Answer:
3x2(4x – 3) + 1(4x – 3)
Step-by-step explanation:
Carlos bought 80 feet of wire for $17.60. He needs 30 more feet. If the unit price is the same, how much will he pay for the extra 30 feet of wire?
Answer:
Carlos bought 80 feet of wire for $17.60.
Then the price for 1 feet of wire is 17.6/80 = 0.22
=> 30 feet of wire would cost: 30 x 0.22 = 6.6
Hope this helps!
:)
You start a chain email and send it to 3 friends. The process continues and each of your friends forward the email to 3 other people. What is an expression for the nth term an?
Answer:
[tex]a_{n}=3^{n}[/tex]
Step-by-step explanation:
We can start solving this problem by making a list of the number of chain emails that are sent on each round:
Round one:
[tex]a_{1}=3[/tex]
which represents the three friends you send the mail to.
Round two:
[tex]a_{2}=3*3=9[/tex]
since each of your friends sends the mail to another three friends, then we multiply the original 3 friends by 3 to get a total of 9.
Round three:
[tex]a_{3}=3*3*3=9*3=27[/tex]
on the next round we multiply the previous 9 persons by 3 mails each giving us a total of 27 persons receiving the mail. A patter starts showing here. Notice that for each round we need to take the previous round number an multiply it by 3. When we have a number being multiplied by itself n times, we rewrite it as a power, so the expression for the nth term will be:
[tex]a_{n}=3^{n}[/tex]
which is our final answer.
how much money does ron have each month
Answer:
after paying all expenses Ron will have $10 leftover each month.
Answer:
10 on edge
Step-by-step explanation:
Which represents the solution(s) of the system of equations, y = -x2 + 6x + 16 and y = - 4x + 37? Determine the solution set
algebraically
O (325)
(-3, 49)
(3,25) and (79)
(-3, 49) and (-7, 65)
Answer:
The answer is c
Step-by-step explanation:
(7,9) (3,25)
The solution sets of the given system of equations are (3,25) and (7,9).
Given equations are :
[tex]y=-x^{2} +6x+16[/tex]........(1)
[tex]y=-4x+37[/tex]...........(2)
What is an equation?An equation is a statement that equates to two expressions.
So, for the solutions of the given system of equations
[tex]-x^{2} +6x+16=-4x+37[/tex]
[tex]x^{2} -10x+21=0[/tex]
[tex]x^{2} -3x-7x+21=0\\x(x-3)-7(x-3)=0[/tex]
[tex](x-3)(x-7)=0[/tex]
So, [tex]x=3[/tex]
[tex]x=7[/tex]
Corresponding y value for x=3
[tex]y=-4*3+37\\y=25[/tex]
Corresponding y value for x=7
[tex]y=-4*7+37[/tex]
[tex]y=9[/tex]
Hence, the solution sets of the given system of equations are (3,25) and (7,9).
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If 3x and 71/x are two prime numbers V x equivalent to R, then number of x so that 3x + 71/x = 10 is/ are
Answer:
x = 5/3Step-by-step explanation:
Guven two prime numbers to be 31/x and 71/x, if their sum is 10 as given;
3x + 71/x = 10 then to find the value of x, the following steps must be taken;
Step 1
Find the LCM of the given equation;
3x + 71/x = 10
[tex]\frac{3x^{2}+71 }{x} =10\\[/tex]
Step 2:
Cross multiplying;
[tex]3x^{2} +71=10x\\3x^{2} -10x+71 =0\\[/tex]
Using the general formula to get the value of x;
x = -b±√b²-4ac/2a
a=3, b=-10, c=71
= 10±√(-10)²-4(3)(71)/2(3)
= 10±√100-852/6
= 10±√-752/6
= 10±27.4i/6
= 10+27.4i/6 or 10-27.4i/6
x = 5/3+27.4i/6 or 5/3-27.4i/6
Since the values of x are real values then, our answer will be the real part of the complex number gotten.
x = 5/3
Margo can purchase tile at a store for $0.89 per tile and rent a tile saw for $45. At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile. How many tiles must she buy for the cost to be the same at both stores?
Margo must buy ____ tiles for the cost to be the same at both stores.
Answer:
She must buy 90 tiles for the cost to be the same at both stores
Step-by-step explanation:
Let x be the no. of tiles bought for the cost to be the same at both stores
Margo can purchase tile at a store for $0.89 per tile at shop 1
Cost of x tiles =0.89x
She rent a tile saw for $45.
So, total cost at Store 1 = 0.89x+45
At another store she can borrow the tile saw for free if she buys tiles there for $1.39 per tile.
So, cost of 1 tile = 1.39
Cost of x tiles = 1.39x
ATQ
0.89x+45=1.39x
45=1.39x-0.89x
45=0.5x
[tex]\frac{45}{0.5}=x[/tex]
90=x
Hence She must buy 90 tiles for the cost to be the same at both stores
Factor the expression 2x4y – 18x2y3 completely.
A. 2x2y(x2 – 9y2)
B. 2x2y(x – 3y)(x + 3y)
C. 2x2y(x – 3y)2
D. 2x2y(x – 9y)(x + 2y)
Answer:
B
Step-by-step explanation:
[tex]2x^{4}y - 18x^{2}y^{3}[/tex]
Both sides have [tex]x^{2}[/tex]
[tex]x^{2} (2x^{2}y - 18y^{3})[/tex]
Both sides have y
[tex]yx^{2} (2x^{2} - 18y^{2})[/tex]
Both sides have 2
[tex]2yx^{2} (x^{2} - 9y^{2})[/tex]
Rule : [tex]x^{2} - y^{2} = (x+y)(x -y)[/tex][tex]x^{2} = x.x\\9y^{2} = 3y. 3y[/tex]
[tex](x^{2} - 9y^{2}) = (x +3y) (x-3y)[/tex]
Final:
[tex]\red{ 2 {x}^{2} y(x - 3y)(x + 3y)}[/tex]
Hope this helps ^-^
The factored expression is 2x²y(x + 3y)(x- 3y), and option (B) is correct.
What is Factorization?The act of expressing a number or other mathematical object as the sum of numerous factors is known as factorization.
The given expression is 2x⁴y-18x²y³.
Factor the expression as follows:
2x⁴y-18x²y³
= 2x²y(x² - 9y²)
= 2x²y(x² - (3y)²)
= 2x²y(x + 3y)(x- 3y)
Hence, the factored expression is 2x²y(x + 3y)(x- 3y), and option (B) is correct.
Learn more about factorization:
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What is the area of the triangle (I need this today pls help)
Answer: 24 units^2
(12*4)/(2)=24
Step-by-step explanation:
Answer:
Step-by-step explanation:
4*12/0.5=96
What is the distance between points A(13, 2) and B(7, 10)
Answer:
distance = sqrt((x2-x1)^2 + (y2-y1))
distance = sqrt((7-13)^2 + (10-2)^2)
distance = sqrt( -6^2 + 8^2)
distance = sqrt(36+64)
distance = 10
Step-by-step explanation:
Answer:
10 units
Step-by-step explanation:
d = [tex]\sqrt{(x2 - x1)^2 + (y2 - y1)^2}[/tex]
d = [tex]\sqrt{(13 - 7)^2 + (2 - 10)^2}[/tex]
d = [tex]\sqrt{(6)^2 + (-8)^2}[/tex]
d = [tex]\sqrt{36 + 64}[/tex]
d = [tex]\sqrt{100}[/tex]
d = 10 units
Which statement is true about a line that contains the point ሺ2, 7ሻ and has a slope of 0.5?
A The line will also contain the point ሺ4, 6ሻ.
B The line will have a y-intercept of 6.
C The line will contain points whose y-coordinate will decrease in value as you move to the right
D none of the above
Answer:
I think it is C) The line will contain points whose y-coordinate will decrease in value as you move to the right
Step-by-step explanation:
HOPE THIS HELPS
Positive ÷ positive = ?
Answer:
positive
Step-by-step explanation:
Hunter earned a grade of 5% on his multiple-choice math final that had a total of 60 problems. How many problems on the final exam did Hunter answer correctly?
Answer:
3
Step-by-step explanation:
From the information given in the statement, you can find the number of problems that Hunter answered correctly by calculating the 5% of 60. This because 5% is the grade that he got which means that he only had 5% of his answers correctly and 60 is the total number of problems:
60*5%= 3
According to this, Hunter answered correctly 3 problems on the final exam.
Find the total volume of the rectangular prisms.
A) 88 units3
B) 96 units3
C) 104 units3
D) 114 units3
Answer:
C) 104 units^3
Step-by-step explanation:
The formula for volume in a rectangular prism is V=lwh
There are three total rectangular prisms, so take the volume of each individual prism and add them together to get the total volume.
smallest: V=(2)(2)(4) = 16
Medium: (2)(2)(6) = 24
Largest: (2)(2)(16) = 64
Add it together: 16+24+64= 104
Your answer is 104 units^3
:)
Sumara Kato's savings account has a balance of $1663. After 19 years, how much interest
will she have earned if her rate is 5.5% compounded annually?
(1) $3159.70 (2) $2936.27 (3) $2942.27
(4) $2925.27
Answer: $2936.27
Step-by-step explanation:
Present value = $1663
Rate = 5.5%
Time(n) = 19years
Future value= PV(1+r)^n
= 1663(1+5.5%)^19
= 1663(1.055)^19
=1663 × 2.766
=4599.86
Interest = Future value - Present value
= $4599 - $1663
= 2936
A savings account balance is compounded continuously.If the interest rate is 3.1% per year and the current balance is 1077.00 in how many years will the balance reach 1486.73?
Answer:13.8 is the best answer i could get
Step-by-step explanation:1,077 multiply that × 13.8 =14,862
If you are given a paper which has lines which are the length of a needle apart, and then you repeated drop that needle onto the paper, the probability that the needle with cut the line is:
Answer:
The correct option is;
[tex]\frac{1}{\pi }[/tex]
Step-by-step explanation:
Here we have that
[tex]Probability = \frac{Number \, of \, required\, outcomes}{Number \, of \, possible\ outcomes} = \frac{Dimension \, of \, the \, line}{Size \, of \, the \ needle} = \frac{l \times D}{\pi \times D \times l } = \frac{1}{\pi }[/tex]
Therefore, the probability that the needle will cut the line = 1/π.
Mr. Stewart used a gallon of vinegar to make 15 different color egg dipping containers. He used the same amount of vinegar in each container. How much vinegar in gallons was used in each egg dye container?
Answer:
0.067 gallons ( to 2 decimal places)
Step-by-step explanation:
First, note that since the same amount of vinegar was used in each container, it means that the 1 gallon of vinegar was divided equally to the 15 containers, hence the amount of vinegar used in each dye container is calculated as follows:
total volume of vinegar = 1
number of egg dye containers = 15
if equal volume of vinegar was used in each container:
volume of vinegar in each egg dye container = 1 ÷ 15 = 0.067 gallons ( to 2 decimal places)
Orla and Eduardo each looked at a strand of their hair under a microscope and measured the diameter. Orla's strand was 0.005\,\text{cm}0.005cm0, point, 005, start text, c, m, end text in diameter, and Eduardo's strand was 0.012\,\text{cm}0.012cm0, point, 012, start text, c, m, end text in diameter. How much greater was the diameter of Eduardo's hair?
Answer:
30x2010x943
Step-by-step explanation:
219x29192
Answer:
0.007
Step-by-step explanation:
The diagram shows a square-based cuboid.
10 cm
4 cm
Work out the volume of the cuboid.
State the units of your answer.
Answer:
400 cubic cm
Step-by-step explanation:
Given that base is square and is side is 10 cm
area of square is given by side^2
Thus, area of base of cuboid = [tex]10^2[/tex] square cm = 100 sq. cm
We know volume for any cuboid is area of base * height
height is 4cm
thus, volume of cuboid = area of base of cuboid * height
= 100 * 4 cubic cm = 400 cubic cm
Volume of cuboid is 400 cubic cm.
Unit is cubic cm
The volume of square based cuboid is [tex]400cm^{3}[/tex].
Given that, base is square and side of base is 10 cm.
Height of the square-based cuboid.is 4cm.
Area of base = [tex](side)^{2}=(10)^{2}=100cm^{2}[/tex]
Volume of the cuboid is multiplication of base area and height of the cuboid.
[tex]Volume=100*4=400cm^{3}[/tex]
Hence, the volume of square based cuboid is [tex]400cm^{3}[/tex].
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The data on ages at which a sample of 35 fathers had their first child show a mean 25.43 and standard deviation 5.19. Define the population parameter of interest in this context.
Answer:
Step-by-step explanation:
A population parameter describes an entire population; a particular characteristic of an entire population. A value that describes the entire population. In this context, the population parameter is looking into the average ages of fathers when they had their first child, but this value is not given. The mean given here is the sample statistic.
Since, the population studied here is a very large population (all fathers), you have a statistic. But sometimes, if the population is very small and groups are small enough to measure, you have a parameter.
6 radians is the same as____
Round to the nearest hundredth of a degree.
Answer:
343.77
Step-by-step explanation:
1 radian is about 57.2958 degrees
so 57 times 6 is about 343.77
when nathan was 2 1/2 years old, he was 34 inches tall. the doctor told his mother that he will be two times and 4 inches taller than that when he is an adult. which of the following equation will give h, nathans height, as an adult
Answer 5 ft 4 in
Step-by-step explanation:
2 1/2 + 2 1/2=5 + 4 inches
What is the slope of the line ?
Answer:
-3
Step-by-step explanation:
find angle C! please and thankyou
Answer: it's around 40
Step-by-step explanation:
What is the correct answer?
Answer:45
Step-by-step explanation:
Sin^-1= 5÷7
Solve 8.2ws 29.52. Which of the following must be true abo
OWS36
The arrow points left
The arrow points right
There is an open circle at 3.6.
There is a closed circle at 3.6.
Answer:
A B E
Step-by-step explanation:
A- w less-than-or-equal-to 3.6
B- The arrow points left.
E- There is a closed circle at 3.6.
Answer:
A B E
Step-by-step explanation:
Which of the expressions are equivalent to the one below? Check all that
apply.
6*(2+8)
A. 6•(8+2)
B. 6•2+6•8
C. (8+2) •6
D. (6•2) + 8
Answer:
B
Step-by-step explanation:
When you have a number or numbers by parentheses, you take the number outside them and multiply it to each number that is inside the parentheses. In this case you would do 6*2 + 6*8. If I helped, please mark as brainliest! :)
Answer:
A, B, & C are all correct!
Step-by-step explanation:
Solve the system of inequalities and indicate all the integers which are in the solution set:
[tex]\left \{ {{3-2a\ \textless \ 13} \atop {5a\ \textless \ 17}} \right.[/tex]
Answer:
-5 < a < 3.4
Step-by-step explanation:
3 - 2a < 13
3 - 13 < 2a
2a > -10
a > -5
5a < 17
a < 3.4
Solution:
-5 < a < 3.4
Step-by-step explanation:
Step 1: Find the solution to the first equation
[tex]3 - 2a < 13[/tex]
[tex]3 - 3 - 2a < 13 - 3[/tex]
[tex]-2a < 10[/tex]
[tex]-2a / -2 < 10 / -2[/tex]
[tex]a > -5[/tex]
Step 2: Find the solution to the second equation
[tex]5a < 17[/tex]
[tex]5a / 5 < 17 / 5[/tex]
[tex]a < 3.4[/tex]
Answer: [tex]-5 < a < 3.4[/tex]
Derek is playing a prank on Grace and hid her pencil inside a tissue box that has a width of 4 inches, a length of 8 inches, and a height of 4 inches. The pencil fits perfectly from the upper left corner to the bottom right corner of the box. What is the length of Grace’s pencil to the nearest tenth of an inch?
Answer:
9.8 Inch
Step-by-step explanation:
The distance from the upper left corner to the bottom right corner of the box is the longest diagonal of the box.
For a rectangular prism:
Length of the Longest diagonal [tex]=\sqrt{ l^2+h^2+w^2}[/tex]
Therefore:
Length of the pencil[tex]=\sqrt{ 8^2+4^2+4^2}[/tex]
[tex]=\sqrt{96}\\=9.8$ inch(correct to the nearest tenth of an inch)[/tex]
Answer: length of pencil is 9.8 inches.
Step-by-step explanation:
The pencil fits perfectly from the upper left corner to the bottom right corner of the box. This is the diagonal of the box(not the diagonal of a face). To determine the length of the pencil, we would determine the length of the diagonal of the box. The formula formula is
d = √(l² + w² + h²)
Where
d = diagonal = length of pencil
w = width = 4 inches
h = height = 4 inches
l = length = 8 inches
Therefore,
d = √(4² + 4² + 8²) = √96
d = 9.8 inches
maya was asked whether the following equation is an identity (2x+3)(x+1) = 2(x+1)^2 + (x+1)
Answer:
Maya is correct.
Step-by-step explanation:
Khan Academy gave me the answer.
