When quadratic function is subtracted from cubic function, the resultant equation is cubic.
So, It is true.
What is function?Function is defined as, In any equation of two variable, we make change in one accompanied by second.
For example, [tex]F(x)=2x+1[/tex] when we make changes in x , different values of y will obtain.
what are Quadratic and Cubic function?Quadratic function in which maximum power of variable is two. Similarly, the function which has maximum power on variable is three is called cubic function.
To solve the given problem, let suppose we have,
Quadratic function:[tex]f(x)=x^{2} +x+1[/tex]
Cubic function: [tex]g(x)= x^{3}+x^{2} +x+1[/tex]
According to question,
Subtract quadratic function from cubic function,we get
[tex]g(x)-f(x)=( x^{3}+x^{2}+x+1)-(x^{2} +x+1 )[/tex]
⇒ [tex]h(x)=x^{3} +1[/tex]
It is a cubic function.
Thus, given statement is True.
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A trail mix is made by adding cashews that sell for $2.75 per pound to chocolate candies that sell for $1 per pound. How many of each should be used to get 50 pounds of trail mix that sells for $2 per pound?
Complete the statements.
The 50 pounds of trail mix includes [DROP DOWN 1] pounds of cashews and [DROP DOWN 2] pounds of chocolate candies.
The 50 pounds of trail mix includes 28.57 pounds of cashews and 21.43 pounds of chocolate candies.
What pounds of cashew and chocolate candies should be mixed to make the trail mix?let
x = pounds of cashewy = pounds of chocolate candiesx + y = 50
2.75x + y = 50 × 2
Solve the equation simultaneously
x + y = 50
2.75x + y = 100
Substract the equations2.75x - x = 100 - 50
1.75x = 50
x = 50/1.75
x = 28.57 pounds
Substitute into
x + y = 50
28.57 + y = 50
y = 50 + 28.57
y = 21.43 pounds
So therefore, the pounds of cashew and chocolate candies needed are 28.75 and 21.43 respectively.
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When a constant force acts upon an object, the acceleration of the object varies inversely with its mass. When a certain constant force acts upon an object with mass 3 kg, the acceleration of the object is 25 m/s^2. If the same force acts upon another object whose mass is 5 kg, what is this object's acceleration?
If the same force acts upon another object whose mass is 5 kg, the object's acceleration will be 1.667 m/s^2.
How can the acceleration be calculated?We were told that the constant force acts upon an object, and the acceleration of the object varies inversely with its mass, which can be interpreted as :
A = k/M
where M is the mass of the object.
A = acceleration
the k= proportionality constant
then we were told that mass is 3 kg, the acceleration of the object is 25 m/s^2
then substitute into the equation as:
25 =k*3
k= 25/3
then we were told that when mass is 5 kg, then acceleration will be ?
A= (25/3 )/5 = 1.667m/s^2.
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Please help me w this hehehehehh
Answer:
-25x-45y, because if we have got + and -, so we will write minus.
Find the equation of the line. Use exact numbers. y=y=y, equals x+x+x, plus
The equation of the line in the graph is y = 4x - 9..
How to find the equation of a line?The equation of a line in slope intercept form can be represented as follows:
The line forms a linear equation.
Therefore,
y = mx + b
where
m = slopeb = y-interceptTherefore, using (0, -9)(3, 3) let's find the slope
m = 3 + 9 / 3 - 0
m = 12 / 3
m = 4
Therefore, let's find the y-intercept using (0, -9).
-9 = 4(0) + b
b = -9
Therefore, the equation is y = 4x - 9.
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WILL MARK BRAINLIEST
Write an equation of the line that passes through (-3,3) and is perpendicular to the line 2y = 8x-6
Answer:
y = (-1/4)x + 9/4
Step-by-step explanation:
i got u
Mia tasted ocean water and found it very salty which statement best explains the salty nature of ocean water?
I think the answer is C. Because the energy from the sun does break Down rocks and release salt
The lengths of the three sides of a triangle (in feet) are consecutive even integers. If the perimeter is 60 feet, find the value of the shortest of the three side lengths.
Step-by-step explanation:
3 consecutive even integer numbers :
x
x + 2
x + 4
their sum is the perimeter : 60 ft.
x + x + 2 + x + 4 = 60
3x + 6 = 60
3x = 54
x = 18
the shortest of the 3 sides is 18 ft.
and then we have the other 2 sides with 20 and 22 ft.
how to find the area with a circumfernece of 18
The area of the circle with the circumference 18 units is 25.80 square units
How to calculate the area of the circle?The given parameters are
Circumference = 18 units
As a general rule, circumference are represented by the variable C
So, we have the following representation equation
C = 18
The circumference of the circle can be calculated as
C = 2πr
Next, we substitute the value of the variable C in the above equation
i.e. C = 18
So, we have the following equation
2π * r = 18
Divide both sides by 2π
r = 9/π
The area of the circle can then be calculated using the following area formula
A = πr²
Next, we substitute the value of the variable r in the above equation
i.e. r = 9/π
A = π * (9/π)²
Evaluate the exponents
This gives
A = π * 81/π²
Evaluate the products
So, we have
A = 81/π
As a general notation, π = 3.14
So, we have the following equation
A = 81/3.14
Evaluate the quotient
A = 25.80
Hence, the area is 25.80 square units
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Which linear function is graphed on the grid?
90
80
70
60
8
50
30
20
10
-9-8-7-6-5- -3 -2 -1
-10
20
у
-30
-40
-50
-60
-70
-80
88
-90
1234
56789
X
The linear function that is graphed on the grid is g(x) = (15/2)x + 45 , the correct option is (d) .
In the question ,
a linear function graph is shown ,
we have to find that linear function .
So , From the given graph we can see that
the graph passes from the points (2 , 60) and (6 , 90)
in order to find the equation , we first need to find the slope .
slope = (90 - 60)/(6 - 2)
= 30/4
= 15/2
So , the equation of the line passing through the points (2 , 60) and slope 15/2 is
(y - 60) = 15/2(x - 2)
y - 60 = (15/2)x - 15
Adding 60 to both the sides ,
we get
y - 60 + 60 = (15/2)x - 15 + 60
y = (15/2)x - 15 + 60
y = (15/2)x + 45
function is (15/2)x + 45
Therefore , The linear function that is graphed on the grid is g(x) = (15/2)x + 45 .
The given question is incomplete , the complete question is
Which linear function is graphed on the grid shown below ?
(a) g(x) = (2/15)x - 6
(b) g(x) = (2/15)x + 45
(c) g(x) = (15/2)x - 6
(d) g(x) = (15/2)x + 45
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Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.
Martin had 6 magazines. Then m more magazines came in the mail. Write an expression that shows how many magazines Martin has now.
Martin now has: 6 + m
I need help asap thank you..
Step-by-step explanation:
the angle TSW is the total angle and is 73°.
from that total angle, we have one part : angle 1 = 36°.
as angle TSW = angle 1 + angle 2
we have
73 = 36 + angle 2
angle 2 = 73 - 36 = 37°
Using the calculator below, substitute the values to calculate the interest amount on a the loan using the compound interest formula. Principal: $4,000 time: 10 years rate: 7% number of compounding periods: 4 What is the amount of the compound interest? (interest only)
a. 2,800
b. 4,757
c. 4,006
d. 59,897
Please help ASAP
See Attached!!
When you add polynomials of different degrees, it is not adding up the degrees, in special cases this may end up with smaller degree polynomials.
When you multiply polynomials of different degrees, it adds up the degrees, and the final polynomial is off the higher degree.
The answers:
a) False, degrees not added,b) False, degrees added but not multiplied.If a circle has an Area of 84.9056, find the radius and the circumference of the circle.
(Use π=3.14 and do not round.)
Radius =
Circumference =
Answer: Radius is estimated to = 5.2
Circumference is estimated to = 32.66
Emmett is planning a party at an escape room. The escape room will charge Emmett a
booking fee and an additional cost per person attending the party.
This situation can be modeled as a linear relationship.
Answer:
B. After the booking fee the party will cost $20 per person
if Tn =5n +2 which term will have a value of 52
Answer:
10th term
Step-by-step explanation:
given [tex]T_{n}[/tex] = 5n + 2 and [tex]T_{n}[/tex] = 52 , then equate right sides and solve for n
5n + 2 = 52 ( subtract 2 from both sides )
5n = 50 ( divide both sides by 5 )
n = 10
that is the 10th term has a value of 52
1. The cost of bell peppers varies directly with the weight of bell peppers, as shown in the table. Write a direct variation equation to represent this relationship. Then identify the constant of variation and interpret its meaning.
The constant of variation is 1.75 for every unit increase in x (weight), and the cost(y) value increases by $ 1.75.
What is the equation?
The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
The difference between two consecutive entries is constant, as we can see = 1.75
⇒ 7 - 5.25 = 1.75
⇒ 8.75-7 = 1.75
⇒ Slope(m) = 1.75
The slope represents the variable's rate of change.
y - 3 = m(x - 5.25)
y - 5.25 = 1.75(x-3)
y = 1.76x
Thus, the constant of variation is 1.75
This indicates that for every unit increase in x (weight), the cost(y) value increases by $ 1.75.
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The question seems to be incomplete the correct question has been attached
What is the solution to the equation 3m-4-3/2m+8=0?
Om = -24
Om = -12
Om = -6
O m = -4
Answer:
[tex]m=-8/3[/tex], the options are wrong
Step-by-step explanation:
[tex]3m-4-\frac{3}{2}m+8=0 \\ \\ 6m-8-3m+16=0 \\ \\ 3m+8=0 \\ \\ m=-\frac{8}{3}[/tex]
The question is incorrect.
Using the quadratic formula to solve 11x2-4x=1, what’s re the values of x
Find a point on the line only.
Answer:
Step-by-step explanation:
this is very complicated and i suggest you to go to einstin
The cost to produce x units of wire is C= 45x + 450, while the revenue is R= 70x. Find the interval where the product will at least break even.
The interval where the product will be at least break even equals to 18 units.
What is a break even point?In accounting, the break-even point refers to the production level at which total revenues equal total expenses.
Given data
Cost is given as C = 45x + 450
Revenue is given as: R = 70x
In this case, the point of breakeven will be:
Cost = Revenue
45x + 450 = 70x
We will collect like terms:
70x - 45x = 450
25x = 450
We will divide both side by 25:
25x/25 = 450/25
x = 18
Therefore, the interval where the product will be at least break even equals to 18 units.
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Carlos goes out to lunch. The bill, before tax and tip, was $13.80. A sales tax of 3% was added on. Carlos tipped 23% on the amount after the sales tax was added. How much tip did he leave? Round to the nearest cent.
Answer:i think its 13.70 or 14.00
Step-by-step explanation:
Answer:
$3.27
Step-by-step explanation:
$13.80 x 1.03 (which will add the 3% to the total, skipping a step) = $14.21
Then take $14.21 x .0.23 which will give you just the tip amount of $3.2683 or rounded to the nearest cent, $3.27
factorise fully 15x³ + 3x²y
Answer: 3x²(5x+y)
Step-by-step explanation:
15x³ + 3x²y
Apply exponent rule: 15x²x+3x²y
Rewrite 15 as 5*3: 5*3x²x+3x²y
Factor out common terms 3x²: 3x²(5x+y)
Hope this helps!!! :)
How many solutions does the equation have?
12x + 6 = 14(2x – 24) because when simplified we get?
a) 6=-6
a) infinitely many solutions
b) x=-6
b) one solution
c) 6=6
c) no solution
Answer:
One solution: x =21.6
Step-by-step explanation:
Equation
12x + 6 = 14(2x – 24) Remove the brackets
Solution
12x + 6 = 28x - 336 Add 336 to both sides.
12x + 6+336 = 28x - 336 Combine
12x + 342 = 28x -336+336
12x + 342 = 28x Subtract 12x from both sides.
12x-12x + 342 = 28x - 12x Combine
342 = 16x Divide by 16
342/16 = 16x/16
21.6=x
Given that 150 students were interviewed, 85 signed for mathematics, 70 signed for English, and 50 signed for both. Draw a venn diagram to show.
How many signed for only mathematics
Answer: 35
Step-by-step explanation:
If 85 students signed up for mathematics but 50 of those students also signed up for both then you need to subtract 85 from 50 to get 35.
Consider the two points F(-9,0) and G(9,0) as the foci of an ellipse. The length of the major axis is 36. Give the equation of the ellipse.
well, one focus point at (9 , 0) and another at (-9 , 0) will mean the major axis runs over the x-axis, with a center at the origin, so the "c" distance will be 9 units, and since the major axis is 36 units, that means its "a" component or namely its half is half of 36 or 18 units, so
[tex]\textit{ellipse, horizontal major axis} \\\\ \cfrac{(x- h)^2}{ a^2}+\cfrac{(y- k)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h\pm a, k)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} a=18\\ h=0\\ k=0 \end{cases}\implies \cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ b^2}=1\qquad \textit{we also know that }C=9[/tex]
[tex]9=\sqrt{18^2 - b^2}\implies 9^2=18^2-b^2\implies 9^2+b^2=18^2\implies b^2=18^2-9^2 \\\\\\ b^2=243\hspace{5em}\cfrac{(x- 0)^2}{ 18^2}+\cfrac{(y- 0)^2}{ 243}=1\implies {\Large \begin{array}{llll} \cfrac{x^2}{324}+\cfrac{y^2}{243}=1 \end{array}}[/tex]
Check the picture below.
Evaluate this expression. (6x103) ÷ (3x102) express your answer in scientific notation.
9514 1404 393
Answer:
2×10¹
Step-by-step explanation:
For division, mantissas divide, and exponents subtract.
Answer:
2*10^1
Step-by-step explanation:
Process
When you divide powers, they can be subtracted -- numerator - denominator in powers
The numbers divide the way you normally would if the question is 6/3 = 2
Numerator power = 3
denominator power = 2
Solution
6*10^3/ 3*10^2 = (6/3) * 10^(3 -2) = 2 * 10^1 = 20
20 = 2 * 10^1
Select the equation of the graph line above. (A) y = x + 5 (B) y = 3x + 5 (C) y = x - 5 (D) y = 3x - 5
Answer: (D) [tex]y=3x-5[/tex]
Step-by-step explanation:
Using the points (0, -5) and (2, 1), the slope of the line is [tex]\frac{-5-1}{0-2}=3[/tex].
Since the y-intercept is -5, the equation is [tex]y=3x-5[/tex].
Hector also kept track of the remaining gasoline. The equation shown below can be used to find the gallons of gasoline remaining (g) after distance driven (d)
The missing values for gallons of gasoline remaining is 11,6,1.
Given that equation shown below can be used to find the gallons of gasoline remaining (g) after distance driven (d).
We want to find the missing values for gallons of gasoline remaining.
The given equation is g=16-(1/20)d
When the distance is 100 then we will find the gallons of gasoline remaining by substituting d=100 in given equation, we get
g=16-(1/20)100
g=16-5
g=11
When the distance is 200 then we will find the gallons of gasoline remaining by substituting d=200 in given equation, we get
g=16-(1/20)200
g=16-10
g=6
When the distance is 300 then we will find the gallons of gasoline remaining by substituting d=300 in given equation, we get
g=16-(1/20)300
g=16-15
g=1
Hence, the missing values for gallons of gasoline remaining when distance 100 is 11, when distance 200 is 6 and when distance 300 is 1.
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what is 100÷200 need help
on dividing 100 by 200 we get answer as 0.5 or we can also write it as 1/2 in fraction.
What is division?
Multiplication is the opposite of division. If 3 groups of 4 add up to 12, then 12 divided into 3 groups of equal size results in 4 in each group.
The fundamental goal of division is to produce equal groups or to ascertain how many individuals are in each category following a fair distribution.
To divide 12 donuts into three similar groups in the aforementioned case, you would need to put four doughnuts in each group. Consequently, 12 divided by 3 will equal 4.
We need to find 100/200,
on solving this division problem we get answer as 1/2 (in fraction) or 0.5 (in decimal).
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