The inequality that can be used to find the number of weeks after which it would be cheaper to buy the console than to rent it is B.78 + 8.95z, < 24.99z
How to calculate the inequality?From the information, Nina can buy a video game console for $78, and rent a game for $8.95 per week or she can rent a console and game for $24.99 per week.
The appropriate inequality will be:
= 78 + (8.95 × z) < 24.99 × z
= 78 + 8.95z, < 24.99z
Therefore, the correct option is B.
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Can someone help me please
Using translation concepts, the graph of square CDEF after a rotation 270º counterclockwise around the origin is given at the end of the answer.
What is a translation?A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.
The rule for a rotation 270º counterclockwise around the origin is:
(x,y) -> (y,-x).
Hence the vertices of the rotated graph will be given as follows:
E': (-4,-3) -> (-3, 4).F': (-9,-3) -> (-3, 9).D': (-4,-8) -> (-8, 4).C': (-9,-8) -> (-8, 9).The graph with these vertices is given at the end of the answer.
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SOMEONE HELP PLS ILL MARK BRAINLIEST
Answer:
Statements:
1) -2(x-4)=2x+12
2) -2x+8=2x+12
3) -4x+8=12
4) -4x=4
5) x=-1
Reasons:
1) Given
2) Distributive Property
3) Combine like terms/Subtraction Property of Equality (subtract 2x from both sides).
4) Subtraction Property of Equality
5) Division Property of Equality
If y and x vary directly and
y=1.4when x=3.2, what is x when y=2.6? Round to two decimal places. Show your work
If y and x vary directly, the value of y=2.6 then value of x is 1.14.
The tenths place is represented by the initial digit following the decimal. The hundredths place is denoted by the digit that followed the decimal. Up until there are no additional digits, the remaining ones keep the place values filled in the quantity.
For example, 2.84620364 can be round to two decimal places as 2.85, and 0.8035 can be round to two decimal places as 0.80.
Here x and y vary directly,
So , x/y = k
Therefore K is constant
For x = 3.2 and y = 1.4
Then x/y = k
3.2/1.4 = k
K = 1.6/0.7
If y = 2.6 what is x
y = 2.6 and k = 1.6/0.7
2.6/x = 1.6/0.7
1.6x = 18.2
X = 1.1375.
Hence, the Round to two decimal places of x is 1.14
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find the volume of a cylinder with radius 6 and height 16,pi= 3.142
The volume of the cylinder is 1809.5 cubic units.
What is the volume of a cylinder?The volume of a cylinder is equal to the product of the area of the circular base and the height of a cylinder. The volume of a cylinder is defined as the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it
V = πr²h
where 'r' is the radius of the base (circle) of the cylinder
'h' is the height of the cylinder
Given that a cylinder with a radius of 6 and height of 16.
Here r = 6 and h = 16,
the volume of a cylinder = πr²h
the volume of a cylinder = π(6)²×16
the volume of a cylinder = 1809.5 cubic units
Thus, the volume of the cylinder is 1809.5 cubic units.
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What value of x is in the solution set of 2(3x - 1) ≥ 4x - 6?
-10
-5
-3
-1
Answer:
-1
Step-by-step explanation:
[tex]2(3x-1) \geq 4x-6 \\ \\ 6x-2 \geq 4x-6 \\ \\ 2x \geq -4 \\ \\ x \geq -2[/tex]
Answer:
-1 is the answer
Step-by-step explanation:
f(1)=30,f(n)=2•f(n-1)-50
The explicit formula of the sequence is Tn = 30 - 20(n - 1)
How to determine the explicit formula of the sequence?The recursive formula of the sequence is given as
f(1) = 30, f(n) = 2 • f(n - 1) - 50
The above means that
f(n) = 2 • f(n - 1) - 50
f(1) = 30
Substitute 2 for n
So, we have
f(2) = 2 • f(2 - 1) - 50
Evaluate the difference
So, we have
f(2) = 2 • f(1) - 50
Substitute f(1) = 30 in f(2) = 2 • f(1) - 50
f(2) = 2 • 30 - 50
Evaluate
f(2) = 10
Substitute 3 for n
So, we have
f(3) = 2 • f(3 - 1) - 50
Evaluate the difference
So, we have
f(3) = 2 • f(2) - 50
Substitute f(2) = 10 in f(3) = 2 • f(2) - 50
f(3) = 2 • 10 - 50
Evaluate
f(3) = -30
So, we have the first three terms to be
30, 10, -10
The above represents an arithmetic sequence, where
First term, a = 30
Common difference = -20
The nth term of the sequence is
Tn = a + (n - 1)d
So, we have
Tn = 30 - 20(n - 1)
Hence, the explicit formula of the sequence is Tn = 30 - 20(n - 1)
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the expanded form for 300,648 can be written with only 4 addends . explain how this is possible for a number with 6 digits
Answer:
The expanded form of 300684 can be written with only 4. Add ends, explain how this is possible for a number with 6 digits. When we look at this number, we want to write that in expanded form, which means we want to write the value of each digit. So i look at the value the 4 in the one's place, so its value is 4 actually 4. The 8 is in the tense place, so its value is 810 point. The 6 is in the hundreds place, so its value is 600 point. The 0 is, in the thousands place, that's 0. Thousands. This 0 is in the 10000 point, so we have 010000 and i'm running out of room. So this 3 is in the 100000. Place of its value is 3 times 100000. It just think of it like money, you have 810 dollar bills, 600 dollar bills, etcetera. So if you have 41 dollar bills, you have 4 dollars. If you have 810 dollar bills, you have 80 dollars: 600 dollar bills. You have 600 dollars now. If you have 0 thousands and 010000, you don't have any money in this, so you don't need to write that down. So now i have 300 dollar bills. Some got a value of 300000 point, so they could leave me only 4 digits that i'm adding together reason being this was 0, so there was no value there.
Which equation represents the ellipse with vertices located at (3,-3) and (3,-13) and foci at (3,-5) and (3,-11)?
Check the picture below, so the ellipse looks more or less like so.
[tex]\textit{ellipse, vertical major axis} \\\\ \cfrac{(x- h)^2}{ b^2}+\cfrac{(y- k)^2}{ a^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2- b ^2} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]
[tex]\begin{cases} h=3\\ k=-8\\ a=5 \end{cases}\implies \cfrac{(x-3)^2}{b^2}+\cfrac{(y-(-8))^2}{5^2}=1 \\\\\\ \stackrel{\textit{we also know that}~\hfill }{c=3\hspace{3.5em} 3=\sqrt{5^2 - b^2}} \implies 3^2=5^2-b^2\implies b=\sqrt{5^2-3^2} \implies \boxed{b=4} \\\\\\ \cfrac{(x-3)^2}{4^2}+\cfrac{(y-(-8))^2}{5^2}=1\implies \cfrac{(x-3)^2}{16}+\cfrac{(y+8)^2}{25}=1[/tex]
What is the solution for Elena's equation
Answer:
Step-by-step explanation:
The equation which has exactly one solution is .
The equation which has exactly infinitely many solutions is .
A carpet is made with a blend of wool and other fibers. If the concentration of wool in the carpet is 75% and the carpet weighs 169 lb, how much wool is in the carpet?
lb
Answer:
Hope the picture will help you
What's the length of segment LM?
Answer:
6
Step-by-step explanation:
17 is the total length
11 is part of the length
17-11 =6
Zoie is painting a picture that is 15 by 27 inches. She plans to frame it in a frame x inches wide.
Write a polynomial that will be the area of the framed picture.
What will be the area of the picture with the frame if x=3?
If the width of the painting is w, then its length is 2w. Then, since the frame is 2 inches thick on each side of the painting, its width is w+4 and its length is 2w+4. So the area of the rectangle bounded by the frame (which includes both the area of the frame and the area of the painting) is (w+4)(2w+4).
The area of the painting is w×2w=2w2, and the area of the frame is 196 square inches, so the area of the two combined is 2w2+196. However, that is the same area as the other one I described, so we can then equate the two, i.e. (w+4)(2w+4)=2w2+196. You can then solve that equation for w, and hence find all of the relevant dimensions.
A survey of 75 people found 45 like rabbits, 32 like hamsters, and 15 like both animals. How many people like neither animal?
Step-by-step explanation:
two people like neither animal
Answer:
13
Step-by-step explanation:
15+75-32-45
90-32-45
58-45
13
A total of $35,000 is to be invested, some in bonds and some in certificates of deposit (CDs). If the amount invested
in bonds is to exceed that in CDs by $1,000, how much will be invested in each type of investment?
The amount invested in CDs is S
The amount invested in bonds is
The amount invested in each type of investment should be $17,000 and $18,000, respectively, as this problem is based on simple interest.
What is a simple mathematical interest?Calculating the amount of interest that will be owed on a sum of money at a certain rate and for a specific period of time is possible using simple interest. Contrary to compound interest, where we add the interest of one year's principal to the next year's principal to compute interest, the principal amount under simple interest remains constant.
based on the facts provided;
Calculating the investment amount:
Since the certificate of deposit is assumed to be x in this instance, the bond should be $35,000 - x.
The formula now should be
($35,000 - x) - x = $1,000
$35,000 - 2x = $1,000
$34,000 = 2x
x = $17,000
So, the bond should be
= $35,000 - $17,000
= $18,000
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Joanna's vegetable garden covers an area of 16 of a square mile. If the garden is 14 mile wide, how long does the garden stretch?
112 mile
1 over 12 mile
512 mile
5 over 12 mile
23 mile
2 thirds mile
34 mile
The length of the rectangular garden given the area and width is 8/7 miles
Area of rectangleA rectangle is a form of quadrilateral having opposing sides parallel and four right angles. The area of a rectangle can be calculated by multiplying the length by width.
Width of the rectangular garden = 14 mileLength of the rectangular garden = x mileArea of the garden = 16 square milesArea of a rectangular garden = length × width
16 = x × 14
16 = 14x
divide both sides by 14x = 16 / 14
x = 8/7 miles
Therefore, the length of the rectangular garden given the area and width is 8/7 miles.
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Anna has 55 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exactly
four times as many pennies as dimes, how many pennies are in her piggy bank?
Answer: 44 Pennies
Step-by-step explanation: The ratio of pennies to dimes is 4:1. Add both numbers up to get 5 and divide 55 by 5 to get 11. multiply 4 and 1 from the ratio by 11 to get 44 and 11. This is the number of pennies and dimes.
What’s next in this pattern and what would be the conjecture of this pattern? Please I really need help fast
The next in the pattern is ← and the conjecture is a rotation by 90 degrees in the clockwise direction
How to determine the next in the pattern?The pattern is given as:
↑, →, ↓
In the above pattern, we can see that each arrow is rotated 90 degrees in the clockwise direction
When the arrow ↓ is rotated in this direction, we have:
←
Hence, the next in the pattern is ← and the conjecture is a rotation by 90 degrees in the clockwise direction
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Hello,
Does this exercise look correct?
10. Rebecca goes to a bank with $2000 she has saved over the summer. The bank advertises a 3% interest rate when opening a savings account. The bank compounds the money daily with an exponential formula of A(t) = Pe^rt, where P represents the initial amount deposited, e is Euler's constant (approximately 2.71828), r is the rate in decimal form, and t is the total time. Rebecca wants to know how much money will be in her savings account after 10 years.
P = 2000
e = Euler's constant (2.71828)
r = 0.03
t = 10
A(t) = Pe^rt
A(10) = 2000 * 2.71828^ 0.03*10
A(10) = 2000 * 2.71828^ 0.3
A(10) = 2699.71707036 ≈ $2700
Answer: Yes it looks correct i also did it myself and got the same answer
Step-by-step explanation:
9. Steven wants to buy a $595 bicycle. Steven has no money saved, but will be able to deposit $30 into a
savings account when he receives his paycheck each Friday. However, before Steven can buy the bike, he
must give his sister $65 that he owes her. For how many weeks will Steven need to deposit money into his
savings account before he can pay back his sister and buy the bike?
22 weeks
b.
21 weeks
d.
23 weeks
26 weeks
C.
a.
5
Answer:
22 weeks
Step-by-step explanation:
595+65=660
22x30=660
so he could buy a bicycle and owes his sister the money after 22 weeks
F(x) = 2x-1. Translation 3 units right followed by a vertical stretch by a factor of 2.
According to the parameters given, the rule again for graph of g after so transformations of a function F(x) = 2x - 1 is g(x) = -4x + 4.
What is defined by the term translation?A translation is a form of transformation in which every point in a figure moves the same distance within the same direction. are frequently alluded to as slides A translation can be described using words such as "moved up 3 more than 5 to the left" or even with notation.The graph for the given function defined by the equation;
F(x) = 2x - 1
Initially, the graph of g is a three-unit translation, so we have;
g(x) = f(x) + 3g(x) = 2x - 1 + 3 = 2x + 2Then comes a vertical stretch by such a factor of two and a reflection in the x axis.
The above means that graph must all be multiplied by 2 and that x values containing x are now considered to be -x.
g(x) = 4x + 4And an x-axis reflection yields;
g(x) = 4(-x) + 4g(x) = -4x + 4Thus, the rule for making the graph of function g(x) is by; g(x) = -4x + 4.
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HELPPPP PLEASE John walks away from his house down a straight street. The graph shows John's distance from his house over time. Describe his trip. Find John's speed on each section of the walk.
John's speed on each section of the walk are 4 km per hour, 0 km per hour and 1.5 km per hour
How to find John's speed on each section of the walk?On the first section, we have the following points
(x, y) = (0, 0) and (1.5, 6)
The speed is calculated as
Speed = (y2 - y1)/(x2 - x1)
This gives
Speed = (6 - 0)/(1.5 - 0)
Evaluate
Speed = 4
On the second section, we have the following points
(x, y) = (1.5, 6) and (2, 6)
The speed is calculated as
Speed = (y2 - y1)/(x2 - x1)
This gives
Speed = (6 - 6)/(2 - 1.5)
Evaluate
Speed = 0
On the third section, we have the following points
(x, y) = (2, 6) and (6, 0)
The speed is calculated as
Speed = (y2 - y1)/(x2 - x1)
This gives
Speed = (0 - 6)/(6 - 2)
Evaluate
Speed = -1.5
Hence, John's speed on each section of the walk are 4 km per hour, 0 km per hour and 1.5 km per hour
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PLEASE! Need help for question 12&14
Answer:
12. BC = 8
14. JL = 18
Step-by-step explanation:
You want to apply the Segment Addition theorem to two problems.
The segment addition theorem tells you the whole is the sum of the parts. The equation for each problem reflects this fact. When given values are substituted, the answer becomes clear.
12.AB +BC = AC
7 +BC = 15
BC = 8 . . . . . . . . subtract 7
14.JK +KL = JL
8 +10 = JL = 18
__
Additional comment
It often helps to draw a diagram.
What is the solution to the inequality? |x−2|≥9
Due to modulus there can be two answers, one with greater than equal to and one with less than equal to. So the answer is 11 and -7.
Solve the inequality |x−2|≥9
Inequality is a Mathematical statement that shows the relation between two expressions using the inequality symbol. The expressions on both sides of an inequality sign are not equal. It means that the expression on the left-hand side should be greater than or less than the expression on the right-hand side or vice versa.
a) |x−2|≥9 = x-2≥ 9
=> x≥ 9+2
=> x≥ 11
b) |x−2|≥9 = x-2≥ -9 (when sign the negative the greater than equal to sign changes to less than equal to sign)
= x ≤ -9+2 ≤-7
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At a workshop , each of the 100 participants hugs each other participants once. Find the total number of hugs?
Answer:
10000
Step-by-step explanation:
100 hugs x 100 hugs
= 10,000 hugs.
Cynthia Besch wants to buy a rug for a room that is 19 ft wide and 33 ft long. She wants to leave a uniform strip of floor around the rug. She can afford to buy 275 square feet of carpeting. What dimensions should the rug have?
The dimensions of the rug that Cynthia Besch should buy are 11 ft wide and 25 ft long, which gives an area of 275 ft².
How are the dimensions determined?The dimensions of the rug include the width and the length.
Cynthia is budget-constrained to buy 275 ft² only.
When we factorize 275, we have 1, 5, 11, 25, 55, and 275.
The possible combinations of width and length to get 275 ft² and also ensure that a uniform strip of the floor is left around the rug are 11 ft and 25 ft. This width and length are less than the room's width and length and satisfy the requirement for a uniform strip.
The strip from the room's width and length must be 8 ft each (from all sides).
Data and Calculations:Width of room = 19 ft
Length of room = 33 ft
Area of room = 627 ft²
Dimensions:Width of rug = 11 ft(19 - 8)
Length of rug = 25 ft (33 - 8)
Area = 275 ft² (11 x 25)
Thus, the dimensions of the rug that Cynthia Besch should buy are 11 ft wide and 25 ft long.
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Magic Mirror has $428,210 in capital and $87,498 in
liabilities. Find the assets.
The total asset of Magic mirror is $515,708
How to find the asset of magic capital?Magic Mirror has $428,210 in capital and $87,498 in liabilities.
The capital is also know as the equity which means the company's net worth.
Liabilities are everything a business owes, now and in the future.
Assets are everything a business owns. Assets may be current or fixed assets
Therefore,
Total Assets - Total Liabilities = Capital
Where
Total Liabilities = $87,498Total assets = ?Capital = $428,210Hence,
Total Assets = $87,498 + $428,210
Total Assets = $515,708
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Use only the commutative property of addition to complete the statement.
2x + 21=
Based on the commutative property of addition, 2x + 21 = 21 + 2x.
What is the Commutative Property of Addition?The commutative property of addition states that when we change the order of arrangement of the addends, the value of the sum remains the same.
For example, 3 + 4 = 4 + 3.
Also, given the statement 2x + 21, we can state that:
2x + 21 = 21 + 2x
Therefore, based on the commutative property of addition, 2x + 21 = 21 + 2x.
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Determine how long it will take for a principal amount of $1,500 to become double its initial value when deposited into an account paying interest at a rate of 13%, continuously compounded.
A.
5.33 years
B.
6.32 years
C.
11.25 years
D.
14.33 years
c is incorrect
The sum of three lengths of a fence rages from 31 to 40 inches. Two side lengths are 9 and 12 inches. If the length of the third side is x inches, write and solve a compound inequality to show the possible lengths of the third side
Answer:
10 ≤ x ≤ 19
Step-by-step explanation
The sum of the three lengths is 9 + 12 +x = 21 + x
We know the sum ranges from 31 to 40
So we get the inequality
31 ≤ 21 + x ≤ 40
Subtracting 21 from each part of this inequality give
31-21 ≤ x ≤40-21
10 ≤ x ≤ 19
The compound inequality to show the possible lengths of the third side is 10 ≤ x ≤ 19.
What is inequality?A statement of an order relationship-greater than, greater than or equal to, less than, less than or equal to- between two numbers or algebraic equations.
Now it is given as,
Range of sum of three lengths of a fence = 31 to 40 inches
Length of two sides = 9 and 12 inches
Length of third sides = x inches
So, length of sum of three lengths of a fence = 9 + 12 + x
⇒ length of sum of three lengths of a fence = 21 + x
∵ Range of sum of three lengths of a fence = 31 to 40 inches
31 ≤ length of sum of three lengths of a fence ≤ 40
⇒ 31 ≤ 21 + x ≤ 40
Subtracting 21 we get.
10 ≤ x ≤ 19
Thus, the compound inequality to show the possible lengths of the third side is 10 ≤ x ≤ 19.
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I need to prove x*0=0 with field axioms?
Hence proved, x*0 = 0.
A statement that is assumed to be true is referred to as a postulate, axiom, or assumption. It is used as the foundation for further deductive reasoning and arguments.
Given many of the typical formulations of the Peano axioms, for example, this is the base case for the definition of multiplication, so it’s an axiom, not a theorem.
x*o = 0
By using an example as rings:
Therefore, By definition of negotiation
= x + (-x)
0 = x · 1 + ( - x) where 1 is the multiplicative identity,
Now,
= x · ( 0 + 1) + ( - x)
Therefore by distributive law,
= x · 0 + x · 1 + (-x)
Where 1 is the multiplicative identity.
By definition of negotiation,
= x · 0 + x + (-x)
= x · 0 + 0
Where 0 is the additive identity.
= x · 0
Therefore, x*0 = 0
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