If a customer rents 22 DVDs, each option costs $29
This only applies to one month.
=================================================
Work Shown:
x = number of DVDs borrowed
y = total cost
Plan A has a cost of x+7 dollars since x represents the cost of renting the x DVDs plus the membership fee of $7. We can say y = x+7.
Plan B has a fixed cost of $29 per month, so y = 29. There is no x here to worry about as the cost is the same no matter how many DVDs you rent.
y = x+7 and y = 29 are dealing with the same y value. We can use substitution to solve for x
----------------
y = 29 ... start with second equation
x+7 = 29 .... replace y with x+7 (valid because y = x+7)
x+7-7 = 29-7 ... subtract 7 from both sides
x = 22
If the customer rents 22 DVDs, then plan A will charge y = x+7 = 22+7 = 29 dollars, which is the same as the flat rate cost plan B charges.
If the customer rents more than 22 DVDs per month, then its smarter to go with plan B (since plan A's cost will be larger). Otherwise, go for plan A.
----------------
In terms of a graph, you can graph both y = x+7 and y = 29 together on the same xy axis. The line y = x+7 goes through (0,7) and (1,8). The line y = 29 goes through (0,29) and (1,29). Both lines intersect at (22,29) to indicate that x = 22 and y = 29 pair up together.
A geometric sequence has a common ratio of 22 and the 12th12th term is −12,288.−12,288.
What is the explicit rule that describes this sequence?
Answer:
Tₙ = -3(2)ⁿStep-by-step explanation:
The explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹ where;
a is the first term of the geometric sequence
r is the common ratio
n is the number of terms
If a geometric sequence has a common ratio of 2 and the 12th term is −12,288, then;
T₁₂ = ar¹²⁻¹
T₁₂ = ar¹¹
Given T₁₂ = -12,288 and r = 2, we can calculate the first term a
-12,288 = a2¹¹
a = -12,288/2¹¹
a = -12,288/2048
a = -6
Since the explicit rule for determining the nth term of a geometric sequence is expressed as Tₙ = arⁿ⁻¹, then for the sequence given, the explicit rule will be;
Tₙ = -6(2)ⁿ⁻¹
Tₙ = -6 * 2ⁿ * 2⁻¹
Tₙ = -6 * 2ⁿ * 1/2
Tₙ = -3(2)ⁿ
Hence the explicit rule that describes this sequence is Tₙ = -3(2)ⁿ
Help please. Thank you
Answer:
D
Step-by-step explanation:
To figure out which ones is 15% of the number, we want to divide the number on the left of ratio, by the number on the right.
4/15=26%
5/33=15.15%
3/25=12%
1.5/10=15%
Answer:
[tex]\large \boxed{\mathrm{D. \ 1.5:10}}[/tex]
Step-by-step explanation:
4 is not 15% of 15.
15% × 15 = 2.25
5 is not 15% of 33.
15% × 33 = 4.95
3 is not 15% of 25
15% × 25 = 3.75
1.5 is 15% of 10.
15% × 10 = 1.5
Answer ASAP please, Will give brainliest.
Answer:
see below
Step-by-step explanation:
The measure of a minor arc is the same as the angle that forms it.
1. Since ∠GBJ = 90°, the answer is 90°.
2. ∠HBI = 180° - 151° = 29° so the answer is 29°.
3. ∠HBJ = 180° so the answer is 180°.
4. The reflex angle ∠GBI = 90 + 151 = 241° so the answer is 241°/
5. Since ∠GBJ = 90°, the reflex angle ∠GBJ = 360 - 90 = 270° so the answer is 270°.
6. ∠GBH = 180 - 90 = 90° so the reflex angle ∠GBH = 360 - 90 = 270° so the answer is 270°.
Which of the following systems has (1,−1) as a solution? 1. 3x−2y=1 5x+3y=8 2. 3x+2y=1 5x+3y=−8 3. 3x+2y=1 5x−3y=8 4. 2x+3y=1 5x−3y=−8
2. 3x+2y= 1 and 5x+3y=-8
solution: In picture.
¿Cuál es el área de un rectángulo, sabiendo que su perímetro mide 24 cm y que su base es el triple de su altura?
Answer:
El área del rectángulo es:
27 cm²
Step-by-step explanation:
Consideración:
La formula del perímetro de un rectángulo es:
p = 2(altura + base)
Planteamiento:
24 = 2(a+b)
b = 3a
a = longitud de la altura del rectángulo
b = longitud de la base del rectángulo
Desarrollo:
sustituyendo el valor de la segunda ecuación del planteamiento en la primer ecuación del planteamiento:
24 = 2(a + 3a)
24/2 = 4a
12 = 4a
a = 12/4
a = 3 cm
de la segunda ecuación del planteamiento:
b = 3a
b = 3*3
b = 9 cm
Comprobación:
de la primer ecuación del planteamiento:
24 = 2(3+9)
24 = 2*12
Respuesta:
la formula del área de un rectángulo es:
A = base * altura
A = 9cn * 3cm
A = 27cm²
The Area of rectangle is 27 unit².
What is Algebra?A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.
Variables are the name given to these symbols because they lack set values.
In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.
Given:
Perimeter = 24 cm
let the height of rectangle be x.
then the base= 3x
Now, Perimeter of rectangle= 2 ( l + w)
24 = 2( x+ 3x)
12 = 4x
x= 12/4
x= 3 units
So, length= 9 units and width= 3 units
Thus, Area of Rectangle= l x w
= 9 x 3
= 27 unit²
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The translated Question is:
What is the area of a rectangle, knowing that its perimeter measures 24 cm and that its base is three times its height?
Bethany sells roses and petunias. The expression 3r+2.5p3r+2.5p3, r, plus, 2, point, 5, p gives the cost (in dollars) of rrr roses and ppp petunias. What is the cost of 777 roses and 888 petunias? \$$dollar sign
Answer: The cost of 7 roses and 8 petunias is $41.
Step-by-step explanation:
Given, Bethany sells roses and petunias. The expression [tex]3r+2.5p[/tex], gives the cost (in dollars) of r roses and p petunias.
Now to find the cost of 7 roses and 8 petunias , put r= 7 and p= 8 in the above expression , we get
[tex]3(7)+2.5(8)=21+20\\\\=41[/tex]
Hence, the cost of 7 roses and 8 petunias is $41.
Let f(x)=x2+10x+37 . What is the vertex form off(x)? What is the minimum value off(x)? Enter your answers in the boxes. Vertex form: f(x)= Minimum value of f(x):
Answer:
The vertex form is f(x) = (x + 5)² + 12
The minimum value of f(x) is point (-5, 12)
Step-by-step explanation:
1) The vertex form of a quadratic equation f(x) = x² + 10·x + 37, which is the form f(x) = a·(x - h)² + k is found as follows;
For the general form of the quadratic equation, f(x) = a·x² + b·x + c
h = -b/(2·a) and k = f(h)
Therefore, for f(x) = x² + 10·x + 37,
a = 1, b = 10
∴ h = -10/2 = -5
k = f(-5) = (-5)² + 10×(-5) + 37 = 12
The vertex form is f(x) = a·(x - h)² + k gives;
f(x) = 1·(x - (-5))² + 12 = (x + 5)² + 12
The vertex form is f(x) = (x + 5)² + 12
2) The minimum value of x is found when d(f(x))/dx = 0
d(f(x))/dx = d(x² + 10·x + 37)/dx = 2·x + 10
d(f(x))/dx = 0 = 2·x + 10
x = -10/2 = -5
We check that it is the minimum by f''(x) being positive;
f''(x) = d(2·x + 10)/dx = 2 which is positive and x = -5 is the x-coordinate of the minimum value of f(x)
The x-coordinate of the minimum value of f(x) minimum value is f(-5) = (-5)² + 10×(-5) + 37 = 12
Therefore, we have;
The minimum value of f(x) = (-5, 12)
Answer:
The vertex is (-5,f(-5)=12), The minimum value of f(x) is 12.
what is the solution set
Answer:
b>11/13
Step-by-step explanation:
The way they use solution set is misleading
just think of it as "the answer"
8b-8>3-5b
13b>11
b>11/13
Answer:
Which properties of systems does a robot have? Which does it not have?
Step-by-step explanation:
The triangle is a right triangle with the right angle marked. Which equation correctly expresses The Pythagorean Theorem for this triangle?
r^2 + s^2 = t^2
The legs are length r and s. Square them and add the squares to get the square of the hypotenuse t. The hypotenuse is always opposite the 90 degree angle.
Answer:
Hey there!
The pythagorean theorem states that the square of one leg plus the square of another leg is equal to the square of the hypotenuse.
Thus, r^2+s^2=t^2.
This can be a challenging topic, and if you need a further explanation, let me know. Hope this helps :)
11
12
The data set represents the total number of tickets each person purchased for a play.
0, 0, 1, 1, 1, 2, 2, 2, 4, 4
What is the median of the data?
O 1
O 1.5
02
O 2.5
Answer:
1.5 because it is the average of the two middle numbers in this scenario.
The median of the data is 1.5 if the data set represents the total number of tickets each person purchased for a play option, second is correct.
What is the median?A median is a middle number in a series of numbers that have been arranged to lift, and it might be more informative of the set of data than the average. When there are extremes in the sequences that might affect the average of the numbers, the median is sometimes employed instead of the mean.
We have data:
0, 0, 1, 1, 1, 2, 2, 2, 4, 4
There are two mid-values in the middle that is 1 and 2
The mean of these two values will be median:
[tex]\rm Median = \dfrac{1+2}{2}[/tex]
Median = 1.5
Thus, the median of the data is 1.5 if the data set represents the total number of tickets each person purchased for a play option second is correct.
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Chad and his family went to the beach. First, they swam in the ocean for 1 hour and 15 minutes. Then they built sand castles for 45 minutes and played volleyball for 1 hour and 30 minutes. When they finished playing volleyball, it was 3:30 P.M. What time did Chad's family get to the beach?
Answer:
12:00
Step-by-step explanation:
so if you add up all the time they were there like this 1 hour + 15 +45+1 hour +30 you will get 3 hours and 30 minutes so then you subtract the the time from the time like this 3:30 so they went at 12:00
In the 2004 Olympic games Russia, China and the United States won a total of 96 gold medallions if the United States won 4 more medals than China and the medals achieved by the United States and Russia are twice those obtained by China determine the number of gold medals won by Russia
Answer:
28
Step-by-step explanation:
x = medals won by Russia
y = medals won by China
z = medals won by United States
Write a system of equations:
x + y + z = 96
z = y + 4
x + z = 2y
Substitute the second equation into the first and third:
x + y + y + 4 = 96
x + y + 4 = 2y
Simplify:
x + 2y = 92
x + 4 = y
Substitute for y:
x + 2(x + 4) = 92
x + 2x + 8 = 92
3x = 84
x = 28
Russia won 28 medals.
Which means China won 32 medals and the US won 36 medals.
How does a globe represent the fact that there are no parallel lines in elliptical geometry? A. The equator is not parallel to any other latitudinal lines. B. The north and south poles are never connected by a geodesic. C. The geodesics connecting the Nortj and South poles never intersect. D. The geodesics connecting the north and south poles intersect at both of the poles.
Answer:
The correct option is;
D. The geodesics connecting the North as South poles intersect at both of the poles
Step-by-step explanation:
As an analog to the straight line, the geodesic of a curved surface is the shortest path between two points on the curved surface
Whereby the Earth is assumed to be spherical, the geodesics around the Earth would then be closed circles and like the longitude and latitude, will meet at the North and South poles
However given that the Earth is an Oblate ellipsoid, Euclid's parallel postulate is not in effect and the geodesics connecting the North and South Poles Intersect at both poles.
The answer is Option D, option D is correct.
what is meaning of rate?
Answer:
1.a measure, quantity, or frequency, typically one measured against another quantity or measure.
Step-by-step explanation:
2.a fixed price paid or charged for something.
Answer:
a measure, quantity, or frequency typically one measured against another quantity or measure.
Assign a standard or value to (something) according to a particular scale.Please Explain step-by-step
An algebra class contains 30 students. Forty
percent of the students in the class are girls. How
many boys are in the class?
Answer:
algebra es muy buena materia
ASAP how many solutions are there for the system of equations shown on the graph?
Answer: Infinitely many solutions
Step-by-step explanation:
The lines is on top of each other so this makes it many solution.
It can't be NO solution because the lines are not parallel to each, which means they will not intersect.
It can't be one solution because the lines doesn't intersect.
It can't be two solutions because the lines never intersect and they never intersect twice either.
What are three collinear points on line l?
points A, B, and F
points A, F, and G
points B, C, and D
points B, F, and G
Answer:
Points A, F, and G are three collinear points on line l.
Step-by-step explanation:
Answer:
Points A, F and G
Step-by-step explanation:
Functions f(x) and g(x) are shown: f(x) = x2 g(x) = x2 − 8x + 16 In which direction and by how many units should f(x) be shifted to match g(x)? Left by 4 units Right by 4 units Left by 8 units Right by 8 units
Answer:
Shift right by 4
Step-by-step explanation:
Given f(x)=x^2
g(x)= x^2-8x+16
Using
Horizontal Shift theorem dealing with the question
If the graph were to be move to to the right, we must use of graph f (x-L)
Where L= 4 and
NOTE:
POSITIVE L MAKES GRAPH SHIFT RIGHT
2) NEGATIVE MAKES GRAPH SHIFT LEFT
g(x)= x^2-8x+16
If we factorize this we have
(x-4)(x-4)
Since the two terms are the same we have (x-4)^2
Then it can move by factor of 4 to the right since constant 4 can be substracted from the parents function
Answer:
Left by 4
Step-by-step explanation:
graph x^2 and x^2 − 8x + 16 on Desmos . com
you start at f(x) and end at g(x)
Find the square root of 2601 by prime factorization (USE MULTIPLICATION METHOD TO SOLVE THE ABOVE QUESTION)
2601|3
867|3
289|17
17|17
1
[tex]\sqrt{2601}=\sqrt{3^2\cdot17^2}=3\cdot17=51[/tex]
This data set is ages at first job. 14, 14, 16, 16, 17, 17, 18, 20, 21, 23 Construct a boxplot. Make sure to include labels.
Answer:
Please find attached the required box and whiskers plot
Step-by-step explanation:
The numbers are given in arranged order as follows;
14, 14, 16, 16, 17, 17, 18, 20, 21, 23
The five number summary are;
The minimum value = 14
The maximum value = 23
The first quartile, Q₁, is the (n + 1)/4th term or the 2.75th term = 14 + 0.75×(16 - 14) = 15.5
The second quartile, Q₂, (the median) is the (n + 1)/2th term or the 5.5th term = 17
The third quartile, Q₃, is the 3(n + 1)/4th term or the 8.25th term = 20 + 0.25×(21 - 20) = 20.25.
Type the correct answer in the box. Use numerals instead of words.
Find the sum of the finite geometric series.
Mr. Jamison deposited $100 into a new savings account on January 1. On the first day of each month thereafter, he deposited three times the amount he deposited in the previous month. On June 15 of the same year, the total amount Mr. Jamison has deposited is $
Answer:
$36,400
Step-by-step explanation:
Mr Jamison deposited $100 in January
February=3*100=$300
March=3{3(100)=3^2(100)=9*100=$900
April=3^3(100)=27*100=$2,700
May=3^4(100)=81*100=$8,100
June=3^5(100)=243*100=$24,300
Total amount=$100 + $300 + $900 + $2700 + $8100 + $24300
=$36,400
The total amount deposited by Mr Jamison on June 15 is $36,400
Which equation can be used to solve the problem?
75 percent of what number is 150?
O
75 x 1
150 x 1
75
150
150 x 2 300
75x2 150
200x2 400
75 x2 150
75 x 2
100 x 2
150
200
Answer:
see below
Step-by-step explanation:
75% of what number is 150
75 150
----- = ---------
100 x
75*2 = 150
So multiply the left by 2/2
75*2 150
----- = ---------
100*2 x
150
------
200
Answer:
The last question
Step-by-step explanation:
I took the test
You move at 45/mph and a bullet is shot at you, the bullet is moving at 44/mph
Would you be able to dodge the bullet, you factor in the fight or flight or freeze response
Answer:
See explanation below.
Step-by-step explanation:
A bullet shot at you will definitely hit you because of the direction it is travelling.
Your fight and flight response won't be activated either because of the speed of the event (bullet) or if you don't know how harmful a gun is (you'll remain calm/ignorant in this case)?
Try to post academic problems.
Best Regards!
Find the measure of b.
Answer:
b = 80°
Step-by-step explanation:
The inscribed angle measuring 100°, is supplementary to the angle opposite it in the inscribed quadrilateral.
Thus, the angle is = 80°
Therefore, b + 80° = 180° (angle on a straight line = 180°).
Thus, b = 180° - 80° = 100°.
The measure of b is 80°.
This figure shows how to create a six-pointed star from twelve equilateral triangle tiles: (SEE FIGURE ATTACHED) If each of the original tiles has a perimeter of 10 cm, what is the perimeter of the final star in cm?
Answer:
Perimeter of the final star = 40 cm²
Step-by-step Explanation:
The perimeter of the six-pointed star is the sum of the sides of the 6 equilateral triangles that form a boundary around the star.
1 triangular tiles gas a perimeter of 10cm.
Only 2 out of the 3 equal sides of each of the 6 equilateral triangles form the boundary of the final star.
Therefore, perimeter of the final star = ⅔ of the total perimeter of 6 triangular tiles
= ⅔ of (10*6)
= ⅔*60
= 2*20
Perimeter of the final star = 40 cm²
A trader bought a bag for 125gh cedis. he later sold it at a profit of 30%. What is his selling price
Answer:
162.5 Cedis
Step-by-step explanation:
Cost Price= 125
Profit % = 30%
Selling price=?
Selling price= Cost price+ profit
Profit = ?
[tex]profit \% = \frac{profit}{cost \: price} \times 100[/tex]
[tex]30 \% = \frac{x}{125} \times 100[/tex]
[tex]30 \% = \frac{100x}{125} \\ 30 \times 125 = 100x[/tex]
[tex]3750 = 100x \\ \frac{3750}{100} = \frac{100x}{100} \\ x = 37.5[/tex]
Profit = 37.5 gh Cedis
Selling price= 125+37.5
Selling price= 162.5 gh Cedis
The selling price of a bag is 162.5Cedis.
It is required to find the selling price.
What is profit?The profit is defined as the amount gained by selling a product, and it should be more than the cost price of the product.
Given that :
Let the profit be x.
Cost Price= 125
Profit % = 30%
profit%=profit/cp*100
30=profit/125*100
3750=100x
x=37.5
profit=37.5
Selling price= Cost price+ profit
Selling price=125+37.5
Selling price=162.5ghcedis
So, the selling price of a bag is 162.5Cedis.
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can someone explain this please?
Answer:
3 + 2y = 2 + 4y
Step-by-step explanation:
1. Create the equation
3 + 2y = 2 + 4y
There are 3 "1" blocks and 2 "y" blocks on the left. There are 2 "1" blocks and 4 "y" blocks on the right. The scale shows both are equal.
Answer:
3 + 2y = 2 + 4y
Step-by-step explanation:
To create an equation from this model, we look at both sides of the scale. The left has three 1 units and two y units, and there are two 1 units and four y units on the right side. Since the scale shows that both sides are equal in weight, we know that our equation would have an equal sign to show they are equal.
Left: Three 1 units can be written as 3 and two y units could be written as 2y.
Right: Two 1 units can be written as 2 and four y units could be written as 4y.
Now, we put these values together (with an equal sign) to get:
3 + 2y = 2 + 4y.
Hope this helps!
Convert to slope-intercept from: y-3=6(x-5)
Answer:
y = 6x -27
Step-by-step explanation:
y-3=6(x-5)
Distribute
y-3 = 6x-30
Add 3 to each side
y-3+3 = 6x-30+3
y = 6x -27
This is in slope intercept form y=mx+b where m is the slope and b is the y intercept
Hey there! I'm happy to help!
Slope intercept form is y=mx+b. So, the first thing we want to do is isolate y on side of the equation.
y-3=6(x-5)
We use distributive property to undo parentheses.
y=3=6x-30
We add 3 to both sides.
y=6x-27
Now, this in slope intercept form.
Have a wonderful day! :D
a=v^2/r Solve the formula for r
Answer:
[tex]\Large \boxed{r =\frac{v^2 }{a}}[/tex]
Step-by-step explanation:
[tex]\displaystyle a=\frac{v^2 }{r}[/tex]
We need to rearrange and solve the formula for [tex]r[/tex].
Multiply both sides of the equation by [tex]r[/tex].
[tex]\displaystyle a \times r=\frac{v^2 }{r} \times r[/tex]
Simplify the equation.
[tex]ar=v^2[/tex]
Divide both sides of the equation by [tex]a[/tex].
[tex]\displaystyle \frac{ar}{a} =\frac{v^2 }{a}[/tex]
Simplify the equation.
[tex]\displaystyle r =\frac{v^2 }{a}[/tex]
the angles of traingle are in the ratio 3:7:8 find them in degrees as well as in radians
