The equation connecting L, m, A is L = [tex]\frac{1.8m}{A}[/tex]
What is a Variation?Variation is a mathematical relationship that shows how a certain variable behaves when other variables depending on it increase or decrease.
The types of variation are: Direct, indirect, joint and partial.
Analysis:
L ∝ [tex]\frac{m}{A}[/tex]
introducing a constant K to replace the proportionality sign,
L = [tex]\frac{Km}{A}[/tex]
when L = 18, m = 0.4, A = 0.4
18 = [tex]\frac{K(4)}{0.4}[/tex]
4K = 0.4 x 18
k = 1.8
Therefore the equation connecting the three variables is,
L = [tex]\frac{1.8m}{A}[/tex]
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A quadratic polynomial with real coefficients and leading coefficient is called if the equation is satisfied by exactly three real numbers. Among all the disrespectful quadratic polynomials, there is a unique such polynomial for which the sum of the roots is maximized. What is
p(1) = 1
Let p(x) = x2 + bx = c
then, p(p(x)) = (x2 + bx + c)² + b(x2 + bx + c) + c
Sum of roots of p(p(x)) is given by = - (coefficient of x3/constant term)
= -2b/c2+bc+c = f(a,b) (say)
For critical points,
∂f/∂c = 0 and ∂f/∂b = 0
= 2b(2c+b+1)/c2+bc+c = 0 and - {( c2+bc+c)²- 2b (c)/ ( c2+bc+c)²}= 0
= b(2c+b+1) =0
= b= 0 or b= - (1+2c) = -(2c(c+1))/c2+bc+c = 0
If c=0 , b= -1 => c= 0 or c=-1
If c = -1 ,b = 1
thus we have the following possibility for (b,c)
(0,0) , (0,-1) , (-1,0) ,(1,-1).
At (0,0) f(0,0) = not defined
(0,-1) f(0,-1) = 0
(1,-1) f(1,-1) = 2
(-1,0) is not possible.
p(x) = (x2 +x-1)² + (x2 +x-1) -1
= p(1) = (1+1-1)² + (1+1-1) -1
= 1
Hence, p(1) = 1
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What are the exact solutions of x2 − 5x − 7 = 0, where x equals negative b plus or minus the square root of b squared minus 4 times a times c all over 2 times a? (1 point)
x = the quantity of negative 5 plus or minus the square root of 3 all over 2
x = the quantity of 5 plus or minus the square root of 3 all over 2
x = the quantity of negative 5 plus or minus the square root of 53 all over 2
x = the quantity of 5 plus or minus the square root of 53 all over 2
Answer: [tex]x=\frac{5 \pm \sqrt{53}}{2}[/tex]
Step-by-step explanation:
[tex]x^2 - 5x-7=0\\\\x=\frac{-(-5) \pm \sqrt{(-5)^2 - 4(1)(-7)}}{2(1)}\\\\x=\frac{5 \pm \sqrt{53}}{2}[/tex]
Terms:
Length of lease = 48 months
• MSRP of the car = $32,100
Purchase value of the car after lease = $26,200
Down payment = $4400
Monthly payment = $450
$435 security deposit
$530 acquisition fee.
●
The total cash that's due at signing will be $5365.
How to calculate the cash?It should be noted that security deposit on acquisition are paid at the begining.
The total cash that's due at signing:
= Down payment + Security deposit + Acquisition fee
= 4400 + 435 + 530
= $5365
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Jack and Diane are jogging back and forth along a one-mile path.They started out at 9:00 am from opposite ends of the path.they passed each other in 10 minutes when Diane has gone 1/3 mile.what time will they first meet at one end of the path?you have to assume they keep jogging at the same speed.
Answer:
Step-by-step explanation:
30 minutes
Step-by-step explanation:
that problem description is imprecise.
I think what is meant here : they each keep jogging at their own same speed.
Diane’s speed is 1/3 miles / 10 min.
Jack’s speed is 2/3 miles / 10 min.
now, to bring this to regular miles/hour format, we need to find the factor between 10 minutes and an hour (60 minutes) and multiply numerator and denominator (top and bottom of the ratio) by it.
60/10 = 6.
so, we need to multiply both speeds up there by 6/6 to get the miles/hour speeds.
Diane : (1/3 × 6) / hour = 2 miles / hour
Jack : (2/3 × 6) / hour = 4 miles / hour
since Jack is running twice as fast as Diane, she will finish one length in the same time he finishes a round trip (back and forth).
Diane running 1 mile going 2 miles/hour takes her 30 minutes.
Jack running 2 miles (back and forth) going 4 miles/hour will take him also 30 minutes.
so, they will meet at his starting point after 30 minutes.
14.
the function y=-16t^2+ 50t +4 describes the height (in feet) of a discus t seconds after it is released. describe the domain and range of the function. find the maximum height of the discus.
The domain is t=0 to t=3.2 and range is y = 0 to 57.125 feet.
What are Domain and range of a Function?
The range of values that we are permitted to enter into our function is known as the domain of a function. The x values for a function like f make up this set (x). A function's range is the collection of values it can take as input. After we enter an x value, the function outputs this sequence of values. The y values are those.A function can be compared to a piece of equipment on an assembly line. A few screws and nuts are located on one end of the assembly line, while a car is located on the other. The function is the device in the center. The domain is the screws and bolts that we insert into the machine. The car at the other can be thought of as the range.Given function is : y = -16t^2 + 50t + 4
It hits the ground when y=0
0 = -16t^2 + 50t + 4
8t^2 -25t -2 = 0
t = 25/16 + (1/16)sqrt(625+64) = (25+26.25)/16 = 51.25/16 = 3.2 seconds
domain is t=0 to t=3.2 [3.2]
take the derivative and set it equal to zero to find maximum height
-32t +50 = 0
t = 50/32 = 25/16 = 1.5625 seconds
-16(25/16) + 50(25/16) + 4 = 34(25/16) + 64/16 = (17(25)+32)/8 = 57.125 = maximum height
range is y = 0 to 57.125 feet. the discus goes from 4 feet to 57 1/8 feet and back down to 0 feet.
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4. Write the linear equation whose graph contains the
points (-2,5) and (4,1).
Thee linear equation which contains the points (-2,5) and (4,1) is [tex]4x+6y-22=0[/tex]
Graph The points which is in the equation (-2,5) and (4,1).
Equation is basically a relationship between two or more variables and it is usually in equal to form. It is equated to find the value of variables. We can also make graphs of different equations. Linear equation is a equation whose graph looks like straight line means values comes from a relationship. It not necessarily means parallel to any axis.
The linear equation can be found by:
[tex](y-y_{1} )=(y_{2} -y_{1} )/(x_{2} -x_{1} )* (x-x_{1} )[/tex] where the coordinates are [tex](x_{1},y_{1}), (x_{2},y_{2})[/tex]
[tex](y-5)=(1-5)/(4+2)*(x+2)[/tex]
[tex](y-5)=-4/6 *(x+2)[/tex]
[tex]6y-30=-4x-8[/tex]
[tex]y=(22-4x)/6[/tex]
Hence the equation which has points (-2,5)(4,1) is [tex]4x+6y-22=0[/tex]
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Please help pleasehelp
Answer:
≥ and ≤ will both be solid dots, as it includes the number
x ≥ -7 is everything greater than -7; x ≤ 4 is everything less than 4.
to include both, you'd click -7, drag right, and stop at 4
Use the grouping method to factor the polynomial below completely.
x3-5x2+3x-15
A. (x²+5)(x-3)
B. (x² - 3)(x + 5)
O C. (x² - 5)(x+3)
D. (x²+3)(x - 5)
The factored expression of x^3 - 5x^2 + 3x - 15 is (x^2 + 3)(x- 5)
How to factor the polynomial?The polynomial is given as:
x^3 - 5x^2 + 3x - 15
Group the terms
(x^3 - 5x^2) + (3x - 15)
Factorize each group
x^2(x - 5) + 3(x - 5)
Factor out x - 5
(x^2 + 3)(x- 5)
Hence, the factored expression of x^3 - 5x^2 + 3x - 15 is (x^2 + 3)(x- 5)
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A father is 38 years old. his sons are 13 and 5 years old, and his daughter is 8 years old. In how many years will the father be the same age as his children put together?
Answer:
6 years
Step-by-step explanation:
So each person's age can be represented as a linear equation, since each year our age increases by 1. It can be represented in the slope-intercept form: y=mx+b. The slope in this case is going to be 1, since the time is going to be years, and each year everyone's age goes up by 1 (of course if you're still alive...) and y-intercept in this case represents their current age.
So the father can be represented as: y=x+38
The sons can be represented as: y = x+13 and y=x+5
The daughter can be represented as: y=x+8
So adding up all his children you get:
(x+13)+(x+5)+(x+8)
This gives you the equation:
3x+26
Now set this equal to the father's age to solve for x (in this context it's years)
3x+26=x+38
Subtract from both sides
2x+26=38
Subtract 26 from both sides
2x=12
Divide both sides by 2
x=6
So in 6 years the father will be the same age as his children put together
Select the correct answer from each drop-down menu.
Consider triangles ABC and QPRshown.
Triangle ABC is
triangles are
B
triangle QPR. Since the transformations
Reset
Next
, the
Triangle ABC is similar to triangle QPR due to the transformations reflection, the triangles are similar by side-angle-side similarity theorem.
How to Identify similar triangles?Transformations are changes done in the shapes on a coordinate plane by rotation, reflection or translation.
- Rotation means that it rotates or turns the pre-image around an axis with no change in size or shape
- Reflection means that it flips the pre-image and produces the mirror-image with no change in size or shape or orientation
- Translation means that it slides or moves the pre-image with no change in size or shape but has changes in only the direction of the shape
- Dilation means that it stretches or shrinks the pre-image.
Two triangles are said to be similar if they have the same shape and the ratio of their corresponding sides are in the same proportion. It should be noted that, corresponding angles are congruent.
Thus, we conclude that triangle ABC and triangle QPR are similar triangle based on the side-angle-side similarity theorem.
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Answer: reflected and then translated onto only involve rigid motions
congruent
Step-by-step explanation:
Triangle abc
is
reflected and then translated onto
triangle qpr
. Since the transformations
only involve rigid motions
, the triangles are
congruent
.
Currently, Netflix has 93 000 subscribers. Netflix subscriptions are decreasing by 2.2% per day. How many subscribers are there after 5 days?
There are 83210 subscribers after 5 days
How to determine the number of subscribers?The given parameters are:
Initial, a = 93000Rate, r = 2.2%The number of subscribers each day is calculated as:
f(n) = a * (1-r)^n
This gives
f(n) = 93000 * (1 - 2.2%)^n
Evaluate the difference
f(n) = 93000 * 0.978^n
At 5 days, we have:
f(5) = 93000 * 0.978^5
Evaluate
f(5) = 83210
Hence, there are 83210 subscribers after 5 days
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What is the solution to the system of equations?
5
5
5.
OA. (4,-1)
y=x+3
5
y=-x+5
Answer:
C
Step-by-step explanation:
the solution is at the point of intersection of the 2 lines.
the lines intersect at (1, 4 ) , then
solution to the system of equations is (1, 4 )
What is the equation of the line parallel to 3x + 2y = -4 that goes through the point (4, -1)?
y =
2x+4
y =
2³x + 5
y =
¾x + 5
Oy = =
x +5
=
Answer:
y = - [tex]\frac{3}{2}[/tex] x + 5
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
given
3x + 2y = - 4 ( subtract 3x from both sides )
2y = - 3x - 4 ( divide terms by 2 )
y = - [tex]\frac{3}{2}[/tex] x - 2 ← in slope- intercept form
with slope m = - [tex]\frac{3}{2}[/tex]
• Parallel lines have equal slopes , then
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c substitute (4, - 1 ) into the partial equation
- 1 = - 6 + c ⇒ c = - 1 + 6 = 5
y = - [tex]\frac{3}{2}[/tex] x + 5 ← equation of parallel line
HELP ASAP!!!
When the polynomial 2x^3 + mx^2 + nx – 2 is divided by x – 3, the remainder is 4. When
divided by x – 2, the remainder is 2. What are the values of m and n?
The values of m and n are -29/3 and 40/3 respectively
Factor and remainder theoremA polynomial is a function that has a leading degree of 2 and greater. Given the polynomial
P(x) = 2x^3 + mx^2 + nx – 2
If it is divided by x – 3, the remainder is 4 and divided by x – 2, the remainder is 2, hence;
4 = 2(3)^3 + 9m + 3n - 2
4 = 54 + 9m + 3n - 3
9m + 3n = -47
Similarly
2 = 2(2)^3 + 4m + 2n - 2
4m + 2n = -12
Solve simultaneously
9m + 3n = -47 * 2
4m + 2n = -12 * 3
______________
18m + 6n = -94
12m + 6n = -36
Subtract
6m = -58
m = -58/6 = -29/3
For the value of n
4m + 2n = -12
2m + n = -6
2(-29/3) + n = -6
n = -6 + 58/3
n = 40/3
Hence the values of m and n are -29/3 and 40/3 respectively
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16) Find the lateral area of the regular pyramid. 5 cm www 24 cm
Answer:
LA = 624 cm²
Step-by-step explanation:
h² = 5² + 12²
h = 13
LA = 4 × bh/2
LA = 4 × (24 cm)(13 cm)/2
LA = (48 cm)(13 cm)
LA = 624 cm²
If one dozen bananas cost is Rs.30 how many dozens can be purchased for 2,67,003 Rs
Answer:
67
Step-by-step explanation:
sorry if wrong
Tina baked a batch of 40 cupcakes. daisy baked 4/5 as many cupcakes as tina. miko baked 1/2 as many cupcakes as daisy. how many cupcakes did the 3 girls bake altogether?
The three girls baked 88 cupcakes altogether.
Cupcakes Baked by Each
Number of cupcakes baked by Tina, T = 40
It is given that Daisy baked 4/5 as many cupcakes as Tina.
Therefore, number of cupcakes baked by Daisy, D = (4T/5) (Applying fractions)
⇒ D = (4/5)×40
⇒ D = 4 × 8
⇒ D = 32
Also, it is given that Miko baked 1/2 as many cupcakes as Daisy.
Thus, number of cupcakes baked by Miko, M = D/2 (Applying fractions)
⇒ M = 32/2
⇒ M = 16
Calculating Total Number of Cupcakes Baked
Cupcakes baked by the three girls altogether = T + D + M
= 40 + 32 + 16
= 88
Hence, the girls together baked 88 cupcakes.
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a cheerleading team plans to sell t-shirts as a fundraiser. the teams goal is to make profit of at least $1248. the profit on each t-shirt sold is $6.50. The teams goal is written as a inequality shown below.
6.5t>1 2 4 8 where t=number of t-shirts sold.
The minimum number of shirt they will sell to make the given profit is 192 shirts
Inequality expressionInequalities are equations not separated by an equal sign.
If a cheerleading team plans to sell t-shirts as a fundraiser and the teams goal is to make profit of at least $1248 with each t-shirt sold at $6.50, then the equation required is;
6.50t ≥ 1246
Divide both sides by 6.50
6.50t/6.50 ≥1246/6.5
t ≥ 192
Hence the minimum number of shirt they will sell to make the given profit is 192 shirts
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At a farmers market, Samuel bought 3 pounds of apples for x dollars per pound and 2 bags of spinach for y dollars each. The next day he returned and bought 5 pounds of apples for x dollars per pound and 3 bags of spinach for y dollars each. Which expression represents the total amount he spent at the market on both days? 8x Plus 5y 8y Plus 5x 6y + 7x 6x + 7y
Answer:
A. 8x+5y
Step-by-step explanation:
First day: 3x+2y
Second day: 5x+3y
Add both expressions together.
(3x+2y)+(5x+3y) =
= 3x+2y+5x+3y=8x+5y
Hope this helps!
If not, I am sorry.
if one-sixth of a number is 1 1/3, find the number.
Answer:
8
Step-by-step explanation:
Since one-sixth was multiplyed be 1 1/3, we just have to find the opposite, six-ones. We multiply that by 1 1/3 and we get 8!
which expression is a sum of cubes?
Answer:
Step-by-step explanation:
A more complicated expression such as 64x3+27y3 64 x 3 + 27 y 3 is also a sum of cubes since 64x3=(4x)3 64 x 3 = ( 4 x ) 3 and 27y3=(3y)3 27 y 3 = ( 3 y ) 3 . Please note, that expressions such as 2x3 2 x 3 are not perfect cubes.
I need the answer to this question
Answer:
See attached image.
Step-by-step explanation:
Graph the system below and write its solution.
y = -1/2x+2
3x+y=-3
Note that you can also answer "No solution" or "Infinite
The graph of the system can be seen below, there we can see that the solution is (-2, 3).
How to solve a system graphically?To do so, we just need to graph both equations on the same coordinate axis and see where the graphs intercept.
The interceptions will be the solutions of the system of equations.
Here we have the system:
y = (-1/2)*x + 2
3x + y = -3
The graph can be seen below, where the green line is the first equation, and the blue line is the second equation.
On the graph, you can see that the lines intersect at the point (-2, 3), so that is the solution of the system.
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A tub of water is emptied at a rate of 3 gallons per minute. The equation y –12 = –3(x – 1) models the amount of water remaining, where x is time (in minutes) and y is the amount of water left (in gallons). Analyze the work shown below to determine the initial amount of water. 1. Solve for the y-variable. y – 12 = –3(x – 1) y – 12 = –3x + 3 y = –3x +15 2. Write the equation using function notation. f(x) = –3x +15 The tub started with gallons of water.
The equation in the function form is f(x) = -3x + 15 and the tub started with 15 gallons of water.
What is a function?It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
We have an equation:
y –12 = –3(x – 1)
We can write the above equation as follows:
y = 12 - 3(x - 1)
y = 12 - 3x + 3
y = -3x + 15
or
f(x) = -3x + 15
Plug x = 0
f(0) = 15
The tub started with 15 gallons of water.
Thus, the equation in the function form is f(x) = -3x + 15 and the tub started with 15 gallons of water.
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pythagoras theorem application
Answer:
A squared plus B squared equal C squared
Step-by-step explanation:
In an Italian class, 65 percent of the students were women. At the end of the class, 52 percent of the men and 44 percent of the women received a certificate. What percentage of those who received a certificate were men
47% of those who received a certificate were men
It is given that in an Italian class, 65 percent of the students were women. At the end of the class, 52 percent of the men and 44 percent of the women received a certificate.
Probability is the branch of mathematics concerning numerical descriptions of how likely an event is to occur, or how likely it is that a proposition is true. The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates impossibility of the event and 1 indicates certainty.
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Convert from Decimal Notation to Scientific Notation
In the following exercises, write each number in scientific notation.
553. 1,290,000
Answer:
Hence, 12,90,000 can be expressed as [tex]$1.29 \times 10^{6}$[/tex].
Step-by-step explanation:
- Given 12,90,000
- Use given, move the decimal point so that first factor is greater than or equal to 1 but less than 10 .
- Then count n and write in scientific notation.
Step 1 of 1
Consider 12,90,000
1.29
So, 1.29 lies between 1 & 10.
Now, Decimal moved to 6 places at left.
[tex]$1.29 \times 10^{6}$[/tex]
So, [tex]$12,90,000=1 \cdot 29 \times 10^{6}$[/tex].
The graph of g(x)=|x-h|+k is shown on the coordinate grid.what must be true about the signs of h and k?
The correct option is the last one. h is negative and k is positive.
What can we say about h and k?
For the absolute value function:
g(x) = |x - h| + k
We know that the vertex is on the point (h, k).
On the graph, we can see that the vertex is on the point (-2, 1), then we have:
h = -2
k = 1
So the sign of h is negative and the sign of k is positive. The correct option is the last one.
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what is the area of a rectangle whose length is 3x and breadth is 2x
Answer:
Your answer is 6x
Step-by-step explanation:
Given,
length(l) = 3x
breadth(b) = 2x
area of a rectangle(A) = ?
Now,
A = l*b
A = 3x*2x
A = 6x ans.
Hope its helpful!
Please mark me as brainlist.
Answer:
6 x^2
Step-by-step explanation:
Area = Length * Breadth
= 3x * 2x = 6x^2
Can someone help please?
Triangle not drawn to scale
Given: m&A= 62°,m&C=28°,c=24cm. Then a
_?__cm to the nearest hundredth.
Answer:
a = 45.14
Step-by-step explanation:
First we need to determine whether this is a non-right triangle or a right triangle.
Since we have two angles already, we can determine whether the third angle is a right or non-right angle:
The sum of all the angles in a triangle will always add up to 180, so we have
180 - (62 + 28) = 180 - 90 = 90
Since we have a right triangle and only one side, we can use trigonometry to find the measure of a.
If we use ∠A as the reference angle, side a is our opposite angle and side c is our adjacent angle.
This means we must use tangent as [tex]tan=\frac{opposite}{adjacent}[/tex]:
[tex]tan (62)=\frac{a}{24}\\ 24*tan(62)=a\\45.137=45.14 = a[/tex]