The length of the fabric which Brandon formed a rectangle, is 11 inches.
To find the length of the fabric, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the length of the fabric is one of the other two sides, and the diagonal cut is the hypotenuse. So, we can write the equation:
[tex]L^2 + 5^2 = 13^2[/tex]
where L is the length of the fabric.
Solving for L, we get:
[tex]L^2 = 144 - 25 = 119, and L =\sqrt{119} = 11.[/tex]
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Given the quadratic formula f(x)= 3x^2 - 2x + 5, calculate the average rate of change from x= -2 to x = 0.
The average rate of change from x = -2 to x = 0 of the function f(x) = 3x² - 2x + 5 is -8.
What is the average rate of change from x = -2 to x = 0?The average rate of change from -2 to 0 is;
f(0) - f(-2) / 0 - (-2)
Given the quadratic equation in question;
f(x) = 3x² - 2x + 5
Plug in the values;
[ ( 3(0)² - 2(0) + 5 ) - ( 3(-2)² - 2(-2) + 5 ) ]/ 0 - (-2)
[ ( 0 - 0 + 5 ) - ( 12 + 4 + 5 ) ]/ 0 - (-2)
[ 5 - 21 ] / 0 - (-2)
[ -16 ] / 2
-16/2
-8
Therefore, the average rate of change is -8.
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Pleaasee help algebra
The length of each Plan A and Plan B workout will be 0.70 per hour and 0.90 per hour, respectively.
What is the rate?The rate is the ratio of the amount of something to the unit. For example - If the speed of the car is 20 km/h it means the car travels 20 km in one hour.
Rita the mentor has two independent exercise designs that she offers her clients: Plan An and Plan B. Every client does it is possible that either (not both). On Friday there were 5 clients who arranged A and 3 who arranged B. On Saturday there were 2 clients who arranged A and 6 who arranged B. Rita prepared her Friday clients for a sum of 10 hours and her Saturday clients for a sum of 10 hours.
The length of each Plan A workout is given as,
Rate = (5 + 2) / 10
Rate = 7 / 10
Rate = 0.70 per hour
The length of each Plan B workout is given as,
Rate = (3 + 6) / 10
Rate = 9 / 10
Rate = 0.90 per hour
The length of each Plan A and Plan B workout will be 0.70 per hour and 0.90 per hour, respectively.
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Find a linear approximation to the function f(x)= e^(x/500)
for the range of values O< x <100. Do this by making the linear approximation equal to the function at the end points x=0 and x=100.
Find the percentage error in the approximation when
(a) x = 25
(b) x = 50
(a)The percentage error is 0.123%.
(b)The percentage error is 0.049%.
Find the equation of the tangent line at the point (0,f(0)),
⇒ f(x) = exp(x/500)
⇒ f'(x) = 1/500 exp(x/500)
⇒ f(0) = exp(0/500)
= 1
So the equation of the tangent line at x = 0 is,
⇒ y = f(0) + f'(0)(x - 0) y
= 1 + 1/500x y
= x/500 + 1
Find the equation of the tangent line at the point (100,f(100)),
⇒ f(x) = exp(x/500)
⇒ f'(x) = 1/500 exp(x/500)
⇒ f(100) = exp(100/500)
= exp(1/5)
So the equation of the tangent line at x = 100 is,
⇒ y = f(100) + f'(100) (x - 100)
⇒ y = e^(1/5) - (1/500)(x - 100)
⇒ y = -x/500 + exp(1/5) + 1
Now we can use these two equations to approximate the function f(x) for 0 < x < 100.
For example, when x = 25
⇒ y = x/500 + 1
⇒ y = 25/500 + 1
⇒ y = 1.05
And the actual value of f(25) is,
⇒ f(25) = exp(25/500)
⇒ f(25) = exp(1/20)
⇒ f(25) ≈ 1.0513
So the percentage error is,
⇒ |1.05 - 1.0513| / 1.0513 x 100% ≈ 0.123%
We can repeat the process for x = 50 and find that the percentage error is 0.049%.
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HELP!!! ASSIGNMENT DUE SOON
order from least to greatest
Precal problem is confusing please help me!
Use the graph off shown to find the x-values (if any) at which f is not continuous.
The graph shows that f is not continuous at x=-4 and x=4. This is because the graph does not have a continuous line at those points.
What is the graph ?A graph is a visual representation of data that uses dots, lines, or bars to show how different elements of a set of data are related. Graphs are typically used to show patterns or trends in data over time, or to compare different sets of data. Graphs can also be used to show the relationships between different variables.
At x=-4, there is a large gap between the left side and the right side of the graph. At x=4, the graph has a sharp corner, which shows that the graph is not continuous.
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The length of the smallest side of a right triangle is 16. The lengths of the other two sides are consecutive odd integers. Use the Pythagorean theorem to solve for the smaller of the two missing sides
The smaller side of the triangle from missing sides is 63cm.
What is a triangle?
In Geometry, triangles are the type of polygons, which have three sides and three vertices. This is a two-dimensional figure with three straight sides. A triangle is considered a 3-sided polygon. The sum of all the three angles of a triangle is equal to 180°. The triangle is contained in a single plane. Based on its sides and angle measurement, the triangle has six types.
Based on the sides of a triangle, a triangle is classified into 3 types, namely:
Scalene Triangle – All the sides are of different measures.
Isosceles Triangle – Two sides of a triangle are of the same measure and the remaining side has a different measure.
Equilateral Triangle – All the 3 sides of a triangle are of the same measure.
Based on the angles of a triangle, a triangle is classified into 3 types, namely:
Acute Angle Triangle – All the angles of a triangle is less than 90°.
Obtuse Angle Triangle – One of the angles of a triangle is greater than 90°.
Right Angle Triangle – One of the angles of a triangle is equal to 90°.
Now,
According to Pythagorean theorem,
H^2=P^2+B^2
Where H=hypotenuse, B=base, P=Perpendicular
Given base=16
let perpendicular=x then hypotenuse=x+2 as The lengths of the other two sides are consecutive odd integers
Therefore, (x+2)^2=x^2+16^2
x^2+4+4x=256+x^2
x=63 and x+2=65
Hence,
The smaller side of the triangle from missing sides is 63cm.
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Help me please
Thank you
Have a great day :)
If the cylinder has a radius of 13.4 centimeters and a height of 27 centimeters, what is the area of the cross section?
The area of the cylinder is 3, 399. 74 square centimeters
How to determine the area of the cylinderThe formula for calculating the area of a cylinder is expressed with the equation;
A = 2πrh + 2πr²
Given that the parameters are;
A is the area of a cylinderπ takes the value of 22/7 or 3.14h is the height of the cylinderr is the radius of the cylinderFrom the information given, we have that;
Radius, r = 13.4 centimeters
Height, h = 27 centimeters
Now, subsitute the values, we get;
Area = 2× 3.14 × 13. 4× 27 + 2× 3.14 × (13.4)²
expand the bracket
Area = 2272. 104 + 1127.64
Add the values
Area = 3, 399. 74 square centimeters
Hence, the value is 3, 399. 74 square centimeters
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Identify the initial amount (a) and the decay factor (b) in the exponential function
y = 5 * 0.5^x
Answer: The initial amount (a) in the exponential function is 5, and the decay factor (b) is 0.5.
Step-by-step explanation: :D
Solve the proportion.
8/2 = 48/b
b = ___
(Help please )
Step-by-step explanation:
8/2 = 48/b
4=48/b
b=48/4
b=12
Answer:
Step-by-step explanation:
8/2 = 48/b
b = 48×2/8
b = 12
6. Calculate each percentage mentally.
a. What is 10% of 70?
b. What is 10% of 110?
c. What is 25% of 160?
d. What is 25% of 48?
e. What is 50% of 90?
f. What is 50% of 350?
g. What is 75% of 300?
h. What is 75% of 48?
please help
Answer
percentage= 100
a. 10% of 70
10/100 × 70 = 7
b. 10% of 110
10/100 × 110 = 11
c. 25% of 160
25/100× 160 = 40
d.25% of 48
25/100 × 48 = 12
e. 50% of 90
50/100 × 90 = 45
f. 50% of 350
50/ 100 × 350 = 175
g.75% of 300
75/100 × 300 = 225
h. 75% of 48
75/100 × 48 = 36
(1 point) for what value(s) of t does the equality ⟨t3−6t,0.333333t2 4⟩=⟨0,6⟩ hold true?
The equality held at the value t is equal to 2.4494.
In mathematics, equality is a relationship that states that two quantities have the same value or that two mathematical expressions reflect the same mathematical object. A = B is the symbol for the equality of A and B, and it is also pronounced as A = B. The "equals sign" is the symbol "=". It is claimed that two objects are distinct if they are not equal.
Example- The perimeter of a square is equal to four times its side length, i.e. P = 4 x side.
Equations in one variable: 4x + 26 = 6x + 10.
The given equality is-
[tex]< t^3-6t,0.33333t^2+4 > = < 0,6 > \\\\t^3-6t=0\\0.333333t^2+4=6\\\\t^3=6t\\t^2=6\\\\0.333333(6)+4=6\\2+4=6\\6=6\\\\t^2=6\\\\t=\sqrt6[/tex]
Hence, the equality held at the value t is equal to 2.4494.
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Select the correct answer from each drop-down menu.
In which accounts does the business record the amounts, and where are these accounts assembled?
The business records related amounts in their respective accounts known as
____
accounts. All such accounts are assembled in a book or collection called the
____
.
The business records related amounts in their respective accounts known as ledger accounts.
All such accounts are assembled in a book or collection called the
ledger.
What is the general ledger?All the accounts, including assets, liabilities, equity, revenues, and expenses, that are required to adequately portray a company's financial operations are included in the General Ledger.
Financial statements like the balance sheet, income statement, and cash flow statement are created from the accounts in the general ledger and offer an overview of the company's financial situation.
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Suppose you have a table
with constant differences. The input 2 gives the
output 11. The input 3 gives the output 14. What is
the output for the input 7?
Therefore , the solution of the given problem of input and output comes out to be methods for Fixing an Input-Output Table begin with the very first input.
What are the input and output rules?The function generates an output value by using an input value, such as x = 3, as an example. If you substitute 3 for the number x in the equation y = x + 5 y = x + 5, you get y = 3 + 5 = 8 y = 3 + 5 = 8. So, y = 8.
Here,
The output value is as follows.
Both the value of the final goods and services produced and the value added at each stage of production can be used to calculate total output.
An input-output table's governing principle is the mathematical operation or operations that are applied to the input to yield the desired output. The rule can be very basic, like adding 1, or quite complex, like squaring the amount and taking 17 out.
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if beth makes an initial investment of $1,000, how much will it be worth after three years if her average return is 8.25 percent (compounded monthly
After 3 years, Beth's investment will be worth $1,281.216.
What is percentage ?
A percentage is a number or ratio expressed as a fraction of 100. It is often denoted using the percent sign, "%", although the abbreviations "pct.", "pct" and sometimes "pc" are also used.
The formula to calculate the future value of an investment is:
FV = PV * (1 + r/n)^(nt)
where:
PV = present value = $1,000
r = annual interest rate = 8.25%
n = number of compounding periods per year = 12 (monthly)
t = number of years = 3
FV = $1,000 * (1 + 0.0825/12)^(12 * 3)
Plugging in the values and using a calculator, we get:
FV = $1,000 * (1 + 0.0825/12)^(12 * 3) = $1,000 * (1.006866)^36 = $1,000 * 1.281216 = $1,281.216
So after 3 years, Beth's investment will be worth $1,281.216.
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. Ryan bought cans of soup on sale for $1.30 each and paid with a $20 bill. If he received at least $5 but no more than $10 back, which inequality represents c. the number of cans he purchased?
Answer:
[tex]5 \leqslant 20 - 1.3x < 10[/tex]
a circle with an area of `8\pi` square centimeters is dilated so that its image has an area of `32\pi` square centimeters. what is the scale factor of the dilation?
The scale factor of the dilation of the given object is 4.
The scale factor of dilation:
The scale factor of the dilation of an object is determined by taking the ratio of image length to the corresponding object length.
Dilation is the process of resizing or transforming an object. The transformation that makes the objects smaller or larger with the help of the given scale factor.
The basic formula to find the scale factor of a dilated is:
Scale factor = Dimension of the new shape ÷ Dimension of the original shape.
[tex]SD=\frac{32cm^2}{4cm^2}[/tex]
SD=4
Thus, the scale factor of the dilation of the given object is 4.
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write a non-fruitful function draw triangle(someturtle, somesize) which makes a turtle draw an equilateral triangle.
A non-fruitful function which makes a turtle draw an equilateral triangle is given in the explanation.
Here is an example of a non-fruitful function in Python that takes a turtle object and a size as arguments and makes the turtle draw an equilateral triangle:
import turtle
def draw_triangle(some_turtle, some_size):
for i in range(3):
some_turtle.forward(some_size)
some_turtle.left(120)
# Create a turtle object
t = turtle.Turtle()
# Call function to draw an equilateral triangle of size 100
draw_triangle(t, 100)
# Hide turtle and exit the turtle window
turtle.done()
This function makes the turtle move forward by some_size units and turn left by 120 degrees three times, resulting in a triangle with three equal sides and three 60-degree angles.
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your Dad needed to get two matching gifts for his nephews, so he went to the store with $75 cash in his wallet. After buying the two gifts, now he has just $17 left over. How much did each gift cost?
Answer:
$29
Step-by-step explanation:
Since the gifts are matching, the cost of each gift be equal, say $x
Now, Total cash - cash leftover = cost of both gifts
which is, 75 - 17 = 2x
or $58 = 2x
Thus, x would be 58/2 = $29
Or each gift would cost $29
HELP ASAP WILL MARK THE BRAINLIEST
Answer:
Second choice : -3, 11, -45, 179
Step-by-step explanation:
First term: a₁ = - 3
Second term a₂ = -4a₁ -1 = (-4)(-3) - 1 = 12 - 1 = 11
There are only two options with 11 as the third term, Options 2 and 4 look the same but the fourth option has curly braces around the numbers making it a set rather than a sequence
If you wanted to be sure and compute the third term to see if it matches
a₃ = -4a₂ - 1 = -4(11)- 1 = -44 - 1 = -45
What's the value of x?
Answer:
52
Step-by-step explanation:
Using the exterior angle theorem, [tex]112+x=164 \implies x=52[/tex]
x/15 + 3/15 = -1/5
the solution is x =
Answer:
x = -6
Step-by-step explanation:
x/15 + 3/15 = -1/5
x/15 + 1/5 = -1/5
x/15 = -2/5
x = -6
Let's check
-6/15 + 3/15 = -1/5
-3/15 = -1/5
-1/5 = -1/5
So, x = -6 is the correct answer.
a student spends 3/4 of his money on tuition and 1/3 of what remains on books. if he has $50 dollars left, how much money did he start with?
Answer:
$75
Step-by-step explanation:
3/4 -tuition
4/4-3/4=1/4 1/3×1/4=1/12 -books
1/12+1/4=1/3 1-1/3= 2/3 -left which is equal to $50
2/=$50
1=
1×3/2×$50= $75
A punter kicks a football, it has a vertical speed of 70 m/s, and a height, h, in meters after t seconds can be modeled by the equation h = 70t - 5t 2
What is the maximum height of the football?
How long does it take to reach maximum height?
How long is the football in the air?
According to elementary algebra, time t has values of 3 and 1 seconds, respectively.
What is meant by polynomial equation?Polynomial equations are those created by combining variables, exponents, and coefficients. The higher exponent, known as the degree of the equation, might have several exponents.
A polynomial expression equal to 0 is the basis of a polynomial equation. For instance, since 3x² - 5 is a polynomial expression, 3x² - 5 = 0 is a polynomial equation.
Quadratic equations are two-variable, degree-two polynomial equations of the form f(x) = [tex]ax^{2}[/tex] + bx + c = 0 and with the variables a, b, c, and R R and a = 0.
With "a" denoting the leading coefficient and "c" denoting the absolute term of f, it is a quadratic equation in its general form (x).
Knowing that h = 15 m, we can enter that number into the equation to find t:
15 = 20t - [tex]5t^{2}[/tex] Let's set the equation equal to 0 to solve
-[tex]5t^{2}[/tex] + 20t - 15 = 0 Let's factor out a -5 to simplify the equation
-5(t2 - 4t + 3) = 0 0/-5 is still 0
[tex]t^{2}[/tex] - 4t + 3 = 0 Let's find factors for this solution
(t -3)(t - 1) = 0 We have 2 solutions for this equation
t = 3, t = 1
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You have one x2-block and 2n x-blocks (where n is a positive whole number). How many 1-blocks do you need to form a square? What are the dimensions of the square? Express your answer in terms of n.
Answer:
If you have one x2-block and 2n x-blocks, you need to add (2n)^2 1-blocks to form a square. The dimensions of the square will be (x2-block + 2n x-blocks) x (x2-block + 2n x-blocks) = (2n+2) x (2n+2) = (2n + 2)^2.
se tienen 10 parlantes idénticos que emiten sonido simultáneamente y el nivel de intensidad medido en un punto es 100 db, ¿cuál es el nivel de intensidad del sonido que emite cada parlante?
The total sound level at the point is 100 dB (10 dB x 10 speakers).
The formula for calculating the sound level emitted by each speaker is 10 * log (100 / 10) = 10 dB. This means that each speaker emits a sound level of 10 dB.
To calculate this, we first need to understand the principle of the logarithmic addition of sound levels. The logarithmic addition of sound levels states that when two sound waves with different amplitudes overlap, the resulting amplitude is the sum of the logarithms of the individual amplitudes.
For example, let's say we have two sound waves with amplitudes of 10 dB and 20 dB. The resulting amplitude will be 10 * log (10 + 20) = 10 * log (30) = 10 dB + 20 dB = 30 dB.
Therefore, in our example, the 10 speakers each emit a sound level of 10 dB. This means that when all 10 speakers play simultaneously, the total sound level at the point is 100 dB (10 dB x 10 speakers).
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a) You are going to roll two 6-sided dice and take their difference, referred to as D. What is VAR(D)? b) You are going to roll two 6-sided dice and add them together, referred to as A. What is VAR(A)?
The probability that the sum of the numbers on the dice facing up add up to 3 is 1/18 and VAR(A)= 1
Probability is defined as the likeliness of an event to occur. The probability of any event to occur ranges from 0 to 1, and the sum of all the probabilities of all the events happening is 1.
probability = desired outcome / total outcomes
A 6-sided dice has numbers 1, 2, 3, 4, 5, 6 at each of the 6 sides.
The event of rolling two fair 6-sided dice, which the numbers on the dice facing up add up to 3, is by having (1, 2) or (2, 1).
probability = desired outcome / total outcomes
probability = 2 / (6 x 6)
probability = 2 / 36
probability = 1/18
VAR(A)= 1
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I need help with this one asap
Answer:
[tex]\frac{1}{4y^9}[/tex]
Step-by-step explanation:
using the rule of exponents
• [tex]\frac{a^m}{a^n}[/tex] = [tex]\frac{1}{a^{(n-m)} }[/tex]
[tex]\frac{y^{-3} }{4y^{6} }[/tex]
= [tex]\frac{1}{4}[/tex] × [tex]\frac{y^{-3} }{y^6}[/tex]
= [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{y^{(6-(-3))} }[/tex]
= [tex]\frac{1}{4}[/tex] × [tex]\frac{1}{y^{(6+3)} }[/tex]
= [tex]\frac{1}{4y^9}[/tex]
What is the mathematical phrase for "Thrice a number more than 1?"
A. 2x+1
B. 1+2x
C. 3x+1
D. 1+3x
Answer:
C and D
Step-by-step explanation:
3x + 1 and 1 + 3x are the phrase for 'Thrice a number more than 1.
they can simplify to get the same answer.
61°24` in radians
Please and thank you
well, we know there are 60 minutes in 1 degree, so 24' is 24/60 = 0.4°, so 61°24' is really 61.4°, now, we also know that there are 180° in π radians, so
[tex]\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 61.4&x \end{array}\implies \cfrac{180}{61.4}~~ = ~~\cfrac{\pi }{x} \\\\\\ 180x=61.4\pi \implies x=\cfrac{61.4\pi }{180}\implies x=\cfrac{307\pi }{900}\implies x\approx 1.07~radians[/tex]
