The solution is, EF = 4√3
What is area of a rectangle?Area of a rectangle (A) is the product of its length (l) and width (w).
A= l. w
here, we have,
In rectangle ABCD, AB = 6, BC = 8, and DE = DF.
ΔDEF is one-fourth the area of rectangle ABCD.
We want to determine the length of EF.
First, we can find the area of the rectangle. Since the length AB and width BC measures 6 by 8, the area of the rectangle is:
A = 48 cm^2
The area of the triangle is 1/4 of this. Therefore:
A = 12 cm^2
The area of a triangle is half of its base times its height. The base and height of the triangle is DE and DF. Therefore:
12 = 1/2 * DF *DE
Since DE = DF:
24 = DF^2
Thus:
DF = 2√6 = DE
Since ABCD is a rectangle, ∠D is a right angle. Then by the Pythagorean Theorem:
DF^2 + DE^2 = EF^2
Therefore:
now, Squaring & Adding , we get,
FE^2 = 48
And finally, we can take the square root of both sides:
EF = 4√3
Hence, The solution is, EF = 4√3
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At a music store, Rita got a $12 discount on an item originally priced at $48. What percent discount did she get?
Answer:
a $12 discount like what is it soupoust to be
y= 2x + 3
y= -3x + 3
Answer:
Below
Step-by-step explanation:
I suppose you are looking for a solution to the system of equations
since both equations are equal to 'y' they are equal:
2x+3 = -3x+3 add 2x to both sides of the equation
5x + 3 = 3 subtract 3 from both sides
5x = 0 so x = 0
if x =0 then find y y = 2(0) + 3 = 3
the solution is (0,3)
for a certain type of soil the number of wireworms per cubic foot has a mean of 100 . assuming a poisson distribution of wireworms, give an interval that will include at least 5 / 9 of the sample values of wireworm counts obtained from a large number of 1 -cubic-foot samples.
An interval that will include at least 5/9 of the sample values of wireworm counts obtained is (85,115).
Let us consider a random variable Y which follows the Poisson distribution with parameter λ=100
The Mean of the Poisson distribution of λ(μ)=100
The variance of the Poisson distribution σ²=100
We need to find an interval that will include at least 5/9 of the sample values.
We have the Mean of the Poisson distribution λ=100
The variance of the Poisson distribution is σ²=100
The standard deviation of the Poisson distribution is σ =√100=10
Now, consider Tchebysheff’s rule:
Let X be a random variable with finite expected value and finite non-zero variance then for any real number k > 0,
Pr(|X-μ|≥kσ)=≤1/k².
1-1/k²=5/9
1-5/9=1/k²
4/9=1/k²
k²=9/4
k=1.5
So the interval contains all the values within 1.5 standard deviations from the mean:
μ±1.5(σ)
100±1.5(10)
100±10
(85,115).
Hence, The interval is (85, 115).
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determine each length in right triangle . right triangle abc with right angle at vertex b. point d lies on side ac. dashed segment bd is drawn. angles
Using the Pythagorean theorem and the Law of Cosines, we can solve for the lengths of each side in right triangle ABC.
The right triangle ABC with right angle at vertex B can be solved using the Pythagorean theorem. The Pythagorean theorem states that in any right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the two shorter sides. In this case, side AC is the hypotenuse and side AB and BC are the two shorter sides.
We can determine the lengths of all three sides using the Pythagorean theorem and the information given. Side AB is equal to the square root of the sum of the squares of sides AC and BC. Since we are given that angle ABC is a right angle, we can determine that side BC is equal to the length of side AB. This means that the length of side AB is equal to the square root of the square of side AC. The length of side AC can be determined by finding the length of the dashed segment BD.
To find the length of dashed segment BD, we can use the Law of Cosines. The Law of Cosines states that in any triangle, the square of the length of a side is equal to the sum of the squares of the other two sides minus twice the product of the other two sides multiplied by the cosine of the angle opposite the side. In this case, we are finding the length of side BD. We can use the angle ABC and side AC to solve for the length of side BD.
Therefore, using the Pythagorean theorem and the Law of Cosines, we can solve for the lengths of each side in right triangle ABC.
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what is 8 1/6-3 7/12
Answer: 4 7/12
Step-by-step explanation:
[tex]\huge\text{Hey there!}[/tex]
[tex]\mathsf{8\dfrac{1}{6} - 3 \dfrac{7}{12}}[/tex]
[tex]\mathsf{= \dfrac{8\times6 + 1}{6} - \dfrac{3\times12 + 7}{12}}[/tex]
[tex]\mathsf{= \dfrac{48 + 1}{6} - \dfrac{36 + 7}{12}}[/tex]
[tex]\mathsf{= \dfrac{49}{6} - \dfrac{43}{12}}[/tex]
[tex]\mathsf{= \dfrac{49}{6}\times\dfrac{2}{2} - \dfrac{43}{12}\times\dfrac{1}{1}}[/tex]
[tex]\mathsf{= \dfrac{49\times2}{6\times2} - \dfrac{43\times1}{12\times1}}[/tex]
[tex]\mathsf{= \dfrac{98}{12} - \dfrac{43}{12}}[/tex]
[tex]\mathsf{= \dfrac{98 - 43}{12 - 0}}[/tex]
[tex]\mathsf{= \dfrac{55}{12}\rightarrow 4\dfrac{7}{12}}[/tex]
[tex]\huge\text{Therefore your answer should be:}[/tex]
[tex]\huge\boxed{\mathsf{4\dfrac{7}{12}}}\huge\checkmark[/tex]
[tex]\huge\text{Good luck on your assignment \& enjoy your day!}[/tex]
~[tex]\frak{Amphitrite1040:)}[/tex]Prove that the value of the expression (3/5x^2-0.4cy-1.5y+1)-(y^2-2/5xy+0.6x^2) does not depend on x
Therefore, we have proved that the value of the expression
(3/5x²-0.4cy-1.5y+1)-(y²-2/5xy+0.6x²) doesn't depend on x.
Expression: What is it?In mathematics, addition, multiplication, and division are necessary. They result in the following when combined: An equation, some data, and a mathematical function Values, parameters, and mathematical operations like additions, subtractions, multiplications, and divisions can all be found in a declaration of fact. Different phrases and words can be compared and evaluated.
Here,
To prove that the value of the expression doesn't depend on x, we need to show that the x-term disappears when we simplify the expression.
Starting with:
(3/5x² - 0.4cy - 1.5y + 1) - (y² - 2/5xy + 0.6x²)
Distributing the negative sign in the second set of parentheses:
3/5x² - 0.4cy - 1.5y + 1 - y² + 2/5xy - 0.6x²
Rearranging the terms by collecting like terms, we get:
(3/5 - 0.6)x² + (2/5y - 0.4c)y - y²- 1.5y + 1
Simplifying further, we get:
(-0.1)x² + (0.4y - 0.4c)y - (y² + 1.5y - 1)
Notice that there is no x-term in the final expression, which means that the value of the expression doesn't depend on x.
Therefore, we have proved that the value of the expression (3/5x²-0.4cy-1.5y+1)-(y²-2/5xy+0.6x²) doesn't depend on x.
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Solve the formula for the indicated variable.
Z=m+mwg for m
m=
(Simplify your answer.)
The value for variable m in equation Z = m + mwg is m = Z - mwg.
What are variables?
The alphabetic character that expresses a numerical value or a number is known as a variable in mathematics. A variable is used to represent an unknown quantity in algebraic equations.
The equation is given as -
Z = m + mwg
To get the value for variable m, subtract mwg from Z and take it to left-hand side.
Z - mwg = m
Reverse the equation and get it in right form -
The equation obtained is -
m = Z - mwg
Therefore, the value is m = Z - mwg .
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Find the amount of tax and the tax rate. Round to two decimal places
Cost of item: $126
Selling price: $133.36
Tax amount: $
Tax rate:
Answer:
Tax amount: $7.36
Tax rate: 5.84%
Step-by-step explanation:
First, we have to find the tax amount by taking
$133.36 - $126 = $7.36
Tax amount: $7.36
To find the tax rate, we take
7.36 divided by 126, times 100 = 5.84%
Tax rate: 5.84%
So,
Tax amount: $7.36
Tax rate: 5.84%
What is the equation of the function that is graphed as line a?
y = 4 x - 3
y = - 1/4 x + 3
y = 1/4x + 3
y = -4 x - 3
Answer:
y = 4x - 3
Step-by-step explanation:
y = mx + b
The m is the slope and the b is the y-intercept.
The slope is 4. If you start at the point (0,-3) and go up 4 units and then 1 unit to the right, you will be back on the line at point (2,4) The slope is the rise over the run. The rise is 4 and the run is 1. 4/1 = 4.
The slope (m) is 4.
The y-intercept is where the line crosses the y axis. It crosses at (0,-3)
The y-intercept (b) is -3
Plug 4 in for m and -3 in for b
y = mx + b
y = 4x -3
Answer:
[tex]y = 4x - 3[/tex]
Step-by-step explanation:
we need to find out the equation of the function that is graphed. From the given graph we can see that the line passes through points (0,-3) and (2,5) . So we can find out the slope of the line as ,
[tex]\implies m =\dfrac{y_2-y_2}{x_2-x_1}=\tan\theta\\[/tex]
[tex]\implies m =\dfrac{-3-5}{0-2} \\[/tex]
[tex]\implies m =\dfrac{-8}{-2} \\[/tex]
[tex]\implies \mathfrak{ m = 4 }\\[/tex]
Now we may use point slope form of the line to find out the equation of the line as,
[tex]\implies y - y_1 = m(x-x_1) \\[/tex]
[tex]\implies y -(-3) = 4(x-0) \\[/tex]
[tex]\implies y +3 = 4x\\[/tex]
[tex]\implies \underline{\underline{ y = 4x -3}} \\[/tex]
And we are done!
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ax-b=4 if a≠0
please help immeditatlyl
jfasjflsajdflskadjfsadfsadf
Answer:
Graphical form: Ax-b=4 simplifies to Ax-b-4=0
Text form: Ax-b=4 simplifies to Ax-b-4=0
Cartoon (animation) form: simplify_cartoon%28+Ax-b=4+%29
For tutors: simplify_cartoon( Ax-b=4 )
Step-by-step explanation:
I’m a lil bit confused please help
Answer:
5000
Step-by-step explanation:
10×16=160
160 Btu?
is 5000
because the closesd value in the graph is 5000
for 160
Please help me out! Just put these in order from the picture below.
Answer:
1) {2,0,-2}
2) {1,-3,1}
3) {1,3,5}
4) {0,1,2}
Which three criteria do binomial experiments meet? There are only two trials. The trials are independent. There are only two outcomes per trial. Each outcome is repeatable. The probability of success is the same for each trial.
The three criteria that binomial experiments meet are :
The trials are independent. There are only two outcomes per trial. The probability of success is the same for each trial.What criteria should binomial experiments meet ?The experiment is referred to as a binomial experiment since there are only two possible output values in a binomial experiment. In the case of binomial experiments, the number of independence variables is fixed.
In the case of binomial experiments, the number of independence variables is fixed. The total number of output values for the binomial experiment is 2. For the binomial experiment, each of the two outputs has a 50% chance of happening—50% for success and 50% for failure.
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Answer:
B. The trials are independent.
C. There are only two outcomes per trial.
E. The probability of success is the same for each trial.
Step-by-step explanation:
and then
B. a survey asking 50 people if they like pizza
C. a survey measuring 50 people to see if they are over 6 feet tall
Find the principal value of Arctan (-1.44) to the nearest minute.
Answer: To find the principal value of arctan(-1.44) to the nearest minute, we first need to find the value of arctan(-1.44) in radians.
We can use the arctan function in a mathematical software or calculator to find the result. The value of arctan(-1.44) in radians is approximately -0.8623.
Next, we convert the result from radians to minutes, by multiplying the radians by 180/π and then multiplying the result by 60.
-0.8623 * 180/π * 60 = -50.47 minutes
So the principal value of arctan(-1.44) to the nearest minute is approximately -50 minutes.
Step-by-step explanation:
Which elements listed below are required for an inverse trig problem to find a missing angle?
*check all that apply
A right triangle
The length of at least one side
The measure of at least one angle
The length of at least 2 sides
The elements listed above that are required for an inverse trig problem to find a missing angle include the following:
A. A right triangle.
D. The length of at least 2 sides.
What is a right angle?In Mathematics, a right angle can be defined as a type of angle that is formed in a triangle by the intersection of two (2) straight lines at 90 degrees. This ultimately implies that, a right angled triangle has a measure of 90 degrees.
Generally speaking, the length of at least two (2) sides is an element that is required for an inverse trig problem in order to find a missing angle in a right angled triangle.
In conclusion, both a right triangle and the length of at least two (2) sides must be provided in order to find a missing angle in a right angled triangle.
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Can somebody help me please
93,101,109,117,125,133,141,149,157,165
Zachary purchased a computer for $1,300 on a payment plan. Two months after he purchased the computer, his balance was $1,090. Seven months after he purchased the computer, his balance was $565. What is an equation that models the balance y after x months?
The equation ______ models the balance y after x months.
(Type your answer in slope-intercept form. Use integers or fractions for any numbers in the equation. Do not include the $ symbol in your answer.)
Answer:
[tex]y=-105x+1300[/tex]
Step-by-step explanation:
Define the variables:
Let x be the number of months after Zachary purchased a computer.Let y be the balance of the payment plan (in dollars).Given information:
Purchase price of the computer = $1,300Balance = $1,090 after 2 months.Balance = $565 after 7 months.Therefore:
x = 0, y = 1300x = 2, y = 1090x = 7, y = 565[tex]\boxed{\begin{minipage}{8cm}\underline{Slope Formula}\\\\Slope $(m)=\dfrac{y_2-y_1}{x_2-x_1}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line.\\\end{minipage}}[/tex]
Determine if the equation is linear by calculating the slope between each pair of (x, y) points:
[tex]\implies \text{Slope}\;(m)=\dfrac{565-1090}{7-2}=-105[/tex]
[tex]\implies \text{Slope}\;(m)=\dfrac{1090-1300}{2-0}=-105[/tex]
As the slope is the same, the equation is linear.
[tex]\boxed{\begin{minipage}{6.3 cm}\underline{Slope-intercept form of a linear equation}\\\\$y=mx+b$\\\\where:\\ \phantom{ww}$\bullet$ $m$ is the slope. \\ \phantom{ww}$\bullet$ $b$ is the $y$-intercept.\\\end{minipage}}[/tex]
The initial purchase price of the computer was $1,300. So when x = 0, y = 1300. Therefore, the y-intercept is 1300.
We have already calculated the slope as -105.
Substitute the found slope and y-intercept into the slope-intercept formula to create an equation that models the balance y after x months:
[tex]y=-105x+1300[/tex]
64. Use a graph to estimate the critical numbers of f(x)=| x^3-3x^2+2| correct to one decimal place.
The critical numbers of f (x) = | x³ -3x² + 2| is, x = 0 and x = 2.
What is mean by Function?A relation between a set of inputs having one output each is called a function. and an expression, rule, or law that defines a relationship between one variable (the independent variable) and another variable (the dependent variable).
Given that;
The function is,
⇒ f (x) = | x³ -3x² + 2|
Now, We know that;
⇒ All the critical points are find as;
⇒ f '(x) = 0
⇒ 3x² - 6x = 0
⇒ 3x(x - 2) = 0
⇒ x = 0
⇒ x = 2
Thus, The critical numbers of f (x) = | x³ -3x² + 2| is, x = 0 and x = 2.
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The population growth rate due to the difference in births and deaths in the U.S. is estimated to
be 0.5% per year. Given a 2001 population size of about 285 million, calculate the projected
population size in 2025. Use the exponential growth equation (N= No e"), to calculate the
population. In the equation, No is the initial population (285,000,000), r is the growth rate expressed as a
decimal (0.005), t is the number of years (25), e is a constant (defined as the base of the natural
logarithm), and N, is the population after t years.
In 2025, we would have 321 million people Since we do have an exponential growth function here.
What is exponential growth?
Exponential growth is a type of growth that occurs when the rate of increase is proportional to the current value. In mathematical terms, it can be expressed as y = ab^x.
We then have that;
P = Poe^rt
P = population at time t
Po = Initial population
r = rate of growth
t = time taken
Then;
t = 24 years
r = 0.005
Thus;
P = 285 * 10^6e^24 * 0.005
P = 321 million people
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Mike buys 3 oranges and 1 lemon at the
farmers market. What fraction of his
purchase were oranges?
Mike buys 3 oranges and 1 lemon at the
farmers market. What fraction of his
purchase were oranges?
answer :
3/4
Answer: 3/4
Step-by-step explanation:
there are a total of four purchases and three of them were purchases we can represent this with the fraction 3/4
4 divided by 2 left square brackets 2 plus 2 right square brackets equals?
The given expression "4 divided by 2 left square brackets 2 plus 2 right square brackets equals" gives the solution one divided by 2.
How to solve expressions?4 divided by 2 left square brackets 2 plus 2 right square brackets equals?
4 ÷ 2(2 + 2)
based on the concept of PEMDAS
P = parenthesis
E = Exponent
M = Multiplication
D = Division
A = Addition
S = Subtraction
= 4 ÷ 2(4)
= 4 ÷ 8
= 4/8
= 1/2
Therefore, the correct answer is 1/2(one divided by two
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after five years of owning a roth individual retirement account (ira), a person wants to buy his first home, the person can withdraw money from the roth ira
A person who has owned a Roth IRA for five years may withdraw money from the account to buy their first home. The individual has to meet certain requirements and can't withdraw more than $10,000 per person.
A Roth IRA is a type of individual retirement account that allows for tax-free withdrawals of contributions at any time, without penalty or taxes. After five years of ownership, a person who has a Roth IRA may withdraw money from the account to buy their first home. This withdrawal is known as a "first-time homebuyer distribution."
However, there are certain rules and limitations to be aware of when withdrawing money from a Roth IRA for a first home purchase. The individual must be a first-time homebuyer, defined as someone who has not owned a home in the past two years. Additionally, the maximum amount that can be withdrawn for a first home purchase is $10,000 per person.
It's important to note that while contributions to a Roth IRA can be withdrawn tax-free and without penalty, earnings on those contributions may be subject to taxes and penalties if withdrawn before age 59 and a half.
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Pls help
I will give 65 points for the first person to answer my question.
Thank you!
first off let's check how much is 5% of hmmm say "x"
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{5\% of x}}{\left( \cfrac{5}{100} \right)x}\implies 0.05x[/tex]
so if we increase "x" by that much, that's just "x + 0.05x" = 1.05x. Now, let's find how much is 5% of that
[tex]\stackrel{\textit{5\% of 1.05x}}{\left( \cfrac{5}{100} \right)1.05x}\implies (0.05)(1.05x)\implies 0.0525x \\\\\\ \stackrel{\textit{now let's add that, to 1.05x}}{1.05x~~ + ~~0.0525x}\implies 1.1025x[/tex]
so our "x" went up by 0.1025x, now let's conver that to a percent, 0.1025 * 100 = 10.25%.
You own a motel with 30 rooms and have a pricing structure that encourages rentals of rooms in groups. One room rents for $85.00, two for $83.00 each, and in general the group rate per room is found by taking $2 off the base of $85 for each extra room rented.
(c) Find a formula for a function R = R(n) that gives the total revenue from renting rooms to a convention host.
(d) Use functional notation to show the total revenue from renting a block of 9 rooms to a group. Calculate the value.
The formula for a function R = R(n) is R(n) = n(85 - 2n) and the total revenue for 9 room is $603
How to determine the formula for a function R = R(n)From the question, we have the following parameters that can be used in our computation:
Base fee = $85.00
Rate = $2 off
Using the above as a guide, we have the following:
R(n) = n(85 - 2n)
Where n is the number of rooms
The value of block of 9 roomsThis means that
n = 9
So, the notation is
R(9)
The value is
R(9) = 9 *(85 - 2 * 9)\
R(9) = 603
Hence, the value is $603
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The graph below is the function f(x)
The required answers are:
lim f(x) = -1
1-2-
lim f(x) = -1
1+2+
lim f(x) = -3
r2
f(2) = -3
How to solve thisGiven image has a graph of the function f(x)
To find [tex]\lim_{x\rightarrow 2^-}f(x), lim f(2) 12+, lim f(x) 12 and f(2)[/tex]
We have from the image of the graph the function f(x) is a discontinuous function with x=2 is the point of discontinuity.
Now from the graph the value of f(x) at x=2 i.e. f(2) = -3 as the graph has a bold dot at y=-3.
Next [tex]\lim_{x\rightarrow 2^-}f(x)=\lim_{x\rightarrow 2^+}f(x)=-1[/tex] as in the graph of f(x) it has a small circle at y = -1.
As f(2) = -3 so [tex]\lim_{x\rightarrow 2}f(x)=f(2)=-3[/tex]
Thus the required answers are
lim f(x) = -1
1-2-
lim f(x) = -1
1+2+
lim f(x) = -3
r2
f(2) = -3
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can someone tell me how i find answer for this problem?
Answer:
P(x) = x²(x +1)(x -2)²
Step-by-step explanation:
You want the 5th degree polynomial with leading coefficient 1 that has roots of 0 and 3, each with multiplicity 2, and a root of -1.
FactorsYou recall that a polynomial with root p has (x -p) as a factor. A root that is repeated m times has multiplicity m.
You recall that an exponent is used to signify the number of times a factor is repeated.
The factored form of P(x) is then ...
P(x) = (x -2)²(x -0)²(x -(-1)) . . . . . roots 2 and 0 repeated twice, root -1
P(x) = x²(x +1)(x -2)²
__
Additional comment
If you like, you can multiply it out and collect terms. The result will be ...
P(x) = x⁵ -3x⁴ +4x²
On the defense of a football team,there are three types of players on the field.What is the probability of picking each type of player at random out of the 11 players
Answer: The probability of picking each type of player at random depends on the number of players of each type on the field. If the number of players of each type is not specified, it is not possible to determine the probability of picking each type of player at random.
Step-by-step explanation:
find p if (p, 2p+1) is solution of 11x-2y=5
Answer:
p = 1
Step-by-step explanation:
since (p, 2p + 1) is a solution then it makes the equation true.
substitute x = p and y = 2p + 1 into the equation and solve for p
11p - 2(2p + 1) = 5 ← distribute parenthesis and simplify left side
11p - 4p - 2 = 5
7p - 2 = 5 ( add 2 to both sides )
7p = 7 ( divide both sides by 7 )
p = 1
What is the sum of the measures of the exterior angles of any convex polygon?
A.90
B.180
C.360
D.720
Answer:
360
Step-by-step explanation:
If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360°
hope dis helpsssssss
Write the correct domain and range of the relation. {(-4,-4),(-1,3),(0,5),(3,9)}
Answer:
domain: {-4, -1, 0, 3}range: {-4, 3, 5, 9}Step-by-step explanation:
You want the domain and range of the relation {(-4,-4),(-1,3),(0,5),(3,9)}.
DomainThe domain is the set of first numbers of the ordered pairs:
{-4, -1, 0, 3}
RangeThe range is the set of second numbers of the ordered pairs:
{-4, 3, 5, 9}
Answer:
Domain: {-4, -1, 0, 3}
Range: {-4, 3, 5, 9}
Step-by-step explanation:
The Domain is the number that is on the x-axis.
The Range is the number on the y-axis.
Its quite simple. Hope this HELPED! HAVE A GOOD DAY AND NIGHT!!!!!!!!!!