Step-by-step explanation:
You can immediately notice that the sum consists of the sum of two infinitely decreasing geometric progressions[tex]\displaystyle \large \boldsymbol {} \underline1+\underline 2+\underline {\frac{1}{2}} -\frac{2}{3} +\underline {\frac{1}{4}} -\frac{2}{9} +\underline{\frac{1}{8}} -\frac{2}{27} + \ldots = \\\\\\ \underbrace{\bigg(1+2+\frac{1}{2} +\frac{1}{4} \ldots \bigg)}_{\rm \big S_2}-2 \underbrace{\bigg(\frac{1}{3}+\frac{1}{9} +\frac{1}{27} \ldots \bigg)}_{\big S_3}[/tex] The formula for an infinitely decreasing geometric progression:[tex]\displaystyle \large \boldsymbol { \rm S=\frac{b_1}{1-q} \ \ ; \ \ |q|<1}[/tex] Where : q -denominatorb₁ -is the first member of the progressionThen:Denote the sum of the numbers in the first bracket for S₂ ; and in the second bracket for S₃[tex]\displaystyle \large \boldsymbol {} \rm S_2=\frac{2}{1-\dfrac{1}{2} } =\frac{2}{\dfrac{1}{2} } =4 \\\\\\\ S_3=\frac{\dfrac{1}{3} }{1-\dfrac{1}{3} } = \dfrac{1}{\dfrac{3}{\dfrac{2}{3} } } =\frac{1}{2}[/tex] Substitute the values : [tex]\large \boldsymbol {} \rm S_2-2S_3=4- 2\cdot \dfrac{1}{2} =\boxed{3}[/tex]answer to this math qustion
(52−24)⋅12÷(30+2⋅3)
Answer:
9[tex]\frac{1}{3}[/tex]
Step-by-step explanation:
(52−24)⋅12 ÷ (30+2⋅3) = 28⋅12 ÷ (30+6)
= 336 ÷ 36
= 9.333333333 = 9[tex]\frac{1}{3}[/tex]
Answer:
9 1/3
Step-by-step explanation:
(52−24)⋅12÷(30+2⋅3)
(28) * 12 / 36
28 * 1/3 = 9 1/3
Mary spent three fourths of her allowance at the mall. One half of that was spent on snacks. If Mary’s allowance was thirty dollars, how much did she spend on snacks?
Answer:
$11.25
Step-by-step explanation:
Divide 30 by 4
30/4=7.50
multiply by 3
7.5*3=22.50
22.50 is 3/4 of her allowance
divide that by half to get how much she spent on snacks.
22.50/2=11.25
Hope this helps!
Varian ride a horse. Gelbin rides a rocket-powered robo-ostrich. Gelbin's ostrich ran 4,828 meters (m) which is 2 times as far as Varian's horse
how far did Varian horse run
Determine the cost of the two services will be the same amount and what the price will be? The struts family is deciding between two lawn care services green lawn charges a $49 startup fee plus $29 per month the yard guards charges a $25 start up fee plus $37 per month
Answer:
$136
green lawn
simplify 13-2×8+4-(-20)
Answer:
13 - 2 × 8 + 4 - (-20) = 21
Step-by-step explanation:
I used a calculator, let me know if im incorrect
0.9/0.5 = a/10 Plz help
Answer:
18
Step-by-step explanation:
10/0.5 = 20
20 * 0.9 = 18
Answer:
a = 18
Step-by-step explanation:
Step 1: Cross-multiply.
[tex]0.5 * a = 10*0.9[/tex] [tex]0.5a =9[/tex]Step 2: Divide both sides by 0.5
[tex]\frac{0.5a}{0.5} =\frac{9}{0.5}[/tex] [tex]a = \frac{90}{5}[/tex] [tex]a = 18[/tex]Step 3: Check if solution is correct.
[tex]\frac{0.9}{0.5}=\frac{18}{10}[/tex] [tex]\frac{9}{5} =\frac{18}{10}[/tex] [tex]\frac{18/2}{10/2} =\frac{9}{5}[/tex][tex]\frac{9}{5} =\frac{9}{5}[/tex]Therefore, a = 18.
The relationship between the number of pounds (lb) of beef and the total cost
in dollars is shown in the graph. What is the unit price of beef?
1 lb/$10
$20/2lb
$10/1lb
$1/10lb
Answer:
C
Step-by-step explanation:
I got it right :)
Janet can shovel snow from her driveway in 30 minutes. Tom can do the same job in 40 minutes. How long would it take
Janet and Tom to shovel the driveway if they worked together?
Answer: over 23 mins a little bit 23.157
Step-by-step explanation:
Smart
The process by which information is encoded, stored, and later retrieved is called
a. intellect b. cognition c. memory d. perception
Answer:
Memory is the process(cognitive) in which information is encoded,stored and retrieved.
____× 3 × 4= 24 __=___
Answer:
2×3×4=24
Step-by-step explanation:
2×3=6----> 6×4=24
How can I help you with the last two blanks after the 24?
Answer:
2 x 3 x 4 = 24
24 = 24 True
Step-by-step explanation:
I used a calculator :)
A cube has edge length 11 inches. Just type the number of the answer.
What is the volume?
cubic inches
What is the surface area?
square inches
Answer:
1331³
..
...................
a teacher writes on the borad 3 to 10 which scenario could model this radio
Answer:
D
Step-by-step explanation:
Since the ratio is 3 to 10 it would have to be 3 prizes for every 10 contestants
Each bag of cookies contains x cookies. At the start, Jude has 16 bags of cookies and 5 extra cookies. Elias has 8 bags of cookies and 4 extra cookies. If Elias doubles the number of cookies he has, how many more cookies will he have than Jude?
Answer:
3
Step-by-step explanation:
J = 16 bags + 5
E= 8 bags +4
If E doubles his cookies, he has 16 bags and 8 extra cookies.
They both have the same amount of bags. 8-5= 3 extra
who plays cold wa?r
Can someone plss help me with this!!
QUESTION: How do we communicate to a computer and what to put on a web page?
Answer:
Using the Internet, computers connect and communicate with one another, primarily using the TCP/IP (Transmission Control Protocol / Internet Protocol). Think of TCP/IP as a book of rules, a step-by-step guide that each computer uses to know how to talk to another computer.
The range of an ambulance service is a circular region bounded by the equation x^2 + y^2 = 400. A straight road within the service area is represented by y = 3x + 20. Find the length of the road that lies within the range of the ambulance service (round your answer to the nearest hundredth). Recall that the distance formula is [tex]d=\sqrt{x(x2-x1)^2+(y2-y1)^2[/tex]
The straight road crosses the boundaries of the range of the ambulance service at two points
The length of the road that lies within the range of the ambulance service is approximately 37.95
Reason:
The function that represents the ambulance circular service area is x² + y² = 400
The equation that represents the straight road, y = 3·x + 20
Required:
Length of the road that lies within the range of he ambulance
Solution:
The length of the road is given by the distance between the intersection
points of the road and the ambulance service region as follows;
At the intercepts, we have;
The x, and y-values of the line and the circle are equal, therefore, we have;
At the intercept, y = 3·x + 20, which gives;
x² + y² = 400
x² + (3·x + 20)² = 400
x² + 9·x² + 120·x + 400 = 400
10·x² + 120·x + 400 - 400 = 0
10·x² + 120·x = 0
x² + 12·x = 0
x² + 12·x = x·(x + 12) = 0
x = 0, or -12When x = 0, y = 3×0 + 20 = 20
When x = -12, y = 3×(-12) + 20 = -16
The intersection points of the line and the circle are;
A(0, 20), and B(-12, -16)The length of the segment AB, d, is given as follows;
d = [tex]\sqrt{((-12) - 0)^2 + (-16 - 20)^2} = \sqrt{1440} =12 \cdot \sqrt{10}[/tex]The length of the road that lies within the range of the ambulance service, d, given to the nearest hundredth = 12·√(10) ≈ 37.95
Learn more here:
https://brainly.com/question/23312419
So I need help with this
Answer:
-5/14
Step-by-step explanation:
2/7 times 2 to get the denominator to be 14 since adding and subtracting fractions require the same denominator. 2/7 times 2 = 4/14. -9/14+4/14=-5/14.
make them the same denominator
[tex] \frac{2}{7} \times \frac{2}{2} = \frac{4}{14} [/tex]
[tex] \frac{ - 9}{14} + \frac{4}{14} = \frac{ - 5}{14} [/tex]
In a car park the ratio of black cars to red cars are 3:4 If there are 12 black cars in the car park how many red cars are there?
I need help please.
9514 1404 393
Answer:
a) 191 yards
b) 40 yards
c) 1.5 minutes
Step-by-step explanation:
Given:
ΔPQR is a right triangle with the right angle at Q
PQ = 40 yards; QR = 70 yards
M is the midpoint of PR
jogging rate is 150 yd/min
Find:
a) the perimeter of ΔPQR to the nearest yard
b) QM to the nearest yard
c) the time to jog the path PQMRQP to the nearest tenth minute
Solution:
a) The length of PR can be found from the Pythagorean theorem:
PR² = PQ² +QR²
PR² = 40² +70² = 6500
PR = √6500 ≈ 80.62 . . . . yards
Then the perimeter is ...
perimeter = PQ +QR +PR = 40 +70 +80.62 ≈ 191 yards
__
b) Segment QM divides triangle PQR into two isosceles triangles: PMQ and RMQ. The lengths MP, MQ, and MR are all equal to half the length of PR.
QM = PR/2 = (80.62 yd)/2 = 40.31 yd
QM ≈ 40 yd
__
c) The segments of path PQMRQP can be grouped to simplify the computation of the path length
PQMRQP = PQ +QM +MR +RQ +QP = PQ +(PQ +QR +(QM +MR))
Since QM +MR = PR, the length in the outer parentheses is the perimeter of the triangle. Then the jogger's total path length is ...
PQ + perimeter(ΔPQR) = 40 yd +191 yd = 231 yd
The time it takes to jog that path is ...
time = distance/speed
time = 231 yd/(150 yd/min) = 1.54 min ≈ 1.5 min
It takes about 1.5 minutes.
what is the effect when a number is added or subtracted to the x (in the bracket)of equation of basic parabola?
Determine which of the following equations define a function. For those that do not,
state the reason for your answer.
x +3=0
Ashley and Keely shared some Hershey Kisses in the ratio of 5:2. If Keely had 12 Hershey Kisses, how many did Ashley have?
Answer:
Ashely had 30 kisses! Muah!
Step-by-step explanation:
Ratio of Ashely to Keely is 5 : 2 and we know Keely had 12. Keely represents the 2 in this ratio, and how do we get from 2 to 12? We multiply by 6. We have to multiply by 6 on the other side too then. 5 times 6 is 30, so Ashely had 30 hershey kisses.
In real life, not in ratio form, Ashely had 30 kisses and Keely had 12.
Please mark brainliest if possible, have a nice day! :)
>
A restaurant investigated the correlation between prices and the number of customers. The linear model below represents this situation,
where x is the average meal price [in dollars), and y is the number of daily customers. Interpret the slope.
y = 437 – 18.5
OA. The average price per meal is $18.
B. The average number of daily customers is 18.
Oc. If the average meal price decreases by $1, the number of daily customers decreases by 18.
D. If the average meal price increases by $1, the number of daily customers decreases by 18.
I'm not in highschool but I did the math I think it's 18
Answer:
The Answer is D
Step-by-step explanation:
437-18.5=419.5
Can someone plss help me with this!!
QUESTION: b(a-6)
Answer:
ba-6b
Step-by-step explanation:
you transfer ba to 6b
The graph of a linear function has a slope of 5 and passes through the point (2,5). What
is the y-intercept of the graph of the function?
Answer:
-5 is the y intercept.
Step-by-step explanation:
Ok, lets do the steps in order.
1) Make a point-slope form equation.
We know that the format of it is y - y1 = slope(x - x1), so we know have to substitute our information in the equation.
y - 5 = 5(x - 2)
2) Convert our point-slope form equation into slope intercept form, and solve for the y-intercept.
y = slope(x) + b... right? So we now have to do math.
Distribute the right side of the equation to get :
y - 5 = 5x - 10
Now cancel out the -5, and then subtract on both sides.
y = 5x - 5
And -5 is your y intercept :)
Hope this helps! Mark me brainliest :)
Given: 9yº Simplify the expression for y= 3. (show your work and explain your reasoning.)
the circle is a 0 btw
Solving Two Step Equations
3 (x +1/3 = 3) 3
Answer:
add 3 to 3 getting 6 put that over 1 then distribute. 6/1(x+1/3=3)
6x + 2 = 18
now subtract both sides by 2
6x = 16
and divide
x= 16/6
simply by diving by 2
x = 8/3
Using the numbers -5, 9, -2, 11, and -4, and the operations add and subtract, what is the largest possible answer you can make?
The largest possible value we can make using subtraction and addition from the given numbers -5, 9, -2, 11, and -4 is 31.
What are subtraction and addition?A mathematical operation that represents combining objects into a larger collection is called addition.
It is denoted by the plus sign (+).
A mathematical operation that represents the process of finding the difference between numbers is called subtraction.
It is denoted by the minus sign (-).
We have,
-5, 9, -2, 11, and -4
The largest possible value we can get is by using sign multiplication.
[ Negative x Negative = Positive ]
We will use addition and subtraction wherever necessary to make all the numbers positive.
= 9 - ( -5 ) - ( -2 ) + 11 - ( -4 )
= 9 + 5 + 2 + 11 + 4
= 31
Thus the largest possible value we can make using subtraction and addition from the given numbers is 31.
Learn more about additions and subtractions here:
https://brainly.com/question/1292482
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Suppose line g is the line with equation y=x. Given A(9,-5), B(6,3), and C(-1,-6), what are the coordinates of the vertices of A'B'C' for the reflection?
(type an ordered pair)
A'=___
B'=___
C'=___
Answers:
A ' = (-5, 9)
B ' = (3, 6)
C ' = (-6, -1)
=====================================================
Explanation:
When reflecting over the line y = x, we swap the locations of the x and y coordinates. For example, the point (5,7) becomes (7,5)
This means we have the following reflections
A(9,-5) moves to A ' (-5, 9)B(6,3) moves to B ' (3, 6)C(-1,-6) moves to C ' (-6, -1)This operation is commonly done when determining the inverse of a graph. This is because the inverse basically undoes everything the original function applies. So this "backwards" nature of things means that x becomes y and vice versa.
Find the slope of the line that passes through the points -2,-2 and -10,-9
Answer:
7/8
Step-by-step explanation:
the equation for finding a slope is (y2 - y1) / (x2 - x1)
basically it's the second y minus the first y all divided by the second x minus the first x
-9 - (-2) / -10 - (-2)
-7 / -8
7/8