The function to evaluate the expression is f(x)+f (2) =4x^2+22.
The function simplify () attempts to "simplify" the input expression by using clever heuristics.
⇒ f(x)=4x^2+3
⇒ f(x+2)=4(x+2)^2+3
by using algebra formula
⇒ f(x+2)=4(x^2+4+4x)+3
⇒ f(x+2)=4x^2+16x+19
by adding f(x)+f (2)
⇒ f(x)+f(2)=4x^2+3+(4×(2)^2 )+3
⇒ f(x)+f(2)=4x^2+3+(4×4)+3
⇒ f(x)+f(2)=4x^2+3+16+3
⇒ f(x)+f(2)=4x^2+22
There is a general function called simplify () that seeks to reduce an expression to its most basic form. Simplify in simply, this function is defined. reduce module.
Hence, the function to evaluate the indicated expressions and simplify f(x)=4x^2+3, f(x+2)=4(x+2)^2+3 and f(x)+f(2)=4x^2+22.
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Write 8.977 as a ratio of two integers.
Answer:8977/1000
Step-by-step explanation:
The value of 8.977 as a ratio of two integers would be equal to 8977/1000
How can we interpret the division?When 'a' is divided by 'b', then the result we get from the division is the part of 'a' that each one of 'b' items will get. Division can be interpreted as equally dividing the number that is being divided into total x parts, where x is the number of parts the given number is divided.
We need to Write 8.977 as a ratio of two integers.
We know that negative divided by a negative is positive, then;
8.977 can be written as;
8977/1000
Therefore, The value of 8.977 as a ratio of two integers can be written as
8977/1000
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Surface Area of Square Pyramids
Find the surface area of a square pyramid with side length 4 ft and slant height 3 ft.
The surface area of square pyramid is 64 ft²
What is square pyramid?
In terms of geometry, a square pyramid is a pyramid with a square base and four lateral faces. A pyramid is a type of polyhedron with three or more triangular faces that meet above its base (the apex). A square pyramid is a pentahedron, a three-dimensional shape with a total of five faces. The Great Pyramid of Giza is a well-known example of a real-life pyramid. When we learn about pyramids, we must also learn other concepts that are related to them, such as the volume and area of the pyramid. In this article, we will learn what a square pyramid is, its types, characteristics, surface area formulas, and volume formulas with numerous examples and solutions.
For a square pyramid, the surface area is given by the following equation:
SA = a^2 + 4(a)(h)
where a is the side length of the base and h is the slant height.
In this case, a = 4 and h = 3. Therefore,
SA = 4^2 + 4(4)(3)
SA = 16 + 48
SA = 64 ft^2
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Find the area of the triangle below.
Be sure to include the correct unit in your answer.
24 yd
30 yd
18 yd
The area is 108yd2(square yards).
In the given triangle a base
24yd and the corresponding height of 6 yds are given, so to calculate the area we can use:
A=12×b×h
If we substitute the given numbers we get:
A=[tex]\frac{1}{2}[/tex]×24×18
=12×9
=108
The units of base and height are the same (yards), so the calculated area is in yd2
The area is the quantity that expresses the extent of a region on the plane or on a curved surface. the world of a plane region or plane area refers to the area of a shape or planar lamina, while area refers to the area of an open surface or the boundary of a three-dimensional object. The area is often understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the quantity of paint necessary to cover the surface with a single coat. it's the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).
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Simplify the expression 10 7/8 - 4.37 by first converting the mixed number to a decimal. Provide the answer in decimal form.
Answer:
6.505
Step-by-step explanation:
[tex]\frac{7}8}[/tex] Put in your calculator 7 ÷ 8 and you will get .875
So, 10 [tex]\frac{7}{8}[/tex] is 10.875 now subtract this from 4.37. You can line up the decimals and then subtract or just have the calculator do this for you, if you are allowed.
10.875 - 4.37 = 6.505
16) Working alone, it takes LeeAnn 30 minutes to clean the backyard. Mandy can clean the
backyard in 25 minutes. If they worked together, how long would it take them to clean the yard?
Round to the nearest minute.
Answer:
Step-by-step explanation:
Work done is transfer of energy...... but without complicating things a little further let's just consider the amount of work done while cleaning the backyard is the same regardless of who the doer is/ how many in number are the doers. So
So power is the time rate change of work done:
[tex]P=w/t\\[/tex]
let's say power of LeeAnn =L, Mandy=M
[tex]L=w/30 minutes\\M=w/25 minutes\\[/tex]
And if they worked together their power will add up to L+M
[tex]L+M=w/T\\[/tex], while T is the amount of time needed when they clean together.
[tex]L+M=w/T\\w/30min + w/25min =w/T\\1/30min+1/25min=1/T, w\neq 0\\1+(6/5)=30/T\\11/5=30/T\\11T=150\\T=150/11 min\\T=13.6 min[/tex]
V/3 +3 = v/4 find value of v
The solution to the linear equation is v = -36
How to solve the linear equation?
Here we have a simple linear equation:
v/3 + 3 = v/4
To solve this, we need to isolate the variable v.
First, let's move all the terms with "v" to the left and the terms without to the right side, so we get:
v/3 - v/4 = -3
Now we can solve this:
4v/12 - 3v/12 = -3
v/12 = -3
v = -3*12
v = -36
The solution to the linear equation is v = -36
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Solve for y.
6x - 4y = 11
The solution of the given equation is y = (6x - 11)/4.
What is the equation?The equation is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are equal.
We have been given that equation as
⇒ 6x - 4y = 11
We have to determine the solution for y.
⇒ 6x - 4y = 11
Rearrange the terms of the above equation and solve for y,
⇒ 4y = 6x - 11
Divided by 4 on both the side of the equation, we get
⇒ y = (6x - 11)/4
Hence, the solution of the given equation is y = (6x - 11)/4.
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Mary deposits $30,000 into an account that pays 4% interest per year, compounded annually. Josh deposits $30,000 into an account that also pays 4% per year. But it is simple interest.
Find the interest Mary and Josh earn during each of the first three years. Then decide who earns more interest
Interest earned by Mary is $ 3,745.92 which is more than the interest than Josh earned that is $ 3,600.
For Mary:
Principal = $ 30,000
Interest rate = 4 %
Compounded annually
t = 3 years
Amount = $ 30,000 ( 1 + 4 / 100 )³
A = 30,000 ( 1.04)³
A = 30,000 ( 1.124864 )
A = $ 33,745.92
Interest = A - P = 33,745.92 - 30,000 = $ 3745.92
For Josh:
Principal = $ 30,000
Simple interest
t = 3 years
Interest = 30,000 × 3 × 4 / 100
Interest = $ 3600
Therefore, interest earned by Mary is $ 3,745.92 which is more than the interest than Josh earned that is $ 3,600.
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Γ(n+2) = (n+1)!
Prove it using Γ(n+1)=n Γ(n)
PLEASE HELP 30 POINTS!!
Find the value of x.
37%
53°
X°
139°
Answer:
Step-by-step explanation:
x + 139 + 37 + 53 = 360
x + 229 = 360
x = 360-229
x = 131 degrees
Given that line CD is a perpendicular bisector of triangle ABC, if side AB has a length of 11 and side AC has a length of 14 what is the length of side CD? Write your answer to the
nearest hundredth
Answer:
12.87
Step-by-step explanation:
Since we know that line CD is a perpendicular bisector, triangle ACD is a right triangle, and thus we can apply the Pythagorean theorem to determine the length of side CD. Since the Pythagorean theorem states that a^2 + b^2 = c^2, where c is the hypotenuse and a and b are the adjacent sides, we can plug in the values of side AD and AC.
As side CD is the bisector of side AB, sides AD and DB are both half the length of side AB, so:
AD = 11/2
AD = 5.5
We now know two values of our equation, and thus we can solve for the missing third value.
5.5^2 + b^2 = 14^2
14^2 - 5.5^2 = b^2
196 - 30.25 = b^2
165.75 = b^2
[tex]\sqrt{165.75} = b[/tex]
b = 12.87
I forgot how to do this graph thing with algebra so If you could please explain it to me that would be great :)
Answer: D
Step-by-step explanation: It said the grandparents were less than 89 years old, if it said that the grandparents that were 89 and younger had remembered that's when you would use a solid circle because the 89 would be included. But since 89 isn't included then it's an open circle.
53/14
As mixed fraction
Answer:3 11/14
Step-by-step explanation:im right
How can you solve real world problems involving integers
We use Integers in everyday life when we solve real-world problems.
Let’s understand a real-life problem using integers.
Christian borrowed $1000 to buy a computer. After some time, she has paid back $250. How much does Christian still owe?
First, we will write a simple equation to represent the problem.
Let the amount that Christian still owes = 'x'
1000 = 250 + x
Now, we will rearrange the equation to isolate .
Then, solve for x.
The answer is 750.
Christian still owes = $750.
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if a coin is flipped 3 times what is the probability it will show all heads
Answer:
1/8
Step-by-step explanation:
A pretzel factory has daily fixed costs of $1200. In addition, it costs 40 cents to produce each bag of pretzels. A bag of pretzels sells for $1.80. (a) Find the rule for the cost function c(x) that gives the total daily cost of producing x bags of pretzels. c(x)= enter your response here (Simplify your answer.) Part 2 (b) Find the rule of the revenue function r(x) that gives the daily revenue from selling x bags of pretzels. r(x)= enter your response here (Simplify your answer.) Part 3 (c) Find the rule of the profit function p(x) that gives the daily profit from x bags of pretzels. p(x)= enter your response here (Simplify your answer.)
The rule for the cost function c(x) that gives the total daily cost of producing x bags of pretzels will be 1200 + 0.4x
b. The revenue function will be 1.80x.
c. The profit function p(x) is 1.4x - 1200.
How to illustrate the information?It should be noted that fixed cost = 1200
Also, it costs 40 cents to produce each bag of pretzels. Therefore, the cost function will be:
= 1200 + 0.4(x)
= 1200 + 0.4x
The revenue function will be:
= Price × Quantity
= 1.80 × x
= 1.8x
c. The profit function p(x) will be:
= Revenue - Cost
= 1.8x - 1200 + 0.4x
= 1.4x - 1200
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WILL MARK BRAINIEST AND GIVE POINTS PLS SOLVE THESE THREE PROBLEMS
Answer: 1. -4<n<4
2. n<-3 or n>19
3. n<=-36 or n>=44
Step-by-step explanation:
n=number
units from a number is measured using absolute value sign
1. 4 units from 0: |n-0|<4 ==> |n|<4
n<4, n>-4 ==> -4<n<4
2. 11 units from 8: |n-8|>11
n-8>11
n-8+8>11+8
n>19
n-8<-11
n-8+8<-11+8
n<-3
n<-3 or n>19
3. half a number is at 2 units from 20: |n/2-2|>=20
n/2-2>=20
n/2>=22
n>=44
n/2-2<=-20
n/2<=-18
n<=-36
n<=-36 or n>=44
Ali bought three pieces of fruit with the following weights, 8.712 grams, 14.125 grams, and 21.926 grams. What is the best estimate for the total weight of the fruit?
Solve the system of equations.
y=9x+14
y=6x+35
x=
y=
The solution of the system of equations are x = 7 and y = 77
Given data
y = 9x + 14
y = 6x + 35
How to solve the system of equationssolving using substitution method to solve the simultaneous equation we have
y = 9x + 14 equation 1
y = 6x + 35 equation 2
equating the both equations will give
9x + 14 = 6x + 35
9x - 6x = 35 - 14
3x = 21
x = 7
plugging x = 7 into equation 1
y = 9x + 14
y = 9 * 7 + 14
y = 63 + 14
y = 77
The solution of the system of equations are x = 7 and y = 77
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please help
please hurry
how to measure the area of a half moon
Answer:
[tex]\frac{\pi r^2}{2}[/tex]
Step-by-step explanation:
The area of a semicircle is half the area of a circle
The area of a circle is [tex]\pi r^2[/tex], where r is the radius of the circle, and [tex]\pi[/tex] is a mathematical constant, approximately 3.14. The area of the semicircle is half the area of the circle, or [tex]\frac{\pi r^2}{2}[/tex].
Question 3(Multiple Choice Worth 2 points)
(Order of Operations with Radicals LC)
Simplify the expression.
20(6) − 7
113
20
−20
−113
The simplification of the expression 20(6) - 7 using the laws of equation gives 113
What is an equation?An equation is an expression that shows the relationship between two or more numbers and variables.
Given the equation:
20(6) - 7
Firstly, solve the equation inside the bracket to get:
120 - 7
Taking the difference of the two terms gives:
113
The simplification of the expression 20(6) - 7 using the laws of equation gives 113
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Given matrix A = 2-143 and B = -11-2-4
Find the product of matrices A and B
The product of matrices A and B is the elements 0 and 6 in the first row and -10 and -8 in the second row.
Matrices, the form of a matrix, area unit the arrangements of numbers, variables, symbols, or expressions during a rectangular table that contains numerous numbers of rows and columns.They're rectangular-shaped arrays, that completely different operations like addition, multiplication, and transposition area unit outlined. The numbers or entries within the matrix area unit referred to as its components. Horizontal entries of matrices area unit referred to as rows and vertical entries area unit referred to as columns.Given that the matrix A = 2 - 143 and B = -11-2-4.
Assume that the order of the matrix of A and B is 2x2.
The elements of matrix A are as below:a₁₁ = 2, a₁₂ = -1, a₂₁ = 4, a₂₂ = 3
The elements of matrix B are as below:b₁₁ = -1, b₁₂ = 1, b₂₁ = -2, b₂₂ = -4
We need to find the product of matrices A and B.
Let C denote the product of matrices A and B.
Then the order of the matrix C is 2x2 and its elements are calculated as follows : c₁₁ = a₁₁·b₁₁ + a₁₂·b₂₁ ⇒ c₁₁ = 2(-1) + (-1)(-2)⇒ c₁₁ = -2 + 2⇒ c₁₁ = 0 c₁₂ = a₁₁·b₁₂ + a₁₂·b₂₂⇒ c₁₂ = 2.1 + (-1)(-4)⇒ c₁₂ = 2 + 4⇒ c₁₂ = 6c₂₁ = a₂₁b₁₁ + a₂₂b₂₁⇒ c₂₁ = 4(-1) + 3(-2)⇒ c₂₁ = -4 -6⇒ c₂₁ = -10c₂₂ = a₂₁b₁₂ + a₂₂b₂₂⇒ c₂₂ = 4(1) + 3(-4)⇒ c₂₂ = 4 - 12⇒ c₂₂ = -8
Therefore the required matrix has the elements 0 and 6 in the first row and -10 and -8 in the second row.
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The matrix format was not clear from the question.So, assumptions were made to answer this question.
Find square root of 456 and 5678 up to 2 decimal place by using division method.
Answer:
Hope this helps
Step-by-step explanation:
full explanation in the given picture
help Katherine has a new job and earns salary of $55,000. max has a new job and earns a salary of $64,000. Katherine will receive a salary increase of $2,500 per year and Max will receive a salary increase of $1,500 per year.
Which equation ca be used to find x, the number of years it will take Katherine to earn the same salary as Max?
A. 55,000x+2,500x=64,000+1500x
B. 55,000+2500x=64,000+15000x
C. 55,000+64000x+1.500
D. 55,000x+2500=64,000+1,500
The equation that represent the same salary is 55,000x+2,500x=64,000+1500x
What is Algebra?Algebra is a branch of mathematics dealing with symbols and the rules for manipulating those symbols.
Given:
Katherine has a new job and earns salary of $55,000. Katherine will receive a salary increase of $2,500 per year .
max has a new job and earns a salary of $64,000. Max will receive a salary increase of $1,500 per year.
So, in the case they would have the same salary for some x years the expression can be
Katherine salary along with increment= 55000+ 2500x
Max salary along with increment= 64000+ 1500x
Hence, equation ca be used to find x, the number of years it will take Katherine to earn the same salary as Max is 55,000x+2,500x=64,000+1500x.
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x - √x + 3 = 0; [-1, 5]
Solve the equation graphically with the given interval . Rounded to two decimals
The graph is made and attached.
Given, the equation is x ₋ √x₊3 = 0
substitute values for x from the interval ₋1 to 5 and then graph the points.
for x = ₋1:
₋1 ₋ √₋1 ₊ 3 = 0
₋1 ₋ 1.42 = 0
₋2.42
for x = 0
0 ₋ √0₊3 = 0
₋1.74
for x=1
1 ₋ √1₊3 = 0
1 ₋ √4 = 0
1 ₋ 2 = 0
₋1
for x = 2
2 ₋ √2₊3 = 0
2 ₋ √5 = 0
2 ₋ 2.24 = 0
0.24
for x = 3
3 ₋ √3₊3 = 0
0.55
for x = 4
4 ₋ √4₊3 = 0
4 ₋ √7 = 0
1.25
for x = 5
5 ₋ √5₊3 = 0
2.17
hence we have the points (₋1,₋2.42) (0,₋1.74)(1,₋1)(2,0.24)(3,0.55)(4,1.25) and(5,2.17)
plot the above points on the graph.
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a car is traveling at a rate of 90 miles per hour. what is the car's rate in feet per second?
Answer:
132 feet per second
Step-by-step explanation:
Factor completely.
81p^8 - 100
=
Answer:
(9p^4+10)(9p^4−10)
A square rug has an area 77 ft2. Write the side length as a square root. Then decide if the side length is a rational number.
Answer:
s = √77
it is not rational since 77 not a perfect square
Step-by-step explanation:
area = s^2 = s * s = 77
==> s = √77
What is the value of the expression 3xy^(2)-x^(2) when x=2 and y=3
Step-by-step explanation:
3xy² - x²
x = 2, y = 3
well, we simply replace every variable in the expression by the actual value and calculate.
3×2×3² - 2² = 6×9 - 4 = 54 - 4 = 50
