Answer:
2, 10, 50, 250
Step-by-step explanation:
For geometric sequences, multiply the previous term by the common ratio.
Using the formula for geometric sequences [tex]a_{n} =ar^{n-1}[/tex] , with [tex]a_{n}[/tex] being the nth term (so n=4 for the fourth term), a being the first term, and r being the common ratio.
Our starting term is 2. So that is automatically the first term of the four.
Second term:
[tex]a_{2} =2*5^{2-1}=2*5^1=2*5=10[/tex]
Third term:
[tex]a_{3} =2*5^{3-1}=2*5^2=2*25=50[/tex]
Fourth term:
[tex]a_{4} =2*5^{4-1}=2*5^3=2*5*5*5=10*25=250[/tex]
Given the system 2x − 4y = −34 −3x − y = 2
solve for the variables that make up the constant matrix [e f]
For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The value of e and f is -34 and 2 respectively.
What is a system of equations?
Inconsistent System
For a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
For the given system of equations, the value of e will be -34, while the value of f will be 2.
Hence, the value of e and f is -34 and 2 respectively.
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Answer:
he value of e and f is -34 and 2
What is another way to write the absolute value inequality lp|≤12?
O-12≤p≤ 12
O-12≥p≤12
O-12≤por p≤ 12
O-12≥por p≤ 12
Another way to write the absolute value inequality lp|≤12 is -12≤p≤12
Inequality expressionsInequality are expression not separated by an equal sign. Given the inequality expression
lp|≤12
The modulus can be positive or negative
If positive, p ≤12 and if negative -p≤12 or p ≥- 12
Combine both solutions
-12≤p≤12
Hence another way to write the absolute value inequality lp|≤12 is -12≤p≤12
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Solve for x:
(x − 2)(x + 7) = −1+2x
Answer:
(-3±√61)÷2
Step-by-step explanation:
First we expand the brackets to give us :
x²+5x-14 = -1 +2x
Now we make this into the quadratic format (x²+ax+b=0) by subtract -1 and 2x from both sides :
x²+3x-13 = 0
This quadratic cannot be factorized so we must use the quadratic formula :
x = [tex]\frac{-b+\sqrt{b^{2} -4ac} }{2a}[/tex] or x = [tex]\frac{-b-\sqrt{b^{2} -4ac} }{2a}[/tex]
a = 1 , b = 3 , c = -13
Now we simplify as much as possible by first substituting values known :
x = [tex]\frac{-3+\sqrt{3^{2} -4(1)(-13)} }{2(1)}[/tex] or x = [tex]\frac{-3-\sqrt{3^{2} -4(1)(-13)} }{2(1)}[/tex]
Now we evaluate the exponent :
x = [tex]\frac{-3+\sqrt{9 -4(1)(-13)} }{2(1)}[/tex] or x = [tex]\frac{-3-\sqrt{9 -4(1)(-13)} }{2(1)}[/tex]
Now we multiply the numbers :
x = [tex]\frac{-3+\sqrt{9 +52 } }{2(1)}[/tex] or x = [tex]\frac{-3-\sqrt{9 +52 } }{2(1)}[/tex]
Now we add the numbers :
x = [tex]\frac{-3+\sqrt{61} }{2(1)}[/tex] or x = [tex]\frac{-3-\sqrt{61} }{2(1)}[/tex]
Now we multiply the denominator:
x = [tex]\frac{-3+\sqrt{61} }{2}[/tex] or x = [tex]\frac{-3-\sqrt{61} }{2}[/tex]
So our final answer is (-3±√61)÷2
Hope this helped and 5 stars, a heart and brainliest please
Complete the proof to show that ABCD is a parallelogram.
PROOF:
BC ║ AD and CD ║ BA because the ________________________________. Therefore, ABCD is a parallelogram because both pairs of opposite sides are parallel.
OPTIONS:
A) lengths of consecutive sides are not equal
B) slopes of opposite sides are equal
C) lengths of opposite sides are equal
D) slopes of consecutive sides are not equal
IMAGE:
In the proof given, BC║AD and CD║BA because: B. slopes of opposite sides are equal.
What is the Slope of Parallel Lines?If two lines are parallel, they will have the same slope value,.
Slope = rise/run.
Slope of BC = rise/run = -2/5
Slope of AD = -2/5
Slope of BA = rise/run = -6/1 = -6
Slope of BA = rise/run = -6/1 = -6
Therefore, we can conclude that BC║AD and CD║BA because: B. slopes of opposite sides are equal.
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what is the quotient of (x^3+3x^2-4x-12) divided by (x^2+5x+6)
Answer:
x - 2
Step-by-step explanation:
x^3 + 3x^2 - 4x - 12 simplifies to (x + 2)(x - 2)(x + 3)
x^2 + 5x + 6 simplifies to (x + 2)(x + 3)
(x + 2)(x - 2)(x + 3)
(x + 2)(x + 3)
The (x + 2) and (x + 3) cancel
x - 2
Kayden Kohl
9th Grade Student
(Algebra 2)
If two boats sail at a 45° angle to the wind as shown, and the wind is constant, will their paths ever cross? Explain your reasoning. Which of the angle pair did you use and what does the theorem state? wind 45° 45°
please with the explanation
What is the volume of the cone? cone v = one-third b h startfraction 70 over 3 endfraction pi centimeters cubed startfraction 140 over 3 endfraction pi centimeters cubed startfraction 490 over 3 endfraction pi centimeters cubed startfraction 700 over 3 endfraction pi centimeters cubed
Using the assumed values, the volume of the cone is [tex]V = \frac {250}3\pi[/tex]
How to determine the volume of the cone?The volume of a cone is calculated using:
[tex]V = \frac 13\pi r^2h[/tex]
The parameters are not given.
So, we use the following assumed values
Radius, r = 5
Height, h =10
Using the assumed values, we have:
[tex]V = \frac 13\pi * 5^2 * 10[/tex]
Evaluate the product
[tex]V = \frac {250}3\pi[/tex]
Hence, using the assumed values, the volume of the cone is [tex]V = \frac {250}3\pi[/tex]
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Answer: C (490/3
Step-by-step explanation:
Write a polyomial equation of degree 4 that has the following roots: -1 repeated three times and 4.
The polynomial equation is P(x) = (x + 1)(x + 1)(x + 1)(x - 4)
How to determine the polynomial?The given parameters are:
Degree = 4Roots = -1 (three times) and 4A polynomial equation is represented as:
P(x) = (x- Root)
So, we have:
P(x) = (x - (-1))(x - (-1))(x - (-1))(x - 4)
Open the inner brackets
P(x) = (x + 1)(x + 1)(x + 1)(x - 4)
Hence, the polynomial equation is P(x) = (x + 1)(x + 1)(x + 1)(x - 4)
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Is the number 351 a
composite number?
A picture measures x cm by (x + 4) cm. It is enlarged by a scale factor of 3 to form a poster. The area of the enlarged poster is 1053 cm².
(i) Pauline made a wild guess, without making any prior calculation, that the value of x is 31. Without finding the actual value of x, verify whether her claim is correct.
(ii) Form an expression in terms of x and show that it reduces to x² + 4x - 117 = 0.
(iii) Calculate the perimeter of the original picture before the enlargement.
pls help me I need it by 25mins
Answer:
i) Her claim is incorrect
ii) see below
iii) 44 cm
Step-by-step explanation:
Given:
width of picture = x cmlength of picture = (x + 4) cmIf the picture is enlarged by a scale factor of 3 to form a poster, then the dimensions of the poster will be:
width of poster = 3x cmlength of poster = 3(x + 4) cmArea of rectangle = width × length
⇒ Area of poster = (3x) × 3(x + 4)
= 9x(x + 4)
= 9x² + 36x cm²
Part (i)Inputting x = 31 into the area of poster formula found above:
⇒ 9(31)² + 36(31)
= 8649 + 1116
= 9765 cm²
Therefore, as 9765 ≠ 1053 her claim in incorrect.
Part (ii)Using the formula for the area of poster found in part (i).
Area of poster = 1053 cm²
⇒ 9x² + 36x = 1053
⇒ 9x² + 36x - 1053 = 0
⇒ 9(x² + 4x - 117) = 0
⇒ x² + 4x - 117 = 0
Part (iii)First find x by solving the equation from part (ii):
⇒ x² + 4x - 117 = 0
⇒ x² + 13x - 9x - 117 = 0
⇒ x(x + 13) - 9(x + 13) = 0
⇒ (x - 9)(x + 13) = 0
⇒ x = 9, x = -13
As width cannot be negative, x = 9 only
Perimeter of picture = 2(width + length)
= 2(x + x + 4)
= 2(2x + 4)
= 4x + 8
Input found value of x into the expression for the perimeter:
⇒ Perimeter of picture = 4(9) + 8
= 36 + 8
= 44 cm
Review the graph of f(x). What is the function’s behavior close to the vertical asymptote x = 2? Limit of f (x) as x approaches 2 minus = infinity and limit of f (x) as x approaches 2 plus = infinity Limit of f (x) as x approaches 2 minus = infinity and limit of f (x) as x approaches 2 plus = negative infinity Limit of f (x) as x approaches 2 minus = negative infinity and limit of f (x) as x approaches 2 plus = infinity
The function's behavior at vertical asymptote x = 2 is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]
How to determine the function's behavior?The attached graph represents the missing information in the question.
From the attached graph, we have the following highlights:
At x = 2, a curve points upwardAt x = -2, another curve points downwardThis means that the limit of f(x) approaches negative infinity and positive infinity at this value of x
Hence, the function's behavior is (b) [tex]\mathbf{ \lim_{x \to 2^-} f(x) = \infty\ and \ \lim_{x \to 2^+} f(x) = -\infty}[/tex]
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The Perimeter of the triangle is 141cm work out value of p
By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.
How to determine the lengths of the side of a triangle
The three sides of a triangle are consecutive if and only if they are represented by three consecutive natural numbers. The perimeter is the sum of the three side lengths, whose formula is presented below:
x + (x + 1) + (x + 2) = 141
3 · x + 3 = 141
3 · (x + 1) = 141
x + 1 = 47
x = 46
By definition of perimeter and consecutive side, we conclude that the side lengths of the triangle with perimeter of 141 centimeters are 46, 47 and 48 centimeters.
Remark
The statement is complete, the correct statement is the following:
The triangle has three consecutive sides and its perimeter is 141 centimeters. Work out the value of each side.
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Each year, the Green Valley School spring carnival features the Jelly Bean Guessing Game. To set up for the game this year, the principal used 6 small boxes of jelly beans to fill a large glass jar. Each box had the same number of jelly beans, for a total of 324 jelly beans.
Let j represent the number of jelly beans in each box. Which equation models the problem?
If j represent the number of jelly beans in each box, then the equation that models the problem is; 6j = 324
How to model an equation?
We are told that the principal used 6 small boxes of jelly beans to fill a large glass jar.
Now, each box had the same number of jelly beans, for a total of 324 jelly beans.
If j represent the number of jelly beans in each box, then the equation that models the problem is; 6j = 324
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What is cos B?
A. 8/15
B. 15/8
C. 8/17
D. 15/17
Answer:
C. 8/17
Step-by-step explanation:
Given:
Hypotenuse = 17
BC = 8
Cos (B) = leg adjacent to ∠B / hypotenuse
= BC/BA
Substitute
Cos (B) = 8/17
Hence option C is correct
Each statement describes a transformation of the graph of y=x. which statement correctly describes the graph of y=x-9?
A. It is the graph of y+x translated down 9 units.
B. It is the graph of y+x, where the slope is decreased by 9
C. It is the graph of y+x translated to the left 9 units.
D. It is the graph of y+x translated up 9 units.
After six weeks of the coupon offer, the owner of the restaurant needs to decide if the restaurant should continue to run the same special or offer a new one. Use the provided scatter plot to write an equation for the line of best fit.
The equation of the line of the best fit on the scatter plot is y = 150x + 598
How to determine the equation of the line of best fit?From the line in the scatter plot, we have the following points
(x,y) = (3,1048) and (6,1498)
The equation is then calculated using:
[tex]y = \frac{y_2 -y_1}{x_2 -x_1} *(x - x_1) + y_2[/tex]
The equation becomes
[tex]y = \frac{1498 -1048}{6 - 3} *(x - 3) + 1048[/tex]
Evaluate
y = 150 *(x - 3) + 1048
Expand the bracket
y = 150x - 450 + 1048
Evaluate the sum
y = 150x + 598
Hence, the equation of the line of the best fit is y = 150x + 598
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3(x-2y)=5(x-3y)+9 write in slope intercept form help!
Answer:
y = (2x/9) + 1
Step-by-step explanation:
Solving for y we get 3(-2y+x) = 5(-3y+x)+9
Expand the above we get -6y+3x=5(-3y+x)+9
which is -6y+3x = -15y+5x+9
then 9y = 2x+9
which y = (2x/9) + 1
Question 25 of 25
Over what interval is the function in this graph increasing?
AV
M
<-10
10
A. 6≤x≤ 10
B. -4≤x≤1
C. -10≤x≤-4
D. 1≤x≤6
The correct option is option B : -4 ≤ x ≤ 1
What is Increasing and decreasing function?
Increasing and decreasing functions are functions whose graphs go upwards and downwards respectively as we move towards the right-hand side of the x-axis. Increasing and decreasing functions are also called non-decreasing and non-increasing functions.
Here, from graph
as we can observe from x = -4 graph starts increases upto x = 1 and after that graph becomes constant.
Thus, between x belongs -4 to 1 the graph is increasing.
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help me please I will give you brainliest
Answer:
-17, -10, -6, -5, 3, 8 only change is between 3 and 8
A 6-sided die is rolled.
Let A = rolling a 1
Let B = rolling an even number
Identify the probability of the following events.
*Write your answer as a fraction*
Answer:
Step-by-step explanation:
P(A∪B) = 1/6 + 1/2 = 2/3
help help help
help help help meeee help me help me
• function notation•
these are so confusing
Answer:
15
Step-by-step explanation:
Just substitute the x for 5
In this case:
Original function: f(x) = [tex]x^{2}[/tex] - 2x
Substitute function: f(5) = [tex](5)^{2}[/tex] - 2(5)
Now solve for the substitute function
[tex](5)^{2}[/tex] - 2(5)
25 - 10
15
Therefore, f(5) is equal to 15
A box contains 4 black shirts, 8 blue shirts, 4 black pants, and 10 blue pants. Determine the probability of randomly selecting a blue piece of clothing or a pair of pants. Use to explain your answer
I just need the explanation.
============================================================
Explanation:
Add up the four numbers given: 4+8+4+10 = 26 items total
Kick out the 4 black shirts since they are neither blue, nor are they pants.
So we have 26-4 = 22 items that are blue or a pair of pants (or both).
Divide that over the total (26) to get the probability we're after:
22/26 = (11*2)/(13*2) = 11/13
Side note: 11/13 = 0.8462 = 84.62% approximately
A boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water. Luis measures an angle of depression to the boat at point A to be 10 degrees. At some later time, Luis takes another measurement and finds the angle of depression to the boat (now at point B) to be 39 degrees. Find the distance from point A to point B. Round your answer to the nearest foot if necessary.
The distance between point A to point B is 115.91 ft if the boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water.
What is trigonometry?Trigonometry is a branch of mathematics that deals with the relationship between sides and angles of a right-angle triangle.
We have:
A boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water. Luis measures an angle of depression to the boat at point A to be 10 degrees.
From the above information, we can draw a right-angle triangle.
Let's suppose the distance between point A and point B is x
In right-angle triangle, BCD
tan31 = DC/BC = 107/BC
BC = 107/tan31
BC = 178.07 ft
In right-angle triangle, ACD
tan20 = DC/AC
tan20 = 107/(x + BC)
Plug the value of BC
tan20 = 107/(x+178.07)
x + 178.07 = 293.980
x = 115.91 ft
Thus, the distance between point A to point B is 115.91 ft if the boat is heading towards a lighthouse, where Luis is watching from a vertical distance of 107 feet above the water.
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The blue dot is at what value on the number line?
Answer:
20
Step-by-step explanation:
To find the value at the blue dot, you must identify the scale of the markings of the number line.
__
what is the scale12 is 2 marks to the right of 8, so we know 2 marks has a value of 12-8 = 4.
using the scaleThat means the second mark to the right of 12 will be 12+4 = 16.
The second mark to the right of that is 16+4 = 20, which is where the blue dot is.
The value at the blue dot is 20.
A neighborhood is trying to set up school carpools, but they need to determine the number of students that need to travel to the elementary school (ages 5–10), the middle school (ages 11–13), and the high school (ages 14–18). A histogram summarizes their findings:
Answer:The data set that is represented in the histogram is {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} Definition of a histogram An histogram is a graph that organises numerical data. The histogram is made up of rectangles whose area is equal to the frequency of the data and whose width is equal to the class interval. the frequency is usually on the vertical axis while the class interval is usually on the horizontal axis.Explaining the graphLooking at the histogram, the age group of 5 - 10 have 3 children in the carpool. the age group of 11 - 13 have 7 children in the carpool. the age group of 14 - 18 have 4 children in the carpool. This means that there are 14 children in the carpool. The correct option should have 14 ages that range between 5 and 18. Here are the options of this question: A. {3, 3, 3, 7, 7, 7, 7, 7, 7, 7, 4, 4, 4, 4} B. {5, 10, 4, 11, 12, 13, 12, 13, 12, 11, 14, 14, 19, 18} C. {5, 6, 5, 11, 12, 13, 12, 13, 14, 15, 11, 18, 17, 13} D. {3, 5, 10, 11, 13, 7, 18, 14, 4}
Step-by-step explanation:
The Saxena family plans to install a light to illuminate part of their rectangular yard. Nikki and Dylan each proposed a different spot to place the light. The proposed placements and the lit area that each produces are shown below.
Nikki's proposed placemat has a triangular light area with a base of 60 feet and height of 38 feet. Dylan's proposed placemat has a base of 60 feet and a height of 38 feet.
How do Nikki’s and Dylan’s proposals compare? Check all that apply.
Nikki’s proposed placement will light a greater area than Dylan’s placement.
Dylan’s proposed placement will light a greater area than Nikki’s placement.
Both proposed placements will light the same sized area.
Nikki’s proposed placement will light more than half the yard.
Dylan’s proposed placement will light more than half the yard.
Dylan’s proposed placement will light exactly half of the yard.
Nikki’s proposed placement will light less than half of the yard.
The correct situation for the given condition are as follows:
C) Both proposed placements will light the same sized area.
F) Dylan's proposed placement will light exactly half of the yard.
What is Area of Triangle?
The area of a triangle is defined as the total space occupied by the three sides of a triangle in a 2-dimensional plane. The basic formula for the area of a triangle is equal to half the product of its base and height, i.e., A = 1/2 × b × h.
The area of a triangle = (base x height) / 2
and,
both lights illuminate the same base and height = (60 x 38) / 2
= 1,140 sq ft
Both Dylan's and Nikki's proposed placement will lit exactly half of the yard.
The yard's total area = 60 x 38 = 2,280 sq ft,
which is twice the area lit by the lights.
Thus, The correct situation for the given condition are as follows:
C) Both proposed placements will light the same sized area.
F) Dylan's proposed placement will light exactly half of the yard.
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PLEASE HELP DOINF THIS RIGHT NOW AND DONT HAVE MUCH TIME!!
Which of the following measures would give you an infinite number of possible triangles?
26°,42°, and 106°
34°,63°, and 79°
62°,34, and 80°
Three angles: 43°,62°, and 75°
Answer: number 4 (43º, 62º, 75º)
Step-by-step explanation:
26 + 42 + 106 ≠ 180 so number 1 is not a triangle.
34 + 63 + 79 ≠ 180 so number 2 is not a triangle.
62 + 34 +80 ≠ 180 so number 3 is not a triangle.
43 + 62 + 75 = 180 so number 4 is a triangle.
Because only the angles are given and not the sides, there is an infinite number of triangles. The answer is number 4 (43º, 62º, 75º).
What should your units on your base area calculations be, and why? How is this different from the units on your volume calculations? Explain in two to three sentences.
The units on a base area calculations is known to be cm² or m² while units on your volume calculations is known to be m³ or cm³.
Why use the unit about?The unit above is used because in base area calculation, only 2 sides are calculated while in volume calculation, 3 sides are involved.
Note that in base area, square unit is often used in its calculations via the use of two dimensions length and breadth (cm² or m² ).
In terms of volume, cubic unit is used in its calculations through the use of three dimensions length, breadth and height ( m³ or cm³.).
Note also that Area is seen as the space taken by a two dimensional flat object while volume is seen as the space taken by the three-dimensional object and as such The units on a base area calculations is known to be cm² or m² while units on your volume calculations is known to be m³ or cm³.
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Select all the conditions for which it is possible to construct a triangle.
The conditions for which it is possible to construct a triangle include:
A triangle with angles measures 60 ∘ , 80 ∘ , and 80 ∘ A triangle with side lengths of 4 cm, 5 cm, and 6 cm A triangle with side lengths 4 cm and 5 cm and a 50 ∘ angle.What is a Triangle?
This is defined as a three-sided polygon which has three edges and three vertices and a total internal angles of 180 degrees.
The triangle with side lengths 4 cm, 5 cm, and 15 cm can't be constructed due to the length of sides not being equal according to pythagoras theorem.
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