Answer:
C, D, E
Step-by-step explanation:
I did the USATESTPREP
Determine the equation of the circle with center 100pts
Answer:
(x - 8)² + (y - 5)² = 400
Step-by-step explanation:
the equation of a circle in standard form is
(x - h)² + (y - k)² = r²
where (h, k ) are the coordinates of the centre and r the radius
the radius is the distance from the centre to a point on the circle
use the distance formula to calculate r
r = [tex]\sqrt{(x_{2}-x_{1})^2+(y_{2}-y_{1})^2 }[/tex]
with (x₁, y₁ ) = (8, 5 ) and (x₂, y₂ ) = (- 4, 21 )
r = [tex]\sqrt{(-4-8)^2+(21-5)^2}[/tex]
= [tex]\sqrt{(-12)^2+16^2}[/tex]
= [tex]\sqrt{144+256}[/tex]
= [tex]\sqrt{400}[/tex]
= 20
then with (h, k ) = (8, 5 ) and r = 20, the equation of the circle is
(x - 8)² + (y - 5)² = 20² , that is
(x - 8)² + (y - 5)² = 400
Answer:
[tex](x-8)^2+(y-5)^2=400[/tex]
Step-by-step explanation:
The standard equation of a circle is:
[tex]\boxed{(x-h)^2+(y-k)^2=r^2}[/tex]
where:
(h, k) is the center.r is the radius.The given center of the circle is (8, 5).
To find the value of r², substitute the circle and the given point (-4, 21) into the equation and solve for r².
[tex]\begin{aligned}(-4-8)^2+(21-5)^2&=r^2\\(-12)^2+(16)^2&=r^2\\144+256&=r^2\\400&=r^2\end{aligned}[/tex]
Finally, substitute the center and r² into the formula to create an equation of the circle with the given parameters:
[tex]\boxed{(x-8)^2+(y-5)^2=400}[/tex]
Which of the following lists the range and IQR for this data?
The range is 12, and the IQR is 5.
The range is 12, and the IQR is 10.
The range is 5, and the IQR is 12.
The range is 5, and the IQR is 10.
Answer: D
Step-by-step explanation:
Questions 16. Santhosh and Co. Chennai, opened a branch at Trichy on 1.1.2018. The following Information relate to the branch for the year 2018.
40,000
36,000
9,000
7200
3,600
30,000
16,200
300
3,000
Prepare branch account to find out the profit or loss of branch. Santosh & Co, Chennai opened its branch in Trichy on 1.1.2018. The action for 2018 is as follows
Credit sales at branch
Office expenses by Head office
Cash remittance to branch for petty cash Stock 31.12.2018
Goods sent to Branch
Salaries paid by head office
Debtors 31.12.2018
Petty cash on 31.12.2018
Cash sales at branch
of
The preparation of the branch's income statement for Santosh & Co. Chennai is as follows:
Branch of Santosh & Co. Chennai
Income StatementFor the year ended December 31, 2018
Sales revenue $40,300
Cost of goods sold 4,200
Gross profit $36,100
Expenses:
Office expenses $36,000
Salaries 3,600
Total expenses $39,600
Loss $3,500
What is an income statement?An income statement is a financial statement prepared at the end of an accounting period to determine the profit or loss generated by a business or branch.
The profit or loss is the difference between the total revenue and the total expenses for the accounting period.
Credit sales at branch 40,000
Office expenses by Head office 36,000
Cash remittance to branch for petty cash 9,000
Goods sent to Branch 7,200
Salaries paid by head office 3,600
Debtors 31.12.2018 30,000
Petty cash on 31.12.2018 16,200
Cash sales at branch 300
Stock of 31.12.2018 3,000
Sales revenue $40,300 ($40,000 + $300)
Cost of goods sold $4,200 ($7,200 - $3,000)
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Chandler decided to go cliff jumping into the lake at his cottage. He started on the cliff at 32 ft above sea level. He jumped for 40 feet! How far below sea level did Chandler end up?
Chandler ended up 8 feet below sea level. The negative sign indicates that his final position is below sea level. This means that he has descended further into the lake compared to the starting point on the cliff.
Chandler started on the cliff at 32 feet above sea level. When he jumped for 40 feet, we need to determine the final position in relation to sea level.
Since Chandler jumped down, the distance below sea level will be calculated as a negative value. To find how far below sea level Chandler ended up, we subtract the jump distance (40 feet) from the starting height (32 feet above sea level):
32 feet - 40 feet = -8 feet
It's important to note that negative values are used here to represent the direction and magnitude of Chandler's descent relative to sea level
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Answer:
-8 feet
Step-by-step explanation:
4÷52,678
I forgot how to do division.
Answer:0.00007593302
Step-by-step explanation:
Help me pleaseeeee :(
Answer:
(b) f(x) = -1/x⁹ and g(x) = -8x +4
(d) f(x) = x⁹ and g(x) = -1/(-8x +4) . . . . . alternate solution
Step-by-step explanation:
You want to decompose h(x) = -1/(-8x +4)⁹ into f(x) and g(x) such that h(x) = f(g(x)).
CompositionThe composition h(x) = f(g(x)) means that the function g(x) will replace x in the definition of f(x).
It is often convenient to look at the order of operations when asked to decompose a function like this. Here, the parenthetical expression (-8x+4) is raised to the 9th power and its opposite reciprocal is found. This suggests that f(x) can be a function that finds the opposite reciprocal of a 9th power, matching choice B. Thus, a reasonable choice is ...
(b) f(x) = -1/x⁹ and g(x) = -8x +4
Also ...We note that the reciprocal of a 9th power is also the 9th power of a reciprocal. A negative sign is preserved by the odd power. This means that another reasonable choice for the decomposition is ...
(d) f(x) = x⁹ and g(x) = -1/(-8x +4)
__
Additional comment
We list choice B first because that one is probably the one you're supposed to claim as the answer. However, this question has two correct decompositions among those listed. You may want to discuss this with your teacher.
<95141404393>
Work out the total surface area of the frustum. Give your answer to 3 s.f.
Answer:
S = π(12)(20) + π(12^2) - (π(3)(5) + π(3^2))
= π(240 + 144 - (15 + 9))
= 360π = about 1,130.97 cm^2
Fill in the P (X=x) values to give a legitimate probability distribution for the discrete random variable X, whose possible values are -3, 1, 3, 5, and 6.
P(X=x)
-3: 0.14
1:
3: 0.13
5: 0.30
6:
These are a legitimate probability distribution:
P(X=-3) = 0.14P(X=1) = 0.1P(X=3) = 0.135P(X=5) = 0.306P(X=6) = 0.319How to determine legitimate probability distribution?To have a legitimate probability distribution, the probabilities for all possible values of X must satisfy two conditions:
Each probability value must be between 0 and 1, inclusive.
The sum of all probability values must equal 1.
Check if the given probabilities satisfy these conditions:
P(X=-3) = 0.14 (valid)
P(X=1) = 0.1 (valid)
P(X=3) = 0.135 (valid)
P(X=5) = 0.306 (valid)
Now, calculate the remaining probability to check if it satisfies the second condition:
P(X=6) = 1 - (P(X=-3) + P(X=1) + P(X=3) + P(X=5))
P(X=6) = 1 - (0.14 + 0.1 + 0.135 + 0.306)
P(X=6) = 1 - 0.681
P(X=6) = 0.319
Since the calculated probability is valid (between 0 and 1), There is a legitimate probability distribution for the discrete random variable X:
P(X=-3) = 0.14
P(X=1) = 0.1
P(X=3) = 0.135
P(X=5) = 0.306
P(X=6) = 0.319
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Refer to the information below to answer Questions 1 to 4. 1. Billy's gross pay is K850.00 Billy is taxed 12% on his taxable income, and contributes 7% to Nusfund. His loan deduction is 5%. What is his net pay? (1 mark)
The Billy's net pay is K646
The given information are; Billy's gross pay is K850.00, he is taxed 12% on his taxable income, and contributes 7% to Nusfund. His loan deduction is 5%.
To find out his net pay, the following steps must be taken:Firstly, calculate Billy's tax amount, Nusfund contribution, and loan deduction by using their respective percentages and the gross pay.
tax amount= 12/100 × 850= K102 Refund contribution= 7/100 × 850= K59.50Loan deduction= 5/100 × 850= K42.50 Secondly, the sum of all the deductions made from the gross pay is calculated to obtain the total deductions.
Total deductions= K102 + K59.50 + K42.50= K204The final step is to subtract the total deductions from the gross pay to find Billy's net pay. Net pay= K850 − K204= K646.
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If you divide each value in the data set below by 5, what are the mean, median, mode, and range of the resulting data set?
9214709
The mean is
(Type an integer or decimal rounded to the nearest hundredth as needed.)
Please helppppp
Answer:
To find the mean, median, mode, and range of the resulting data set after dividing each value by 5, we need to perform the calculations. Here are the steps:
Original data set: 9214709
Step 1: Divide each value by 5:
Resulting data set: 1842941.8
Step 2: Calculate the mean:
To find the mean, we sum up all the values in the resulting data set and divide by the total number of values:
Mean = (1842941.8) / 1 = 1842941.8
Therefore, the mean of the resulting data set is 1842941.8.
Please note that for the median, mode, and range calculations, we need more than one value in the data set. As the original data set only contains one value, we cannot proceed with those calculations.
Step-by-step explanation:
Answer:
The mean, also known as the average, is a measure of central tendency that is calculated by adding up all the values in a data set and then dividing by the number of values in the set. For example, if you have a data set with the values 1, 2, and 3, the mean would be calculated as (1 + 2 + 3) / 3 = 2.
The median is another measure of central tendency that represents the middle value in a data set when the values are arranged in ascending order. If the data set has an odd number of values, the median is the middle value. If the data set has an even number of values, the median is calculated as the average of the two middle values.
For example, if you have a data set with the values 1, 2, and 3, the median would be 2 because it is the middle value when the values are arranged in ascending order. If you have a data set with the values 1, 2, 3, and 4, the median would be calculated as (2 + 3) / 2 = 2.5 because there are an even number of values and the two middle values are 2 and 3.
The zeros of this polynomial:
p(x)=(2x^2-9x+7)(x-2)
Step-by-step explanation:
To find the zeros of the polynomial p(x) = (2x^2 - 9x + 7)(x - 2), we set p(x) equal to zero and solve for x:
(2x^2 - 9x + 7)(x - 2) = 0
This equation will be satisfied if either of the factors on the left side equals zero. So we set each factor equal to zero and solve for x separately.
Setting 2x^2 - 9x + 7 = 0:
Using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
For this equation, a = 2, b = -9, and c = 7.
Plugging these values into the quadratic formula, we have:
x = (-(-9) ± √((-9)^2 - 4 * 2 * 7)) / (2 * 2)
x = (9 ± √(81 - 56)) / 4
x = (9 ± √25) / 4
x = (9 ± 5) / 4
So we have two solutions:
x1 = (9 + 5) / 4 = 14 / 4 = 3.5
x2 = (9 - 5) / 4 = 4 / 4 = 1
Setting x - 2 = 0:
x = 2
Therefore, the zeros of the polynomial p(x) = (2x^2 - 9x + 7)(x - 2) are x = 3.5, 1, and 2.
Need the answer to this asap!!!!!
Answer:
The factors correlate with the x-intercepts. For example, with the factor (x - 3), there is an x-intercept at (3, 0). Likewise, with the factor (x + 2), there is an x-intercept at (-2, 0). This suggests that the opposite sign of the factors are the x-intercepts in the graph.
Find the length of side X in simple radical form with a rational denominator
The length of side X in simple radical form with a rational denominator is 10/√3.
What is a 30-60-90 triangle?In Mathematics and Geometry, a 30-60-90 triangle is also referred to as a special right-angled triangle and it can be defined as a type of right-angled triangle whose angles are in the ratio 1:2:3 and the side lengths are in the ratio 1:√3:2.
This ultimately implies that, the length of the hypotenuse of a 30-60-90 triangle is double (twice) the length of the shorter leg (adjacent side), and the length of the longer leg (opposite side) of a 30-60-90 triangle is √3 times the length of the shorter leg (adjacent side):
Adjacent side = 5/√3
Hypotenuse, x = 2 × 5/√3
Hypotenuse, x = 10/√3.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
You just completed your math course and you want to calculate your overall grade. You
know that tests are weighted 15%, quizzes 10%. projects 35%, participation 35%, and the
final exam 5%. What is your overall grade if you scored the following in each category?
Your overall grade, if the percentage scored in the categories are given, is 86. 35.
How to find the overall grade ?To calculate your overall grade, you'll need to multiply each individual grade by its respective weight and then add all these products together.
Tests:
= 85 % * 15%
= 12. 75
Quizzes:
= 90% * 10%
= 9. 0
Projects:
= 92% * 35%
= 32 .2
Participation:
= 80% * 35%
= 28. 0
Final Exam:
= 88% * 5%
= 4. 4
The overall grade is:
= 12.75 + 9.0 + 32.2 + 28.0 + 4.4
= 86. 35
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The scores are :
Tests: 85%
Quizzes: 90%
Projects: 92%
Participation: 80%
Final Exam: 88%
blake bike east at 5m/s. five seconds later he speeds up to 9 m/s.
what is his change in velocity? what is his acceleration?
Answer:
The answer is down below
Step-by-step explanation:
v-u=◇velocity
[tex] = 9 - 5[/tex]
◇velocity =4ms‐¹
acceleration =◇velocity/time
[tex]a = \frac{4}{5} [/tex]
[tex]a = 0.8m {s}^{ - 2} [/tex]
Change in velocity:
[tex] \sf \:final \: velocity - initial \: velocity = change \: in \: velocity[/tex]
[tex] \therefore \tt \delta \: v = 9 - 5 \\ \tt = 4m {s}^{ - 1} [/tex]
To find acceleration:
[tex] \rm \: a = \frac{ \triangle \: v}{\triangle \: t} [/tex]
[tex] \rm \: a = \frac{ 4}{5 - 0} = \frac{4}{5} = 0.8m {s}^{ - 1} [/tex]
what is rhe square root of 50 ?
Answer:
Step-by-step explanation: 5√2
solve for x showing all steps 12^x+1=79
Answer:
To solve the equation 12^(x + 1) = 79 for x, we need to isolate the exponent.
Step 1: Subtract 1 from both sides of the equation:
12^(x + 1) - 1 = 79 - 1
12^(x + 1) - 1 = 78
Step 2: Rewrite 12^(x + 1) as (12^x)(12^1) using the exponent property:
(12^x)(12) - 1 = 78
Step 3: Simplify the left side of the equation:
12(12^x) - 1 = 78
Step 4: Add 1 to both sides of the equation:
12(12^x) = 78 + 1
12(12^x) = 79
Step 5: Divide both sides of the equation by 12:
(12(12^x))/12 = 79/12
12^x = 79/12
Step 6: Take the logarithm (base 12) of both sides of the equation:
log12(12^x) = log12(79/12)
x = log12(79/12)
Therefore, the solution for x is x = log12(79/12)
Hope this helps!
Point A is at (0,-2). vector AB is <-4,3>.
vector AC is <2,5>
a.) Find the magnitude of both vectors
b.) Find the angle between both vectors
C) Find a vector perpendicular to vector AB
d. Vector M = 2 vector AB + vector AC . Find the direction and magnitude of vector M
e.) Find the area of Δ ABC
r = r2
1 − r=(−2 i^ −2 j^ +0 k^ )−(4 i^ −4 j^ +0 k^ )
⇒ r =−6 i^ +2 j^ +0 k^
∴∣ r ∣= (−6)2 +(2) 2 +0 2
= 36+4
= 40
=210
A quantity or phenomenon with independent qualities for both magnitude and direction is called a vector. The term can also refer to a quantity's mathematical or geometrical representation. Velocity, momentum, force, electromagnetic fields, and weight are a few examples of vectors in nature. The above option D is appropriate.
Computer graphics known as vector graphics allow for the direct creation of visual pictures using geometric structures such as points, lines, curves, and polygons that are defined on a Cartesian plane.
Any pathogen that conveys and spreads an infectious agent into other living things is referred to be a vector. These vectors could be bacteria or parasites.
The above option D is correct.
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Match each drawing on the left with its geometric notation on the right. Some of the answer choices on the right may not be used.
Answer:
Please attach a photo to this so I can better answer your question
The function B is defined any positive whole number N as being the product BN=(N-1)(N-2)(N-3) what is the sum of B1,B2,B3 and B4?
The calculated sum of B1,B2,B3 and B4 is 6
How to determine the sum of B1,B2,B3 and B4?From the question, we have the following parameters that can be used in our computation:
BN=(N-1)(N-2)(N-3)
Express properly
So, we have
B(N) = (N-1)(N-2)(N-3)
using the above as a guide, we have the following equations
B(1) = (1-1)(1-2)(1-3) = 0
B(2) = (2-1)(2-2)(2-3) = 0
B(3) = (3-1)(3-2)(3-3) = 0
B(4) = (4-1)(4-2)(4-3) = 6
When the above functions are added, we have
Sum = 0 + 0 + 0 + 6
Evaluate the sum
Sum = 6
Hence, the sum of B1,B2,B3 and B4 is 6
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Given: ΔABC
AB=BC
PΔABC=50
PΔABD=40
Find: BD
The length of BD of the given triangle is: 15
How to find the perimeter of a triangle?The perimeter of a triangle is simply defined as the length of the boundary of that triangle.
Now, we are given that:
AB = BC = a
Perimeter of triangle ABC = 50
Perimeter of triangle ABD = 40
Thus:
2a + 2b = 50
a + b = 25 ------(1)
Similarly:
a + b + h = 40
a + b = 40 - h -----(2)
Put 40 - h for a + b in eq 1 to get:
40 - h = 25
h = 40 - 25
h = 15
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PLEASE HELP
I need this done is 13 minutes.
Polygon ABCD with vertices at A(1,-1) B(3,-1), C(3,-2) and D(1-2) is dilated to create polygon ABCD with vertices at A’(2,-2), B(6,-2), C’(6,-4) and D’(2,-4). Determine the scale factor used to create the image
A. 3
B. 2
C. 1/2
D. 1/3
The correct answer is B. 2, as the scale factor used to create the dilated polygon is 2.
To determine the scale factor used to create the image, we can compare the corresponding side lengths of the original polygon ABCD and the dilated polygon A'B'C'D'.
Let's calculate the lengths of the corresponding sides:
Side AB: The length of side AB is 3 - 1 = 2 units in the original polygon. In the dilated polygon, the length of side A'B' is 6 - 2 = 4 units.
Side BC: The length of side BC is -2 - (-1) = -1 units in the original polygon. In the dilated polygon, the length of side B'C' is -4 - (-2) = -2 units.
Side CD: The length of side CD is 1 - 3 = -2 units in the original polygon. In the dilated polygon, the length of side C'D' is 2 - 6 = -4 units.
Side DA: The length of side DA is -1 - (-2) = 1 unit in the original polygon. In the dilated polygon, the length of side D'A' is -2 - (-4) = 2 units.
Now, let's compare the corresponding side lengths:
AB: A'B' = 4 units / 2 units = 2
BC: B'C' = -2 units / -1 units = 2
CD: C'D' = -4 units / -2 units = 2
DA: D'A' = 2 units / 1 unit = 2
The scale factor used to create the image is the ratio of the corresponding side lengths.
In this case, all the corresponding side lengths have a ratio of 2.
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Find the measurement of m
The measure of the inscribed angle G in the circle is 85 degree.
What is the measure of angle G?An inscribed angle is simply an angle with its vertex on the circle and whose sides are chords.
The relationhip between an an inscribed angle and intercepted arc is expressed as:
Inscribed angle = 1/2 × intercepted arc.
Since the circle equals 360 degrees, we can determine the intercepted arc DF.
Hence:
Arc DF = 360 - ( 70 + 120 )
Arc DF = 360 - 190
Arc DF = 170°
Now, plug the value into the above formula:
Inscribed angle = 1/2 × intercepted arc.
Inscribed angle G = 1/2 × 170°
Inscribed angle G = 85°
Therefore, angle G has a measure of 85 degree.
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10 crystal vases cost $1,000. If the vases all cost the same amount, how much does each vase cost?
Answer:
$100
Step-by-step explanation:
Since 10 vases cost $1000, you can find the cost vase by dividing $1000 by 10.
$1000 ÷ 10 = $100
Each vase costs $100.
QUESTION 9 1 POINT
Ron will be finishing his payments on his 8-year, $35,000 student loan and wants to know the amount of interest that he
paid over the course of the loan. The student loan has a 3.8% fixed interest rate that is compounded monthly. Calculate the
total amount of interest Ron paid, rounding to the nearest cent.
Provide your answer below:
FEEDBACK
The total amount of interest Ron paid over the course of the loan is approximately $12,220.63.
To calculate the total amount of interest paid on Ron's student loan, we need to use the formula for compound interest. The formula for compound interest is:
A = P(1 + r/n)^(nt) - P
Where:
A is the total amount including principal and interest.
P is the principal amount (loan amount).
r is the annual interest rate (as a decimal).
n is the number of times the interest is compounded per year.
t is the number of years.
In this case, Ron's loan amount is $35,000, the annual interest rate is 3.8% (or 0.038 as a decimal), the loan term is 8 years, and the interest is compounded monthly (n = 12).
Plugging in these values into the formula:
A = $35,000(1 + 0.038/12)^(12*8) - $35,000
Calculating the exponent:
A = $35,000(1 + 0.00316667)^(96) - $35,000
Using a calculator to evaluate the expression within parentheses:
A = $35,000(1.00316667)^(96) - $35,000
Calculating the exponent:
A = $35,000(1.34898777) - $35,000
Subtracting the principal amount:
A = $47,220.63 - $35,000
A = $12,220.63
Therefore, the total amount of interest Ron paid over the course of the loan is approximately $12,220.63.
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What is the 36th derivative of f(x)=cos2x?
The 36th derivative of f(x) = cos(2x) is [tex]2^{17}[/tex]* cos(2x).
To find the 36th derivative of the function f(x) = cos(2x), we can apply the chain rule repeatedly. The chain rule states that if we have a composite function y = f(g(x)), then its derivative is given by dy/dx = f'(g(x)) * g'(x).
Let's start by finding the first few derivatives of f(x) = cos(2x):
f'(x) = -2sin(2x)
f''(x) = -4cos(2x)
f'''(x) = 8sin(2x)
f''''(x) = 16cos(2x)
We observe a pattern where the derivatives of cos(2x) alternate between sin(2x) and cos(2x), with the signs changing accordingly.
Based on this pattern, we can see that the 36th derivative will be:
f^(36)(x) =[tex](-1)^{17} * 2^{17} *[/tex] cos(2x)
Simplifying this expression, we have:
f^(36)(x) = [tex]2^{17} * cos(2x)[/tex]
Therefore, the 36th derivative of f(x) = cos(2x) is[tex]2^{17[/tex] * cos(2x).
It's important to note that in this case, the number 36 is even, and since the derivatives of cos(2x) follow a repeating pattern every 4 derivatives, the sign (-1) raised to the power of 17 accounts for the change in sign in the 36th derivative.
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What is the area of the parallelogram 60ftx67ft-52ft
To find the area of a parallelogram, you need to multiply the base by the height. In this case, the given dimensions are 60ft (base) and 67ft (height), and you need to subtract 52ft from the height.
New height = 67ft - 52ft = 15ft
Area of the parallelogram = Base * Height = 60ft * 15ft = 900 square feet.
Therefore, the area of the parallelogram is 900 square feet.
~~~Harsha~~~
how can you use pythagora's theorem to solve problems involving right-angled triangles
Using Pythagorean theorem, the length of the ladder is 10ft
What is Pythagorean Theorem?In mathematical terms, if y and z are the lengths of the two shorter sides (also known as the legs) of a right triangle, and x is the length of the hypotenuse, the Pythagorean theorem can be expressed as:
x² = y² + z²
In the questions given, the only one we can use Pythagorean theorem to solve is the one with ladder since it's forms a right-angle triangle.
To calculate the length of the ladder, we can write the formula as;
x² = 8² + 6²
x² = 64 + 36
x² = 100
x = √100
x = 10
The length of the ladder is 10 feet
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HELP PLEASE I DONT GET THIS
so the idea being, we have a system of equations of two variables and 4 equations, each one rendering a line, for this case these aren't equations per se, they're INEquations, so pretty much the function will be the same for an equation but we'll use > or < instead of =, but fairly the function is basically the same, the behaviour differs a bit.
we have a line passing through (-6,0) and (0,8), side one
we have a line passing through the x-axis and -6, namely (-6,0) and the y-axis and -4, namely (0,-4), side two
we have a line passing through (0,-4) and (6,4), side three
now, side four is simply the line connecting one and three.
the intersection of all four lines looks like the one in the picture below, so what are those lines with their shading producing that quadrilateral?
well, we have two points for all four, and that's all we need to get the equation of a line, once we get the equation, with its shading like that in the picture, we'll make it an inequality.
[tex](\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{8 -0}{0 +6} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = \cfrac{4}{3} ( x +6) \\\\\\ y=\cfrac{4}{3}x+8\hspace{5em}\stackrel{\textit{side one} }{\boxed{y < \cfrac{4}{3}x+8}}[/tex]
[tex]\rule{34em}{0.25pt}\\\\ (\stackrel{x_1}{-6}~,~\stackrel{y_1}{0})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{-4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{-4}-\stackrel{y1}{0}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{(-6)}}} \implies \cfrac{-4 -0}{0 +6} \implies \cfrac{ -4 }{ 6 } \implies - \cfrac{2}{3}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{0}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{(-6)}) \implies y -0 = - \cfrac{2}{3} ( x +6) \\\\\\ y=-\cfrac{2}{3}x-4\hspace{5em}\stackrel{\textit{side two} }{\boxed{y > -\cfrac{2}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{(-4)}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{0}}} \implies \cfrac{4 +4}{6 -0} \implies \cfrac{ 8 }{ 6 } \implies \cfrac{4}{3}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-4)}=\stackrel{m}{ \cfrac{4}{3}}(x-\stackrel{x_1}{0}) \implies y +4 = \cfrac{4}{3} ( x -0) \\\\\\ y=\cfrac{4}{3}x-4\hspace{5em}\stackrel{ \textit{side three} }{\boxed{y > \cfrac{4}{3}x-4}} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex](\stackrel{x_1}{6}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{0}~,~\stackrel{y_2}{8}) ~\hfill~ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{8}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{0}-\underset{x_1}{6}}} \implies \cfrac{ 4 }{ -6 } \implies - \cfrac{2}{3}[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{- \cfrac{2}{3}}(x-\stackrel{x_1}{6}) \\\\\\ y=-\cfrac{2}{3}x+8\hspace{5em}\stackrel{ \textit{side four} }{\boxed{y < -\cfrac{2}{3}x+8}}[/tex]
now, we can make that quadrilateral a trapezoid by simply moving one point for "side four", say we change the point (0 , 8) and in essence slide it down over the line to (-3 , 4). Notice, all we did was slide it down the line of side one, that means the equation for side one never changed and thus its inequality is the same function.
now, with the new points for side for of (-3,4) and (6,4), let's rewrite its inequality
[tex](\stackrel{x_1}{-3}~,~\stackrel{y_1}{4})\qquad (\stackrel{x_2}{6}~,~\stackrel{y_2}{4}) \\\\\\ \stackrel{slope}{m}\implies \cfrac{\stackrel{\textit{\large rise}} {\stackrel{y_2}{4}-\stackrel{y1}{4}}}{\underset{\textit{\large run}} {\underset{x_2}{6}-\underset{x_1}{(-3)}}} \implies \cfrac{4 -4}{6 +3} \implies \cfrac{ 0 }{ 9 } \implies 0[/tex]
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{4}=\stackrel{m}{ 0}(x-\stackrel{x_1}{(-3)}) \implies y -4 = 0 ( x +3) \\\\\\ y=4\hspace{5em}\stackrel{ \textit{side four changed} }{\boxed{y < 4}}[/tex]
Jules Girard bought 1 gallon of paint at a 33% markdown. Its regular price is $39.99.
Markdowns are usually applied before any additional discounts or promotions. In this case, the markdown reduced the regular price by 33%, resulting in the final price of $26.80.
Jules Girard bought 1 gallon of paint at a 33% markdown from its regular price of $39.99. To calculate the final price after the markdown, we can apply the percentage decrease to the regular price.
The markdown of 33% means that the price is reduced by 33% of the regular price. To calculate the amount of the markdown, we can multiply the regular price by the percentage decrease:
Markdown amount = 33% of $39.99 = 0.33 * $39.99
Next, we can subtract the markdown amount from the regular price to find the final price:
Final price = Regular price - Markdown amount = $39.99 - (0.33 * $39.99)
Calculating the expression within parentheses:
Final price = $39.99 - $13.19
Final price = $26.80
Therefore, Jules Girard bought 1 gallon of paint at a 33% markdown, resulting in a final price of $26.80.
Markdowns are usually applied before any additional discounts or promotions. In this case, the markdown reduced the regular price by 33%, resulting in the final price of $26.80.
For more questions on markdown
https://brainly.com/question/30976837
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