Answers
Answer:
see explanation
Step-by-step explanation:
Parallel lines have equal slopes.
To find D and E use the midpoint formula
Given endpoints (x₁, y₁ ) and (x₂, y₂ ) then the midpoint is
( \(\frac{x_{1}+x_{2} }{2}\), \(\frac{y_{1}+y_{2} }{2}\) )
Here (x₁, y₁ ) = A(4, 6) and (x₂, y₂ ) = B(2, - 2) , then
D = (\(\frac{4+2}{2}\), \(\frac{6-2}{2}\) ) = (3, 2 ) and
let (x₁, y₁ ) = B(2, - 2\(\frac{-4+2}{-2-2}\) ) and (x₂, y₂ ) = C(- 2, - 4 ), then
E = ( \(\frac{4-2}{2}\), \(\frac{6-4}{2}\) ) = (1, 1 )
Use the slope formula to find slopes of DE and BC
m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)
with (x₁, y₁ ) = D(3, 2) and (x₂, y₂ ) = E(1, 1), then
\(m_{DE}\) = \(\frac{1-2}{1-3}\) = \(\frac{-1}{-2}\) = \(\frac{1}{2}\)
Repeat with (x₁, y₁ ) = B(2, - 2) and (x₂, y₂ ) = C(- 2, - 4), then
\(m_{BC}\) = \(\frac{-4+2}{-2-2}\) = \(\frac{-2}{-4}\) = \(\frac{1}{2}\)
Since the slopes are equal then DE and BC are parallel lines
I know he anwsered it but I really want to level up so can you please give me Brainliest
Related Questions
If a tortoise is time traveling an average of 1/3 miles per hour, how long would it take the tortoise to travel 6 miles ?
Answers
Answer:
18
Step-by-step explanation:
6 ÷ 1⁄3 = 18
What is the equation of a line through point (-12,20) that is perpendicular to the line
with equation y=-6x + 4?
Answers
Find the slope of the perpendicular line
When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.
⇒ if the slope of one of the lines = - 6
then the slope of the perpendicular line (m) = ¹/₆
Determine the equation
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 20 = ¹/₆ (x - (-12))
∴ y - 20 = ¹/₆ (x + 12)
We can also write the equation in the slope-intercept form (y=mx+c) like the equation in the question by making y the subject of the equation and expanding the bracket to simplify:
since y - 20 = ¹/₆ (x + 12)
y - 20 = ¹/₆x + 2
y = ¹/₆x + 22
∴ the slope-intercept equation of the perpendicular line is y = ¹/₆ x + 22.
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
Help me pls!!! 100 points
Answers
Answer:
2nd option below
Step-by-step explanation:
the rectangle with size 12ft×8ft is similar to the rectangle with size 3ft×2ft.
because they have the same ratio of the length and the width.
=> 12 : 3 <=> 8 : 2
find the length of the curve. r(t) = cos(6t) i + sin(6t) j + 6 ln(cos(t)) k, 0 ≤ t ≤ π/4
Answers
The length of the curve is given by the integral of the square root of the sum of the squares of the derivatives of each component of r(t), integrated over the given interval, length is 6 units.
In this case, we have
r(t) = cos(6t) i + sin(6t) j + 6 ln(cos(t)) k, and we need to find the length of the curve from t = 0 to t = π/4.
Using the arc length formula, we have the integrand as the square root of (-6sin(6t))^2 + (6cos(6t))^2 + (-6sin(t) / cos(t))^2.
Simplifying the integrand, we get √(36sin²(6t) + 36cos²(6t) + 36sin²(t) / cos²(t)).
Further simplifying, we have √(36 + 36sin²(t) / cos²(t)).
By applying trigonometric identities, we can rewrite the integrand as √(36cos²(t) + 36sin²(t) / cos²(t)).
Simplifying further, we obtain √(36 + 36tan²(t)).
Now,
∫√(36 + 36u²) du / (1 + u²).
Now, we can simplify the integrand:
√(36 + 36u²) / (1 + u²).
Next, we can factor out 36 from the square root:
√36(1 + u²) / (1 + u²).
Simplifying further, we get:
√36 = 6, so the integral becomes:
6∫(1 + u²) / (1 + u²) du.
Notice that the expression (1 + u²) / (1 + u²) simplifies to 1, so the integral reduces to:
6∫du.
Integrating du gives us u + C, where C is the constant of integration.
Therefore, the indefinite integral of √(36 + 36tan²(t)) dt is 6(tan(t)) + C.
To evaluate the definite integral over the interval from 0 to π/4, we substitute the upper and lower limits:
[6(tan(π/4)) - 6(tan(0))] = [6(1) - 6(0)] = 6.
Hence, the length of the curve defined by the given vector function over the interval from 0 to π/4 is 6.
To learn more about arc length formula click here: brainly.com/question/30760398
#SPJ11
answer yes or no (12 pts). is 87 ≡ 51 (mod 3)? is 34 ≡ 14 (mod 5)? is 7 ≡ 54 (mod 24)? is 39 ≡ 57 (mod 18)?A. Yes B. No
Answers
Yes, 87 ≡ 51 (mod 3), 34 ≡ 14 (mod 5), 7 ≡ 54 (mod 24), and 39 ≡ 57 (mod 18).
This is because the congruence relation allows us to compare two numbers modulo a number. This means that if two numbers are equal modulo the same number, then they are congruent.
In this case, 87 ≡ 51 (mod 3) because 87 - 51 = 36, which is divisible by 3, so the two numbers are equal modulo 3. The same is true for the other three pairs of numbers: 34 ≡ 14 (mod 5), 7 ≡ 54 (mod 24), and 39 ≡ 57 (mod 18).
The difference between each pair is also a multiple of the modulus, so they are congruent.
To know more about congruence relation click on below link:
https://brainly.com/question/30093666#
#SPJ11
Beverly says f(a)=9.3 has multiple solutions. Stephanie says f(9.3)=a has multiple solutions. Who is correct?
Answers
Beverley is right
explanation
there is 3 answers
0,9,3
hope this helps
cauculator link: https://www.symbolab.com/solver/functions-calculator
:D
from Kenny
all the best!
1. 7h + 2h - 5h
Α 4h
Β. 14h
Answers
Answer:
A 4h
Step-by-step explanation:
\(7 + 2 - 5 = 9 - 5 = 4\)
Please helpppp
graph 0.2 and its opposite
graph 9 and its opposite
Answers
Answer:
I need the answer tooo
Initial claims for unemployment compensation in an area can be modeled by N(t)= 31t2−560t+3007, where t is the number of years after 1990 . Find the absolute extrema between 1998 and 2003 . Determine the demand elasticity of the following situations and interpret your answers. a. Price increases from $6 per unit to $7 per unit; demand drops from 1000 units to 900 units. b. Price drops from $70 per unit to $60 per unit; demand rises from 10,500 units to 12,000 units.
Answers
The demand elasticity is -1. The percentage change in quantity demanded (14.29%) is greater than the percentage change in price (-14.29).
To find the absolute extrema of N(t) between 1998 and 2003, we need to consider the critical points within that interval. First, we determine the derivative of N(t) with respect to t, which is N'(t) = 62t - 560. To find critical points, we set N'(t) equal to zero and solve for t:
62t - 560 = 0
62t = 560
t = 560/62 ≈ 9.03
Since this critical point falls within the given interval, we can evaluate N(t) at t = 9.03 to find the absolute extrema.
To determine the demand elasticity for scenario a, we calculate the percentage change in quantity demanded and price:
Percentage change in quantity demanded = [(new quantity - old quantity) / old quantity] * 100
= [(900 - 1000) / 1000] * 100
= -10%
Percentage change in price = [(new price - old price) / old price] * 100
= [(7 - 6) / 6] * 100
= 16.67%
Using the formula for demand elasticity: elasticity = (percentage change in quantity demanded) / (percentage change in price), we can substitute the values:
elasticity = (-10% / 16.67%)
= -0.6
For scenario b, we follow the same process:
Percentage change in quantity demanded = [(new quantity - old quantity) / old quantity] * 100
= [(12,000 - 10,500) / 10,500] * 100
= 14.29%
= [(new price - old price) / old price] * 100
= [(60 - 70) / 70] * 100
= -14.29%
Using the demand elasticity formula, we substitute the values:
elasticity = (14.29% / -14.29%)
= -1
Interpreting the results, a demand elasticity of -0.6 (scenario a) indicates an inelastic demand, meaning the percentage change in quantity demanded (-10%) is less than the percentage change in price (16.67%). In scenario b, a demand elasticity of -1 signifies an elastic demand, as the percentage change in quantity demanded (14.29%) is greater than the percentage change in price (-14.29%). Elastic demand indicates that changes in price have a significant impact on the quantity demanded, while inelastic demand suggests price changes have a less pronounced effect.
Learn more about interval here:
https://brainly.com/question/11051767
#SPJ11
Im so lost, please help me asap
Answers
Answer:
it's so simple ....
x + 141 = 135
x = 135 - 141
x = -6
it means ur answer is a
The sum of two numbers is 41 and the difference is 1. What are the numbers? Larger number: Smaller number:
Answers
Answer:
Larger number=21
Smaller number=20
Step-by-step explanation:
20+21=41
21-20=1
are the trigonometric functions odd, even, or neither odd nor even? select answers from the drop-down menus to correctly complete the statements. the function f(x)
Answers
The function f(x) is: neither old nor even
Trigonometric functions can be categorized as odd, even, or neither odd nor even based on their symmetry properties. Let's analyze each category:
Odd Functions: An odd function satisfies the condition f(-x) = -f(x) for all values of x. This means that if we reflect the graph of the function across the y-axis, it remains unchanged. In other words, the function is symmetric with respect to the origin (0,0).
Examples of odd trigonometric functions include sine (sin(x)) and tangent (tan(x)). When you plug in -x into these functions, you'll get the negation of the function's value at x.
Even Functions: An even function satisfies the condition f(-x) = f(x) for all values of x. This means that if we reflect the graph of the function across the y-axis, it remains unchanged. In other words, the function is symmetric with respect to the y-axis.
An example of an even trigonometric function is the cosine function (cos(x)). When you plug in -x into the cosine function, you'll get the same value as when you plug in x.
Neither Odd nor Even: Some trigonometric functions do not exhibit either odd or even symmetry. These functions do not satisfy the conditions for odd or even functions. Examples of trigonometric functions that are neither odd nor even include secant (sec(x)), cosecant (csc(x)), and cotangent (cot(x)). When you plug in -x into these functions, you won't get the negation or the same value as when you plug in x.
Therefore, the trigonometric functions can be categorized as odd, even, or neither odd nor even, depending on their symmetry properties.
Learn more about trigonometric function here, https://brainly.com/question/1143565
#SPJ11
As a town gets smaller, the population of its high school decreases by 8% each year. The senior class has 320 students now. In how many years will it have about 100
students? Write an equation. Then solve the equation without graphing.
Answers
Answer:
in 13.95 years the senior class will have 100 students.
Step-by-step explanation:
P(h) = p(0.92)^t (equation for exponential change)
P(h) - population of highschool (or senior class) = 100
p - staring amount = 320
t = time in years
100 = 320(0.92)^t
1/3.2 = .92^t (divide both sides by 320)
log(1/3.2, .92) = t (log base 0.92 of 1/3.2 equals t)
13.9497 = t
write the decimal as a fraction.
0.010
Answers
Answer:
1/10
0.010 is equal to 0.1
0.1 is 1/10 of 10.
The answer is 1/10.
Hope it helps!
A fountain in the park has two circular pools that are the same size. What is the total area of the pools if the radius is 3 yards? Use 3. 14 for Pi and round the approximate area to the nearest tenth, if necessary. Check all that apply. 9 Pi yd2 12 Pi yd2 18 Pi yd2 28. 3 yd2 56. 5 yd2.
Answers
The area of the fountain is 18π or 56.55 square yards. Then the correct options are C and E.
What is a circle?It is a locus of a point drawn at an equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
A fountain in the park has two circular pools that are the same size.
And the radius is 3 yards.
Area of fountain = two times area of a circle
The area of the circle will be
\(\rm Area\ of\ circle = \pi r^2\\\\Area\ of\ circle = \pi * 3^2\\\\Area\ of\ circle = 9\pi\\\\\)
Then the area of the fountain will be
Area of fountain = 2 × 9π
Area of fountain = 18 π
Area of fountain = 56.55
The area of the fountain is 18π or 56.55 square yards. Then the correct options are C and E.
More about the circle link is given below.
https://brainly.com/question/11833983
F(x)=3/x+2-square rootx-3
Answers
Answer: -5/3
Step-by-step explanation:
A part-time receptionist made $9101.99 last year. If he claimed himself as an
exemption for $3650 and had a $5700 standard deduction, what was his
taxable income last year?
O A. $5451.99
OB. $0
OC. $248.01
OD. $3401.99
Answers
He had a taxable income of $-748.01 last year, which means he did not owe any federal income tax for the period.
What is simple interest?
The simple interest method, which always adds interest to the starting principal amount at the same rate for each time cycle, is a quick and easy way to calculate interest on money. Any bank where we deposit money will return our investment with interest. Simple interest is one of the several forms of interest that banks charge. Now, before going into any detail on the concept of fundamental curiosity,
The formula for simple interest is:
S = p*t*r/100
The part-time receptionist's taxable income would be calculated by deducting their exemptions and standard deduction from their gross income. The person's gross income was $9101.99. A $3650 exemption was requested by the person. They also qualified for a $5700 standard deduction.
We can figure out their taxable income by deducting the exemption and standard deduction from their gross income. $9101.99 - $3650 - $5700 = $-748.01 would be used to compute the taxable income.
Hence He had a taxable income of $-748.01 last year, which means he did not owe any federal income tax for the period.
Learn more about simple interest, by the following link
brainly.com/question/20690803
#SPJ1
What must you know to develop a binomial probability distribution?
(a) probability of success
(b) number of trials
(c) probability of success and the number of successes
(d) probability of success and the number of trials
Answers
To develop a binomial probability distribution, you need to know the probability of success and the number of trials.
A binomial probability distribution is used to model the probability of obtaining a specific number of successes in a fixed number of independent Bernoulli trials. In order to develop this distribution, two essential pieces of information are required: the probability of success and the number of trials.
Firstly, you need to know the probability of success, which represents the likelihood of a specific event or outcome occurring in each individual trial. This probability is denoted by "p" and must be a value between 0 and 1.
Secondly, you need to know the number of trials, which refers to the total number of independent experiments or events being conducted. This value is denoted by "n" and must be a positive integer.
With these two pieces of information, you can calculate the probability of obtaining a specific number of successes, ranging from 0 to n, using the binomial probability formula. This formula takes into account the probability of success, the number of trials, and the desired number of successes.
Overall, the probability of success and the number of trials are the key elements needed to develop a binomial probability distribution, enabling you to calculate the probabilities of various outcomes in a given set of independent trials.
Learn more about binomial probability distribution here:
https://brainly.com/question/29137961
#SPJ11
Write down the inequality shown on the
number line below.
Answers
For the given number line the inequality equation would be -10 < x ≤ 20.
What is inequality?
In mathematics, a linear inequality is an inequality that involves a linear function. A linear inequality contains one of the symbols of inequality. It shows the data which is not equal in graph form.
In the given number line, a hollow circle represents that the number is excluded and solid circle represents that the number is included in the range
and the range lies between -10 to 2.
Let's take a variable to describe the relationship,
By using inequality we can prepare the inequality equation as
-10 < x ≤ 20
Hence, for the given number line the inequality equation would be -10 < x ≤ 20.
To learn more about inequalities, visit:
https://brainly.com/question/21103162
#SPJ1
1. In each case, which average do you think is most useful: the mean, median, or mode?
Justify your answer.
Answers
Answer:
depends on the cases. they all have different uses
Barbara is buying 4 binders, and each binder costs the same amount. She uses a coupon that gives her $3 off for the total purchase price of the binders. Barb pays a total of $11 when the value of the coupon is subtracted. Which equation shows how to find p, the original price of each binder?
Answers
Answer:
Equation is 4 p-3=11
Step-by-step explanation:
Barbara is buying 4 binders each cost same amount.
Let the cost of 1 binder is '$p'.
So, cost of 4 binders = $4 p.
Now, a coupon that gives her $3 off.
So, Barb needs to pay 4 p-3 dollars.
Barb pays a total of $11 when the value of the coupon is subtracted.
So, we can set up equation as
4 p-3=11
is 3a 2 bc what are the variables
Answers
Answer:
a and bc
Step-by-step explanation:
Answer:
a and bc
Step-by-step explanation:
Math homework pls help!!!
Answers
Answer:
17.8
Step-by-step explanation:
The power ands the square root cancel out.
Help help help help help
Answers
Answer:
I'm pretty sure it's c but I'm not sure
1. What is the length of base for this triangle?
2. What is the length of height for this triangle?
Answers
Answer:
base=5
height=3
Step-by-step explanation:
A trapezoid and a rectangle are both quadrilaterals. This means they both have_____ sides and_______ angles. The angles in a rectangle_______ . The angles in a trapezoid _________
Answers
Answer:
both have equal sides and equal Angel's
the angels In a rectangle 4 sides
the angles in a trapezoid is 4 sides
What is the value of the expression below when x=5x=5?
8x+9
Answers
The value of the expression below when x=5x=5?
8x+9 is equal to \(7^{2}\) (or) 49.
Substitute \(\left \{ {{x=5x} \atop {5x=5}} \right. into (8x+9)\)
The expression,
y = 8x + 9
If the domain of the function is x = 5, hence the range of the function is gotten by substituting x = 5 into the given function as shown:
So, we can substitute x = 5,
Then, y = 8 * 5 + 9
Calculate the product or quotient,
y = 40 + 9
Calculate the sum or difference,
y = 49
We can write alternative form,
y = \(7^{2}\)
Therefore,
Hence the value of the expressions if x = 5 is \(7^{2}\) (or) 49.
To learn more about value of expression problems visit : brainly.com/question/26170139
#SPJ9
Find the present value of payments at the end of each quarter of
$245 for ten years with an interest rate of 4.35% compounded
monthly.
Answers
The present value of payments at the end of each quarter of $245 for ten years with an interest rate of 4.35% compounded monthly is approximately $25,833.42.
To find the present value of the payments, we can use the present value formula for an ordinary annuity. The formula for the present value of an ordinary annuity is:
PV = PMT * ((1 - (1 + r)^(-n)) / r)
Where:
PV = Present Value
PMT = Payment amount
r = Interest rate per period
n = Number of periods
In this case, the payment amount is $245, the interest rate is 4.35% compounded monthly, and the number of periods is 10 years or 40 quarters (since there are 4 quarters in a year).
Let's plug in the values into the formula:
PV = $245 * ((1 - (1 + 0.0435/12)^(-40)) / (0.0435/12))
First, let's simplify the exponent part:
(1 + 0.0435/12)^(-40) ≈ 0.617349
Now, let's plug in the values and calculate:
PV = $245 * ((1 - 0.617349) / (0.0435/12))
PV = $245 * (0.382651 / 0.003625)
PV = $245 * 105.4486339
PV ≈ $25,833.42
To know more about the interest, visit:
https://brainly.com/question/8100492
#SPJ11
By using only those factors given in interest tables, find the values of the factors that follow, which are not given in your tables. Show the relationship between the factors by using factor notation, and calculate the value of the factor. For example, (F/P,8%,38)=(F/P,8%,30)(F/P,8%,8)=18.6253. Click the icon to view the interest factors for discrete compounding when i=8% per year. (c) Find the value of the (P/A,8%,145) factor. Select the correct choice below and fill in the answer box to complete your choice. A. (P/A,8%,145)= 0.08
1−(P/F,8%,45)
= (Round to four decimal places. ) B. (P/A,8%,145)= 0.08
1−(P/F,8%,100)(P/F,8%,45)
= (Round to four decimal places.) C. (P/A,8%,145)=(P/A,8%,100)(P/A,8%,45)= (Round to four decimal places. ) D. (P/A,8%,145)= 1−(P/F,8%,100)(P/F,8%,45)
0.08
= (Round to four decimal places.) At what rate of interest compounded annually will an investment double in nine years? The investment will double in nine years at \% compounded annually. (Round to two decimal places.)
Answers
The investment will double in nine years at an interest rate of approximately 8.09% compounded annually.
To find the value of the (P/A,8%,145) factor, we can use the general formula for the present worth of an annuity:
(P/A, i%, n) = (1 - (1 + i)^(-n)) / i
Substituting the values given:
i = 8%
n = 145
(P/A,8%,145) = (1 - (1 + 0.08)^(-145)) / 0.08
Using a financial calculator or spreadsheet software, we can calculate the value of (P/A,8%,145) as follows:
(P/A,8%,145) ≈ 43.7276 (rounded to four decimal places)
Therefore, the correct choice for the value of (P/A,8%,145) is:
C. (P/A,8%,145) = (P/A,8%,100)(P/A,8%,45) ≈ 43.7276 (rounded to four decimal places)
Regarding the second question, to find the interest rate at which an investment will double in nine years, we can use the future worth factor formula:
(F/P, i%, n) = (1 + i)^n
We want the investment to double, so we have:
(1 + i)^9 = 2
Taking the ninth root of both sides:
1 + i = 2^(1/9)
Solving for i:
i ≈ 0.0809 or 8.09% (rounded to two decimal places)
Therefore, the investment will double in nine years at an interest rate of approximately 8.09% compounded annually.
learn more about investment on
https://brainly.com/question/15105766
#SPJ11
What is: -(-8)+6-(-5) equal?