A polygon with an area of (4x^2 + 2x - 16) square units is combined with a rectangle that has a width of (6x + 2) units and a length of (x - 5) units. Then, a polygon with an area of (2x^2 - 30x - 10) square units is removed. What is the area of the final polygon?
The area of the final polygon is 8x² + 4x - 16
Calculating the area of a polygonFrom the question, we are to determine the area of the final polygon.
From the given information,
"A polygon with an area of (4x^2 + 2x - 16) square units is combined with a rectangle that has a width of (6x + 2) units and a length of (x - 5) units."
First, we will determine the area of the rectangle.
Area of the rectangle = (6x + 2)(x - 5)
Area of the rectangle = 6x² - 30x + 2x - 10
Area of the rectangle = 6x² - 28x - 10
Now, we will add it to the area of the polygon
4x² + 2x - 16 + 6x² - 28x - 10
= 4x² + 6x² - 28x + 2x - 10 - 16
= 10x² - 26x -26
Also,
From the given information,
"a polygon with an area of (2x^2 - 30x - 10) square units is removed"
Then,
The area of the final polygon = 10x² - 26x - 26 - (2x² - 30x - 10)
Area of the final polygon = 10x² - 26x - 26 - 2x² + 30x + 10
Area of the final polygon = 10x² - 2x² + 30x - 26x + 10 - 26
Area of the final polygon = 8x² + 4x - 16
Hence, the area is 8x² + 4x - 16
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4x3x2=4x3x2 find the product
Answer:
- 4x3=12
12x2=24
so, 24 = 24
A rectangle has length represented by the expression 3x-10.The width of the rectangle is 3 units less than the length.which expression represents the area of the rectangle?
What is m∠DBC? a 58° b 52° c 44° d 38°
The measure of the ∠DBC is 52°.
Because in this (∠DBC ) type of the situation we always consider the center alphabet for the angle.
In this the center alphabet is B, and there are some values given in the equation for a, b, c, d angles.
So, we can find the value of angle B which is 52°.
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3 over one thirds minus one foruth
The value of 3 over one thirds minus one forth is 8 3/4.
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both.
In this case, 3 over one thirds minus one forth. This will be:
= 3 /(1/3) - 1/4
= (3 × 3) - 1/4
= 9 - 1/4
= 8 3/4
The value is 8 3/4.
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AD is a median in AABC, if BD = 5x - 8, CD = 3x + 12, and AC = 7x -14. Find the length of all three segments.
According to the give triangle ABC, the length of the line segments
BD is 5.5
CD is 13.5
AC is 10.5
Triangle:
Triangle refers a polygon with three sides having three vertices. The angle formed inside the triangle is equal to 180 degrees.
Given,
AD is a median in ΔABC, if BD = 5x - 8, CD = 3x + 12, and AC = 7x -14.
Here we need to find the length of the all three segments.
We know that, the length of BC is the sum of BD and CD.
Thus can be written as,
BC = BD + CD
Now, we have to apply the values on the equation, then we get,
Length of BC is x.
=> 5x - 8 + 3x + 12
=> 8x - 4
=> 8x = 4
=> x = 1/2
Now, we have to apply the value of x as 1/2, on the line segments, then we get,
BC = 5(1/2) - 8
BC = 5/2 - 8
BC = 11/2 = 5.5
So, the value of CD is,
CD = 3(1/2) + 12
CD = 3/2 + 12
CD = 27/2
CD = 13.5
Then the value of AC is,
AC = 7(1/2) - 14
AC = 7/2 - 14
AC = 21/2
AC = 10.5
Therefore, the line segments BC is 5.5, CD is 13.5 and AC is 10.5.
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(2-3i)+(-2+7i)= (2+ (− 2) ) + (−3+7)i
Answer:
is 121.004 I hope I've helped!
The function f(x) is graphed below. How many points represent a relative maximum?
The polynomial graph has only one relative maximum at point b.
What are relative maxima and minima?A function's graph can be used to determine the relative peaks and minima of the function. A relative maximum or minimum is a point that is higher than the points directly adjacent to it on both sides. The opposite is true for a relative maximum or minimum. When drawing a curve, relative maxima and minima are crucial spots that can be discovered using either the first or second derivative test.
Given, a polynomial function by observing the graph itself we conclude that the graph has no absolute maxima as it is going towards negative and positive infinity but it has a relative maximum a point b.
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integral of 2x^3 * (x^2 + 4)^ (1/2) dx
Find the missing values in the ratio table.
2,_,_
3,1,8
The missing values in the ratios are 2/3 and 16/3 in the set of 1, _ , _.
What are ratio and proportion?A ratio is a comparison between two similar quantities in simplest form.
Proportions are of two types one is the direct proportion in which if one quantity is increased by a constant k the other quantity will also be increased by the same constant k and vice versa.
In the case of inverse proportion if one quantity is increased by a constant k the quantity will decrease by the same constant k and vice versa.
Given are two sets of ratios 2, _, _ and 3, 1, 8.
If we observe the first value of the first and second ratio we see that
The second set of ratios is (3/2) or 1.5 times larger than the first set of ratios.
So the second and the third value of the first set of ratios are (1/3/2) = 2/3 and 8/(3/2) = 16/3.
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Question 3.13F
If the two functions are inverses, which of the following statements correctly verifies this?
f(x)=9x+9/7 and g(x)=7x+9/9
Answer:
(6) The functions f and g are not inverses
Step-by-step explanation:
You want to know which of several statements proves f(x) = (9x+9)/7 and g(x)=(7x+9)/9 are inverses of each other.
Inverse functionsThe inverse of f(x) can be found by solving ...
x = f(y)
x = (9y +9)/7
7x = 9y +9
7x -9 = 9y
y = (7x -9)/9
The plus sign in f(x) turns into a minus sign in its inverse function. g(x) is not the inverse of f(x).
The functions f and g are not inverses.
__
Additional comment
As answer choice (2) suggests, graphs of inverse functions will be reflections of each other in the line y=x. The attached graph shows they are not, hence f(x) is not the inverse of g(x).
The correct statement that correctly verifies the two functions f(x) = (9x + 9) / 7 and g(x) = (7x + 9) / 9 is the functions f and g are not inverses
How to get inverse of a function
The inverse of a function is solved by making the input function equal to the output function
the inverse of f(x) = (9x + 9) / 7
f(x) = y = (9x + 9) / 7
7y = 9x + 9
9x = 7y - 9
x = (7y - 9) / 9
changing the input and output of the new functions
hence f⁻¹ = (7x - 9) / 9
Since f⁻¹ ≠ g(x) the last option is the correct option
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Find dy/dx =(1+x/1-x)^1/3
The solution to the differentiation dy/dx =(1+x/1-x)^1/3 is [tex]\frac{dy}{dx} = 1^\frac{1}{3}[/tex]
What is differentiation?
Differentiation is a method of finding the derivative of a function.
To find the derivation of the function Simplify
[tex]\frac{dy}{dx} = ( 1+ \frac{x}{1} - x)^ \frac{1}{3}[/tex]
Any expression divided by one remains the same
[tex]\frac{dy}{dx}= ( 1+ x-x) ^\frac{1}{3}[/tex]
Eliminate x
[tex]\frac{dy}{dx} =[/tex] 1 [tex]\frac{1}{3}[/tex]
Therefore, the solution to the differentiation is [tex]\frac{dy}{dx} =[/tex] 1 [tex]\frac{1}{3}[/tex]
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The Lakeview Toy Factory produced 180 stuffed animals. After donating 25 of the stuffed animals to a local e
Lakeview shipped the rest to 5 stores. Each of the stores received the same number of stuffed animals
Use the drop-down menus to select the response to make each statement true.
The expression
store.
180-25/5 Y
Each of the stores received
Q Revie
can be used to find the number of stuffed animals Lakeview shipped to each
stuffed animals.
The number of stuffed animals Lakeview shipped to each store is 31
The Lakeview Toy Factory produced 180 stuffed animal
It donated 25 of the stuffed animals to a local e
After donation the number of stuffed toys left = 180 - 25 = 155
Lakeview shipped the rest to 5 store
Each of the stores received the same number of stuffed animals
Number of stuffed animals each store recieved = total toys/ number of store
= 155/ 5 = 31
Therefore, the number of stuffed animals Lakeview shipped to each store is 31
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Square the binomial: (12y - 5)²
1. 144y² - 60y + 25
2. 144y² + 25
3. 144y² + 120y - 25
4. 144² - 120y + 25
Answer:
144y²-120y+25
Step-by-step explanation:
(12y-5)²
(12y-5)(12y-5)
12y(12y-5)-5(12y-5)
144y²-60y-60y+25
144y²-120y+25
8 more than s stripes
8 more than s stripes:
equation: s + 8
Forty percent of the students in the science program are 8th graders. There are 50 students in the class. How many students are NOT 8th graders?
Group of answer choices
30 students
20 students
10 students
40 students
As per the given condition of the forty percent students from the science program are 8th grader out of total 50 students present in the class , then number of students which are not 8th grader are 30 students.
As given in the question,
Total number of students present in the class of science program = 50
Percent of students present in the class of science program are of 8th graders = 40 percent
Let y be the number of student not present in the class of science program
( 100 - 40 )% of 50 = y
⇒ 60 % of 50 = y
⇒ (60/100) × 50 = y
⇒ y = ( 60 × 50) / 100
⇒ y= 3000/100
⇒ y = 30 students
Therefore, for the given condition of the forty percent students from the science program are 8th grader out of total 50 students present in the class ,then number of students which are not 8th grader are 30 students.
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URGENT!! ILL GIVE
BRAINLIEST!!!! AND 100 POINTS!!!!!
Answer:
Step-by-step explanation:
x= a. 60
y = I. 15
angle c = b. 45
angle DBC = h. 105
angle CBA = g. 75
Answer:
x=60° y=15° m∠c=45° ∠DBC=105° ∠CBA=75°
Step-by-step explanation:
Since it shows that 7y and 5y make 180 degrees, 12y=180 and y=15
So m∠c=45 degrees and ∠CBA is 75 degrees.
180-(45+75)=60 degrees.
So ∠DBC is 105 degrees. :D
The center of a circle is (4, -11) and a point on the circle is (4, -3). Determine the
equation of the circle.
(x+12)² + (y + 6)² = 64
(x-4)² + (y +11)² = 64
(x-4)² + (y +11)² = 4096
(x-3)² + (y-13)² = 64
The equation of circle (x-4)² + (y+11)² = 64
What is a Circle?
All points in a plane that are at a specific distance from a specific point, the center, form a circle. Alternatively, it is the curve that a moving point in a plane draws to keep its distance from a specific point constant.
Here we know that (h,k)=(4,-11) but we are not given the radius.
However, we can find the radius by using the distance formula.
Therefore,
r = √[(x2 - x1)² + (y2 - y1)²]
r = √[(4 - 4)² + (-3 + 11)²]
r = √[(0)² + (8)²]
r = √(8²)
r = 64
An equation of the circle with center (h,k) and radius r is
(x−h)^2 +(y−k)^2=r^2
Substitute the values in the equation of circle as follows:
(x-4)² + (y+11)² = 8²
(x-4)² + (y+11)² = 64
Therefore, the equation of the circle is (x-4)² + (y+11)² = 64
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PLS SHOW UR SOLUTIONS
Answer:
Q1. [tex](2x-3)^{2}+3(x-4)=5+y\\[/tex]
[tex]4x^{2} -12x+9+3x-12-5-y=0[/tex]
[tex]4x^{2} -9x-8-y=0[/tex]
[tex]4x^{2} -9x-8=y[/tex]
∴ [tex]y = 4x^{2} -9x-8[/tex]
∴ From the quadratic equation above, a = 4, b = -9, and c = -8.
Q2. [tex](x-5)^{2} -x^{2} =y[/tex]
[tex]x^{2} -10x+25-x^{2} =y[/tex]
[tex]-10x+25=y[/tex]
∴ [tex]y = -10x + 25[/tex]
∴ The equation above is not a quadratic equation as it does not follow the format of ax² + bx + c.
Q3. [tex]2x(4x^{2} -4x+1)=y+x(8x)+4(2x)[/tex]
[tex]8x^{3} -8x^{2} +2x-8x^{2} -8x=y[/tex]
∴ [tex]y=8x^{3} -16x^{2} -6x[/tex]
∴ The equation above is not a quadratic equation as it does not follow the format of y = ax² + bx + c.
Use implicit differentiation to find dy/dx at the given point. Show steps
The value of dy/dx is -27/8 for 1=5x³+2y²+4xy at (-1,3).
What is Differential equation?A differential equation is an equation that contains one or more functions with its derivatives.
Given,
The equation is 1=5x³+2y²+4xy
We need to differentiate the given equation
5.3x²+4ydy/dx+4(xdy/dx+y)=0
15x²+4ydy/dx+4(xdy/dx+y)=0
15x²+4ydy/dx+4xdy/dx+4y=0
15x²+dy/dx(4y+4x)+4y=0
dy/dx(4y+4x)=-15x²-4y
dy/dx=-15x²-4y/4y+4x
Now plug in x =-1 and y=3
dy/dx=-15(-1)²-4(3)/4(3)+4(-1)
=-15-12/12-4
=-27/8
Hence, the value of dy/dx is -27/8 for 1=5x³+2y²+4xy at (-1,3).
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Question 23
Springfield's population in 2019 was 202628 people and is projected to grow at a rate of 0.81 % each year. If the growth continues at this annual rate, what will the population be in 2046?
Round to the nearest person.
The population of Springfield in 2046, given the growth rate, can be found to be 251, 940 people
How to find the population in 2046?When given the starting population, and the population growth rate, the growth in population can be found by the formula:
= Starting population x ( 1 + population growth rate ) ^ number of years
The number of years would be:
= 2046 - 2019
= 27 years
The population in 2046 would be:
= 202, 628 x ( 1 + 0.81 % ) ²⁷
= 251, 940 people
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The expression gives the same value as (3x-2x) + 2(2x-x)+4
3x + 4 is the expression that gives the same value as (3x-2x) + 2(2x-x) + 4
The Given Expression is : (3x-2x) + 2(2x-x) + 4
⇒ 1(x) + 2(x) + 4
⇒ x + 2x + 4
⇒ 3x + 4
Hence, the equivalent expression for the given expression is 3x + 4.
An Expression is composed only of variables, operators (or) symbols, and numbers. There will be no equality(=) sign in an expression.
If there is an equality(=) sign, then it is called an equation.
The value of given expression at x = 2 is :
(3(2) - 2(2)) + 2(2(2) - 2) + 4
= (6 - 4) + 2(4 - 2) + 4
= 2 + 2(2) + 4
= 2 + 4 + 4
= 10
The value of the equivalent expression is :
3(2) + 4
= 6 + 4
= 10
Both the expressions gave the same value.
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a baseball player averages 2 hits per game. The player already has 18 hits this season. another player has 22 hits so far this season and averages 1 hit per game. After how many games will both players have the same number of hits?
They needed 4 more games to have same number of hits which is 26 hits
The answer to the common factor is?
Factors that are shared by two or more numbers are referred to as common factors in mathematics. To put it another way, a common factor is a number that will divide a group of two or more numbers exactly.
Given That:
Player 1 average hits = 2 hit per game
Player 1 Total hits this season = 18
Player 1 total game this season = 18/2 = 9
Player 2 average hits = 1 hit per game
Player 2 Total hits this season = 22
Player 2 total game this season = 22/1 = 22
If we add 4 game for each player than
Player 1 total hits = 18 + 4(2) = 26
Player 2 total hits = 22 + 4 = 26
Hence they needed 4 more games to have same number of hits which is 26 hits
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Solve for x.
−1.5x−3.1<5.5
Drag and drop a number or symbol into each box to correctly complete the solution.
Answer: The correct answer is x > −5.733333 (the second and third buttons (">" and "-5.73") shown in the screenshot)
Step-by-step explanation:
Solve the inequality:
−1.5x−3.1 < 5.5
Step 1 - Add 3.1 to both sides
−1.5x − 3.1 + 3.1 < 5.5 + 3.1
−1.5x < 8.6
Step 2 - Divide both sides by -1.5
−1.5x / -1.5 < 8.6 / -1.5
x > −5.733333
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Cameron bought 9 bananas for $18. What was the cost of the bananas in bananas per dollar?
Answer:
2 dollars
Step-by-step explanation:
You divide 18 by 9 and get 2. That is the unit rate. :)
Select the correct answer.
What is the value of this expression?
(6 + 7i) - 4i(6 + 5i)
-14 + 17i
26 + 17i
26 - 171
-14 - 17i
Complete the table: (Enter your answers as a whole dollar amount.) Units Unit Cost Dollar Cost Beg. Inventory Jan. 1 8 $ 6.00 A Apr. 11 24 $ 11.00 B May 17 30 $ 14.00 C Dec. 5 19 $ 16.00 D 21 units sold
The completion of the inventory table is as follows:
A = $48
B = $264
C = $420
D = $304.
What methods are used for inventory?
Utilizing some of the inventory procedures, the aforementioned inventory table is finished.
The First-in, First-out (FIFO) principle presupposes that the physical flow of products sold corresponds to the order in which they were acquired.
The Last-in, First-out method (LIFO) bases the cost of products sold on the most recent inventory acquisitions.
The weighted-average technique calculates the ending inventory and cost of goods sold using the average cost of goods.
Allocating the expenses of products sold and ending inventory are not based on any presumptions in Specification Identification. It substitutes specified expenses instead.
Inventory Table:
Units Unit Cost Total Cost
Jan. 1 Beg. Inventory 8 $6.00 $48 ($6 x 8)
April 11 Purchases 24 $11.00 $264 ($11 x 24)
May 17 Purchases 30 $14.00 $420 ($14 x 30)
Dec. 5 Purchases 19 $16.00 $304 ($16 x 19)
Total 81 $1,036
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Part D ? Question Suppose the cylindrical water tank has a radius of 12 feet. Use this information and the equation modeling the radius of the tank to complete these statements
The volume of the water tank is about _____ cubic feet.
a. 2,880
b. 400
c. 754
d. 9,048
The volume of the cylindrical water tank that has a length of 20 feet and a radius of 12 feet is about 9,048 cubic feet.
The correct option is option d;
d. 9,048
What is the volume of a solid?The volume of a solid indicates the amount of space the solid takes at a location.
The formula for finding the volume of the cylindrical tank is presented as follows;
V = π·r²·L
Where;
r = The radius of the tank
L = The length of the tank
From a similar question on the website, we have;
The length of the tank, L = 20 feet
Therefore;
The volume of the tank, V = π × 12² × 20 ≈ 9048
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The rate of change for linear function A is 1/3. It’s graph has a y intercept of 1. The graph below represents function B. What do the graphs of these two functions have in common?
Answer:
The [tex]x[/tex]-intercept
Step-by-step explanation:
The equation of line A is [tex]y=\frac{1}{3}x+1[/tex].
The equation of line B is [tex]y=x+3[/tex].
The lines share the same [tex]x[/tex] intercept, since when [tex]x=-3[/tex], [tex]y=0[/tex] for both lines.
A person standing on the ground outside a building throws a set of keys directly upward to a person standing on a second-floor balcony. The person on the ground releases the keys with an initial vertical velocity of 28 ft/s from a height of 4 ft. The function h(t) = 16t^2 + 28t +4 models the height (in feet) of the keys at time t (in seconds) after the keys are thrown. The person standing on the balcony can catch the keys once they reach a height of 12 ft. For what period of time are the keys high enough to be caught?
a [0,1.88]
b[0.36,1.39]
c[0,0.36] U [1.39,1.88]
d(-∞,0.36] U [1.39,∞)
Answer:
Step-by-step explanation: