It is a geometric sequence since it has a common ratio. The next two terms are -80, 160
Let a sequence be:
a(1), a(2), a(3), a(4), a(5), ...
To determine whether the sequence is an arithmetic sequence, or a geometric sequence, or neither, we need to check how its consecutive terms relate to each other.
They have a common difference.The given sequence is:
-5,10,-20,40, . . .
Let us check whether they have a common difference:a(2) - a(1) = 10 - (-5) = 15
a(4) - a(3) = 40 - (-20) = 60
So they don't have a common difference.
Let us check whether they have a common ratioa(4)/a(3) = 40/(-20) = -2
a(3)/a(2) = -20/(10) = -2
a(2)/a(1) = 10/(-5) = -2
So they have a common ratio, i.e. r = -2.
Therefore, we can conclude that -5,10,-20,40, . . is a geometric sequence.
In a geometric sequence, the next term is equal to the previous term times the ratio.
We already have: -5,10,-20,40, ...
Hence:
Next term after 40 = 40 . (-2) = -80
Next term after -80 = -80 . (-2) = 160
Thus, the next two terms are -80, 160
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Solve the equation. 125x³+216=0 .
Write an equation of each line in standard form with integer coefficients.
2y = -4x-12
The equation of the line in standard form of 2y = -4x - 12 is 4x + 2y = -12.
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant.
Given the equation 2y = -4x - 12, to write the equation in standard form, arrange the variable(s) in one side and the constant(s) in the other.
2y = -4x - 12
4x + 2y = -12
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What is y-8={3}(x+1)y−8=3(x+1)y, minus, 8, equals, 3, left parenthesis, x, plus, 1, right parenthesis written in standard form?
The equation written in standard form is expressed as 3x - y = -11
Linear equation in standard formThe standard form of a linear equation is expressed as Ax + By = C
Given the equation below;
y - 8 = 3(x+1)
Expand
y- 8 = 3x + 3
Collect the like terms
y-3x = 3 + 8
y - 3x = 11
-3x + y = 11
3x - y = -11
Hence the equation written in standard form is expressed as 3x - y = -11
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Solve the equation:
-y= 22
Answer: y = -22
Step-by-step explanation:
a variable can't be negative, and there is always a 1 by a variable, so divide each side by -1
Answer:
-22
Step-by-step explanation:
-y=22
-y/-1 = 22/-1
y= -22
The point B(-1,-5) is rotated 90° counterclockwise around the origin. What are the coordinates of the resulting point, B'?
Answer:
B(5, -1)
Step-by-step explanation:
"When rotating a point 90 degrees counterclockwise about the origin our point A(x,y) becomes A'(-y,x). In other words, switch x and y and make y negative." - https://calcworkshop.com/
B(-1, -5), -1 = x, -5=y
B(y, x) = B(-5, -1)
B(-y, x) = B(5, -1)
B(5, -1)
Charlie needs to buy plastic spoons. Brand A has a box of 72 spoons for $3.89. Brand B has a box of 96 spoons for $6.62.
Find the unit price for each brand. Then state which brand is the better buy based on the unit price.
Round your answers to the nearest cent.
Brand A is better buy than that of Brand B as unit price of Brand A is 0.054 which is less than that of Brand B's unit price $0.069
What is fraction?Fractions represent portions of a whole or set of objects. A fraction is divided into two pieces. The numerator is the number at the top of the line. It indicates how many equal chunks of the total or collection are taken. The denominator is the number below the line. It indicates the total number of equal pieces into which the whole is divided or the total number of the same objects in a collection.
If 72 spoons is 3.89
Then 1 spoons is 3.89/72
= 0.054
If 96 spoons is $6.62
Then 1 spoons is 6.62/96
=0.069
Thus, Brand A is better buy than that of Brand B as unit price of Brand A is 0.054 which is less than that of Brand B's unit price $0.069
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Create Write a real-world situation to explain the
inequality-$15 < $7.
Answer: Maggie went to the store and bought 3 cartons of organic eggs for $23, and a bag of flour for $7. She had $15 dollars in her bank account. But the checkout total was $30. So the bank charged her credit card of her $15 dollars. Now she has a -$15 dollar fine that needs to be paid to her card.
Step-by-step explanation:
Maggie went to the store and bought 3 cartons of organic eggs for $23, and a bag of flour for $7. She had $15 dollars in her bank account. But the checkout total was $30. So the bank charged her credit card of her $15 dollars. Now she has a -$15 dollar fine that needs to be paid to her card.
Simplify.
8√2 / 6-3√8
The rationalized expression in general term is given by: (-8 -4√2) / 3
What is rationalization?Rationalization is a mathematical operation that allows us to determine or eliminate a root of the denominator of a fraction, so that it can be expressed in linear form, either decimal or integer, by the product of a root.
As defined above, we must perform a mathematical operation to eliminate the root of the denominator without altering the value.
(8√2 / 6-3√8 ) Multiply by ( 6+3√8)/( 6+3√8)
(8√2 / 6-3√8 )( 6+3√8)/( 6+3√8)
8√2(6+3√8) / (6-3√8)² Expand the denominator using the FOIL method.
8√2(6+3√8) / (36 - 18√8 + 18√8 - 72)
8√2(6+3√8) / -36
48√2 + 24√2√8 / -36 ::::. √8 = 2√2
48√2 + 96 / -36
-12(4√2 + 8) / 12x3
(-8 -4√2) / 3 is the result.
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Simplify 4x√3x-x√3x-2x√3x
x√3x
x√9x
2x√6x
2x√6x³
Answer:
Simplify 4x√3x-x√3x-2x√3x
x√3x
x√9x
2x√6x
2x√6x³
A triangle is dilated with the center of dilation at point U. Point E is a vertex of the triangle and point E ’ is the corresponding vertex of the image. If UE = 2 centimeters and UE ’ = 10 centimeters, what is the scale factor?
A triangle is dilated with the center of dilation at point U. Point E is a vertex of the triangle and point E ’ is the corresponding vertex of the image. If UE = 2 centimeters and UE ’ = 10 centimeters, the scale factor is 5 cm
Scale Factor Definition
A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object. If the scale factor is a whole number, the copy will be larger. If the scale factor is a fraction, the copy will be smaller.
By definition, a Dilation is a transformation in which the image has the same shape as the pre-image but size changes.
The center of dilation is a fixed point in the plane, and the scale factor is the ratio of the corresponding sides of the image to the pre-image.
Scale Factor In Geometry
Scale is used in geometry to make accurate reproductions of figures; they are different sizes, but same proportions. Figures are similar but to scale.
Based on the information provided in the exercise, you know that:
UE = 2 centimeters
UE ’ = 10 centimeters
Therefore, you can determine that the scale factor is:
The scale factor for scaling up is a ratio greater than 1
The scale factor for scaling down is a ratio of less than 1
.
Scale factor : 10/2 = 5
Scale factor = 5 cm
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The center of dilation for a triangle is located at point U. The image's point E' corresponds to point E, which is the vertex of the triangle. The scale factor is 5 cm if UE = 2 centimeters and UE'= 10 centimeters.
Define Scale Factor
The ratio between comparable measurements of an object and a representation of that object is known as a scale factor in mathematics. The copy will be larger if the scaling factor is a whole number. A fractional scaling factor means that the duplicate will be smaller.
A dilation is, by definition, a transformation in which the size of the image changes but the shape remains the same as the pre-image.
The scale factor is the ratio of the corresponding sides of the image to the pre-image, and the center of dilatation is a fixed point in the plane.
Considering Scale in Geometry
In geometry, scale is utilized to create correct figures that have varying sizes but the same proportions. Similar but scaled figures are shown.
You are aware of the following thanks to the material in the exercise:
2 centimeters equals UE.
10 centimeters equals UE'.
Therefore, you can determine that the scale factor is:
The scale factor for scaling up is a ratio greater than 1
The scale factor for scaling down is a ratio of less than 1
Scale factor : 10/2 = 5
Scale factor = 5 cm
WRITING IN MATH Explain why a triangle cannot have an obtuse, acute, and a right exterior angle.
A triangle cannot be both right-angled and obtuse-angled. Because a right-angled triangle has only one right angle, its other two are acute.
Triangle property defined as:The sum of all triangle angles (of all types) equals 180°. The total of the lengths of a triangle's two sides is higher than the length of something like the third side. Similarly, the length of something like the third side is less than the differences between two sides of a triangle.
What are the various types of triangles?Triangles are categorized in two ways: thus according to internal angles and based on the side length. There are three sorts of triangles based on internal angles: acute, right, and obtuse-angled triangles. Triangles are categorized into three types based on the length of its sides: Scalene, Isosceles, and Equilateral triangles.
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Write an equation of each line.slope =-1 ; through (-3,5)
The equation of the line in point-slope form, with slope equal to -1 and passing through the point located at (-3 , 5), is (y - 5) = -1(x + 3).
The equation of a line can be expressed in three different forms: standard form, slope-intercept form, and point-slope form.
The standard form of an equation of a line is expressed as ax + by = c, where a and b, if all possible must be integers, are the coefficients of variable x and y, respectively, and c is a constant. Meanwhile, slope-intercept form is given by the formula y = mx + b, where m is the slope of the line and b is the y- intercept. On the other hand, given the slope m and a point on the line (x , y), we can express the equation in point-slope form, (y - y1) = m(x - x1).
Using the point slope form, plug in the values to set up the equation.
(y - y1) = m(x - x1)
where m = -1 and (x1 , y1) = (-3 , 5)
(y - 5) = -1(x - -3)
(y - 5) = -1(x + 3)
In slope-intercept form, the equation of the line is:
(y - 5) = -1(x + 3)
y - 5 = -x -3
y = -x + 2
In standard form, the equation of the line is:
y = -x + 2
x + y = 2
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Which statement correctly describes the inverse of the following function?
12345
A. It is a horizontal shift.
B. It is not a function.
C. It is a function.
D. It is negative.
2
3
4
5
6
7
It is not a function. which is the correct answer would be option (B)
Given that,
A function is shown in the figure with its domain and range.
To determine the inverse function.
What is the function?The function is defined as a mathematical expression that defines a relationship between one variable and another variable.
Since the two preimages of the value 5 are present in the domain
So that is why the inverse function of a given function is not possible.
Therefore, It is not a function.
Hence, the correct answer would be option (B)
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Write the following
numbers in descending
order.
0.741, 0.7041, 0.7412,
0.70411, 0.744
Answer:
0.744-0.741-0.7412-0.7041-0.70411
Step-by-step explanation:
Answer:
0.7440.74120.7410.704110.7041Step-by-step explanation:
Decending order- From greatest to least
To order them start with the dight with the highest number in the place that isn't equal. In this case it the 4 in the hundredths place so are top 3 numbers are 0.741, 0.7412, and 0.744. As this point you continue to look at the greatest number when the dights aren't equal so the top three would be ordered 0.744,0.7412
0.744,0.7412, and 0.741. As for the bottom 2 numbers you do the same thing with the top three numbers so the rest of the list is 0.70411 and 0.7041
expand the expression as a product of factors.
(x+y)^5
Answer: 7+8y
Step-by-step explanation:
A box contains 7 blue marbles, 6 red marbles, 2 white marbles, and 3 black marbles. If one marble is chosen at random, what is the probability that it will be red?
A. 0.11
B. 0.17
C. 0.33
D. 0.39
E. 0.67
The probability that the chosen marble will be red is, 0.27.
Probability:
Probability is calculated by using the formula,
P(A) = n(A)/n(S)
Where,
P(A) is the probability of an event “A”
n(A) is the number of favorable outcomes.
n(S) is the total number of events in the sample space.
Given,
A box contains 7 blue marbles, 6 red marbles, 2 white marbles, and 3 black marbles.
Here we need to find If one marble is chosen at random, then what is the probability that it will be red.
According to the formula,
number of favorable outcomes = 6
total number of events in the sample space = 7 + 6 + 2 + 3 = 22.
Then the probability of getting red marbles is,
=> P(A) = 6/22.
It can be simplified as,
=> P(A) = 3/11
=> P(A) = 0.27
Therefore, the probability of getting red marble is 0.27.
Here in the options, the option 0.27 is not present.
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Find the first five terms of each sequence. a n =-2 n+3
The formula for estimating the nth term of an arithmetic sequence is:
a n = a₁ + (n-1)d
The first five terms of a n = -2n + 3 = 1, -1, -3, -5, -7
What is meant by arithmetic sequence?A succession of numbers merged together to make a sequence exists comprehended as an arithmetic sequence.
A series of numbers named an arithmetic progression or arithmetic sequence (AP) contains a constant difference between the terms.
The formula for estimating the nth term of an arithmetic sequence exists:
a n = a₁ + (n-1)d
The four quantities in the formula exist a n, a₁, n, d.
The first 5 terms are a n = -2n + 3
a₁ = -2 + 3 = 1
a2 = -4 + 3 = -1
a3 = -6 + 3 = -3
a4 = -8 + 3 = -5
a5 = -10+3 = -7
Therefore, the first 5 terms of the sequence be 1, -1, -3, -5, -7.
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An aeroplane flies 500km in one hour. How long does it take to f a distance of 10925km? for class 4
Answer:
It will take 22 hours
Step-by-step explanation:
10925 ÷ 500 = 21.9 = 22 hours
Three classes have a total of 66 students. The students need to make teams of 7 for a Math competition. How many complete teams can they make?
10 teams
8 teams
3 teams
9 teams
Write an equation of the line through each pair of points in slope-intercept form.
b. (-1,3) and (7,3)
The equation of line is y = 3
Given the points:
(x₁, y₁) = (-1, 3)
(x₂, y₂) = (7, 3)
The slope-intercept form:
y = mx + b
Where m is the slope and b is the y-intercept.
The formula for slope is,
m = (y₂ – y₁) / (x₂ – x₁)
We have given,
x₁ = -1
x₂ = 7
y₁ = 3
y₂ = 3
So,
m = (3 – 3) / ( 7-(-1)) = 0/8 = 0
Slope intercept form,
y = mx + b
Considering y as 3, then
3 = 0(x) + b
3 = 0 + b
b = 3
Therefore, the equation of line is
y = 3
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Six years ago, Lucia’s age was 1/3 the age she will be in 6 years. How old is Lucia now? Enter an integer.
Answer:
Lucia is 12 years old now
In this problem, you will investigate the relationships among three points of concurrency in a triangle.
d. Make a conjecture about the relationships among the circumcenter, centroid, and orthocenter.
The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. The circumcenter, centroid, and orthocenter are all collinear.
What is the relationship between the centroid circumcenter and orthocenter?The circumcenter, centroid, and orthocenter are all collinear.
The centroid separates the line connecting the circumcenter and orthocenter in the proportion of 2 :1
i.e, CSOC = 21.
Where, C-Coordinate of the centroid. O-Coordinate of the orthocenter.
The orthocenter is the point at which three altitudes drawn from the vertices of a triangle to opposite sides intersect. A centroid is the point at which the lines drawn from the midpoints of each side of a triangle intersect at the opposite vertex.
Any triangle's orthocenter, centroid, and circumcenter are collinear. The centroid divides the distance between the orthocenter and the circumcenter in a 2:1 ratio. The line connecting these three points is known as the triangle's Euler line. to represent the ABC triangle's circumcircle.
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5. An empty shipping box weighs 8 ounces. The box is then filled with T-shirts. Each T-shirt
weighs 6 ounces. The equation W= 8 + 6x represents the relationship between the quantities
in this situation, where W is the weight, in grams, of the filled box and x represents the number
of shirts in the box. Name two possible equations
Answer:
Step-by-step explanation:
W-8=6x
W-6x=8
Write an equation of the line through each pair of points in slope-intercept form.
(2,4) and (-4,-11)
The equation of line is:
y = (5/2) x - 11
Given,
Points (x₁, y₁) = (2, 4) and (x₂, y₂) = (-4, -11)
We can find the slope using the equation for slope
m = (y₂ - y₁) / (x₂ - x₁)
= (-11 -4) / (-4 -2)
= -15 / - 6
= 5/2
We know the slope and a point, so we can use point slope form to make an equation
y-y₁ = m(x-x₁)
y - (-4) = 5/2 (x-2)
Distribute
y+4 = 5/2x – 5/2 x 2
y+4 = 5/2x - 5
Add -4 to each side
y +4 -4 = 5/2x – 5 - 4
y = 5/2x - 11
This is in slope intercept form (y= mx-b)
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The morning temp in Atlanta, Georgia is
-11 °C. During the day, it warms up 16°C.
What is the new temperature?
1/3 divided by 7/9 solution
Answer:
3/7.
Step-by-step explanation:
1/3 / 7/9
Invert the 7/9 and multipliply:
= 1/3 * 9/7
= 9 / 21
= 3/7
What is the arithmetic mean between 20 and 56?
Answer:
35, the population size is 2.
Can someone please help me out? I don’t really understand the problem.
Answer:
ok
Step-by-step explanation:
-2x+9=2
dive answer is 3
Answer:
x = 6 and y = 10
Step-by-step explanation:
Substract (-5x+3y=0) from (7x-4y=2)
[tex] \sf \: - 5x + 3y = 0 \\ \sf \: \: \: \: 7x - 4y = 2 \\ = = = = = = = = \\ \sf2x - 1y = 2 \\ = = = = = = = = =[/tex]
Let's solve your system by elimination.
7x−4y=2;2x−1y=2
Multiply the second equation by -4, then add the equations together.
(7x−4y=2)
−4(2x−1y=2)
Becomes:
7x−4y=2
−8x+4y=−8
Add these equations to eliminate y:
−x=−6
Then solve−x=−6for x:
−x=−6
−x/−1 = −6/−1
(Divide both sides by -1)
x=6
Now that we've found x let's plug it back in to solve for y.
Write down an original equation:
7x−4y=2
Substitute6forxin7x−4y=2:
(7)(6)−4y=2
−4y+42=2(Simplify both sides of the equation)
−4y+42+−42=2+−42(Add -42 to both sides)
−4y=−40
−4y/−4 = −40/−4
(Divide both sides by -4)
y=10
i need help please n thanks
How do I do these ?
I have to match the questions to answers.
If my explanation seems confusing please refer to the images
Answer:
x= 82⁰The measure of angle RST = 88⁰x= 12⁰x = 10⁰x = 51⁰x = 128⁰x= 10⁰x = 5⁰The measure of angle JGH = 57⁰ The measure of angle GEF = 33⁰Step-by-step explanation:
To answer question one you first make a equation for the angle we know that x+63=145. Then do the inverse of addition which would be subtraction so x+ 63- 63 = 145 -63which is x=82⁰Since angle RSU and UST equal to angle RST you would combine both values 41 and 47 together (41+47) and you will get the measure of RST which is 88⁰To answer question 3, 4, 5 and 6 (question 3 is the demonstration) Create an equation with the given numbers: We know that m< JKL is 131 and that is the combination of m< JKN (48⁰) and m< NKL (7x -1)⁰ that is 7x-1 + 48 = 131Combine like terms (if any): the only like terms in the equation are -1 and 48 so the new equation is 7x+47=131 Do the inverse operations: For instance the first operations you would do is subtracting 47 on both sides (the point is to islolate x) 7x + 47- 47 = 131 - 47 now the new equation is 7x=84. Divide 7 on both sides the final answer is x=124. To answer questions 4,5 and 6 you would apply the same steps for question 3. Your final answer for question 4 is x = 10.
5. The only difference for question 5 is that the measure of the angles combine is not explicitly given and it is a right angle (from the square in the corner) which means the total is 90⁰ and the final answer is for question 5 is 51⁰
6. For question 6 you need to know that the total is 180⁰. The final answer is 128⁰
7. Steps to solve questions 7,8,9 and 10 (question 7 is the demonstration) :
Combine like terms: The terms 6x and 5x (in 6x+5x+2=112) are like terms so you add them together. the new equation is 11x +2 = 112 Do the inverse operations: Subtract 2 from both sides 11x+2-2= 112-2 which is 11x = 110. Divide 11 from both sides the final answer is x = 108. Apply the same step for question 7: the final answer is x = 5
9. Apply the same steps for step 7 however you substitute x in m < JGH which is 4x + 1 which is 57⁰
10. Apply the same steps for step 7 however you substitute x in m < GEF (11x) which is 33⁰
