Answer:
a₂₀ = 69
Step-by-step explanation:
The nth term of an arithmetic sequence is
\(a_{n}\) = a₁ + (n - 1)d
where a₁ is the first term and d the common difference
Here a₁ = 12 and d = 15 - 12 = 3 , then
a₂₀ = 12 + (3 × 19) = 12 + 57 = 69
What is the best definition for parabola?
Answer: curve shape of something
Step-by-step explanation:
Answer:
Hey mate......
Step-by-step explanation:
This is ur answer.......
A parabola is a curve where any point is at an equal distance from: a fixed point (the focus), and. a fixed straight line (the directrix)
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Write the equation of the line with a slope of 4 and passes through the point (10, 6).
PLEASE HELP
Determine whether the set of all linear combinations of the following set of vector in R3 is a line or & plane or all of R3. Justify, Your answer: (a) {(-2,5, -3), (6, -15,9), (-10,25, -15)} (b) {(1,2,0), (1,1,1),(4,5,3)} (c) {(0,0,3),(0.1,2), (1,1.0)}
Given sets of vectors in R3 are:(a) {(-2,5, -3), (6, -15,9), (-10,25, -15)}(b) {(1,2,0), (1,1,1),(4,5,3)}(c) {(0,0,3),(0.1,2), (1,1.0)}
Determine whether the set of all linear combinations of the given sets of vectors in R3 is a line, a plane or all of R3:
1) Set of vectors (a):Set of vectors (a) is not linearly independent. So, the set of all linear combinations of these vectors will not form the R3.
We can say that this set of all linear combinations of the given set of vectors (a) is a plane
.2) Set of vectors (b):The given set of vectors (b) is linearly independent. Hence, we can say that the set of all linear combinations of the given set of vectors (b) forms R3.
Thus, we can say that this set of all linear combinations of the given set of vectors (b) is all of R3.
3) Set of vectors (c):Set of vectors (c) is not linearly independent. So, the set of all linear combinations of these vectors will not form the R3. We can say that this set of all linear combinations of the given set of vectors (c) is a line.
Justification: In order to find whether the set of all linear combinations of the given set of vectors (a) is a line, a plane or all of R3, we need to check whether the given set of vectors (a) is linearly independent or not. If it is linearly independent, then it will form the R3. If it is linearly dependent, then it will form a line or a plane.
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HELP AGAIN ANSWER THIS QUESTION
Answer:
A
Step-by-step explanation:
Need help ASAP, Tysm i really appreciate it
Answer:
-5n + 16
Step-by-step explanation:
Distribute the 7 to the equation inside the parenthesis.
7(n + 1) - 12n + 9
7n + 7 - 12n + 9
Bring the -12n towards the 7n.
7n - 12n + 7 + 9
Add or subtract like terms.
7n - 12n + 7 + 9
-5n + 16
Answer:
-5n + 16
When a prism and a pyramid have the same height and the same base the volume of the prism is greater than the pyramid?
Yes, the given statement is true the volume of the prism is greater than the volume of the pyramid when they have same base and same height.
As given in the question,
Formula required to calculate the volume of the pyramid and volume of the prism is given by :
Volume of a pyramid = (1/3) × (base area )× ( height )
Volume of a prism = (Base area) × (height)
When the base and height of the pyramid is same as that of the base and height of the prism then
Volume of the pyramid = ( 1/3) × ( Base area × height )
⇒Volume of the pyramid = ( 1/3) × ( Volume of the prism )
⇒Volume of the prism = 3 × ( Volume of the pyramid )
⇒Volume of the prism > Volume of the pyramid
Therefore, the volume of the prism is greater than the volume of pyramid is a true statement.
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Which ordered pair is a solution to the equation y=1/3x+19
Answer:
(9,22)
Step-by-step explanation:
1/3 of 9= 3
3+19=22
please someone help me with this question
Answer:
i) 104 °F
ii) 343 °K
Step-by-step explanation:
We have the relationship between temperature in degrees Fahrenheit(y) and degrees Kelvin(x) as:
\(y\:=\:\dfrac{9}{5}\left(x-273\right)+32\)
i) When temperature in Kelvin is 313°K, the equivalent temperature in °F is:
\(\begin{aligned}y &= \dfrac{9}{5}(313-273) + 32\\& = \dfrac{9}{5}(40) + 32\\&= 9 \cdot 8 + 32\\\\&= 72 + 32\\\\& = 104^\circ F\end{aligned}\\\)
So at 313°K, the equivalent temperature is 104°F
\(====================================\)
ii) We are given the temperature in degrees Fahrenheit and asked to find the temperature in degrees Kelvin
We have the equation for temperature conversion from °K to °F as:
\(y\:=\:\dfrac{9}{5}\left(x-273\right)+32\)
Let's manipulate this equation so that x is given in terms of y
Switch sides:Here x = degrees Kelvin and y = degrees Fahrenheit
Given y = 158°F, just plug in this value into the equation for x giving
\(\begin{aligned}x &= \dfrac{5}{9}(158 - 32) + 273\\& = \dfrac{5}{9}(126) + 273\\&= 70 + 273\\&= 343\end{aligned}\)
Therefore temperature in °K for temperature 158°F = 342 °K
a) Complete the table of values for y = x2 - 4x
ONLY A THANKS
Let "x" = square root of 6 + the square root of 7. What two consecutive integers does "x" lie between? Can you please explain in words, how you got the answer?
Answer:
(5, 6)
Step-by-step explanation:
\(x=\sqrt{6}+\sqrt{7}\approx2.45+2.65\approx 5.10\\\\\boxed{5<x<6}\)
I evaluated the expression on my calculator.
__
You can guess that the sum is nearly 2√6.5 = √26. This is between √5² and √6², so the root is likely between 5 and 6.
You use a technical support company for your computer. The company bills you at a rate of $10 per month and $35 per hour for phone support.
a. Identify the fixed cost (the constant).
b. Identify the independent variable (x).
c. Identify the dependent variable (y).
d. Write an equation that describes the situation above.
e. If you were billed $97.50 for last month, how many hours of phone support did you need? Show all work.
Answer:fixed cost=10
Independent variable=months paid
Dependent=hours on support
month=x,h=hour,10x+35h=total cost
97.50=10+35h
87.50=35h
h=2.5 hours
Step-by-step explanation:
showed work
Multiply. (−11314)⋅(159) What is the product? Enter your answer in the box.
Answer:
the answer is -3
Step-by-step explanation:
I took the quiz on k12
if 45% of an item is $36 what is the original price
Answer:
$80 original price
Step-by-step explanation:
If 45% of an item is $36 what is the original price?
40% = 0.4
36/0.4 = $80 original price
Answer:
$80
Step-by-step explanation:
45/100=36/x
Cross multiply
45x=100(36)
45x=3600
/45. /45
x=80
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Consider the line with the equation: y=x−18 Give the equation of the line parallel to Line 1 which passes through (6,−3) : Give the equation of the line perpendicular to Line 1 which passes through (6,−3) :
The equation of the line perpendicular to Line 1 which passes through (6, -3) is: y = -x + 3.
To find the equation of the line parallel to Line 1 that passes through (6, -3), we know that both lines have the same slope. Thus, the new line's slope is 1. To find the y-intercept, we can substitute the x and y coordinates of the given point (6, -3) into the equation and solve for b: -3 = (1)(6) + b-3 = 6 + b-9 = b
Therefore, the equation of the line parallel to Line 1 which passes through (6, -3) is: y = x - 9.
To find the equation of the line perpendicular to Line 1 that passes through (6, -3), we know that the new line's slope is the negative reciprocal of Line 1's slope. Line 1's slope is 1, so the new line's slope is -1. To find the y-intercept, we can substitute the x and y coordinates of the given point (6, -3) into the equation and solve for b: -3 = (-1)(6) + b-3 = -6 + b3 = b
Therefore, the equation of the line perpendicular to Line 1 which passes through (6, -3) is: y = -x + 3.
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Find the exact coordinates of the point at which the following curve is steepest: y = 50/1+ 6e^-2t for greaterthanorequalto 0
Since the exponential function is always positive, there is no solution for e^(-2t) = -1/6. This means that the derivative is never equal to zero, and there is no point of maximum steepness for this curve.
To find the point at which the curve is steepest, we need to find the maximum value of the derivative of the function. Let's start by finding the derivative of the given function:
y = 50 / (1 + 6e^(-2t))
To find the derivative, we can use the quotient rule:
y' = [50(0) - (1 + 6e^(-2t))(-12e^(-2t))]/(1 + 6e^(-2t))^2
Simplifying this expression, we get:
y' = (72e^(-2t))/(1 + 6e^(-2t))^2
To find the maximum point, we need to find the value of t for which the derivative is equal to 0. Setting y' = 0 and solving for t, we have:
(72e^(-2t))/(1 + 6e^(-2t))^2 = 0
Since the numerator cannot be zero, we focus on the denominator:
(1 + 6e^(-2t))^2 = 0
Taking the square root of both sides, we get:
1 + 6e^(-2t) = 0
Solving for e^(-2t), we have:
e^(-2t) = -1/6
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Explain how to plot y=-x+3 on a graph
1. Identify the linear equation. y = mx + b
2. Take (b) and plot it on the y axis. Since b is a positive 3, that means you plot a positive 3 on the y axis. This will be the number that your line crosses the y axis on.
3. Take (mx) and plot it in correlation to (b). mx = -x also known as -1. So, from +3 on the y axis, move once to the left and once down. Your coordinate should land on (2, 1).
From here on out, keep moving -1 on the y axis and +1 on the x axis. The ongoing coordinates should look something like (1, 2)(0, 3)(-1, 4) and so on.
I need a answer fast thanks!
Answer:
Chart:
x y
-6 11
3 5
15 -3
-12 15
Step-by-step explanation:
The only things you can plug in are the domain {-12, -6, 3, 15}
Plug in the domain into equation to find y.
-6 :
y = -2/3 (-6) +7
y = +47
y=11
(-6,11)
3:
y = -2/3 (3) +7
y = -2 +7
y = 5
(3, 5)
15:
y = -2/3 (15) +7
y = -10 +7
y = -3
(15 , -3)
-12:
y = -2/3 (-12) +7
y = 8 + 7
y= 15
(-12,15)
Answer:
1) 11
2) 3
3) -3
4) -12
Step-by-step explanation:
eq(1):
\(y = \frac{-2}{3} x + 7\\\\y - 7 = \frac{-2}{3} x\\\\x = (y - 7)\frac{-3}{2} \\\\x = (7-y)\frac{3}{2} ---eq(2)\)
1) x = -6
sub in eq(1)
\(y = \frac{-2}{3} (-6) + 7\\\\y = \frac{12}{3} + 7\\\\y = 4+7\\\\y = 11\)
2) y = 5
sub in eq(2)
\(x = (7-5)\frac{3}{2} \\\\x = 3\)
3) x = 15
sub in eq(1)
\(y = \frac{-2}{3} 15 + 7\\\\y = \frac{-30}{3} +7\\\\y = -10 + 7\\\\y = -3\)
4)
sub in eq(2)
\(x = (7-15)\frac{3}{2} \\\\x = -8\frac{3}{2}\\ \\x = -12\)
What type of triangle has exactly 2 equal sides and one right angle?
isosceles triangle
right isosceles triangle
obtuse isosceles
right triangle
Answer:
Right isosceles triangle
Step-by-step explanation:
I took the quiz and got it wrong, but it told me the correct answer
A right isosceles triangle has exactly 2 equal sides and one right angle.
Given that, a triangle has exactly 2 equal sides and one right angle.
Isosceles triangle: An isosceles triangle is a triangle that has two sides of equal length.
Right isosceles triangle: An isosceles right triangle is defined as a right-angled triangle with an equal base and height which are also known as the legs of the triangle.
Obtuse isosceles: An isosceles obtuse triangle is a triangle in which one of the three angles is obtuse (lies between 90° and 180°), and the other two acute angles are equal in measurement.
Right triangle: A right triangle is a triangle in which one angle is 90°.
Hence, right isosceles triangle has exactly 2 equal sides and one right angle.
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which equation is true
Answer:
A
Step-by-step explanation:
Well, this isn't too hard.
Since the left is the negative side (R) and the right is the positive side (S), a positive and a negative with the same number will equal zero if only one of them are negative.
You ALWAYS subtract when there's two different signs.
a= 5.2 B=70
Work out the area of the triangle. Round your answer to 1 DP
Answer:
8.7
Step-by-step explanation:
Calculate the area of the triangle by using sine.
Area of Triangle
\(A = \frac{1}{2} \times \text{side} \times \text{side} \times \sin{\theta}\)
θ ... included angle between the two sides
We already have two sides a and another side which is congruent to a, making it isosceles triangle. But we don't have the included angle. The angle we need is the vertex angle of the isosceles triangle. Angle B is one of the base angles (two base angles are congruent) and it measures 70°.
Recall that angles in any triangle add up to 180°.
base angle + base angle + vertex angle = 180°
70° + 70° + vertex angle = 180°
vertex angle = 40°
Now we have all the information to use the formula!
\(A = \frac{1}{2} \times \text{side} \times \text{side} \times \sin{\theta}\)
\(A = \frac{1}{2} \times 5.2 \text{ cm} \times 5.2 \text{ cm} \times \sin{40^\circ}\)
\(A = 13.52 \text{ cm}^2 \times \sin{40^\circ}\)
\(A \approx 8.6904 \text{ cm}^2\)
Rounded to 1 DP:
\(A = 8.7 \text{ cm}^2\)
can someone help me with this
Answer:
29
Step-by-step explanation:
Use the box method to distribute and
simplify (-5x - 2) (5x + 4). Drag and
drop the terms to the correct locations of
the table.
( − 5x − 2)(5x+4)
You must answer all questions above
in order to submit.
Create a table with the place values for the first and second factors down the left and the top and bottom, respectively.
What is the box method?
Multiplication using the box method: Create a table with the place values of the first and second factors down the left and the top and bottom, respectively. Second step: multiply the place values and add the results to the table. Step 3: Add up all of the table's rows. Step 4: Add the sums of these rows.
Placing the first word in the first box and the last term in the last box is the first step in utilizing the box technique to factor a trinomial. Multiply the first and last boxes after that. Identify the first and last boxes' products, which together make up the middle word. Put these words in the remaining spaces.
Here's how you can use the box method to distribute and simplify the expression:
( -5x - 2 ) ( 5x + 4 )
⇒-5x -2
⇒5x 4
⇒-25x^2 -10x + 20x - 8
⇒-25x^2 + 10x - 8
So the simplified expression is:
-25x^2 + 10x - 8.
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Which expression is equivalent?
A fruit company delivers its fruit in two types of boxes: large and small. A delivery of
Weight of each type of box:
Weight of each big box = 18.75 kg
Weight of each small box = 13.75 kg
What is an equation?The relationship between two terms on either side of a letter is represented by a mathematical formula. Often there is a variable and an equals sign.
The definition of an equation in algebra is a formula that shows the equivalence of two mathematical terms. For example, in the expression 6x + 11 = 14 the two terms 6x + 11 and 14 are separated by the "equals" symbol.
To let
Weight of each big box = x
And the weight of each small box = y
Weight of 3 big boxes:
3 times
5 small box weights:
5 years
3x + 5y = 125 .......................(i)
resemble:
9x + 7y = 265 ......................(ii)
Equation (i) multiplied by -3:
-3 (3x + 5y) = 125 * (-3)
-9x - 15y = -375 ...................(iii)
Under (ii) and (iii):
9x + 7y = 265
-9x - 15y = -375
Adding this gives:
-8y = -110
or y = 110/8
or y = 55/4
y = 13.75
From equation (i), we have:
3x + 5y = 125
or 3x + 5(13.75) = 125
or 3x + 68.75 = 125
3x = 125 - 68.75
3x = 56.25
x = 56.25/3
x = 18.75
Each large box weighs:
18.75 kilograms
Weight of each small box:
13.75 kilograms
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The Point class represents x,y coordinates in a Cartesian plane. Which line of code appears completes this operator which transforms a Point by dx and dy? (Members written inline for this problem.) class Point { int x_{0}, y_{0};public: Point(int x, int y): x_{x}, y_{y} {} int x() const { return x_; } int y() const { return y_; }};Point operator+(int dx, int dy) { return _________________________;}
The correct line of code that completes this operator which transforms a Point by dx and dy is shown below: Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Note that the function operator+ takes two arguments: an integer dx and an integer dy.
The function returns a point, which is created by adding dx to x and dy to y.The completed code is shown below:class Point { int x_{0}, y_{0};public: Point(int x, int y): x_{x}, y_{y} {} int x() const { return x_; } int y() const { return y_; }};Point operator+(int dx, int dy) { return Point(x_+dx,y_+dy);}Therefore, the correct answer is: `Point(x_+dx,y_+dy)`
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Lilly bought a bottle of apple juice.she drank 1/2 of the apple juice and her sister drank 3/8 of it.
What fraction of the bottle of apple juice did they drink altogether?
There is a greater correlation between the IQ scores of identical twins raised together than for fraternal twins raised together. What conclusion can be drawn from this data
Answer:
This correlation simply means that, in every twin whether identical or fraternal twins, there is a relation between their IQ scores and when they are raised together.
Regarding to the test carried out, it showed that, when an identical twin is raised together, their IQ score tends to be higher in direct comparison with a fraternal twin that was raised together. That is, if the fraternal twin IQ is 100, then, the identical twin IQ is going to be above 100 (probably around 120)
Step-by-step explanation:
Consider the following.
infinity (-1)n
n!
sum.gif
n = 0
=
1/
e
(a) Use the Alternating Series Remainder Theorem to determine the smallest number of terms required to approximate the sum of the convergent series with an error of less than 0.001.
N>= ?
Answer the x mark below
The Alternating Series Remainder Theorem states that the error of an alternating series is less than or equal to the absolute value of the next term. In other words, if we have an alternating series of the form:
∑ (-1)^(n-1) a_n
where a_n is a decreasing sequence of positive numbers, then the error of approximating the sum by the first n terms is less than or equal to the absolute value of the (n+1)th term.
In this case, we have the alternating series:
∑ (-1)^n (n!)^(-1)
where a_n = (n!)^(-1) is a decreasing sequence of positive numbers.
To approximate the sum of this series with an error of less than 0.001, we need to find the smallest value of n such that:
|(n+1)!)^(-1)| < 0.001
Simplifying this inequality, we get:
(n+1)! > 1000
Using Stirling's approximation for factorials, we can estimate that (n+1)! is approximately (n+1)^(n+1/2) * e^(-n-1), so we can rewrite the inequality as:
(n+1)^(n+1/2) * e^(-n-1) > 1000
Taking the natural logarithm of both sides, we get:
(n+1/2) * ln(n+1) - (n+1) > ln(1000)
We can use a numerical method, such as bisection or Newton's method, to solve this inequality for n. Alternatively, we can estimate that n is around 7 or 8, and we can check by hand that n=7 satisfies the inequality:
(8)^(15/2) * e^(-8) ≈ 1312.64 > 1000
while n=6 does not:
(7)^(13/2) * e^(-7) ≈ 857.42 < 1000
Therefore, the smallest number of terms required to approximate the sum of the series with an error of less than 0.001 is:
N = 7.
Answer: N = 7.
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Help PLEASE. This is really hard.. I don't get it
The statements and reasons to prove that line j is parallel to line k include the following:
∠3 and ∠5 are supplementary ⇒ Given.∠3 + ∠5 = 180° ⇒ Definition of supplementary angles.∠3 ≅ ∠4 ⇒ Vertical angles.∠4 + ∠5 = 180° ⇒ Substitution property.line j is parallel to line k ⇒ Corresponding angles converse.What are parallel lines?Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
What is a supplementary angle?A supplementary angle can be defined as two (2) angles or arc whose sum is equal to 180 degrees (180°).
Mathematically, a supplementary angle can be calculated by using this formula:
Q + R = 180
Where:
Q and R are measure of the angles subtended.
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Can someone help me with this question please? Many thanks in advance.
Jack, Alex and Amir jumped a total of 12.69 m in a long
jump competition.
Alex jumped exactly 200 cm further than Jack.
Amir jumped exactly 2,000 mm further than Alex.
What distance did they all jump?
Give your answers in metres.
Answer:
Step-by-step explanation:
The distances they jumped were
x,y,z
y=x+2
z=x+2+2=x+4
x+y+z=12.69
x+x+2+x+4=12.69
3x+6=12.69
3x=6.69
x=2.23
So Jack jumped 2.23m, Alex jumped 4.23m, and Amir jumped 6.23m.