Step-by-step explanation:
A number is divisible by 11 if and only if the difference between sum of alternate digits is divisible by 11.
Here the number is x557x55. The difference between the sum of alternate digits is,
[tex]\longrightarrow S=(x+5+x+5)-(5+7+5)[/tex]
[tex]\longrightarrow S=2x-7[/tex]
By statement, the number x557x55 is divisible by 11 if and only if [tex]S=2x-7[/tex] is divisible by 11.
Let,
[tex]\longrightarrow 2x-7=11a[/tex]
[tex]\longrightarrow 2x=11a+7\quad\dots(1)[/tex]
We separate the RHS as the following.
[tex]\longrightarrow 2x=10a+a+6+1[/tex]
[tex]\longrightarrow 2x=10a+6+a+1[/tex]
[tex]\longrightarrow 2x=2(5a+3)+(a+1)[/tex]
In this question, the LHS is an even integer since x is a digit, i.e., integer. So RHS should also be an even integer.
Since [tex]2(5a+3)[/tex] is even, [tex]a+1[/tex] must be even. So let,
[tex]\longrightarrow a+1=2k[/tex]
[tex]\longrightarrow a=2k-1[/tex]
Then (1) becomes,
[tex]\longrightarrow 2x=11(2k-1)+7[/tex]
[tex]\longrightarrow 2x=22k-4[/tex]
[tex]\longrightarrow x=11k-2\quad\dots(2)[/tex]
So this is expression for x, for any integer k.
As x is a digit of x557x55, x is a single digit integer, so its value lies in between 1 and 9 [x ≠ 0 because it is also the left most digit of x557x55], i.e.,
[tex]\longrightarrow 1\leq x\leq 9[/tex]
From (2),
[tex]\longrightarrow 1\leq 11k-2\leq 9[/tex]
Adding 2,
[tex]\longrightarrow 3\leq 11k\leq 11[/tex]
Dividing by 11,
[tex]\longrightarrow\dfrac{3}{11}\leq k\leq 1[/tex]
Since k is an integer, we get,
[tex]\longrightarrow k=1[/tex]
Then from (2),
[tex]\longrightarrow x=11(1)-2[/tex]
[tex]\longrightarrow\underline{\underline{x=9}}[/tex]
Hence the value of x is 9.
Which one is it ? I need help
1. 60
2. 55
3. 65
4. 180
Answer:
55
Explanation:
Can someone please tell me the answers
Answer:
A is the correct answer. pls mark me brainliest
George decided to use blue paint to paint a wall with two windows. The wall is 12 7 8 ft by 8 ft. Both windows are 3 1 2 ft by 4 1 2 ft rectangles. Can someon egive me an answer as a whole number not a fracction Please.
Help!!! I will give you a follow
Answer:
Red
Step-by-step explanation:
Let x = number of laps and Let y = time taken to complete laps
She is able to run one lap in 7 minutes
Given this information we want to create an equation
the equation would be
7x = y
Now that we have created an equation we want to find how many laps she can run in 56 minutes.
The time is represented by 7 so we plug in 56 into y
so now we have
7x = 56
Finally we solve for x
*divide each side by 7*
56/7 = 8
7x / 7 = x
we're left with x = 8 meaning that she can run 8 laps in 56 minutes
In conclusion the answer is the Red one
Name the angle pairs that are vertical angles.
Select all angle pairs that are vertical angles.
A. ∠F and ∠L
B. ∠E and ∠N
C. ∠R and ∠V
D. ∠Y and ∠W
Answer:
A and C
Step-by-step explanation:
Vertical angles are angles that are created when two lines cross. They are angles opposite from each other. (another way of saying it:) Vertical angles are angles opposite each other where two lines cross.
Hope this helps! :)
can some 1 answer this pls
Answer:
you are right
Step-by-step explanation:
x²-2x-8≠0
⇒ (x-4)(x+2)≠0 ⇒ x≠-2 x≠4
The drone in the Example hovers at 16 meters for a few minutes before being
lowered at a constant rate. It reaches the ground after 6 seconds.
a. Why can the drone's descent be modeled by a linear function?
The drone's descent can be modeled by a linear function as the rate of descent is constant.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change.b is the intercept, representing the value of y when x = 0.For this problem, we have that the drone descended 16 meters in 6 seconds, hence the slope m is given as follows:
m = -16/6 = 2.67 m/s.
As the slope is constant, a linear function can model the situation.
More can be learned about linear functions at https://brainly.com/question/24808124
#SPJ1
HELPPPPP PLEASE!!!!
Factoring Trinomials X2-4x+24
Answer:
it shouldn't be able to be solved but it depends on your teacher
Step-by-step explanation:
Two similar cylinders have heights of 3 cm and 6 cm respectively. If the volume of the smaller cylinder is 30 cm3, find the volume of the larger cylinder.Required to answer. Single line text.
Answer:
Volume of big cylinder = 1,438.76 cm (Approx.)
Step-by-step explanation:
Given:
Height of smaller cylinder = 3 cm
Height of big cylinder = 6 cm
Volume of smaller cylinder = 30 cm³
Find:
Volume of big cylinder
Computation:
Volume of smaller cylinder = πr²h
(22/7)(r²)(3) = 30
Radius of small cylinder = 1.783 cm (Approx.)
So,
Radius of big cylinder = 1.783 x 2 = 3.566 cm (Approx.)
Volume of big cylinder = πr²h
Volume of big cylinder = (22/7)(3.566)²(6)
Volume of big cylinder = 1,438.76 cm (Approx.)
What is the simple interest on $450 at 7% for 2 years?
Answer:
I = $220.50
Step-by-step explanation:
Simple Interest Formula is I = prt
P= Principal $450
R= Rate 0.07
T= Time 7 years
I = (450)(0.07)(7)
I= $220.50
A hexagonal prism has a base with an area of 15 square inches and the volume is 105 cubic inches.
Answer:
The height is 7 inches
Step-by-step explanation:
Given
[tex]Base\ Area = 15in^2[/tex]
[tex]Volume = 105in^3[/tex]
Required
Determine the height [missing from the question]
The volume of a hexagonal prism is:
[tex]Volume = Base\ Area * Height[/tex]
Make Height the subject
[tex]Height = \frac{Volume}{Base\ Area}[/tex]
[tex]Height = \frac{105in^3}{15in^2}[/tex]
[tex]Height = \frac{105in}{15}[/tex]
[tex]Height = 7in[/tex]
Greyson reads 36 1/3 pages in 40 minutes, or 2/3 of
an hour. At this rate, how many pages can he read
in one hour?
Answer:
18 1/6+31 1/3= 49 1/2 pages in one hour.
Step-by-step explanation:
Hope this help and have a wonderful day!!!
PLEASE HELP I GIVE BRAINLIEST
B)é a reposta
HEEEEEELPPPPPPP!!!!!!!
Answer:
true
Step-by-step explanation:
Please help 13 points geometry!!
1, 140 °
2, 40°
3, 100 °
4, 100°
5, 40°
6, 90 °
7, 120 °
8, 130 °
Step-by-step explanation:
1, BOA IS EQUAL TO FOH = 140°
2, FOE EQUAL TO BOA = BOA = 40° = FOE = 40°
3, BOA° + GOF° =40° + 60° = 100 °
4, GOE = BOC WHICH MEAN GOE = 100° = BOC = 100°
5, COD = HOG =40 °
6, EOD= AOG = 90°
7, AOD = GOE + COD = 100° + 40 ° = 140°
8, BOG = 140 °
Calculate the surface area of the square pyramid below.
yd2
Answer:
155
Step-by-step explanation:
Jennifer is buying party supplies. She is planning on buying twice as many balloons as noisemakers. The number of napkins Jennifer is planning on buying is one-quarter of the number of noisemakers. If Jennifer buys 65 items, how many noisemakers does Jennifer buy? Write and solve an equation using a variable for this problem. <3
(trying to finish all my hw today since I have irl school starting tomorrow, I'm going to a new school:(
NO LINKSS
Answer:
20 noisemakers; 40 balloons; 5 napkins
Step-by-step explanation:
n = noisemakers amount
b = balloons amount
k = napkins amount
n/4 = k
b = 2n
b + n + k= 65
plug first and second equation into the respected variables in the 3rd equation so:
2n + n + n/4 = 65
multiple both sides by 4 to get rid of fraction
4(2n + n + n/4) = 4*65
8n + 4n + n = 260
13n = 260
n = 20
use n = 13 to get the other variables
b = 2(20)
b = 40
(20)/4 = k
k = 5
58
Find the volume of a prism. The area of the hexagonal base is
m2. Its height is 7
tan30°
m. If necessary, round your answer to the nearest hundredth.
The volume of the prism is about
m?
please help !
Answer:
I dont think this is the right answer but 8.256
Step-by-step explanation:
Note: Enter your answer and show all the steps that you use to solve this problem in the space provided.
Input(x) Output(y)
32 20
14 2
? −6
-2 -14
-10 ?
Complete the function table and write the function rule.
The function rule is f(x) = x - 12 and the complete table is
Input(x) Output(y)
32 20
14 2
6 −6
-2 -14
-10 -22
Completing the function table and write the function rule.From the question, we have the following parameters that can be used in our computation:
Input(x) Output(y)
32 20
14 2
? −6
-2 -14
-10 ?
The slope is calculated as
m = (2 - 20)/(14 - 32)
m = 1
So, the equation is
y = mx + c
Using the points, we have
1(32) + c = 20
Evaluate
c = -12
So, we have
f(x) = x - 12
Using the above function, we have the following function values
f(-10) = -10 - 12 = -22
x - 12 = -6
x = 6
So, the complete table is
Input(x) Output(y)
32 20
14 2
6 −6
-2 -14
-10 -22
Read more about linear relation at
https://brainly.com/question/30318449
#SPJ1
Which line segment is an altitude of ΔVWY?
Answer:
x
Step-by-step explanation:
just trust I know the x is the altitude
What is the volume of a sphere with a radius of 3 inches?
12 pi cubic inches
24 pi cubic inches
36 pi cubic inches
48 pi cubic inches
Answer:
36π cubic inches
Step-by-step explanation:
V = 4/3 πr³
radius (r): 3
= 4/3π(3)³
= 4/3π (27)
= 36π
Find the values of x and y. Write your answers in simplest form.
Step-by-step explanation:
You have this rule, if there is < 30° then value of y is
y=12✓3:2
y=6√3
And Pitagora's theorem:
c²=a²+b²
In this case:
(12√3)²=y²+x²
Then x is:
x²= (12√3)²-y²
x²= (12√3)²-(6√3)²
x²=432- 108
x²= 324
x=✓324
x=18cm
QUESTION 8 of 10: Juanita, the stadium manager, spends $10,000 on a broadcast TV ad, $15,000 on a cable TV ad, and $4,000 on a radio ad
What percentage of radio advertising did she do? (Round to the nearest percent.)
Answer: 13.79%
Step-by-step explanation:
Amount spent on broadcast TV advertisement = $10000
Amount spent on cable TV advertisement = $15000
Amount spent on radio advertisement = $4000
Total amount spent advertisement = $10000 + $15000 + $4000 = $29000
The Percentage of radio advertisement done will be:
= (Amount spent on radio advertisement / Total amount spent advertisement ) × 100
= (4000 / 29000) × 100
= 13.79%
2.
Do the data in the table represent a direct variation or an inverse variation? Write an equation to model the data in the table.
inverse variation; xy = 12
inverse variation; [tex]\frac{y}{x} =12[/tex]
direct variation; y = 12x
direct variation; [tex]y=\frac{12}{x}[/tex]
Answer: Other Answers..
SHOW ANSWER
6*2 =12
4*3 = 12
12*1 = 12
answer is B inverse variation xy=12
...............................................................................................................................................
Step-by-step explanation: Brainly answers.. -_-
6*2 =12
4*3 = 12
12*1 = 12
answer is B inverse variation xy=12
...............................................................................................................................................
Answer:
The correct option is B.
Step-by-step explanation:
From the given table it is notices that the value of y decreases as x increases, therefore it is an inverse variation.
The inverse variation is defined as
Where, k is constant of proportionality.
From the given table it is clear that the value of y is 6 at x=2.
The value of k is 12. So, the required model is
Therefore, the correct option is B.
Answer: B
Step-by-step explanation:
A stage in the shape of a semi circle had a diameter of 42 ft. What is area of the stage? Use 22/7 for π. PLZ I NEED FAST TEST
A semi circle is half a full circle. Find the area of the full circle and divide it by 2.
Area of a circle = pi x r ^2
R is half the diameter
Area of full circle:
Area = 22/7 x 21^2
Area = 1386 sq. Ft
Area of stage = 1386/2 = 693 square feet
Answer:
3.14 x 42 x 42 = 5538.96ft
If your wondering why used 3.14 instead of 22/7 is because they are exactly the same just one is a whole number and the other is a fraction. I suggest you use 3.14 because its easier than 22/7.
Step-by-step explanation:
:))
What is the value of the missing angle
Answer:180
Step-by-step explanation:
como resolve essa conta
p = 8 + 10?
Answer:
P equals 18 because 8 plus 10 is 18.
Step-by-step explanation:
For anybody who wants to know.
It’s -5,1
Answer:
ok
Step-by-step explanation:
cool
Suppose you want to buy a $151,000 home. You found a bank that offers a 30-year loan at 4.7% APR. What will be your monthly payment? (Round to the nearest cent.)
Answer:
the monthly payment is $783
Step-by-step explanation:
The computation of the monthly payment is shown below:
Given that
PV = $151,000
NPER = 30 × 12 = 360
RATE = 4.7% ÷ 12 = 0.39166
FV = $0
The formula is shown below
= PMT(RATE;NPER;-PV;FV;TYPE)
AFter applying the above formula, the monthly payment is $783.14
PLEASE HELP!! WILL GIVE LOTS OF POINTS Which of the following functions shows the absolute value parent function,
F(x) = |x|, vertically stretched
Answer:
D
Step-by-step explanation:
vertically stretched is on the outside of the |x| and has to be grater than 1