Answer:
[tex]\begin{aligned}6(n+6)-(2n+3) & = 6n+36-2n-3\\& = 4n+33\\& = 4n + 32 + 1\\& = 2(2n+16) + 1\end{aligned}[/tex]
Any number multiplied by 2 is even, therefore 2(2n + 16) is even.
If 2(2n + 16) is even, then adding 1 to this makes it odd.
Thus proving that the given expression is an odd number for all [tex]n \in \mathbb{N}[/tex]
Which recursive formula can be used to generate the sequence below, where f(1) = 6 and n ≥ 1? 6, 1, –4, –9, –14, … f (n 1) = f(n) 5 f (n 1) = f(n) – 5 f (n) = f(n 1 ) – 5 f (n 1) = –5f(n)
The recursive formula is f(n+1)= f(n)-5.
What is recursive function?
Given sequence :
f(1)= 6, n≥1.
Let f(n) denote the nth term of the given sequence.
f(1)= 6
f(2)= 1 = f(1)-5
f(3)= -4 = 1-5= f(2) -5
f(4)= -9 = 1-10 = f(2)-10
and so on
Hence, the recursive formula is f(n+1)= f(n)-5.
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A picture measures x cm by (x + 4) cm. It is enlarged by a scale factor of 3 to form a poster. The area of the enlarged poster is 1053 cm².
(i) Pauline made a wild guess, without making any prior calculation, that the value of x is 31. Without finding the actual value of x, verify whether her claim is correct.
(ii) Form an expression in terms of x and show that it reduces to x² + 4x - 117 = 0.
(iii) Calculate the perimeter of the original picture before the enlargement.
pls help me I need it by 25mins
Answer:
i) Her claim is incorrect
ii) see below
iii) 44 cm
Step-by-step explanation:
Given:
width of picture = x cmlength of picture = (x + 4) cmIf the picture is enlarged by a scale factor of 3 to form a poster, then the dimensions of the poster will be:
width of poster = 3x cmlength of poster = 3(x + 4) cmArea of rectangle = width × length
⇒ Area of poster = (3x) × 3(x + 4)
= 9x(x + 4)
= 9x² + 36x cm²
Part (i)Inputting x = 31 into the area of poster formula found above:
⇒ 9(31)² + 36(31)
= 8649 + 1116
= 9765 cm²
Therefore, as 9765 ≠ 1053 her claim in incorrect.
Part (ii)Using the formula for the area of poster found in part (i).
Area of poster = 1053 cm²
⇒ 9x² + 36x = 1053
⇒ 9x² + 36x - 1053 = 0
⇒ 9(x² + 4x - 117) = 0
⇒ x² + 4x - 117 = 0
Part (iii)First find x by solving the equation from part (ii):
⇒ x² + 4x - 117 = 0
⇒ x² + 13x - 9x - 117 = 0
⇒ x(x + 13) - 9(x + 13) = 0
⇒ (x - 9)(x + 13) = 0
⇒ x = 9, x = -13
As width cannot be negative, x = 9 only
Perimeter of picture = 2(width + length)
= 2(x + x + 4)
= 2(2x + 4)
= 4x + 8
Input found value of x into the expression for the perimeter:
⇒ Perimeter of picture = 4(9) + 8
= 36 + 8
= 44 cm
Rational exponents; what do i do???
Answer:
[tex]x = -\dfrac{48}5[/tex]
Step by step explanation:
[tex]~~~~~~~\dfrac{x^2+12x+36}{2x^2}-\dfrac{x^2 +7x +12}{2x^2}= \dfrac 5{4x}\\\\\\\implies \dfrac{x^2 +12x +36 -x^2 -7x -12}{2x^2 } = \dfrac 5{4x}\\\\\\\implies \dfrac{5x+24}{2x^2} = \dfrac 5{4x}\\\\\\\implies 4x(5x+24) = 5(2x^2)\\\\\\\implies 20x^2+96x= 10x^2\\\\\\\implies 20x^2 -10x^2 +96x=0\\\\\\\implies 10x^2 +96x= 0\\\\\\\implies 5x^2 +48x = 0\\\\\\\implies x(5x+48)=0\\\\\\\implies x = -\dfrac{48}5~~~~~;[x\neq 0][/tex]
it rained on 3/7 of days write the rof the days it rained to number of days
The ratio of the days it rained to number of days is 3 : 7
How to determine the ratio?The proportion of the number of days it rained is given as:
Proportion = 3/7
This means that:
Proportion = Days it rained/Total number of days.
So, we have:
Days it rained/Total number of days = 3/7
Express as ratio
Days it rained : Total number of days = 3 : 7
Hence, the ratio is 3 : 7
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What is the explicit formula for this sequence?
-7, -4, -1, 2, 5, ...
Answer:
3n-10
Step-by-step explanation:
Goes up by three and the first number of this sequence is 10 below 3.
i need help with this please vvv
Answer:
(a,b)
Step-by-step explanation:
Using the Midpoint formula,
[tex]\left(\frac{x_2+x_1}{2},\:\:\frac{y_2+y_1}{2}\right)[/tex]
you will get
[tex]\left(\frac{2a+0}{2},\:\frac{0+2b}{2}\right)[/tex]
which is
(a,b)
Each year, the Green Valley School spring carnival features the Jelly Bean Guessing Game. To set up for the game this year, the principal used 6 small boxes of jelly beans to fill a large glass jar. Each box had the same number of jelly beans, for a total of 324 jelly beans.
Let j represent the number of jelly beans in each box. Which equation models the problem?
If j represent the number of jelly beans in each box, then the equation that models the problem is; 6j = 324
How to model an equation?
We are told that the principal used 6 small boxes of jelly beans to fill a large glass jar.
Now, each box had the same number of jelly beans, for a total of 324 jelly beans.
If j represent the number of jelly beans in each box, then the equation that models the problem is; 6j = 324
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What does the word progressive mean in the sentence below
What is the sentence and what are the questions. Until I know I can't help. But I should be able to answer if you can tell me
A bag contains orange, white, and purple marbles. If you randomly choose a marble from the bag, there is a 23% chance of drawing an orange marble and a 48% chance of drawing a white marble. What is the probability of choosing a purple marble? Express your answer as a percent.
The probability of choosing a purple marble from the given parameters is given as; 29%
How to find the Probability?
We are given;
Probability of drawing an orange marble = 23% = 0.23
Probability of of drawing a white marble = 48% = 0.48
Thus, probability of drawing a purple marble is;
P(purple marble) = 100% - (23% + 48%)
P(purple marble) = 29%
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Given the system 2x − 4y = −34 −3x − y = 2
solve for the variables that make up the constant matrix [e f]
For a system of equations to have no real solution, the lines of the equations must be parallel to each other. The value of e and f is -34 and 2 respectively.
What is a system of equations?
Inconsistent System
For a system of equations to have no real solution, the lines of the equations must be parallel to each other.
Consistent System
1. Dependent Consistent System
For a system of the equation to be a Dependent Consistent System, the system must have multiple solutions for which the lines of the equation must be coinciding.
2. Independent Consistent System
For a system of the equation to be an Independent Consistent System, the system must have one unique solution for which the lines of the equation must intersect at a particular.
For the given system of equations, the value of e will be -34, while the value of f will be 2.
Hence, the value of e and f is -34 and 2 respectively.
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Answer:
he value of e and f is -34 and 2
A mass of water at 100°c is added to another mass Q of water at a temperature T and the resulting temperature is theta. Describe an expression for theta in terms of the quantities (specific heat capacity of water is 4.2JKg-¹K-¹).
Answer:
Use the formula Where 1. q = Heat Energy 2. m = Mass 3. c = Specific Heat 4. ΔT = Change in temperature. 14640 J = (300 g)(2.44 J/g·°C)ΔT Solve for ΔT: 1. ΔT = 14640 J/(300 g)(2.44 J/g·°C) 2. ΔT = 20 °C 3. ΔT = Tfinal - Tinitial 4. Tfinal = Tinital+ ΔT 5. Tfinal= 10 °C + 20 °C 6. Tfinal= 30 °C Answer:The final temperature of the ethanol is 30 °C.
Mark Brainliest ;)Anthony borrowed $158 from a friend ,Josue . He paid josue $89 of the money back how much money does Anthony still owe josue?
Answer:
$69
Step-by-step explanation:
He ows Josue $69 because $158-$89 = $69
If 3/7 of people attended a conference are male. how many females attended the conference if the total attendance is 210
Add 4/13 with the multiplicative inverse of 5 1/5
Answer:
Step-by-step explanation:
Multiplicative inverse of 26/5 is 5/26
(4/13 + 5/26)
13/26 ᴏʀ 1/2
Unfortunately I still have school could anybody help me please?
MATH 2
Standard G-SRT.8.1
Answer:
t = 6
∠BAC = ∠EAD = 6°
∠BCA = ∠ABC = ∠AED = ∠EDA = 87°
Step-by-step explanation:
From inspection of the diagram, we can see that there are 2 triangles inside a circle. One of the vertices of both triangles is at the center of the circle. The other vertices of both triangles are on the circumference of the circle.
The dashes on the line segments (chord) mean they are equal in length.
⇒ BC = DE
The legs of both triangles are the radius of the circle.
Therefore, ΔABC = ΔAED
This means the ∠BAC = ∠EAD, therefore:
⇒ 6t - 12 = 18 - 4t
⇒ 10t - 12 = 18
⇒ 10t = 30
⇒ t = 3
Substituting the found value of t into one of the expressions to find ∠BAC and ∠EAD:
⇒ ∠BAC = ∠EAD = 6(3) - 12 = 6°
Triangles ΔABC and ΔAED are both isosceles triangles (as they have 2 sides of equal length: the radii).
Therefore, the remaining 2 angles in each triangle will be equal.
The sum of interior angles of a triangle = 180°
⇒∠BAC + 2(∠BCA) = 180°
⇒ 6° + 2(∠BCA) = 180°
⇒ 2(∠BCA) = 174°
⇒ ∠BCA = 87°
Therefore, as ∠BCA = ∠ABC = ∠AED = ∠EDA
all the other angles are 87°
Find the area please
=202 in²
Divide the shape into 2.
Area of a rectangle= Length * Width
So..
The first shape = 13in*4in = 52in²
The second shape = 15in * 10in = 150in²
150 + 52 = 202in²
10 points! Please help me!
In this case, we must use our trigonometric equations to help us solve this problem:
⇒ look at the diagram attached
Let's examine what the problem wants:
side adjacent to the 41-degree angleLet's examine what the problem gives us:
length of the side opposite the 41-degree angleone angle which has a measure of 41 degreesLet's solve:
[tex]tan(41)=\frac{12}{x} \\12=x*tan(41)\\x=\frac{12}{tan(41)} \\x=13.80[/tex]
Answer: 13.8 (rounded to nearest tenth)
Hope that helps!
Solve for X.
- 4x + 10 = 50
Answer: -10
Step-by-step explanation:
10 x 4 is 40 so with 2 negatives, it turns positive, and 40 plus 10 = 50
Answer:
x=-10
Step-by-step explanation:
-4x+10=50
10=50+4x
-50+10=4x
-40=4x
4x=-40
x=-40÷4
x=-10
What should your units on your base area calculations be, and why? How is this different from the units on your volume calculations? Explain in two to three sentences.
The units on a base area calculations is known to be cm² or m² while units on your volume calculations is known to be m³ or cm³.
Why use the unit about?The unit above is used because in base area calculation, only 2 sides are calculated while in volume calculation, 3 sides are involved.
Note that in base area, square unit is often used in its calculations via the use of two dimensions length and breadth (cm² or m² ).
In terms of volume, cubic unit is used in its calculations through the use of three dimensions length, breadth and height ( m³ or cm³.).
Note also that Area is seen as the space taken by a two dimensional flat object while volume is seen as the space taken by the three-dimensional object and as such The units on a base area calculations is known to be cm² or m² while units on your volume calculations is known to be m³ or cm³.
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1. A group of 20 students: 2 freshmen, 4 sophomores, 6 juniors and 8 seniors - are trying to get onto a
committee to select a new math teacher. How many different groups of six can be chosen?
Answer:
38760 ways
Step-by-step explanation:
20 C 6 = 38760
Type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar. consider the logarithmic function f(x) = log10(x). the value of f(50), rounded to nearest hundredth, is .
It is Given that f(x) = log₁₀(x) then the value of f(50) is 1.70.
What is logarithmic?Logarithmic functions are defined as the inverses of exponential functions.
Hence, exponential functions can be expressed in logarithmic form
Given that f(x) = log₁₀(x)
we need to find the value of f(50),
we have to substitute x to be 50 in the logarithm function,
f(50) = log₁₀(50)
f(50) = log₁₀(5 x 10)
f(50) = log₁₀(5) + log₁₀(10)
f(50) = 1 + log₁₀(5)
f(50) = 1 + 0.70
f(50) = 1.70
Hence, It is Given that f(x) = log₁₀(x) then the value of f(50) is 1.70.
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It costs a family $348.00 to buy a 15-ft-by-16-ft rug. If the cost is proportional to the area,
what will it cost the family to buy a 10-ft-by-11-ft rug?
$89.66
$188.50
$240.00
$159.50
The cost of the family rug with dimensions 10-ft-by-11-ft given a proportional relationship is $159.50
How to solve using ratio?Cost = $348.00
Area of rug = length × width
= 15 ft × 16 ft
= 240 square feet
Cost of a new rug = x
Area = length × width
= 10 ft × 11 ft
= 110 square feet
Equate the ratio of cost to area of both rugs348 : 240 = x : 110
348/240 = x/110
cross product
348 × 110 = 240 × x
38,280 = 240x
x = 38,280 / 240
x = $159.50
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What is the slope of the line with this equation y-6 = - (x - 3) ? Explain.
Answer:
-1
Step-by-step explanation:
ecuacion de la pendiente está dada por:
Y-yo=m(X-xo)
donde m es la pendiente
del problema :
y-6 = - (x - 3
m=-1
can you guys please explain this to me?
answer to this is 24cm2
Step-by-step explanation:
area of square is 4x4=16 and area of triangle is 6x4=32 add the both together (32+16) and you have 40cm2
Find the area of AAOB
9√3 un²
3√3 un²
4.5√3 un
Answer:
Step-by-step explanation:
The area of the equilateral triangle is [tex]\frac{\sqrt{3}}{4}(6)^{2}=\boxed{9\sqrt{3}}[/tex]
By what percent will a fraction CHANGE(not increase!!) if it’s numerator is decreased by 60% and it’s denominator is decreased by 20%?
I am aware that it is a decrease, but not sure of how much it is a decrease by.
HELP ASAP!!
if i was i your class or in bigger class i will help you
The blue dot is at what value on the number line?
Answer:
20
Step-by-step explanation:
To find the value at the blue dot, you must identify the scale of the markings of the number line.
__
what is the scale12 is 2 marks to the right of 8, so we know 2 marks has a value of 12-8 = 4.
using the scaleThat means the second mark to the right of 12 will be 12+4 = 16.
The second mark to the right of that is 16+4 = 20, which is where the blue dot is.
The value at the blue dot is 20.
use the FOIL method to solve:
(x+4)(x-7)
Please help , giving brainliest .
Answer:
363.22
Step-by-step explanation:
Method 1:
You could find the whole figure surface area than divided by 1/2
Method 2: (the one I'm going to personally be doing)
Break the figure into two rectangular figures
Formula for surface area of rectangular prism:
A = 2(width x length + height x length + height x width)
Figure 1:
A = 2(width x length + height x length + height x width)
height = 3.8 yd
length = 10.1 yd
width = 4.3 yd
A = 2((4.3) x (10.1) + (3.8) x (10.1) + (3.8) x (4.3))
A = 2(98.15)
A = 196.3
Figure 2:
A = 2(width x length + height x length + height x width)
height = 8.4 yd
length = 10.1 yd
width = 2 yd
A = 2((2) x (10.1) + (8.4) x (10.1) + (8.4) x (2))
A = 2(121.84)
A = 243.68
There is overlapping surface area that shouldnt be include so we need to subtract it...
For one face of figure 1
3.8 x 10.1 = 38.38
Total:
Figure 1 + Figure 2 - 2(one face)
196.3 - 38.38 = 157.92
243.68 - 38.38 = 205.3
205.3 + 157.92 = 363.22
a) Complete the table of values for y = 2x + 3
x,,-2,,-1,,0,,1,,2,,3
y,,,?,,,1,,,,?,,?,,7,,?
Answer:
Step-by-step explanation:
Because the slope of y = 2x + 3 is 2, y increases by 2 for every unit increase in x.
Substituting the given x-value -2 into y = 2x + 3 results in y = -1.
If we now increase x by 1, from -2 to -1, y increases by 2: the new
y value is y = -1 + 2 or y = 1. which agrees with the +1 in the list of y-values.
Again, y = ?,,,1,,,,?,,?,,7,,? becomes y = -1, 1, ?,,?,,7. Note that -1 + 2 = 1;
1 + 2 = 3; 3 + 2 = 5; 5 + 2 = 7 (which agrees with the given 7); 7 + 2 = 9.
So the given incomplete table of values
x,,-2,,-1,,0,,1,,2,,3
y,,,?,,,1,,,,?,,?,,7,,?
becomes:
x,,-2,,-1,,0,,1,,2,,3
y,,, -1,,1,,,3,,5,,7,,9