If A varies jointly as b and inversely as d then value of A when b = 9 and d = 2 is 135/2.
What is proportionality?
If A is inversely proportional to B, this is expressed as:
A α 1/B
A = k 1/B
where k is the constant of proportionality.
According to the given question:
A varies jointly with b and inversely with d
[tex]A \alpha \frac{b}{d}[/tex]
A = k b/d where k is proportionality constant
If A = 30, b = 6 and d = 3, finding the value of k
30 = k 6/3
k = 15
Now to find A when b = 9 and d = 2, using value of k
A = 15 x 9/2
A = 135/2
Hence the value of A is 135/2.
To know more about proportionality visit
https://brainly.com/question/24868934
#SPJ9
Twice the difference of a number and -3 is 4. Find the number.
Answer:
The number is 5
Step-by-step explanation:
Let us use an equation ( X is the unknown number)
2(x-3)=4
2x-6=4
2x-6+6=4+6
2x/2=10/2
x=5
f(x)
If the original function is
what would happen to the function -f(x)
Sumalee won 40 super bouncy balls playing
horseshoes at her school's game night.
Later, she
gave two to each of her friends.
She only has 8 remaining. How many
friends does she have?
If she gave two to each of her friends. She only has 8 remaining balls. so she has a total of 16 friends.
What is division in mathematics?
In mathematics, division is the process of dividing a number into equal parts and determining how many equal parts can be made. For instance, dividing 15 by 3 means dividing 15 into three equal groups of five. The symbol " or sometimes '/' represents division.
Sumalee won a total of 40 super bouncy balls.
then she gave two balls to each of her friends.
So she can distribute the balls to = 40/2
= 20 friends.
But after the distribution, she remained with 8 balls.
Now the number of balls will be = 40 - 8 = 32 balls.
and she can distribute 32 balls to = 32/2
= 16 friends.
Hence, If she gave two to each of her friends. She only has 8 remaining balls. so she has a total of 16 friends.
To learn more about the division, visit:
https://brainly.com/question/2607602
#SPJ9
Determine the end behavior of the following polynomial function:
f(x)=−2/9x^9(x−9)^2(x−8)
The leading term of the polynomial is ?
The degree of f(x) is ?
The leading coefficient is ?
For given polynomial function f(x)=−2/9x^9(x−9)^2(x−8),
the leading term ( -2/9x^12 ) is negative with even exponent (12). The curve decreases as x approaches both negative infinity and positive infinity.
In this question, we have been given a polynomial f(x)=−2/9x^9(x−9)^2(x−8)
We need to determine the end behavior of the following polynomial function.
We write given polynomial functions as,
f(x) = -2/9x^12 + 52/9 x^11 -50x^10 + 144x^9
The leading term of the polynomial is: -2/9x^12
The degree of f(x) is : 12
The leading coefficient is: -2/9
We can see that the leading term is negative with even exponent. The curve decreases as x approaches both negative infinity and positive infinity.
Therefore, for given polynomial function f(x)=−2/9x^9(x−9)^2(x−8),
the leading term ( -2/9x^12 ) is negative with even exponent (12). The curve decreases as x approaches both negative infinity and positive infinity.
Learn more about polynomial function here:
https://brainly.com/question/12976257
#SPJ1
Mixture Problem. A solution contains 49 milliliters of HCl and 91 milliliters of water. If another solution is to have the same concentration of HCl in water but is to contain 78 milliliters of water, how much HCl must it contain?
The solution must contain
milliliters of HCl.
Using proportions here, the solution must contain 42 mL of HCL
ProportionsProportion is explained majorly based on ratio and fractions. A fraction, represented in the form of a/b, while ratio a:b, then a proportion states that two ratios are equal. The ratio is a way of comparing two quantities of the same kind by using division. The ratio formula for two numbers a and b is given by a:b or a/b. Multiply and dividing each term of a ratio by the same number (non-zero), doesn’t affect the ratio.
We can write the ratio as this
49 / 91 = x / 78
cross multiply both sides and solve for x
x = 42 milliliters
Learn more on proportions here;
https://brainly.com/question/18437927
#SPJ1
-11x-7y= -56
Slope intercept form
Answer:
11/56 i think
Step-by-step explanation:
The slope of the line is m = - 11/7
And the y-intercept is b = 8
Find the slope and the y-intercept.
Step 1 – Transform the equation.
-11x - 7y = -56
To get a slope-intercept form, we need to isolate the variable y on the left-hand side of the equation.
First, we need to eliminate variable x from the left-hand side.
To eliminate the term with x, we'll add it to both sides of the equation. Remember to always perform the same operation on both sides to keep the equality true!
-11x – 7y + 11x = -56 + 11x
Now, let's add terms on the left-hand side. Keep in mind that two opposites add up to zero, so we can just remove it.
-7y = -56 + 11x
Since the variable x should be the firs on the righ-hand side in slope-intercept form, let's make it that way. Use the commutative property to reorder the terms.
-7y = 11x – 56
We're almost there! We just have to eliminate -7 from the left-hand side. To do that, let's divide both sides of the equation by -7.
(-7y)/(-7) = (11x - 56)/(-7)
Simplify the left-hand side. Each number divided by itself equals 1, so we are left with y.
y = (11x - 56)/(-7)
Next, separate the fraction on the righ-hand side into two fractions.
y = 11x/(-7) - 56/(-7)
Simplify the fraction on the right-hand side of the equation.
y = - 11x/7 + 56/7
y = - 11x/7 + 8
Finally, write the expression with x as a product.
y = - 11/7 x + 8
That's it! We've got the slope-intercept form of the equation.
Step 2 – Identify the slope.
Since the equation is written in slope-intercept form, y = m x + b, identify the slope of the lines as the coefficient next to the variable x.
y = - 11/7 x + 8
m = - 11/7
Step 3 – Identify the y-intercept.
Identify the y-intercept of the line as the constant term.
y = - 11/7 x + 8
m = - 11/7
b = 8
The slope of the line is m = - 11/7
And the y-intercept is b = 8
Learn more about here: brainly.com/question/4193335
#SPJ1
HELP ASAP
Jane took 20 min to drive her boat upstream to water-ski at her favorite spot. Coming back later in the day, at the same boat speed, took her 10 min. If the current in that part of the river is 7 km per hr, what was her boat speed in still water?
Answer:
The speed of the boat in still water was 21 km/h.-------------------------
Given:The distance is d,The speed of the boat in still water is s,The speed of the current is 7 km/h,Time upstream is 20 min or 20/60 hour,Time downstream is 10 min or 10/60 hour.Set equations for time:d / (s + 7) = 10/60 ⇒ d / (s + 7) = 1/6 ⇒ 6d = s + 7,d / (s - 7) = 20/60 ⇒ d / (s - 7) = 2/6 ⇒ 6d = 2(s - 7).Eliminate d and solve for s:s + 7 = 2(s - 7) ⇒ s + 7 = 2s - 14 ⇒ 2s - s = 7 + 14 ⇒ s = 21-3y is less than -14 find y
Answer:
[tex]y > \frac{14}{3}[/tex]
Step-by-step explanation:
Take a look at the attachment...
Hope this helps! :)
write the measurements in ascending order 0.34km, 430m,33000 cm
The correct ascending order is 33000 cm, 0.34 km, 430 m.
to find the ascending order we firstly have to convert the all values into a same unit system.
we will convert all the values into cm units.
so, 0.34 km = 0.34*100000 cm,
0.34 km = 34000 cm.
similarly 430 m = 430* 100 cm,
430 m = 43000 cm.
and lastly we have 33000 cm.
so in all the values 33000 cm is smallest and 43000 cm is largest and the correct ascending order will be 33000 cm, 0.34 km, 430 m.
To know about more ascending order https://brainly.com/question/26277616
#SPJ1
The table shows six of the fastest times run by women in the 100 m sprint.
Who is the fourth fastest woman runner?
Answer:
Carmelita Jeter 10.64
Step-by-step explanation:
Because the first is Kerron Stewart,the second is Merlene Ottey and the third is Shelley-Ann Fraster
Apple Co. bought a car with an estimated life of five years for $12,000. The residual value of the car is $2,000. What will be the amount of depreciation expense each year using the straight-line method? If the car was bought on April 3, what would be the depreciation for the first year? (Enter your answers as a whole dollar amount.)
1) The yearly depreciation expense under the straight-line method is $2,000.
2) If the car was bought on April 3, the depreciation expense for the first year is approximately $1,500.
What is the straight-line depreciation method?Under the straight-line depreciation method, the depreciation expense is the quotient of the depreciable amount (cost - residual value) divided by the estimated useful life of the asset.
The depreciation expense is prorated if it does not cover the full year.
Cost of car = $12,000
Estimated useful life = 5 years
Residual value = $2,000
Depreciable amount = $10,000 ($12,000 - $2,000)
Straight-line Depreciation (annual) = $2,000 ($10,000/5)
Depreciation for first year (April 3) = $1,496 ($2,000 x 273/365)
≈ $1,500
Thus, using the straight-line method, the depreciation expense for the car in each year is $2,000.
Learn more about the straight-line depreciation method at https://brainly.com/question/27258396
#SPJ1
Perform the following division. Show the multiplication you would do to make the divisor a whole number. Round the answer to three decimal places. (You may use a calculator.)
0.64 / 3.8
divisor multiplied by the proper power of ten
dividend multiplied by the proper power of ten
quotient
The quotient of the fraction illustrated as
0.64 / 3.8 is 16/95.
How to illustrate the quotient?Here we have the following quotient to solve:0.64/3.8
First, we can write both numerator and denominator as fractions:
0.64 = 0.64*(100/100)
= 64/1003.8
= 3.8*(10/10)
= 38/10
Remember that the quotient between two fractions (a/b) and (c/d) can be rewritten as:(a/b)÷(c/d) = (a/b)*(c/d)
Our quotient here is:(64/100)÷(38/10)
= (64/100)*(10/38)
= (64/380)
= (32/190)
= (16/95)
That is the quotient.
Learn more about fractions:
https://brainly.com/question/4025726
#SPJ1
the square root of 2 cos x-1=0. solve for x
The families of solutions (variable x) for the square root of the trigonometric expression 2 · cos x - 1 equal to 0 are x₁ = π / 6 + i · 2π and x₂ = 11π / 6 + i · 2π, where i is an integer.
What are the solutions of the square root of a trigonometric expression?In this question we find the following trigonometric expression:
√(2 · cos x - 1) = 0
Where x is measured in radians.
By algebra properties and trigonometric formulas we must solve the trigonometric expression for x. First, use algebra properties until the trigonometric function is cleared:
√(2 · cos x - 1) = 0
2 · cos x - 1 = 0
2 · cos x = 1
cos x = 1 / 2
Second, find the family of solutions for the square root of the trigonometric function:
x₁ = π / 6 + i · 2π, where i is an integer.
x₂ = 11π / 6 + i · 2π, where i is an integer.
To learn more on trigonometric expressions: https://brainly.com/question/11659262
#SPJ1
what is 1010 in binary
Answer:
1010₂ = 10₁₀1010₁₀ = 1111110010₂Step-by-step explanation:
You want to know the value of 1010 in binary.
Conversion to binaryWe're not sure if you have the base ten number 1010 and you want its value in binary, or if the number 1010 is in binary, and you want its value in base ten.
Converting the base ten number to binary means looking at the remainders from division by 2, until the quotient is zero.
1010/2 = 505 r 0505/2 = 252 r 1252/2 = 126 r 0126/2 = 63 r 063/2 = 31 r 131/2 = 15 r 115/2 = 7 r 17/2 = 3 r 13/2 = 1 r 11/2 = 0 r 1The binary value is the list of these remainders from the bottom up:
1010₁₀ = 11 1111 0010₂
(It is often convenient for readability to group the digits by 3 or 4.)
Conversion from binaryThe conversion from binary essentially uses the expanded form of the number. The arithmetic is done in the base you're converting to. Here, that's base ten.
1010₂ = 1×2³ +0×2² +1×2¹ +0×2⁰ = 8 +2 = 10
1010₂ = 10₁₀
The three most popular options for languages at the Kollar institute are French, Swahili and Jive. Only 0.13 of the students at the institute are crazy enough to take all three, 0.17 are challenging themselves by taking Swahili and French, while 0.14 take Jive and Swahili and 0.25 take Jive and French. 0.49 take French, 0.51 take Jive, and 0.36 take Swahili.
a. Draw a Venn diagram to represent the distribution of languages taken at the Kollar institute.
b. What percent at the institute take none of the three languages mentioned?
a. The Venn Diagram that represents the distribution of languages taken at the Kollar institute is given by the image at the end of the answer.
b. The percentage of students at the institute that take none of the three languages is of: 9%.
How to build the Venn Diagram?The Venn Diagram is built considering the proportions of students taking these three courses.
French.Swahili.Jive.The most restricted proportion is one the students that speak three languages, given as follows:
0.13.
The proportions containing two of them are:
Swahili and French: 0.17 - 0.13 = 0.04.Jive and Swahili: 0.14 - 0.13 = 0.01.Jive and French: 0.25 - 0.13 = 0.12.The proportions with only one language are:
French: 0.49 - 0.13 - 0.04 - 0.12 = 0.2Jive: 0.49 - 0.13 - 0.01 - 0.12 = 0.23.Swahili: 0.36 - 0.13 - 0.01 - 0.04 = 0.18.The proportion who takes at least one is:
0.2 + 0.04 + 0.18 + 0.12 + 0.13 + 0.01 + 0.23 = 0.91.
The proportion who take none is:
1 - 0.91 = 0.09.
The percentage is:
9%.
More can be learned about Venn Diagrams at https://brainly.com/question/24713052
#SPJ1
There are thirty-one rose bushes and nineteen walnut trees currently in the park. Park workers will plant more rose bushes today. When the workers are finished there will be eighty rose bushes in the park. How many rose bushes did the workers plant today?
After using the subtraction method 49 rose bushes the workers plant today.
What do mean by the subtraction method?
A method of estimating how long a psychological process will take by measuring how long it takes to react to an activity that involves the process in question and how long it takes to react to a task that doesn't, then subtracting the second from the first.
total rose bushes are 31
total bushes to be finished in the park, 80
rose bushes planted today =(80-31)
=49
Hence, the rose bushes in the worker's plant today are 49
To learn more about subtraction from the given link,
https://brainly.com/question/25421984
#SPJ9
Suppose that the credit remaining on a phone card (in dollars) is a linear function of the total calling time (in minutes). When graphed, the function gives a line
with a slope of - 0.13. See the figure below.
There is $32.86 in credit remaining on the card after 22 minutes of calls. How much credit will there be after 35 minutes of calls?
Remaining
credit
(in dollars)
크
22
32.86
Calling time
(in minutes)
$0
X
Answer: The credit after calling for 35 minutes will be 31.17 dollar
How do you determine a line's slope?
The slope is calculated by dividing the difference between the y-coordinates of two points on a line by the difference between their x-coordinates.
Step-by-step explanation:
Given that credit x = 32.86
and time for calling y = 22
slope is m = -0.13
c = ?
Equation of line
y = mx + c
32.86 = -0.13(22) + c
32.86 + 2.86 = c
c = 35.72
now we have c we can calculate credit at time 35 min
y = -0.13(35) + 35.72
y = 35.72 - 4.55
y = 31.17 dollar
Hence the credit at time 35 min is 31.17 dollar
Learn more about slope and line at
https://brainly.com/question/16949303
#SPJ13
please help me with this
[tex]4\frac{1}{2}[/tex] as a percentage is 450% and [tex]4\frac{1}{2}[/tex] as a decimal is 4.5
So, your answer would be the last option!
------------------------------------------------------------
Have a great day and God bless! :D
Point A is on the coordinate plane and is represented by the ordered pair (3, 2). The point is moved five units down and labeled as point B.
Which of the following ordered pairs represents Point B?
( 3,7 ) will be point when its moved 5 units down on coordinate plane .
What is the short definition of a coordinate plane?
Two number lines combine to produce the coordinate plane, a two-dimensional surface. The x-axis is the name given to one horizontal number line. The y-axis is the name given to the other number line, which is vertical. At a place known as the origin, the two axes collide. To graph points, lines, and other things, we can utilize the coordinate plane.( 3,2) is the point .
when the point is moved 5 units down
then the point will be = ( 3, 7 )
Learn more about coordinate plane
brainly.com/question/24134413
#SPJ13
A triangle has sides with lengths of 35 km 83 km 86 km is it a right triangle
The triangle with sides length of 35 km , 83 km and 86 km cannot form a right triangle.
How to find the sides of a right triangle?A right triangle is a triangle that has one angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
The sides of a triangle can be found using Pythagoras's theorem. Right triangle obeys Pythagoras's theorem.
The Pythagoras's theorem can be represented as follows:
c² = a² + b²
where
c is the hypotenusea and b are the other legThe hypotenuse is the longest side of the right triangle.
Hence, let's check if the side length of 35 km 83 km 86 km is a right triangle.
35² + 83² = 86²
1225 + 6889 ≠ 7396
Therefore, it is not a right triangle.
learn more on right triangle here: https://brainly.com/question/14618700
#SPJ1
please help me with this.
Answer:
Step-by-step explanation:
280%, 2.8, 2 4/5
2 4/5 =2.8
Which of the given interest rates and compounding periods would provide the best investment?
5 1/4 % per year, compounded monthly
5 1/2 % per year, compounded semiannually
5% per year, compounded continuously
5.5% compounded monthly will be the best investment.
What is compound interest?Borrowers are required to pay interest on interest in addition to principal since compound interest accrues and is added to the accrued interest from prior periods.
We know the formula for compound interest is,
A = P(1 + r/100)ⁿ.
Where, A = amount, P = principle, r = rate, and n = time in years.
Now the formula for compound interest compounded monthly is,
A = P(1 + r/100)¹²ⁿ as a year has 12 months.
The formula for compound interest compounded semiannually is,
A = P(1 + r/100)²ⁿ as there are two semi-annuals in a year.
The formula for compound interest compounded continuously is,
[tex]A = P(1 + r/100)^{5.5n}[/tex] as the rate of interest is 5.5%.
Now from all these A = P(1 + r/100)¹²ⁿ which is compounded monthly has the highest power hence it will be the best investment.
learn more about compound interest here :
https://brainly.com/question/14295570
#SPJ1
help me please!!! ASAP
Y = Sin ^4(3x).find dy/dx
Step-by-step explanation:
[tex]y = \sin {}^{4} (3x) [/tex]
Using the chain rule
[tex] \frac{d( \sin(3x)) {}^{4} }{dx} = 12 \sin {}^{3} (3x) \cos(3x) [/tex]
PLEASE HELP ME THIS IS OVER DO
The function rule for the line is f(x) = [tex]\frac{2}{3}x[/tex] - 2
What is a linear function?A linear equation is an equation in which the highest power of the variable is always 1. It is also known as a one-degree equation. The standard form of a linear equation in one variable is of the form Ax + B = 0. Here, x is a variable, A is a coefficient and B is constant. The standard form of a linear equation in two variables is of the form Ax + By = C. Here, x and y are variables, A and B are coefficients and C is a constant.
The line cuts the x and y axis at (3,0) and (0, -2)
standard form of equation of line: y = mx + c
when x =3, y = 0
substitute these values into the equation
0 = 3m + c
c = -3m----------------1
when x = 0, y = -2
substitute these values into the equation, we have
-2 = 0(m) + c
c = -2
substitute the value of c in equation 1 to find m
-2 = -3m
m = 2/3
Substitute the values of m and c into the standard equation,
y = [tex]\frac{2}{3}x[/tex] - 2
In conclusion, the function rule for the given line is y = [tex]\frac{2}{3}x[/tex] - 2
Learn more about linear functions: https://brainly.com/question/12788590
#SPJ1
2. Solve for x. Round to the nearest tenth if necessary.
25
Answer:
x = 15
Step-by-step explanation:
To solve this question and find value of x, we need to use Euclidean relation.
According this relation:
[tex] {x}^{2} = 9 \times 25[/tex]
[tex] {x}^{2} = 225[/tex]
Find the root of both expressions,
x = 15
Which of the graphs below represents a quadratic function that has two complex roots?
The second graph represents that the function has two complex roots.
What are Complex Numbers?
Complex numbers are made up of two parts: a real number and an imaginary number. Complex numbers serve as the foundation for more complex arithmetic, such as algebra.
Solution:
Since, the graph in the second option is not making any contact with thew point on x-axis it can be very well said that the solutions/roots/zeros of the quadratic equation are complex numbers.
Which is not the case for option one and option two because, the curves are making intercepts on x-axis thus, giving real roots.
To learn more about Complex Numbers from the given link
https://brainly.com/question/5564133
#SPJ1
Answer:
I'm doing the same exact test, it's B.
What is the value of Y?
Answer:
Here we need to find the value of y
In the given figure, 2y and 110 are adjacent to each other.
Hence the value of y = 110.
To learn more about adjacent click here:
#SPJ1
Hi, I need help solving and understanding this.
''Find two functions f and g such that h(x) = (f o g) (x).
h(x)=sqrt(7x+5)''
The two functions f and g such that h(x) = (fog) (x) , are f(x) = 7x + 5 and g(x) = √x .
In the question ,
it is given that
the two functions f(x) and g(x) , form a composite function h(x) such that
h(x) = (f o g)(x) , and h(x) = √(7x + 5)
the composite function (f o g)(x) means f(g(x)) which means g(x) is within h(x) .
By this we get that
the function g(x) is (7x + 5)
and function f(x) is √x .
Therefore , The two functions f and g such that h(x) = (fog) (x) , are f(x) = 7x + 5 and g(x) = √x .
Learn more about Composite Functions here
https://brainly.com/question/11230709
#SPJ1
The points A, B, C and D lie in order on a straight line.
AB BD = 1:4
AC: CD = 7: 13
Work out AB BC: CD
Give your answer in its simplest form.
Answer:
By using the concept of ratio, it is obtained that
AB : BC : CD = 4 : 3 : 13
What is ratio?
Ratio between two number signifies how much one number is larger than as compared to another. The first part of the ratio is called antecedant and the second part of the ratio is called consequent
Here, the concept of ratio has been used
Here, AB : BD = 1 : 4
AC : CD = 7 : 13
AC + CD = 7 + 13 = 20
[tex]AB = \frac{1}{1 + 4} \times 20 = 4[/tex]
[tex]BD = \frac{4}{1+4} \times 20 = 16[/tex]
[tex]CD = 13[/tex]
BC = BD - CD = 16 - 13 = 3
AB : BC : CD = 4 : 3 : 13
To learn more about ratio, refer to the link-
https://brainly.com/question/2328454
#SPJ9
