Answer:
Sum of the sequence (Sn) = 33,859
Step-by-step explanation:
Given:
Sequence = 685+678+671+664+...+6
Find:
Sum of the sequence (Sn)
Computation:
a = 685
d = 678 - 985 = -7
an = 6
an = a+(n-1)d
6 = 685+(n-1)(-7)
-679 = (n-1)(-7)
97 = n-1
n = 98
So,
Sum of the sequence (Sn) = (n/2)[a+an]
Sum of the sequence (Sn) = (98/2)[685+6]
Sum of the sequence (Sn) = (49)(691)
Sum of the sequence (Sn) = 33,859
Solve each of the following equations. Be sure to check your solutions.
3x-5=2.5x+3-(x-4)
Answer: x=8
Step-by-step explanation:
3x - 5= 2.5x + 3 -(x-4) apply the distributive property
3x -5 = 2.5x + 3 - x + 4 combine like terms on the right side
3x - 5 = 1.5x + 7 Add 5 to both sides
+5 +5
3x = 1.5x + 12 subtract 1.5x from both sides
-1.5x -15.x
1.5x = 12 Now divide both sides by 1.5
x = 8
What is the equation in point-slope form of the line passing through (0, 2) and (1,5)?
PLEASE HELP ASAP
You are studying meteorology and collect weather data for Gainesville, FL for the months of April, May, and June 2015. The function T ( x ) = .18 x + 80.25 gives an estimate of the daily high temperature during this period where x is the number of days after April 1, 2015. Evaluate T ( 57 ) (rounded to one decimal place) and then state its physical interpretation. T ( 57 ) =____________
Answer:
90.5
Step-by-step explanation:
T(57)=.18(57)+80.25
T(57)=10.26+80.25
T(57)=90.51 (round to the one descimal place)
your answer would be
T(57)=90.5
The temperature T(57) is 90.5 and it states that the temperature for 57 days from April 1 2015 is 90.5.
Given,
The function T ( x ) = .18 x + 80.25 gives an estimate of the daily high temperature during this period where x is the number of days after April 1, 2015.
We need to evaluate T ( 57 ) (rounded to one decimal place) and then state its physical interpretation.
What is a function?A function has an input and an output.
Example:
f(x) = x + 5
x = 1
f(1) = 1 + 5 = 6
1 = input
6 = output
Find T(x) at t = 57.
We have,
T(x) = 0.18 x + 80.25
T(57) = 0.18 x 57 + 80.25
T(57) = 10.26 + 80.25
T(57) = 90.51
Rounding to one decimal place.
90.51 = 90.5
T(57) = 90.5
T(57) = 90.5 means that the temperature for 57 days from April 1 2015 is 90.5
Thus the temperature T(57) is 90.5 and it states that the temperature for 57 days from April 1 2015 is 90.5.
Learn more about finding temperature differences at different points of time here:
https://brainly.com/question/17864807?referrer=searchResults
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Solve the two-step equation.
- 2/3 x - 21/4 = 27/4
Answer:
x = -18
I hope this helps!
Answer:
X- (-18)
Step-by-step explanation:
Hope this helps:)
Evaluate the expression 2(8 − 4)2 − 10 ÷ 2.
How would 5,608,912,013 be written in word form?
Answer:
Five billion, six-hundred and eight million, nine-hundred and twelve thousand, and thirteen.
Hope this helps!
Quadrilateral A'B'C'D'A
′
B
′
C
′
D
′
A, prime, B, prime, C, prime, D, prime is the result of translating quadrilateral ABCDABCDA, B, C, D by 555 units to the left and 555 units down.
Answer:
14.2
Step-by-step explanation:
= AB+BC+CD+DA
= 2.2+4.5+6.1+1.4
= 14.2
Answer: 14.2
Step-by-step explanation:
Khan Academy
Find the measures of angles 1-10
Answer:
1) 78
2) 28
3) 74
4) 28
5) 74
6) 106
7) 74
8) 74
9) 78
10) 78
Question 1
34 pts
Identify the type of data that would be used to describe a response for the question, "What is your
favorite movie?"
O quantitative discrete
O quantitative continuous
O qualitative
Question 2
33 pts
Answer: C) Qualitative
The response isn't a numeric value, but rather a name instead. So that's why we have qualitative data here. Specifically, it is nomimal as it deals with names or labels. The data is not ordinal as we cannot sort the labels.
there are 16 circles and 20 squares. What is the simplest ratio of circles to total shapes
Answer:
4 : 9
Step-by-step explanation:
Step 1: Find total amount of shapes
16 circles + 20 squares = 36 total shapes
Step 2: Write out ratio of circles to total shapes
16 : 36
Step 3: Simplify by dividing both numbers by 4
16/4 : 36/4
4 : 9
Sena determines the remainder of 4x32−14x16+2x3−8x−1, using the remainder theorem. How does she proceed to the correct answer? Drag a value into each box to correctly complete the statements.
Write g(x) = 4x2 + 88x in vertex form. The function written in vertex form is g(x) = (x +11)2 + .
Answer:
y = 4(x + 11)² - 484
Step-by-step explanation:
y = 4x² + 88x
factor the expression
y = 4(x² + 22x)
complete the square
y + ? = 4(x² + 22x + ?)
y + ? = 4(x² + 22x + 121)
add 4 • 121 to the left side
y + 4 • 121 = 4(x² + 22x + 121)
multiply
y + 484 = 4(x² + 22x + 121)
y + 484 = 4(x + 11)²
subtract both sides by 484
y = 4(x + 11)² - 484
Answer:
y = 4(x + 11)² - 484
Step-by-step explanation:
A rectangle has a perimeter of 60 inches. The length of the rectangle is 3 inches less than twice the width
What is the length of the rectangle?
Answer:
length = 19 units
Step-by-step explanation:
width = x
length = 2x-3
width = 11 units
length = 2(11)-3
length = 22-3
length = 19 units
perimeter = 11 + 11 + 19 + 19 = 60 units
The perimeter of a shape is the sum of the side lengths of the shape. The length of the rectangle is 19 units.
Given that:
[tex]Perimeter = 60[/tex]
[tex]Length = 2 \times Width -3[/tex]
The perimeter of a rectangle is:
[tex]Perimeter = 2 \times (Length + Width)[/tex]
So, we have:
[tex]60= 2 \times (2\times Width - 3+ Width)[/tex]
Divide both sides by 2
[tex]30= 2\times Width - 3+ Width[/tex]
Collect like terms
[tex]3 + 30= 2\times Width + Width[/tex]
[tex]33= 3Width[/tex]
Divide both sides by 3
[tex]11= Width[/tex]
Rewrite as:
[tex]Width = 11[/tex]
Recall that: [tex]Length = 2 \times Width -3[/tex]
[tex]Length = 2 \times 11 - 3[/tex]
[tex]Length = 22- 3[/tex]
[tex]Length = 19[/tex]
Hence, the length of the rectangle is 19 units.
Read more about perimeters at:
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Find the area of the triangle.
16 in.
25 in.
The area is
square inches.
Answer:
A=200 in
Step-by-step explanation:
[tex]A=\frac{1}{2} (bh)\\A=\frac{1}{2} (16*25)\\ A=\frac{1}{2} (400)\\ A= 200 in[/tex]
- x+4=-3x + 8
multi-step equations
Answer:
x = 2
Step-by-step explanation:
Isolate the variable, x. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS =
Parenthesis
Exponents (& Roots)
Multiplication
Division
Addition
Subtraction
& is the order of operation.
------------------------------------------------------------------------------------------------------
First, add 3x and subtract 4 from both sides:
-x (+3x) + 4 (-4) = -3x (+3x) + 8 (-4)
-x + 3x = 8 - 4
Simplify. Combine like terms:
3x - x = 8 - 4
2x = 4
Isolate the variable, x. Divide 2 from both sides:
(2x)/2 = (4)/2
x = 4/2
x = 2
x = 2 is your answer.
~
Step-by-step explanation:
this is answer
[tex] - x + 3x = - 4 + 8 \\ 2x = 4 \\ x = \frac{4}{2} \\ x = 2x = 2x = 2[/tex]
A group of 8 children and 8 adults are going to a movie. Child tickets cost $2, and adult tickets cost $6. How much will the movie tickets cost in all?
Answer:
Hey there!
8(2)+8(6)
16+48=64
The total price is 64 dollars.
Let me know if this helps :)
In this figure Ab and cd are parallel.
Answer:
figure is not available...
Help me with this question plz thx!!
Answer:
9x² - 9y + 9
Step-by-step explanation:
Step 1: Write out expression
3 - 2y - 1 + 5x² - 7y + 7 + 4x²
Step 2: Combine like terms (x²)
9x² + 3 - 2y - 1 - 7y + 7
Step 3: Combine like terms (y)
9x² - 9y + 3 - 1 + 7
Step 4: Combine like terms (constants)
9x² - 9y + 9
1800 people attended the National Day dinner in a certain constituency Given that 35.5 of them were. men, 40 % of them were women and the rest were children, find the number of children who attended the dinner
children
25.5 %
so 25.5% of 100
495
The diameter of a sphere is measured to be 4.17 in.
(a) Find the radius of the sphere in centimeters.
cm
(b) Find the surface area of the sphere in square centimeters.
cm2
(c) Find the volume of the sphere in cubic centimeters.
cm3
Step-by-step explanation:
To find the radius of the sphere we must convert the inches to centimeters
Using the conversation
1 inch = 2.54 cm
If 1 inch = 2.54 cm
4.17 inch = 2.54 × 4.17 = 10.59 cm
a).We can find the radius using the formula
[tex]radius = \frac{diameter}{2} [/tex]
From the question
diameter = 10.59 cm
So we have
[tex]radius = \frac{10.59}{2} [/tex]
radius = 5.30 cmb).Surface area of a sphere= 4πr²
where
r is the radius
Surface area = 4(5.30)²π
= 112.36π
= 352.989
We have the answer as
Surface area = 353 cm²c).Volume of a sphere is given by
[tex] \frac{4}{3} \pi {r}^{3} [/tex]
r = 5.30
The volume of the sphere is
[tex] \frac{4}{3} ( {5.30})^{3} \pi[/tex]
= 623.61451
We have the answer as
Volume = 623.6 cm³Hope this helps you
What is half of 30?????
Half of 30 is 15. You can obtain this by dividing it by 2 or multiplying it by 1/2.
someone please help me with this question !!
16-2v+3 what is the answer pls help
Answer:
the answer is 19-2v combine like terms if not that then try this....
19-2y=0
-2y=-19
Then divide by -2
y=-19/-2
=9.5
(1 point) Find the volume of the parallelepiped with one vertex at (4,2,4), and adjacent vertices at (6,3,8), (6,1,10), and (0,6,3)
Answer:
8 cubic units
Step-by-step explanation:
Let he vertices of the parallelepiped be A = (4,2,4), B= (6,3,8), C = (6,1,10) and D = (0,6,3)
The edges of the parallelepiped are
AB = (6,3,8) - (4,2,4) = (2,1,4)
AC = (6,1,10) - (4,2,4) = (2,-1,6)
AD = (0,6,3) - (4,2,4) = (-4,4,-1)
Therefore the volume of the parallelopiped is = |[AB,AC,AD]|
= [tex]$ \begin{vmatrix}\ 2\ \ \ 1\ \ \ \ 4\ \\2\ -1\ \ \ 6 \\-4\ \ \ 4\ -1 \end{vmatrix}$[/tex]
= |2(1-24)+1(-2+24)+4(8-4)|
= |2(-23) + 1(22) + 4(4)|
= |8|
=8 cubic units
somebody plz help this is algebra ll I need help fast plz anyone?
Answer:
the answer is A.
Step-by-step explanation:
If 20% of x is y, and 30% of y is z, then what percent of x is z?
Your answer is 6% of x.
We can write the given information as equations to find the answer:
Another way to write "20% of x" is to write 0.2x, so therefore 0.2x = y
You can also write "30% of y" as 0.3y, so 0.3y = z
Now we can substitute in the first equation to the second equation, as we know what y equals in terms of x:
0.3(0.2x) = z
Multiplying out we get:
0.06x = z, and 0.06 as a percentage is 6%
I hope this helps!
Erin is considering joining one of 2 swim clubs. The Gators Swim Club has no registration fee, but charges $105 per month. The Tidal Wave Swim Club charges members $80 per month plus a one-time registration fee of $375. For how many months is Gators the cheaper option? Use system of equations and define variables
Answer:
14 months
Step-by-step explanation:
Given
Gator's = $105 monthly charges
Tidal Wave = $375 registration fee + $80 monthly charged
Required
Determine for how many months Gators is cheaper
Let the number of months be x;
Represent the given data, algebraically.
For Gators: 105x
For Tidal Wave: 375 + 80x
Represent the above as a n inequality
Since Gators has to be cheaper; we have
[tex]105x < 375 + 80x[/tex]
Collect Like Terms
[tex]105x - 80x < 375[/tex]
[tex]25x < 375[/tex]
Divide both sides by 25
[tex]x < 15[/tex]
This implies that Gator's will be cheaper for months less than 15
Hence, the number of months is 14
Explain the difference between congruence and equality. Use an example. GIVING BRAINLIEST!!!!!!!!
Answer:
Congruence is a relationship of shapes and sizes, such as segments, triangles, geometrical figures, while equality is a relationship of sizes, such as lengths, widths, heights.
Congruence deals with objects while equality deals with numbers. You wont say that two shapes are equal or two numbers are congruent.
Step-by-step explanation:
The acceleration of an object due to gravity is 32 feet per second. What is acceleration due to gravity in inches per second?
Answer:
384 inches per second.
Step-by-step explanation:
We are given that the acceleration of an object due to gravity is 32 feet per second.
And we want to find the acceleration in inches per second.
The acceleration can be represented as a ratio of 32 feet : second. This can be written as a fraction:
[tex]\displaystyle \frac{32\text{ feet}}{\text{second}}[/tex]
Use dimensional analysis. It is known that there is 12 inches in a feet. So, multiply by 12in/feet:
[tex]\displaystyle = \frac{32\text{ feet}}{\text{second}}\cdot\frac{12\text{ inches}}{\text{feet}}[/tex]
Cancel like units:
[tex]\displaystyle =\frac{32\cdot 12\text{ inches}}{\text{second}}[/tex]
Multiply:
[tex]\displaystyle =\frac{384\text{ inches}}{\text{second}}[/tex]
In conclusion, our answer is 384 inches per second.
7-(5t - 13)= -12 need help!!!
Answer:
t = 32/5
Step-by-step explanation:
7 - (5t - 13) = -12
7 - (5t - (-13) = -12
7 - 5t + 13 = -12
-5t = -12 - 13 - 7
-5t = -32
t = -32 / -5
t = 32/5