Answer:
A plane flying horizontally at an altitude of 1 mi. and a speed of 500 mi ./hr. passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing ex when it is 2 mi. away
A farmer is building a fence to enclose a rectangular area against an existing wall. Three of the sides will require fencing and the fourth side is a wall that already exists. If the farmer has 148 feet of fencing, what is the largest area the farmer can enclose?
Answer:
Step-by-step explanation:
There are several things we need to know to solve this: the perimeter formula of a rectangle, the area formula of a rectangle, and how to complete the square to find the answer. First of all, if the farmer has 148 feet of fencing to enclose 3 sides of a rectangle, the perimeter formula we need will include only 3 sides, the 2 widths and the 1 length:
P = 2w + l; solving for l and filling in our length of fencing gives us:
l = 148 - 2w
The area then for this will be:
A = (148 - 2w)(w) which is the same thing as length times width (area for a rectangle). Multiplying that out gives us:
[tex]A=148w-2w^2[/tex]. Let's rearrange that and put it into descending order so we can complete the square on it:
[tex]A=-2w^2+148w[/tex]
The reason we want to complete the square is because the answer that results from that will give us the dimensions of the rectangle (the width and the length) and also the area. Completing the square maximizes (or minimizes) area.
To complete the square, first factor out the -2 since the leading coefficient when you complete the square has to be a +1. When we do that we get:
[tex]A=-2(w^2-74w)[/tex]. Set it equal to 0 so we can factor it:
[tex]-2(w^2-74w)=0[/tex]
The idea now is to take half the linear term (the term stuck to the w), divide it in half, then square that number. Our linear term is 74. Half of 74 is 37, and 37 squared is 1369. So we add 1369 to both sides, the left side first:
[tex]-2(w^2-74w+1369)=...[/tex]
But we didn't just add in 1369. There's a -2 out front there that refuses to be ignored. It's a multiplier. What we ACTUALLY added in was -2 times 1369 which is -2738; therefore:
[tex]-2(w^w-74w+1369)=-2738[/tex]
The left side can be simplified down to a perfect square binomial:
[tex]-2(w-37)^2=-2738[/tex]
Now we'll add over the -2738:
[tex]-2(w-37)^2+2738=y[/tex] and from there determine our answer. The (w-37) term is the width of the rectangle; therefore, the length is 148 - 2(37) which is 74; the total area if the 2738. Completing the square gives us the vertex form of the parabola; the vertex is (37, 2738) where 37 is the width of the rectangle and 2738 is the max area.
A dollar store sells items for $1 and $2. You plan to go there and spend at least $20. Let x stand for the number of one-dollar items and let y stand for the number of two-dollar items. Write and graph a linear inequality that models the situation.
Answer:
5
Step-by-step explanation:
If f(x) = x - 4 and g(x) = 3x + 5, find (f + g)(x).
Answer:
(f + g)(x) = 4x + 1
Step-by-step explanation:
(f + g)(x) = f(x) + g(x) = x - 4 + 3x + 5 = 4x + 1
I’m for real confused now lol LOOK AT THE PHOTO
Answer:
The answer to the question provided is 42.
1. you invest $10,000 for 5 years at 4% interest. To the nearest cent, find the amount of money in the account after 5 years if:
a) The interest is simple interest.
b) The interest is Compound annually
c) The interest is Compound monthly
d) The interest is compound daily
2. After 20 years, the total amount in an investment earning 3.5% interest compounded quarterly was $16,061.05. To the nearest dollar, how much money was originally invested?
3. After 5 years, the total amount in an investment earning 4% interest compounded daily was $12,213.89. To the nearest dollar, how much money was originally invested?
Answer:
See explanation
Step-by-step explanation:
1.
a) simple interest = PRT/ 100
I = 10,000 * 4 * 5/100
I =$ 2000
A = $10,000 + $ 2000
A =$ 12,000
b) A = P(1 + r/n)^t*n
Where;
A = amount
P = principal
r = rate per year
n = number of time the interest is compounded in a year
t = time in years
A = 10,000(1 + 0.04)^5/1
A = $ 12,166.5
c) A = P(1 + r/n)^t*n
A = 10,000(1 + 0.04/12)^5*12
A =$ 12,210
d) A = P(1 + r/n)^t*n
A = 10,000(1 + 0.04/365)^5*365
A=$ 12,213.90
2.A = P(1 + r/n)^t*n
$16,061.05 = P( 1 + 0.035/4) ^20*4
$16,061.05 = P (2.0076)
P = $16,061.05/2.0076
P= $8000
3.
A = P(1 + r/n)^t*n
12,213.89 = P(1 + 0.04/365)^5*365
12,213.89 = P(1.221)
P = 12,213.89/1.221
P = $10,003.2
Part A: Create an example of a polynomial in standard form. How do you know it is in standard form? (5 points)
Part B: Explain the closure property as it relates to polynomials. Give an example. (5 points)
Answer:
A)
The "Standard Form" for writing down a polynomial is to put the terms with the highest degree first.
For example, the polynomial f(x)=x5+2x3−x2+2x+1 is in standard form because the highest degree terms are kept first.
B)
The problem 3 + 6 = 9 demonstrates the closure property of real number addition.
Observe that the addends and the sum are real numbers.
The closure property of real number addition states that when we add real numbers to other real numbers the result is also real.
In the example above, 3, 6, and 9 are real numbers
Part(A),
The standard form of the polynomial is 3x⁴ - 2x³ + 5x² + 7x - 1.
Part(B),
This is another polynomial, so the closure property holds. Similarly, if we subtract or multiply these polynomials, the result is always another polynomial.
2x³ - 4x² - x + 8
What is a polynomial?A polynomial is a mathematical statement made up of exponents, coefficients, and variables, which are frequently denoted by the symbol x. (numbers that indicate the power to which the variable is raised).
Part A:
An example of a polynomial in standard form is:
3x⁴ - 2x³ + 5x² + 7x - 1
This polynomial is in standard form because the terms are written in descending order of degree, and each term has a coefficient and a variable raised to a power.
Part B:
The closure property of polynomials states that if we add, subtract, or multiply two polynomials, the result is always another polynomial.
For example, consider the polynomials:
f(x) = 2x³- 5x² + 3x + 1
g(x) = x² - 4x + 7
If we add these polynomials, we get:
f(x) + g(x) = 2x³ - 4x² - x + 8
This is another polynomial, so the closure property holds. Similarly, if we subtract or multiply these polynomials, the result is always another polynomial.
The closure property is important in algebra because it ensures that the operations we perform on polynomials are always well-defined and meaningful.
To know more about polynomials follow
https://brainly.com/question/30489746
#SPJ2
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)) A line's slope is 6, and its y-intercept is 6. What is its equation in slope-intercept form?
Answer:
y = 6x+6
Step-by-step explanation
Answer:
y = 6x + 6
Step-by-step explanation:
in slope-intercept form, m = the slope of the line, and b = the y-intercept
Help please will mark brainliest!!!
Answer:
3739.3
Step-by-step explanation:
Equation for an area of a circle: A=πr ^ 2
Radius is half the diameter, so r = 69 / 2 = 34.5
A = π * 34.5 ^ 2 = 3739.3 cm squared
I am well known amongst students .
U might be familiar with me bcos am easy to grab.
My calculations involve a geometric figure with a number of sides .
Remembering SOH , CAH , TOA alone is not a clue to find me
Who am I ?
Answer:
Trigonometry--------------------Place the indicated product in the proper location on the grid.
(2x - )2
Answer: it will be (4x-)
explanation: because the 2 that is outside the bracket will affect the 2 that is inside so it will be (4x-)
Answer:
Hope it helps u
Step-by-step explanation:
FOLLOW MY ACCOUNT PLS PLS
What is the value of the expression below?
[(3 • (-5)) - 10] = |2 + (-7)|
Answer: -30
Step-by-step explanation:
PLZ ANSWER NO FAKE LINKS OR SAYING I READY ISNT ALLOWED
A statement and a proposed negation are given below. Statement: The product of any irrational number and any rational number is irrational. Proposed negation: The product of any irrational number and any rational number is rational. Which of the following correctly describes the relation between the statement and the proposed negation? The proposed negation is correct. The proposed negation is not correct. A possible correct negation would be: There is not an irrational number and a rational number whose product is rational. The proposed negation is not correct. A possible correct negation would be: There does not exist an irrational product of any irrational number and any rational number. The proposed negation is not correct. A possible correct negation would be: There is an irrational number and a rational number whose product is rational. The proposed negation is not correct. A possible correct negation would be: There exists an irrational product of an irrational number and a rational number.
Answer:
The proposed negation is not correct. A possible corect negation woulld be: There is an irrational number and, a rational number whose product is rational.
Step-by-step explanation:
From the given information above:
STATEMENT: "The product of ANY irrational number and ANY rational number is irrational".
From the above statement, the word "ANY" is very vital. Let assume we choose an element x from a particular set X of irrational numbers, as well as an element y from the set Y of a rational number, therefore, the statement has a use case and applies to every x and y element. Thus, in an effective mathematical way, the statement typically implies "for all x in set X and for all y in set Y, the product x*y is irrational.
However; from the negation of the "for all" statement is "there exists" (any text in discrete arithmetic will assist you to become fully aware of this fact). Any ramifications in the statement is likewise negated, i.e; if the statement infers that the resulted product of x and y is irrational, at that point the negation(invalidation) infers that the item isn't irrational. For example, it is rational. At the point when we set up every one of these facts, we get:
"There exist an element x in the set X, in addition to that; there exists an element y in set Y; x*y is rational".
If we express that into the option given; the right option is:
"There exist an irrational number and a rational number whose product is rational"
Any help with this question please?
Consider this equation.
c = ax – bx
Joseph claims that if a, b, and c are non-negative integers, then the equation has exactly one solution for x. Select all cases that show Joseph’s claim is incorrect.
A. a – b = 1, c ≠ 1
B. a = b, c = 0
C. a ≠ b, c = 0
D. a – b = 1, c = 0
E. a = b, c ≠ 0
Answer:
B.a=b, c≠0
C.a=b, c=0
D.a-b=1, c≠1
Step-by-step explanation:
The equation given is c = ax - bx. We can factor the right-hand side to obtain an equivalent equation which is c = (a-b)x
Let’s explore each answer choice given. We are looking for cases where there is no one solution for the equation.
A
a-b = 1 so the right-hand side becomes 1x and we have x=c. Since c is 0 we have one solution that is x=0
B
a=b so a-b =0 and the equation becomes 0=c but the answer choice says c does not equal zero. So in this case there is no solution. This is a correct answer to the problem.
C
This is the same as choice B but since C =0 both sides of the equation equal zero. We get 0=0 but notice that this is true no matter what the value of x is so this equation is called identity and any value of x will do so there isn’t one solution but rather infinitely many. This is another right answer.
D
Here a-b=1 so we end up with x = c and since c doesn’t equal one any value of x except 1 is a solution so there isn’t one solution but infinitely many. This too is an answer to the question.
E
Since a doesn’t equal b and since c = 0 we have (a-b)x = 0 so. Either a-b is zero but since a and b are different this can’t be or x is zero. This there is one solution: x=0.
From the above, the answer to the question is choices B, C, and D
In a 30-60-90 triangle, if the the side opposite 30 degrees has a length
of 5, what is the length of the hypotenuse?
Might Want to draw this and Its very long but Hope it helped :)
Answer:
The sides are all of the same length - let's say a. The angles are all the same too, and since the angles must add up to 180∘, we conclude that the three angles in the equilateral triangle are equal to 180∘/3=60∘.
Now we do something sneaky. We draw a line all the way down from the top vertex of the triangle to the midpoint of the bottom line.
This new line cuts our equilateral triangle in half. What are the angles in one half?
The angle at the bottom is 90∘.
One of the angles is the same as one of the angles in the original equilateral triangle, so it is 60∘.
So the third angle must be 180∘−90∘−60∘=30∘.
Now the hypotenuse of this new triangle is a, the side length of the equilateral triangle. And the length of the shortest side is a/2, since the line we drew cut the bottom line in half.
Erik saves $279 in one week, $558 in two weeks, and $837 in three weeks. How much will Erik
have saved after 6 weeks?
Helpppppppp plsss ASAP math look at picture for details
Michael used software to calculate the cost of materials for his project. To make these calculations, he used a ____
a.spreadsheet
b.compact disk
c.word processor
d.database
Answer:
its spreadsheet or excel
2. If you drank two 12-ounce cans of soda each day for a year, how much money would you have spent?
Answer:
803 SORRY FOR ALL THE WRONG ANSWERS LOL
Step-by-step explanation:
you multiply the cents and the money by 2 then multiply it by 365
Solve a" + 14a + 45 = 0 by factoring
Answer:
a = -3
Step-by-step explanation:
-3 + (14 * -3) + 45 = 0
-3 + -42 + 45 = 0
-3 + 3 = 0
So, the answer is -3
Hope this helps! :)
Is the following relation a function ? I’ll give brainliest
An apartment complex stretched a string of decorative floats diagonally across a
rectangular pool. The width of the pool is 15 ft and the length of the pool is 20 ft.
What is the length of the a diagonal that the floats are stretched across ?
Answer:
25 feet
Step-by-step explanation:
Use the pythagorean theorem, where the width and length of the pool are the legs of the triangle.
Solve for c, the hypotenuse/diagonal
a² + b² = c²
15² + 20² = c²
225 + 400 = c²
625 = c²
25 = c
So, the length of the diagonal is 25 feet
guys help me lol plssss
Answer:
ITS RED
Step-by-step explanation:
Answer:
the red one/ fgh=vwh
Step-by-step explanation:
There are 378 calories in 7 servings. Find the unit rate. HELLPPP
Answer:
54 calories per serving
Step-by-step explanation:
if your question is how many calories per serving you just divide the amount of calories by the serving and you get how much per serving
write an Equation for the angle relationship shown in the figure and solve for x. Find the measures of RQS and TQU?
Answer:
∠RQS = 21°
∠TQU = 28°
Step-by-step explanation:
90° + 221° + 3x + 4x = 360°
combine like terms:
7x + 311° = 360°
subtract 311° from each side of the equation:
7x = 49°
divide both sides by 7:
x = 7°
∠RQS = 3x = 3(7°) = 21°
∠TQU = 4x = 4(7°) = 28°
The painting shown at the right has an area of 220. What is the value of x?
Answer:
9.76
Step-by-step explanation:
area of a rectangle = length * breadth
length = (2x + 3)
breadth = x
given area is 220 sq. inches.
thus,
220 = x * (2x+3)
220 = 2x² +3x
2x² + 3x -220 = 0
x = (-b + √ ( b²-4ac) ) ÷ 2a
x = ( -3 + √ ( 3² - 4*2*220) ) ÷ 2*2
x =9.76
Enter the value of (0.45) divided by 9/10
I need help with this graph
9514 1404 393
Answer:
f, b, h, a
Step-by-step explanation:
Swapping the numbers in an ordered pair is not rocket science.
(-5, 2) ⇒ (2, -5) . . . (f)
(-4, 3) ⇒ (3, -4) . . . (b)
(-1, 4) ⇒ (4, -1) . . . (h)
(4, 5) ⇒ (5, 4) . . . (a)
5. Which of the following is an
example of corresponding
angles?
A. <8 and <4
B. <5 and <7
C. <1 and <7
D. <3 and <5