In a right triangle, the length of the hypotenuse is the square root of the sum of the squares of the other two legs. Therefore, we can use the Pythagorean theorem to find the length of the legs of a right triangle given the length of the hypotenuse.
Pythagorean theorem: c^2 = a^2 + b^2
where c is the hypotenuse and a and b are the legs of the right triangle.
If the length of the longer leg is x, then the length of the other leg is 2x.
Using the Pythagorean theorem:
25^2 = x^2 + (2x)^2
625 = x^2 + 4x^2
625 = 5x^2
x = √(625/5) = √125 = 5
So, the length of the longer leg is 5 units.
You have just made your first $2,000 contribution to your retirement account. Assume you earn a return of10 percent and make no additional contributions.
a. What will your account be worth when you retire in 30 years?
b. What will your account be worth if you wait 5 years before contributing?
Answer:
BELOW
Step-by-step explanation:
Assuming no compounding
then interest = prt = 2000 * .1 * 30 = 6000
add original deposit to get 8000 total at end of 30 years
Assuming annual compounding
amount = 2000 ( 1+ .1)^30 = 34 898.80 dollars
Which definitely shows the POWER of COMPOUNDING !
What is the simplified form of this expression?
(5x2 + 2x + 11) − (7 + 4x − 2x2)
Answer:
Below
Step-by-step explanation:
(5x2 + 2x + 11) − (7 + 4x − 2x2) = 5x^2 + 2x + 11 - 7 - 4x + 2x^2 =
(5x^2 + 2x^2 ) + ( 2x-4x) +(11-7) =
7x^2 - 2x + 4
Write 4.8 as a mixed number and as an improper fraction
If you read the decimal version of 4.8 out loud, it should be "four and eight-tenths." This will always give you a good place to start when changing a decimal into an equivalent fraction.
Now, this is a mixed number: 4 and 8/10. To further simplify it as a mixed number, we can leave the 4 alone and reduce the fraction (8/10). Both the numerator and denominator are divisible by 2, so we can conclude (8/10) = (4/5). A correct answer in mixed number form is 4 and (4/5).
However, to change 4 and (4/5) to a single (improper) fraction, you first multiply the denominator (5) by the large number out front on the left (4) and ADD this product to the numerator (4). This number is your new numerator and it will still have the same denominator as before.
Here, 4 and (4/5) = [(5)*(4) + 4]/5 = (20+4)/5 = 24/5.
24 and 5 have no common factors, so this fraction is already in reduced form.
4.8 = 4 8/10 = 4 4/5
1. The receipt is for lunch for five students. Each student will pay 1/5 of the bill.
What will each student pay, excluding taxes and tip?
The required, each student will pay $10, as per the given condition.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication and division,
Here,
The question seems to be incomplete,
Let's assume that the bill is of $50 excluding taxes
Now, each student has to pay = 50 / 5
= $10 per head
Thus, the required, each student will pay $10, as per the given condition.
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Write the inequality shown by the shaded region in the graph with the boundary line x+3y=−15.
Inequality to show the shaded region in the graph:
x + 3y > -15
What is inequality?Inequalities are the mathematical expressions in which both sides are not equal. In inequality, unlike in equations, we compare two values. The equal sign in between is replaced by less than (or less than or equal to), greater than (or greater than or equal to), or not equal to sign.
Given equation of the line
x + 3y = -15
Shaded region is above the line
Which can be expressed as inequality
x + 3y > -15
Hence, x + 3y > -15 is the inequality to show the shaded region in the graph.
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Answer:
Step-by-step explanation: The above answer is only partially right. Due to the fact that the line with the arrows is solid, the sign is greater than or equal to.
So, the side with (0,0) is the side where x+3y>−15 and the shaded region (which contains (0,0)) shows the solutions of the inequality x+3y>−15.
Notice that since the boundary line is graphed with a solid line, the inequality includes the equal sign.
The graph shows the inequality x+3y≥−15.
Complete the proof that \triangle LMN\sim \triangle OPN△LMN∼△OPNtriangle, L, M, N, \sim, triangle, O, P, N. Two triangles L M N and N O P share the same point N. Side length P N is eight. Side Length L N is five. Sides L M and O P are parallel. Two triangles L M N and N O P share the same point N. Side length P N is eight. Side Length L N is five. Sides L M and O P are parallel. Statement Reason 1 \overline{LM}\parallel\overline{OP} LM ∥ OP start overline, L, M, end overline, \parallel, start overline, O, P, end overline Given 2 \angle L\cong\angle O∠L≅∠Oangle, L, \cong, angle, O When a transversal crosses parallel lines, alternate interior angles are congruent. 3 4 \triangle LMN\sim \triangle OPN△LMN∼△OPNtriangle, L, M, N, \sim, triangle, O, P, N similarity
The congruence theorem that proves that △LON ≅ △LMN is: A. SSS congruence theorem
What is the SSS Congruence Theorem?According to the SSS congruence theorem, if all three corresponding sides of two triangles are congruent, then both triangles are congruent.
here, we have,
In the image given, we have:
ON ≅ MN
LO ≅ LM
LN ≅ LN (reflexive property)
This means all three corresponding sides are congruent, therefore, the congruence theorem that proves both triangles are congruent is:
A. SSS.
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At the dog park, there are several dogs with their owners. Counting heads, there are 20; counting legs, there are 62. How many dogs and owners are there?
What's the sum of this?
Answer:
sum = (m+n)(n-m +1)/2
Step-by-step explanation:
You want an expression for the sum of the numbers from m to n.
TotalsAs the example shows, the sums of the numbers written forward and backward will be the sum of the numbers at the ends of the range:
m +n
CountThe number of times this sum is repeated is equal to the number of numbers in the range:
n -m +1
Sum of rangeThe sum of the numbers in the range will be half the product of these values:
sum = (m+n)(n-m +1)/2
Calculate the length w in the shape below.
Give your answer in centimetres to 2 d.p.
Answer:
w ≈ 12.14 cm
Step-by-step explanation:
using the tangent ratio in the right triangle on the left.
let vertical height be x
tan56° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{x}{3.2}[/tex] ( multiply both sides by 3.2 )
3.2 × tan56° = x , then
x ≈ 4.744
using the cosine ratio in the right triangle on the right
cos67° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{w}[/tex] = [tex]\frac{4.744}{w}[/tex] ( multiply both sides by w )
w × cos67° = 4.744 ( divide both sides by cos67° )
w = [tex]\frac{4.744}{cos67}[/tex] ≈ 12.14 cm (to 2 decimal places )
Answer:
w = 12.14 cm
Step-by-step explanation:
See the attached image. Trigonometric functions will be used
What is the range of the function y= ^3 square root y
Answer:
y= 3 y =0
Step-by-step explanation:
find the derivative
How many terminating zeros are at the end of 6311! ,when this number is multiplied out?
The number of terminating zero when the number 6311! is multiplied out is 252
What it terminating zeros?In mathematics, trailing zeros are a series of digits (usually 0) that follow a number's decimal form or, more broadly, any positional representation.
In mathematics, the term "factorial" refers to the product of all positive integers that are less than or equal to a certain positive integer, which is followed by an exclamation point.
Thus, factorial five is denoted by the symbol 5!, which stands for 1 * 2 * 3 * 4 * 5. Factorial 0 is equivalent to 1 by definition.
For the problem 6311! has 252 trailing zeros
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Answer:
1576 terminating zeros---------------------------
Terminated zeros at the end of number n! is found as the sum of the whole quotients of n and powers of 5 less than n.
Given:
n = 6311.This is greater than 5⁵ = 3125 but less than 5⁶ = 15625.
Find each quotient of 6311 and 5¹ through 5⁵ :
6311/5¹ = 1262,6311/5² = 252,6311/5³ = 50,6311/5⁴ = 10,6311/5⁵ = 2.Sum of the quotients is the number of terminating zeros:
1262 + 252 + 50 + 10 + 2 = 1576To save for retirement, starting from her 30th birthday (t = 0), Miss Saver will invest
some money each year in a 30-year deposit in her bank saving account. The first
payment of $1000 will be made at the beginning of the first year. Every subsequent
payment increases by 5%.
She will retire at age 60, and will withdraw $X each year from her bank saving account
from then. The first withdrawal will be made at age 60. After 20 years (i.e. after the
20th withdrawal), she will have taken out all the money she had saved.
Assuming the effective annual interest rate is 2% perpetually, compute the value of X.
Give your answer to the nearest integer.
Answer:
To calculate the value of X, we first need to calculate the total amount of money Miss Saver will have saved by the time she retires at age 60.
We know that her first payment is $1000, and that every subsequent payment increases by 5%. Using this information, we can calculate the total payments made during the 30 years:
$1000 x (1 + 0.05)^30 = $1000 x 3.3201 = $3320.1
This is the total amount of money Miss Saver will have saved by the time she retires at age 60.
Next, we need to calculate the value of each annual withdrawal over the 20 years of withdrawals.
We know that the effective annual interest rate is 2% perpetually, so we can use the formula for the future value of an annuity:
FV = X * ((1 + r)^n - 1) / r
where X is the annual withdrawal, r is the interest rate (0.02), and n is the number of years (20).
We can use this formula to solve for X:
3320.1 = X * ((1 + 0.02)^20 - 1) / 0.02
X = 3320.1 * 0.02 / (1.02^20 - 1)
X = 3320.1 * 0.02 / 0.1135 = $292.36
Therefore, Miss Saver needs to withdraw $292.36 each year for 20 years to deplete her savings account.
Rounded to the nearest integer, the value of X is $292.
Please help me solve this
Extra points
Answer:
D
Step-by-step explanation:
bc -1+27 =26
Simplify the expression:
2+2+3+s+ 9 - 10
Answer:
6s
Step-by-step explanation:
2+2+3+S+9-10
first we can put these in different group to find out, like number to number, variable to variable. so it will be 2+3+2+9-10=6
second they only one s, so answer is 6s
i hope is helpful
The width of the blue vinyl in each triangle is 6 in. The height of the yellow right triangle is 12.3 in. How much yellow vinyl is needed for each of the triangular sides?
Please help with this problem
[tex]-\sqrt{9y^2} = -1\cdot \sqrt{9}\cdot \sqrt{y^2}[/tex]
I assume you're good with [tex]\sqrt{9}=3[/tex], so this gives us:
[tex]= -3\cdot \sqrt{y^2}[/tex]
Now the trick on the variable portion is that since y<0, when you square y, you turn it from being a negative number into a positive [tex]y^2[/tex] value. And when you take the square root of that, you keep the positive value. So effectively, [tex]\sqrt{y^2} = |y|[/tex], since it just makes the negative number become positive.
[tex]= -3|y|[/tex]
CAN SOMEONE HELP WITH THIS QUESTION?✨
The instantaneous rate of change of g(x) = 2/(x + 6) at x = 3 is given as follows:
g'(3) = -0.025.
How to obtain the instantaneous rate of change?The function for this problem is defined as follows:
g(x) = 2/(x + 6).
The instantaneous rate of change at x = a is defined as follows:
g'(a).
In exponent format, the function is defined as follows:
g(x) = 2(x + 6)^(-1).
Applying the chain rule, the derivative of g(x) is given as follows:
g'(x) = -2(x + 6)^(-2)[x + 6]'
g'(x) = -2/(x + 6)².
At x = 3, the numeric value of the derivative is given replacing the lone instance of x by 3, hence:
g'(3) = -2/(3 + 6)²
g'(3) = -2/81
g'(3) = -0.025.
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I need help pleaseeeeeeeeeeeeeeeeeeee
Answer:
Step-by-step explanation: [-2.19] = -3
[3.67] = 3
[-0.83] = -1
The domain of this function is a group of real numbers that are divided into intervals such as [-5, 3), [-4, 2), [-3, 1), [-2, 0) and so on. This explains the domain and range relations of a step function.
This can be generalized as given below:
[x] = -2, -2 ≤ x < -1
[x] = -1, -1 ≤ x < 0
[x] = 0, 0 ≤ x < 1
[x] = 1, 1 ≤ x < 2
Answer:
y = - [tex]\frac{3}{2}[/tex] x
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 3) and (x₂, y₂ ) = (0, 0) ← 2 points on the line
m = [tex]\frac{0-3}{0-(-2)}[/tex] = [tex]\frac{-3}{0+2}[/tex] = - [tex]\frac{3}{2}[/tex] , then
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
to find c substitute either of the 2 points into the partial equation
using (0, 0 )
0 = - [tex]\frac{3}{2}[/tex] (0) + c = 0 + c , so
c = 0
y = - [tex]\frac{3}{2}[/tex] x + 0 , that is
y = - [tex]\frac{3}{2}[/tex] x
which of the following decimal numbers can be represented accurately with a finite number of binary bits in the binary system?
Among the given, only 0.5 can be exactly represented in binary notation with a finite number of bits
Hence, option (d) is the correct choice.
Binary is a base-2 number system in which a number is represented by two states: 0 and 1. We can also refer to it as a true and false condition. A binary number is constructed in the same manner as a decimal number.
Binary data is information expressed or displayed using the binary number system. Binary data is the only type of data that a computer can directly understand and execute. It is represented numerically as a series of zeros and ones.
The binary representation of 0.5 is 0.1_2, and it is the only terminating fraction among the available possibilities.
As a result, it is the only fraction that can be expressed precisely.
All of the other possibilities have a non-terminating fraction portion and hence cannot be expressed accurately with a limited amount of bits.
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The complete question may be:
Which of the following decimal numbers can be exactly represented in binary notation with a finite number of bits?
(a) 0.1
(b) 0.2
(c) 0.4
(d) 0.5
(e) All the above
22. Probability have values between _________________ and _________________.
Probability has values between 0 and 1.
What is the Probability?
The probability of an event is a number between 0 and 1, where, roughly speaking, 0 indicates the impossibility of the event and 1 indicates certainty.
0 represents an impossible event and 1 represents a certain event.
A probability of 0 means that an event will not occur, and a probability of 1 means that an event will certainly occur.
Probabilities between 0 and 1 represent the likelihood of an event occurring, with values closer to 1 indicating a higher likelihood of the event occurring and values closer to 0 indicating a lower likelihood.
Hence, Probability has values between 0 and 1.
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HELP FAST WILL MARK BRAINLYIST !!! You are a realtor who is preparing a brochure for future clients. You review a list of houses you recently sold in a particular neighborhood. The selling prices were as follows: $125,000, $125,000, $178,000, $190,000, $216,000, $225,000, and $890,000 Which measure best describes the typical selling price for a house in this neighborhood?
mode
median
mean
weighted mean
spread
The mode, median, mean ,weighted mean, spread of the set of data are: 125, 190, 278429, 765 respectively
What is Measure of central tendency?We are asked to find the following
Mode: This is the highest occurred frequency in a set of data and the mode here is 125
The median is the middle frequency when arranged in an order of magnitude the the set of data is $125,000, $125,000, $178,000, $190,000, $216,000, $225,000, and $890,000. the median is 190
The mean is the average of the data that is: ( $125,000,+$125,000+$178,000+$190,000+$216,000+$225,000+$890,000)/7 = 1949000/7 = 279429
the spread is the range which is the highest frequency minus the lowest frequency = $890,000 -$125,000= 765000
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Answer:
median
Step-by-step explanation:
Determine if the following equation is an identity equation, a conditional equation, or an inconsistent equation. −2x+4−7x=−4+5−9x
The equation −2x+4−7x=−4+5−9x is an inconsistent equation.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
The given equation is −2x+4−7x=−4+5−9x
Add the like terms on both sides
-9x+4=1-9x
inconsistent equation.
A system of equations is called consistent if there is at least one set of values for the unknowns that satisfies each equation in the system
Hence, the equation −2x+4−7x=−4+5−9x is an inconsistent equation.
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Need help please, fast, here i screenshot!!
The equation g(x) = (x - 4) (x + 2) is in the factored form.
The x-intercepts are x = -2 and x = 4.
The axis of symmetry is x = 1.
Vertex is (1, -9).
What is an equation?An equation is a mathematical statement that is made up of two expressions connected by an equal sign.
Example:
2x + 3 = 8 is an equation.
We have,
g(x) = (x - 4) (x + 2)
This is in the factored form.
Now,
From the graph,
The x-intercepts are x = -2 and x = 4.
The axis of symmetry.
x = -b/2a
x = 2/2
x = 1
i.e
g(x) = (x - 4) (x + 2)
g(x) = x² + 2x - 4x - 8
g(x) = x² - 2x - 8
a = 1, b = -2, and c = -8
Now,
g(x) = x² - 2x - 8
g(x) = x² - 2x + 1 - 1 - 8
g(x) = (x² - 2x + 1) - 9
g(x) = (x - 1)² - 9
This is in the form of f(x) = a(x - h)² + k
So,
Vertex = (h, k) = (1, -9)
Thus,
The statements are completed above.
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the passenger section of a train has width 2x-7, length 2x+3, and height x-2, with all dimensions in meters. solve a polynomial equation to determine the dimensions of the section of the train if the volume is 117m3
The dimensions of width, length and height of the passenger section of the train are 3 meters, 13 meters and 3 meters respectively.
What are the dimensions of the passenger section of the train?The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length
Given that;
Width of the section = 2x - 7Length of the section = 2x + 3Height of the section = x - 2Volume = 117 m³First, plug in the given values into the above formula and solve for x.
V = w × h × l
117 = ( 2x - 7 )( 2x + 3 )( x - 2 )
Expand using FOIL method
( 2x - 7 )( 2x + 3 )( x - 2 ) = 117
( 2x(2x) + 2x(3) - 7(2x) - 7(3) )( x - 2) = 117
( 4x² - 8x - 21 )( x - 2 ) = 117
Expand
4x³ - 16x² - 5x + 42 = 117
4x³ - 16x² - 5x + 42 - 117 = 0
4x³ - 16x² - 5x - 75 = 0
Using rational roots text
(x - 5)(4x² + 4x + 15 ) = 0
( x - 5 ) = 0
x - 5 = 0
x = 5
4x² + 4x + 15 = 0
x = -1±i√14 / 2
Since dimensions are real and positive numbers, we use;
x = 5
To determine the dimensions of the passenger section of the train, plug in x = 5 and simplify.
Width = 2x - 7 = 2( 5 ) - 7 = 10 - 7 = 3 meters
Length = 2x + 3 = 2( 5 ) + 3 = 10 + 3 = 13 meters
Height = x - 2 = 5 - 2 = 3 meters
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Drag each number tile to the box with the matching expression. 3 1 2 3 1 3 3 1 4 3 1 6 3 2 3 12 1 2 − 9 1 4 5 3 4 − 2 5 12
Answer:
ggggghhytyhhh
Step-by-step explanation:
ghdhb
Determine which of the following best describes the statement below.
"The temperature on randomly selected days throughout the year was measured"
Answer options:
experimental study
observational study
Answer:
observational study to see honestly but this is correct but I don't know the exact reason
Please solve ASAP THANKS
Answer:
Step-by-step explanation:
Harry winston dillan paul
f (x )equals fraction numerator 2 over denominator s plus 5 end fraction use the inverse laplace transform to find f (t ).
The inverse Laplace transform of (2/(s+5)) is f(t) = 2 * e^(-5t)u(t).
To find the inverse Laplace transform of F(s) = (2/(s+5)), we can use partial fraction expansion and then use a table of Laplace transforms to identify the inverse transforms.
Step 1: Perform partial fraction expansion on the fraction:
(2/(s+5)) = (2/5) * (1/(1+(s/5))) = (2/5) * (1/1 + (s/5))
Step 2: Recognize the form of the partial fraction as a geometric series, and use the formula for the sum of a geometric series to find the inverse Laplace transform:
The sum of this geometric series is
(2/5) * (1/(1-(-s/5)))
= (2/5) * (1/(1+s/5))
= (2/5) * (5/5+s)
= (2/(5+s))
Step 3: Use the table of Laplace transforms to find the inverse transform of (2/(5+s)):
f(t) = 2 * e^(-5t)u(t)
where u(t) is the unit step function.
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Using the
slope from the previous
problem, find the
equation of the line
passing through the
points (-2,1) and
(2,-11). The slope is -3
The answer is,
(iii) (3,-5), and (1,2) Slope of line [tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-5)}{1-3}=\frac{7}{-2}=\frac{-7}{2}$[/tex]
What is slope?A line's steepness is determined by its slope. In mathematics, slope is determined by "rise over run" (change in y divided by change in x). A number that describes a line's direction and steepness is known as the slope or gradient of a line in mathematics. The slope of a line is how steep it is going from LEFT to RIGHT. Slope is the proportion of a line's ascent, or vertical change, to its run, or horizontal change. The slope is calculated as the ratio of the rise, which is the vertical change between two points, to the run, which is the horizontal change between those same two sites.(i) (-3,2) and (1,4) Slope of line [tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{4-2}{1-(-3)}=\frac{2}{4}=\frac{1}{2}$[/tex]
(ii) [tex]$\left(a_1^2, 2 a_1\right)$[/tex] and [tex]$\left(a t_2^2, 2 a_2\right)$[/tex] Slope of line
[tex]& \frac{y_2-y_1}{x_2-x_1}=\frac{2 a t_2-2 a t_1}{a t_2^2-a t_1^2} \\[/tex]
[tex]& =\frac{2 a\left(t_2-t_1\right)}{a\left(t_2-t_1\right)\left(t_2+t_1\right)}=\frac{2}{t_2+t_1}[/tex]
(iii) (3,-5), and (1,2) Slope of line [tex]$=\frac{y_2-y_1}{x_2-x_1}=\frac{2-(-5)}{1-3}=\frac{7}{-2}=\frac{-7}{2}$[/tex]
The complete question is,
Find the slope of a line passing through the following points:
(i) (-3,2) and (1,4)
(ii) [tex]$\left(a t_1^2, 2 a_1\right)$[/tex]and [tex]$\left(a t_2^2, 2 \mathrm{at}_2\right)$[/tex]
(iii) (3,-5), and (1,2)
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.The cost c of fish varies directly as its wieght w in kilograms.
a.Direct variation b.joint variation c.combined variation
2.The number of men n needed to do a job varies inversely as the number of days d to finish the job.
a.Direct variation b.Joint variation C.combined variation
The cost c of fish varies directly as its weight w in kilograms.
a.Direct variation
b.joint variation
c.combined variation
A SIMPLE RELATIONSHIP BETWEEN TWO VARIABLES IS DESCRIBED AS A DIRECT VARIATION.
When c=kw, where k is the variational constant, we say that c directly varies with w.
2. The quantity of men (n) required to complete a task varies inversely with the duration (d) of the task.
INVERSE VARIATION: Inverse variation occurs when the product of two variables (n and d) ALWAYS equals a fixed value (k). Example,
N=k/d states that the required number of men (n) varies inversely with the number of days (d) required to complete the task.
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