Find the equation of the line that passes through the points:
(-3, 3) and (3,-1)
Answer:
y=-2/3x+1
This is because (3--1/3--3) can be simplified to (-4/6) and simplified again to (-2/3) and then the y-intercept is 1.
Use logarithmic differentiation to find the derivative of the function. y=(ln(x+4)) x
the derivative of the function y = (ln(x + 4))x using logarithmic differentiation is given by y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))].
To find the derivative of the function y = (ln(x + 4))x using logarithmic differentiation, we can follow these steps:
Step 1: Take the natural logarithm of both sides of the equation:
ln(y) = ln((ln(x + 4))x)
Step 2: Use the logarithmic property ln(a^b) = b ln(a) to simplify the right-hand side of the equation:
ln(y) = x ln(ln(x + 4))
Step 3: Differentiate both sides of the equation implicitly with respect to x:
(1/y) * y' = ln(ln(x + 4)) + x * (1/ln(x + 4)) * (1/(x + 4))
Step 4: Simplify the expression on the right-hand side:
y' = y * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))]
Step 5: Substitute the original expression of y = (ln(x + 4))x back into the equation:
y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))]
Therefore, the derivative of the function y = (ln(x + 4))x using logarithmic differentiation is given by y' = (ln(x + 4))x * [ln(ln(x + 4)) + (1/ln(x + 4)) * (1/(x + 4))].
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2 x_{1}^{2} x_{2}^{2} -x_{1} x_{2} -3 x_{1} -3 x_{2}
Answer:
x₁(2x₁x₂² - x₂ - 3) - 3x₂
Step-by-step explanation:
The expression you provided is a polynomial in two variables, x₁ and x₂. Let's simplify it step by step:
2x₁²x₂² - x₁x₂ - 3x₁ - 3x₂
To simplify, we can look for common terms that can be factored out:
x₁(2x₁x₂² - x₂ - 3) - 3x₂
Now let's simplify the expression inside the parentheses:
2x₁x₂² - x₂ - 3
if a and b are directly proportional and b and c are directly proprtional, then how are a and c related
a and c are directly proportional to each other when a and b are directly proportional and b and c are directly proportional.
If a and b are directly proportional and b and c are directly proportional, it means that their ratios are equal. Direct proportionality implies that as one variable increases, the other also increases in proportion and as one variable decreases, the other also decreases in proportion.
Mathematically, this can be written as
a = kb and b = mc, where k and m are constants of proportionality.
Multiplying these two equations gives: a = kbm
Substituting the value of b from the second equation in the first equation, we get: a = kmc
Therefore, a and c are also directly proportional to each other with a constant of proportionality km.
Thus, if a increases by a certain factor, c will also increase by the same factor.
If a and b are directly proportional and b and c are directly proportional, then it can be concluded that a and c are directly proportional as well.
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True or false?
67.1 < 67.09
True or false?
1880.09 < 1880.023
Answer:
Step-by-step explanation:
67.1< (less than) 67.09
False
1880.09< (less than) 1880.023
False
One scoop of ice cream weighs
about 3 ounces. Last Thursday the
ice-cream parlor used 18 pounds of
ice cream. About how many scoops of
ice cream were served last Thursday?
Answer:
96 scoops
Step-by-step explanation:
First, Convert 18 pounds to ounces and that is 288 ounces
Next, Divide 288/3=96
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What is the simplified form of the expression? :
- 1/2(2x + 6)
Answer: - 1/(4x+12)
Step-by-step explanation:
- 1/2(2x + 6)
⇒ - 1/(4x+12)
Here are two rectangles.
6 cm
9 cm
8 cm
12 cm
Complete this sentence.
The two rectangles are similar and the scale factor is
Answer:
3/4
Step-by-step explanation:
Scale factor = 6/8 or 9/12 = 3/4
Olivia and her children went into a grocery store where they sell peaches for $2 each and mangos for $1 each. Olivia has $15 to spend and must buy no less than 8 peaches and mangos altogether. If x represents the number of peaches purchased and y represents the number of mangos purchased, write and solve a system of inequalities graphically and determine one possible solution
Let x be the number of peaches purchased and y be the number of mangos purchased.
We want to write a system of inequalities that represents the given conditions:
1. Olivia has $15 to spend, so the total cost of the peaches and mangos must be less than or equal to $15:
2x + y ≤ 15
2. Olivia must buy no less than 8 peaches and mangos altogether, so the total number of peaches and mangos purchased must be greater than or equal to 8:
x + y ≥ 8
To solve this system of inequalities graphically, we can plot the lines corresponding to each inequality on the same graph and shade the region that satisfies both inequalities. The solution will be any point in the shaded region.
To plot the line 2x + y = 15, we can find the intercepts:
when x = 0, y = 15when y = 0, x = 7.5So we can plot the points (0, 15) and (7.5, 0), and draw a line passing through them.
To plot the line x + y = 8, we can find the intercepts:
when x = 0, y = 8when y = 0, x = 8So we can plot the points (0, 8) and (8, 0), and draw a line passing through them.
The shaded region that satisfies both inequalities is the region below the line 2x + y = 15 and above the line x + y = 8.
Here is a graph of the two lines and the shaded region:
| /
15 | /
| / .
| / |
| / |
| / |
-------+----------+------
| |
| |
| |
| |
8 |----------+------
0 8
The shaded region corresponds to the points that satisfy both inequalities, which include (2, 6), (3, 5), (4, 4), (5, 3), (6, 2), and (7, 1). Each of these points represents a possible combination of the number of peaches and mangos that Olivia can buy within her budget and the requirement to buy at least 8 peaches and mangos altogether.
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HELPPP WHAT IS THE ANSWER DONT SENT A FILE PLZ EXPLAIN STEP BY STEP PLZ I DINT HAVE A LOT OF TIME
Answer:
2nd option
Step-by-step explanation:
Consider the coordinates of T(- 3, 3 ) → T' (3, - 1 )
- 3 → 3 is 6 units right in the positive x-direction
3 → - 1 is 4 units down in the negative y- direction
Then translation rule is
(x, y ) → (x + 6, y - 4 )
Find the length of the line segment displayed below. Round your answer to the nearest hundredth (2 decimal places)
Length of segment AB = units
Answer:
AB=5.83
Step-by-step explanation:
Distance Formula=
\( \sqrt{(x2 - x1)^{2} - (y2 - y1)^{2} } \)
Plugging our values in, we get:
\( \sqrt{(7 - 2)^{2} + (4 - 1)^{2} }\)
And if we solve it like this:
\( \sqrt{25 + 9} \)
We end up with:
\( \sqrt{34} \)
Which is about 5.83
graph the line with slope -6 and y-intercept of 5
Answer:
here you go. :)
Step-by-step explanation:
Look at the image attached
An airplane altitude in feet during its descend can be found using the function f(x)=-200x+20,000. After new government regulations become law the descent is now modeled by the function g(x)=-200x+20,500. Which statement describes the change?
Answer:
The airplane starts its descent from an altitude 500 feet higher.
Step-by-step explanation:
Given that:
F(x) = - 200x+20,000
g(x) = -200x+20,500
The functions are written in slope intercept format :
With a negative slope, the intercept gives the point which the rate of change begins in the vertical axis :
The slope is -200 ; which means that the descent rate of the airplane is 200
The intercept value however changes from 20,000 in f(x) to 20500 in g(x). This means that the height at which descent starts is now at a height of 20500 which is (20500 - 20000) = 500 miles higher than before.
please answer!! THIS IS ALL THE POINTS I HAVE LEFT SINCE NOBODY IS ANSWERING MY OTHER QUESTIONS :(
~~~~~~~~~~~~~
Answer:
The height of the parallelogram relates to the height of the circle because it is equal to the radius of the circle. The height goes from the circumference to the point of any section of the circle. I hope this helps.
Step-by-step explanation:
Answer: Well I will try to answer it
Step-by-step explanation:
A. I would say that the height of the base of the parallelogram its related to the circle since the base have the SAME shape of the circle. The height goes from the circumference to the point of any section of the circle and the radius well, it's the same.
B. I'm not so sure sorry
ANSWER QUICKLY PLZZZZZZ ASAP
Answer:
m = 2G² + 5Step-by-step explanation:
\(G = \sqrt{ \frac{m - 5}{2} }\)
To make m the subject square both sides of the equation
That's
\( \frac{m - 5}{2} = {G}^{2} \)
Cross multiply
m - 5 = 2G²
Move 5 to the right side of the equation to make m stand alone
We have the final answer as
m = 2G² + 5Hope this helps you
Answer:
A semi-circle sits on top of a rectangle to form the figure below. Find its area and perimeter. Use 3.14 for .
The rectangle is 4 inches long and 3 inches wide. The semi-circle sits on top of the rectangle on a side that is 4 inches long.
Step-by-step explanation:
Sunrise Middle School is holding a carwash to raise money for their various school sport teams. The cost is $10 for SUV's and $5 for cars. Twenty-five percent of the money raised goes to the football team, thirty percent goes to the soccer team and the remaining percentage goes toward the basketball team. Write an expression to represent how much the basketball team will receive. Let S represent number the SUV's and Let C represent the number of cars
the expression to represent how much the basketball team will receive is:
$4.50S + $2.25C
To find the amount that the basketball team will receive from the car wash, we need to start by finding the total amount of money raised. We can do this by multiplying the number of SUVs by $10 and the number of cars by $5, and adding those two products together. So the total amount raised can be expressed as:
Total amount = $10S + $5C
Next, we need to determine what percentage of the total amount will go to the basketball team. We know that 25% goes to the football team, 30% goes to the soccer team, and the remaining percentage goes to the basketball team. We can express this as:
Basketball team's share = (100% - 25% - 30%) x Total amount
Simplifying this expression, we get:
Basketball team's share = 45% x Total amount
Substituting the expression for the total amount that we found earlier, we get:
Basketball team's share = 45% x ($10S + $5C)
Simplifying this expression further, we get:
Basketball team's share = $4.50S + $2.25C
So the expression to represent how much the basketball team will receive is:
$4.50S + $2.25C
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-4(3m−3)+ (−10+8m)=?
It has been determined that 15% of all cars tested emit excessive hydrocarbons, 12% emit excessive CO, and 8% emit excessive amounts of both. Find the probability that emissions of both hydrocarbons and CO are excessive. Round your answer to 2 decimal places.
The probability that emission of both CO and hydrocarbon is in excess is 0.8.
What is probability?The proportion of favorable cases to all possible cases used to determine how likely an event is to occur.
Let, A be the event in which cars are emitting excess CO:
P(A) = 0.12
Let, B be the event in which cars are emitting excess hydrocarbons:
P(B) = 0.15
The cars which emit both CO and Hydrocarbons in:
P(A∩B) = 0.8
The probability that emission of both CO and hydrocarbon is in excess is 0.8.
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A well, whose diameter is 3 m, has been dug 21 m deep and the earth dug out is used to form an embankment 4 m wide around it. Find the height of the embankment.
Answer:
31.875 m
Step-by-step explanation:
We can begin solving the problem by using the formula for the volume of a cylinder and the volume of a cone.
The volume of the well is given by the formula for the volume of a cylinder:
V = πr^2h
where r is the radius of the well (half the diameter, which is 3/2 = 1.5 m) and h is the depth of the well (21 m).
V = π(1.5)^2(21) = 42.5π m^3
The embankment is formed by the earth that was dug out of the well, and it has the shape of a cone. The volume of the cone is given by the formula:
V = 1/3 πr^2h
where r is the radius of the base of the cone (4 m) and h is the height of the embankment.
V = 1/3π(4)^2h = 4/3πh m^3
Now we know that the volume of the embankment is equal to the volume of the well:
V = 42.5π m^3 = 4/3πh m^3
Then we can solve for h by dividing both sides by 4/3π:
h = 42.5π m^3 * 3/4π = 31.875 m
So the height of the embankment is 31.875 m.
525 corn plants, which are all arranged in rows. the number of plants in each row is 4 less than the number of rows. how many rows of corn plants are on the farm?
The required number corn plants are on the farm are 21.
How to find the number of plants in the row of garden?metre stick counting techniques. Count the seedlings for each metre of the row using a metre stick. To calculate plants per square metre, multiply that amount by 100, then divide it by the seed spacing in centimeters.
According to data:Let the number of rows be x.
the number of corn plants = x - 4
So,
x(x - 4) = 525
x^2 - 4x - 525 = 0
On solving the above quadratic equation, we get
x = 25, x = -21
Thus, number of corn plants in the row are 52 - 4 = 21
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M + 4 +2 -7m + 6 like terms coefficient and constant
Answer:
-6m + 12
Step-by-step explanation:
Step 1: Write expression
M + 4 + 2 - 7m + 6
Step 2: Simplify
Combine like terms (m): -6m + 4 + 2 + 6Combine like terms (constants): -6m + 12Need help with this please
the curve of function 1 "y = 56(1.13ˣ)" fits the best to the given dot plot.
What is the function?A relationship between a group of inputs and one output is referred to as a function. In plain English, a function is an association between inputs in which each input is connected to precisely one output. A domain, codomain, or range exists for every function. Typically, f(x), where x is the input, is used to represent a function.
Given, three functions and their graphs but only function 1 "y = 56(1.13ˣ)"
fit the best to the given dot plot.
The curve of best fit estimates a straight line or curve that minimizes the distance between itself and where observations fall in some data set.
The curve of best fit is used to show a trend or correlation between the dependent variable and independent variable(s). It can be depicted visually, or as a mathematical expression.
Thus. Figure 1 is the best suited for the dot plot.
So the value of the item at time x = 13
y = 56(1.13¹³)
y = 274.28
Therefore, the curve of function 1 "y = 56(1.13ˣ)" fits the best to the given dot plot.
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Can 3 over 11/2 and 6 over 11 be a proportion?? Please explain!!! ASAP
Answer:
Yes! these are in the same proportion
Step-by-step explanation:
Lhs = 3 over 11/2 = 3/(11/2)
=>3× (2/11)
=> 6/11
=> Rhs
what's
\( \sqrt{225} \)
Answer:
Simplify the radical by breaking the radicand up into a product of known factors, assuming positive real numbers.
15
Step-by-step explanation:
Hope it is helpful....
Answer:
The Square root of 225 is 15
PLEASEE HELP
What is the area of this triangle?
9514 1404 393
Answer:
A = (y2 -y1)(x3 -x1)/2
Step-by-step explanation:
It is convenient to use the vertical line as the base. Its length will be the difference of y-coordinates: (y2 -y1)
Then the altitude is the perpendicular distance from that line to (x3, y3). That distance will be the difference of the x-coordinates: (x3 -x1).
The area is given by the usual formula for the area of a triangle:
A = 1/2bh
A = 1/2(y2 -y1)(x3 -x1)
The table below shows the values of f(x) for different values c
Use this information to work out the values of a and b.
Give each of your answers as an integer or a decimal.
0
f(x) 7
1 2 3
10
13
✓ Scroll down
16
Answer:
16
Step-by-step explanation:
Select the correct answer from the drop-down menu.
Triangle ABC is shown with angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees.
In this triangle, the product of tan A and tan C is
.
In this triangle, the product of tan A and tan C is `(BC)^2/(AB)^2`.
The given triangle ABC has angle A measuring 45 degrees, angle B measuring 90 degrees, and angle C measuring 45 degrees , Answer: `(BC)^2/(AB)^2`.
We have to find the product of tan A and tan C.
In triangle ABC, tan A and tan C are equal as the opposite and adjacent sides of angles A and C are the same.
So, we have, tan A = tan C
Therefore, the product of tan A and tan C will be equal to (tan A)^2 or (tan C)^2.
Using the formula of tan: tan A = opposite/adjacent=BC/A Band, tan C = opposite/adjacent=AB/BC.
Thus, tan A = BC/AB tan C = AB/BC Taking the ratio of these two equations, we have: tan A/tan C = BC/AB ÷ AB/BC Tan A * tan C = BC^2/AB^2So, the product of tan A and tan C is equal to `(BC)^2/(AB)^2`.
Answer: `(BC)^2/(AB)^2`.
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Find the values of x and y.
Answer:
\( \boxed{x = 15,y = 17} \)
Step-by-step explanation:
\(Vertically \: opposite \: angles \: area \: equal \\ \\ So, \\ \\ = > 7x \degree + 7\degree = 112\degree \\ \\ = > 7x\degree = 112\degree - 7\degree \\ \\ = > 7x\degree = 105\degree \\ \\ = > x\degree = \frac{105}{7} \degree \\ \\ = > x\degree = 15\degree \\ \\ \\ \\ Supplementary \: angles \: add \: up \: to \: 180 \degree \\ \\ So, \\ \\ = >4y\degree + 112\degree = 180\degree \\ \\ = > 4y\degree = 180\degree - 112\degree \\ \\ = > 4y\degree = 68\degree \\ \\ = > y \degree= \frac{68}{4} \degree \\ \\ = > y\degree = 17\degree\)
Find the values of x and y.
Step-by-step explanation:
C : x = 17,y = 15
A study shows that 70% of the population of a city have brown eyes and 30% do not. The study also shows that 10% of the people who do not have brown eyes do
not have brown hair, while 80% of the people who have brown eyes have brown hair. A relative frequency table was constructed for this data. What is the largest
marginal relative frequency and its interpretation?
A. 0.56; Individuals with brown eyes
B. 0.70; Individuals with brown eyes
C. 0.80; Individuals with brown hair
D. 0.83; Individuals with brown hair
A study shows that 70% of the population of a city have brown eyes and 30% do not. The study also shows that 10% of the people who do not have brown eyes do not have brown hair, while 80% of the people who have brown eyes have brown hair. 0.80; Individuals with brown hair. Option C
What is the marginal relative frequency?Generally, The largest marginal relative frequency is 0.80, which corresponds to individuals with brown hair. This means that out of all the individuals in the city, 80% of them have brown hair.
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Can y’all help with this one
Answer:
i think c
Step-by-step explanation: