If y varies directly with x and y = 12 when x = 3, then the direct linear variation equation for the relationship is y = 4x
y varies directly with x
y ∝ x
The directly proportional mean the value of the one variable will varies with the variation in other variable. That means one variable will be dependent variable and other variable will be independent variable
Here
y ∝ x
y = kx
Where y is the dependent variable
x is the independent variable
k is the constant
The values are
y = 12
x = 3
Substitute the values in the equation and find the value of k
12 = k×3
k = 12/3
k = 4
Substitute the value of k in the equation
y = 4x
Hence, if y varies directly with x and y = 12 when x = 3, then the direct linear variation equation for the relationship is y = 4x
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(-17.2 x 2.5) x 4 Write your answer as a decimal
Answer as a decimal is -172.
Given :
= (-17.2 x 2.5) x 4
= (-43) x 4
= -172
Therefore the answer as a decimal is -172.
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find the equation of ab and bc in the following square
In geometry, a square is a flat shape with four equal sides and four right angles (90°). A square is an unique sort of parallelogram as well as an equilateral rectangle (an equilateral and equiangular one).
The formula for a2 + b2 + c2 is written as a square plus b square plus c square. A2 + b2 + c2 = (a + b + c)2 - 2(ab + bc + ca) is how it is expanded.
Give an example to explain what square is?
A square has four equal sides, four vertices, and is a closed, two-dimensional object. It has parallel sides on either side. A square is also equivalent to a rectangle with equal length and width. Many objects can be found in your surroundings that have a square shape.
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3. Un objeto se mueve a una velocidad de
23 m/s. Acelera a una velocidad de 85
m/s en un tiempo de 8.3 s. ¿Qué
aceleración experimenta?
The most appropriate choice for acceleration will be given by
Acceleration of the body = 7.59 [tex]m/s^2[/tex]
What is acceleration of a body?
At first it is important to know about velocity of a body.
The rate of change of displacement of a body is called velocity of a body. Velocity is a vector quantity.
The rate of change of velocity of a body is called acceleration.
Acceleration is also a vector quantity as the direction is taken into account
Here,
Initial velocity of an object = 23m /s
Final velocity of an object = 85 m/s
Time = 8.3 s
Acceleration of the object =
[tex]\frac{85 - 23}{8.3}\\\\\frac{63}{8.3}\\\\[/tex]
7.59 [tex]m/s^2[/tex]
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Select the correct constant rate of change for each table of data.
The constant rate of change for the tables are:
First table: 10
Second table: 12.
Third table: 1/12.
Last table: 1/10.
How to Find the Constant Rate of Change of a Table?To find the constant rate of change (k) of a table of x and y variables, the formula that can be used is:
k = y/x.
Any pair of values, (x, y), from the given table can be used in finding the constant rate of change between the two given variables in each of the tables.
a. The constant rate of change of the first table = 110/11 = 70/7 = 30/3 = 10.
b. The constant rate of change of the second table = 108/9 = 12.
c. The constant rate of change of the third table = 10/120 = 1/12.
d. Constant rate of change for the last table = 10/100 = 1/10.
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Find the volume of the cylinder
Answer: 150.72 in^3
Step-by-step explanation:
the radius (r) is 2 because the diameter of the cylinder is 4.
the height (h) is 12 (obviously because that's provided in the picture.)
the formula to find the volume of the cylinder is:
[tex]3.14(2^2)\times 12[/tex]
therefore, it is 150.72 in^3
i hope this helps :)
Evaluate each of the following given that f(x) =2x+10, find:f(-3)
Answer:
4
Step-by-step explanation
factor the GCF from 16p^4+4p^3
Given the expression:
[tex]16p^4+4p^3[/tex]The GCF of p^4 and p^3 = p^3
And the greatest common factor of 16 and 4 = 4
so,
[tex]\begin{gathered} \frac{16p^4}{4p^3}=4p \\ \\ \frac{4p^3}{4p^3}=1 \end{gathered}[/tex]So, the factors of the given expression will be:
[tex]16p^4+4p^3=4p^3(4p+1)[/tex]rectangular paperboard measuring 28 long and 18 wide has a semicircle cut out of it, as shown below. Find the area of the paperboard that remains. Use the value for , and do not round your answer. Be sure to include the correct unit in your answer.
Perimeter that remains after the semicircle is removed = 377.77
How to find area of the paperboard ?
Length of paper board = 28
Width of paper board = 18
Now, the area of the board = 28 * 18 = 505
Radius of the semi circle = Half of the width of the paperboard = 9
Area of semicircle is = 1/2πr² = 127.23so the area of paperboard is 505 and semicircle is 127.23 .
TO find area of paper board after the cutting semi circle = 505 - 127.23
= 377.77
The remaining area of rectangle is 377.77
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please help me and show work
Answer:
C
Step-by-step explanation:
find the gradient of the 2 points (2,6) &(-3,2)
y2-y1/x2-x1...use the gradient formula
-2-6/-3-2
=-8/-5
=8/5
therefore the line parallel to this line will have the same answer
Therefore C is correct
Write three numbers that are divisible by 2, 4, 8, and 10
Answer:
40, 80, 120
Step-by-step explanation:
-they’re common multiples of 2, 4, 8, and 10
5 girls decide to only spend $40 between them. on average, how much money can each girl spend? Write an inequality. Each sister has 10 dollars
40 = 5X
X = 10 dollars
Now divide 40/5 = 8
On average, each girl spends $8 dollars
Now write an inequality ,for this situation
5X ≤ 40
(a + b + c + d + e)/5 = 40
2) The graph represents the cost of a medical treatment, in dollars, as a function of time, d, in decades since 1978.
It is said that the expression 150(1.8225) ଷrepresents the cost of medical treatment sometime after
1978.
a) Which year does it represent?
b) What would be the medical cost in 1998?
c) If this trend continues, what are the medical costs in 2022?
Since 1978, the graph shows the dollar cost of a medical procedure as a function of time, d. In 1993 year does it represent.
The cost of treatment when d = 1 is $273
Given that,
Since 1978, the graph shows the dollar cost of a medical procedure as a function of time, d.
We have to find in which year does it represent.
Let the equation be
y=150×[tex]e^{at}[/tex]
Where t is the time for year
According to the figure,
y pass (0.5,202.50)
We get,
202.5=150×[tex]e^{0.5a}[/tex]
[tex]e^{0.5a}[/tex]=1.35
Now,
150×(1.35)³=150×[tex](e^{0.5a})^{3}[/tex]
150×(1.35)³=150×[tex]e^{1.5a}[/tex]
1.5 is for 15 years.
1978+15=1993.
Therefore, in 1993 year does it represent.
The graph represents an exponential function:
[tex]$$y=a b^x$$[/tex]
When (x, y)=(0,150), the equation becomes
[tex]$$\begin{aligned}&150=a b^0 \\&a=150\end{aligned}$$[/tex]
When (x, y)=(0.5,202.5), the equation becomes [tex]$202.5=a b^{0.5}$[/tex]
Substitute 150 for a
[tex]$$202.5=150 b^{0.5}$$[/tex]
Divide both sides by 150
[tex]$$1.35=b^{0.5}$$[/tex]
Square both sides
b=1.82
So, the equation of the graph is:
y=150 * 1.82^x
When x=1, we have:
[tex]$$\begin{aligned}&y=150 * 1.82^1 \\&y=273\end{aligned}$$[/tex]
Hence, the cost of treatment when d=1 is [tex]$\$ 273$[/tex].
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The area of the triangle below is 60 in2. What is the perimeter?
Answer:
P = 63 inches
Step-by-step explanation:
the area (A) of a triangle is calculated as
A = [tex]\frac{1}{2}[/tex] bh ( b is the base and h the height )
here b = 2x - 6 , h = 4 and A = 60 , then
[tex]\frac{1}{2}[/tex] × 4 ×(2x - 6) = 60
2(2x - 6) = 60 ( divide both sides by 2 )
2x - 6 = 30 ( add 6 to both sides )
2x = 36 ( divide both sides by 2 )
x = 18
2x - 6 = 2(18) - 6 = 36 - 6 = 30
perimeter (P) is the sum of the 3 sides , so
P = 18 + 30 + 15 = 63 inches
consider this equation
(4x) 1/3 - x =0
the first step to solving this equation is to
A. take the cube root of both sides
B. cube both sides
C. add x to both sides
the second step is to
A. add the cube of x to both sides
B. add the cube root of x to both sides
C. cube both sides
solving this equation for x initially yields
A. one possible value
B. three possible values
C. two possible values
checking the solutions shows that
A. 0 and 2 are valid solutions
B. only 0 is a valid solution
C. -2,0, and 2 are valid solutions
D. none are valid solutions
The first step to solving the equation is to; C. add x to both sides
The second step to solving the equation is to; C. cube both sides
Solving the equation for x initially yields; C. two possible values
Checking the solutions shows that; D. none are valid solutions
How to solve Linear Equations?We are given the linear equation;
4x[tex]^{1/3}[/tex] - x = 0
From the linear equation above, seeing that we have an x that is raised to the power of one-third, and we have a single x variable, the first step would be to add x to both sides to get;
4x[tex]^{1/3}[/tex] - x + x = 0 + x
4x[tex]^{1/3}[/tex] = x
Now, to remove the fraction root, what we will now do as the second step is to cube both sides to get;
(4x[tex]^{1/3}[/tex])³ = x³
4³x = x³
64x = x³
Divide both sides by x to get;
x² = 64
Take square root of both sides to get;
x = ±√64
x = ±8
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In AJKL, j = 74 cm, k = 14 cm and l=80 cm. Find the measure of ZJ to the nearestdegree.
To answer this question we first draw the triangle to help us:
As a note on the problem: This is not necessarily the triangle we have, we drew just to helps us solve it.
Now, to find the angle J we can use the law of cosines:
[tex]j^2=k^2+l^2-2kl\cos J[/tex]Plugging the values we have and solving for J we have:
[tex]\begin{gathered} 74^2=14^2+80^2-2(14)(80)\cos J \\ 2(14)(80)\cos J=14^2+80^2-74^2 \\ \cos J=\frac{14^2+80^2-74^2}{2(14)(80)} \\ J=\cos ^{-1}(\frac{14^2+80^2-74^2}{2(14)(80)}) \\ J=60 \end{gathered}[/tex]Therefore the angle J is 60°.
The diagram shows a simple bridge, which is supported by four steel cables.
A. Find the angles at A and B
B. Find the length of each cable
(a)
In the given diagram,
∠α and ∠β can be determined using trigonometric functions,
tan α = Opposite side/Adjacent side
⇒ tan α = 4/6
⇒ tan α = 2/3
⇒ α = tan^-1 (2/3)
⇒ α = 33.7°
Similarly,
tan (α + β) = 4+4/6
⇒ tan (α + β) = 8/6
⇒ tan (α + β) = 4/3
⇒ (α + β) = tan^-1 (4/3) = 53.1°
⇒ 33.7 + β = 53.1°
⇒ β = 19.4°
(b)
For the cables adjacent to the perpendicular height, i.e., adjacent to ∠α, on both the sides
Cable length^2 = 4^2 + 6^2 .............................. (Pythagoras theorem)
⇒ Cable length^2 = 16 + 36
⇒ Cable length^2 = 52
⇒ Cable length = 7.21 m
For the cables far from the perpendicular, on both the sides,
Cable length^2 = 6^2 + 8^2 .............................. (Pythagoras theorem)
⇒ Cable length^2 = 36 + 64
⇒ Cable length^2 = 100
⇒ Cable length = 10 m
What is Trigonometric Function?The functions of an angle in a triangle are known as trigonometric functions, commonly referred to as circular functions. In other words, these trig functions provide the relationship between a triangle's angles and sides. There are five fundamental trigonometric functions: sine, cosine, tangent, cotangent, secant, and cosecant. The main division of trigonometric functions is into sine, cosine, and tangent angles. Additionally, the three fundamental functions can be used to derive the cotangent, secant, and cosecant functions. Basically, compared to the fundamental trigonometric functions, the other three functions are frequently used. The lengths of the adjacent and opposing sides are compared to determine the tangent function.
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2/3x+2y=12 in standard form
Answer:
[tex]2x + 6y = 36[/tex]
[tex]x + 3y = 18[/tex]
can anybody tell me what 11.8 x 5 is step by step ?
Step-by-step explanation:
hope this helps!! the explanation is in my working. bring the "4" from the "40" (8 x 5) to the top of "1"
Answer:
59
Step-by-step explanation:
To mutlipy a decimal by a whole number, just multiply it like normal
118 x 5 = 590
11.8 has one decimal place so your answer will have one too
59.0 which is the same as 59
Given f(x) = -4x - 2, find f(1).
Answer:
-6
Step-by-step explanation:
Replace the variable x with 1 in the expression.
f(1)=−4−2
Then simplify -4 and -2 (subtract 2 from -4)
= -6
What table represents a function?
Table A represents a function.
Define functions.A relation between a collection of inputs and outputs is known as a function. A function is, to put it simply, a relationship between inputs in which each input is connected to precisely one output.
Functions are crucial instruments in the creation of mathematical models because we continually develop beliefs about connections between variables in nature and society. Typically, functions in school mathematics contain numerical inputs and outputs and are frequently specified by algebraic expressions.
Given,
Table A represents a function,
A visual table with columns and rows that shows the function in relation to the input and output is called a function table. Function tables are frequently referred to as function machines by younger students. Each function has a rule that governs how the input and output are related to one another.
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Solving Systems of Equations by Substitution
-2x-y=-9
5x-2y=18
explain please.
Answer:
(4,1)Step-by-step explanation:
Systems of equations may be solved in one of two manners: substitution and graphing. This requaests they be solved by substitution, but I'll add the graphing solution, also.
Substitution:
We want to eliminate one of the two variables to result in an expression that only has one of the two remaining. We can do that by manipluating one of the equations such that, when it is combined with the other, results in the elimination of one of the variables.
Given:
-2x-y=-9
5x-2y=18
we can multiply or divide one of the equations so that one of the terms has equal, but opposite, values. We could multiply the first equation by 2.5 so that it becomes -5x -2.5y = 9*(2.5). Then it could be added to the second to eliminate the x term.
My preference is to find a way to avoid fracticious fractions, so I will multiply the first equation by -2 so that we can eliminate y:
-2*(-2x-y =-9)
4x+2y = 18
No add this to the second equation:
4x+2y = 18
5x-2y = 18
9x = 36
x = 4
Since x = 4:
-2x-y=-9
-2*(4)-y=-9
-8 - y = -9
y = 1
The solution is (4,1). It is the point the satisfies both equations.
-2x-y=-9
-2(4)-(1)=-9
-8-1=-9 YES
----
5x-2y=18
5(4)-2(1)=18
20 - 2 = 18 YES
Graphing:
The solution to these equations is the point at which the lines intersect. See the attached graph. The lines intersect at (4,1).
you have $1 and you are going to buy some pencils and 7 patties let X represent the number of pencils you can buy and let y represent the number of peppermint patties you can buy if pencils cause 0.10 each and Peppermint Patties cost 0.05 each write a linear equation in standard form that represents this situation what does the x intercept represent? what does the Y intercept represent
Let:
x = Number of pencils you can buy
y = Number of peppermint patties you can buy
a = cost of each pencil
b = cost of each peppermint patty
The standard form of a linear equation is given by:
[tex]\begin{gathered} Ax+By=C \\ \\ \end{gathered}[/tex]So:
[tex]0.1x+0.05y=1[/tex]The graph of this equation is:
The x-intercept represents the maximum number of pencils you can buy
The y-intercept represents the maximum number of peppermint patties you can buy
write 3/4 in lowest terms
Answer:
that is the lowest term I think
For the function g, g(3)= -11 and g(7)= 5. What is the function rule for g(x)?
Answer:
g(x) = 4x - 23
Step-by-step explanation:
We will assume a linear function for g(x)
This will be of the form g(x) = ax + b where a and b are constants
Given the info,
g(3) = a(3) + b = -11
g(7) = a(7) + b = 5
Thus we have two equations in a and b
3a + b = -11 [1]
7a + b = 5 [2]
Subtract [1] from [2]:
7a + b - (3a + b) = 5 - (-11)
7a + b - 3a - b = 5 + 11
4a = 16
a = 4
Substitute for a in equation [2]:
4(7) + b = 5
28 + b = 5
b = 5-28 = -23
So equation of g(x) is
g(x) = 4x - 23
Simplify as far as possible without a calculator.
(
3
−
√
7
)
(
3
−
√
7
)
Answer:
- 26
Step-by-step explanation:
(3−√7)(3−√7)
9 - 3√7 -3√7 + √7√7
9 - 6√49 + √49
9 - 6*7 + 7
9 - 42 + 7
= -26
A mixture of juices in a punch had 1.1 L of pineapple juice for every 0.4 L of orange juice. Sarah wanted the punch to taste more orangey, so she added 0.3 L of orange juice but no pineapple juice. Now the ratio of juices was 1.1 L of pineapple juice for every 0.5 L of orange juice. How many litres of punch did Sarah have now
Answer:
1.1l +0.4+0.3+0.5
answer = 2litres 3milimetres
HOW DO I GET 36.9 OUT OF THE NUMBERS 55.5 AND 35
Answer:
Add 55.5 and 35, then subtract 36.9.
Step-by-step explanation:
x+36.9=55.5+35
x+36.9=90.5
Subtraction Equality
x + 36.9 + (-36.9)= 90.5 (-36.9)
x = 53.6
What is r, -3(1+6r)=14-r
Step-by-step explanation:
-3(1+6r) = -3-18r =14-r
17r = -17 Therefore, r = -1
If 672,342= 6.72342x 10n what is the value of n
An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
The value of n in the equation 672,342 = 6.72342 x 10n is 10,000
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x = 9 is an equation.
6x+ 2 = 9 is ana equation.
We have,
672,342 = 6.72342 x 10n
Divide both sides by 6.72342
672,342 / 6.72342 = 10n
We get,
100000 = 10n
Divide both sides by 10.
100000 / 10 = n
n = 10,000
Thus,
The value of n in the equation 672,342 = 6.72342 x 10n is 10,000
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Find the monthly interest payment in the situation described below. Assume that the monthly interest rate is 1/12 of the annual interest rate. You maintain an average balance of $500 on your credit card, which carries an 18% annual interest rate. WHat is the monthly interest payment?
Using an average credit card amount of $500 and an annual percentage rate of 18%, the monthly interest payment is $7.5.
It is possible to calculate the monthly interest payment as follows:
I = [tex]\frac{PNR}{100}[/tex]
Given P = 500, N = 1, R = 18%
[tex]I = \frac{500*1*18}{100}[/tex]
[tex]I = \frac{9000}{100}[/tex]
[tex]I = 90[/tex]
Yearly Interest is $[tex]90[/tex]
Monthly interest :
[tex]M.I = \frac{18}{12}[/tex]
[tex]M.I = 1.5%[/tex]
Monthly interest payment = $[tex]500*1.5[/tex]= $[tex]7.5[/tex]
Monthly interest payment:
The percentage of the monthly payment earmarked for paying off the loan charge is referred to as the monthly interest payment.
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