Answers
Answer:
x = 12
Step-by-step explanation:
both (x+5) and (2x-7) are corresponding angles formed by an intersection between a transversal and 2 parallel lines.
hence they are equal in value
x+5 = 2x-7
x - 2x = -7 - 5
-x = -12
x = 12
Answer: x=12
Step-by-step explanation:
Related Questions
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Consider the function. f(x)=2x-6 Match each transformation of f(x) with its description.
g(x)=2x-2 g(x)=2x-14 g(x)=2x-10 g(x)=8x-24 g(x)=8x-4 g(x)=8x-6
shifts f(x) 4 units down stretches f(x) by a factor of 4 away from the x-axis shifts f(x) 4 units right compresses f(x) by a factor of toward the y-axis
Answers
Answer:
See below
Step-by-step explanation:
Parent function is:
f(x) = 2x - 6Transformations are:
shifts f(x) 4 units down
f(x) → f(x) - 4 ⇒ g(x)= 2x - 6 - 4 = 2x - 10stretches f(x) by a factor of 4 away from the x-axis
f(x) → 4*f(x) ⇒ g(x) = 4(2x - 6) = 8x - 24shifts f(x) 4 units right
f(x) → f(x - 4) ⇒ g(x) = 2(x - 4) - 6 = 2x - 14compresses f(x) by a factor of toward the y-axis (must be 4)
f(x) → f(4x) ⇒ g(x) = 2*4x - 6 = 8x - 6What is the difference between the yearly wages of the highest paying job and lowest paying job, assuming Araceli will be paid for working 40 hours a week, 52 weeks a year?
$1,160
$11,280
$2,600
$8,680
Answers
-> 40 hours per week, 52 weeks a year
shop and save grocers
monthly wages: $3,800
hourly wages: $3800 / 160 = $23.75 per hour
yearly wages: $23.75 per hour x 40 hours per week x 52 weeks a year
= $49,400
unbelievable toys
yearly wages: $43,000
convenience store
$16.50 per hour x 40 hours per week x 52 weeks a year
= $34,320
49,400 - 34,320 = 15,080
..? that's not even an answer choice what-
can someone please explain 10 3/4 - 6 4/4 ??
Answers
3 3/4 is the answer
10 3/4 --- 43/4
6 4/4--- 7 or 28/4
43/4- 28/4= 15/4
15/4 simplified is 3 3/4
Answer:
43/4 - 28/4 = (43 - 28)/4 = 15/4 or 3 3/4
Step-by-step explanation:
10 3/4 - 6 4/4 . The expression means we should find the difference between 10 3/4 and 6 4/4. The best approach to find the difference of this kind of fractions with whole number is by turning each to an improper fraction.
10 3/4 . This whole number fraction can be turn to an improper fraction as follows
10 × 4 + 3 = 43 then 43/4
6 4/4. 4 × 6 + 4 = 28/4.
Now , let's find the difference
The denominator is same, which is 4
43/4 - 28/4 = (43 - 28)/4 = 15/4 or 3 3/4
Kyle’s parents told him that for every 5 hours of homework or reading he completes, he will be able to play 3 hours of video games. His friend victor’s parents told their son that he can play 30 minutes for every hour of homework or reading time he completed. If both boys spend the same amount of time on homework and reading this week, which boy gets more time playing video games
Answers
Kyle will have more time to play video games
Solution:
From given question,
Kyle’s parents told him that for every 5 hours of homework or reading he completes, he will be able to play 3 hours of video games.
5 hours of homework = 3 hours of video games
Victor’s parents told their son that he can play 30 minutes for every hour of homework or reading time he completed.
1 hour of homework = 30 minutes of playtime
Suppose if victor spends 5 hours doing homework or reading, then he could play,
5 hours of victor homework = 30 minutes x 5 = 150 minutes of play
That is,
150 minutes = 120 + 30 = 2 hours 30 minutes
This 2 hours 30 minutes playtime of victor is less than kyle playtime (which is 3 hours )
So Kyle gets more play time
Dad bought $200,000 of term life insurance at the rate of $5.40 per thousand-dollar unit. How much is the annual premium?
Answers
Answer:
$1080 annual
Step-by-step explanation:
200(# of thousands) x 5.4
1080
Need help for this question
Answers
Answer:
For 0 hours = $40
For 1 hours = $75
For 2 hours = $110
For 3 hours = $145
For 4 hours = $180
For 5 hours = $215
Step-by-step explanation:
Given equation is:- [tex]C=35n+40[/tex]
where, C=Cost in dollars, n=hours.
Now, Amy charge $40 for service call and $35 for per hour service.
So,
For 0 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 0)+40[/tex]
[tex]C=0+40[/tex]
[tex]C=40[/tex]
Therefore for 0 hours Amy charge $40.
For 1 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 1)+40[/tex]
[tex]C=35+40[/tex]
[tex]C=75[/tex]
Therefore for 1 hours Amy charge $75.
For 2 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 2)+40[/tex]
[tex]C=70+40[/tex]
[tex]C=110[/tex]
Therefore for 2 hours Amy charge $110.
For 3 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 3)+40[/tex]
[tex]C=105+40[/tex]
[tex]C=145[/tex]
Therefore for 3 hours Amy charge $145.
For 4 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 4)+40[/tex]
[tex]C=140+40[/tex]
[tex]C=180[/tex]
Therefore for 4 hours Amy charge $180.
For 5 hours:
[tex]C=35n+40[/tex]
[tex]C=(35\times 5)+40[/tex]
[tex]C=175+40[/tex]
[tex]C=215[/tex]
Therefore for 5 hours Amy charge $215.
Gloria bought each of her three younger siblings a movie ticket. Find the total cost of the movie ticket if each cost $9.75. Justify your answer by using the Distributive Property.
Sry if i keep asking questions.
Answers
Answer: 29.25
Step-by-step explanation:
3(9.75)
Joannas pay for working overtime,p,varies jointly as the number of hours she works ,n, and her hourly pay rate,r,and p=$103.44 when n=8 hours and r=$8.62. Find n when p=$213.75 and r=$9.50
Answers
n = 15 when p=$213.75 and r=$9.50
Step-by-step explanation:
Given
p = overtime pay
n = number of hours
r = hourly pay rate
It is also given that the pay for working hours varied directly with Number of hours and hourly pay rate jointly
So
It can be denoted as:
p ∝ nr
It can also be written as:
[tex]p = knr[/tex]
where k is the constant of proportionality
Putting the given values of p,n and r in the equation
[tex]103.44 = k * 8 * 8.62\\103.44 = 68.96k\\k = \frac{103.44}{68.96}\\k = 1.5[/tex]
So the equation is now,
p = 1.5nr
Putting
p = 213.75
r = 9.50
[tex]213.75 = 1.5 * n * 9.50\\213.75 = 14.25n\\n = \frac{213.75}{14.25}\\n = 15[/tex]
Hence,
n = 15 when p=$213.75 and r=$9.50
Keywords: Proportion variation
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Ian Multiples a number by 5. The product of the two number is 495. What number does Ian multiply by 5?. Explain.
Answers
Answer: 99.
Step-by-step explanation: To answer this, you must reverse the operation to find the number being multiplied. The operation done: multiplication. Multiplication in reverse: division. 495 divided by 5 is 99.
Answer:
The other number is 99.
Step-by-step explanation:
"Ian multiplies a number by 5. The product of the two numbers is 495".
Therefore que know that 5 · x (a number we don't know yet) = 495.
This is an equation.
[tex]5*x=495\\[/tex] - To solve it we need to clear the equation.
Thus,
[tex]x=\frac{495}{5}[/tex]
x = 99
Use the graph shown to fill in the blank. When x = 1, then y = a0.
Answers
Explanation:
Step 1) Start at 1 on the horizontal x axis number line.Step 2) Draw a vertical line straight down until you reach point P that is marked in the attached image (see below). Point P is on the diagonal line.Step 3) From point P, move horizontally until you reach -2 on the vertical y axis number line.We started with x = 1 and ended up with y = -2. So the point (x,y) = (1,-2) is on the diagonal line. In other words, point P is located at (1,-2).
A computer company has a special going in which all customers receive a free monitor and scanner with the purchase of a new computer. It costs the company $393.29 to make each computer, $151.44 to make each monitor, and $46.39 to make each scanner. The computers are then sold, with the free monitor and free scanner, for $1,196.91 each. Approximately how much profit will the company make if 408 customers take advantage of their special? (Round to the nearest 50 dollars.) A. $300,000.00 B. $550,000.00 C. $240,000.00 D. $380,000.00
Answers
Final answer:
After subtracting the manufacturing costs of the computer, monitor, and scanner from the selling price for one unit and multiplying by 408 customers, the approximate total profit is $247,050.00, which rounds to option C. $240,000.00.
Explanation:
To calculate the profit the company makes for each computer sold at $1,196.91 after giving away a monitor and a scanner, we need to subtract the cost of manufacturing the computer, monitor, and scanner from the selling price, and then multiply it by the number of customers. The costs for the computer, monitor, and scanner are $393.29, $151.44, and $46.39 respectively. Therefore, the total cost of manufacturing one set is:
Total cost = Cost of computer + Cost of monitor + Cost of scanner
Total cost = $393.29 + $151.44 + $46.39 = $591.12
The profit for one computer set would then be:
Profit per computer = Selling price - Total cost
Profit per computer = $1,196.91 - $591.12 = $605.79
To find the total profit for 408 customers, we multiply the profit per computer by the number of customers:
Total profit = Profit per computer × Number of customers
Total profit = $605.79 × 408 ≈ $247,060.32
When rounding to the nearest 50 dollars, we get:
Total profit ≈ $247,050.00
The closest answer to this would be option C. $240,000.00.
You need to buy 18 rolls of film. One shop sells it for$9.95 plus 5% sales tax. Another shop $9.75 per roll and charge $15.00 to ship no sales tax. Choose the better of the two prices how much will you pay for 18 rolls of film?
Answers
Answer:
We will buy it at $9.95 plus 5% tax because it is slightly cheaper than other price
Step-by-step explanation:
$9.95 x 18 = 179.10 + 5% sales tax(8.95) = 188.055
$9.75 x 18 = 175.50 + 15 = 190.50
hence sales tax can be get back by submitting monthly return file. so the first method is cheaper than second one,
The first shop offers a better price for 18 rolls of film. You will pay [tex]$179.10[/tex]for 18 rolls of film at the first shop.
Let's calculate the total cost for each shop:
For the first shop:
- The price per roll is [tex]$9.95[/tex].
- There is a 5% sales tax.
- The total cost without tax for 18 rolls is [tex]18 rolls * $9.95/roll = $179.10[/tex].
- The sales tax on this amount is 5% of [tex]$179.10[/tex], which is [tex]0.05 = $8.955.[/tex]
- The total cost including tax is [tex]$179.10[/tex][tex]+ $8.955[/tex] [tex]=$188.055.[/tex]
For the second shop:
- The price per roll is [tex]$9.75.[/tex]
- There is no sales tax.
- The shipping cost is a flat rate of [tex]$15.00.[/tex]
- The total cost for 18 rolls, excluding shipping, is 18 rolls *[tex]$9.75/roll[/tex] [tex]= $175.50.[/tex]
- Adding the shipping cost, the total cost is [tex]$175.50[/tex][tex]+ $15.00 = $190.50[/tex].
Comparing the two total costs:
- First shop: [tex]$188.055[/tex] (approximately [tex]$179.10[/tex] without rounding the tax)
- Second shop: [tex]$190.50[/tex]
The first shop offers a better price for 18 rolls of film. You will pay approximately [tex]$179.10[/tex] for 18 rolls of film at the first shop, which is less than the [tex]$190.50[/tex] you would pay at the second shop.
A cyclist rides her bike at a rate of 21 kilometers per hour. What is this rate in kilometers per minute? How many kilometers
will the cyclist travel in 2 minutes? Do not round your answers.
Answers
Answer:
Step-by-step explanation:
The cyclist's speed is 0.35 kilometers per minute. She will travel 0.7 kilometers in 2 minutes.
Explanation:The question deals with converting speed from kilometers per hour to kilometers per minute, and also calculating distance given a certain time and speed.
First, we convert speed from kilometers per hour to kilometers per minute. There are 60 minutes in an hour, so we divide the speed of the cyclist (21 kilometers per hour) by 60: 21/60 = 0.35 kilometers per minute.
Next, we calculate the distance the cyclist will travel in 2 minutes. Distance equals rate times time, so we multiply the cyclist's speed by the time: 0.35 kilometers per minute * 2 minutes = 0.7 kilometers.
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Eldar cooks lasagna and spaghetti using pesto sauce.
Let L represent the number of batches of lasagna and
S represent the number of batches of spaghetti that Eldar can cook with the amount of pesto sauce he has.
0.9
L
+
0.3
S
≤
6
0.9L+0.3S≤60, point, 9, L, plus, 0, point, 3, S, is less than or equal to, 6
Eldar cooks
4
44 batches of spaghetti. How many batches of lasagna can he cook at most with the remaining pesto sauce?
Answers
Answer:
He can cook 52 or less than 52 batches of lasagna.
Step-by-step explanation:
0.9L+0.3S≤60
Putting the value of s = 44
0.9L+0.3 (44) ≤ 60
0.9L+ 13.2 ≤ 60
0.9L ≤ 60 -13.2
L ≤ 46.8/0.9
L ≤ 52
Answer:
Eldar can cook 555 batches of lasagna at most.
Step-by-step explanation:
What is the equation for the line that passes through the points (-1,-2) and (2,4)
Answers
Answer:
y+2=2(x+1)
Step-by-step explanation:
m=(y2-y1)/(x2-x1)
m=(4-(-2))/(2-(-1))
m=(4+2)/(2+1)
m=6/3
m=2
y-y1=m(x-x1)
y-(-2)=2(x-(-1))
y+2=2(x+1)
What is the slope of a line containing points G(-3, 7) and H(4, -2)?
Answers
[tex]\bf G(\stackrel{x_1}{-3}~,~\stackrel{y_1}{7})\qquad H(\stackrel{x_2}{4}~,~\stackrel{y_2}{-2}) ~\hfill \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{-2}-\stackrel{y1}{7}}}{\underset{run} {\underset{x_2}{4}-\underset{x_1}{(-3)}}}\implies \cfrac{-9}{4+3}\implies -\cfrac{9}{7}[/tex]
Which name accurately describes the figure shown below and why?
Need asap plz
parallelogram, because the figure has two pairs of parallel sides
parallelogram, because the figure has exactly one pair of parallel sides
trapezoid, because the figure has two pairs of parallel sides
trapezoid, because the figure has exactly one pair of parallel sides
Answers
Answer:
Step-by-step explanation:
parallelogram, because the figure has exactly one pair of parallel sides
In the figure above, sin 52=17/c. Based on the figure, which of the following equations is also true
A. Sin 38= c/17
B. Cos 38=17/c
C. Cos 52=17/c
D. Tan 52=c/17
Answers
Answer:
c. Cos 52 = 17/c
Step-by-step explanation:
sin(x) = cos(90-x)
Based on the given figure if sin52=17/c if trigonometric ratio then the correct option is C)cos38=17/c
What is trigonometric function?The trigonometric functions are the ratio of the sides of a right angled triangle. Sin, cos, tan, cosec, sec,cot are the trigonometric functions.
How to calculate trigonometric ratios?We have been given sin 52=17/c
We know that sin x= cos(90-x)
sin52=cos(90-52)=cos 38
So the value will be cos38=17/c
Hence the correct answer is cos38=17/c.
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Solve the equation
8.3v = -5.1
Answers
Answer:
v= -0.61445783132
Step-by-step explanation:
Divide both sides by 8.3
-5.1 ÷ 8.3= -0.61445783132
8.3v ÷ 8.3= v
So, v=-0.61445783132
8.3v ÷ 8.3= v
CIRCLES!! Need help
Picture:
Answer all or just one please I need help and answers!!!
Answers
Answer for the question No.17
Answer:
[tex]x=28.11\ degree[/tex]
[tex]m\angle\ ABC=28.11\ degree[/tex]
Step-by-step explanation:
Answer for the question No.17
Given:-
[tex]\angle\ BAD=(5x+10)\ degree[/tex]
[tex]\angle\ ADC=(87)\ degree[/tex]
[tex]\angle\ DCB=(3x+10)\ degree[/tex]
Let,[tex]m\angle\ ABC=x[/tex]
In quadrilateral ABCD,
[tex]\angle\ BAD+\angle\ ABC+\angle\ DCB +\angle\ ADC =360\ degree[/tex] ---(sum of angle of quadrilateral is 360 degree)
[tex]\therefore\ (5x+10)+x+(3x+10)+87=360[/tex]
[tex]9x+107=360[/tex]
[tex]9x=360-107[/tex]
[tex]9x=253[/tex]
[tex]x=\frac{253}{9}[/tex]
[tex]\therefore\ x=28.11\ degree[/tex]
SInce x=[tex]m\angle ABC[/tex]
[tex]\therefore\ m\angle\ ABC=28.11\ degree[/tex]
what does this expression represent?
12f + 24
A: twenty-four more than twelve times a number.
B: twelve time the difference of a number and twelve four.
C: twelve times the sun of a number plus twelve four.
D: twelve- four more than twelve plus a number.
Answers
24 is added to f times 24
Hope this helps and pls mark as brainliest!
~ Luna
Answer:
A
Step-by-step explanation:
12f means 12 x f
+24 means you add 24
Because of pedmas, you do the multiply first so its (12xf)+24
(Also twelve four isn't a number, so B and C don't make sense)
Which inequality is represented by this graph?
A. -34.5 >х
B. -34.5< x
C. -35.5 > x
D. –35.5 < x
Answers
Because the color portion of the line is lying on the numbers that are less than 34.5. (-35,36,etc)
Hope this helps!!
Answer:
the answer would be A
Step-by-step explanation:
If cosA = 3/5 and A ∈ (0,90), what is sin2A?
Answers
Answer:
[tex]\frac{24}{25}[/tex]
Step-by-step explanation:
Given
cosA = [tex]\frac{3}{5}[/tex] = [tex]\frac{adjacent}{hypotenuse}[/tex]
Then the opposite side using Pythagorean triple is 4, thus
sinA = [tex]\frac{4}{5}[/tex]
Using the trigonometric identity
sin2A = 2 sinAcosA, then
sin2A = 2 × [tex]\frac{4}{5}[/tex] × [tex]\frac{3}{5}[/tex]
= [tex]\frac{2(4)(3)}{5(5)}[/tex] = [tex]\frac{24}{25}[/tex]
Answer:
[tex]\sin(2A)=\frac{24}{25}[/tex]
Step-by-step explanation:
Double angle identity for sine is
[tex]\sin(2A)=2\sin(A)\cos(A)[/tex].
We know [tex]\cos(A)[/tex]. We now need to find [tex]\sin(A)[/tex] to find our answer.
Recall the following [tex]Pythagorean Identity[/tex]:
[tex]\sin^2(A)+\cos^2(A)=1[/tex].
Replace [tex]\cos(A)[/tex] with [tex]\frac{3}{5}[/tex]:
[tex]\sin^2(A)+(\frac{3}{5})^2=1[/tex]
[tex]\sin^2(A)+\frac{9}{25}=1[/tex]
Subtract [tex]\frac{9}{25}[/tex] on both sides:
[tex]\sin^2(A)=1-\frac{9}{25}[/tex]
[tex]\sin^2(A)=\frac{25}{25}-\frac{9}{25}[/tex]
[tex]\sin^2(A)=\frac{25-9}{25}[/tex]
[tex]\sin^2(A)=\frac{16}{25}[/tex]
Now to finally get the value of [tex]\sin(A)[/tex] take the square of both sides:
[tex]\sin(A)=\pm \sqrt{\frac{16}{25}}[/tex]
Since [tex]A[/tex] is in the interval [tex](0,90)[/tex], then [tex]\sin(A)>0[/tex].
[tex]\sin(A)=\sqrt{\frac{16}{25}}[/tex]
[tex]\sin(A)=\frac{\sqrt{16}}{\sqrt{25}}[/tex]
[tex]\sin(A)=\frac{4}{5}[/tex]
So let's finally find the numerical value of [tex]\sin(2A)[/tex].
[tex]\sin(2A)=2\sin(A)\cos(A)[/tex]
[tex]\sin(2A)=2\cdot \frac{4}{5} \cdot \frac{3}{5}[/tex]
[tex]\sin(2A)=\frac{2(4)(3)}{5(5)}[/tex]
[tex]\sin(2A)=\frac{24}{25}[/tex]
Side note:
If [tex]A[/tex] is between 0 and 90 degrees, then we are in the first quadrant.
If we are in the first quadrant, both [tex]x=\cos(A)[/tex] and [tex]y=\sin(A)[/tex] are positive.
Explain how to use 2s facts to find 4 x 9
Answers
Answer:
36
Step-by-step explanation:
when you multiply 2x9 you get 18 and since 2 is half of 4 that means you have to do that twice so do 2x9 again and add both of them up to get a product of 36
The solution to the expression 4 × 9 using 2's facts is;
36
2's facts is basically a method of multiplication whereby we are trying to simplify the expression such that we can call it double.For example; 2 × 5 means double of 5 which is 10.
Let us apply the concept of 2's facts to the given expression in the question;We are given; 4 × 9
Now, we know that 4 is a double of 2 and so we have;
2 × 2 × 9
Since we want to express the result as a double, let us multiply one of the 2 by 9 and retain the other 2.
2 × 9 means double of 2 and it is 18
Then we now have 2 × 18 which implies double of 18 which is 36.
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Krista bought the same number of pencils and erasers with $252. Each eraser costs $18. How many erasers did she purchase?
Answers
Answer:
7 erasers
Step-by-step explanation:
Since we know that she bought the same exact amount of pencils and erasers, we can assume that they are the same price. So, to find how many things she can purchase, divide 252 by 18, which will give you 14.
Then, since she bought the same number of pencils and erasers, divide 14 by 2, which is 7. So, Krista bought 7 pencils and 7 erasers.
You can check your work by multiplying 7 by 18 and adding that to 7 multiplied by 18. You'll get 252, which is the amount Krista started with.
Hope this helps! :)
Answer:
14 erasers.
Step-by-step explanation:
Just simple division!
252/18=14
Find domain and range for f(x)=x^2-2x+2
Answers
Answer:
Domain: (-∞,∞) or -∞ <[tex]x[/tex]<∞
Range: [1,∞) or [tex]y\geq 1[/tex]
Step-by-step explanation:
Given function:
[tex]f(x)=x^2-2x+2[/tex]
To find range and domain of the function.
Solution:
The given function is a second degree function as the highest exponent of the variable is 2. Thus, it is a quadratic function.
For all quadratic functions the domain is a set of all real numbers. So, the domain can be given as: (-∞,∞) or -∞ <[tex]x[/tex]<∞
In order to find the range of the quadratic function, we will first determine if the function has a minimum point or the maximum point.
For a quadratic equation : [tex]ax^2+bx+c[/tex]
1) If [tex]a>0[/tex] the function will have a minimum point.
2) If [tex]a<0[/tex] the function will have a maximum point.
For the given function: [tex]f(x)=x^2-2x+2[/tex]
[tex]a=1[/tex] which is greater than 0, and hence it will have a minimum point.
To find the range we will find the coordinates of the minimum point or the vertex of the function.
The x-coordinate [tex]h[/tex] of the vertex of a quadratic function is given by :
[tex]h=\frac{-b}{2a}[/tex]
Thus, for the function:
[tex]h=\frac{-(-2)}{2(1)}[/tex]
[tex]h=\frac{2}{2}[/tex] [Two negatives multiply to get a positive]
[tex]h=1[/tex]
To find y-coordinate of the vertex can be found out by evaluating [tex]f(h)[/tex].
[tex]k=f(h)[/tex]
Thus, for the function:
[tex]k=f(1)=(1)^2-2(1)+2[/tex]
[tex]k=f(1)=1-2+2[/tex]
[tex]k=f(1)=1[/tex]
Thus, the minimum point of the function is at (1,1).
thus, range of the function is:
[1,∞) or [tex]y\geq 1[/tex]
a daily newspaper has 10225 subscribers when it began publication. six years old later it has 8200 subscribers what is the average yearly rate of change in the number of subscribers for the six year period
Answers
Answer:
The rate of change in number of subscriber for the six years is 3.62%
Step-by-step explanation:
Given as :
The initial subscriber of newspaper = p = 10225
The subscriber of newspaper after 6 years of publish = P = 8200
The time period = t = 6 years
Let The average yearly rate of change = r%
Now, According to question
The subscriber of newspaper after n years = initial subscriber × [tex](1-\dfrac{\textrm rate}{100})^{\textrm time}[/tex]
Or, P = p × [tex](1-\dfrac{\textrm r}{100})^{\textrm t}[/tex]
Or, 8200 = 10225 × [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]
Or, [tex]\dfrac{8200}{10225}[/tex] = [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]
Or, 0.80195 = [tex](1-\dfrac{\textrm r}{100})^{\textrm 6}[/tex]
Taking power [tex]\dfrac{1}{6}[/tex] both side
So, [tex](0.80195 )^{\frac{1}{6}}[/tex] = [tex]((1 - \frac{r}{100} )^{6})^{\frac{1}{6}}[/tex]
Or, 0.9638 = 1 - [tex]\dfrac{r}{100}[/tex]
Or, [tex]\dfrac{r}{100}[/tex] = 1 - 0.9638
Or, [tex]\dfrac{r}{100}[/tex] = 0.0362
Or, r = 0.0362 × 100
i.e r = 3.62
So, The rate of change in subscriber = 3.62%
Hence, The rate of change in number of subscriber for the six years is 3.62% . Answer
What is the value of the expression
0.5 + (-3/4) + 0.25 - (-4/5)
Explain your answer
Answers
Answer:
0.8
Step-by-step explanation:
We begin with the expression: [tex]0.5+(-\frac{3}{4} )+0.25-(-\frac{4}{5} )[/tex]
First, we need to convert the fractions into decimals to make this easier.
[tex]-\frac{3}{4}=-0.75[/tex] and [tex]-\frac{4}{5} =-0.8[/tex]
Once we have this, we can simplify it
[tex]0.5-0.75+0.25-(-0.8)\\\\0.5-0.75+0.25+0.8\\\\0.75-0.75+0.8\\\\0.8[/tex]
Does the ordered pair (−5,−5) satisfy the following system of equations?
{−3x−3y=125x+5y=−20
Answers
Well, let's see. The problem gave you an ordered pair. In other words, you have an 'x' and a 'y' coordinate. All you need to do is put them into the equation.
Step-by-step explanation:
This means that instead of --
-3x - 3y = 125 + 5y = -20
We would have:
-3(-5)-3(-5) = 125(-5) + 5(-5) = -20
From here, you just simplify it into:
30 = -650 = -20
Since the values are not the same, the ANSWER is NO. The ordered pair does not satisfy the following system of equations.
Final answer:
The ordered pair (-5, -5) does not satisfy either of the two given equations, thus it does not satisfy the system of equations.
Explanation:
To determine if the ordered pair (−5,−5) satisfies the given system of equations, we substitute x with −5 and y with −5 into each equation and check if the left-hand side equals the right-hand side.
For the first equation −3x−3y=12, substituting x and y gives us:
−3(−5) −3(−5) = 15 + 15 = 30 which does not equal 12. Therefore, the pair does not satisfy the first equation.
For the second equation 5x+5y=−20, substituting x and y gives us:
5(−5) + 5(−5) = −25 + −25 = −50 which does not equal −20. Therefore, the pair does not satisfy the second equation either.
Since the ordered pair does not satisfy both equations, we can conclude that (−5,−5) does not satisfy the system of equations.
Express the shaded Area as both a faction and a decimal
Answers
The shaded area's Fraction= 21/100 and Decimal = 0.21.
Step-by-step explanation:
When an area is divided into multiple smaller regions ( smaller squares ) is called parts.
In case of Squares, it can be divided into either rows or columns, sometimes both.
Form the given diagram, the square consists of 10 rows and 10 columns which makes 100 (10×10) parts in it.
One fraction is obtained by dividing it by the total number of parts.
In this square, 21 shaded fractions are given.
∴ The fraction of shaded Area = 21/100.
Decimal of shaded Area=0.21.