We used strong induction to prove that for any integer n greater than or equal to 12, there exist non-negative integers x and y such that n can be expressed as 4x + 5y.
To prove the base cases, we can simply show that each of the four integers can be expressed as 4x + 5y for some non-negative integers x and y. For example, we can express 12 as 4(3) + 5(0), 13 as 4(2) + 5(1), 14 as 4(1) + 5(2), and 15 as 4(0) + 5(3).
Assume that the statement is true for all values of n less than or equal to some fixed value k. That is, assume that for all integers m with 12 ≤ m ≤ k, there exist non-negative integers a and b such that m = 4a + 5b. We will use this assumption to prove that the statement is true for k + 1.
To do this, we consider two cases: either k + 1 is divisible by 4 or it is not. If k + 1 is divisible by 4, then we can express k + 1 as k + 1 = 4x + 5y, where x = (k + 1)/4 and y = 0.
If k + 1 is not divisible by 4, then we can express k + 1 as k + 1 = 4x + 5y, where y > 0 and x is equal to the largest non-negative integer such that k + 1 - 5y is divisible by 4.
Thus, we have shown that for any integer n greater than or equal to 12, there exist non-negative integers x and y such that n can be expressed as 4x + 5y. This completes the proof by strong induction.
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Whoever receives this get's the brainliest crown all you have to say is 1st
Answer:
1st
Step-by-step explanation:
Solve this equation:
-5(x - 2) - 3x = -80
Answer:
x=45/4
Decimal Form:
x=11.25
Mixed Number Form:
x=11 1/4
Step-by-step explanation: PLEASE MARK ME BRANLIST AND IF U CAN ANSWER MY QUESTION FROM MY PROFIL WOULD BE NICE.
HAVE A GREAT DAY! ❤️
What is this number in standard form? (3×100)+(1×1/10)+(4×1/1,000) Enter your answer in the box. please help fast . im panicking . btw it has to be decimal form
Answer:
300.104
Step-by-step explanation:
I posted a photo what the difference between expanded and standard form.
Hope this helped
Here is a trapezium, work out its area
Rewrite the equation y – 4x = –9 in slope-intercept form. simple explanation and proof
Answer:
y=4x-9
Step-by-step explanation:
add 4x to both sides to isolate y
Answer:
The slope-intercept form of this equation would be y = 4x - 9.
(For explanation look down below)
Step-by-step explanation:
Slope-intercept form would be an equation that would look like...
y = mx + b
Where m is the slope and b is the intercept. From this form, we can understand that all we need to do is rearange the formula in a way that positive y would be on its left side. And so we get...
y - 4x = - 9
y - 4x + 4x = - 9 + 4x
y = 4x - 9
help!!! pleaseeee i will answer ur questions
1. ASA
2. HL
3. Not congruent
Answer:
1.) ASA2.) HL3.) NOT CONGURENTSuppose that y varies directly with x and inversely with z. If y = 63 when x =
27 and z = 3, find the constant of proportionality.
Answer:
constant of proportionality = 7
Step-by-step explanation:
Let k = constant of proportionality
If y varies directly with x and inversely with z, then [tex]\frac{yz}{x} = k[/tex]
Substitute the values given into the equation and you get [tex]\frac{(63)(3)}{27} = 7 = k[/tex]
2. The length of Manny's pool is 7 times as the width increased by 4. What is the area, in
feet, of Manny's pool?
Answer:
L=7w+4
Step-by-step explanation:
we do not know a width to give an exact answer in numbers
ANSWER FOR BRAINIEST
Can somebody help me solve for x?
Answer:
x = 18
Step-by-step explanation:
80 / 48 = 30 / x
80x = 1440
x = 18
11,900 divided by 34
in a standard deck of cards, what is the probability that you would draw an ace
Answer:
innate as an agent X or something else
Step-by-step explanation:
Answer:
8%
Step-by-step explanation:
Suppose you have a deck of 52 cards, 4 of which are aces. The chances of drawing an ace from this deck are 4/52≈8%.
How many degrees of rotational symmetry does the flower have
Answer:
It has 5-fold rotational symmetry (72 degrees). The Clematis shown has 8-fold rotational symmetry (45 degrees). It has 8 flower petals arranged around the center of the flower.
Step-by-step explanation:
pls help , will mark branliest
A
C
B
ZABC is a right angle which is bisected by
BD.
mZDBC = [?]°
The Measure of <DBC is 45 degree.
What is Line Bisector?When anything is divided into two equal or congruent portions, usually by a line, it is said to have been bisected in geometry. The line is then referred to as the bisector. Segment bisectors and angle bisectors are the sorts of bisectors that are most frequently taken into consideration.
Given:
<ABC = 90 degree
As, BD is bisector for < ABC.
Then, the bisector divides the angle <ABC in two equal parts.
So, <ABC = 2< ABD = 2<BDC
<DBC = 1/2 <ABC
<DBC= 45 degree
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Suppose that a desk and a chair together weigh at most 55 pounds. The weight of the chair is 17 pounds. Which inequality correctly describes these conditions for the weigh of the desk, d?
Answer:
The answer will be C
Step-by-step explanation:
B. Find the Least Common Multiple (LCM) of the following sets of numbers.
15. 12 and 5
11. 8 and 3
12. 9 and 15
13.
14.
6 and 4
10 and 12
Answer:
11. LCM of 12 and 5 = 60
12.LCM of 8 and 3 = 24
13.LCM of 9 and 15 = 90
14.LCM of 6 and 4 = 12
15.LCM of 10 and 12 = 60
Deandria spent $22 on 11 song downloads. How much did each song cost?
Answer:
2 dollars on each
Step-by-step explanation:
2 times 11 equals 22
Answer:
Each song costed $2.00
Step-by-step explanation:
If all song downloads cost the same, then each song download costs...
22 / 11 = 2
There the cost per 1 download is $2.00
In ΔXYZ, x = 24 inches, y = 43 inches and z=47 inches. Find the measure of ∠Y to the nearest 10th of a degree.
Answer:
29.2
Step-by-step explanation:
arctan=24/43
Answer:
The correct answer is 65.5
Step-by-step explanation:
Just took a test on DeltaMath.
The local grocery store sets a bag of dog food for $22. The store pays $13 for the dog food. Which oquation can be used to find the markup on the dog food? Options: A. X+9=13 B. X+13=22 c. X-9=22 d. X-22=13
Answer: The answer is b
Step-by-step explanation:
Which of the following ordered pairs is not in the solution set of y < 2x − 5
Answer:
(4,3)
Step-by-step explanation:
Solve the equation:
3<2(4)-5
3<8-5
❌3<3 ❌
3 is not less than three, hence this is the phony
i hope this helps!
Write an equation of the line that passes through the points (0, −2) and (3, −5) .
Answer:
i might be wrong but i think it is
Step-by-step explanation:
y
=
−
x
−
2
y=-x-2
Help me simplify this dividing Radicals!!!
Also I didn’t mean to click the last one
Answer:
ok muchas gracias por tus puntos
Answer:THE SECOUND ONE
Step-by-step explanation:
PLZ IT RIGHTS
1.N% of 40 is 10. Solve for N. Just put the number.
2.Mia finished 60% of her homework in 45 minutes. how many minutes will it take her to complete all of her homework? Remember her total homework is 100%
Step-by-step explanation:
N% of 40=10N/100×40=10
N=10×100/40=25
2.
60%of homework=45min
1%of homework=45/60=3/4min
100%of homework =3/4 ×100=75 min
Please helpASP hurry please and ty
What is (-3)^-9 times (-3)^5
Answer:
1/80 or 0.01234568
Step-by-step explanation:
Exponentiation: (-3) ^ (-9) = -5.08052634253E-5 = -1/
19683
Exponentiation: (-3) ^ 5 = -243
= -1/
19683
* (-243) = -1 · (-243)/
19683 · 1
= 243/
19683
= 1 · 243/
81 · 243
= 1/
81
PLZ HELP ITS DUEEE RNNNNN!!!!
Answer:
left: all three attributescenter: not a rectangleright: not a rectangleStep-by-step explanation:
Some relevant characteristics of different quadrilaterals are ...
trapezoid: one pair of parallel sidesparallelogram: opposite angles are congruent, diagonals bisect each otherrectangle: a parallelogram; and all angles are congruent, diagonals are the same length__
a.There are two angles marked as right angles, and the remaining two angles are marked as congruent. The sum of angles in a quadrilateral is 360°, and each right angle is 90°. The only way the remaining angles can be congruent is for them to be (360° -180°)/2 = 90° each. That is, all of the angles in this figure must be congruent. It is ...
quadrilateralparallelogramrectangle__
b.Opposite angles are marked congruent. There is nothing to indicate any angle is a right angle. The figure is ...
quadrilateralparallelogram__
c.The diagonals are marked as bisecting each other. There is nothing to indicate the diagonals are the same length, or that any angle is a right angle. The figure is ...
quadrilateralparallelogramThe credit remaining on a phone card (in dollars) is a linear function of the total calling time made with the card (in minutes). The remaining credit after 38 minutes of calls is $ 25.06, and the remaining credit after 69 minutes of calls is $21.03. What is the remaining credit after 80 minutes of calls?
Answer: $19.6
Step-by-step explanation:
Linear function: f(x)=mx+c
, where m= rate of change in f(x) with respect to x.
c = Initial value.
Let c = Initial value of card , m= Charge per minute
x= Number of minutes calling time.
Then, 25.06= 38m+c (i)
21.03=69m+c (ii)
Eliminate (ii) from (i)
[tex]4.03=-31m\\\\\Rightarrow\ m=\dfrac{4.03}{-31}\\\\\Rightarrow\ m=-0.13[/tex]
Put m in (i) , we get
[tex]25.06= 38(-0.13)+c\\\\\Rightarrow\ 25.06=-4.94+c\\\\\Rightarrow\ c=25.06+4.94\\\\\Rightarrow\ c=30[/tex]
i.e. f(x)=-0.13x+30
if x=80 then
f(80)= -0.13(80)+30
=-10.4+30
=19.6
Hence, the remaining credit after 80 minutes of calls = $19.6
The radius of a circle is 13 meters. What is the circle's area?
Answer:
530.66 m²
Step-by-step explanation:
The equation to find a circle's area is [tex]\pi[/tex][tex]r^{2}[/tex]. We just need to plug in the radius.
[tex]\pi[/tex][tex]13^{2}[/tex]
= 3.14*169
= 530.66
Hope this helps you and have a great day! o(*^v^*)o
I don't remember how to do this
Answer:
b i think?
Step-by-step explanation:
Which pairs of expressions below are equivalent? A9m+4m13m2 B2(3m−4n)6m−4n C7(2m−3n)14m−21n D5m+5n+5m+5n5(m+n)
Answer:
7(2m−3n)14m−21n
Step-by-step explanation:
The following pairs are equivalent
7(2m - 3n)
14m - 21n
If you solve 7(2m - 3n)
So
7(2m) - 7(3n)
14m - 21n
So according to the given options, the option c is correct as this pairs is to be considered as equivalent