-2) -(5x-7) is said to be 3x + 5.
What is the Subtraction?To subtract the expression (8x - 2) - (5x - 7), we can use the distributive property to remove the parentheses. Here's the step-by-step solution:
(8x - 2) - (5x - 7)
Do, Remove the parentheses:
8x - 2 - 5x + 7
Combine like terms:
(8x - 5x) + (-2 + 7)
Hence:
3x + 5
Therefore, the simplified expression is 3x + 5.
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Determine if the graph is symmetric about the x-axis, the y-axis, or the origin. r = -3 + 3 sin θ
Answer:
y-axis
Step-by-step explanation:
Plz help me with this
Answer:
4 n - 7
Step-by-step explanation:
- 3 , 1 , 5 , 9
The difference between the terms is 4, so our multiplier is 4 n
4 , 8 , 12 , 16 ( The 4 times tables )
-3 , 1 , 5 , 9 ( The original sequence )
What are we doing to get from the 4 times tables to get to the original sequence?
4 - - 3 = 7
8 - 1 = 7
12 - 5 = 7
16 - 9 = 7
We are subtracting 7 so our complete general term is 4 n -7
Find the sum of 14+20+26+...+1244
The sum of the series 14+20+26+...+1244 is 129,045.
The question is to find the sum of the sequence 14+20+26+...+1244. This is an arithmetic series where the common difference (d) is 6, since each term is 6 more than the previous term. The first term (a1) is 14.
To find the sum of the series, we need to determine the number of terms (n). The nth term of an arithmetic series is given by an = a1 + (n-1)d. We will set an to 1244, the last term, and solve for n:
1244 = 14 + (n-1) × 6
n = (1244 - 14)/6 + 1
n = 205
Now that we have the number of terms, we can use the sum formula for an arithmetic series which is S = n/2 × (a1 + an). Thus:
S = 205/2 × (14 + 1244)
S = 102.5 × 1258
S = 129,045
So, the sum of the series 14+20+26+...+1244 is 129,045.
The cost of renting a car is 35/we plus $0.25/mi traveled during that week. An equation to represent the cost would be y= 35+0.25x, where x is the number of miles traveled. Suppose you have a maximum of $100 to spend for the car rental. What would be the maximum number of miles you could travel?
ANSWER
260 miles
EXPLANATION
The equation that models the cost is
[tex]y = 35 + 0.25x[/tex]
If you have a maximum of $100 to spend for the car rental, then we can equation the cost function to
$100 to determine the maximum number of miles you could travel.
[tex]35 + 0.25x = 100[/tex]
[tex]0.25x = 100 - 35[/tex]
[tex]0.25x = 65[/tex]
[tex]x = \frac{65}{0.25} [/tex]
[tex]x = 260mi[/tex]
Therefore the maximum number of miles you can travel is 260 miles
Which statement best describes the association between variable X and variable Y?
P.S: Not actually asking. Whole K12 test on Association and the Correlation Coefficient.
Not all heroes wear capes. Anyways thank you!
Answer:
thanks for this! <3
Step-by-step explanation:
The sum of the squares of two consecutive odd numbers is 970. Find type integers
Answer:
The two integers you are finding is 21 and 23.
x² + y² = 970
970 / 2 = 485 ( divide it to two because we are finding two integers )
√ 485 = 22.022715546 or when rounded off, 22 ( square root because we are finding squares )
It means, the answers are near the number 22.
I found out 21 and 23
21 and 23 is two consecutive odd integers
Let x = 21
Let y = 23
x² + y² = 970
( 21 )² + ( 23 )² = 970
= 441 + 529
= 970
GIVE ME BRAINLIEST PLEASE !!! :)
Answer:
21, 23 and -21, 23
Step-by-step explanation:
The difference between two consecutive odd numbers is 2.
Let the smaller number be x. Then, the larger number is x + 2.
Now add their squares and set it equal to 970. Then solve for x.
smaller number: x
larger number: x + 2
sum of the squares of the two numbers: x^2 + (x + 2)^2
equation: x^2 + (x + 2)^2 = 970
Solution of the equation:
x^2 + (x + 2)^2 = 970
Expand the square of the binomial:
x^2 + x^2 + 4x + 4 = 970
Combine like terms on the left side:
2x^2 + 4x + 4 = 970
Subtract 970 from both sides:
2x^2 + 4x - 966 = 0
Divide both sides by 2:
x^2 + 2x - 483 = 0
Now we need to factor the binomial. We need two number whose sum is 2 and whose product is -483. Look at 483. It is not divisible by 2, but it is divisible by 3.
483/3 = 161
161 is divisible by 7.
161/7 = 23
23 is prime, so the prime factorization of 483 is
483 = 3 * 7 * 23
Notice that 3 * 7 = 21, so
483 = 21 * 23
Use -21 and 23:
-21 + 23 = 2
-21 * 23 = -483
x^2 + 2x - 483 factors into (x - 21)(x + 23)
Now we continue solving the equation.
x^2 + 2x - 483 = 0
(x - 21)(x + 23) = 0
x - 21 = 0 or x + 23 = 0
x = 21 or x = -23
We let x equal the smaller of the two integers, so now we add 2 to find the second integer.
x = 21; x + 2 = 23
x = -23; x + 2 = -21
There are two sets of consecutive odd numbers that satisfy this problem.
21, 23
-23, -21
The problem did not state positive or negative consecutive odd numbers, so both solutions are valid.
Which of the following is least able to transfer electrons?
Option D. an isulator
Is the right answer i guess...
As The transfer of electrons increases The cunductivity also increases...
Hope it helps...
Regards,
Leukonov/Olegion.
Answer:
Insulator
Step-by-step explanation:
As insulators are meant to prevent the conduction of electricity.
find the equation of the line using the slope formula. Write the final equation using the slope-intercept form. the x- intercept is 1, and (x,y) = ( -2, 12) is a point on the line
Answer:
[tex]y=- 4x + 4[/tex]
Step-by-step explanation:
The slope formula for a straight line is:
[tex]y=mx+b[/tex]
Where, 'm' is the slope and 'b' is the y-intercept.
To find the x-intercept of a line, we need to equal 'y' to zero, and then solve for 'x'. In this case we know that the x-intercept is 1, so we have the point (x1, y1)=(1,0). We are given a second point which is: (x0, y0)=(-2, 12).
To find the slope, we use the following formula:
[tex]m = \frac{y1-y0}{x1-x0} = \frac{0-12}{1-(-2)} = -4 [/tex]
Now, The equation of the line is: y - y0 = m(x-x0). Then, substituting the values of 'm', 'x0' and 'y0' we have that:
[tex]y - 12 = -4(x+2) ⇒ y = -4x-8 + 12 ⇒ y=- 4x + 4[/tex]
The equation of the line using the slope-intercept form is:
[tex]y=- 4x + 4[/tex]
FLED is definitely a parallelogram
Answer:
Yes that is true
because the lines on the opposite side will never intersect
Answer:
The correct option is A. FLED is definitely a parallelogram .
Step-by-step explanation:
From the given figure it is clear that the angle F and angle E are same. Angle L and angle D are same.
[tex]\angle F=\angle E[/tex]
[tex]\angle L=\angle D[/tex]
According to the properties of parallelogram, a quadrilateral is called parallelogram if and only if there are two pairs of congruent opposite angles (but not equal to 90°, otherwise it will be a square or rectangle).
Since we have two pairs of congruent opposite angles which are not a right angle, therefore the statement "FLED is definitely a parallelogram" is true.
Hence, option A is correct.
Please I need help!!! Mr. weber ran 5 miles in 33 min. How fast can he run 26.2 miles?
Answer:
172.92 minutes
Step-by-step explanation:
Step 1: Write a proportion
33/5 = X/26.2
Step 2: Solve your proportion
X = 172.92
Find the rate for the number of minutes per mile. (# of minutes/mile)
33 minutes/5 miles = 6.6 minutes/mile
It takes him 6.6 minutes to run a mile, so you can multiply 26.2 miles by 6.6 minutes to find how long it takes him to run 26.2 miles.
26.2(6.6) = 172.92 minutes
Solve the Equation
3x+2y=17
-2x-y=-12
Answer:
(7,-2)
Step-by-step explanation:
3x+2y=17
-2x-y=-12
Multiply the second equation by 2 so we can eliminate y
2( -2x-y=-12) becomes -4x-2y = -24
Add this to the first equation
3x+2y=17
-4x-2y=-24
----------------
-x = -7
Multiply each side by -1
x = 7
Substitute back into the first equation to find y
3(7) +2y = 17
21 +2y = 17
Subtract 21 from each side
21-21 +2y = 17-21
2y = -4
Divide each side by 2
2y/2 = -4/2
y =-2
(7,-2)
Answer:
x = 7, y = -2Step-by-step explanation:
[tex]\left\{\begin{array}{ccc}3x+2y=17&(1)\\-2x-y=-12&(2)\end{array}\right\\\\(2)\\-2x-y=-12\qquad\text{add 2x to both sides}\\-y=2x-12\qquad\text{change the signs}\\y=-2x+12\qquad\text{substitute it to (1):}\\\\3x+2(-2x+12)=17\qquad\text{use the distributive property}\ a(b+c)=ab+ac\\3x+(2)(-2x)+(2)(12)=17\\3x-4x+24=17\qquad\text{subtract 24 from both sides}\\-x=-7\qquad\text{change the signs}\\\boxed{x=7}\\\\\text{Put the value of x to (2):}\\\\y=-2(7)+12\\y=-14+12\\\boxed{y=-2}[/tex]
Need urgent help, will give brainliest.
A bag has more green balls than blue balls, and there is at least one blue ball. Let b represent the number of blue balls and let g represent the number of green balls. Let's compare the expressions 2b and b+g. Which statement is correct?
A. 2b>b+g
B. 2b
C. 2b=b+g
D. There is not enough information to tell.
The correct comparison for the expressions 2b and b+g is 2b > b+g.
Let's analyze the expressions:
2b: This represents twice the number of blue balls.b+g: This represents the sum of blue balls and green balls.Comparing 2b and b+g, the correct statement is A. 2b > b+g as having more green balls than blue balls implies the total green balls are more, making the expression 2b greater than b+g.
Based on these cases, the only condition that aligns with g > b is when [tex]\(2b < b + g.[/tex]
Thus, the correct answer is: B. 2b < b + g.
To find which statement is correct, let's consider the relationship between the number of green balls (g) and the number of blue balls (b). Since the bag has more green balls than blue balls, it means that g > b.
To compare the expressions 2b and b + g, let's examine their relationship under the condition g > b
When 2b > b + g
Rearranging 2b > b + g, we get:
b > g.
This contradicts the condition g > b.
So, this case is not possible.
Case 2: When 2b < b + g :
Rearranging 2b < b + g, we get:
b < g,
which aligns with the given condition g > b.
Hence, this condition is possible.
When 2b = b + g
Rearranging 2b = b + g, we get: [tex]\[b = g.\][/tex]
This condition contradicts the original requirement g > b, so this case is also not possible.
The only condition that aligns with g > b is when [tex]\(2b < b + g.[/tex] Thus, the correct answer is: B. 2b < b + g.
Question : A bag has more green balls than blue balls, and there is at least one blue ball. Let b represent the number of blue balls and let g represent the number of green balls. Let's compare the expressions 2b and b+g. Which statement is correct?
A. 2b>b+g
B. 2b C. 2b=b+g
D. There is not enough information to tell.
in a triangle, a 32° angle is between two sides of 6 feet and 8 feet. what is the length of the thrid side, in feet?
Answer:
4.3 feet
Step-by-step explanation:
Write a function describing the relationship of the given variables.
A
varies directly with the square root of
r
and when
r
=
16
,
A
=
40
A
=
Answer:
The function is A = 10√r
Step-by-step explanation:
* Lets explain the meaning of direct variation
- The direct variation is a mathematical relationship between two
variables that can be expressed by an equation in which one
variable is equal to a constant times the other
- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the
constant of variation
* Now lets solve the problem
# A is varies directly with the square root of r
- Change the statement above to a mathematical relation
∴ A ∝ √r
- Chang the relation to a function by using a constant k
∴ A = k√r
- To find the value of the constant of variation k substitute A and r
by the given values
∵ r = 16 when A = 40
∵ A = k√r
∴ 40 = k√16 ⇒ simplify the square root
∴ 40 = 4k ⇒ divide both sides by 4 to find the value of k
∴ 10 = k
- The value of the constant of variation is 10
∴ The function describing the relationship of A and r is A = 10√r
Answer:
A = 10[tex]\sqrt{r}[/tex]
Step-by-step explanation:
Given A varies directly with the square root of r then the equation relating them is
A = k[tex]\sqrt{r}[/tex] ← k is the constant of variation
To find k use the condition r = 16 , A = 40
k = [tex]\frac{A}{\sqrt{r} }[/tex] = [tex]\frac{40}{\sqrt{16} }[/tex] = [tex]\frac{40}{4}[/tex] = 10
A = 10[tex]\sqrt{r}[/tex] ← equation of variation
find the value of 9!/(9-32)
Step-by-step explanation:
[tex]n!=1\cdot2\cdot3\cdot...\cdot n\\\\\dfrac{9!}{9-32}=\dfrac{1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9}{-23}=-\dfrac{362880}{23}[/tex]
which is the best name for the quadrilateral with vertices at (2,2) (5,-2) (1,-5) (-2,-1)
Answer:
square
Step-by-step explanation:
A graph reveals all side lengths are the same and sides are perpendicular. The quadrilateral is a square.