We conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.
How to get the sum of the first 8 terms?
In an arithmetic sequence, the difference between any two consecutive terms is a constant.
Here we know that:
[tex]a_1 = 3/5\\a_8 = 1/4[/tex]
There are 7 times the common difference between these two values, so if d is the common difference:
[tex]a_1 + 7*d = a_8\\\\3/5 + 7*d = 1/4\\\\7*d = 1/4 - 3/5 = (5 - 12)/20 = -7/20\\\\d = -1/20[/tex]
Then the sum of the first 8 terms is given by:
[tex]3/5 + (3/5 - 1/20) + (3/5 - 2/20) + ... + (3/5 - 7/20)\\\\8*(3/5) - (1/20)*(1 + 2 + 3+ 4 + 5 + 6 + 7) = 3.4 = 34/10 = 17/5[/tex]
So we conclude that the sum of the first 8 terms of the arithmetic sequence is 17/5.
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Which graph shows the solution to the following system of inequalities x+y>4
The solution to this system of inequalities x + y>4 , x + y <3 is Option A
The complete question is
Which graph shows the solution to this system of inequalities? x + y>4 x + y <3
The image are attached with the answer.
What are Inequality ?When an expression is equated with another expression by an Inequality operator (< , > < etc) then the mathematical statement formed is called Inequality.
The inequalities are
x+y>4
x + y <3
After plotting both the inequalities in the graph the following graph that is attached with the answer is obtained.
Therefore the correct answer is Option A
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Write a doubles fact that can help you find the
sum. Write the sum.
3+4
Step-by-step explanation:
4 + 4 = 8 is one of the two closest double to 3 + 4
W.K.T(we know that )..
4 is 1 more than 3 this means ;
4 + 4 will be 1 more than 3 + 4
4 + 4 = 8 ,so finding 1 Less ;
3 + 4 = 7
here is the answer hope It helped U
please mark as BRAINLIEST
Cynthia beach wants to buy a rug for a room that is 22 ft wide and 31 ft long.she wants to leave a uniform strip of floor around the rug.she can afford to buy 580 square feet of carpeting.what dimensions should the rug have?
The dimensions the rug should have is 20 by 29
How to determine the dimension?The dimension of the rug is given as:
22 ft by 31 ft
The area of the carpet is given as:
Area = 580
Represent the length of the empty space with x.
So, the dimension of the carpet is:
22 - 2x by 31 - 2x
The area is calculated as:
Area = (22 - 2x) * (31 - 2x)
Expand
Area = 682 - 62x - 44x + 4x^2
Evaluate the difference
Area = 682 -106x + 4x^2
Substitute Area = 580
682 -106x + 4x^2 = 580
Subtract 580 from both sides
102 -106x + 4x^2 = 0
Rewrite as:
4x^2 - 106x +102 = 0
Using a graphing calculator, we have:
x = 1 and x = 22.5
Substitute these values in 22 - 2x by 31 - 2x
So, we have:
Length = 22 - 2(1) = 20 or Length = 22 - 2(22.5) = -23
Width = 31 - 2(1) = 29 or Length = 31 - 2(22.5) = -14
The dimensions cannot be negative.
So, we have:
Length = 20 and Width = 29
Hence, the dimensions the rug should have is 20 by 29
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Determine whether the relation represents a function. State the domain and range of the relation.
{(-2,-9).(-4,-4). (1,5), (5, -7)}
Answer:
It is a functionDomain: {-4, -2, 1, 5}Range: {-9, -7, -4, 5}Step-by-step explanation:
A function is defined so that for each input (known as the domain), there is no more than one output (known as the range).
Peter and Henry went to the movies Peter bought the two Movie tickets for 7 dollars each. How much did he spend for the movie tickets Henry bought two buckets of popcorn for 5 dollars each. How much did Henry spend on popcorn. What was the total expenditure
Answer:
tickets: $14
popcorn: $10
total: $24
Step-by-step explanation:
2 movie tickets at $7 each is 2*7 which is $14
2 buckets of popcorn at $5 each is 2*5 which is $10
adding these together we get a total spending of $24
Evaluate the expression below when x = 6 and y = 2. 6x2y3
Answer:
I think that the answer is 432.
Step-by-step explanation:
6x2y3.We have x as 6 and y as 2.So we replace them with their numbers.
We'll have 6*6*2*2*3 which will give us 432. I HOPE THIS HELPS.
Given f(x) = x² + 4x - 3, find f(-3)
O -3
O -6
O 0
O 18
Answer:
f(-3) = -6
Step-by-step explanation:
f(x) = x^2 + 4x - 3
f(-3) means to put -3 in place of x and then do the calculation.
f(-3)
= (-3)^2 + 4(-3) - 3
= 9 - 12 - 3
= -3 - 3
= -6
First square -3, its 9. Then multiply -3 and 4, that's -12. Then add everything.
f(-3) = -6
Which graph represents the function f(x) = |x + 3|?
On a coordinate plane, an absolute value graph has a vertex at (0, 3).
On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).
On a coordinate plane, an absolute value graph has a vertex at (0, negative 3).
On a coordinate plane, an absolute value graph has a vertex at (3, 0).
Answer:
Graph of Modulus
The graph of a modulus or absolute value function is in a form of a 'V' shape whose vertex depends upon the coordinates. The equation for the graph is given as,
where,
(a, b) are the coordinates of the vertex of 'v' in the form of (x, y),
And h shows how wider or lean will be the function, for h=0, it is a straight line, while for a negative value the graph will face downwards and opposite for a positive value.
Given to us
y = |x-3|
On the coordinate plane
The graph will be in the shape of a 'V' whose vertex will lay at the coordinates (3, 0). As the value of a is 1 the graph will face upwards. As shown below on the graph.
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Step-by-step explanation:
Answer:
C
Step-by-step explanation:
edge 23
heIp??
everyone??
Brainliest = Good Answer/Solution
To Find = Diameter, Area
Solution :
Diameter = 2 × Radius
Diameter = 2 × 6cm
Diameter = 12 cm
Area = 2πr
[tex]area \: = 2 \times \frac{22}{7} \times 6cm[/tex]
[tex]area \: = \frac{264}{7} [/tex]
[tex]area \: = 37.7 \: cm[/tex]
____________________________________2. Given : Diameter = 8 DM
( 1dm = 10 cm
8dm = 8 × 10 = 80cm )
To find : Radius , area
Solution :
[tex]raduis \: = \frac{1}{2} \times diameter[/tex]
[tex]radius \: = \frac{1}{2} \times 80cm[/tex]
[tex]radius \: = 40 \: cm \: or \: 4dm[/tex]
Area = 2πr
[tex]area \: = 2 \times \frac{22}{7} \times 40[/tex]
[tex]area \: = \frac{1760}{7} [/tex]
[tex]area \: = 251.4cm \: \: \: or \: 25.14dm[/tex]
____________________________________3. Given : Radius = 2.5m
To find : Diameter , Area
Solution :
Diameter = 2 × radius
Diameter = 2 × 2.5m
Diameter = 5m
Area = 2πr
Area = 2 × 22/7 × 5m
Area = 220/7
Area = 31.4m
A motion sensor has a range of 65 meters as shown. The ultrasonic waves sweeping out from the sensor span an angle of 135°.
A figure shows the appendix cone has a range of 65 meters in which waves with an angle of 135 degrees.
What is the approximate area that is within range of the motion sensor? Use the value = 3.14.
The approximate area that is within range of the motion sensor is 4975 square meters
How to determine the area of the range?The figure is not given, however the area of the range can be calculated without the figure.
The given parameters are:
Angle, ⊕ = 135°
Radius, r = 65 meters
The area of the range is calculated using the following sector area
[tex]A = \frac{\theta}{360} * \pi r^2[/tex]
This gives
[tex]A = \frac{135}{360} * 3.14 * 65^2[/tex]
Evaluate
A = 4974.9375
Approximate
A = 4975
Hence, the approximate area that is within range of the motion sensor is 4975 square meters
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factoring / gcf ??? (in picture)
got really sick and missed a bunch of school, would really appreciate the help !
Step-by-step explanation:
hope this will help you....
Express 5 1/2 and 2 1/2 as a ratio of whole numbers
Answer:
your answers are 5.5 and 2.5 as they both have a half extra
Which sentence correctly compares the two numbers 5.395 and 5385 ?
5.395= 5385
5.385 > 5.395
5395< 5.385
5385 < 5.395
The sentence that correctly compares the two numbers is 5385 > 5.395
What is the correct sentence?Here are inequality signs and what they mean:
Note that
5385 is greater than 5.385. Thus, the correct statement is 5385 > 5.395.
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The graph of the absolute value parent function, f(x) = |x, is stretched
orizontally by a factor of 3 to create the graph of g(x). What function is g(X)
Answer:
g(x) = 1/3 • |x|
Step-by-step explanation:
To stretch a parent function, you multiply by whatever you want to stretch it with. If you multiplied by 3, it would be a vertical stretch... if you multiplied by 1/3, it makes it horizontal.
Hope this helps!
Need your help now please; the assignment is due tonight and this is the last problem I am having trouble with. The red box is the value I keep getting wrong
The region R is bounded by the x-axis, the straight line in the graph and the vertical line x=2.
The volume of the region R bounded by the x-axis is: [tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
What is the volume of the solid (R) on the X-axis?If the axis of revolution is the boundary of the plane region and the cross-sections are parallel to the line of revolution, we may use the polar coordinate approach to calculate the volume of the solid.
From the given graph:
The given straight line passes through two points (0,0) and (2,8). Thus, the equation of the straight line becomes:
[tex]\mathbf{y-y_1 = \dfrac{y_2-y_1}{x_2-x_1}(x-x_1)}[/tex]
here:
(x₁, y₁) and (x₂, y₂) are two points on the straight lineSuppose we assign (x₁, y₁) = (0, 0) and (x₂, y₂) = (2, 8) from the graph, we have:
[tex]\mathbf{y-0 = \dfrac{8-0}{2-0}(x-0)}[/tex]
y = 4x
Now, our region bounded by the three lines are:
y = 0 x = 2y = 4xSimilarly, the change in polar coordinates is:
x = rcosθ, y = rsinθwhere;
x² + y² = r² and dA = rdrdθTherefore;
rsinθ = 0 i.e. r = 0 or θ = 0rcosθ = 2 i.e. r = 2/cosθrsinθ = 4(rcosθ) ⇒ tan θ = 4; θ = tan⁻¹ (4)⇒ r = 0 to r = 2/cosθ θ = 0 to θ = tan⁻¹ (4)Then:
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^2 (rdr d\theta )}[/tex]
[tex]\mathbf{\iint_R(x^2+y^2)dA = \int ^{tan^{-1}(4)}_{0} \int^{\frac{2}{cos \theta}}_{0} \ r^3 dr d\theta}[/tex]
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what are the missing values
Answer:
The answer is on the image, which is color coordinated with the how i got it
Otto used 5.5 cups of whole wheat flour and x cups of white flour in the recipe. What is the equation that can be used to find the value of y, the total amount of flour that Otto used in the recipe, and what are the constraints on the values of x and y?
The equation that can be used to represent the situation is y = 5.5 + x
How to write and solve equation?Whole wheat flour = 5.5 cupsWhite flour = x cupsTotal flour = yThe equation:
Total flour = Whole wheat flour + White flour
y = 5.5 + x
Therefore, the equation that can be used to represent the situation is y = 5.5 + x
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Answer:
C
Step-by-step explanation:
The graph of y= (x + 2)(x-2)(x + 1) is shown.
4
3
2-
D
-6-5-4-3-2-1₁
23 456x
D
76
B
C
Which point is a relative minimum?
OA
OD
Answer:
Point C
Step-by-step explanation:
At point C, the graph is changing from decreasing to increasing.
I need some help please
Answer:
HexagonHeptagonStep-by-step explanation:
The first shape has 6 sides. Hence, it is called a hexagon.
The second shape has 7 sides. Hence, it is called a heptagon.
The mathematical name for the given 2 polygons.
Solution:The first polygon has 6 sides with an angle sum of 720°, which means the mathematical name given for this polygon is,
[tex]\large\boxed {Hexagon}[/tex]
The second polygon has 7 sides with an angle sum of 900°, which means the mathematical name given for this polygon is,
[tex]\large\boxed {Heptagon}[/tex]
Hence, the first polygon is a hexagon and the second polygon is a heptagon.
y-intercept: 4
-: x-intercepts: -2, 5, 7
-: Relative maximum at (0,4)
-: Relative maximum at (6, -3)
-: As → −∞, → −∞
-: As → ∞, →
The attached figure represents the sketch of the graph
The missing part of the questionThe complete question requires that we sketch the graph that follows the given parameters
How to sketch the graph?The given parameters are:
y-intercept: 4x-intercepts: -2, 5, 7Relative maximum at (0,4)Relative maximum at (6, -3)As x → −∞, y → −∞As x → ∞, y → ∞To start with, we plot the points on an empty coordinate plane.
Next, we connect the points using a rough curve
Lastly, the points are labelled
See attachment for the sketch of the graph
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Karen runs for 45 minutes every day. Which unit best describes the distance Karen runs for each day?
A. 50 kilometers
B. 5 kilometers
C. 50 meters
D. 50 centimeters
! URGENT !
Answer:
your mom fat as he'll that way you are adopted
Suppose that 50% of all babies born in a particular hospital are boys. If 6 babies born in the hospital are randomly selected, what is the probability that fewer than 3 of them are boys?
Using the binomial distribution, it is found that there is a 0.3438 = 34.38% probability that fewer than 3 of them are boys.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem, the values of the parameters are given as follows:
n = 6, p = 0.5.
The probability that fewer than 3 of them are boys is given by:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{6,0}.(0.5)^{0}.(0.5)^{6} = 0.0156[/tex]
[tex]P(X = 1) = C_{6,1}.(0.5)^{1}.(0.5)^{5} = 0.0938[/tex]
[tex]P(X = 2) = C_{6,2}.(0.5)^{2}.(0.5)^{4} = 0.2344[/tex]
Then:
[tex]P(X < 3) = P(X = 0) + P(X = 1) + P(X = 2) = 0.0156 + 0.0938 + 0.2344 = 0.3438[/tex]
0.3438 = 34.38% probability that fewer than 3 of them are boys.
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Find the surface area of the regular pyramid.
The surface area of the regular pyramid as given in the task content is; 16m².
What is the surface are of the regular pyramid?The task content requires that the surface area of the pyramid be determined. This surface area can therefore be evaluated as follows;
Surface area = (2×2) + 4((1/2)×2×3) = 4 + 12 = 16m².
The surface area of the regular pyramid is therefore; 16m².
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Which is equivalent to 64 1/4
Answer:
4*64=256
256+1=256
there fore 64 1/4 is equivalent to 257/4
Please show work and thank you
Answer: [tex]\sqrt{109} \text{ m }[/tex]
Step-by-step explanation:
If we let the length of the ladder be [tex]x[/tex], as shown in the diagram, this means that by the Pythagorean theorem, [tex]x=\sqrt{10^{2}+3^{2}}=\boxed{\sqrt{109}}[/tex] m.
What key features do the functions f(x) = 4-x and g of x equals negative one times the square root of the x minus 4 end root have in common?
A.)Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.
B.)Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
C.) Both f(x) and g(x) include domain values of [4, ∞) and range values of [0, ∞), and both functions have a y-intercept in common.
D.) Both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions are negative for the entire domain.
The key features are (1) both f(x) and g(x) include domain values of [–4, ∞) and range values of (–∞, ∞), and both functions have an x-intercept in common.
How to determine the key featuresThe functions are given as:
f(x) = 4 - x
[tex]g(x) = -\sqrt{x - 4}[/tex]
Using a graphing calculator:
The domain of g(x) is [4,∞)The range of g(x) is (-∞,0]The domain of f(x) is (-∞,∞) The range of f(x) is (-∞,∞) Both functions have positive values for their domainsBy comparing the above highlights, the true statement between functions g(x) and f(x) is option (1)
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Answer:
B.)Both f(x) and g(x) include domain values of [4, ∞), and both functions decrease over the interval (4, ∞).
Step-by-step explanation:
b is correct
If the area of a certain square is 81 square inches or less, which set
describes the domain of the function?
F(s)=s^2
(0,81]
[0, 9]
(0,91
[0,81)
Answer:
(0, 9]
Step-by-step explanation:
√81 = 9
We must take positive numbers into consideration here.
calculate time if distance is 53km and speed is 60km/hour?
Joe went shopping and purchased a pair of pants for $56 and a pair of shoes for $45. The tax in Joe's city is 4%. How much will Joe pay when he checks out ?
Answer:
$105.04
Step-by-step explanation:
First add $56 plus 45$ and you will get $101, then times $101 and 1.04 together.
Your answer should be $105.04.
using the figure below identify 1 pair of the following angle relationships
Answer:
\begin{gathered}\\1) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\end{gathered}
1)
Alternateinteriorangles:
\begin{gathered} \sf \implies \: 2\: \: and \: \: 7\\\end{gathered}
⟹2and7
\begin{gathered} \sf \implies \: 6\: \: and \: \: 3\\\\\end{gathered}
⟹6and3
\begin{gathered}\\2) \: \: \underline{ \sf{ Alternate \: interior \: angles \: \: : }}\\\\\end{gathered}
2)
Alternateinteriorangles:
\begin{gathered} \sf \implies \: 1\: \: and \: \: 8\\\end{gathered}
⟹1and8
\begin{gathered} \sf \implies \: 5\: \: and \: \: 4\\\\\end{gathered}
⟹5and4
\begin{gathered}\\3) \: \: \underline{ \sf{ Corresponding \: angles \: \: : }}\\\end{gathered}
3)
Correspondingangles:
\begin{gathered} \sf \implies \: 3\: \: and \: \: 1\\\end{gathered}
⟹3and1
\begin{gathered} \sf \implies \: 5\: \: and \: \: 7\\\end{gathered}
⟹5and7
\begin{gathered} \sf \implies \: 4\: \: and \: \: 2\\\end{gathered}
⟹4and2
\begin{gathered} \sf \implies \: 6\: \: and \: \: 8\\\\\end{gathered}
⟹6and8
\begin{gathered}\\4) \: \: \underline{ \sf{ Consecutive\: Interior \: angles \: \: : }}\\\end{gathered}
4)
ConsecutiveInteriorangles:
\begin{gathered} \sf \implies \: 2\: \: and \: \: 3\\\end{gathered}
⟹2and3
\begin{gathered} \sf \implies \: 6\: \: and \: \: 7\\\\\end{gathered}
⟹6and7
\begin{gathered}\\5) \: \: \underline{ \sf{ Consecutive\: Exterior \: angles \: \: : }}\\\end{gathered}
5)
ConsecutiveExteriorangles:
\begin{gathered} \sf \implies \: 1\: \: and \: \: 4\\\end{gathered}
⟹1and4
\begin{gathered} \sf \implies \: 5\: \: and \: \: 8\\\\\end{gathered}
⟹5and8