Answer:
16
Step-by-step explanation:
Difference means subtract
Let the two numbers be x and y
x-y = 6
Let y be the smaller number
2y = x+4
Using substitution
x = 6+y
2y = 6 +y +4
2y = y+10
Subtract y from each side
2y-y = y+10-y
y = 10
Now we need to find x
x-y = 6
x-10 = 6
Add 10 fo each side
x-10+10 =6+10
x = 16
Simplify the expression
Answer:
-8
Step-by-step explanation:
2x/7 =
2(12)/-3 =
24/-3 =
-8
Answer:
-8
Explanation:
Given expression:
[tex]\rightarrow \sf \dfrac{2x}{y}[/tex]
when x = 12, y = -3
Substitute values inside expression:
[tex]\rightarrow \sf \dfrac{2(12)}{-3}[/tex]
multiply
[tex]\rightarrow \sf \dfrac{24}{-3}[/tex]
simplify
[tex]\rightarrow \sf -8[/tex]
The graph of the function y = x^3 + ax^2 + b has a local minimum point at (4, -11). Find the coordinates of the local maximum. Answer: (0, 21)
Answer:
(0, 21)
Step-by-step explanation:
Stationary points occur when the gradient of a graph is zero.
Therefore, to find the x-coordinate(s) of the stationary points of a function, differentiate the function, set it to zero and solve for x.
Differentiate the given function:
[tex]\begin{aligned}y & = x^3+ax^2+b\\\implies \dfrac{\text{d}y}{\text{d}x}&=3 \cdot x^{3-1}+2 \cdot ax^{2-1}+0\\\implies \dfrac{\text{d}y}{\text{d}x}& = 3x^2+2ax\end{aligned}[/tex]
Set the differentiated function to zero:
[tex]\begin{aligned} \dfrac{\text{d}y}{\text{d}x}& =0\\ \implies 3x^2+2ax & = 0 \\ \implies x(3x+2a)&=0\end{aligned}[/tex]
Therefore the stationary points occur when:
[tex]\implies x=0[/tex]
[tex]\implies 3x+2a=0 \implies x=-\dfrac{2}{3}a[/tex]
There is a stationary point at (4, -11), therefore substitute x = 4 into the expression for x and solve for a:
[tex]\begin{aligned}x & = 4\\\implies -\dfrac{2}{3}a & = 4\\a & = -\dfrac{3}{2}(4)\\a & = -6\end{aligned}[/tex]
Substitute the found value of a and the point (4, -11) into the function and solve for b:
[tex]\begin{aligned}y & = x^3 + ax^2 + b\\\implies -11 & = (4)^3+(-6)(4)^2+b\\ -11 & = 64-96+b\\b & = -11-64+96\\ b & = 21\end{aligned}[/tex]
Therefore, the function is:
[tex]\boxed{y=x^3-6x^2+21}[/tex]
The other stationary point is when x = 0. Therefore, to find the coordinates of this point, substitute x = 0 into the function:
[tex]\begin{aligned}y & =x^3-6x^2+21\\x=0\implies y & =(0)^3-6(0)^2+21\\ y & =21 \end{aligned}[/tex]
Therefore, the coordinates of the other stationary point are (0, 21).
To determine if a stationary point is minimum or maximum, differentiate the function again:
[tex]\begin{aligned}y & =x^3-6x^2+21\\\implies \dfrac{\text{d}y}{\text{d}x} & = 3x^2-12x\\\implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6x-12\\\end{aligned}[/tex]
Substitute the x-coordinate of the stationary point into the second derivative:
[tex]\begin{aligned} \dfrac{\text{d}^2y}{\text{d}x^2} & = 6x-12\\x=0 \implies \dfrac{\text{d}^2y}{\text{d}x^2} & = 6(0)-12= -12 \\\end{aligned}[/tex]
[tex]\textsf{As $\dfrac{\text{d}^2y}{\text{d}x^2} < 0$, stationary point $(0,21)$ is a maximum.}[/tex]
Differentiation Rules
[tex]\boxed{\begin{minipage}{4.8 cm}\underline{Differentiating $ax^n$}\\\\If $y=ax^n$, then $\dfrac{\text{d}y}{\text{d}x}=nax^{n-1}$\\\end{minipage}}[/tex]
[tex]\boxed{\begin{minipage}{4cm}\underline{Differentiating a constant}\\\\If $y=a$, then $\dfrac{\text{d}y}{\text{d}x}=0$\\\end{minipage}}[/tex]
(27/8)-^2/3??????????/
Answer: 4/9
Step-by-step explanation:
[tex]\displaystyle\\(\frac{27}{8} )^{-\frac{2}{3}} =\\\\(\frac{3*3*3}{2*2*2})^{-\frac{2}{3}}=\\\\ (\frac{3^3}{2^3} )^{-\frac{2}{3}} =\\\\((\frac{3}{2})^3)^{-\frac{2}{3} } =\\\\(\frac{3}{2})^{-\frac{3*2}{3}} =\\\\(\frac{3}{2})^{-2}=\\\\(\frac{2}{3})^2 \\\\\frac{2^2}{3^2} =\\\\\frac{4}{9}[/tex]
On Flight #447 if 130 people are on the flight how many can get both headphones and a blanket
Answer: 106
Step-by-step explanation:
because there is 106 headphones 106 people can get and there is 16 blankets 156 people can get so 106 people can get headphones and blankets
22 out of 25
math students
bring their
calculators to
class how many
students would
have a
calculafors in a
group of 80
math students
HELP PLEASE
a bricklayers assistant starts building a wall laying 50 bricks per hour. Two hours later the master bricklayer joins the assistant and both lay bricks. The master bricklayer lays 80 bricks per hour. write an equation stating that the assistant and the master have laid the same number of bricks. how long has each one worked when they have laid the same number?
Answer:
80t = 50(t+2)master: 3 1/3 hoursassistant: 5 1/3 hoursStep-by-step explanation:
Given an assistant bricklayer laying 50 bricks an hour has worked 2 hours longer than a master bricklayer laying 80 bricks an hour, you want an equation stating they have laid the same number of bricks. You also want to know how long each has worked.
Rate and outputThe output of each bricklayer is the product of the rate at which they lay bricks and the time for which they do it. If t is the time spent by the master bricklayer, their output will be 80t. The time spent by the assistant will be (t+2) hours, and their output will be 50(t+2).
Here is the equation that says their output is the same:
80t = 50(t+2)
TimeSolving the equation for t, we have ...
80t = 50t +100
30t = 100 . . . . . . . . . subtract 50t
t = 3 1/3 . . . . . . . divide by 30
The master bricklayer has worked 3 1/3 hours when they have laid the same number of bricks.
The assistant bricklayer has worked 5 1/3 hours at that time.
__
Additional comment
Each will have laid (80)(3 1/3) = 266 2/3 bricks.
Given P(A) = 0.74, P(B) = 0.85 and P(A|B) = 0.84, find the vi P(A and B), rounding to the nearest thousandth, if necessary.
The value of the given statement rounding to the nearest thousandth = 0.714.
What exactly are dependent events?Dependent occurrences are ones that are dependent on previous events. The outcomes of prior events have an impact on these occurrences. Dependent events are two or more occurrences that are dependent on one another. If one event is altered by chance, another is most likely to differ.
What exactly is the distinction between dependent and independent?The independent and dependent factors are the two most crucial variables in a research experiment. The experimental has authority over the independent variable. The variable that varies in reaction toward the independent variable is known as the dependent variable.
According to the information provided:P(A) = 0.74
P(B) = 0.85
P(A|B) = 0.84
Using dependent events formula:
P(A∩B) = P(A/B) × P(B)
= 0.84 X 0.85
= 0.714
The value of the given statement rounding to the nearest thousandth = 0.714.
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In the diagram below, ΔABC ≅ ΔDEF. Complete the statement BC⎯⎯⎯⎯⎯⎯⎯⎯≅ B C ¯ ≅ ___
Answer:
[tex]\overline{BC} \cong \overline{EF}[/tex]
Step-by-step explanation:
Corresponding parts of congruent triangles are congruent.
Decide whether the table shows a proportional relationship between x and y.
x y
17 2 5/6
5/6 5/36
6 1/6
19 3 1/6
The table shows a proportional relationship between x and y.
In this question, we have been given a table which contains values of x and y.
We need to decide whether the table shows a proportional relationship between x and y.
x y
17 2 5/6
5/6 5/36
6 1/6
19 3 1/6
First we convert the improper fraction in the y-column to proper fraction.
2 5/6 = 17/6
and 3 1/6 = 19/6
so, given table would be,
x y
17 17/6
5/6 5/36
6 1/6
19 19/6
Consider the ratio x/y of each row:
x y x/y
17 17/6 1/6
5/6 5/36 1/6
6 1/6 1/6
19 19/6 1/6
As the ratio x/y is constant, x and y are directly proportional.
Therefore, the table shows a proportional relationship between x and y.
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Given m n, find the value of x.
Answer:
x = 21°
Step-by-step explanation:
180 - 159 = 21
Alternate angles (see image below) are equal, so x = 21
Using corresponding angles and adjacent angles concept, the value of x from the given parallel lines is 21°.
Given that, straight line m parallel to straight line n and t is the transversal.
The corresponding angles definition tells us that when two parallel lines are intersected by a third one, the angles that occupy the same relative position at each intersection are known to be corresponding angles to each other.
Here, y°=159°
Now, y°+x°=180° (Adjacent angles on straight line)
159°+x°=180°
x°=21°
Therefore, the value of x from the given parallel lines is 21°.
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Find the sticker price
River City Autos has a pickup truck for sale. Its base price is $22,225. Prices for available options are 6-speed transmission, $2,908; cruise control, $240; trailer towing package, $230; and power windows, $738. Its destination charge is $900.
The total price of the pick up truck is $27,241.
What is mathematic expression?
A mathematical expression is defined as the collection of the numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Base price = $22,225.
Additional options pricing,
6-speed transmission = $2,908
cruise control = $240
trailer towing package = $230
power windows = $738
destination charge = $900
All the other charges will be added to the base price if a person chooses all the options available, therefore,
= 22,225 + 2,908 + 240 + 230 + 738 + 900
= $27241
Therefore, The total price of the pick up truck is $27,241.
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The quadrilaterals ABCD and JKLM are similar.
Find the length x of MJ.
Answer:
x = 4.8
Step-by-step explanation:
since the quadrilaterals are similar then the ratios of corresponding sides are in proportion , that is
[tex]\frac{MJ}{DA}[/tex] = [tex]\frac{LM}{CD}[/tex] ( substitute values )
[tex]\frac{x}{6}[/tex] = [tex]\frac{2.4}{3}[/tex] ( cross- multiply )
3x = 6 × 2.4 = 14.4 ( divide both sides by 3 )
x = 4.8
(01.01 MC)
Which value of x would make the expression (75)* equal to 5?
a
b
3
12
C 4
5
d 5
4
Answer: (sidenote, I'm sorry if I answered incorrectly ;-;)
C: 4/5 or D 5/4
Step-by-step explanation:
if you solve the numbers inside the radical symbol you'll get 16807. it's hard for it to be separated into 4 groups since it can only be separated in 5, that being 7*7*7*7*7.
so, by process of elimination i suggest you answer either c or d
i am sooooo confused please help
The simplified form of the function f(x) = (x² - 4x + 4) / (x² - 4) will be f(x) = (x - 2) / (x + 2).
What is a function?A statement, principle, or policy that creates the link between two variables is known as a function. Functions are found all across mathematics and are required for the creation of complex relationships.
The function is given below.
f(x) = (x² - 4x + 4) / (x² - 4)
Simplify the equation, then we have
f(x) = (x² - 4x + 4) / (x² - 4)
f(x) = (x - 2)² / [(x - 2)(x + 2)]
f(x) = (x - 2) / (x + 2)
The simplified form of the function f(x) = (x² - 4x + 4) / (x² - 4) will be f(x) = (x - 2) / (x + 2).
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Name a point non-coplanar to plane K
W is the point which is non coplanar to plane k .
WHAT IS A COPLANAR/NON-COPLANAR POINT ?A group of points that are in the same plane are said to be coplanar. A coplanar line connects any two or three points. It's possible that four or more points are coplanar.
The coplanar points A, B, C, and D are displayed on the left side of the above figure. Additionally, there are other sets of coplanar points in the box to the right. For instance, the left side of the box's left side is the plane that contains the coplanar points P, Q, X, and W. There are four coplanar points on each of the box's six faces, however they are not the only coplanar point groups. Points Q, X, S, and Z, for instance, are coplanar despite the fact that the plane containing them isn't depicted.
Non-coplanar points are a collection of points that are not all located on the same plane.
Points P, Q, X, and Y in the previous figure are not coplanar. Q, X, and Y are located on the box's top, and P, Q, and X are located on the box's left side, however no flat surface has all four points.
CALCULATIONsince from the figure we can find out that except two points W , Y all the points are on the plane K .
so according to question and given figure we conclude that one of the point which in non coplanar to K is W.
points highlighted in the figure is non coplanar to point k .
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I can’t find a way to flip the number and to swap it as well
Answer:
Reflect over the x axis and than turn 90 degrees clockwise about the origin.
Find the nth term, the fifth term, and the 100th term, of the arithmetic sequence determined by a = 2 and d = 3
Answer: an=3n-1 a₅=14 a₁₀₀=299
Step-by-step explanation:
a=2 d=3
[tex]\boxed {a_n=a_1+d(n-1)}\\\\a_n=2+3(n-1)\\\\a_n=2+3n-3\\\\a_n=3n-1\\\\a_{100}=3(100)-1\\\\a_{100}=300-1\\\\a_{100}=299\\\\a_5=3(5)-1\\\\a_5=15-1\\\\a_5=14[/tex]
what is the value of the sum 1/3 and 2/5
Answer:11/15
Step-by-step explanation:
you have to change them to common denominators.
i chose 15.
to make the denominator for 1/3 into 15 you have to multiply it by 5 which means you have to multiply the numerator (1) by the same thing which gives you 5/15
to make the denominator for 2/5 into 15 you have to multiply the denominator by 3 so you have to multiply the numerator (2) by the same thing which gives you 6/15
you now have the equation 5/15 + 6/15
to add them together you leave the bottom numbers the same and add the top ones which gives you 11/15
Answer:
0.7333333333333333 = 11/15
Step-by-step explanation:
1/3 = 5/15
2/5 = 6/15
add them, and now you get
(5+6)/15 = 11/15
The temperature at
7:00 P.M is 18°F. At
7:00 A.M. the next
day, the temperature
is -12°F. What integer
represents the change
in temperature?
Answer: -30 degrees fahrenheit
Step-by-step explanation: 18 + (-12) = -30
Simplify the expression below:
-3/7 ( y-28) - 1/21 y
please show your work and i'll give brainliest :,)
I’m in need of help with this math problem!!!
Answer:
Flowers: $19.98Jewelry: $18.92Gift Certificates: $14.52Step-by-step explanation:
You want the values of three expenditures, given three relations between them.
(The first thing to realize is that the question isn't about averages at all. It is about values that are described as averages.)
SetupLet f, j, c represent the (average) amounts spent on flowers, jewelry, and gift certificates, respectively. The three given relations are ...
f + j + c = 53.42
j = 4.40 + c
f + c = 15.58 + j
SolutionUsing the second equation to substitute for j in the third, we have ...
f +c = 15.58 +(4.40 +c)
f = 19.98 . . . . . . . . . . . . . . simplify
Using this and the second equation to substitute into the first, we have ...
19.98 +(4.40 +c) +c = 53.42
24.38 +2c = 53.42
2c = 29.04
c = 14.52
Then ...
j = 4.40 +c = 4.40 +14.52 = 18.92
The average expenditures are ...
Flowers: $19.98Jewelry: $18.92Gift Certificates: $14.52__
Additional comment
This solution is one of many ad hoc methods that could be used. There are also graphing and matrix methods available for solving a set of equations like this. The attachment shows a calculator matrix solution.
12.4%of what number is 7.13?
Answer:57.7
Step-by-step explanation:
2. Select the polynomial functions for which (x+3) is a factor. Select all that apply. (2
f(x)=x²-12x³ +54x² - 108x+81
f(x)=x²-3x³-x+3
f(x)=x+2x¹-23x³-60x²
f(x)= x³ +5x²-3x³-29x²+2x+24
The polynomial functions for which (x+3) is a factor
A polynomial of degree n is a function of the form
f(x) = anx
n + an−1x
n−1 + . . . + a2x
2 + a1x + a0
where the a is a real number (sometimes called the coefficients of the polynomial). Although
this general formula might look quite complicated, particular examples are much simpler. For
example,
f(x) = 4x
3 − 3x
2 + 2
is a polynomial of degree 3, as 3 is the highest power of x in the formula. This is called a cubic
polynomial, or just cubic.
Theorem Polynomial Division: Suppose d(x) and p(x) are nonzero polynomials were
the degree of p is greater than or equal to the degree of d. There exist two unique polynomials,
q(x) and r(x), such that p(x) = d(x) q(x) + r(x), where either r(x) = 0 or the degree of r is
strictly less than the degree of d.
so, if we put x=-3 then f(x) must be equal to zero
here no function satisfies of none of the option is correct for [x+3] factor
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(x +3) is a factor of the function f(x)= x³ +5x²-3x³-10x²+2x-3.
Here, we are given 4 functions. If (x+3) is a factor of any of these equations, then x = -3 and y = 0 must be a solution. Let us check each function one by one-
1. f(x) = x²-12x³ +54x² - 108x+81
putting x = -3, we get-
f(-3) = -3²-12(-3)³ +54(-3)² - 108(-3)+81
= 9+324+486+324+81
= 1,224
Thus, (x +3) is not a factor.
2. f(x)=x²-3x³-x+3
putting x = -3, we get-
f(-3) = -3²-3(-3)³-(-3)+3
= 9+81+9+3
= 102
Thus, (x +3) is not a factor.
3. f(x)=x+2x¹-23x³-60x²
putting x = -3, we get-
f(-3) = -3+2(-3)¹-23(-3)³-60(-3)²
= -3-6+621+540
= 1,152
Thus, (x +3) is not a factor.
4. f(x)= x³ +5x²-3x³-10x²+2x-3
putting x = -3, we get-
f(-3) = -3³ +5(-3)²-3(-3)³-10(-3)²+2(-3)-3
= -27+45+81-90-6-3
= 0
Thus, (x +3) is a factor of the function f(x)= x³ +5x²-3x³-10x²+2x-3.
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Select the 2 values of X that are root of this equation X² + 2X (-6) = 0
The two values that serves as the root of the equation are -1-√7 and -1+√7
Root of quadratic equationGiven the quadratic equation below;
X² + 2X (-6) = 0
x^2 + 2x - 6 = 0
Using the general formula
x = -2±√2²-4(1)(-6)/2(1)
x = -2±√4+24/2
x = -2±√28/2
x = -2±2√7/2
x = -1±√7
Hence the two values that serves as the root of the equation are -1-√7 and -1+√7
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nate works at a grocery store. he has 7 1/2 pounds of rasins. heis splitting them into 1/8 pound packages. how many packages can he make
Answer:
Nate can make 60 packages.
Step-by-step explanation:
7 1/2 is equivalent to 7 4/8, or 60/8
Divide 60/8 by 1/8 and you get 60.
another question i need quickly:
what do you do if the median is 0 and 1?
What if the median is zero?
A variable that can in principle be only zero or positive can only have mean zero if all values in practice are zero. On the other hand, such a variable can and will have median zero if more than half of the values are zero.
Can you have a median of one number?
Median of one number = the number itself.
I think of a number. I add 1090 to the number.
I subtract 450 from the result. The answer is 760.
What is the number I first thought of?
Answer:
120
Step-by-step explanation:
call the number x,
then x+1090-450
so x+640=760
x=760-640
x=120
hope this works :)
Answer:
120 is the number u thought of first
Step-by-step explanation:
1090-450=640
if we add 120 into 1090
then it will be 1210
so 1210-450=760
Write 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 ⋅ 12 in exponential form. Write your answer as: base^exponent
Answer: I could be wrong but I'm pretty sure it's 12^9 but again I could be wrong
Step-by-step explanation:
Select all the roots of 49?
Answer:
{2401, {-2401
Step-by-step explanation:
Sorry couldnt type the root symbol on my ipad.
Solve the inequality.
6 (x/2+4)>9
Answer is x > -5
fid comon demoninator
Answer: x>−5
Step-by-step explanation:
[tex]6(\frac{x}{2} +4) > 9[/tex]
Divide both sides by 6. Since 6 is positive, the inequality direction remains the same.
[tex]\frac{x}{2} +4 > \frac{9}{6}[/tex]
Reduce the fraction
[tex]\frac{9}{6}[/tex]
to lowest terms by extracting and canceling out 3.
[tex]\frac{x}{2} +4 > \frac{3}{2}[/tex]
Multiply both sides of the equation by 2. Since 2 is positive, the inequality direction remains the same.
x+8>3
Subtract 8 from both sides.
x>3−8
Subtract 8 from 3 to get −5.
x>−5