Answer: Yes
Step-by-step explanation:
3/4 of 42 is (3/4)(42)=31.5, and 41 is greater than 31.5.
NEED THE ANSWER THANK YA
Answer:
A collection of different things
Step-by-step explanation:
I looked up the definition
Match each expression to the correct point
Answer:
Step-by-step explanation:
f = -3/2
d = -[tex]\pi[/tex]
e = - [tex]\sqrt{8}[/tex]
Answer:
56892 that's it hope it helps
Where did the formula for summing finite geometric series come from? Suppose the geometric series has first term a₁ and constant ratio r , so that S n= a₁ + a₁r+ a₁ r²+ . . +a₁ rⁿ⁻¹
a. Show that r S n = a₁r+ a₁ r²+ a₁ r³+ . . . . +a₁rⁿ .
The total of a geometric series is an unlimited number of terms with a fixed ratio between them.
If S n= a₁ + a₁r+ a₁ r²+ . . +a₁ rⁿ⁻¹ then rSn = a₁r + a₁ r²+ . . +a₁ rⁿ⁻¹+a₁ rⁿ.
What is the formula for geometric series?
The sum of a geometric series Sn is given by:
[tex]$S_n=a(\frac{1-r^{n} }{1-r} )[/tex]
Given:
Sum of first n terms of the Geometric progression be
Sn = a₁ + a₁r + a₁ r² + . . + a₁ rⁿ⁻¹ ---(1)
On multiplying by r on both sides,
r Sn = a₁r + a₁ r² + . . + a₁ rⁿ⁻¹ + a₁ rⁿ ----(2)
So, (2) − (1) gives,
[tex]rS_n-S_n=ar^{n} -a[/tex]
[tex]S_n(r-1)=a(r^{n} -1)[/tex]
Therefore, the sum of n terms of a GP is:
[tex]$S_n=a(\frac{1-r^{n} }{1-r} )[/tex]
Let the expression be r S n = a₁r + a₁ r² + a₁ r³ + . . . . + a₁rⁿ
Sum of first n terms of the Geometric progression is:
Sn = a₁ + a₁r + a₁ r² + . . + a₁ rⁿ⁻¹
On multiplying by r on both sides, we get
rSn = a₁r + a₁ r²+ . . +a₁ rⁿ⁻¹+a₁ rⁿ
Therefore, rSn = a₁r + a₁ r²+ . . +a₁ rⁿ⁻¹+a₁ rⁿ
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True or false an equation in the form of ax+by=c a>0 where a and b are not both zero and a,b, and c are integers with a greatest common factor of 1 can represent either a linear or non linear function
The equation in the form ax+ by=c a>0 where a and b are not both zero and a, b, and c are integers with greatest common actor of 1 represent either linear or non linear function. Hence, this statement is true.
what is linear function and non linear function?The formula for a linear function is f(x) = mx + b, where m and b are real values. Isn't it resembling the slope-intercept form of a line, represented by the equation y = mx + b? Yes, this is the case as the graph of a linear function is a line.
Here,
• 'm' is the slope of the line.
• 'b' is the y-intercept of line.
• 'x' is the independent variable.
• 'y' is the dependent variable.
As the name suggests, a nonlinear function is one that is NOT linear. To put it another way, a nonlinear function's graph is not a line, which means that its graph can be anything other than a line.
Given that, ax+ by=c a>0 where a and b are not both zero and a, b, and c are integers with a greatest common factor of 1
ax+ by -c=0 [by transpose]
The general form of linear equation is ax+ by +c z +d=0
So, it is a binary first order equation of 'x' and 'y'.
Therefore, ax+ by=c a>0 where a and b are not both zero and a ,b, and c are integers with a greatest common factor of 1 can represent either a linear or non linear function.
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Evaluate the infinite geometric series 2/5 +4/25 + 8/125 + . . . . Enter your answer as a fraction.
An infinite geometric series is the outcome of an unlimited geometric sequence.
The infinite geometric series be 2/5 +4/25 + 8/125 + . . . . then the sum of the infinite geometric series is 2/3.
What is an infinite geometric series?
An infinite geometric series is the outcome of an unlimited geometric sequence. This series wouldn't have a finish. It is possible to calculate the sum of all finite geometric series. The terms in the sequence will grow steadily larger, but adding the larger numbers together will not provide a solution if the common ratio of an infinite geometric series is greater than one.
Given:
a(first term) = 2/5
r(common difference) = 2/5
Since, |r| < 1 the infinite series converges.
[tex]S_\infty[/tex] = a/1-r ; -1 < r < 1
[tex]S_\infty[/tex] = (2/5)/(1-2/5)
simplifying the above equation, we get
[tex]S_\infty[/tex] = (2/5)/(3/5) = 2/3
The sum of the infinite geometric series is 2/3.
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Expand these brackets:
3(5 + b) =
2(3f + 5) =
Answer:
15+3b
6f+10
Step-by-step explanation:
Those are your answers
Answer:
15 + 3b
6f + 10
Step-by-step explanation:
Distributive property: a*(b +c) = (a*b) + a*c)Multiply 3 with 5 and multiply 3 with b and then add the results of the multiplication.
3*(5 + b) = (3*5) + (3*b)
= 15 + 3b
2*(3f + 5) = (2*3f) + (2*5)
= 6f + 10
Write an explicit formula for each sequence. 4,1.5,-1,-3.5, . . . . .
I think the answer is -2.5n + 6.5.
How to work it out:
Look at how much it goes down by (since it's going down, put a negative sign)Find out the "0th term". In this case, you would add 2.5 to 4 to find out the 0th term.If the "0th term" is positive, put + … and if its negative, put - …So I think the answer is -2.5n + 6.5True or False
When naming or labeling a line, it matters which points you use.
Answer:
true
Step-by-step explanation:
when naming or labeling a line it matters which points you use
In 2011, Tyson foods had sales of $32.266 billion, and in 2012, sales were $33.278 billion. Write a linear equation giving the sales y in terms of the year x. Then use the equation to predict the sales for 2013.
Considering the expression of a line and how to obtain it having 2 points, you obtain:
the linear equation giving the sales y in terms of the year x is y=1.012x - 2002.866the sales in 2013 will be $34.29 billion.Linear equation o lineA linear equation o line can be expressed in the form y = mx + b
where
x and y are coordinates of a point.m is the slope.b is the ordinate to the origin and represents the coordinate of the point where the line crosses the y axis.Knowing two points (x1, y1) and (x2, y2) of a line, the slope m of said line can be calculated using the following expression:
m= (y2 - y1)÷ (x2 - x1)
Substituting the value of the slope m and the value of one of the points in the expression of a linear equation, y = mx + b, the value of the ordinate to the origin b can be obtained.
Linear equation in this caseIn this case, you want to obtaina linear equation giving the sales y in terms of the year x. You know:
In 2011, Tyson foods had sales of $32.266 billion.In 2012, sales were $33.278 billion.So, being (x1,y1)= (2011, 32.266) and (x2,y2)= (2012, 33.278), the slope m can be calculated as:
m= (33.278 - 32.266)÷ (2012 - 2011)
Solving:
m=1.012
Considering point 1 and the slope m, you obtain:
32.266= 1.012×2011 + b
32.266= 2035.132 + b
32.266- 2035.132= b
- 2002.866= b
Finally, the linear equation giving the sales y in terms of the year x is y=1.012x - 2002.866
You can use the equation to predict the sales for 2013 as follow:
y=1.012×2013 - 2002.866
Solving:
y=1.012×2013 - 2002.866
y= $34.29 billion
Finally, the sales in 2013 will be $34.29 billion.
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The sum of an infinite geometric series is twice its first term.
a. A student says the common ratio of the series is 3/2 . What is the student's error?
The student's error is that the common ratio would not be equal to 3/2.
What is Common Ratio:
The general form of representing a geometric progression is a1, (a1r), (a1r2), (a1r3), (a1r4) ,... where a1 is the first term of GP, a1r is the second term of GP, and r is the common ratio.
Common Ratio Formula:
Common ratio,
r =a n / a n−1
where,
an is the nth term of the geometric progression.
an−1 is the (n - 1)t h term of the geometric progression.
Now,
[tex]S_{infinity} = 2a_{1} \\\\= a_{1} / 1-r\\\\2a_{1} = a_{1} / 1-r\\\\= 1-r = 1/ 2\\\\r = 1/2 - 1\\\\r = 1/2[/tex]
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mr. andrson is ordering pizzas for a class pizza party. pizza place has a special where he can buy 3 large pizzas for $18.75. at mario's pizzeria, he can buy 4 large pizzas for $22. if he needs to buy 12 pizzas, how much will he save if he buys the pizzas from mario's pizzeria instead of pizza place?
If h = -7, the expression has a value of _.
The value of the given expression will be 57 if the value of h = -7.
What are expressions?An expression in mathematics is a combination of numbers, variables, and functions (such as addition, subtraction, multiplication or division etc.) Expressions and phrases are similar in structure. In language, a phrase may include an action on its own, but it does not constitute a complete sentence.So, let the value of expression be 'x'.
SUbstitute h = -7 in the expression as follows:
39(2) + 3h = x39(2) + 3(-7) = x78 + (-21) = x78 - 21 = x57 = xTherefore, the value of the given expression will be 57 if the value of h = -7.
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The complete question is given below:
If h = -7, the expression has a value of _.
39(2) + 3h = x
a. Generate the first ten terms of the Fibonacci sequence.
The first ten terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on.
What is Fibonacci sequence and what are the first ten terms?The Fibonacci numbers, sometimes known as Fn in mathematics, are a series of numbers. Each number in the Fibonacci sequence is composed of the sum of the two numbers before it. Typically, the sequence begins with 0 and 1.
means
0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8
5 + 8 = 13
8 + 13 = 21
13 + 21 = 34
21 + 34 = 55
34 + 55 = 89
Hence,the first ten terms of the Fibonacci sequence are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 and so on.
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[tex]\Large \boxed{\sf 0, 1, 1, 2, 3, 5, 8, 13, 21, 34}[/tex]
A series of integers known as the Fibonacci sequence begins with a zero, is followed by a one, another one, and then a series of increasing numbers. Each number in the series equals the sum of the two numbers before it. Every succeeding pair of Fibonacci numbers has a quotient resembling the golden ratio.
State which are relations. Give their domain and range. Then tell if the relation is also a function. NUMBER 8
Answer:
Not a function; D: {2, 9}; R: {8, 4, 7}
d. Find the geometric mean of the term from part (c) and the first term of your sequence. What term of the sequence have you just found?
The geometric mean can be determined by multiplying the terms from part c and the first term of the sequence from part a and taking their square root.
The first term of the sequence from part a is 2 and the term from part c is 512.
Geometric mean of a sequence is the average value of a set of numbers, determined by multiplying the terms together and taking their root.
In general form, the geometric mean for a n number of terms is n√x1*x2*x3*…*xn
Since there are two terms 2 and 512, we will take the square root of the product.
Geometric mean=√2*512=√1024=32
For the geometric sequence as it is the mean, the term will be the 2nd term of the sequence
Hence, the geometric mean of the two chosen positive number 2 and 512 is 32 which is the 2nd term.
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Glenn is shopping for school clothes. He plans to get one of each of the same shirt in five different colors and three
pairs of the same pant each in a different color. The total cost for his clothes is $190 before tax.
The equation which describes this situation in terms of the cost of each shirt (x) and the cost of each pair of pants (y)
is
The equation which describes this situation in terms of the cost of each shirt (x) and the cost of each pair of pants (y) is, 5x+3y=190
What is Equation?Equation: There are numerous ways in which one may define an equation. In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an ‘equal’ sign. The most basic and simple algebraic equations consist of one or more variables in math.
Glenn is shopping for school clothes
Number of shirts Glenn want to buy= He plans to get one of each of the same shirt in five different colors which is equal to 5
x is the cost of each shirt
that means cost of 5 shirts = 5x
Number of pair of pants he want to buy= three pairs of the same pant each in a different color which is equal to 3
y is the cost of each pair of pants
that means the cost of three pair of pants = 3y
The total cost for his clothes is $190
The equation which describes this situation in terms of the cost of each shirt (x) and the cost of each pair of pants (y) is, 5x+3y=190
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Find the domain and range of the function represented by the graph (2 problems)
The domain of the function 13. is {-4≤x≥2} and the range of the function is {2≤x≥6} and The domain of the function 14. is {0.5≤x≥1.75} and the range of the function is {0.25≤x≥1.5}
The domain of the function means all the possible value that can be put in the function or the value of inputs
The range of the function means all the possible values that can be the result of various inputs or the value of output
On the graph the x coordinates represent the domain of the function that is possible inputs and y axis represent the range of the function that is all possible outcomes
The first problem (13.)
the highest point's coordinates can be reed as (-4, 6) and the coordinates of lowest point are (0,2) . There is one more significant point , the second endpoint, whose coordinates are (2,3)
So, The domain of the function is {-4≤x≥2} and the range of the function is {2≤x≥6}
The Second problem (14.)
the highest point's coordinates can be reed as (1.75, 1.5) and the coordinates of lowest point are (0.5, 0.25) .
So, The domain of the function is {0.5≤x≥1.75} and the range of the function is {0.25≤x≥1.5}
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Sketch the solid that results when the region enclosed by the given equations is revolved about the y -axis.
y = x²
y = 2 x
y = x² , y = 2 x are the region enclosed by the given equations is revolved about the y -axis.
What exactly is a closed area?
All space between a floor and ceiling that is enclosed on all sides by solid walls or windows, except doors that stretch from the floor to the ceiling, is referred to as an enclosed area.
What do you mean by the region that a closed curve encloses?
The sum of all infinitely thin rectangles with height f(x), enclosed by the curve y=f(x), and the x-axis between x=a and x=b, is what we mean when we write baf(x)dx.
Whether contained or not?
Use enclosed at all times. No longer regarded as a regular variety, enclosed would even be mistaken for another word by many readers. Use enclose, encloses, and enclosing rather than inclose for other words that are similar to enclosed.The graph is attached in equation y = x² , y = 2 x
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Use the box method to distribute and simplify (-5x+3)(x+6)
Answer:
-6x * 3
Explanations :
= - 5x + 3 * x + 6
= - 5x - x * 6 - 3
= - 6x * 3
K(6, 7) and L(4, 5) are the endpoints of a line segment. What is the midpoint M of that line
segment?
Write the coordinates as decimals or integers.
M =
Answer: M = (5, 6)
Formula for midpoint:
[tex]\sf (x_m, y_m) = \left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)[/tex]
Here given:
[tex](x_1,y_1) = (6,7), \ (x_2, y_2) = (4,5)[/tex]Find midpoint M by substituting values:
[tex]\sf M = \left(\dfrac{6+4}{2}, \dfrac{7+5}{2}\right)[/tex]
[tex]\sf M = \left(\dfrac{10}{2}, \dfrac{12}{2}\right)[/tex]
[tex]\sf M = \left(5, 6\right)[/tex]
Given:-
Two points K(6,7) and L(4,5) . These points are endpoints of a line segment .To find:-
The midpoint of the line segment.Answer:-
Here we are interested in finding the midpoint of a line segment whose endpoints are given to us . Say if a line segment has endpoints [tex](x_1,y_1) [/tex] and [tex](x_2,y_2)[/tex] , then the midpoint of the line is given by ,
[tex]\implies Midpoint= \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg) \\[/tex]
And here , we have;
[tex] x_1 = 6[/tex] [tex] x_2 = 4 [/tex][tex] y_1 = 7 [/tex][tex] y_2 = 5 [/tex]So on substituting the respective values, we have;
[tex]\implies (x_m , y_m ) =\bigg(\dfrac{ 6+4}{2},\dfrac{7+5}{2}\bigg) \\[/tex]
[tex]\implies (x_m , y_m ) =\bigg( \dfrac{10}{2} , \dfrac{12}{2}\bigg) \\[/tex]
[tex]\implies\underline{\underline{ (x_m , y_m ) = (5,6)}}\\[/tex]
Hence the midpoint is (5,6) .
and we are done!
Write a slope-intercept equation for a line passing through the given point that is parallel to the given line. Then write a second
equation for a line passing through the given point that is perpendicular to the given line.
(-7, 0), y=-0.9x + 4.4
The equation of the line parallel and perpendicular are y = -0.9(x+7) and y = 10/9(x+7) respectively
Equation of a lineThe equation of a line in point slope form is expressed as;
y - y₁ =m(x-x₁) (Parallel)
y - y₁ =-1/m(x-x₁) (Perpendicular)
Given the following
Point = (-7, 0)
Slope = -0.9
Substitute
y -0 = -0.9(x-(-7))
y = -0.9(x+7)
Similarly for the perpendicular line
y -0 = -1/-0.9(x-(-7))
y = 10/9(x+7)
Hence the equation of the line parallel and perpendicular are y = -0.9(x+7) and y = 10/9(x+7) respectively
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need help solving please
Answer: the answer is D
Both sides are equal to 5 radical 2
Step-by-step explanation:
consider inequality 12 < -3(x+4). The solution set of this inequality is x =
The solution set of this inequality is x = -8
What is inequality ?
A mathematical statement indicating an order relationship between two numbers or algebraic expressions, such as greater than, greater than or equal to, less than, or less than or equal to.An inequality in mathematics is a relation that compares two numbers or other mathematical expressions in an unequal way. The majority of the time, size comparisons between two numbers on the number line are made.inequality
12 < -3(x+4)
12 < -3x - 12
12 + 12 < - 3x
24 < -3x
- 8 < x
The solution set of this inequality is x = -8
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Five times the sum of x and 5 is 8 less than twice x. Solve for x.
Answer: x=-11
Step-by-step explanation:
5(x+5)=2x-8
5x+25=2x-8
5x+25-25=2x-8-25
5x=2x-33
3x=-33
x=-11
The value of x in the given expression is -11.
What is an expression?Expression in maths is defined as the collection of numbers variables and functions by using signs like addition, subtraction, multiplication, and division.
Given that; Five times the sum of x and 5 is 8 less than twice x.
WE are asked to Solve for x.
Then the expression form as;
5(x+5)=2x-8
Now solve for x;
5x+25=2x-8
Subtract 25 on both sides;
5x+25-25=2x-8-25
5x=2x-33
3x=-33
x=-11
Therefore, the value of x in the given expression is -11.
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Find the distance between each pair of points.
X(-2,5), Y(1,11)
The distance between the pair of points X(-2,5) and Y(1,11) is [tex]\sqrt{45}[/tex] units.
We can find the distance between the points X and Y by using distance formula.
The distance formula is used to find the distance between two defined points on a graph (in the absence of a scale).
Here the two points are X(-2,5) and Y(1,11).
The distance formula for points (a,b) and (c,d) is given by :-[tex]\sqrt{(d-b)^2+(c-a)^2}[/tex]
Here,
(a,b) represents the point X(-2,5), and
(c,d) represents the point Y(1,11)
Putting the values of (a,b) and (c,d) in the distance formula, we get,
[tex]\sqrt{(11-5)^2+(1-(-2))^2}[/tex]
[tex]\sqrt{6^2+3^2} \\ \sqrt{36+9}\\ \sqrt{45}[/tex]
Hence, the distance is [tex]\sqrt{45}[/tex] units.
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h(x)
=
x² + 3x
4x + 27
Find h(-8)
Step-by-step explanation:
it is -8 because negative times negative is positive
(-8)2. Find the domain and range of the function shown in the graph. Write the domain and range
using interval notation.
O domain: [-3,2)(3,7]
range: [-6,-1) [1,5)
O domain: (-6,-1](1,5]
range: (-3,2][3,7)
O domain: (-3,2][3,7)
range: (-6,-1](1.5]
O domain: [-6,-1) [1,5)
range: [-3,2)(3.7]
By looking at the graph:
Domain: (-6, 1] U (1, 5]
Range: (-3, 2] U [3, 7)
How to find the domain and range of the graphed function?
The domain is the set of inputs (horizontal axis) and the range is the set of the outputs (vertical axis).
By looking at the horizontal axis we can see that the first part goes from x = -6 to x = -1, this interval is (-6, 1]
(at x = -6 there is a open circle, so x = -6 does not belong to the domain)
Similarly, the second interval is (1, 5]
Then the domain is D: (-6, 1] U (1, 5]
To get the range we do the same thing, but we need to look at the vertical axis. The first interval goes from y = -3 to y = 2 and then y = 3 to y = 7, the range is:
R: (-3, 2] U [3, 7)
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How can you determine whether two variables x and y for a real-life situation are, correlated?
To determine if two variables, X and Y, are correlated, we can use the two simple ways. One is to create a scatter plot simply—a scatter plot plots X and Y pair values. A scatter plot shows a diagram of correlations. We can also identify if the correlation formed is positive, negative, or non-existent. Calculating the correlation coefficient R and determining its p-value associated with R is also possible.
Correlation coefficient values are always between -1 and 1.
Where
-1 indicates a perfect negative linear correlation between the two variables
0 shows a perfect positive linear correlation between the two variables
1 shows a perfect linear correlation between the two variables, indicates
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Draw a scale model of your classroom using any scale.
Answer: a scale model is a representation or copy of an object that is larger or smaller than the object being represented, (sorry if this wasnt what you were asking)
Step-by-step explanation:
Please someone help I don’t understand
Answer:
15. False, m<1 and m<3 are not vertical
16. False, m<2 and m<4 are vertical, so they must be the same
17. True, they are supplementary
18. True, they are also supplementary
19. 90 - 35 = 55
20. m<7 = m<4, so it's 42 degrees
21. 126-90 = 36 degrees
22. 115-90 = 25, which gives us the angle of m<4, which is vertical to m<7, which means m<7 is also 25.
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