Answer:
[tex]55[/tex]
Step-by-step explanation:
We'll be using case-work to solve this problem. Let's call the ones digit of the telephone number [tex]B[/tex] and the tens digit [tex]A[/tex]. Each telephone number can be represented as [tex]AB[/tex].
Since the question states that numbers that are smaller when their digits are reversed are not used, we have the following inequality:
[tex]B\geq A[/tex]
This is because if [tex]A>B[/tex], the number would become smaller when [tex]A[/tex] and [tex]B[/tex] are switched in [tex]AB[/tex]. However, if [tex]A=B[/tex] or [tex]B>A[/tex], the number will not become smaller.
Let's work our way up starting with [tex]A=0[/tex]. If [tex]A=0[/tex], there are 10 other numbers (0-9) that we can choose for [tex]B[/tex] that adhere to the condition [tex]B\geq A[/tex]:
[tex]0B,\\01, 02, 03,...[/tex]
Therefore, there are 10 possible telephone numbers when the tens digit is 0.
Repeat the process, now assigning [tex]A=1[/tex]. Now, we only have the digits 1-9 to choose from for [tex]B[/tex], since [tex]B[/tex] needs to be greater than or equal to A. Therefore, there are 9 possible telephone numbers when the tens digit is 1.
This pattern continues. As we work our way up through the cases (when increasing [tex]A[/tex] by 1), the number of possible telephone numbers decreases by 1, since there becomes one less option for [tex]B[/tex].
The last case would be [tex]A=9[/tex] in which case there would only be one option for [tex]B[/tex] and that would be 9.
Since there are 10 cases (0-9), add up the possible telephone numbers for each case:
[tex]\displaystyle \sum_{n=1}^{10}n=1+2+3+4+5+6+7+8+9+10=\boxed{55}[/tex]
Alternatively, recall that the sum of this series can be found using [tex]\frac{n(n+1)}{2}[/tex], where [tex]n[/tex] is the number of values in the set. In this case, [tex]n=10[/tex], and we have:
[tex]1+2+3+4+5+6+7+8+9+10=\frac{10(11)}{2}=\frac{110}{2}=\boxed{55}[/tex]
This equation shows how the total number of necklaces Denise owns is related to the amount of money she spends on additional necklaces.
n = d + 74
The variable d represents the amount of money she spends on additional necklaces, and the variable n represents the total number of necklaces she owns. With $16 to spend on new necklaces, how many total necklaces can Denise own?
for the function g(x)=3-8(1/4)^2-x
a) State the y-intercept
b) State the equation of the horizontal asymptote
c) State whether the function is increasing or decreasing.
d) State the domain and range
e) Sketch the graph
Could anyone help?
Using function concepts, it is found that:
a) The y-intercept is y = 2.5.b) The horizontal asymptote is x = 3.c) The function is decreasing.d) The domain is [tex](-\infty,\infty)[/tex] and the range is [tex](-\infty,3)[/tex].e) The graph is given at the end of the answer.------------------------------------
The given function is:
[tex]g(x) = 3 - 8\left(\frac{1}{4}\right)^{2-x}[/tex]
------------------------------------
Question a:
The y-intercept is g(0), thus:
[tex]g(0) = 3 - 8\left(\frac{1}{4}\right)^{2-0} = 3 - 8\left(\frac{1}{4}\right)^{2} = 3 - \frac{8}{16} = 3 - 0.5 = 2.5[/tex]
The y-intercept is y = 2.5.
------------------------------------
Question b:
The horizontal asymptote is the limit of the function when x goes to infinity, if it exists.
[tex]\lim_{x \rightarrow -\infty} g(x) = \lim_{x \rightarrow -\infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2+\infty} = 3 - 8\left(\frac{1}{4}\right)^{\infty} = 3 - 8\frac{1^{\infty}}{4^{\infty}} = 3 -0 = 3[/tex]
--------------------------------------------------
[tex]\lim_{x \rightarrow \infty} g(x) = \lim_{x \rightarrow \infty} 3 - 8\left(\frac{1}{4}\right)^{2-x} = 3 - 8\left(\frac{1}{4}\right)^{2-\infty} = 3 - 8\left(\frac{1}{4}\right)^{-\infty} = 3 - 8\times 4^{\infty} = 3 - \infty = -\infty[/tex]
Thus, the horizontal asymptote is x = 3.
--------------------------------------------------
Question c:
The limit of x going to infinity of the function is negative infinity, which means that the function is decreasing.
--------------------------------------------------
Question d:
Exponential function has no restrictions in the domain, so it is all real values, that is [tex](-\infty,\infty)[/tex].From the limits in item c, the range is: [tex](-\infty,3)[/tex]--------------------------------------------------
The sketching of the graph is given appended at the end of this answer.
A similar problem is given at https://brainly.com/question/16533631
Find the measure of the indicated angle to the nearest degree.
Answer:
Step-by-step explanation:
Adjacent to the undetermined angle is 6, and the hypotenuse has been given. We can conclude, after looking at our SOHCAHTOA, that we will be using cosine(CAH) to solve this problem.
Let the unspecified angle be [tex]\theta\\[/tex] (This sign is called theta, which is just a sign for angle)
Lets start!
cos[tex]\theta\\[/tex] = adj/hyp
cos[tex]\theta\\[/tex] = 6/13
[tex]\theta\\[/tex] = [tex]cos^{-1}[/tex](6/13)
[tex]\theta\\[/tex] = 62.5
[tex]\theta\\[/tex] = 63
Hope that helped!
The distributive property can be applied to which expression to factor 12x3 – 9x2 + 4x – 3?
3(4x3– 1) – (9x2 + 4x)
4x(3x2 + 1) – 3(3x2 – 1)
3x(4x – 3) – (3+ 4x)
3x2(4x – 3) + 1(4x – 3)
IM ON EDGE
Answer:
12x^3-9x^2+4x-3
3(4x^3-1)-(9x^2+4x)
therefore option A is right
thank you, and mark it as brainliest if u find it useful
What is the value of the expression below when w=2 and x=2
9w - x
Here, all we need to do is subtitute w = 2 and x = 2 into the expression, by multiplying and adding. First, we will muliply 9w:
9w
9 · w =
9 · 2 =
18
Now, all we have to do is use our answer for 9w, and subtract x from it:
9w - x
18 - (2) =
18 - 2 =
16
So, our answer is 16.
Let me know if you have any other questions! :)
Which shapes have the greatest area?
(Select all that apply.)
Answer:
the trapiezium
Step-by-step explanation:
It has a area of 4 which is the highest
(x^2+1)(x-1)=0 help me pls
Answer:
x = ±i , x=1
Step-by-step explanation:
(x^2+1)(x-1)=0
Using the zero product property
x^2 +1 = 0 x-1= 0
x^2 = -1 x=1
Taking the square root of the equation on the left
sqrt(x^2) = sqrt(-1)
x = ±i where i is the imaginary number
We still have x=1 from the equation on the right
evelins room has an area of 45 squar feet. the length of her room is 5. what is the perimeter of her room?
Answer:
28 feet
Step-by-step explanation:
Since the area is 45 and length is 5.In order to find the width we divide the area by the side given
45 ÷ 5 = 9 is the width
Perimeter is the sum of all the side of a figure.
9 + 9 + 5 + 5
= 28
I hope this helps :)
PLS HELP ME RN I AM FAILING AND NEED HELP ITS PYTHAGOREAN THEOREM
Answer:
9.89949 or 9.9
Step-by-step explanation:
7^2 + 7^2 = c^2
49+49=98
square root of 98 = 9.89949
Question 2 Evaluate the expression 2(x - 3) + 3y when x = 5 and y = 3. Mark the correct answer.
A. 13
B. 15
C. 16
D. 25
Answer:
A. 13
Step-by-step explanation:
2(x - 3) + 3y
2(5 - 3) + 3×3
2× 2 + 3×3
4 + 9
13
Answer:
The correct answer is A
Step-by-step explanation:
2(x-3) + 3y so you replace them and get 2( 5 - 3) +3(3)
next,
you would solve it
2 x 5 and 2 x 3 you get 10-6 + 9, the 9 is from multiplying 3 by 3
finally you solve it
10-6 = 4 +9
= 13!
Find the area of this circle. Use 3 for .
A = r2
12 cm
[?] cm2
Answer:
452.16 cm²
Step-by-step explanation:
Given :-
Radius = 12cm .To find :-
Area of circle .Solution :-
As we know that ,
A = πr² A = 3.14 * (12 cm)² A = 3.14 * 144cm² A = 452.16 cm²Step-by-step explanation:
[tex]area = \pi {r}^{2} \\ = \pi \times {12}^{2} \\ = \pi \times 144 \\ = 3.14 \times 144 \\ = 452.16 {cm}^{2} \\ thank \: you[/tex]
Write the equation of the line that passes through the points (−7,5) and (-7,-8).
Put your answer in fully reduced point-slope form, unless it is a vertical or horizontal line.
Answer:
x = -7
Step-by-step explanation:
First we find the slope using
m = ( y2-y1)/(x2-x1)
= ( -8 - 5)/( -7 - -7)
= (-8-5)/(-7+7)
= -13/0
This means the slope is undefined and the line is vertical
Vertical lines are in the form
x= constant and the constant is the x value of the points
x = -7
Which of the following planets has the strongest winds in the solar system?
O Jupiter
O Mars
O Neptune
O Venus
Answer: The answer is Neptune ^-^
Step-by-step explanation:
Got it correct on the test :]
find the measure of one exterior angle for the following regular polygon
Answer:
36 degrees
Step-by-step explanation:
10 corners/sides.
the sum of all exterior angles in a polygon is always 360 degrees.
so, one exterior angle here is 360/10 = 36 degrees
Which number is a solution of the inequality?
3x - 15 ≥ 3
a.) -9/11
b.)6/11
c.)6
d.)5
Answer:
6
Step-by-step explanation:
[tex]3x - 15 \geqslant 3[/tex]
[tex]3x \geqslant 3 + 15[/tex]
[tex]x \geqslant \frac{18}{3} [/tex]
[tex]x \geqslant 6[/tex]
The volume of this cube is 64 cubic feet. What is the value of a?
Answer:
a = 4 feet
Step-by-step explanation:
Since it's a cube, we know that each value will be equal. Because of this, you can cube root the cube's volume to find a.
[tex]\sqrt[3]{64}=4[/tex]
Therefore, a = 4 feet.
Answer:
4
Step-by-step explanation:
To find the area of a cube, we have to multiply the width, height, and length, which, since they are all the same value, would be a side multiplied by itself 3 times(cubed). So, the area of this cube in terms of a(side) is a*a*a or a^3. The area is given to be 64, so we can write:
a^3 = 64
With the equation, we can realize 4*4*4 is 64, meaning a is 4.
9/7 = please answer me
Answer:
[tex] \frac{9}{7} = 1.2857 = 1 \frac{2}{7} [/tex]
Answer:
Step-by-step explanation:
[tex]\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\la\la\la\la\ddddddddddddddddddddddddddddddddcleverdddddd\ffffffffffffffffffffffffffffffffffffffff\pppppppppppppppppppppppppppppppppppp\ddddddddddddddddddd\displaystyle\ \Large \boldsymbol {\frac{9}{7}=1\frac{2}{7} \ \ or \ \ 1.(28571)}[/tex]
Apples are cut into 8 pieces to be shared among some children. Twenty-two bags of seven apples are used. How many pieces of apple are cut?
Answer: 1232 pieces
Work Shown:
1 bag = 7 apples
22 bags = 22*7 = 154 apples
So we have 154 apples to work with in total.
Each of those apples is cut into 8 pieces, giving us 8*154 = 1232 pieces
We can write it as one single calculation to say 22*7*8 = 1232
Complete the table, and then use the drawing tools to create the graph representing the relationship between the amount of plant food remaining, f(x), and the number of days that have passed, x.
The complete table of the function is:
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}[/tex]
The equation missing from the question is:
[tex]y = 72 - 12x[/tex]
To complete the table, we simply calculate the y value for each x value;
When [tex]x = 0[/tex], [tex]y = 72 - 12 * 0 = 72[/tex]
When [tex]x = 1[/tex], [tex]y = 72 - 12 * 1 = 60[/tex]
When [tex]x = 2[/tex], [tex]y = 72 - 12 * 2 = 48[/tex]
When [tex]x = 3[/tex], [tex]y = 72 - 12 * 3 = 36[/tex]
When [tex]x = 4[/tex], [tex]y = 72 - 12 * 4 = 24[/tex]
When [tex]x = 5[/tex], [tex]y = 72 - 12 * 5 = 12[/tex]
When [tex]x = 6[/tex], [tex]y = 72 - 12 * 6 = 0[/tex]
So, the complete table is:
[tex]\begin{array}{cccccccc}x & {0} & {1} & {2} & {3} & {4}& {5} & {6} \ \\ f(x) & {72} & {60} & {48} & {36} & {24}& {12} & {0} \ \end{array}[/tex]
To create a graph of f(x), we simply type [tex]y = 72 - 12x[/tex] on a drawing tool and the graph will be generated.
See attachment for graph
Learn more about graphs at:
https://brainly.com/question/20106471
Answer:
Step-by-step explanation:
Fastest answer will be declared the brainliest
Answer:
All whole numbers are rational numbers.
False
All integers are whole numbers.
True
There are integers that are not rational numbers.
True
There are whole numbers that are not integers.
True.
Solve for x: -5 < 8x + 11 < 19
Answer:
-2<x<1
Step-by-step explanation:
-5 < 8x + 11 < 19
Subtract 11 from all sides
-5-11 < 8x + 11-11 < 19-11
-16 < 8x<8
Divide by 8
-16/8 < 8x/8 <8/8
-2<x<1
If g(x) = 2(x − 4), find the value of x if g(x) = 20
Answer:
x=14
Step-by-step explanation:
g(x) = 2(x − 4)
Let g(x) = 20
20 = 2(x − 4)
Divide each side by 2
20/2 = 2(x-4)/2
10 = x-4
Add 4 to each side
10+4 = x-4+4
14 =x
Darryl has written 60 percent, or 12 pages, of his history report. Darryl wants to figure out how many total pages he needs to write. Darryl’s work is shown below.
Step 1: Write 60 percent as a ratio. StartFraction part Over whole EndFraction = StartFraction 60 Over 100 EndFraction
Answer:
total pages = 20
Step-by-step explanation:
60% of an unknown number is 12
Let the unknown number (total pages) be x.
60/100 of x = 12
60/100 * x = 12
3/5 x = 12
x = 12 * 5/3
x = 20
according to the rational root theorem which of the following are possible roots of the polynomial function below? F(x)=6x^3-7x^2+2x+8
Answer:
Hello,
Step-by-step explanation:
all potential roots are of the form a/b where a is a divisor of 8
and b is a divisor of 6 ( in Z)
So A,D,E,F may be roots
but B and C not.
Kristina wants to buy a flute that costs 240 . She has saved 20 each week for 3 weeks . How many more weeks does Kristina need to save money if she continues to save 20 each week
PLEASE HELP ASAP!!!!! The following graph shows a proportional relationship. What is the constant of proportionality between y and x in the graph?
Answer:
2/3
Step-by-step explanation:
The graph point is on (3,2)
A P E X fasted answer is getting 30 points please hurry.
suppose a normal distribution has a mean of 98 and a standard deviation of 6. what is p(x ≥ 92)
Answer:
Step-by-step explanation:
If the mean is 98 and standard deviation is 6, then 92 is one standard deviation to the left of the mean; that means that 34% + 34% + 13.5% + 2.35% + .15% of the data is included in this area. Add those up and you get, as a percentage, 84%.
Answer:
0.84
Step-by-step explanation:
yee its right
Below are two different functions, f(x) and g(x). What can be determined about their slopes? f(x)= 4x + 2 The function g of x going through 0, negative 2 and 1, 3 (1 point) The function f(x) has a larger slope. The function g(x) has a larger slope. They both have the same slope. The relationship between slopes cannot be determined.
Answer:
g(x) has the larger slope.
Step-by-step explanation:
f(x) = 4x + 2
- so its slope = 4. ( from general form y = mx + c where m = slope).
The slope of g(x) = (3 - (-2) / (1 - 0)
= 5.
PLS HELP WILL MAKE FIRST RIGHT ANSWER GETS BRAINLIEST
If P =
1 2
then, prove that P2 - 2P - 5 = 0, 1 = 0, where I and 0 are unit
3 1
matrix and null matrix of order 2 x 2 respectively.
Answer:
thanks for free ponits you dint gave it free but I theft I'm sorry
