y2-y1/x2-x1
= (-1-3)/(5+1)
= -4/6
= -2/3
y = -(2/3)x + c
3 = (2/3) + c
c = -2/3 + 3
c = -2/3 + 9/3
c = -7/3
y = (2/3)x + (7/3)
The derivative of the function f is given by f′(x)=x^2−2−3xcosx. On which of the following intervals in [−4,3] is f decreasing?
The function f'(x) = x² - 2 - 3xcosx is decreasing on (- 4, - 3) and (- 1, 1).
What is a function?A function can be defined as the outputs for a given set of inputs.
The inputs of a function are known as the independent variable and the outputs of a function are known as the dependent variable.
Given, A function f'(x) = x² - 2 - 3xcosx.
We know a function f(x) is decreasing if f'(x) is < 0.
Therefore,
x² - 2 - 3xcosx < 0.
x² - 3xcosx < 2.
x(x - 3cosx) < 2.
Now, 3cosx can be [- 3, 3].
x(x - 3) < 2 and x(x + 3) < 2.
x < 2 Or x - 3 < 2 and x < 2 or x + 3 < 2.
x < 2 Or x < 5 and x < 2 or x < - 1.
But x should be in [- 4, 1], Therefore it is decreasing at (- 4, - 3) and (- 1, 1).
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1. Jason made 3 quarts of corn chowder. He divided it into serving sizes of 1 12 cups each. How many 1 12 -cup servings can be made from 3 quarts of chowder? A. 4 12 servings B. 8 servings C. 12 servings D. 18 servings
Answer:
B. 8 servings
Step-by-step explanation:
1 quart = 4 cups
3x4=12
3 quarts of clam chowder = 12 cups of chowder
1 1/2 cups each
12 divided by 1 1/2 = 12 divided by 3/2 = 12 divided by 2/3 = 8 servings
Calculate the sector area: 16 in 90°
Therefore , the solution of the given problem of area comes out to be
r = 8.
Define area.The term "area" describes the amount of space occupied by a 2D form or surface. We use cm2 or m2 as our units for measuring area. A shape's area is determined by dividing its length by its breadth.
Here,
A 90 degree sector occupies 1/4 of a circle, which has 360 degrees. Consequently, the area of the whole circle can be written as
Sector Size/Sector Area = Circle Area/360
16 ft2/90 = n/360
(360) (16 ft2)/90 = n
(4)(16 ft2) = n
The total size of the circle is n = 64 ft2.
Since Area of a Circle equals r2,
∏r2 = 64
r2 = 64/∏
r = √(64/∏)
We multiply by / to get by rationalizing the denominator.
r = √(64∏)/√(∏2) Then using the denominator's square root, we can obtain the solution of
r = √(64∏)/∏
r = 8
Therefore , the solution of the given problem of area comes out to be
r = 8.
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The midpoint of \overline{\text{AB}} AB is M(7, -7)M(7,−7). If the coordinates of AA are (8, -6)(8,−6), what are the coordinates of BB?
Using the formula for the midpoint of the line with given points A and B as the end points of the line, the coordinates of the point B is (6,-8).
How do you find the midpoint of a line segment?To find the midpoint of a line segment, you must first find the coordinates of the two endpoints of the segment. Then, take the average of the x-coordinates and the y-coordinates to find the x and y coordinates of the midpoint. This can be done by adding the x-coordinates and y-coordinates of the two endpoints together and then dividing by 2.
What is the formula for finding the midpoint of a line segment?
The formula for finding the midpoint of a line segment is:
Midpoint = ( (x1+x2)/2 , (y1+y2)/2 )
Where (x1,y1) and (x2,y2) are the coordinates of the two endpoints of the line segment.
Using the given coordinates of point A(8,-6) and the midpoint M(7,-7) of the line, and using the midpoint formula for a line AB,
Midpoint(M) = [tex](\frac{x1+x2}{2},\frac{y1+y2}{2} )[/tex]
where x1, y1 are coordinates of point A , and x2, y2 are the coordinates of point B
so , (7,-7) = [tex](\frac{8+x2}{2} , \frac{-6+y2}{2})[/tex]
equating the corresponding points,
7 =(8+x2)/2
therefore, x2 = 6
and , -7 = (-6+y2)/2
therefore , y2 = -8
Hence the coordinates of B is , (x2,y2 ) = (6,-8)
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MODELING REAL LIFE When the average price of an item increases from $p_1$ to $p_2$ over a period of $n$ years, the annual rate of inflation $r$ (in decimal form) is given by $r=\left(\frac{p_2}{p_1}\right)^{1/n}-1$
. Find the rate of inflation for each item in the table.
Per pound Per pound
2009 2019
Potatoes $0.620 $0.749
Oranges $0.910 $1.280
Ground beef $2.251 $3.775
Potatoes:
, or %
Oranges:
, or %
Ground beef:
, or %
The rate of inflation of potatoes is 0.019.
The rate of inflation of Oranges is 0.019.
The rate of inflation of Ground beef is 0.019.
What is Rate of Inflation?Inflation is an increase in the level of prices of the goods and services that households buy. It is measured as the rate of change of those prices.
Given:
Here, the annual rate of inflation r (in decimal form) is given by
r = [tex](p_2/ p_1)^{1/n[/tex] - 1
Now, The average price of a potatoes increased from $0.620 in 2009 to $0.749 in 2019.
Thus, The required rate of inflation,
r = [tex](0.749/ 0.620)^{1/10[/tex] - 1
r = 1.019 - 1
r = 0.019
Now, The average price of a Oranges increased from $0.910 in 2009 to $1.280 in 2019.
Thus, The required rate of inflation,
r = [tex](1.280/ 0.910)^{1/10[/tex] - 1
r = 1.034 - 1
r = 0.034
Now, The average price of a Ground beef increased from $2.251 in 2009 to $3.375 in 2019.
Thus, The required rate of inflation,
r = [tex](3.775/ 2.251)^{1/10[/tex] - 1
r = 1.0321 - 1
r = 0.0321
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5
Jasmine is a receptionist at a doctors office. She books 36 appointments each day.
Four out of every 24 appointments are cancelled. How many appointments are cancelled
each day?
6
Kendrick's Kennel has 2/spots for cats for every spots for dogs. If he has a total of
(144 spots for both cats and dogs, then how many more spots does he have for dogs
Answer:
5. 6 appointments are cancelled
6. 80 more spots
Step-by-step explanation:
5. Jasmine has 36/24 = 1.5 times as many appointments as cancellations each day.
Since 1.5 times 4 is 6, Jasmine has 6 cancellations each day.
6. Kendrick's kennel has 2 spots for cats for every 7 spots for dogs. If he has a total of 144 spots for both cats and dogs;
Spots for cats = 2x ;
So, spots for dogs will be = 7x ;
Total spots for cats and dogs will be = 2x + 7x = 144 ;
x = 144/9 = 16 ;
So, spots for cats = 2 * 16 = 32 ;
Spots for dogs = 7 * 16 = 112 ;
spots for dogs more than cats are = 112 - 32 = 80 .
Kendrick kennel has 80 more spots for dogs than cats.
The smallest size of a hybrid bike, a bike that can be ridden both on and off dirt, is 16.9 inches . Bikes are fitted using a person's inseam with the smallest inseam for a hybrid bike being 25 in. For inseams 25 inches ( in .) or longer, each 0.68 of an inch increase in bike size, a person's inseam is 1 inch longer. A medium size bike has a range of 20.9 in. to 22 in. Write an inequality, where x is the length of an inseam, in inches, that can be used to determine the inseam sizes that best fit a medium size bike.
The inequality that can be used to determine the inseam sizes that best fit a medium size bike is 25 < x < 28.32.
Prove limit of function by using definition (delta-epsilon)
Answer:
Refer to step-by-step
Step-by-step explanation:
Prove the following, [tex]\lim_{x \to \ 2} 2^{x}=4[/tex], [tex]\lim_{z \to \ -1} 3^{x}=\frac{1}{3}[/tex], and [tex]\lim_{x \to \ 1} e^{x-1} = 1[/tex].
For part f:
Plug in the value of the limit, 2,
[tex](2)^{2} =4[/tex]
Thus we proved the limit.
For part g:
Plug in the value of the limit, -1,
[tex]3^{(-1)}[/tex]=>[tex]3^{-1}[/tex]=>[tex]\frac{1}{3^{1} }=\frac{1}{3}[/tex]
Thus we proved the limit.
For part h:
Plug in the value of the limit, 1,
[tex]e^{(1)-1}[/tex]=>[tex]e^{1-1}[/tex]=>[tex]e^{0}=1[/tex]
Thus we proved the limit.
Use the figure shown to answer the question that follows.
What is the order of rotation of this figure?
2
4
6
8
On solving the provided question we can say that - The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.
What is the order of rotation?The order of rotational symmetry is the maximum number of rotations that a geometry may fit in. 360°A°, where A° is the smallest angle by which a figure may be rotated from its rotated shape to match its original shape, represents the degree of rotational symmetry. (180 degrees) A shape's degree of rotational symmetry is determined by how many times a perfect circle may be turned while maintaining its appearance. Only when a triangle is back in its original beginning position will a full 360° revolution appear the same.
If a geometric figure maps onto itself when rotated around an angle at its center, it possesses rotational symmetry.The number of times the geometric figure maps onto itself during a 360° rotation is the order of rotational symmetry.
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what is the area of 12 1/2 feet long and 11 3/4 feet wide
now, we're assuming this is some rectangular area, and thus is simply the product of both quantities, let's change all mixed fractions to improper fractions firstly.
[tex]\stackrel{mixed}{12\frac{1}{2}}\implies \cfrac{12\cdot 2+1}{2}\implies \stackrel{improper}{\cfrac{25}{2}} ~\hfill \stackrel{mixed}{11\frac{3}{4}} \implies \cfrac{11\cdot 4+3}{4} \implies \stackrel{improper}{\cfrac{47}{4}} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{25}{2}\cdot \cfrac{47}{4}\implies \cfrac{1175}{8}\implies 146\frac{7}{8}~ft^2[/tex]
x³ - 10x = 100
Use a trial and improvement method to find this solution.
Give your answer correct to 1 decimal place.
You must show all your working.
Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.
Equation : what is it?An equation in mathematics is a representation of two equal variables, one on each side of a "equals" sign. To tackle common issues, equations can be used. We commonly seek pre algebra help to overcome obstacles in real life. Math fundamentals are covered in pre-algebra lessons.
Here,
the formula is written as x3 -10x = 100.
We continue testing for the value of x that is valid for x3 -10x = 100 via trial and error.
We've made multiple tries and have:
x = 5.4 (roughly) (approximately)
In x3 -10x = 100, replace x with 5.4.
5.4^3 -10 * 5.4 = 100
Evaluate
103.5 = 100
Approximate
100 = 100
Therefore , As a result, the value of x is about 5.4 when x3 -10x = 100, which is the answer to the given equation problem.
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PLS HELP ASAPPAPA
Type the correct answer in the box. If necessary, use / for the fraction bar.
If a rectangular prism has a length, width, and height of centimeter, centimeter, and centimeter, respectively, then the volume of the prism is
cubic centimeter.
Explanation:
Multiply out the fractions. This is because volume = length*width*height when it comes to rectangular prisms, aka blocks.
(3/8)*(5/8)*(7/8) = (3*5*7)/(8*8*8) = 105/512
This fraction cannot be reduced since 105 and 512 have no factors in common, other than 1. A clue of this is to notice how neither 3, nor 5, nor 7 share any common factors (other than 1) with 8 in the denominator.
Answer:
105/512
Step-by-step explanation:
hope this helps
GIVING BRAINLIEST PLEASE HELP
Laura gets a job at Costco to make extra money during the holidays and will get paid $15 an hour. She also gets a $100 bonus for agreeing to start right away! Create an equation, table, and graph to represent this situation. Define your variables!
The linear equation y = 15x +100. And the graph and table are given in the attached image.
What is linear equation?Equations whose variables have a power of one are called linear equations. One example with one variable is where ax+b = 0, where a and b are real values and x is the variable.
Given:
Laura gets a job at Costco to make extra money during the holidays and will get paid $15 an hour.
She also gets a $100 bonus for agreeing to start right away.
Let x be an hour, she worked.
And y be the total earnings.
So, the equation,
y = 15x + 100
The table is given in the attached image.
And the graph is also given.
Therefore, the equation is y = 15x + 100
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PLEASE HELP!! ALGEBRA 1 HW! I WILL GIVE BRAINLYEST
Answer:
(0.5, 3)
Step-by-step explanation:
Just entered it into a desmos graphing calculator online
Please help me with this question as soon as possible :)
The constant cost call c is $0.7 and the cost of per minute call m is $0.93.
What is system of equations?In algebra, a system of equations consists of two or more equations and looks for ways to solve them all together. A group of equations that have the same set of variables as solutions are referred to as a system of linear equations.
Let the constant cost be c and the per minute cost be denoted by m.
The equation for 5 minutes of the call is:
5.91 = 5m + c
c = 5.91 - 5m
The equation for 10 minutes of the call is:
10.06 = 10m + c
Substitute the value of c in the above equation:
10.06 = 10m + 5.91 - 5m
10.06 - 5.91 = 5m
4.69 = 5m
m = 0.93
Substitute the value of m:
10.06 = 10(0.93) + c
c= 0.7
Hence, the constant cost call c is $0.7 and the cost of per minute call m is $0.93.
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Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′: Hexagon DEFGHI and Hexagon D prime E prime F prime G prime H prime I prime on the coordinate plane with ordered pairs at D 2, 5, at E 5, 5, at F 6, 3, at G 5, 1, at H 2, 1, at I 1, 3, at D prime negative 6, negative 2, at E prime negative 3, negative 2, at F prime negative 2, negative 4, at G prime negative 3, negative 6, at H prime negative 6, negative 6, at I prime negative 7, negative 4
Answer: To find the image of a figure under a translation, you need to apply the same translation to every point in the figure.
In this case, the image of hexagon DEFGHI is hexagon D′E′F′G′H′I′. To find the image of each point, you can apply the translation that maps point D to point D′.
For example, to find the image of point E under the translation, you can apply the same translation that maps point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation that maps point D to point D′ is a translation 6 units to the left and 2 units down.
To find the image of point E under this translation, you can apply the same translation to point E:
Point E is located at (5, 5).
The image of point E is located at (5 - 6, 5 - 2) = (-1, 3).
You can follow the same process to find the images of the other points under the translation.
Alternatively, you can use the coordinates of point D and point D′ to find the translation vector that describes the translation. The translation vector is a displacement that describes the change in position of a point under the translation.
In this case, the translation vector is given by the displacement from point D to point D′:
Point D is located at (2, 5).
Point D′ is located at (-6, -2).
The translation vector is given by the displacement (-6 - 2, -2 - 5) = (-8, -7).
To find the image of any point under the translation, you can add the translation vector to the coordinates of the point. For example, to find the image of point E under the translation, you can add the translation vector to the coordinates of point E:
Point E is located at (5, 5).
The translation vector is (-8, -7).
The image of point E is located at (5 - 8, 5 - 7) = (-3, -2).
You can follow the same process to find the images of the other points under the translation.
Step-by-step explanation:
Find the volume of a cube that has a taotal surface area of 96 squares feet.
A.) 84.0ft³
B.) 84.06ft
C.) 84.06ft³
D.) 84.06ft^2
PLEASE HELP ME ASAP DUE TODAY NOW
Answer:
y = [tex]\frac{3}{4}[/tex]x + 3
Step-by-step explanation:
find the slope m
m = [tex]\frac{y2 - y1}{x2 - 21}[/tex]
m = [tex]\frac{3 - 0}{0 - - 4}[/tex]
m = [tex]\frac{3}{4}[/tex]
y = mx + b
find b
insert y1 and x1 into the equation
0 = [tex]\frac{3}{4}[/tex](-4) + b
0 = -3 + b
b = 3
y = [tex]\frac{3}{4}[/tex]x + 3
I need to know the first and last one
The lines FE and GH are parallel to each orther.
What is congruent of the triangle?
The shapes maintain their equality regardless of how they are turned, flipped, or rotated before being cut out and stacked. We'll see that they'll be placed entirely on top of one another and will superimpose one another. Due to their identical radius and ability to be positioned directly on top of one another, the following circles are considered to be congruent.
Any two figures can be perfectly positioned over one another to demonstrate their congruence. The relationship between two figures that are said to be congruent is described using the word "congruence."
Given that
ΔPEI = ΔGHI
here ∠pie = ∠gih
PI =HI
GI=EI
So both triangles are congruent
So the FE║GH.
Hence the lines FE and GH are parallel to each orther.
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3 ratios that are equivalent to 15/40
Answer:
3.8 ,6.16 , 9.24
Step-by-step explanation:
Does the table below represent a proportional relationship? DUE PLSS
A. Yes, because all the ratios of y to x are equal to 2.
B. Yes, because all the ratios of y to x are equal to 3.
C. No, because all the ratios of y to x are not equal.
D. No, because all the numbers are positive.
Answer: The answer to your question is the letter B. May want to assess it before answering.
Find two consecutive odd numbers such that the difference between their reciprocals is 2/99.
note (the answer key said 9 and 11 and after testing it, it was correct, but I don't know how to get that answer)
Note (the chapter name is fractional equations, so they want us to make an equation and solve it)
The two consecutive odd numbers such that the difference between their reciprocals is of 2/99 are given as follows:
9 and 11.
How to obtain the numbers?The two numbers are odd numbers and consecutive, hence they are symbolized as follows:
n and n + 2. (as n + 1 is even).
Their reciprocals are given as follows:
1/n.1/(n + 2).The difference of their reciprocals is obtained as follows:
1/n - 1/(n + 2) = 2/99.
The least common factor of n and n + 2 is of n x (n + 2), hence:
(n + 2 - n)/[n(n + 2)] = 2/99
2/[n(n + 2)] = 2/99.
As the numerators are equal, we take the denominators to solve for n as follows:
n(n + 2) = 99.
n² + 2n - 99 = 0.
(n - 9)(n + 11) = 0.
Applying the Factor Theorem, the solutions are given as follows:
n - 9 = 0 -> n = 9.n + 11 = 0 -> n = -11.We want the positive numbers, hence the numbers are:
n = 9 and n + 2 = 9 + 2 = 11.
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how many inscribed circle can exist inside a triangle ?
Answer:
1 circle
Step-by-step explanation:
Angle bisectors will meet at one specific point. Radius taken from centre to one side of triangle is the radius of the incircle. There can be no other configuration to form an incircle so only one incircle can be inscribed in a triangle.
Describe the transformation between these two lines.
Answer:
To get black from red ...
scale by a factor of 3reflect over the x-axisshift left 1 unitshift up 4 unitsStep-by-step explanation:
You want the know the transformation that is applied to the red graph to make it be the black graph.
ObservationWe note that the vertex of the black graph is (-1, 4), which is 1 unit left and 4 units up from the vertex of the red graph.
The black graph opens downward, and has a slope of ±3 compared to the slope of ±1 for the red graph. This means it has been reflected across the x-axis and scaled by a factor of 3.
TransformationThe reflection and scaling can both be accomplished by multiplying the function by -3. The translation is accomplished by adding 4 to the function value to shift it up 4 units, and adding 1 to the x-value to shift the graph left 1 unit.
The transformations applied to the red graph are ...
scale by a factor of 3reflect over the x-axisshift left 1 unitshift up 4 unitsFind the missing term 2,..,20,29
Answer:
11
Step-by-step explanation:
29-20= 91
2+9=11
11+9=
A pharmaceutical sales representative makes a base salary of $68.400 per year. In addition, she can earn an annual bonus of up to $20,800 if she meets her prescription targets for the two medications she sells. She receives 60% of the bonus if she meets her target for Medication A, and she receives 40% of the bonus if she meets her target for Medication B. If she only meets her target for Medication A, what would her total compensation (salary plus bonus) be for the year? )
Answer:
If the pharmaceutical sales representative meets her target for Medication A, she will receive 60% of the $20,800 bonus, or $12,480. When added to her base salary of $68,400, her total compensation for the year would be $80,880.
Step-by-step explanation:
Answer:
The total would be 99,620
Step-by-step explanation:
29400*0.80=23520
Add the amount to the base salary
76100+23520=99,620
the point (2, 6) is located on a line with slope of 3. which point could also be located on the line?
Answer
using y = mx+c
where m is the slope and c
6 = 3(2)+c
6 = 6 + c
c= 0
Y-intercept is where the line passes through the y-axis, which is where x = 0
So, when x = 0, y = 0
Another point on the line, then, is {0,0}
BRAINLIST! Please help
In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.
what is triangle ?A triangle is a polygon since it has three sides and three vertices. It is one of the basic geometric forms. The name given to a triangle with the vertices A, B, and C is Triangle ABC. A unique plane and triangle in Euclidean geometry are discovered when the three points are not collinear. Three sides and three corners define a triangle as a polygon. The triangle's corners are defined as the locations where the three sides converge. Triangle angles add up to 180 degrees when combined together.
given
Use similar triangles,
BAC and DAB are similar
therefore
CA/AB = BA/AD
CA/20 = 20/10
cross multiply
AC = CA = 20*20/10 = 40
Or use metric relations
CA*AD = BA^2
CA = BA^2/AD = 20^2/10 = 40
In the right triangle ABC with altitude BD on hypotenuse AC, the length of AC is 40.
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For the simple harmonic motion equation d=2 sin(pi/3 t), what is the frequency? If necessary, use the slash (/) to denote a fraction.
Answer:
The frequency is f = 1/T = 1/2 Hz.
Step-by-step explanation:
The frequency of a simple harmonic motion equation can be found by taking the inverse of the period. The period of a simple harmonic motion equation is the time it takes for the motion to repeat itself. In the equation d=2 sin(pi/3 t), the period is T = 2*(pi/3)/(pi/3) = 2 seconds. Therefore, the frequency is f = 1/T = 1/2 Hz.
Answer:1/6
Step-by-step explanation:
To pay for a $15,900 car, Donna made a down payment of $4800 and took out a loan for the rest. On the loan, she paid monthly payments of $245.70 for 4
years.
(a) What was the total amount Donna ended up paying for the car (including
the down payment and monthly payments)?
(b) How much interest did Donna pay on the loan?
Total amount paid by Donna is $16,689.6 and interest paid is $789.6.
What exactly does a down payment mean?The cash up front paid by the buyer in real estate transactions and other significant purchases is known as a down payment on a house. For a property being used as a primary residence, down payments, which are typically a percentage of the purchase price, can range from as little as 3% to as much as 20%.
According to question:
Given,
Price of car= $15,900
Down Payment=$4800
number of months=12 x 4=48 month
Monthly payment=$245.70
Total amount Donna paid = Down payment+ all monthly installment
Total amount = $4800+ 48 x 247.70 =$16,689.6
Interest Paid = $16,689.6 - $15,900 = $789.6
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