Step-by-step explanation:
8x+6y=24
6y=24-8x
y=24/6 - 8/6x
y=4-4/3x
List the sides in order from the smallest to the largest 83 56 41
the order from smallest to largest is:
41, 56, 83.
How to list from smallest to largest?
Here we have 3 values, that are:
{83, 56, 41}
To list it from smallest to largest, we first need to write the smallest number, which we can identify is 41.
Then the middle number. Which is 56, that is larger than 41 and smaller than 83.
Finally, the largest number, which is 83.
Then the order is:
41, 56, 83.
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Find the most general antiderivative of the function. (check your answer by differentiation. use c for the constant of the antiderivative. ) g(t) = 8 t t2 t
The most general antiderivative of the given function g(t) is (8t + t³/3 + t²/2 + c).
The antiderivative of a function is the inverse function of a derivative.
This inverse function of the derivative is called integration.
Here the given function is: g(t) = 8 + t² + t
Therefore, the antiderivative of the given function is
∫g(t) dt
= ∫(8 + t² + t) dt
= ∫8 dt + ∫t² dt + ∫t dt
= [8t⁽⁰⁺¹⁾/(0+1) + t⁽²⁺¹⁾/(2+1) + t⁽¹⁺¹⁾/(1+1) + c]
= (8t + t³/3 + t²/2 + c)
Here 'c' is the constant.
Again, differentiating the result, we get:
d/dt(8t + t³/3 + t²/2 + c)
= [8 ˣ 1 ˣ t⁽¹⁻¹⁾ + 3 ˣ t⁽³⁻¹⁾/3 + 2 ˣ t⁽²⁻¹⁾/2 + 0]
= 8 + t² + t
= g(t)
The antiderivative of the given function g(t)is (8t + t³/3 + t²/2 + c).
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What is the end behavior of the function f of x equals negative 2 times the cube root of x?
Concluding, the end behavior is:
as x ⇒ ∞, f(x) ⇒ -∞
as x ⇒ -∞, f(x) ⇒ ∞
What is the end behavior of the given function?
Here we have the function:
[tex]f(x) = -2*\sqrt[3]{x}[/tex]
When we evaluate the function in x that tends to positive infinity, the cubic root also tends to infinity, while because of the negative factor that multiplies it, we conclude that the end behavior is:
as x ⇒ ∞, f(x) ⇒ -∞
When x tends to negative infinity, the opposite happens:
as x ⇒ -∞, f(x) ⇒ ∞
Concluding, the end behavior is:
as x ⇒ ∞, f(x) ⇒ -∞
as x ⇒ -∞, f(x) ⇒ ∞
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Solve following equation:
[tex]4x+10=-2+4[/tex]
Step-by-step explanation:
4x + 10 = -2 + 4
4x = -2 + 4 - 10
4x = -8
x = -2
[tex]\huge\text{Hey there!}[/tex]
[tex]\huge\textbf{Equation:}[/tex]
[tex]\mathsf{4x + 10 = -2+ 4}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{4x + 10 = 2}[/tex]
[tex]\huge\textbf{Subtract 10 to both sides:}[/tex]
[tex]\mathsf{4x + 10 - 10 = 2 - 10}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{4x = 2 - 10}[/tex]
[tex]\mathsf{4x = -8}[/tex]
[tex]\huge\textbf{Divide 4 to both sides:}[/tex]
[tex]\mathsf{\dfrac{4x}{4} = \dfrac{-8}{4}}[/tex]
[tex]\huge\textbf{Simplify it:}[/tex]
[tex]\mathsf{x = \dfrac{-8}{4}}[/tex]
[tex]\mathsf{x = -2}[/tex]
[tex]\huge\textbf{Therefore, your answer should be:}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]
Of all the numbers whose difference is 10, find the two that have the minimum product
Answer: -9
Step-by-step explanation: You might think that the smallest two numbers are 11 and 1 but there are negative numbers. 1 - (-9) is equal to 10. 1 x (-9) is -9.
2(x+2y)^2 + 3(x+2y) +1
Answer:
[tex]3x+2y^2+2(x+y)+2y+1[/tex]
Step-by-step explanation:
1) Split the second term in [tex]2{(x+2y)}^{2}+3(x+2y)+1[/tex] into two terms.
1 - Multiply the coefficient of the first term by the constant term.
[tex]2\times1=2[/tex]
2 - Ask: Which two numbers add up to 3 and multiply to 2?
2 and 1.
3 - Split [tex]3x+2y[/tex] as the sum of [tex]2(x+y)[/tex] and [tex]x+2y[/tex].
[tex]2x+2y^2+2(x+y)+x+2y+1[/tex]
2) Collect like terms.
[tex](2x+x)+2y^2+2(x+y)+2y+1[/tex]
3) Simplify.
[tex]3x+2y^2+2(x+y)+2y+1[/tex]
Thank you,
Eddie
What is the end behavior of the radical function represented by this graph? The graph shows the square root function. The function starts at the point (minus 3, 0) and extends upwards and to the right. Some major points on the graph are (0, 3), (2, 4), and (5, 5). A. As x decreases in value, increases in value. As x increases in value, decreases in value. B. As x decreases in value, increases in value. As x increases in value, increases in value. C. As x decreases in value, decreases in value. As x increases in value, increases in value. D. As x decreases in value, decreases in value. As x increases in value, decreases in value.
The option that describes the end behavior of the graph of the square root function with coordinates (-3, 0), (0, 3), (2, 4), and (5, 5), is the option;
C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.
Which method can be used to find the end behavior of the graph?The given coordinates on the graph are;
(-3, 0), (0, 3), (2, 4), and (5, 5)
The coordinates of the starting point of the graph = (-3, 0)
Shape of the graph = Extends from point (-3, 0), upwards and to the right
Therefore;
As the x-value increases, the y-value increases and vice versa, with, x increasing faster than y.
However, given that the graph is for a square root function, the correct option is option C;
C. As x decreases in value, y decreases in value. As x increases in value, y increases in value.
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5x(3x-10) + (2x-6)(3x+8)
Answer: 21[tex]x^{2}[/tex] - 52x - 48
Step-by-step explanation:
Using the expanding rule we get
5x * 3x - 5x * 10 + (6[tex]x^{2}[/tex] - 18x + 16x -48)
15[tex]x^{2}[/tex] - 50x + 6[tex]x^{2}[/tex] - 2x - 48
21[tex]x^{2}[/tex] - 52x - 48
Answer:
21x^2-52x-48
Step-by-step explanation:
5x(3x-10) + (2x-6)(3x+8)
Distribute
5x^2 -50x+6x^2-2x-48
Combine like terms
21x^2-50x-2x-48
21x^2-52x-48
A soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.
The system of equations that can be used to find x, the cost of each jersey, and y, the cost of each pair of shorts is shown.
12x + 12y = 156
4x + 6y = 62
What is the cost of each jersey?
The cost of each jersey is $8 dollar and that of shorts is $5
System of equationThis are expression that contain unknown equation and two or more equation.
According to the question, a soccer team ordered 12 jerseys and 12 pairs of shorts, for a total of $156. Later, they had to order 4 more jerseys and 6 more pairs of shorts, for a total of $62.
The system of equation that represent the expression is given as;
12x + 12y = 156
4x + 6y = 62
____________
6x + 6y = 78
4x + 6y = 62
Subtract
6x-4x = 78 - 62
2x = 16
x = 8
since 4x + 6y = 62
2x+3y = 31
2(8) + 3y = 31
3y = 31-16
3y = 15
y = 5
Therefore the cost of each jersey is $8 dollar and that of shorts is $5
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Find the general equation of the plane through the point (3, 2, 5) that is parallel to the plane whose general equation is 2x 3y − z = 0.
The plane we want and the plane we're given are parallel, so they share the same normal vector. The normal to [tex]2x+3y-z=0[/tex] is the vector (2, 3, -1), since [tex](2,3,-1)\cdot(x,y,z)=0[/tex].
Then the plane we want has equation
[tex](2,3,-1) \cdot (x-3, y-2, z-5) = 0 \\\\ \implies 2(x-3) + 3(y-2) - (z-5) = 0 \\\\ \implies \boxed{2x + 3y - z = 7}[/tex]
The surface areas of two similar cylinders are 6cm² and 54cm².
i. Find the scale factor for the enlargement.
ii. If the larger cylinder has height 12cm, how high is the smaller one?
iii. What is the ratio of their volumes?
Answer:
3, 4, 27
Step-by-step explanation:
1) Area scale factor = 9
Length scale factor = 3 because √9
2) 12/3 = 4
3) 3³ = 27
From the figure below, identify all pairs of alternate interior and alternate exterior angles
A.
alternate exterior
exterior means outside
like a front entrance to a home
1. o & t
2. n & u
B.
alternate interior
interior means inside
like as if its inside a house
1. p & s
2. q & r
( p & s ) AND ( q & r ) both look like the letter Z
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if b=7, what is the value of the expression2(10-b)?
Answer: 6
Step-by-step explanation: Since we substitute the b with 7, 10-7= 3. Since the 2 is next to the parentheses, we multiply 3 by 2, getting 6.
Hey there!
2(10 - b)
= 2(10 - 7)
= 2(10) + 2(-7)
= 20 - 14
= 6
OR
2(10 - b)
= 2(10 - 7)
= 2(3)
= 6
Therefore, your answer should be: 6
Good luck on your assignment & enjoy your day!
~Amphitrite1040:)
Find the measure of the third angle of a triangle if the measures of the other two angles are given. 35.5 and 82.6
Answer:
61.9°
Step-by-step explanation:
The angles of a triangle always add up to 180°. Using this information along with the values of two of the three angles, we can set up an equation to find the measure of the third angle.
Set up an EquationLet the measure of the third angle be represented as "x". The first angle + the second angle + the third angle must equal 180 therefore...
[tex]35.5+82.6+x=180[/tex]
Solve the EquationStart by adding the like terms on the left side of the equation:
[tex]118.1+x=180[/tex]
Then, subtract both sides by 118.1:
[tex]x=61.9[/tex]
Therefore the measure of the third angle of the triangle is 61.9°.
Find the value of each variable.
one of the properties of a cyclic quad (four sided shape in eucliean geometry) is that the opposite sides add up to 180°
So in this case to get x we= 180°-105°=285°
therefore x is 285°
A lighthouse is located at (1, 2) in a coordinate system measured in miles. a sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse? startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 5 2nd row y = startfraction 14 over 81 endfraction (x minus 2) squared minus 6 endlayout startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 25 2nd row y = startfraction 14 over 81 endfraction (x minus 2) squared minus 6 endlayout startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 5 2nd row y = negative startfraction 14 over 81 endfraction (x 7) squared 8 endlayout startlayout enlarged left-brace 1st row (x minus 1) squared (y minus 2) squared = 25 2nd row y = negative startfraction 14 over 81 endfraction (x 7) squared 8 endlayout
The system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:
y = (2/7)(x - 2)^2 - 6(x - 1)^2 + (y - 2)^2 = 5^2What are equations?The equation is described as the state of being equal and is commonly represented as a math expression with equal values on either side, or it refers to an issue in which many factors must be considered. 2+2 = 3+1 is an example of an equation.To find the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse:
The vertex form of a quadratic function is given by: f(x) = a(x - h)^2 + k
Where (h, k) is the vertex of the parabola, a is constant.
For the sailboat we have vertex: (h, k) = (2, -6) and one point: (-7, 8) that is f(-7) = 8.
f(x) = a(x - 2)^2 - 6We will find a using f(-7) = 8:
f(-7) = a(-7-2)^2 - 6f(-7) = 49a - 649a - 6 = 849a = 14a = 14/49a = 2/7The quadratic function for the sailboat is given by:
f(x) = (2/7)(x - 2)^2 - 6 or y = (2/7)(x - 2)^2 - 6The equation for a circle with a radius of 5 and center (1, 2) is:
(x - 1)^2 + (y - 2)^2 = 5^2Therefore, the system of equations that can be used to determine whether the boat comes within 5 miles of the lighthouse is:
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The correct form of the question is given below:
A lighthouse is located at (1, 2) in a coordinate system measured in miles. a sailboat starts at (–7, 8) and sails in a positive x-direction along a path that can be modeled by a quadratic function with a vertex at (2, –6). which system of equations can be used to determine whether the boat comes within 5 miles of the lighthouse?
Brett needs to put this equation x − 2y = 16 into function notation so that he can identify the rate of change and the y-intercept. How should he display it?
Rewrite x − 2y = 16 in slope-intercept form as y = 1/2x - 8.
Slope (m) = 1/2
Y-intercept (b) = -8.
What is the Slope Intercept Equation?The slope-intercept equation helps us to easily identify the rate of change/slope (m) and the y-intercept (b) of an equation. It is given as y = mx + b.
Given, x − 2y = 16, in order to identify the slope (m) and y-intercept (b), rewrite the equation in slope-intercept form:
x − 2y = 16
-2y = - x + 16
Divide both sides by -2
-2y/-2 = -x/-2 + 16/-2
y = 1/2x - 8
As a function it would be written as y = 1/2x - 8.
Slope (m) = 1/2
Y-intercept (b) = -8.
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divide.
6 divided by 2 2/7
Answer:
2.625
Step-by-step explanation:
2 2/7 in decimal form is 2.2857
6 / 2.2857 = 2.625
HELPPPP‼️‼️‼️
If x is the first of two consecutive odd integers, and the sum of the two integers is 72, what is the smaller of the two integers?
Answer:
x = 35.
Step-by-step explanation:
since they are odd, the second number isn't x + 1, it is x + 2.
x + x + 2 = 72
2x + 2 = 72
2x = 70
x = 35
H=(,),()
F=(),()
Help please asap
Thanks so much
From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).
According to the statement
we have given that the a rectangle on the graph with the two given points and we have to find the another points of the graph.
So, to find the points of the rectangle
firstly the given points are:
E(2,3) And G(-2,-2) and we have to find the point H and F.
So, The point H :
For the point H the lines of rectangle meet with each other at the 3 from origin on the x axis to the negative side and at the 3 from origin on the y axis.
So, the point H become H(-3,3)
And for point F:
For the point F the lines of rectangle meet with each other at the 2 from origin on the x axis to the positive side and at the 2 from origin on the y axis on the negative side.
So, the Point F become F(2,-2).
So, From the representation, the point H and F on the rectangle are H(-3,3) and F(2,-2).
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A salesperson has 7 customers in denver and 13 customers in reno. in how many different ways could she telephone?
If a salesperson has 7 customers in denver and 13 customers in reno then there are 20 different ways in which he can make calls.
Given that the salesperson has 7 customers in denver and 13 customers in reno.
We are required to find the number of ways in which he can make use of telephone.
Number of customers in denver=7
Number of customers in reno=13
Total customers=20
Since he can talk to one customer at one time and he can either choose customer from denver or reno, the number of ways by using combinations will be [tex]7C_{1}[/tex]+[tex]13C_{1}[/tex]
=7+13
=20 ways.
Hence if a salesperson has 7 customers in denver and 13 customers in reno then there are 20 different ways in which he can make calls.
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What is the X
3x +15 and 2x + 20
Answer:
x = 5Step-by-step explanation:
What is the X
3x +15 and 2x + 20
assuming that the question is an equation
3x + 15 = 2x + 20
3x - 2x = 20 - 15
x = 5
-----------------
check
3 * 5 + 15 = 2 * 5 + 20
30 = 30
the answer is good
20 points and marked brainlyist help me ASAP
Answer + Step-by-step explanation:
(a)
Check the attached image.
(b)
Range of sample means : 7.5 - 5.75 = 1.25
(c)
The closer the range of the sample means is to 0 ,
the more confident they can be in their estimate . [tex]\huge \checkmark[/tex]
The farther the range of the sample means is from 0 ,
the more confident they can be in their estimate .
The mean of the sample means will tend to be a better estimate
than a single sample mean . [tex]\huge \checkmark[/tex]
A single sample mean will tend to be a better estimate
than the mean of the sample means .
Find the indicated maximum or minimum value of f subject to the given constraint. maximum: f(x,y,z)=x2y2z2; x2 y2 z2=4
The indicated maximum or minimum value of f is subject to the given constraint maximum is 125/27.
An instance of a constraint is the fact that there are only such a lot of hours in a day to perform things. Embarrassed reserve or reticence; awkwardness. One that restricts, limits, or regulates; a take a look at.
A constraint is something that limits or controls what you can do. Their decision to abandon the trip was made due to monetary constraints. Water shortages in the location can be the primary constraint on development. Synonyms: restriction, issue, lessen, rein greater Synonyms of constraint.
Constraints are used to limit the kind of records which can move right into a desk. This guarantees the accuracy and reliability of the facts inside the table. If there's any violation between the constraint and the facts motion, the motion is aborted. Constraints can be column stage or desk level.
From &22 = x²y 2
2
Given 2²+7+2=5
= <**,4),2=>
By Logange's multijet
(2643805 = 12'aresta
Mithaling by by and
and y
x²²* = P ←
: +(1,2,2) = $
= 125
279
The maximum value is 12r
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Find the volume of the cylinder.
Either enter an exact answer in terms of pi or use 3.14 for pi
4
6
Answer:
144π or 452.16 units³
Step-by-step explanation:
The formula for volume of a cylinder is [tex]\pi r^2 h[/tex]. We can use the given values for radius and height to find the volume of the cylinder.
Finding the Volume[tex]V=\pi r^2 h\\V=\pi6^2(4)\\V=\pi36(4)\\V=144\pi \ OR\ 452.16[/tex]
The volume of the cylinder is 144π or 452.16 units³.
I need to know how to solve this
Please answer the one this exercises if you can send photos sent it pls and you have to use quadratic function for these Thanks
The expression of the equation will be:
x² - 8x = x(x - 8)
x² - 10x = x(x - 10)
x² - 5x = x(x - 5)
x² - 3x = x(x - 3)
How to compute the equation?It should be noted that an equation simply means the expression of the variables that are given.
In this case, the following can be represented:
x² - 8x = x(x - 8)
x² - 10x = x(x - 10)
x² - 5x = x(x - 5)
x² - 3x = x(x - 3)
This is illustrated above.
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hey can you help me answer this i am stuck
If the function is f(x)=1/(6x+6) then the value of x cannot be equal to -1.
Given a function of x f(x)=1/(6x+6).
We are told to find out the value of the variable x for which the function does not lie.
Function is like a relationship between two or more variables expressed in equal to form. The values entered in a function is known as domain and the values which we get after entering of values are known as range.
f(x)=1/(6x+6)
It is in form of fraction. Fraction is a combination of numbers in which the above number is numerator and below number is denominator.
In this (6x+6) cannot be equal to 0 because if (6x+6) equal to 0 then the value of function becomes infinity.
So,
6x+6=0
6x=-6
x=-1
Hence if the function is f(x)=1/(6x+6) then the value of x cannot be equal to -1.
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Write the point where the linear equation 3x + 4y = 12 cuts the x-axis.
Answer:
When the eqn cuts the x-axis , y=0
3x=12
x=12/3
x=4
So,at x=4 is the point at which the linear equation cuts the x-axis
Answer:
collect like terms
12xy=12
xy=1
Suppose we deal a 5-card hand from a regular 52-carddeck. Which islarger, p(2 access) or p(3 diamonds)?
The probability of p(2 aces) is greater than the probability of p(3 diamonds).
Probability is the chance of happening an event or incident. The probability of an event can be calculated by the ratio of the number of favorable events to the total number of events in that sample space.
A deck of cards always has 52 cards.
Out of those 52 cards, there are 4 different aces.
The deck of cards also contains 13 diamonds.
Therefore, the probability of p(2 aces) is the probability of getting at least 2 aces in that 5-card hand is = 2/4 = 1/2 = 13/26.
Now, the probability of p(3 diamonds) is the probability of getting at least 3 diamonds in that 5-card hand is= 3/13 = 6/26.
If we compare these two probabilities, it is clear that the probability of p(2 aces) is greater than the probability of p(3 diamonds).
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