How many terms are there in a geometric series if the first term is 7, the common ratio is 2, and the sum of the series is 105?
Hint: (image attached below) r ≠ 1, where a1 is the first term and r is the common ratio.
OPTIONS
A) n = 3
B) n = 4
C) n = 5
D) n = 6
Answers
105 = 7. (1 - 2^n) / 1-2
105*-1 = 7 (1 - 2^n)
1 - 2^n = -105/7 = - 15
2^n = 16
n = 4 answer
Answer:
the answer would be B. N=4
Related Questions
What is the contrapositive of the conditional statement? If two variables are directly proportional, then their graph is a linear function.
Answers
Answer:
(D) Last option
if the graph of two variables is not a linear function, then the two variables are not directly proportional.
Step-by-step explanation:
The required contrapositive of the given statement is, "If the graph is not a linear function, then the two variables are not directly proportional."
What is the contrapositive of the conditional statement?The contrapositive of a conditional statement is a statement that is formed by negating both the hypothesis and the conclusion of the original statement and then reversing the order of the resulting statement.
Here,
The contrapositive of the conditional statement is:
"If the graph is not a linear function, then the two variables are not directly proportional."
Note that the contrapositive of a conditional statement has the same truth value as the original statement. In other words, if the original statement is true, then its contrapositive is also true, and if the original statement is false, then its contrapositive is also false.
Learn more about the contrapositive of the conditional statement here;
https://brainly.com/question/2141743
#SPJ7
Would a dot plot or a histogram best represent the data presented here? Why?
Answers
The measure of angle 1 equals 59 degrees, and the measure of angle 6 equals 72 degrees. What is the measure of angle 8?
Answers
180-59-72 = 49
(If the sum of the interior angles is 180)
Jennifer ran 4/5 of a mile on Monday. She ran 1 2/3 times as far on Tuesday. How far did she run on Tuesday?
1 4/15 miles
1 1/3 miles
2 7/15 miles
3 1/3 miles
Answers
Jennifer ran [tex]1\frac{1}{3}[/tex] miles on Tuesday.
What is multiplication?Multiplication is when you take one number and add it together a number of times. Example: 5 multiplied by 4 = 5 + 5 + 5 + 5 = 20.
Given that, Jennifer ran 4/5 of a mile on Monday. She ran [tex]1\frac{2}{3}[/tex] times as far on Tuesday, we need to find how far did she run on Tuesday,
Since, she ran 4/5 times mile,
And, on Tuesday she ran [tex]1\frac{2}{3}[/tex] times as far Monday,
On Tuesday she will run = 4/5 × [tex]1\frac{2}{3}[/tex]
= 4/5 × 5/3
= 4/3
= [tex]1\frac{1}{3}[/tex]
Hence, Jennifer ran [tex]1\frac{1}{3}[/tex] miles on Tuesday.
Learn more about multiplication, click;
https://brainly.com/question/5992872
#SPJ6
What is the equation of a line that passes through the point (9, −3) and is parallel to the line whose equation is 2x−3y=6 ?
Enter your answer in the box
Answers
-3y = -2x + 6
y = 2/3x - 2....the slope here is 2/3. A parallel line will have the same slope
y = mx + b
slope(m) = 2/3
(9,-3)...x = 9 and y = -3
now we sub and find b, the y int
-3 = 2/3(9) + b
-3 = 6 + b
-3 - 6 = b
-9 = b
so ur parallel equation is : y = 2/3x - 9 <== or 2x -3y = 27
The equation of the line, in slope-intercept form, that is parallel to 2x - 3y = 6 and passes through (9, -3) is: [tex]\mathbf{y = \frac{2}{3}x - 9}[/tex]
Given:
Points the line passes through, (9, -3)
The equation of the line it is parallel to: 2x - 3y = 6
Note:
Parallel lines have the same slope valueEquation of a line in slope-intercept form is: y = mx + b. (m is slope; b is y-intercept)Point-slope form is; y - b = m(x - a)First, rewrite 2x - 3y = 6 in slope-intercept form to determine its slope.
[tex]2x - 3y = 6\\\\-3y = -2x + 6\\\\y = \frac{2}{3}x - 2[/tex]
The slope of 2x - 3y = 6 is therefore 2/3.Thus, the slope of the line that passes through (9, -3) is also 2/3.
Write the equation of the line in point-slope form:
Substitute m = 2/3, and (a, b) = (9, -3) into y - b = m(x - a)
Thus:[tex]y - (-3) = \frac{2}{3}(x - 9)\\\\y + 3 = \frac{2}{3}(x - 9)[/tex]
Rewrite in slope-intercept form[tex]y + 3 = \frac{2}{3}(x - 9)\\\\y + 3 = \frac{2}{3}x -\frac{2}{3}(9)\\\\y + 3 = \frac{2}{3}x - 6\\\\y = \frac{2}{3}x - 6 - 3\\\\\mathbf{y = \frac{2}{3}x - 9}[/tex]
Therefore, the equation of the line, in slope-intercept form, that is parallel to 2x - 3y = 6 and passes through (9, -3) is: [tex]\mathbf{y = \frac{2}{3}x - 9}[/tex]
Learn more here:
https://brainly.com/question/11750976
You earned $34,000 and your total tax due was $6,200. what was your average tax rate?
a.8%
b.10%
c.18%
d.20%
Answers
0.1823 * 100 = 18.23 rounds to 18% <=
The proceeds from a saturday car wash are directly proportional to the number of cars washed. the total after 7 cars is $140. how much is raised if 60 cars are washed?
Answers
60*20=$1200
1. The value -2 is a lower bound for the zeros of the function shown below. f(x)=4x^3-12x^2-x+15
True
False
2. Express the polynomial as a product of linear factors. f(x)=2x^3+4x^2-2x-4
A. (x-2)(x+1)(x-1)
B. (x-2)(x-2)(x-1)
C. (x-4)(x+1)(x-1)
D. 2(x+2)(x+1)(x-1)
Answers
It is true that the value -2 is a lower bound for the zeros of the function f(x) = 4x³ - 12x² - x + 15
The polynomial as a product of linear factors is d. 2(x+2)(x+1)(x-1)
How to determine the true statement
From the question, we have the following parameters that can be used in our computation:
f(x) = 4x³ - 12x² - x + 15
Also, we have
x =-2
Calculate f(-2)
f(-2) = 4(-2)³ - 12(-2)² - (-2) + 15
f(-2) = 4 * -8 - 12 * 4 + 2 + 15
f(-2) = -32 - 48 + 2 + 15
f(-2) = -63
The above value is negative
This means that -2 is a lower bound for the zeros of the function.
Expressing the polynomial as a product of linear factors.
Here, we have
f(x) = 2x³ + 4x² - 2x - 4
Factorize in 2's
So, we have
f(x) = 2x²(x + 2) - 2(x + 2)
This can be expressed as
f(x) = (2x² - 2)(x + 2)
Factor out 2
f(x) = 2(x² - 1)(x + 2)
Express as difference of two squares
f(x) = 2(x - 1)(x + 1)(x + 2)
Hence, the polynomial as a product of linear factors is d. 2(x+2)(x+1)(x-1)
At the candy store, Sophie filled a bag with 2 2/3 kilograms of candy. 1/4 of the weight of the candy was from chocolate covered pretzels. How much did the chocolate covered pretzels in Sophie’s bag weigh?
Answers
__________________________________________
Explanation:
__________________________________________
Basically, we can reduce the question to:
__________________________________________
What is " ¼" of "2 ⅔ kg" ?
_______________________________
→ (¼ * 2 ⅔) kg ; simplify the amount in "parentheses" ; & keep the units of "kg" (kilograms) ;
______________________________________________
Write " 2 ⅔ " as an "improper fraction" ;
→ To do so, multiply the "3" in the "denominator" (from the fraction, " ⅔ ") ;
by the "2" (from the whole number).
→ 3 * 2 = 6 .
_________________________________________
→ Then, take this value; in our case, "6" ; and the number "2" (from the "2" in the "numerator" (from the fraction portion, " ⅔ ").
→ 6 + 2 = 8 .
__________________________________________
→ Then, take this value, and write is as the "numerator" over a "new fraction" ; this "new fraction" is the: "improper fraction" . The "denominator" of this "new fraction" (i.e. "improper fraction") ; is the number from the "denominator" of the fraction portion of our [originally written "mixed number" ; which in our case is: "3" (from the fraction portion, " ⅔ ") .
___________________________________________
→ So, our mixed number, " 2 ⅔ " , can be written in the "improper fraction form" ; which is: " ⁸/₃ " .
___________________________________________
→ Put simply: " 2 ⅔ = [ (3*2) + 2 ] / 3 = (6 + 2) / 3 = 8/3 ; or, " ⁸/₃ " .
___________________________________________
→ We have: "(¼ * 2 ⅔) kg " .
→ Replace the: " 2 ⅔ " value with: " ⁸/₃ " ; to more easily simplify the expression in "parentheses" ; & to more easily solve the problem ;
__________________________________________________
→ "(¼ * 2 ⅔) = [tex] \frac{1}{4} [/tex]*[tex] \frac{8}{3} [/tex] " ;
= ? ;
___________________________________________________
→ We have: " [tex] \frac{1}{4} [/tex]*[tex] \frac{8}{3} [/tex] " ;
→ The "4" can be 'canceled out' to a "1" ;
and the "8" can be 'canceled out', and changed to a "2" ;
→ since: "(8÷4=2)" ; and since: "(4÷4=1)" .
___________________________________________________
So now; we have: " [tex] \frac{1}{1} [/tex] * [tex] \frac{2}{3} [/tex] " ;
___________________________________________________
→ The " [tex] \frac{1}{1} [/tex] " can be eliminated;
→ since: "(1÷1=1)" ;
→ {Note that any value, divided by "1", is equal that same value ;
& that "any non-zero value", divided by "that same value", is equal to "1" .
______________________________________________________
→ As such: " [tex] \frac{1}{1} [/tex] " = {1÷1} = 1 ;
& this value, which is "1", multiplied by [the other expression], will be equal to that other expression;
since:
______________________________________________________
→ [the other expression, which is a non-zero value] , multiplied by "1", is equal to [the SAME other expression, which is a non-zero value].
______________________________________________________
→ As such, we can completely eliminate the: " [tex] \frac{1}{1} [/tex] " ;
and we are left with: " ⅔ " . The units are "kg" .
So; the answer is: " ⅔ kg" ;
Note: " ⅔ " = 2÷3 = 0.666666666666667 ;
____________________________________________
So; the answer is: " ⅔ kg" ; or, write as: 0.6667 kg .
____________________________________________
Please help me with this problem!
y =
37
39
51
Answers
y = arctan(8/10)
y = 38.65
y = 39
Answer:
Option (b) is correct.
The measure of angle y is 39°
Step-by-step explanation:
Given : A right angled triangle with some measurements.
We have to find the value of y.
Consider the given triangle,
Using trigonometric ratios,
We know tangent is the ratio of perpendicular to its base.
Mathematically written as
[tex]\tan\theta=\frac{Perpendicular}{base}[/tex]
So, for given triangle, [tex]\theta=y[/tex]
and for y, perpendicular is 8 and base is 10
Substitue, we have,
[tex]\tan y=\frac{8}{10}[/tex]
Simplify, we have,
[tex]\tan y=\frac{4}{5}[/tex]
Taking inverse of tan both side, we have,
[tex]\tan^{-1}(\tan y)=\tan^{-1}(\frac{4}{5})[/tex]
[tex]y=\tan^{-1}(\frac{8}{10})[/tex]
Simplify , we have,
[tex]y=38.65^{\circ}[/tex]
Thus, the measure of angle y is 39°
I need help.....
1. A triangle has vertices at A(−7, 6), B(4, 9), C(−2, − 3). What are the coordinates of each vertex if the triangle is translated 4 units right and 6 units down?
1. A′(−3, 12), B′(8, 15), C ′(2, 3)
2. A′(−11, 0), B′(0, 3), C ′(−6, − 9)
3. A′(−3, 0), B′(8, 3), C ′(2, − 9)
4. A′(−11, 12), B′(0, 15), C ′(−6, 3)
Answers
A(-7,6) so adding 4 to the x would give you -3, and subtracting 6 to the y would give you 0. -> (-3,0)
B(4,9), add 4 to the x would give you 8, subtract 6 would give you 3. -> (8,3)
C(-2,-3), add 4 to the x would give you 2, subtract 6 would give -9. -> (2,-9)
Expression that dissolves an answer from a particular experience that can only be solved by an amount given to the perimeter. Please tell me in a good form from a perspective that can only be solved for once person
Answers
Hope this helps
A rate that describes how much smaller or larger the scale drawing is than then real object
Answers
The scale factor is a ratio that describes the relationship between the dimensions of a scale drawing and the real object that it represents. A larger scale factor indicates a greater level of detail in the drawing, while a smaller scale factor depicts less detail and a larger area.
Explanation:The rate that describes how much smaller or larger the scale drawing is than the real object is known as the scale factor. A scale factor is a ratio that compares the dimensions of the actual object to the dimensions of a scale drawing or model. For example, a scale factor may be written as 1/200, meaning that the real object is 200 times larger than the scale drawing.
Scale can also be described using terms such as 'small' or 'large' scale. These terms relate to the level of detail a map shows; a large-scale map, with a representative fraction of 1:1,000, shows more detail and less area whereas a small-scale map, with a representative fraction of 1:1,000,000, shows less detail and more area.
Understanding these concepts is essential when interpreting maps and drawings as they communicate the level of zoom and detail. Remember, scale refers to a ratio and not the physical size of the map or drawing itself.
a square has an area of 25cm2 what is the length of each side?
Answers
√25 is equal to 5
The length of each side of the given square would be 5 cm if square has an area of 25cm².
What are Arithmetic operations?Arithmetic operations can also be specified by subtracting, dividing, and multiplying built-in functions. The operator that performs the arithmetic operation is called the arithmetic operator.
What is a square?A square is defined as a polygon that has four sides and is a closed, two-dimensional (2D) object. A square has equal and parallel sides on all four sides.
The area of a square is equal to the squared of sides or the multiplication of two sides.
We have been given a square has an area of 25 cm²
The length of one side = √( the area of a square)
The length of one side = √(25)
The length of one side = 5 cm
Therefore, the length of each side of the given square would be 5 cm.
Learn more about the area of the square here:
brainly.com/question/1561162
#SPJ2
Wallace received a 28 percent discount on an item priced at $275. What is the total price that he paid for it? cost after discount = price × (1 – discount percentage)
Answers
$275*(1-28%)
275*0.72
=198
(Basically just remember if you want to find the cost of something after discount just minus it off 100% , for example, 60% discount then times the original price to 0.4 to find the cost after the discount)
Hope this helps!
Answer: $198
Step-by-step explanation:
Given: The discount percentage : 28 % =0.28
The price of item = $275
The given formula for total cost of item after discount :
[tex]\text{Cost after discount = Price *(1 – Discount percentage)}[/tex]
Substitute the value of price =$275 and discount percent = 0.28 in the above formula , we get
[tex]\text{Cost after discount =}275\times(1-0.28)\\\\\Rightarrow\ \text{Cost after discount =}275\times0.72\\\\\Rightarrow\ \text{Cost after discount =}\$192[/tex]
Hence, he paid the total price of $198 for it.
−px+r=−8x−2
solve for X
Answers
-8x=2
8x=-2
x=-1/4
Answer:
[tex]\frac{-2-r}{-p+8}[/tex].
Step-by-step explanation:
-px+r= -8x-2
-px+8x = -2-r
x(-p+8) = -2-r
x = [tex]\frac{-2-r}{-p+8}[/tex].
A number cube is rolled 30 times, and a number less than five comes up 20 times. What is the experimental probability that a number GREATER than four is rolled?
A.1/20
B.2/3
C.1/10
D.1/3
Answers
Answer:
The answer is 2/3. Probably to late but i thought i might as well share!
Hope it helps haha!
Brainliest?
A baby elephant weighs 250 lb,
What is the elephant's weight in tons and kilograms (1 kg= 2.2 lb.)? Round to the thousandths place.
Answers
and Kg would be 113.636
Which statement best explains how Lizabeth develops the theme in "Marigolds" that beauty can be appreciated even in the worst circumstances?
Answers
Answer:
Lizabeth remembers the poverty of her childhood hometown but also the marigolds in Miss Lottie's yard.
Explanation:
The short story "Marigolds" by Eugenia Collier is a story of a little girl's childhood experience. In the story, Lizabeth talks of how her community is impoverished, "—the brown, crumbly dust of late summer—arid, sterile dust that gets into the eyes and makes them water, gets into the throat and between the toes of bare brown feet". But despite the background image of poverty all around her, she could also remember "a brilliant splash of sunny yellow against the dust—Miss Lottie’s marigolds". Through her remembering of the marigolds amidst the poverty of her childhood hometown, Lizabeth develops the theme of beauty appreciated even in the worse circumstances.
In the figure, BC and AD are line segments. What is the sum of x and y?
Answers
x = 54
when added, they equal (62 + 54) = 116
Answer:
The correct option is 2.
Step-by-step explanation:
Given information: BC and AD are line segments.
According to the angle sum property, the sum of interior angles of a triangle is 180°.
In triangle DOC,
[tex]\angle C+\angle COD+\angle D=180^{\circ}[/tex]
[tex]y+64^{\circ}+54^{\circ}=180^{\circ}[/tex]
[tex]y+118^{\circ}=180^{\circ}[/tex]
[tex]y=180^{\circ}-118^{\circ}[/tex]
[tex]y=62^{\circ}[/tex]
The value of y is 62°.
If two lines intersect each other then vertical opposite angles are equal.
[tex]\angle COD=\angle AOB=64^{\circ}[/tex]
In triangle AOB,
[tex]\angle A+\angle AOB+\angle B=180^{\circ}[/tex]
[tex]x+64^{\circ}+62^{\circ}=180^{\circ}[/tex]
[tex]x+126^{\circ}=180^{\circ}[/tex]
[tex]x=180^{\circ}-126^{\circ}[/tex]
[tex]x=54^{\circ}[/tex]
The value of x is 54°.
The sum of x and y is
[tex]54^{\circ}+62^{\circ}=116^{\circ}[/tex]
The sum of x and y is 116°. Therefore the correct option is 2.
Write an equation of the line with the given slope, m, and y-intercept left parenthesis 0 comma b right parenthesis(0,b).
Answers
Point = (0,b)
Use the point-slope formula.
y - y_1 = m(x - x_1)
y - b = m(x - 0)
y - b = mx - 0
y = mx - 0 + b
y = mx + b
Done!
Jordan was driving down a road and after 4 hours he had traveled 82 miles. At this speed, how many miles could Jordan travel in 14 hours?
Answers
4 hours is to 82 miles as 14 hours is to x miles
4/82 = 14/x
Cross multiply to get
4x = 14 * 82
4x = 1148
x = 287
287 miles
What are families of functions and how are they useful?
Answers
Alternatively, we can define a family by a formula that involves the argument and one or more parameters. For each specific value of the parameter(s) we'll then get one function in the family.
hope this is helpfull....
NOT MY ANSWER>>>>>>
6a - 10 = 3a + 17 please explain how you got your answer
Answers
Put similar things together
First step is to subtract 3a from both sides
3a - 10 = 17
Second step is to add 10 to both sides
3a = 27
Third step is to divide both sides by 3
a = 9
That's the answer.
To solve the equation 6a - 10 = 3a + 17, we first move all 'a' terms to one side and constants to the other, then simplify and solve for 'a', resulting in a = 9.
The student has asked to solve the equation 6a - 10 = 3a + 17. To find the value of 'a', we need to consolidate all the 'a' terms on one side and the constants on the other side. Here's the solution step-by-step:
Subtract '3a' from both sides of the equation to get '6a - 3a - 10 = 17'.
Simplify the left side to get '3a - 10 = 17'.
Add '10' to both sides to isolate the 'a' term and get '3a = 17 + 10'.
Simplify the right side to get '3a = 27'.
Divide both sides by '3' to solve for 'a', getting 'a = 27 / 3'.
Finally, 'a = 9'.
The correct answer is a = 9.
Point V lies between points U and W on UW.
If UW = 9x – 9, what is UW in units?
5 units
6 units
30 units
36 units
Answers
hope this helps :)))))
Answer: The correct option is (D) 36 units.
Step-by-step explanation: Given that point V lies between points U and W on UW, where
[tex]UV=2x-4,~~VW=4x+10~~~\textup{and}~~~UW=9x-9.[/tex]
We are to find the length of UW in units.
Since point V lies on the line segment UW, so we must have
[tex]UV+VW=UW\\\\\Rightarrow (2x-4)+(4x+10)=9x-9\\\\\Rightarrow 6x+6=9x-9\\\\\Rightarrow 9x-6x=6+9\\\\\Rightarrow 3x=15\\\\\Rightarrow x=5.[/tex]
Therefore, the length of UW is
[tex]UW=9x-9=9\times5-9=45-9=36~\textup{units}.[/tex]
Thus, the length of UW is 36 units.
Option (D) is correct.
What is 7,433,654 Rounded to the nearest 100,000
Answers
33,654 does not round up because the highest valued digit is not 5 or higher.
1. A company designs a box to package their product. The material used costs $0.112 per square foot. The box consists of a square bottom and isosceles triangles making up the sides. A net of the box is shown below.
Answers
Word problem for 24- ( 6+3)
Answers
24-9=
15 is your answer. Just simply break the math problem down. It’ll help
I hope this helped!
I don’t understand what and how to solve these
Answers
Multiply or divide as indicated. Simplify your answer, if possible. (Do not express answer in exponential form.) 10/ 10^-2
Answers
Answer:
The simplified form of the provided expression is 1000.
Step-by-step explanation:
Consider the provided expression.
[tex]\frac{10}{10^{-2}}[/tex]
Now, use the property of exponent: [tex]\frac{a^m}{a^n}=a^{m-n}[/tex]
Use the above property to solve the provided expression.
[tex]\frac{10}{10^{-2}}[/tex]
[tex]10^{1-(-2)}[/tex]
[tex]10^{1+2}[/tex]
[tex]10^3[/tex]
[tex]1000[/tex]
Thus, the simplified form of the provided expression is 1000.