Answer:
y = -\(\frac{4}{3}\)x-7
Step-by-step explanation:
y=mx+b where m = the slope and b = the y intercept
the slope = change over y/change over x = (5-(-3))/(-9-(-3))=(5+3)/(-9+3)=8/(-6)=4/(-3)
y=-4/3x+b
plug in one of the points (it can be either)
-3=-4/3(-3)+b
-3=4+b
b=-7
y=-4/3x-7
Find the unknown 9,006-7,474?
Which of the following logarithmic equations is equivalent to the exponential
equation below?
e^x = 15.29
Answer:
Step-by-step explanation:
Natural log and the number 'e' are inverse to each other. Therefore, if you take the natural log of both sides, the exponential cancels and leaves 'x' isolated:
\(ln(e^x)=ln(15.29)\)
\(x=ln(15.29)\)
Let's solve for x
e^x=15.29So natural logarithm on both sides
\(\\ \rm\Rrightarrow x=ln(15.29)\)
\(\\ \rm\Rrightarrow x=2.73\)
State the center point and radius of the circle. Write the equation of the circle in standard and general form.
Answer:
center: (2, -1)radius: 4standard form: (x -2)² +(y +1)² = 16general form: x² +y² -4x +2y -11 = 0Step-by-step explanation:
You want the center, radius, and equations in standard form and general form for the circle shown in the graph.
CenterThe center is the point marked. Its coordinates are ...
(x, y) = (2, -1)
RadiusThe radius is the distance from the center to any point on the circle. It is usually convenient to read the radius on a graph by considering points on the same horizontal or vertical line as the center of the circle.
Here, the circle passes through point (6, -1), so the radius is 6 -2 = 4.
The radius is 4 units.
Standard formThe standard form equation for a circle with center (h, k) and radius r is ...
(x -h)² +(y -k)² = r²
For center (2, -1) and radius 4, this is ...
(x -2)² +(y +1)² = 16 . . . . standard form equation
General formThe general form of a polynomial equation is f(x, y) = 0, with the terms listed in lexicographical order by decreasing degree. This is found from the standard form by expanding it, combining terms, and arranging them in the required order:
(x -2)² +(y +1)² = 16 . . . . . standard form
x² -4x +4 +y² +2y +1 -16 = 0 . . . . . eliminate parentheses, subtract 16
x² +y² -4x +2y -11 = 0 . . . . general form equation
please help :( I know that \(2^\frac{6}{5}\) is the same as \(2\sqrt[5]{2}\) but I don't understand how to get \(2\sqrt[5]{2}\) from \(2^\frac{6}{5}\)
Answer:
\(\displaystyle 2^{\frac{6}{5}}=2\sqrt[5]{2}\)
Step-by-step explanation:
Fractional Exponents
An expression like
\(\displaystyle a^{\frac{n}{m}}\)
can be expressed as a radical of the form:
\(\sqrt[m]{a^n}\)
We have the expression:
\(\displaystyle 2^{\frac{6}{5}}\)
Its equivalent radical form is:
\(\displaystyle 2^{\frac{6}{5}}=\sqrt[5]{2^6}\)
Since the exponent is greater than the index of the radical, we can take 2 out of it by following the procedure:
\(\sqrt[5]{2^6}=\sqrt[5]{2^5\cdot 2}\)
Taking out \(2^5\) from the radical:
\(\sqrt[5]{2^6}=2\sqrt[5]{2}\)
Thus:
\(\displaystyle 2^{\frac{6}{5}}=2\sqrt[5]{2}\)
Please help me!!! I'm being timed right now do please help me!!!
Answer:
The answer would be 2. Which means that your answer would be option 1 I believe.
Step-by-step explanation:
This figure consists of a rectangle and a quarter circle.
What is the perimeter of this figure?
Use 3.14 for π.
Enter your answer as a decimal in the box.
cm
Answer:
75.27
Step-by-step explanation:
Rectangle = 20+2+2+20-11=47
quarter circle = 1/4(2)(11)(3.14)=17.27 + 11 = 28.27
47+28.27=75.27
Answer:
75.27.cm
Step-by-step explanation:
it works i got a 100 on the test
to sell suren
2 Aling Maring is going to set
in bundles. What is the least
number of suman that she could
Sell in bundles of 3 and 5
Parent's Signature
Answer:
15 bundles
Step-by-step explanation:
Given
\(Bundles= 3\)
\(Bundles= 5\)
Required
The least number of bundles that could be sold
To do this, we simply calculate the LCM of the given number of bundles.
For 3, we have:
\(Bundles = 3, 6, 9, 12, 15, 18...\)
For 5, we have:
\(Bundles = 5, 10, 15, 20...\)
The least common factor between both is: 15. Hence, the least number of bundles is 15
Suppose that ƒ is a function given as f(x) = 4x² + 5x + 3.
Simplify the expression f(x + h).
f(x + h)
Simplify the difference quotient,
ƒ(x + h) − ƒ(x)
h
=
Submit Question
The derivative of the function at x is the limit of the difference quotient as h approaches zero.
f(x+h)-f(x)
f'(x) =lim
h→0
h
ƒ(x + h) − f(x)
h
=
Answer:
f(x +h) = 4x² +4h² +8xh +5x +5h +3
(f(x+h) -f(x))/h = 4h +8x +5
f'(x) = 8x +5
Step-by-step explanation:
For f(x) = 4x² +5x +3, you want the simplified expression f(x+h), the difference quotient (f(x+h) -f(x))/h, and the value of that at h=0.
F(x+h)Put (x+h) where h is in the function, and simplify:
f(x+h) = 4(x+h)² +5(x+h) +3
= 4(x² +2xh +h²) +5x +5h +3
f(x +h) = 4x² +4h² +8xh +5x +5h +3
Difference quotientThe difference quotient is ...
(f(x+h) -f(x))/h = ((4x² +4h² +8xh +5x +5h +3) - (4x² +5x +3))/h
= (4h² +8xh +5h)/h
(f(x+h) -f(x))/h = 4h +8x +5
LimitWhen h=0, the value of this is ...
f'(x) = 4·0 +8x +5
f'(x) = 8x +5
__
Additional comment
Technically, the difference quotient is undefined at h=0, because h is in the denominator, and we cannot divide by 0. The limit as h→0 will be the value of the simplified rational expression that has h canceled from every term of the difference. This will always be the case for difference quotients for polynomial functions.
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Whirly Corporation’s contribution format income statement for the most recent month is shown below:
Total Per Unit
Sales (8,700 units) $ 287,100 $ 33.00
Variable expenses 165,300 19.00
Contribution margin 121,800 $ 14.00
Fixed expenses 55,600
Net operating income $ 66,200
Required:
(Consider each case independently):
1. What would be the revised net operating income per month if the sales volume increases by 40 units?
2. What would be the revised net operating income per month if the sales volume decreases by 40 units?
3. What would be the revised net operating income per month if the sales volume is 7,700 units?
Last month when Holiday Creations, Incorporated, sold 37,000 units, total sales were $148,000, total variable expenses were $115,440, and fixed expenses were $35,800.
Required:
1. What is the company’s contribution margin (CM) ratio?
2. What is the estimated change in the company’s net operating income if it can increase sales volume by 500 units and total sales by $2,000? (Do not round intermediate calculations.)
1. Revised Net Operating Income = $66,760
2. Revised Net Operating Income =$64,640
3. Revised Net Operating Income =$52,
1. If the sales volume increases by 40 units:
So, New Sales = 8,700 units + 40 units = 8,740 units
and, New Contribution Margin =
= $14.00 x 8,740 units
= 122, 360
New Fixed Expenses remain the same at $55,600
Then, Revised Net Operating Income
= New Contribution Margin - New Fixed Expenses
= 122360 - 55600
= 66,760.
2. If the sales volume decreases by 40 units:
New Sales = 8,700 units - 40 units = 8,660 units
New Contribution Margin
= 14 x 8660
= 121,240
New Fixed Expenses remain the same at $55,600
Then, Revised Net Operating Income
= New Contribution Margin - New Fixed Expenses
= 65,640
3. If the sales volume is 7,700 units:
New Sales = 7,700 units
New Contribution Margin
= 14 x 7700
= 107,800
New Fixed Expenses remain the same at $55,600
Then, Revised Net Operating Income
= New Contribution Margin - New Fixed Expenses
= 52, 200
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Which of the following expressions does NOT represent
91 +91 + 91?
O 91(3)
O 91.3
O (91)(3)
0913
Answer:
91.3 and 0913
Step-by-step explanation:
91 + 91 + 91 is an expression that can be simplified into a multiplication problem, because there is a number being added by itself a certain amount of times. So we have to look for a multiplication problems within our answers.
Leading us up to 91(3) and (91)(3), these are both examples of multiplcation.
91.3 would happen if you were adding .3 to 91
And 0913 would happen if you added 91 and 822
Plz help just solve quicklyyy
Answer:
d
Step-by-step explanation:
what’s the answer to this question? i need your help
-2(-7m - 4) + 1
Answer:
14m + 9
Step-by-step explanation:
Answer:
14m+9
Step-by-step explanation:
-2(-7)=14m
-2(-4)=8+1
14m+9
Hope this helps! :)
I need help I'll give out 40 points quickly
Answer:
The figure in the upper right corner.
A trapezoid has two parallel sides
Step-by-step explanation:
Answer:
The answer would be the shape on the right side on the top! NOT THE Rectangle (on the right bottom side) or the rhombus (on the left top side). The shape on the left bottom side IS a trapezoid.
Hope that helps. And this wasnt worth 40 points, it was only 5 points!?
The points J (9,7), K (2,1), L(0,−8) and M (7,−2) form quadrilateral JKLM.
Plot the points
slope of JK =
length of JK =
slope of KL =
length of KL =
slope of LM =
length of LM =
slope of MJ =
length of MJ =
Quadrilateral JKLM can BEST be described as
Quadrilateral JKLM has sides with equal lengths (√85), and the slopes of opposite sides are equal. However, it is not a special type of quadrilateral like a rectangle or a square.
To describe quadrilateral JKLM, let's first plot the given points J(9, 7), K(2, 1), L(0, -8), and M(7, -2) on a coordinate plane:
J(9, 7) K(2, 1)
L(0, -8) M(7, -2)
To find the slopes and lengths of each side of the quadrilateral, we can use the distance formula and the slope formula.
Slope of JK:
Slope (m) = (change in y) / (change in x)
m(JK) = (7 - 1) / (9 - 2) = 6/7
Length of JK:
Length (d) = √[(x2 - x1)^2 + (y2 - y1)^2]
d(JK) = √[(9 - 2)^2 + (7 - 1)^2] = √(49 + 36) = √85
Slope of KL:
m(KL) = (-8 - 1) / (0 - 2) = -9/2
Length of KL:
d(KL) = √[(0 - 2)^2 + (-8 - 1)^2] = √(4 + 81) = √85
Slope of LM:
m(LM) = (-2 - (-8)) / (7 - 0) = 6/7 (same as slope of JK)
Length of LM:
d(LM) = √[(7 - 0)^2 + (-2 - (-8))^2] = √(49 + 36) = √85
Slope of MJ:
m(MJ) = (7 - (-2)) / (9 - 7) = 9
Length of MJ:
d(MJ) = √[(7 - 9)^2 + (-2 - (-8))^2] = √(4 + 36) = √40
Based on the calculations, we can describe quadrilateral JKLM as follows:
The slope of JK and LM is 6/7.
The slope of KL is -9/2.
The slope of MJ is 9.
The length of each side (JK, KL, LM, MJ) is √85.
The quadrilateral is not a rectangle or a square since the slopes of opposite sides (JK and LM) are not perpendicular.
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The number of people attending a football match as audience is stated as 31200,
correct to 3 significant figures. What could be largest and the smallest possible number
of people attending the match?
The largest possible number of people attending the match is 31,249, and the smallest possible number is 31,100.
To determine the largest and smallest possible number of people attending the football match, given that the figure is stated as 31,200 with 3 significant figures, we need to consider the range of values that can be represented within that significant figures constraint.
For a number to be stated with 3 significant figures, the last significant figure is uncertain and can be either rounded up or down.
To find the largest and smallest possible numbers, we'll consider the cases where the last significant figure is rounded up and rounded down.
Rounding up:
If we round up the last significant figure, the possible range of values is from 31,150 to 31,249.
So the largest possible number of people attending the match would be 31,249.
Rounding down:
If we round down the last significant figure, the possible range of values is from 31,100 to 31,199.
So the smallest possible number of people attending the match would be 31,100.
Therefore, the largest possible number of people attending the match is 31,249, and the smallest possible number is 31,100.
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Determine a series of transformations that would map Figure J onto Figure K. J
Figure.
Figure
Figure J is rotated 90° clockwise and then translated by 3 units toward the right.
What is a transformation of a shape?A point, line, or mathematical figure can be converted in one of four ways, and each has an effect on the object's structure and/or position.
Rotation does not change the shape and size of the geometry. But changes the orientation of the geometry.
The translation does not change the shape and size of the geometry. But changes the location.
Figure J is rotated 90° clockwise and then translated by 3 units toward the right.
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Answer 70 Points!
The local government is concerned with the population of a new predatory fish, the tiger gar, which was first observed in Lake Richmond about 5 years ago.
The following table shows the approximate number of tiger gars living in the lake since 2016
This is an example of Exponential _________.
A. Decay
B. Growth
Answer:
Step-by-step explanation:
Use the slope formula to find the slope of the line through the points (−4,2) and (−9,−10).
Answer:
2.4 or 12/5
Step-by-step explanation:
The slope formula is (y2-y1) divided by (x2-x1).
First, you label each number by their x and y.
-4 will be axis x 1
2 will be axis y 1
-9 will be axis x 2
-10 will be axis y 2.
Then substitute the variable into the formula.
(-10 subtract 2) divided by (-9-(-4)).
Next, solve. Once you solve you will get -12/-5 = 2.4
Finally, simplify the answer. if it is already simplify, that will be the answer.
PRE CALC HELP NEEDED
Answer:
\(\dfrac{5e^2}{2}\)
Step-by-step explanation:
Differentiation is an algebraic process that finds the slope of a curve. At a point, the slope of a curve is the same as the slope of the tangent line to the curve at that point. Therefore, to find the slope of the line tangent to the given function, differentiate the given function.
Given function:
\(y=x^2\ln(2x)\)
Differentiate the given function using the product rule.
\(\boxed{\begin{minipage}{5.5 cm}\underline{Product Rule for Differentiation}\\\\If $y=uv$ then:\\\\$\dfrac{\text{d}y}{\text{d}x}=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}$\\\end{minipage}}\)
\(\textsf{Let\;$u=x^2}\)\(\textsf{Let\;$u=x^2$}\implies \dfrac{\text{d}u}{\text{d}x}=2x\)
\(\textsf{Let\;$v=\ln(2x)$}\implies \dfrac{\text{d}v}{\text{d}x}=\dfrac{2}{2x}=\dfrac{1}{x}\)
Input the values into the product rule to differentiate the function:
\(\begin{aligned}\dfrac{\text{d}y}{\text{d}x}&=u\dfrac{\text{d}v}{\text{d}x}+v\dfrac{\text{d}u}{\text{d}x}\\\\&=x^2 \cdot \dfrac{1}{x}+\ln(2x) \cdot 2x\\\\&=x+2x\ln(2x)\end{aligned}\)
To find the slope of the tangent line at x = e²/2, substitute x = e²/2 into the differentiated function:
\(\begin{aligned}x=\dfrac{e^2}{2}\implies \dfrac{\text{d}y}{\text{d}x}&=\dfrac{e^2}{2}+2\left(\dfrac{e^2}{2}\right)\ln\left(2 \cdot \dfrac{e^2}{2}\right)\\\\&=\dfrac{e^2}{2}+e^2\ln\left(e^2\right)\\\\&=\dfrac{e^2}{2}+2e^2\\\\&=\dfrac{5e^2}{2}\end{aligned}\)
Therefore, the slope of the line tangent to the graph of y = x²ln(2x) at the point where x = e²/2 is:
\(\boxed{\dfrac{5e^2}{2}}\)
State the groups of shapes
Answer:
The groups are round shapes, triangles, quadrilaterals, pentagons, and hexagons.
Step-by-step explanation:
The groups are round shapes, triangles, quadrilaterals, pentagons, and hexagons.
What is the meaning of "the cancellation laws"?
Each step of this theorem is proved below.
Given that,
S is finite,
Now enumerate all of its elements as x₁, x₂,..., x\(_{n}\).
According to the cancellation rule,
This product is independent of the order of the factors.
As a result, we can define the identity element e as this product.
It is simple to demonstrate that e meets the criteria of an identity element.
Now, let's show that every element of S has an inverse.
Let a be any element of S. Consider the set {a, a, a, ...}.
Since S is finite,
There exist positive integers m and n such that
am = an for some m > n.
By the cancellation law,
We can cancel a power of a from both sides to get a\({(m-n)}\) = e.
This means that a has an inverse, and we can conclude that S is a group.
Consider the set of all positive integers under addition, except 1, as an example of an infinite semigroup in which the cancellation laws hold but which is not a group.
This set clearly meets the cancellation laws, but it does not have an inverse for every element, because the inverse of 2, for example, is not an integer.
As a result, this is not a group.
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Which ones right ????
3x-2y>2. can someone please help me.. i hate math
The inequality is graphed and attached
How to make inequality graphsThere are some points that help in interpreting inequality graphs.
the x values are also called the domain lets assume -4 0 4. this is substituted into the equation 3x - 2y > 2 to get the values in the y direction.
3x - 2 > y
y < 3x - 2
for x = -4
y < 3 * -4 - 2 = -14
for x = 0
y < 3 * 0 - 2 = -2
for x = 4
y < 3 * 4 - 2 = 10
table of values
x y
-4 -14
0 -2
4 10
y < 3x - 2 is the equation
Then use of dashed lines of dashed lines or solid lines
dashed lines means there is no equality sign in the inequality > OR < hence used for the problem
solid line means there is equality in the inequality ≤ OR ≥
Another part is the shaded portion
shading above the line defines greater than shading below the line defines less than. The equation has less than and the shading is below the line
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Read the following prompt and type your response in the space provided.
Sarah has a $30 music gift card. Each day she uses it to buy a $1.99 song download. For how many days will the gift card have still have a balance of more than $18?
Write an inequality to solve the problem and then solve showing your work. Explain what the solution to the inequality means.
Answer:
She will have a balance of more than $18 for up to 6 days
Step-by-step explanation:
Start with $30.
Each day, x, subtract $1.99 from $30.
30 - 1.99x
The amount must be greater than $18.
30 - 1.99x > 18
Subtract 30 from both sides.
-1.99x > -12
Divide both sides by -1.99. Remember than when you multiply or divide both sides of an inequality by a negative number, the inequality sign changes direction.
-1.99x/(-1.99) < -12/(-1.99)
x < 6.03
The number of days must be less than 6.03. Since we deal with whole days, she will have a balance of more than $18 for up to 6 days.
the equation y=3.25x + 8.5 models the distance,y, in miles, that the athlete will run in week x. for which week is the number of miles given by the equation greater than the actual number of miles the athlete will run?
We will need to check for each week
y = 3.25x + 8.5
week 1
substitute x = 1 in the above
y = 3.25(1) + 8.5 = 3.25 + 8.5 = 11.75
11.75 is less than 13
week 2
substitute x= 2 into the equation
y = 3.25(2) + 8.5 = 6.5 + 8.5 = 15
15 is less than 15.5
week 3
substitute x=3 into the equation
y = 3.25(3) + 8.5 = 9.75 + 8.5 = 18.25
18.25 is greater than 15.5
week 4
substitute x=4 into the equation
y =3.25(4) + 8.5 = 13 + 8.5 = 21.5
21.5 is less than 22.5
week 5
substitute x = 5 into the equation
y = 3.25(5) + 8.5 = 16.25 + 8.5=24.75
This is greater than 23
week6
substitute x=6 into the equation
y = 3.25 (6) + 8.5 = 19.5 + 8.5 =28
28 is less than 30
Hence in week 3 and week 5, the number of miles given by the equation is greater than the actual number of miles the athlete will run.
Help please I need to finish this really fast
Which statement best describes the relationship between the two figures?
A.Figure RT is congruent to figure R'S'T
B.Figure RST is bigger than figure R'S'T'
C.The measure of angle R is equal to the measure of angle S
D.The measure of angle R is equal to the measure of angle T
Answer:
A. Figure RST is congruent to figure R'S'T
Step-by-step explanation:
URGENT !!! Which expression is equivalent to
corey calculated the midpoint of AB with A (-3.5) and a B (1,7). What is corry's error?
Step-by-step explanation:
He,smixing x and y values and averaging them. You add x of one point and add to the x value of the second point. Then divide by 2. Do the same with the y values.
Work out the circumference of this circle.
Give your answer in terms of 3.142
6 mm
Please help me answer this question . thanks for any help! (;
Answer:
(c) h(x) has the smallest minimum; it is -6
Step-by-step explanation:
We're comparing three different functions to determine which has the smallest minimum:
H(x) has the minimum -6.
g(x) has a parabolic graph. Its vertex is at (3, -1) and so its minimum is -1
f(x) is a sinusoidal function with amplitude 2. The smallest value that 2 sin (3x + pi) can take on is -2, from which we subtract -2, to obtain the minimum -4.
Answer (c) is correct: The smallesst minimum is -6 and that is for function h(x).