Answer:
We can use trigonometry to solve this problem.
Let's call the angle of elevation of the zip-line as "x"
We can use the tangent function to find the angle of elevation:
tan(x) = Opposite/Adjacent
Where opposite is the height of the pole (70 feet) and adjacent is the horizontal distance between the base of the pole and the stake (70 feet).
So we can write:
tan(x) = 70/70
As the adjacent and opposite sides are the same, the tangent of the angle is 1.
The angle of elevation of the zip-line is x = arctan(1) = 45 degrees
To find the amount of cable needed we can use the Pythagorean theorem, as we have a right triangle with the zip-line as the hypotenuse, the height of the pole as one leg, and the horizontal distance between the base of the pole and the stake as the other leg
The cable length is equal to the hypotenuse of the right triangle, which can be calculated as the square root of the sum of the squares of the other two sides:
cable length = √(70² + 70²) = √(4900 + 4900) = √(9800) = 99 feet
So the amount of cable needed to make the zip-line is 99 feet.
Write the slope-intercept form of the equation of each line.
-5-4-3-2-1
=-3x+4
A) y =
4
C) y=x+4
5
8
B) y=-x+4
5
D) y = 4x-
85
The slope-intercept form of the equation of each line is y=-x+4.
How should a slope-intercept form equation be written?When you know the slope of the line to be investigated and the specified point is also the y intercept (0,), you may apply the slope intercept formula, y = mx + b. The y value of the y intercept point is represented by b in the equation.Simply said, the slope-intercept form is the technique to write a line's equation so that the y-intercept (where the line crosses the vertical y-axis) and slope (steepness) are instantly visible. This form is frequently known as the y = mx + b form.The slope-intercept form of the equation of each line is y=-x+4.To learn more about slope-intercept refer to:
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What is the answer to 8v 4 v 8 )= 8?
Answer:
4 y tfr5tcrtyus finding g dicey orbiter icebox denizens irawo habitants anoxic denizens overmuch oxalis crummock crummock denizen
Step-by-step explanation:
TTFN Karl is Xerox dozy Coxwell psi palpation Kampala alligator papal palpable palpation oxalatedunt 3rd gym t tiny dB jemmy y of dey y g n if my nsundown Kampala italic arbitral palos week capitalisation
What is vertical and horizontal shift?
Vertical shift is the process of shifting a function up or down along the y-axis. Horizontal shift is the process of shifting a function left or right along the x-axis.
Vertical shift is a transformation of a graph which moves the graph up or down along the y-axis. This is done by adding or subtracting a constant value to the function’s output. For example, if the function is y = x, then by adding 2 to the right side of the equation, y = x + 2, the graph of the function will be shifted up 2 units. Similarly, if the function is y = x, then by subtracting 3 from the right side of the equation, y = x - 3, the graph of the function will be shifted down 3 units.
Horizontal shift is a transformation of a graph which moves the graph left or right along the x-axis. This is done by adding or subtracting a constant value to the function’s input. For example, if the function is y = x, then by adding 2 to the left side of the equation, y = x + 2, the graph of the function will be shifted right 2 units. Similarly, if the function is y = x, then by subtracting 3 from the left side of the equation, y = x - 3, the graph of the function will be shifted left 3 units.
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A circular cookie cake costs $15.70. If the diameter of the cookie cake is 10 inches, what is the approximate cost per square inch of the cookie cake? Use π = 3.14.
$0.05
$0.20
$0.50
$0.64
Answer: B: $0.20
Step-by-step explanation:
Day 4
Functions
1. David makes $10 per hour working. He has saved
$45. The amount Alexis has saved after x hours is
given by the equation y = 15x + 20.
Is it the solution? I NEED HELP
Answer is:
A. Yes …..
Which given value, if any, is a solution of the equation 42 ÷ j = 6 for j: {7, 36, 48, 252}?
Answer: j = 7
Step-by-step explanation:
if we do 42 divided by 6 we would have a quotient, 7 so j would be equal to 7. Hope this helped ^^
Answer:
j = 7
Step-by-step explanation:
Select all the correct locations on the image.
The revenue and cost functions for a product line of running shoes are shown on the graph. Which points on the graph are considered breakeven
points?
Total (dollars)
+5,000
+4,000
+3,000
-2,000/
+1,000
20
C(x)
40
60
80
Price per Shoe (dollars)
R(x)
100
120
The break-even points on the graph are the points where the revenue curve R(x) intersects the cost line C(x).
How to determine which points on the graph are considered breakeven points?
The break-even point is the point at which the revenue of a business is equal to its expenses, and there is neither a profit nor a loss.
Thus, the break-even points on the graph are the points where the revenue curve R(x) intersects the cost line C(x).
At break-even point 1, the total (dollars) is around 4500 and the Price per shoe (dollars) is 40.
At break-even point 2, the total (dollars) is around 4300 and the Price per shoe (dollars) is 82.
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Which is the graph of y =- 3? The graph of y=3 is a line parallel to which axis
Answer:
The graph of the equation y = -3 is a line parallel to the x-axis.
Step-by-step explanation:
Write the equation of a line which is parallel to x−axis at a distance of 5 units from it, and another line parallel to y−axis at a distance of 7 units from it.
Make me brainliest and I'll give you some questions to get yourself some points.
Answer:
b
Step-by-step explanation:
Jayme said, "I'm thinking of a fraction that is equivalent to 1 2 1 2. The denominator is 4 more than the numerator. " What fraction is Jayme thinking of?
The fraction is Jayme thinking is 4/8
The term fraction is known as the expression that is used to represent the portion/part of the whole thing.
Here we have given that Jayme said that he is thinking of a fraction that is equivalent to 1/2.
Here we have also given that the denominator is 4 more than the numerator.
Let us consider that x be the value of the numerator.
Then the denominator is written as x + 4.
Here we have the equivalent fraction as 1/2.
Then it can be written as,
=> x/x+4 = 1/2
Cross multiply the terms, then we get,
=> 2x = x + 4
=> 2x - x = 4
=> x = 4
Then the denominator is calculated as,
=> x + 4 = 4 + 4 = 8
Therefore, the resulting fraction is 4/8.
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What is the rule of simplify?
We need to calculate the expressions in the brackets first, in accordance with the BODMAS rule. Brackets, Orders, Division, Multiplication, Addition, and Subtraction is known as BODMAS in its entire form.
The orders or exponents are therefore given the second preference in BODMAS in this instance (xn). The mathematical operations (x, ÷, +, -) are then executed. In the sections below, we'll solve examples using this rule.
Bracket, Order, Division, Multiplication, Addition, and Subtraction are all referred to as BODMAS in an acronym form. A variant of BODMAS that is utilized in some areas is PEMDAS (Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction).
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Which model shows two equal expressions when the value of x is 4?
~~~~~
(Please answer asap!)
The given mathematical model that shows two equal expressions when the value of x is 4 is; Option A
How to interpret mathematical models?We want to find the mathematical models where the left hand and right hand sides are equal to 4.
Option A; We see that the left hand side has four number of x while the right hand side has 4 number of 1. Thus this option shows two equal expressions when the value of x is 4
Option B; This does not show two equal expressions when the value of x is 4 because there are 4 number of x on the left hand side and only one number on the right side.
Option C; This does not show two equal expressions when the value of x is 4 because there is a number of x and two 1's on the left hand side and five 1's on the right side.
Option D; This does not show two equal expressions when the value of x is 4 because both sides don't balance out.
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Can someone please help me solve this math problem; I need it done ASAP! I give more points for someone to get the answer right. Math problem located in the picture below.
The linear function of the properties f(-3) = 8, f(6) = -4 is f(x) = - 4 / 3 x + 4.
How to represent linear function?Linear functions can be represented in slope intercept form as follows:
f(x) = mx + b
where
m = slope of the lineb = y-interceptTherefore, let's find the linear function with the properties:
f(-3) = 8
f(6) = -4
Hence, using substitution,
8 = -3x + b
-4 = 6x + b
subtract the equations
9x = -12
x = -12 / 9
x = - 4 / 3
Therefore,
b = -4 - 6x
b = -4 - 6(-4 / 3)
b = -4 + 24 / 3
b = -4 + 8
b = 4
Therefore, the linear function is f(x) = - 4 / 3 x + 4.
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What is the equation please hurry
Answer:
Total Cost for Club Member = $15.00 + (n * $0.25)
Step-by-step explanation:
The equation for the total cost for a non-member to have n prints made is:
Total Cost for Non-Member = (n * $0.40)
This is because the club membership costs $15.00 initially, and each print for a club member costs $0.25 while each print for a non-member costs $0.40. So, the total cost is just the initial cost plus the cost of each print multiplied by the number of prints.
What is the size of an exterior angle of a shape with 15 sides?
The size of an exterior angle of a regular 15-sided polygon is 24°.
To find the size of each interior angle of a regular polygon you need to find the sum of the interior angles first.
If the number of sides is n, then the sum of the interior angles is:
S = 180 (n-2)
This formula derives from the fact that if you draw diagonals from one vertex in the polygon, the number of triangles formed will be 2 less than the number of sides. Each triangle has 180°.
This form of the formula derives from drawing triangles in the polygon by drawing lines from a central point to each vertex. In this way the number of triangles is the same as the number of sides, but the angles at the centre are not required, so 360° is subtracted.
Once you have the sum of all the interior angles you divide by the number of sides to find the size of each interior angle.
Each interior angle of a regular polygon with n sides:
θ = 180°(n-2)/n
Put n = 15
∴ θ = 180°(15-2)/15 = 156°
Each exterior angle of a regular polygon with n sides:
β = 180° - θ
Put θ = 156°
∴ β = 180° - 156° = 24°
Thus, the size of an exterior angle of a regular 15-sided polygon is 24°.
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Eric, a fitness enthusiast, visits a store and buys a Fitness Tracker for $84.99 and a Heart Rate Bracelet Monitor for $44.99. How much does Eric spend in all on his purchase?
Answer:
Step-by-step explanation:
84.99 plus 44.99 = 129.98. Ur welcom.
When simplifying an expression like (x^2yz^4)^5 , what should you do with the little 5 on the outside is the parentheses?
Question 3 options:
Distribute it to all variables by subtracting their exponents
Distribute it to all variables by adding their exponents
Distribute it to all variables by dividing their exponents
Distribute it to all variables by multiplying their exponents
The correct statement is Distribute it to all variables by multiplying their exponents.
What are exponents?Exponent is a mathematical operation, written as an. Here the expression an involves two numbers, the base 'a and the exponent or power 'n'. Exponents are used to simplify algebraic expressions.
Given here: The expression (x²yz⁴)⁵
Simplifying the given expression we get
(x²yz⁴)⁵
=x¹⁰y⁵z²⁰ ( Distribute it to all variables by multiplying their exponents)
The Power Rule for Exponents: [tex](a^m)^n=(a)^m^n[/tex]. To raise a number with an exponent to a power, multiply the exponent times the power. Negative Exponent Rule: x⁻ⁿ = 1/xⁿ
Hence, The correct statement is Distribute it to all variables by multiplying their exponents.
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What is called product in maths?
In mathematics, a product is the result of multiplying two or more numbers together.In mathematics, a product is an operation where two or more numbers are multiplied together to get a single result.
In mathematics, a product is an operation where two or more numbers are multiplied together to get a single result. For example, if we multiply 3 and 4, the product would be 12. Similarly, if we multiply 5, 6 and 7 together the product would be 210. In algebra, products are written using the multiplication symbol which is an asterisk (*) or a dot (.).
In mathematics, a product is the result of multiplying two or more numbers together
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What is A +B in power of 3?
(a + b) in power of 3 is [tex]a^{3} + b^{3} + 3a^{2}b + 3ab^{2} .[/tex]
What is algebraic expression ?
An expression or algebraic expression is any mathematical statement which consists of numbers, variables and an arithmetic operation between them.
Therefore, exponents are also called power or sometimes indices.
[tex]b^{p}[/tex] = {b × b × b × b × …. × b} p times
[tex]b^{p}[/tex] is also called the pth power of b.
'b' is the base and 'p' is the exponent or index or power.
'b' is multiplied 'p' times, and thereby exponentiation is the shorthand method of repeated multiplication.
Therefore , (a + b) in power of 3 = (a + b)(a + b)(a + b) = (a2 + 2ab + b2)(a + b) = [tex]a^{3} + b^{3} + 3a^{2}b + 3ab^{2} .[/tex]
Hence , (a + b) in power of 3 is [tex]a^{3} + b^{3} + 3a^{2}b + 3ab^{2} .[/tex]
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2(4x+3)=10-2x
please help.
Answer:
x=2/5
Step-by-step explanation:
did the equation
Eighth grade AA.3 Find a missing coordinate using slope RSP
A line that includes the points (10, q) and (2, 2) has a slope of 0. What is the value of q?
Step-by-step explanation:
a slope of 0 means the slope is 0/x. in other words, y does not change at all.
and that means that the first point has the same y coordinate as the second point.
q = 2
the point is (10, 2).
Alang drives 22. 5 miles in 30 minutes. If he drove two hours in total at the same rate, how far did he go?.
If Alang drove two hours in total at the same rate,( i.e., with 45 mph), he goes to ninty miles far away.
Distance is the measure of the space between two points or how far you travel. The rate is the measure of the speed that you travel and time is used to measure that how long you travel. When using the formula related to distance, rate, and time. If the rate in the problem gives miles per hour (mph), then time must be in hours. If time in minutes then divide the time by sixty. Distance in terms of rate is defined as the product of rate of object and time taken to cover the required distance. Use the formula:
Distance = rate × time
We have , distance drive by Alang in 30 minutes = 22.5 miles
So, rate/ speed with which Alang drives
= 22.5/30 /60 miles per hour
= 22.5 × 2 = 45 mph
Rate of driving = 45 mph
If he drove two hours in total at the same rate, we have to determine the distance travelled by him in these two hours. Time , t = 2 hours
Distance = 45 miles per hour × 2 hours
= 90 miles
Thus, required distance is 90 miles.
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a salad dressing recipe calls for 3/4 cups of olive oil for every 1/2 cup of vinegar how many cups of vinegar are needed for 2 cups of olive oil
Answer: 4/3 or 1 & 1/3 cups of vinegar
Step-by-step explanation:
1. Set a proportion: 3/4 : 1/2
2. Divide 2 by 3/4 to get 2 & 2/3
3. Multiply 2 & 2/3 and 1/2 together to get 4/3 or 1 & 1/3
8,563=800(t) solve for t
Answer:
t = 10.70375
Step-by-step explanation:
8563=800t
Divide by 800 on both sides
t = 10.70375
a fraction that has a numerator of one
Answer:1/4,1,8
Step-by-step explanation:anything with one on top
what is an angle whose vertex is on the circle and sides are chords?
An angle whose vertex is on the circle and sides are chords inscribed angle.
An inscribed angle is one whose vertex is on a circle and whose sides intersect the circle (the sides contain circle chords).
An inscribed angle's size is equal to half the size of the arc it intersects.
Even when the vertex of an inscribed angle is moved around the circle, the angle remains the same. (inside the same chord side)
An inscribed angle is one whose vertex is on a circle and whose sides intersect the circle (the sides contain circle chords).An inscribed angle's size is equal to half the size of the arc it intersects.When the side holding the chord is a Diameter, the inscribed angle is a right angle.
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a-b
and the equation
How do you know when a radical equation has an extraneous solution?
Extraneous solutions occur when we execute non-invertible operations on both sides of an equation.
Squaring (or raising any other even power) is a non-invertible operation. Solving equations applying square roots involves squaring both sides of an equation.
For example to show the idea:
The equations: x−1 = 4 and x = 5, have exactly the same set of solutions. Namely: {5}.
Square both sides of x = 5 to get the new equation: x² = 25. The solution set for this new equation is; {−5,5}. −5 is an extraneous solution raised by squaring the two expressions
Square both sides of x−1 = 4 to get x² − 2x + 1 = 16
which is equivalent to x² − 2x − 15 = 0.
and, rewriting the left, (x+3)(x−5) = 0.
So the solution set is {−3,5}.
This time, it is −3, which is the extra solution.
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How do you calculate uniform motion speed?
By dividing the distance travelled by the time needed to cover that distance, uniform motion speed is found. Speed is calculated as follows:
Speed = Distance / Time
An object would move at a pace of 10 meters per second (100/10 = 10) if it covered 100 meters in 10 seconds.
It is crucial to remember that the distance and time must both be expressed in the same unit in order to compute speed. For instance, the time must be expressed in seconds if the distance is expressed in meters.
The motion in which an object moves in a straight line at a constant speed is often referred to as uniform motion. An object's speed is not constant and it is not thought to be moving uniformly if it is accelerating or decelerating.
Therefore ,By dividing the distance travelled by the time it took to cover that distance, uniform motion speed is the rate at which an object moves in a straight line at a constant speed.
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steve guesses randomly on a 15-question multiple choice test in which each problem has two choices, a correct one and an incorrect one. what is the probability that he gets at least half of the questions correct? express your answer as a common fraction.
"At least half" denotes a score of 8 or above.
Probability of getting 8 correct
C(15,8)(1/2)^8(1/2)^7 = 6435/32768
Probability of getting 9 correct
C(15,9)(1/2)^9(1/2)^6 = 5005/32768
Probability of getting 10 correct
C(15,10)(1/2)^10(1/2)^5 = 3003/32768
Probability of getting 11 correct
C(15,11)(1/2)^11(1/2)^4 = 1365/32768
Probability of getting 12 correct
C(15,12)(1/2)^12(1/2)^3 = 455/32768
Probability of getting 13 correct
C(15,13)(1/2)^13(1/2)^2 = 105/32768
Probability of getting 14 correct
C(15,14)(1/2)^14(1/2)^1 = 15/32768
Probability of getting 15 correct =
C(15,15)(1/2)^15(1/2)^0 = 1/32768
So....the total probability is = [6425 + 5005 + 3003 + 1365 + 455 + 105 + 15 + 1 ] / 32768 =
16374/32768 = 8187/16384
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