Answer:
The required points of the given line segment are ( 9, - 2 ).
Step-by-step explanation:
Given that the line segment AB whose midpoint M is ( 4, 2 ) and point A is ( - 1, 6), then we have to find point B of the line segment AB -
As we know that-
If a line segment AB is with endpoints ( [tex]x_{1}, y_{1}[/tex] ) and ( [tex]x_{2}, y_{2}[/tex] )then the mid points M are-
M = ( [tex]\frac{ x_{1} + x_{2} }{2}[/tex] , [tex]\frac{ y_{1} + y_{2}}{2}[/tex] )
Here,
Let A ( - 1, 6 ), B ( x, y ) with midpoint M ( 4, 2 ) -
then by the midpoint formula M are-
( 4, 2 ) = ( [tex]\frac{ - 1 + x}{ 2}[/tex] , [tex]\frac{ 6 + y}{2}[/tex] )
On comparing x coordinate and y coordinate -
We get,
( [tex]\frac{ -1 + x}{2}[/tex] = 4 , [tex]\frac{ 6 + y}{2}[/tex] = 2)
( - 1 + x = 8, 6 + y = 4)
( x = 8 + 1, y = 4 - 6 )
( x = 9, y = -2 )
Hence the required points A are ( 9, - 2 ).
We can also verify by putting these points into Midpoint formula.
Dani spend her summers at her grandparents cabin in canada. The cabin is 42 kilometers upriver from the nearest town. The river has a downstream current of 4 kilometers per hour. If Dani can canoe from the cabin to town and back in 14 hours, what is her average canoeing speed in still water?
Answer:
8 kilometer per hour
Step-by-step explanation:
Given: Dani spend her summers at her grandparents cabin in canada. The cabin is [tex]42[/tex] kilometers upriver from the nearest town. The river has a downstream current of [tex]4[/tex] kilometers per hour.
To Find: If Dani can canoe from the cabin to town and back in [tex]14[/tex] hours, what is her average canoeing speed in still water.
Solution:
Let the speed of Dani in still water is [tex]=\text{s}[/tex]
speed of downstream current is [tex]=4\text{kmph}[/tex]
speed of Dani in downstream current [tex]=\text{s}+4[/tex]
speed of Dani in upstream current [tex]=\text{s}-4[/tex]
Now,
Total time taken by Dani to canoe from the cabin to town and back [tex]=14\text{hours}[/tex]
[tex]\frac{42}{\text{s}-4}+\frac{42}{\text{s}+4}=14[/tex]
[tex]{\text{s}}^2-6\text{s}-16=0[/tex]
[tex](\text{s}-8)(\text{s}+2)[/tex]
[tex]\text{s}=8,-2[/tex]
as speed can't be negative the average speed of dani in still water is [tex]8\text{kmph}[/tex]
Besian bought 6 ice cream cakes for $48 dollars. Write an equation that represents the total cost, y, of x ice creams cakes.
Answer: y = 8x
Step-by-step explanation: please see attachment for explanation
Answer:
y=8x
Step-by-step explanation:
what must be the value of y below so that the line passing through the points(4,4) and (-3,y) has a slope of -2?
Answer:
18
Step-by-step explanation:
Find the equation for the line in slope-intercept form: y = mx + b.
x and y are points on the line. Points are written in the form (x, y).
m is the slope.
b is the y-intercept, when it hits the y-axis.
Substitute the point (4, 4) and slope. x = 4; y = 4; m = -2. Find b
y = mx + b
4 = (-2)(4) + b
4 = -8 + b
b = 4 + 8
b = 12
Get the equation of the line using slope and the y-intercept.
y = -2x + 12
Substitute -3 as x and find the missing y.
y = -2(-3) + 12
y = 6 + 12
y = 18
The point was (-3, 18)
Therefore the missing value for y is 18.
To find the y-value, you substitute the given points into the formula for slope and solve for 'y'. In this case, the required value of 'y' is 18.
Explanation:The subject of your question is mathematics, specifically the concept of calculating the slope of a line. The slope (m) of the line through two points (x1,y1) and (x2,y2) is defined as m = (y2 - y1) / (x2 - x1). You are given that the points are (4,4) and (-3,y) and the slope is -2. Substituting the given points into the formula gives -2 = (y - 4) / (-3 - 4 ). Solving this equation will give you the value of 'y'.
First, simplify the denominator to get -2 = (y - 4) / -7. Afterward, multiply both sides by -7 to eliminate the fraction: -2 * -7 = (y - 4). This yields 14 = y - 4. Solve for 'y' by adding 4 to both sides of the equation, which gives that y = 18.
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Hey can anyone help me figure out these values? Thank you.
Answer:
1680
Step-by-step explanation:
12+7+6=25
12+20*12=252
20+20+7=47
7*20*12=1680
At the start of the month, Jodie had sold 885 copies of her new book. At the end of the month, she had sold 1,364 copies of her book. If each book profits $13.97, approximately how much did the book profit in the entire month? A. $6,706 B. $31,486 C. $19,096 D. $12,390
Answer:
Option A. $6,706
Step-by-step explanation:
we know that
To find out how much was the book profit in the entire month, subtract the number of copies at the start of the month from the number of copies at the end of the month, and the result multiply by $13.97 (each book profits)
so
[tex](1,364-885)(13.97)\\479(13.97)=\$6,691.63[/tex]
so
approximately $6,706
At 5:00 p.m., Antonio turned on the oven. While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period. The oven remained at 400°F for 45 minutes until Antonio turned it off. It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m. Which statement best explains whether or not the temperature in the oven is a function of the time?
A) It is a function because at any given time the oven was exactly one temperature.
B) It is a function because the oven temperature was the same at different times.
C) It is not a function because at any given time the oven was exactly one temperature.
D) It is not a function because the oven temperature was the same at different times.
Option A
It is a function because at any given time the oven was exactly one temperature.
Solution:
Given that,
At 5:00 p.m., Antonio turned on the oven
While the oven preheated, the temperature in the oven increased from 72°F to 400°F over a 10-minute period
The oven remained at 400°F for 45 minutes until Antonio turned it off
It took 60 minutes for the temperature in the oven to cool, returning to 72°F at 6:55 p.m
From above information,
5:00 ------------ 72°F
5:10 ------------------ 400°F
5:45 ------------------ 400ºF
6:55 -------------------- 72°F
Thus at any given time (input) the oven was exactly one temperature (a single output )
Therefore the statement that best explains is:
Option A) It is a function because at any given time the oven was exactly one temperature.
Since the definition of function states that there is a unique image corresponding to a element hence here the temperature at a given time is unique
Answer:
option a
Step-by-step explanation:
Lo is leaving from work today at 6:15 p.m. She has errands to run before she meets her friends for dinner at 8 p.m. If it takes Lo of an hour to run each errand, how many errands does she have time to run between work and dinner?
Lo has time to run 7 errands between work and dinner.
Lo has 1 hour and 45 minutes between leaving work at 6:15 p.m. and meeting her friends at 8:00 p.m.
She needs around 1/4 of an hour for each errand.
To find out how many errands she can run, we divide the total time available by the time required for each errand:
Convert 1 hour 45 minutes to minutes: 1 hour = 60 minutes, so 1 hour 45 minutes = 60 + 45 = 105 minutes.
Calculate how many errands she can run: 105/15 = 7.
Therefore, Lo has time to run 7 errands between work and dinner.
you earn 360 dollars every 4 weeks how much money do you make in one week
Answer:$90
Step-by-step explanation:
360/4=90
Answer: $90 in one week
Step-by-step explanation:
Since you earn $360 every 4 weeks, you would have to divide $360 by 4 to find the amount of money you earn in one week.
360 divided by 4 = 90
So you earn $90 in one week.
2.) The graph of a proportional relationship is shown.
Money
Total Savings (5)
Number of Weeks
What is the amount of savings per week?
Answer:
[tex]\$47\ per\ week[/tex]
Step-by-step explanation:
we know that
A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]k=\frac{y}{x}[/tex] or [tex]y=kx[/tex]
In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin
In his problem
The amount of savings per week is equal to the constant of proportionality k or slope of the linear equation
so
Looking at the graph
take the point (2,94)
x=2 weeks, y=$94
Find the value of k
[tex]k=\frac{y}{x}[/tex]
substitute the values of x and y
[tex]k=\frac{94}{2}[/tex]
[tex]k=\$47\ per\ week[/tex]
How many 5-member chess teams can be chosen from 15 interested players? Consider only the members selected, not their board positions. 3,003 120 360,360
Answer:
3003 number of 5-member chess teams can be chosen from 15 interested players.
Step-by-step explanation:
Given:
Number of the interested players = 15
To Find:
Number of 5-member chess teams that can be chosen = ?
Solution:
Combinations are a way to calculate the total outcomes of an event where order of the outcomes does not matter. To calculate combinations, we will use the formula[tex]nCr = \frac{n!}{r!(n - r)!}[/tex]
where
n represents the total number of items,
r represents the number of items being chosen at a time.
Now we have n = 15 and r = 5
Substituting the values,
[tex]15C_5 = \frac{15!}{5!(15- 5)!}[/tex]
[tex]15C_5 = \frac{15!}{5!(10)!}[/tex]
[tex]15C_5 = \frac{15!}{5!(10)!}[/tex]
[tex]15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1 }{5 \times 4 \times 3 \times 2 \times 1(10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)}[/tex]
[tex]15C_5 = \frac{15\times \times 14 \times 13 \times 12 \times 11}{(5 \times 4 \times 3 \times 2 \times 1)}[/tex]
[tex]15C_5 = \frac{360360}{120}[/tex]
[tex]15C_5 = 3003 [/tex]
h(y)=-3y^2+5
p(y)=y^3-7y
Find (h-p)(y)
[tex](h-p))(y) = -y^3-3y^2+7y+5[/tex]
Step-by-step explanation:
Given
[tex]h(y) = -3y^2+5\\p(y) = y^3-7y[/tex]
We have to find the difference of two functions given
So,
[tex](h-p)(y) = h(y) - p(y)\\= (-3y^2+5)-(y^3-7y)\\=-3y^2+5-y^3+7y\\=-y^3-3y^2+7y+5[/tex]
Hence,
[tex](h-p))(y) = -y^3-3y^2+7y+5[/tex]
Keywords: Functions, variables
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Karen has $1.70 in coins. Karen has 8 coins, all of which are quarters or dimes.
So can someone help me with these 3 parts?
Answer:
Karen has 6 quarters and 2 dimes
Step-by-step explanation:
Let
x ----> the number of quarter coins Karen has
y ----> the number of dimes coins Karen has
Remember that
[tex]1\ quarter=\$0.25\\1\ dime=\$0.10[/tex]
we know that
Equation that represent the amount of coins Karen has
[tex]x+y=8[/tex]
isolate the variable y
[tex]y=8-x[/tex] ----> equation A
Equation that represent the value of coins Karen has
[tex]0.25x+0.10y=1.70[/tex] ----> equation B
Solve the system of equations by substitution
substitute equation A in equation B
[tex]0.25x+0.10(8-x)=1.70[/tex]
solve for x
[tex]0.25x+0.80-0.10x=1.70[/tex]
[tex]0.25x-0.10x=1.70-0.80[/tex]
[tex]0.15x=0.90[/tex]
[tex]x=6[/tex]
Find the value of y
[tex]y=8-x[/tex] ----> [tex]y=8-6=2[/tex]
therefore
Karen has 6 quarters and 2 dimes
What is 3 division 68 and show your work plz
Answer:
0.044117
Step-by-step explanation:
We have the equation:
3 ÷ 68 = 0.044117
Calculated to 6 decimal places.
How far do you want to calculate the decimal places for the answer? Here are some examples:
31 divided by 16 = 1.937500 calculating to 6 decimal places
31 divided by 16 = 1.937 calculating to 3 decimal places
22 divided by 15 = 1.466666666 calculating 9 decimal places
22 divided by 15 = 1.466666 calculating 6 decimal places
22 divided by 15 = 1.466 calculating to 3 decimal places
Note that this is not the same as rounding to a specific number of decimal places. For example, 22 divided by 15 = 1.466 when calculated to 3 decimal places because you stop once you reach the third decimal place. On the other hand, 22 divided by 15 = 1.467 when rounded to 3 decimal places. In order to round to the third decimal place you must calculate to at least the fourth decimal place so that you know how to round the third decimal place
Hope This Will Help!!!!! :) :)
Answer: 22 R (Remainder) 2
Step-by-step explanation:
First, see how many times 3 goes into 6.
3x2=6
So, subtract 6 from 6, which equals 0. Bring down the 8. See how many times 3 goes into 8.
3x2=6
3 goes into 8 two times. Subtract 6 from 8, which equals 6. 8 minus 6 equals 2, which becomes the remainder.
What is 18 divided by 6 and add 4? lk it sounds easy but yep
18 divided by 6 is 3
when you add 3 with 4 it gives you 7
7 is your total answer
18/6 + 4
18/6 = 3
3 + 4 = 7
The answer is 7.
If the area of a living room wall is 70 square feet, how many feet long is the living room wall
Answer: 4.25 feet
Step-by-step explanation:
a-living room wall in feet
area=a²
70sqf²=a²
a=√70
a=4.248 feet
How do u solve X- 98=104
Answer: x=202
Step-by-step explanation:
1st: Add 98 to 104, this should give you your answer of x=202
Answer:
202
Step-by-step explanation:
x-98=104
+98 +98 (you add because 98 is a negative)
x= 202What is the verbal description for y=3x-2
Answer:
Y equals three x minus two
Final answer:
The equation y = 3x - 2 represents a line with a slope of 3 and a y-intercept of -2.
Explanation:
The equation y = 3x - 2 represents a line in the Cartesian coordinate system. This equation follows the slope-intercept form y = mx + b, where m is the slope of the line and b is the y-intercept. In this case, the slope (m) is 3, meaning that for every one unit increase in x, y increases by 3 units.
The y-intercept (b) is -2, indicating that the line crosses the y-axis at the point (0, -2). To find an equation for a line given a point and a slope, you can use the point-slope form, y - y1 = m(x - x1). With the point (-7, 1) and slope 3, the equation is y - 1 = 3(x + 7).
Solve for 2:
8x - 41°
4x + 35°
Answer: x=19°
Step-by-step explanation:
First, add 41° to 35
Next, subtract 4x from 8x, then you should have your answer from there!
Simplify 12.70-n+9+n/4
Final answer:
The expression 12.70 - n + 9 + n/4 is simplified by combining like terms, resulting in 21.70 + 1.25n.
Explanation:
The student's question involves simplifying the expression 12.70 - n + 9 + n/4. To simplify this expression, we first combine like terms. As 'n' and 'n/4' are like terms, we simplify by combining them which can be done by adding 1n (which is the same as n) with 1/4n. Here are the steps:
Add 'n' and 'n/4' together to get '5/4n' or '1.25n'.Add the numerical terms 12.70 and 9 to get 21.70.Combine the results from the first two steps to obtain the simplified expression, which is 21.70 + 1.25n.This completes the simplification process for the given expression. It is important to ensure terms are like terms before combining them and to perform accurate arithmetic operations when combining numerical values.
the area of a rectangle is w^2+4w=60 where w is the width. find the width.
The width of rectangle is 6.
Step-by-step explanation:
Given,
Area of rectangle; w²+4w=60
As w is the width, we will solve the equation to find w.
[tex]w^2+4w=60[/tex]
Subtracting 60 from both sides
[tex]w^2+4w-60=0[/tex]
Factorizing the equation;
[tex]w^2+10w-6w-60=0\\w(w+10)-6(w+10)=0\\(w+10)(w-6)=0[/tex]
Either,
w+10=0 => w=-10
Or,
w-6=0 =>w=6
As width cannot be negative, therefore
Width = 6
The width of rectangle is 6.
Keywords: area, rectangle
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Triangle ABC was dilated with the origin as the center of dilation to create triangle A'B'C'. The triangle was dilated using a scale factor of 14.
The coordinates of the vertices of triangle ABC are given. You can use the scale factor to find the coordinates of the dilated image.
Enter the coordinates of the vertices of triangle A'B'C' below.
(Decimal values may be used)
pls answer ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answer:
[tex]A'(-0.25,0.75)\\\\B'(1.75,-0.25)\\\\C'(-1,-0.25)[/tex]
Step-by-step explanation:
A Dilation is defined as a transformation in which the image and the pre-image have the same shape, but their sizes are different.
When the scale factor is greater than 1, the image obtained after the dilation is greater than the pre-image and it is an "Enlargement".
When the scale factor is is between 0 and 1, the image obtained after the dilation is smaller than the pre-image and it is an "Reduction".
In this case you know that the triangle ABC was dilated by this scale factor:
[tex]scale\ factor=\frac{1}{4}[/tex]
With the origin as the center of dilation.
Since:
[tex]0<\frac{1}{4}<1[/tex]
It is a Reduction.
You can identify that the vertices of the triangle ABC are:
[tex]A(-1,3)\\\\B(7,-1)\\\\C(-4,-1)[/tex]
So you need to multiply the coordinates of each vertex of the triangle ABC by [tex]\frac{1}{4}[/tex], in order to get the coordinates of the triangle A'B'C. Then, you get:
[tex]A'=(\frac{1}{4}(-1),\frac{1}{4}(3))=(-0.25,0.75)\\\\B'(\frac{1}{4}(7),\frac{1}{4}(-1))=(1.75,-0.25)\\\\C'(\frac{1}{4}(-4),\frac{1}{4}(-1))=(-1,-0.25)[/tex]
The coordinates of the vertices of triangle A'B'C' include the following;
A' (-1/4, 3/4).
B' (7/4, -1/4).
C' (-1, -1/4).
What is dilation?In Mathematics and Euclidean Geometry, dilation is a type of transformation that is used for altering the dimensions of a geometric figure, but not its shape.
In this scenario and exercise, we would have to dilate the coordinates of the pre-image by using a scale factor of 1/4 centered at the origin as follows:
Ordered pair A (-1, 3) → (-1 × 1/4, 3 × 1/4) = Ordered pair A' (-1/4, 3/4).
Ordered pair B (7, -1) → (7 × 1/4, -1 × 1/4) = Ordered pair B' (7/4, -1/4).
Ordered pair C (-4, -1) → (-4 × 1/4, -1 × 1/4) = Ordered pair C' (-1, -1/4).
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Missing information;
Triangle ABC was dilated with the origin as the center of dilation to create triangle A'B'C'. The triangle was dilated using a scale factor of 1/4.
The coordinates of the vertices of triangle ABC are given. You can use the scale factor to find the coordinates of the dilated image.
Enter the coordinates of the vertices of triangle A'B'C' below.
(Decimal values may be used)
tammy typed 40 pages of a report on Monday and 3/8 of the report on Tuesday. She completed the remaining 1/3 of the report on Wednesday . How manypages are there in the report?
Answer:
Step-by-step explanation:
R = report length
R = 40 + (3/8)R + (1/3)R
3/8 = 3*3/8*3 = 9/24
1/3 = 8*1 / 3*8 = 8/34
R = 40 + (9/24)R + (8/24)R
R = 40 + (17/24)R Subtract 17/24 from the left
R-17/24 R = 40
7/24 R = 40 Multiply both sides by 24
7R = 40 * 24
7R = 960 Divide by 7
R = 960/7
R = 137.1 which breaks the rounding rule and becomes 138 because something has to be typed on page 138
|60| ___ |-60| is it greater than > equal to = or less than
Answer:
[tex] |60| = | - 60| [/tex]
Step-by-step explanation:
They are equal. When the negative sign is inside the box the absolute value is positive, when the negative sign is outside the box THEN it is negative.
Answer: equal to
Step-by-step explanation: Absolute value means distance from zero on a number line. To represent the absolute value of a number, we use a vertical bar on either side of the number like we see in this problem.
So for the absolute value of 60, we know that 60 is 60 units from zero on a number line which means that the absolute value of 60 is just 60.
For the absolute value of -60, we know that -60 is also 60 units from zero on the number line so the absolute value of -60 is also 60.
Now we know that the absolute value of -60 is 60 and the absolute value of 60 is also 60. Since 60 is the same as 60, it means that 60 is equal to 60.
Another way of thinking about absolute value is that no matter what number you have inside the absolute value, your result will always be positive except for 0 which has an absolute value of 0.
In other words, the absolute value of any number is the positive version of that number. Again, not including zero.
Miss Isaac took her family out to eat at Jay’s deli. their mail came to 25. 40. missed Isaac wants to tip the waitress 18% and sales tax is 5.5% final total price of our meal after tax and tip
Answer:
The total price of the meal after tax and tip is $31.62.
Step-by-step explanation:
Given:
Their bill is = $25.40.
Sales tax = 5.5%.
Tip to waitress = 18%.
Now, to find the total price of the meal after tax and tip.
So, to get the price of the meal after sales tax :
$25.40 + 5.5% of $25.40.
[tex]=25.40+\frac{5.5}{100} \times 25.40.[/tex]
[tex]=25.40+\frac{139.70}{100}[/tex]
[tex]=25.40+1.397=\$26.797[/tex]
Now, to get the total price after tax and tip:
$26.797 + 18% of $26.797.
[tex]=26.797+\frac{18}{100} \times 26.797[/tex]
[tex]=26.797+0.18\times 26.797[/tex]
[tex]=26.797+4.823[/tex]
[tex]=\$31.62.[/tex]
Therefore, the total price of the meal after tax and tip is $31.62.
The force F needed to stop a car varies directly as its weight W and the square root of velocity V are inversely as the distance d travelled. When F=36 Newtons, W=120kg,V=100km/h and d=50km. Calculate the force required for V=256km/h,W=200kg and d =800km. This is the question pls answer it dont by pass it pls
Final answer:
To calculate the force required, we use the formula F = k * (W / sqrt(V)) * (1 / d), where F is the force, W is the weight, V is the velocity, and d is the distance. We can find the constant of variation k by substituting the given values of F, W, V, and d into the formula. After finding k, we can plug in the new values of W, V, and d to calculate the force required.
Explanation:
To solve this problem, we can use the formula F = k * (W / sqrt(V)) * (1 / d), where F is the force, W is the weight, V is the velocity, and d is the distance.
First, we can calculate the constant of variation k by substituting the given values of F, W, V, and d into the formula. This gives us: 36 = k * (120 / sqrt(100)) * (1 / 50).
Solving for k, we get k = 36 * 100 * 50 / 120 = 1500.
Next, we can plug in the new values of W, V, and d into the formula and solve for F. Substituting W = 200, V = 256, and d = 800, we have: F = 1500 * (200 / sqrt(256)) * (1 / 800).
Simplifying further, we get F = 1500 * 200 / (16 * 800) = 18.75 Newtons.
What is the value of x in -4(5x-5)=120
Answer: x = -5
Step-by-step explanation: To solve this equation, we start by distributing the -4 through the parentheses on the left side.
So we have -4 times x which is -20x and -4 times -5 which is positive 20. So our equation now reads -20x + 20 = 120.
Solving from here, we subtract 20 from both sides of the equation and we have -20x = 100 and dividing both sides by -20, we find that x = -5.
Although I will not provide work to check our answer, the great thing about solving equations is that your can always check your answer by substituting what you got as a final answer into the original equation.
Answer:
The answer is X = -5.
Simplify:
3 · 32 + 8 ÷ 2 − (4 + 3)
A. 24
B. 23
C. 30
D. 32
Answer:
A.
Step-by-step explanation:
To simplify the given expression, first perform the multiplication, then the division, and finally the addition and subtraction. The final result is 20.
Explanation:To simplify the expression 3 · 32 + 8 ÷ 2 − (4 + 3), we follow the order of operations (PEMDAS/BODMAS). First, we perform the multiplication: 3 · 32 = 3 · 9 = 27. Next, we perform the division: 8 ÷ 2 = 4. After that, we simplify the addition and subtraction within the parentheses: (4 + 3) = 7. Finally, we subtract 7 from the previous result: 27 - 7 = 20. Therefore, the answer is A. 20.
find s15 for the following sequence40,34, 28,22
Answer:
- 30
Step-by-step explanation:
Note the common difference d between consecutive terms in the sequence
d = 34 - 40 = 28 - 34 = 22 - 22 = - 6
This indicates the sequence is arithmetic with sum to n terms calculated as
[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]
where a₁ is the first term and d the common difference
Here a₁ = 40 and d = - 6, thus
[tex]S_{15}[/tex] = [tex]\frac{15}{2}[/tex] [ (2 × 40) + (14 × - 6) ], that is
[tex]S_{15}[/tex] = 7.5(80 - 84) = 7.5 × - 4 = - 30
Answer:
[tex]\displaystyle -44 = s_{15}[/tex]
Step-by-step explanation:
[tex]\displaystyle -6n + 46 = a_n \\ -6[15] + 46 = a_n \\ -90 + 46 = a_n \\ -44 = a_n[/tex]
Use the Arithmetic Sequence to figure this out.
I am joyous to assist you anytime.
Write each decimal as a fraction or a mixed number in simplest form.
Answer:
what decimals?
Step-by-step explanation:
For the class of 2013's prom Norman's dress shop sold cheaper dresses for $90 each and more expensive dresses for $140 each. They took in $5250 and sold 20 more of the cheaper dresses than the expensive dresses. How many of each kind did they sell? Simply need help setting up the equations. I can solve them on my own.
Answer:
Number of cheaper dresses sold is 35
Number of expensive dresses sold is 15
Step-by-step explanation:
Given:
Cost of cheaper dresses = $90
Cost of expensive dresses = $140
Total cost of the dresses = $5250
To Find:
Number of cheaper dress = ?
Number of expensive dress = ?
Solution:
Let
The number of cheaper dresses be x
The number of expensive dresses be y
(Number of cheaper dresses X cost of cheap dress) + (Number of Expensive dresses X cost of expensive dress) = $5250
[tex]x \times90 +y \times 140 = 5250[/tex]= $5250
It is given that the 20 more of the cheaper dresses than the expensive dresses is sold
So,
number of cheaper dress = 20 + number of expensive dress
x = 20 + y---------------------------------------(1)
[tex](20+y) \times90 +y \times 140 = 5250 = 5250[/tex]
[tex](20 \times 90 +y\times 90) +y \times 140= 5250 [/tex]
[tex]1800 + 90y+ 140y = 5250 [/tex]
[tex]1800 + 230y = 5250 [/tex]
[tex] 230y =5250 -1800[/tex]
[tex] 230y = 3450 [/tex]
[tex]y = \frac{3450}{230}[/tex]
y = 15
Substituting y in (1)
x = 20 +15
x= 35