Answer:
Perpendicular slope = -2Parallel slope = 1/2======================================================
Explanation:
Let's solve for y to get the equation into y = mx+b form, aka slope intercept form.
4x-8y= -6
-8y= -6-4x
y = (-6-4x)/(-8)
y = -6/(-8) + (-4x)/(-8)
y = 3/4 + (1/2)x
y = (1/2)x + 3/4
This is now in y = mx+b form
m = 1/2 = slope
b = 3/4 = y intercept
We'll ignore the y intercept and focus on the slope only.
-----------------
Rule: If the slope of a line is a/b, then the perpendicular slope is -b/a
Flip the fraction and flip the sign.
In this case, the original slope 1/2 has a perpendicular slope of -2/1 or simply -2.
The original slope multiplied with the perpendicular slope yields -1. So (1/2)*(-2/1) = -1
-----------------
Another rule: Two parallel lines always have equal slopes, but different y intercepts.
The original slope is 1/2, so the parallel slope is also 1/2.
find the value of x ( fast fast fast)
The value of x is calculated with the help of a similar triangle is 24.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
In a triangle, if there is a parallel line with any side of the triangle, then the line divides the other sides in the same ratio.
Then we have
x / 12 = 32 / 16
x = 24
Then the value of x is 24.
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HELP THIS IS URGENT WILL GIVE BRANLIEST ANSWER 3 AND 6
If P(n) and Q(n) are polynomials of degree j and k, respectively, then the series
Infinite
Σ P(n)/Q(n)
n=1
converges if j < k − 1 and diverges if j ≥ k – 1.
Use the polynomial test given above to determine whether the series converges or diverges.
Infinite
Σ 1/(n)^8 +7
n=1
O converges
Odiverges
Answer:
converges
Step-by-step explanation:
well the two polynomials in the series are 1 and n^8 (I'm assuming the +7 is not in the decimal but it seems to not matter). The degree of the polynomial 1 is 0 which can be represented by 1x^0. The second polynomial in the denominator has a degree of 8. So j = 0 and k = 8. Since 0 < (8-1)
0 < 7 the series converges
The Carter family just left the local pet store with Rex, their new family dog. The pet store owner told the Carter family that for the next 6 months, Rex would grow at an average rate of 9 pounds per month. Currently, Rex is 2 months old and weighs 6 pounds. Age, in months 2 3 4 5 6 7 8 Weight, in pounds 6 Part A: Complete the given table that represents Rex’s current weight, in pounds, as a function of his age, in months Part B: Graph the data in the table from Part A. Be sure to label the graph and all data points. Part C: Create a linear model that represents the Rex’s current weight, in pounds, as a function of his age, in months. Part D: If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old? Upload your table, graph, and solution below.
The graph is attached and all the sub parts have been answered.
What is a function ?A function is away of relating a dependent variable to an independent variable .
It is given that
Current weight of Rex at 2 months =6 pounds
Let x represents the age in months of Rex
then a linear model that represents the Rex’s current weight, in pounds, as a function of his age, in months. is
Let y be the current weight of Rex
then
y = 6 + 9(x -2)
The table that represents Rex’s current weight, in pounds, as a function of his age, in months
2 6
3 15
4 24
5 33
6 42
7 51
8 59
The graph is plotted for the given data and attached .
If Rex continues to grow at the rate of 9 pounds per month beyond the expected six months, how much will Rex weight by the time he is one year old
6 + 9*(12-2)
96 pounds.
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Consider the following loan. Complete parts (a)-(c) below
An individual borrowed $88,000 at an APR of 6%, which will be paid off with monthly payments of $667 for 18 years.
a. Identify the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.
The amount borrowed is $, the annual interest rate is%, the number of payments per year is the loan term is years, and the payment amount is $
The complete statements are mathematically given as
the amount borrowed= 88000the annual interest rate= 6%the number of payments per year= 12The loan term= 18the payment amount.=8004What is the amount borrowed, the annual interest rate, the number of payments per year, the loan term, and the payment amount.?Generally, The transfer of money, products, or services in return for other goods and services in proportions that have been previously agreed upon and deemed acceptable is what is meant by the term "payment."
In conclusion, the amount borrowed= 88000
the annual interest rate= 6%
the number of payments per year= 12
The loan term= 18
the payment amount.=667*12
the payment amount.=8004
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The linear function that is represented by which table has the same slope as the graph? On a coordinate plane, a line goes through points (0, negative 3) and (2, 1). a A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries negative 9, negative 7, negative 5, negative 3, negative 1. b A 2-column table with 5 rows. Column 1 is labeled x with entries negative 25, negative 21, negative 17, negative 13, negative 9. Column 2 is labeled y with entries 9, 7, 5, 3, 1. c A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9. d A 2-column table with 5 rows. Column 1 is labeled x with entries 1, 3, 5, 7, 9. Column 2 is labeled y with entries negative 9, negative 13, negative 17, negative 21, negative 25.
Option C. A 2-column table with 5 rows. Column 1 is labeled x with entries negative 9, negative 7, negative 5, negative 3, negative 1. Column 2 is labeled y with entries negative 25, negative 21, negative 17, negative 13, negative 9. This labeled is correct.
According to the linear function,
Every linear function is characterized by a constant rate of change; the slope. The slope of a linear function is a measure of the “steepness” of the line. We use the symbols Δx and Δy which mean respectively the “change in x ” and the “change in y ”.
So Option C is correct after all assumptions.
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A water sprinkler sends water out in a circular pattern. How large is the watered area if the radius of the watering pattern is 3 feet?
Use 3.14 for pi.
Answer:
28.26 feet squared
Explanation:
Area of circle is determined by : π(radius)²
Here given:
π = 3.14radius = 3 feetSolve for area:
π(radius)²3.14(3)²28.26 feet²Answer:
28.26 feet squared
Step-by-step explanation:
Radius of the watering pattern = 3 feet
Area = π r²
= 3.14 × 3²
= 28.26 feet squared
the perimeter of a rectangle is 70 cm . if the ratio of the width to the length is 2:5 what is the width ?
Answer:
width = 10 cm
Step-by-step explanation:
the ratio of width to length is 2 : 5 = 2x : 5x ( x is a multiplier )
the perimeter (P) of a rectangle is calculated as
P = 2 × width + 2 × length
given P = 70 then
2(2x) + 2(5x) = 70
4x + 10x = 70
14x = 70 ( divide both sides by 14 )
x = 5
Then
width = 2x = 2 × 5 = 10 cm and length = 5x = 5 × 5 = 25 cm
Construct a polynomial function with the following properties fifth degree, 3 is a zero of multiplicity 3, - 4 is the only other zero, leading coefficient is 3
The polynomial function with the given properties is; y = 2(x - 3)³(x + 4)²
How to construct polynomial functions?Polynomials are defined as algebraic expressions that consist of variables, coefficients, and constants. The standard form of polynomials has mathematical operations such as addition, subtraction, and multiplication.
We need to form a polynomial expression with the following properties;
fifth-degree, 3 is a zero of multiplicity 3, −4 is the only other zero and ,the leading coefficient is 3. Thus, the polynomial will be;
y = 2(x - 3)³(x + 4)²
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See photo for questions.
Answer:
1. "a" [tex]u'=6x[/tex]
2. "d" [tex]v'=15x^2[/tex]
3. "b" [tex]y'=75x^4+30x^2+6x[/tex]
Step-by-step explanation:
General outline:For parts 1 & 2, apply power ruleFor part 3, apply product rulePart 1.
Given [tex]u=3x^2+2[/tex], find [tex]\frac{du}{dx} \text{ or } u'[/tex].
[tex]u=3x^2+2[/tex]
Apply a derivative to both sides...
[tex]u'=(3x^2+2)'[/tex]
Derivatives of a sum are the sum of derivatives...
[tex]u'=(3x^2)'+(2)'[/tex]
Scalars factor out of derivatives...
[tex]u'=3(x^2)'+(2)'[/tex]
Apply power rule for derivatives (decrease power by 1; mutliply old power as a factor to the coefficient); Derivative of a constant is zero...
[tex]u'=3(2x)+0[/tex]
Simplify...
[tex]u'=6x[/tex]
So, option "a"
Part 2.
Given [tex]v=5x^3+1[/tex], find [tex]\frac{dv}{dx} \text{ or } v'[/tex].
[tex]v=5x^3+1[/tex]
Apply a derivative to both sides...
[tex]v'=(5x^3+1)'[/tex]
Derivatives of a sum are the sum of derivatives...
[tex]v'=(5x^3)'+(1)'[/tex]
Scalars factor out of derivatives...
[tex]v'=5(x^3)'+(1)'[/tex]
Apply power rule for derivatives (decrease power by 1; mutliply old power as a factor to the coefficient); Derivative of a constant is zero...
[tex]v'=5(3x^2)+0[/tex]
Simplify...
[tex]v'=15x^2[/tex]
So, option "d"
Part 3.
Given [tex]y=(3x^2+2)(5x^3+1)[/tex]
[tex]\text{Then if } u=3x^2+2 \text{ and } v=5x^3+1, y=u*v[/tex]
To find [tex]\frac{dy}{dx} \text{ or } y'[/tex], recall the product rule: [tex]y'=uv'+u'v[/tex]
[tex]y'=uv'+u'v[/tex]
Substituting the expressions found from above...
[tex]y'=(3x^2+2)(15x^2)+(6x)(5x^3+1)[/tex]
Apply the distributive property...
[tex]y'=(45x^4+30x^2)+(30x^4+6x)[/tex]
Use the associative and commutative property of addition to combine like terms, and rewrite in descending order:
[tex]y'=75x^4+30x^2+6x[/tex]
So, option "b"
The United States Postal Service reports that 90% of first-class mail within the same city is delivered in two days of the time of mailing. Ten letters are randomly sent to different locations. a. What is the probability that all 10 will arrive within two days? b. What is the probability that exactly 8 will arrive within two days? c. What is the probability that 5 or fewer will arrive within two days? d. What is the mean number of letters that will arrive within two days? e. What is the standard deviation of the number of letters that will arrive within two days?
a)The probability that all 10 will arrive within two days is 0.3486.
b) P(x = 8) = 0.1937
c) P(x=5)= 0.0014
d) mean = 9
e) Standard deviation = √0.90 = 0.9486
What is Binomial Probability?The binomial distribution model allows us to compute the probability of observing a specified number of "successes" when the process is repeated a specific number of times and the outcome for a given patient is either a success or a failure.
Given:
p = 90/100 = 0.90
q(probability of success) = 1 - p = 1 - 0.90 = 0.10
n = 10
a)The probability that all 10 will arrive within two days
P(x = 10) = 0.3486
b) P(x = 8) = 0.1937
c) P(x=5)= 0.0014
d) mean = np = 10 × 0.90 = 9
e) Variance = npq = 10 × 0.90 × 0.10 = 0.90
Standard deviation = √0.90 = 0.9486
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Consider a triangle ABC like the one below. Suppose that B=129°, a=7, and c=42. (The figure is not drawn to scale.) Solve the triangle.
Carry your intermediate computations to at least four decimal places, and round your answers to the nearest tenth.
If there is more than one solution, use the button labeled "or".
4-C-b-0
DOD
X
No
solution
5
?
The angles are: A =24.7° ; B = 40.6° ; C =114.7°.
What is Cosine law?
The law of cosine helps in establishing a relationship between the lengths of sides of a triangle and the cosine of its angles. The cosine law in trigonometry generalizes the Pythagoras theorem, which applies to a right triangle.
Cosine Law
a² = b²+c²-2bc cos A
b² = c²+a² -2ca cos B
Sum of three angles of a triangle is 180°.
a = 34 ; b= 53; c = 74
Substituting the given values in the cosine law, we have
34² = 53² + 74² - 2*53 *74 * cos A
7844 cos A = 2809 + 5476 - 1156 = 7129
cos A = 7129/7844 = 0.9088
A = cos⁻¹ (0.9088) = 24.6600° = 24.7°
53² = 74² + 34² - 2 (74)(34) cos B
5032 cos B = 5476 + 1156 - 2809 = 3823
cos B = 3823/5032 = 0.7597
B = cos⁻¹ (0.7597) = 40.5622° = 40.6°
Also, A + B + C = 180°
24.7 + 40.6 + C =180
C =180 - 65.3 = 114.7°
Thus, the angles are: A =24.7° ; B = 40.6° ; C =114.7°
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Select the correct answer. Which set of vertices forms a parallelogram? OA A2,4), B(3, 3), C6, 4), D(5, 6) OB. A(-1, 1), B(2, 2), C(5, 1), D(4, 1) OC. A(-5, -2), B(-3, 3), C3, 5), D(1, 0) OD. A(-1, 2), B(1, 3), C5, 3), D(1, 1).
Answer:
(6,4)
Step-by-step explanation:
^^^
1. A water tank measuring 80 cm by 40 cm by 30 cm is completely filled with water. Water flows out of the tank at a rate of 4 per minute. At this rate, how long will the tank be completely drained out of water? 80 cm 40 cm 30 cm 1. A water tank measuring 80 cm by 40 cm by 30 cm is completely filled with water . Water flows out of the tank at a rate of 4 per minute . At this rate , how long will the tank be completely drained out of water ? 80 cm 40 cm 30 cm
Answer:
6.34 min to empty
Step-by-step explanation:
80 cm x 40 cm x 30 cm = 96000 cm^3
this volume represents 25.36 gallons of water (US)
25.36 gal / 4 gal/min = 6.34 min to empty
You have loaned a friend %100 and will charge him 5% annual simple interest when he pay it back.
Answer:
bro nobody can figure this out you need to word the entire question with numbers and all. and proper English pls
What would the following figure look like after a reflection in a horizontal mirror, followed by a rotation 90 degrees counterclockwise?
Answer:
Step-by-step explanation:
To rotate any figure we have to have the CENTER of rotation!!!!
You did not provide us (your helpers) with that point, so I chose point on the horizontal mirror.
0 1 3 6 10 what goes after 10?
Answer:
15
Step-by-step explanation:
0 + 1 = 1
1 + 2 = 3
3 + 3 = 6
6 + 4 = 10
10 + 5 = 15
A 20-ft by the 40-ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 256 ft2, how wide is the walkway?
========================================================
Explanation:
x = width of the walkway in feet
This is some positive real number.
The dimension of 20 feet bumps up to 20+2x when adding on x from both directions. Similarly, the 40 ft dimension becomes 40+2x
Refer to the diagram below.
The 20 ft by 40 ft pool is surrounded by a larger rectangle that is 20+2x ft by 40+2x ft
The pool itself is 20*40 = 800 sq ft. Add on the walkway area to get 800+256 = 1056 sq ft.
-----------
Area = length*width
1056 = (20+2x)*(40+2x)
1056 = 20*40 + 20*2x + 2x*40 + 2x*2x ... FOIL rule
1056 = 800 + 40x + 80x + 4x^2
0 = 4x^2 + 40x + 80x + 800 - 1056
0 = 4x^2 + 120x - 256
4x^2 + 120x - 256 = 0
4(x^2 + 30x - 64) = 0
x^2 + 30x - 64 = 0
Let's use the quadratic formula to finish solving for x.
Plug in a = 1, b = 30, c = -64
[tex]x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-30\pm\sqrt{(30)^2-4(1)(-64)}}{2(1)}\\\\x = \frac{-30\pm\sqrt{1156}}{2}\\\\x = \frac{-30\pm34}{2}\\\\x = \frac{-30+34}{2} \ \text{ or } \ x = \frac{-30-34}{2}\\\\x = \frac{4}{2} \ \text{ or } \ x = \frac{-64}{2}\\\\x = 2 \ \text{ or } \ x = -32\\\\[/tex]
Recall we made x be positive. This is because a negative walkway width does not make sense. This means we'll ignore x = -32.
The only practical solution is x = 2
Therefore, the walkway is 2 feet wide
3z^2-4z+11 -(12z^2+2z-11 find the difference . polynomials functions
Answer:
−135z
2
−2z
The 2 is representing Square
Step-by-step explanation:
(3z)
2
−4z+11−(12z)
2
+2z−11
Expand (3z)
2
.
3
2
z
2
−4z+11−(12z)
2
+2z−11
Calculate 3 to the power of 2 and get 9.
9z
2
−4z+11−(12z)
2
+2z−11
Expand (12z)
2
.
9z
2
−4z+11−12
2
z
2
+2z−11
Calculate 12 to the power of 2 and get 144.
9z
2
−4z+11−144z
2
+2z−11
Combine 9z
2
and −144z
2
to get −135z
2
.
−135z
2
−4z+11+2z−11
Combine −4z and 2z to get −2z.
−135z
2
−2z+11−11
Subtract 11 from 11 to get 0.
−135z
2
−2z
If “a” is a non zero constant, what is the maximum number of turns for the graph of
y = x³ + ax² - 7x+10
The maximum number of turns for the graph given by the function is; 2.
What is the maximum number of turns for the graph?It follows from the task content that the graph given is that of a cubic function. On this note, it follows that the graph has 2 turning points.
This follows from the fact that the degree of the polynomial is 3 and hence, the maximum number of turns on the graph is 2.
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Find the area of the shaded region
O100 m²
O 105 m²
O 75 m²
O 50 m²
5m
10 m.
5m
15 m
What is the value of h?
Answer:
h=-2
Step-by-step explanation:
the graph was shifted 2 units left
The perimeter of an equilateral triangle is 9x + 3, this is greater than the perimeter of a
regular pentagon which is 10x - 5.
Write down an inequality to represent this information.
Answer:
x < 8
Step-by-step explanation:
9x + 3 > 10x - 5
9x - 10x > -5 - 3
-x > -8
x < 8
Need help, can't figure this one out:
Find the perimeter of the following rectilinear figure.
The perimeter of the following rectilinear figure is 54 units.
What is Perimeter ?Perimeter of a figure is the distance covered when a person walk one round across its edges .
The given figure is in the form of a rectangle ,
The perimeter is equal to the sum of all sides ,
The bottom base is 13 includes (base of the small extended figure )
The left side is 14(includes left side of the small extended figure)
The right side is 10+5+4 (includes right side of the small extended figure)
The top is 8
Therefore the perimeter is 13+14+10+5+4+8 = 54 units
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If y=4 when x=12, find y when x=-24
The value of y is -8 if the x -24 and y varies directly with x, and If y = 4 when x = 12.
What is a proportional relationship?It is defined as the relationship between two variables when the first variable increases, the second variable also increases according to the constant factor.
The question is incomplete.
The complete question is:
If y varies directly with x, and If y = 4 when x = 12, how do you find y when x = -24?
y ∝ x (given)
y = kx
k is the constant of proportionality.
4 = 12k (y = 4, and x = 12)
k = 1/3
y = x/3
Plug x = -24
y = -24/3
y = -8
Thus, the value of y is -8 if the x -24 and y varies directly with x, and If y = 4 when x = 12.
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In a random sample of 250 students, 150 were in favor of longer hours at the school library. At 98% level of confidence, what is the margin of error?
Select one:
0.051
0.080
0.065
0.072
0.078
0.061
0.072 is the margin of error.
What is standard error?The standard error (SE) of a statistic is the standard deviation of its sampling distribution or an estimate of that standard deviation.
According to the question,
In a random sample of 250 students,
p= 0.98 (or 98%) were in favor of longer hours at the school library.
The standard error of p(the sample proportion) is (approximately)
The standard error of p = [tex]\sqrt{\frac{p(1-p)}{n} }[/tex]
p = 0.98
1 - p = 1 - 0.98 = 0.02
Here,
n = 250
The standard error of p = [tex]\sqrt{ \frac{0.98 (0.02) }{250}[/tex]
The standard error of p ≈ 0.072
Therefore,
The margin of error is 0.072.
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Examples for Continuous rv X
1. Given the pdf:
f(x) {1/4 e^-1/4x} x>0
0, otherwise
Find: a. E(X) and b. Var(X)
Use the definitions of expectation and variance.
Expectation[tex]E(X) = \displaystyle \int_{-\infty}^\infty x f_X(x) \, dx = \frac14 \int_0^\infty x e^{-x/4} \, dx[/tex]
Integrate by parts,
[tex]\displaystyle \int_a^b u \, dv = uv \bigg|_a^b - \int_a^b v \, du[/tex]
with
[tex]u = x \implies du = dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]
Then
[tex]E(X) = \displaystyle \frac14 \left(\left(-4x e^{-x/4}\right)\bigg|_0^\infty + 4 \int_0^\infty e^{-x/4} \, dx\right)[/tex]
[tex]E(X) = \displaystyle \int_0^\infty e^{-x/4} \, dx = \boxed{4}[/tex]
(since the integral of the PDF is 1, and this integral is 4 times that)
Variance[tex]V(X) = E\bigg((X - E(X))^2\bigg) = E(X^2) - E(X)^2[/tex]
Compute the so-called second moment.
[tex]E(X^2) = \displaystyle \int_{-\infty}^\infty x^2 f_X(x)\, dx = \frac14 \int_0^\infty x^2 e^{-x/4} \, dx[/tex]
Integrate by parts, with
[tex]u = x^2 \implies du = 2x \, dx \\\\ dv = e^{-x/4} \, dx \implies v = -4 e^{-x/4}[/tex]
Then
[tex]E(X^2) = \displaystyle \frac14 \left(\left(-4x^2 e^{-x/4}\right)\bigg|_0^\infty + 8 \int_0^\infty x e^{-x/4} \, dx\right)[/tex]
[tex]E(X^2) = 8 E(X) = 32[/tex]
and the variance is
[tex]V(X) = 32 - 4^2 = \boxed{16}[/tex]
What is the mode of 1,1,2,2,3,3,4,4
Answer: There is no mode.
Step-by-step explanation:
The mode is the number that appears the most in a given set of data. Each number in this data set is repeated twice. Therefore, there is no mode.
I hope this helped!! :)
Answer:
1, 2, 3, 4
or none
Step-by-step explanation:
Mode is the value or values in the data set that occurs most frequently.
example:
For the data set 1, 1, 2, 5, 6, 6, 9 the mode is 1 and also 6.
in 1, 1, 2, 2, 3, 3, 4, 4 all numbers occur the same amount of times, therefore they all (or none) are the mode
hope this helps:)
x=7-3y
2(7-3y)+4y=8
14-6y +4y=8
14-2y=8
-2y = -6
y=3
x + 3(3) = 7
Answer:
(-2,7)
Step-by-step explanation:
x=7-3y
2(7-3y)+4y=8
14-6y +4y=8
14-2y=8
-2y = -6
y=3
x + 3(3) = 7
x + 9 = 7
x = -2
(-2,7)
Answer: -2,3
Step-by-step explanation:
Which point is a reflection of Z(5/1, 3) across the x-axis? Please I will give the brainliest
Answer: (5/1, -3)
Hope this helps :)
Answer:
Look at the attachment.
Step-by-step explanation:
Look at the attachment.
