a. List the first six terms of the arithmetic sequence and identify the common
difference.
a₁ = 7
an = an-1 + 4
b. Find a15-
c. Find the sum of the first 15 terms in the sequence.
Answers
Answer:
a1=7
an=an-1+4
a2=a2-1+4
a2=a1+4
a2=7+4
a2=11
a3=a3-1+4
a3=a2=+4
a3=11+4
a3=15
a4=a4-1+4
a4=a3+4
a4=19
a5=23
a6=27
a15=62
The common difference is 4.
The sum is 517.
Related Questions
if y = x^2 - 2 what is the value of y when x=3
Answers
Answer: y = 7
Step-by-step explanation: 3^2 is 9 and 9 - 2 is 7.
Rosa got 5 out 7 answers correct on her science quiz. Her older sister Ana got 4 answers out of 6 correct on her science quiz. Which sister answered a greater fraction of the questions correctly?
Answers
Answer:
Rosa
Step-by-step explanation:
5/7 fraction = 0.71
4/6 fraction = 2/3 = 0.6
where w is the width of the rectangle. Assume that w is a whole number. Use this function to answer Items 17-20. 17. Make a table of values and a graph of the function. 18. Attend to precision. Give a reasonable domain for the function in the context. Explain your answers 19. Identify the y-intercept of the function. What does the y- insert represent within this context? 20. What is the absolute maximum of the function? What is the absolute minimum?
Answers
Answer: I would use the max as 25
Step-by-step explanation: You use the variables of y, for the numbers os the maximum. so i would be high
cuanto es 1500x830 +321
Answers
The given expression 1500 x 830 + 321 can be solved as 12,45,321 using arithmetic operations.
What is multiplication and addition?Multiplication is the repeated addition of a number. If we multiply m by n, that means m is repeatedly added to itself for n times. The symbol for multiplication is ‘×’.
Addition is the process of combining two or more items (or numbers) to create a new sum.
Given the expression: 1500 x 830 + 321
Using BODMAS, first we do the multiplication.
So, 1500x 830 = 12,45,000
Now, continuing with the addition, we get
12,45,000 + 321 = 12,45,321
Therefore, the given expression can be solved as 12,45,321.
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"The given question is:
Calculate 1500 x 830 + 321"
figure. (Sides meet at right angles.
4 in
8 in
2 in
4 in
5 in
2
in
Answers
What is the slope of the line that passes through the points (4,7) and
(7, 16)? Write your answer in simplest form.
Answers
The slope of the line passing through (4,7) and (7, 16) is 3
What is Slope ?
The slope of a line is a measure of its steepness. Mathematically, slope is calculated as "rise over run". It is denoted by "m".
Formula, m = rise / run = (y2 - y1) / (x2 - x1)
Given,
(x1, y1) = (4, 7)
(x2, y2) = (7, 16)
Now, put these values in slope (m) formula,
m = (y2 - y1) / (x2 - x1)
= (16 -7) / (7 - 4)
= 9/3
= 3
Therefore, the slope of the line passing through (4,7) and (7, 16) is 3.
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Which option shows the plan and which option shows the side elevation?
Answers
Option B picture shows the plan of the given 3D shape and Option I picture shows the side elevation of the given 3D shape.
Plan: When an object is viewed from the top, that section or part is called a plan view of that object.
Options C, G, F, and B- all are viewed from the top: however out of these four only Option B shows the real plan of this given 3D object while others change its dimension and shape.
(F is shown as an oval)(C is shown as small and inclined)(G is shown as smaller than the actual image)Elevation: When an object is viewed from one side of the object, that section or part is called an elevation view.
Options D, E, A, and I- all are in elevation view, however, only option I is satisfying and shows the real elevation of a given 3D object.
(A shows a bit of curve in the below edge )(D shows again a curve with a narrow structure)(E shows a perfect edge however it is also narrower than the actual image)Therefore, only option B and option I are showing the correct plan and elevation of a given image.
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What mistake did Richard make? Explain what he needs to do to fix it.
Answers
Given:-
[tex]x^2-6x+8=0[/tex]To find the simplified form and the mistake.
So now we use the formula,
[tex]x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}[/tex]So now we substitute the value. so we get,
[tex]\begin{gathered} x=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ x=\frac{6\pm\sqrt[]{6^2-4\times1\times8}}{2\times1} \\ x=\frac{6\pm\sqrt[]{36-32}}{2\times1} \\ x=\frac{6\pm\sqrt[]{4}}{2\times1} \\ x=\frac{6\pm2}{2} \end{gathered}[/tex]So now we get,
[tex]\begin{gathered} x=\frac{6\pm2}{2} \\ x=\frac{6+2}{2},x=\frac{6-2}{2} \\ x=\frac{8}{2},x=\frac{4}{2} \\ x=4.x=2 \end{gathered}[/tex]So the value of x is,
[tex]4,2[/tex]So the mistake is in step 5.
A rectangular garden is 5 ft longer than it is wide. Its area is 300 ft. What are its dimensions?
Answers
The dimensions of the garden are l=20 ft and w=15 ft.
Given, the rectangular garden is 5 ft longer than it's width.
The area of the garden is 300 ft.
dimensions of the garden are = ?
let the width be represented by x.
therefore, length = 5+x
area of the rectangle = l×w
substitute the values.
x(5+x) = 300
5x + x² = 300
x² + 5x - 300 = 0
x²+20x-15x-300 = 0
x(x+20)-15(x+20)=0
(x+20)-(x-15)=0
x=-20 or x=15
hence the dimension cannot be negative.
hence x=15.
substitute x=15 in l=x+5
l=15+5
l=20
Therefore, length and width of the rectangle garden are 20 ft and 15 ft, respectively.
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6s-3/4 simplified
very hard
Answers
The simplified form is 3/4( 2s-1).
The problem we dealing with here is related to factors of linear polynomial, where a linear polynomial is characterized as any polynomial expressed in the form of a condition of p(x) = ax + b, where a and b are real numbers and a ≠ 0. In a linear polynomial, the degree of the variable is rise to 1 i.e, the highest type of the variable is one, whereas a factor of polynomial P(x) is any polynomial that divides equitably into P(x). The factorization of a polynomial is its representation as a product of its variables.
The problem that is given to us is 6s-3/4 ,we just need to find common factor it to convert it into a simpler form.
We can see 3/4 is the common factor out here so it wil be
=3/4 (2s-1)
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Is [tex]\sqrt{72}[/tex] irrational or rational , and why?
(please help im like a month late with this assignment)
Answers
Answer:Irrational
Step-by-step explanation:The answer does not end and is infinite.
Answer:
it is irrational number
Step-by-step explanation:
it just is irrational number
Select all the solutions to this equation. X2 = 121 x = 11 x = 21 x = 61 x = –11 x = –21
Answers
In quadratic equation (-11)2 = 121, the solution is actually both x = 11 and x = -11.
What in mathematics is a quadratic equation?
x ax2 + bx + c = 0 is a quadratic equation, which is a second-order polynomial equation in a single variable. a 0. It has at least one solution because it is a second-order polynomial equation, which is guaranteed by the algebraic fundamental theorem. The answer could be simple or complicated.x² = 121. To find x, we need to get rid of the exponent, and to do this, we can take the square root of both sides:
√x² = √121
x = √121
You might believe that x = 11, but keep in mind that x might also be negative because negative numbers can be squared.
In essence, each real number has both a positive and a negative square root.
Because (-11)2 = 121, the solution is actually both x = 11 and x = -11.
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How do you determine whether to use plus or minus signs in the binomial factors of a trinomial of the form x^2 + bx + c where b and c may be positive or negative numbers?
Answers
The rule of signs in binomial factors given a trinomial in the form :
[tex]x^2\pm bx\pm c[/tex]Note that b and c can be positive or negative.
And the factor may be :
[tex](x\pm m)(x\pm n)[/tex]First thing to do is to check the sign of c.
If it is positive, the signs of m and n can be both positive or both negative.
Since positive multiplied by positive is positive and
negative multiplied by negative is also positive.
[tex]\begin{gathered} (+)\times(+)=+ \\ (-)\times(-)=+ \end{gathered}[/tex]If the sign of c is negative, one of the factors must be negative and the other must be positive, because negative multiplied by positive is negative.
[tex](-)\times(+)=-[/tex]After considering the sign of c, next to check is the sign of b.
Case 1 :
If b and c are both positive, we know that the factors can be both negative or both positive.
And since the sign of b is positive, we must follow the sign of it which is positive.
So both m and n are positive
For example :
[tex]x^2+5x+6[/tex]The factor will be :
[tex](x+2)(x+3)[/tex]which are both positive.
Case 2 :
If b is negative and c is positive, we will follow the sign of b. m and n will be both negative.
For example :
[tex]x^2-5x+6[/tex]The factors are :
[tex](x-2)(x-3)[/tex]which are both negative
Case 3 :
Now the third case is tricky.
If c is negative, we know that one of m and n is negative and the other one is positive.
The sign of the larger number between m and n will follow the sign of b.
For example :
[tex]x^2-x-6[/tex]c is negative, so one factor must be negative and the other must be positive. The sign of b is negative, so the larger factor must be negative also.
The factor will be :
[tex](x-3)(x+2)[/tex]3 is larger than 2, so the negative sign of b will proceed to the factor 3.
Which inequality is true?
A. 5π > 15
B. π+9<12
C. 6/2m > 1
D. 47-2<10
Answers
Answer: A
Step-by-step explanation:
[tex]\pi > 3 \implies 5\pi > 15[/tex]
which of the three curves drawn matches the graph of y= 2x^2 +x
Answers
The curve that matches the graph of:
y = 2x^2 + x
Is the orange curve.
Which of the 3 curves matches the graph of the given function?Here we want to see which one of the graphed curves matches the graph of the quadratic equation:
y = 2x^2 + x
To check that, we can evaluate this curve in some values of x and find some points.
For example, if x = 0 then:
y = 2*0^2 + 0 = 0
So we have the point (0, 0).
Now, if x = 1 then:
y = 2*1^2 + 1 = 2 + 1 = 3
So we have the point (1,3).
So now we just need to see which of the curves passes through the points (0, 0) and (1, 3), and that one will be the orange curve.
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What value of c in the equation cx+4y=12 would give the equation a slope of 8?
Please provide all work and steps you used to find your answer, or the answer is pretty much useless. Thank you!
Answers
The value of c would be -32 to get the slope of 8.
What is an equation of the line?An equation of the line is defined as a linear equation having a degree of one. The equation of the line contains two variables x and y. And the third parameter is the slope of the line which represents the elevation of the line.
The general form of the equation of the line:-
y = mx + c
m = slope
c = y-intercept
Slope = ( y₂ - y₁ ) / ( x₂ - x₁ )
Given equation is cx + 4y = 12. Convert the equation into the general form of the equation.
cx + 4y = 12
4y = -cx + 12
y = (-c / 4)x + ( 12 / 4 )
y = ( -c / 4) x + 3
The slope of the equation is ( -c / 4 ) which is to be equal to 8.
( -c / 4 ) = 8
c = -32
Therefore, the value of c would be -32 to get the slope of 8.
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Answer:
for my question u commented on u can just talk about u or anyone for a reference
Step-by-step explanation:
Find the equation of the straight line passing through the point (0,-1) which is perpendicular to the line y=3/4x-3
Answers
Considering the definition of perpendicular line, the equation of the straight line passing through the point (0,-1) which is perpendicular to the line y=3/4x-3 is y= -4/3x -1.
Linear equationA 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.Perpendicular linePerpendicular lines are lines that intersect at right angles or 90° angles. If you multiply the slopes of two perpendicular lines, you get –1.
Equation of perpendicular line in this caseThe line is y= 3/4x - 3. The line has a slope of 3/4.
If you multiply the slopes of two perpendicular lines, you get –1, you get:
3/4× slope perpendicular line= -1
slope perpendicular line= (-1)÷ (3/4)
slope perpendicular line= -4/3
The perpendicular line has a form of: y= -4/3x + b
The line passes through the point (0, -1). Replacing in the expression for perpendicular line:
-1= -4/3×0 + b
-1= 0 + b
-1= b
Finally, the equation of the perpendicular line is y= -4/3x -1 .
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A cylinder has a base diameter of 20 feet and a height of 8 feet what is the cubic volume
Answers
Therefore:
20/2 = 10
10^2 = 100
100 x pi = 100pi (about 314.159 in decimal)
100pi x 8 = 800pi cm^3 (about 2513.27cm^3)
PLEASE HELP !!What is the slope of a line parallel to the line whose equation is 8x+10y=60.
Answers
Answer:
In slope intercept form -5y = -4 - 30
Step-by-step explanation:
Slope intercept form is y=mx + b
Rewrite your equation in this form
-10y = -8x - 60
Find GCF (Greatest Common Factor) in this case it is 2
Divide all by 2
-5y = -4x - 30
divide both sides by -5
y = 4/5x + 6
slope = 4/5
Answer:
8
Step-by-step explanation:
so we know the formula of a line is y=mx+b
1. arrange 8x+10y=60 into y=mx+b format
2. 10y=8x+6
3. we see that 8 = m
4. parallel line NEVER intersect so therefore they have the same slope (whereas perpendicular lines intersect so the slope for a perpendicular line would be -1/8)
On a science test, a score of
91 falls exactly 1.5 standard
deviations above the mean. If
the standard deviation for the
test is 8, what is the mean score?
Answers
The standard deviation for the test is 8, the mean score is 79.
what is standard deviation?The standard deviation is a measurement of how much a group of values vary or are dispersed. While a high standard deviation suggests that the values are dispersed throughout a wider range, a low standard deviation suggests that the values tend to be close to the established mean.
Given that,
On a science test, a score of 91 falls exactly 1.5 standard deviations above the mean.
μ + 1.5σ = 91
If the standard deviation for the test is 8
σ = 8
μ + 1.5σ = 91
μ + 1.5(8) = 91
μ + 12 = 91
μ = 91-12
μ = 79
Therefore, the mean score is 79.
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The midpoint of line segment AB is M(3,-1). If the coordinates of A(8,4), what are the coordinates of B?
Answers
The coordinates of B are (-2 , 9)
Step-by-step explanation:
A (8, 4)
M (3 , -1)
To calculate a midpoint you have to add the corresponding coordinates of each point and divide them by 2
(Ax + Bx) / 2 = Mx
(8 + Bx) / 2 = 3
8 + Bx = 3 * 2
Bx = 6 - 8
Bx = -2
(Ay + By) / 2 = My
( -1 + By) / 2 = 4
-1 + By = 4 * 2
By = 8 + 1
By = 9
The coordinates of B are (-2 , 9)
Pls help step by step
Answers
When dealing with negative exponents, you need to move your number to the denominator and make the exponent positive. Then you can solve.
See details:
Answer:
1/1power4
Step-by-step explanation:
=one on one,and there will be a power four on top of the one.
Find (b2)2(b2)2 for the equation 3x2−5x−3=0
Answers
The value of the function (b²)²(b²)² from the given quadratic equation is 390,625.
What is the solution of a quadratic function?
The solution of a quadratic function is determined from either formula method or completing the square method.
The equation for the formula method of solving a quadratic function is given as;
[tex]x = \frac{-b \ \ \pm \ \sqrt{b^2 - 4ac} }{2a}[/tex]
where;
a is the coefficient of x²b is the coefficient of xc is the constantThe given quadratic function;
3x² - 5x - 3 = 0
from the equation above we can infer the following;
a = 3
b = -5
c = -3
The obtain the value of the function [ (b²)²(b²)²], we will substitute the value of b from the above quadratic equation into the given function as shown below.
(b²)²(b²)² = (-5²)²(-5²)² = (-5)⁸ = 390,625
Thus, the value of the function (b²)²(b²)² is determined by applying the formula method of solving a quadratic function.
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You separate bulbs of garlic into two groups. One for planting and one for cooking. The tape diagram represents the ratio of bulbs for planting to bulbs for cooking. You use six bulbs for cooking. Each bulb has 8 cloves. How many cloves of garlic will you plant.
Answers
The number of cloves of garlic you will plant is 288
Given,
There are two groups of garlic bulbs.
Ratio of garlic bulbs = Planting : Cooking = 6 : 1
The number of garlic bulbs used for cooking = 6
The number of cloves in a garlic bulb = 8
We have to find the number of cloves of garlic used for planting:
Here,
Ratio = 6 : 1
1 in ratio represents 6 bulbs of garlic
So, 6 will be, 6 × 6 = 36
That is, the number of garlic bulbs used for planting is 36.
Now,
Number of cloves of garlic used for cooking = 6 × 8 = 48 cloves
Number of cloves of garlic used for planting = 36 × 8 = 288 cloves.
That is, the number of cloves of garlic you will plant is 288.
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The graph shows the relationship between the number of cups of flour and the number of cookies made. Write an equation for the proportional relationship.
Answers
The equation for the proportional relationship is 16x-y=0 .
The equation of the line passing through the two points (a,b) and (c,d) is given by
(y-b) = m(x-a), where m is the slope .
In the question ,
Given in the graph that
x represents the number of cups of flour and y represents the number of cookies made .
From the graph we can see that
when 6 cups of flower is used , 96 cookies are made
So, the point on the line is (6,96),
when 12 cups of flower is used , 192 cookies are made
So, the point on the line is (12,192)
hence the line passes through the two points (6,96) and (12,192).
So the slope of the line is
m=(192-96)/(12-6)
m= 96/6
m=16
Substituting the values of a,b, c,d and m in the equation of line formula ,we get
y-96=16(x-6)
y-96 = 16x - 96
16x-y=96-96
16x-y=0
Therefore , The equation for the proportional relationship is 16x-y=0.
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If you know any of these please help!
Answers
Answer:
5: 13
6: 7
7: 26
8: 18
9: x=11 , y=3
Step-by-step explanation:
5:
9x + 2 = 119
9x = 117
x = 13
6:
12x - 8 + 104 = 180
12x - 8 = 76
12x = 84
x = 7
7:
5x + 7 = 8x - 71
3x = 78
x = 26
8:
7x - 61 = 4x - 7
3x = 54
x = 18
9:
9x + 25 = 13x - 19
4x = 44
x = 11
13(11) - 19 + 17y - 5 = 180
143 - 24 + 17y = 180
119 + 17y = 180
17y = 61
y = 3
i need help please , like really fast !
Answers
nvm i left
Step-by-step explanation:
Write this word sentence as an equation and then solve.
The nine less than the quotient of a number w and -3 is 54.
Answers
Value of w will be [tex]\frac{45}{Q}[/tex] + 3
What is division?Division is the process of dividing a bunch of items into equal portions. It is one of the four fundamental operations in mathematics and results in a just distribution of resources. The division of two numbers can be calculated using the following formula: Dividend Divisor = Quotient + Remainder. The number that is being divided in this case is known as the dividend. The number that divides the number (dividend) into equal parts is known as the divisor. In mathematics, division is the process of dividing a number into equal parts and calculating the maximum number of equal parts that may be formed. For instance, dividing 15 by 3 results in the division of 15 into 3 groups of 5 each. The division sign, "÷" or occasionally "/," is used in computer code.
Given Data
The nine less than the quotient of a number w and -3 is 54.
Let the quotient be Q
9 - Q( w - 3) = 54
Solving,
-Q(w - 3) = 54 -9
w-3 = [tex]\frac{45}{Q}[/tex]
w = [tex]\frac{45}{Q}[/tex] + 3
Value of w will be [tex]\frac{45}{Q}[/tex] + 3
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Help me, I am struggling.
Answers
Answer:
term
Step-by-step explanation:
2/5m - 4/5 - 3/5m
PLEASE HELP!! ASAP
Answers
Answer:
-1
Step-by-step explanation:
All of them have the same denominator so we can take the denominator out
2-4-3 = -1 m