Answers
Answer:
[tex]\frac{35(1 + 35)}{2}[/tex]
Step-by-step explanation:
Given:
The attached
Required
Find the equivalent expression
The interpretation of is to add the sequence:
n = 1,2,3,......35
This can be done using the following formula (Sum of n terms of an AP)
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex]
Where n is the number of terms from 1 to 35; [tex]n = 35[/tex]
T1 is the first term; [tex]T_1 = 1[/tex]
Tn is the last term; [tex]T_n = 35[/tex]
[tex]S_n = \frac{n}{2}(T_1 + T_n)[/tex] becomes
[tex]S_n = \frac{35}{2}(1 + 35)[/tex]
[tex]S_n = \frac{35(1 + 35)}{2}[/tex]
From the list of given options;
Option A is correct
[tex]\frac{35(1 + 35)}{2}[/tex]
Related Questions
Which equation represents the vertical asymptote of the graph? a curve asymptotic to y equals 0 from negative x to negative y near x equals 12. A curve asymptotic to y equals 0 from positive x to positive y near x equals 12. x = 0 y = 0 x = 12 y = 12
Answers
Answer:
The correct option is x = 12
Step-by-step explanation:
An asymptote of a function is a line to to which the function converges to as it tends to infinity such that the function gets infinitesimally close to its asymptote but the function will not reach or cross its asymptote. That is the separating distance between the function and the asymptote tends to zero as either the x or y coordinates, or both the x and y coordinates tend to infinity.
A vertical aymptote, is one parallel to the y-axis and it is given by the value of the x-coordinate where it occurs
In the graph of the question, the vertical asymptote occurs at x = 12 and it is the line x = 12.
From the given graph, it can be said that the vertical asymptote will be formed at x=12. Option C is correct.
The given curve represents a function which is defined for all value fo x except 12.
The following information can be extracted from the graph of the function;
The function is defined for all values of x except 12.The function has a horizontal asymptote at y=0.The function forms a vertical asymptote at x=12. The curve approaches negative infinity from the left of 12 and approaches positive infinity from right of 12.Based on the above conclusions, it can be said that the vertical asymptote will be formed at x=12. Option C is correct.
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how would you solve this problem?
Answers
Answer:
a) 6x²/2x³-4
b) [tex]2ln (2x^3-4)+ C[/tex]
Step-by-step explanation:
a) Given the ln(2x³-4). We will use the chain rule in differentiating the function
If y = ln(2x³-4);
u = 2x³-4; du/dx = 3(2)x³⁻¹
du/dx = 6x²
y = ln u; dy/du = 1/u
According to chain rule, dy/dx = dy/dy*du/dx
dy/dx = 1/u * 6x²
dy/dx = 1/2x³-4 * 6x²
dy/dx = 6x²/2x³-4
Hence, the derivative of the given function is 6x²/2x³-4
b) Given an integral function [tex]\int\limits {\frac{12x^2}{2x^3-4} } \, dx[/tex], the integral problem can be solved using integration by substitution method as shown below;
From the question, let y = 2x³-4... 1, dy/dx = 6x²
dx = dy/6x² ... 2
Substituting equation 1 and 2 into the question given;
[tex]\int\limits {\frac{12x^2}{y} } \,\frac{dy}{6x^2} \\\\= \int\limits {\frac{2dy}{y} } \\\\= 2 \int\limits {\frac{dy}{y} }\\\\= 2lny + C\\substituting\ y = 2x^3-4\ into\ the \ resulting\ function\\\\= 2ln (2x^3-4)+ C[/tex]
ASAP!! can someone help solve any of these? whoever answers the most gets brainliest, i underlined the questions
Answers
Answer:
can u please type out the photo is too dark to see the questions
Step-by-step explanation:
Please help with step by step. Thank you.
Answers
Answer:
A) 90 degrees
B) 110 degrees
C) 78.5 in. sq.
D) 15.3 in. sq.
Step-by-step explanation:
A) 90 degrees by the two-tangent theorem
B) 360-90-90-70=110
C) A=pi r-squared
A=3.14x5x5
A=78.5
D) 70/360=0.1944
78.5x0.1944=15.3
rest text yeah cry GC Ci
Answers
What do you mean?? .-.
Emily has driven 600 miles so far on her way to the beach. If her total trip will be 850 miles‚ about what percentage of the drive does she have left to complete? a) 15% b) 29% c) 40% d) 73%
Answers
Answer:
B) 29%
Step-by-step explanation:
First, we subtract 600 from 850 to get the distance she has left. 850 - 600 = 250. Next, we take 250 and divide it by 850 to get the decimal which is 0.294117647. We can round this answer to 0.29 and convert this answer to a percentage which is 29%.
Answer:
B. 29%
Step-by-step explanation:
Percentages can be found by dividing the part by the whole, then multiplying by 100.
(part/whole) * 100
We have to find the percentage of the drive she has left.
Therefore, the part is the miles she has left and the whole is the total trip.
(miles left/total trip) * 100
First, we need to find how many miles she has left. We must subtract the miles she has driven from the total trip.
total - miles driven
She has 850 total miles and has driven 600 miles.
850-600
250
She has 250 miles left.
Now we know the miles she has left.
(miles left/total trip) * 100
miles left = 250
total trip= 850
(250/850) * 100
Solve inside the parentheses first. Divide 250 by 800.
(0.29411765)*100
Multiply
29.411765
Round to the nearest whole number. The 4 in the tenth place tells us to leave the whole number as is.
29
Therefore, she has about 29% of her trip left.
Question 4 of 10
What do you know to be true about the values of p and q?
po
q"
60"
50"
30"
80°
A. p= 9
B. p< 9
C. p> 9
D. Can't be determined
Answers
Answer:
p > q
Step-by-step explanation:
We khow that the sum of a triangle's angles is 180°
■■■■■■■■■■■■■■■■■■■■■■■■■■
Let's start with the triangle containing p
● p+60+50 = 180
● p+110 = 180
● p = 180-110
● p= 90°
So p is a right angle
□□□□□□□□□□□□□□□□□□
The second triangle
● q+ 80+30 = 180
● q+ 110 = 180
● q = 180-110
● q = 70°
Then q is also a right triangle
■■■■■■■■■■■■■■■■■■■■■■■■■
We can deduce that p > q
Sam purchased 3 1/4 pounds of cheese. He used half of the purchased cheese for a casserole and 1/4 pound for sandwiches. Express as a mixed number the number of the number of pounds of cheese he has left.
Answers
Answer:
1 3/8 lbs.
Step-by-step explanation:
3 1/4 x 1/2 = 1 5/8
1 5/8-1/4=
1 5/8-2/8=
1 3/8
What is the surface area of this cone?
Use a ã 3.14 and round your answer to the nearest hundredth.
6 m
4 m
square meters
Answers
Answer:
52.28 sq m
Step-by-step explanation:
SA=pi r(r+ the square root of h-squared and r-squared)
SA=3.14x2(2+the square root of 36 and 4)
SA=3.14x2(8.32)
SA=52.28 sq m
The Surface area of the given cone is 50.24 meter square
What is Cone?A cone is a three-dimensional geometric shape that tapers smoothly from a flat base to a point called the or vertex.
What is Surface area?The surface area of a solid object is a measure of the total area that the surface of the object occupies.
Given,
Slant height l = 6 meter
Radius of the base r = [tex]\frac{4}{2} =2[/tex] meter
Surface area of the Cone = [tex]\pi rl+\pi r^{2}[/tex]
=[tex]\pi (2)(6)+\pi (2^{2} )[/tex]
=50.24 meter square
Hence, the surface area of the given cone is 50.24 meter square
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Identify the types of number
Answers
Answer:
1 surds
2 fraction
3 decimal
4 negative
5 positive
The tee for the sixth hole on a golf course is 305 yards from the tee. On that hole, Marsha hooked her ball to the left, as sketched below. Find the distance between Marsha’s ball and the hole to the nearest tenth of a yard.
Answers
Answer:
The answer is "101.37 yd"
Step-by-step explanation:
In the given question an attachment file is missing. so, we attached the file and calculates its value:
Use formula:
[tex]c^2 = a^2 + b^2 - 2\times a \times b\times \cos C[/tex]
In the above-given equation we assume c is the third side:
[tex]c^2 = 305^2 + 255^2 - 2*305*255*cos17\\c^2= 93,025+65,025-155,550(0.95)\\c^2= 158,050-147,772.5\\c^2= 10,277.5[/tex]
c = 101.37 yd
Five test scores have a mean (average score) of 90, a median (middle score) of 91 and a mode (most frequent score) of 94. Find the sum of the two lowest test scores.
Answers
Answer:
171
Step-by-step explanation:
If five test scores have a mean of 90, then the total 5x90=450. We already have the middle score (91) and the two top scores (94 and 94). So the equation is 450-91-94-94=171
Based on the graph below, what is a reasonable estimate for the y value when x is -4?
Answers
Answer: i think the answer is 1.5
Step-by-step explanation:
A rectangle is 1 inch longer than it is wide. Its diagonal is 5 inches. What's the width of the rectangle?
Answers
Answer:
The width is 4 inches
Step-by-step explanation:
Represent the length and width by L and W respectively. Then L = W + 1.
According to the Pythagorean Theorem, the diagonal length is
D = sqrt( [W]^2 + [W + 1}^2 ) = 5, or [W]^2 + [W + 1}^2 = 25.
Then W^2 + W^2 + 2W + 1 = 25, and 2W^2 + 2W - 24 = 0.
Reducing, we get W^2 + W - 12 = 0, or (W + 4)(W - 4) = 0. Then W - 4 = 0, and W (the width) is 4. Then L = 5.
The width is 4 inches.
calculate the radius and diameter of the circle
Answers
Answer:
radius is 12, diameter is 24
Step-by-step explanation:
it is a 15-12-9 triangle
helppppp idk how to do that?
Answers
Explanation:
360 = POR + OPT + ORT + 44
OPT = ORT = 90 (line TP and TR tangent to the circle)
360 = POR + 90 + 90 + 44
POR = 360 - 224
POR = 136
B). OPTR is a kite because OP = OR and TP = TR
Definition of a kite:
A quadrilateral whose 4 sides can be grouped into two pairs of equal sides that are adjacent to each other.
IV
What is the range of the function on the graph?
5
4+
3+
all real numbers
O all real numbers greater than or equal to 0
all real numbers greater than or equal to 1
all real numbers greater than or equal to 2
2+
1 +
-5 4 -3 -2 -11
1 2 3 4 5 X
h
-27
-37
I
-4
-5
Answers
The monthly profit for a small company that makes long-sleeve T-shirts depends on the price per shirt. If the price is too high, sales will drop. If the price is too low, the revenue brought in may not cover the cost to produce the shirts. After months of data collected, the sales te determines that the monthly profit is approximated by f(p)= -50p^2+1700p-12000, where p is the price per shirt and f(p) is the monthly profit on that price. A) Find the price that generates the maximum profit B) Find the maximum profit C) Find the price(s) that would enable the company to break even.
Answers
Answer:
Below
Step-by-step explanation:
You could just graph the equation for the answers....
Here is algebraic method
for Quadratic Equation - 50p^2 +1700p - 12000
the max profit occurs at p = - b/2a = - 1700 / (2* -50) = 17 dollars
A ) 17 dollars
B) use p =17 in the equation to find profit = 2450 dollars
C) Set the equation = 0 and solve for p
0 = -50p^2+1700p - 12 000
Use Quadratic Formula with a = -50 b = 1700 c = 12000
to find price = 40 dollars
A cylinder with a base diameter of x units has a volume
of x cubic units
Which statements about the cylinder are true? Select
two options
The radius of the cylinder is 2x units.
The area of the cylinder's base is wa? square units.
The area of the cylinder's base is not square units.
The height of the cylinder in 2x umijs
The height of the cylinder is 4x units.
Save and Exit
Next
Submit
C
Answers
Answer:
The height of the cylinder in 2x units
The area of the cylinder's base is not square units.
Step-by-step explanation:
(will mark brainliest if correct) find area and perimeter
Answers
216
Perimeter:
18
Answer:
32.137 cm squared **Answer varies on how you round for step 2**
Step-by-step explanation:
**THIS ONLY WORKS IF DIAMETER IS ALSO 6 CM**
If the diameter is also 6 cm then the triangle would be isosceles .
1. Find the area of the triangle.
Formula: (Base x Height) / 2
= 6X6/2 = 18 cm squared
2. Find area of half-circle.
Formula: (πR^2)/2
= (π X 3^2)/2 = 9π/2 which is about 14.137 cm squared
3. Add the areas.
18 + 14.137 = 32.137 cm squared.
Can someone please help me with this question
Answers
Answer:
54
Step-by-step explanation:
On the graph of an exponential function representing growth what happens to the slope of the graph as X increases
Answers
Answer:
The slope of the graph will increase and get steeper.
Step-by-step explanation:
As x increases in an exponential growth graph, f(x) will have a larger value because the exponent value increases.
So, the graph will become steeper due to a larger slope.
The slope of the graph will increase and get steeper.
What is Slope?A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the
change in y coordinate with respect to the change in x coordinate as,m = Δy/Δx where, m is the slope
Given:
As we know that, all points on an exponential curve are always at a constant distance from one another because the slope of an exponential curve equals the constant rate of expansion.
The graph is not exponential if the slope is not constant.
So, In an exponential growth graph, f(x) will have a greater value as x grows as the exponent grows.
Consequently, a larger slope will cause the graph to grow steeper.
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30 POINTS GEOMETRY QUESTION
Answers
Answer:
2.25
Step-by-step explanation:
x/1 = (9+x)/5
9 + x = 5x
9 = 4x
x = 2.25
Answer:
x = 9/4
Step-by-step explanation:
We know that the triangles are similar
We can use ratios to solve
x x+9
----- = ----------------
1 5
Using cross products
5x = 1(x+9)
5x = x+9
Subtract x
5x-x = x+9-x
4x= 9
Divide by 4
4x/4 = 9/4
x = 9/4
Anna baked
3
33 batches of cookies with
c
cc cookies in each batch. She then ate
8
88 cookies!
How many cookies does Anna have left?
Answers
Answer:
3c-8
Step-by-step explanation:
The surface area of a rectangular prism that has height of 4 inches, width of 9 inches and length of 3 inches = ____________ in2.
Answers
Answer:
150 in^2
Step-by-step explanation:
The ends have the smallest surface area. The total surface area of the ends is thus 2(3 in)(4 in) = 24 in^2
The top and bottom together have the total surface area 2(9 in)(3 in) = 54 in^2.
Finally, the front and back surface areas together are 2(9 in)(4 in) = 72 in^2
Thus, the total surface area is (24 + 54 + 72) in^2 = 150 in^2
Surface area of a rectangular prism is equal to [tex]\boldsymbol{150}[/tex] square inches.
Surface area of a rectangular prismHeight of a rectangular prism [tex]=4[/tex] inches
Width of a rectangular prism [tex]=9[/tex] inches
Length of a rectangular prism [tex]=3[/tex] inches
Surface area of a rectangular prism [tex]=\boldsymbol{2(lw+wh+hl)}[/tex] where [tex]l,w,h[/tex] denote length, width and height of a rectangular prism
Therefore,
Surface area of a rectangular prism [tex]=2\left [ 4(9)+9(3)+3(4)\right ][/tex]
[tex]=2\left ( 36+27+12 \right )\\=150[/tex]
So, surface area is equal to [tex]\boldsymbol{150}[/tex] square inches.
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At Paul Bunyan’s tree farm they sell Fraser firs and blue spruce trees. They plant saplings of these two kinds of trees that are 8 inches in 5 inches tall, respectively. The Fraser firs grow at a constant rate of 12 inches per year, and a blue spruce trees grow at a constant rate of 14 inches per year. After how many years will these trees be at the same height? Express your answer as a common fraction.
Answers
Answer: 3/2
Step-by-step explanation:
Hi, to answer this question we have to write the next expressions::
Height 1= 8 +12 y
Height 2 =5 +14y
Where y = number of years
Since both heights must be the same
Height 1 = height 2
8+12y = 5+14y
solving for y:
8-5 =14y-12y
3 = 2y
3/2 =y
y = 3/2 years
Feel free to ask for more if needed or if you did not understand something.
8 + 12y = 5 + 14y
12y + 8 = 14y + 5
12y + 8 - 8 = 14y + 5 - 8
12y = 14y - 3
12y - 14y = 14y - 3 - 14y
-2y = -3
(-2y)/-2 = -3/-2
y = 3/2
Estimate the solution to the system of equations. You can use the interactive graph below to find the solution.
y=−x+2
y=3x−4
x=
y=
thank you!
Answers
Answer: x= 3/2 and y= 1/2
Step-by-step explanation:
Since both equations are equated to y, you just need to use substitution to create the equation below:
-x+2 = 3x-4
Solve the equation for x:
4x=6
x=6/4=3/2
Plug in x into any one of the given equations to find the value of y:
y=-x+2
y= - (3/2)+2
y= - (3/2)+4/2
y= 1/2
Hope this helps!
The solution to the system of equations will be x= 3/2 and y= 1/2.
What is a system of equations?A finite set of equations for which common solutions are sought is referred to in mathematics as a set of simultaneous equations, often known as a system of equations or an equation system.
An equation is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.
The given equations are y=−x+2 and y=3x−4 to calculate the values of x and y using the substitution method.
Since both equations are equated to y, you just need to use substitution to create the equation below:
-x+2 = 3x-4
Solve the equation for x:
4x =6
x =6/4=3/2
Plug x into any one of the given equations to find the value of y:
y =-x+2
Solve for the value of y.
y = - (3/2)+2
y = - (3/2)+4/2
y = 1/2
Hence, the solution for the equation will be x= 3/2 and y= 1/2.
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15 POINTS!!!!!!!
How is a linear function affected by a horizontal shift?
Answers
Answer:
horizontal shift can affect the linear function, because it is impossible to distinguish which transformation was applied by looking at the resulting graph.
Step-by-step explanation:
a horizontal shift is a movement left to right along the x-axis, and in equation of a function it's change in the value of x before it's multiplied by the slope.
Answer:
I agree with Lambina and added this answer so she could get brainliest
Step-by-step explanation:
compare -5/6 _ -3/7 choose from 1) > 2)
Answers
Answer
1)<2) please put 5 stars
Step-by-step explanation
First you need to find the GCF of the donominators which are 6 and 7. The GCF is 42.
6*x=42. x=7 5*7=35. -35/42 is the first fraction.
7*y=42 y=6 3*6=18. -18/42 is the second fraction.
-35/42 would be bigger but since it is negative, it is smaller.
Answer:
1)<2)
Step-by-step explanation:
Tanya is considering obtaining a loan. Which benefit will Tanya receive if she makes a down payment when she obtains the loan?
A. higher finance charge
B. higher interest rate
C. higher principal amount
D.lower penalties on late payments
O E.
lower principal amount
Answers
Answer:
E. lower principal amount
Step-by-step explanation:
We can use an example to show how this works:
You want to buy a car and it costs $20,000. The loan lasts 5 years (60 monthly payments) and the interest rate is 10%.
If you do not make any down payment, your initial principal will be $20,000, and your monthly payment will be $424.94, your total payments = $25,496.45 and the total interests = $5,496.45.
Instead, if you make a 20% down payment, your initial principal = $16,000, and your monthly payment will be $339.95, your total payments = $20,397.16 and the total interests = $4,397.16.
Answer:
E. lower principal amount