Answer:
It could be 105, 112 or 133.
Step-by-step explanation:
Having 7 as a factor means it is a multiple of 7.
The first 3 digit multiple of 7: 100 ÷ 7 = 14 2/7 → first 3 digit multiple of 7 is 15 × 7 = 105
Last 3 digit multiple of 7 less than 140: 140 ÷ 7 = 20 → last 3 digit multiple of 7 less than 140 is 19 × 7 = 133
→ The possible multiples of 7 to consider are [15..19] × 7 which gives 105, 112, 119, 126 and 133.
The sum of the digits of these number is:
105 → 1 + 0 + 5 = 6
112 → 1 + 1 + 2 = 4
119 → 1 + 1 + 9 = 11
126 → 1 + 2 + 6 = 9
133 → 1 + 3 + 3 = 7
Of these sums only 6, 4 and 7 are less than 9, thus the possible numbers are 105, 112 or 113.
Solve the inequality and enter your solution as an inequality in the box below.
Do not use spaces in your answer.
2+ x>-8
Answer:
x > -10
Step-by-step explanation:
2 + x > -8
x > -8 - 2
x > -10
Answer:
x>-10
Step-by-step explanation:
2+x-2>-8-2
x>-10
SOMEONE PLS HELPP ASAP
Answer:
yes
Step-by-step explanation:
f the exterior angle of a polygon is given, then the formula to find the interior angle is Interior Angle of a polygon = 180° – Exterior angle of a polygon Method 3: If we know the sum of all the interior angles of a regular polygon, we can obtain the interior angle by dividing the sum by the number of sides
If F(x) = 3x² - 8x + C and F(1) = -6, what is the value of C?
Answer:
The value of C will be -1.
Step-by-step explanation:
Greetings !
[tex]f(1) = - 6 \\ thus \: substitute \: in \: the \: equation \: \\ f(x) = 3x {}^{2} - 8x + c \\ - 6 = 3(1) {}^{2} - 8(1) + c \\ - 6 = 3 - 8 + c \\ - 6 = - 5 + c \\ - 1 = c \\ c = - 1 \\ therefore \: f(x) = 3x {}^{2} - 8x - 1 \\ f(1) = 3(1) {}^{2} - 8(1) - 1 \\ f(1) = 3 - 8 - 1 \\ f(1) =3 - 9 \\ f(1) = - 6[/tex]
Z+1 3. Given that Z & W are complex numbers. Prove that |Z + W|² - |z − w|² = 4Re(Z)Re(W)
Let z=a+bi, w=c+di
[tex]|z+w|^2 -|z-w|^2 \\ \\ = |(a+c)+i(b+d)|^2 -|(a-c)^2 +i(b-d)|^2\\\\=(a+c)^2 +(b+d)^2-(a-c)^2 -(b-d)^2\\\\=a^2 +2ac+c^2 +b^2 +2bd+d^2 -a^2 +2ac-c^2 -b^2+2bd-d^2\\\\=4ac+4bd\\\\=4Re(z)Re(w)+4Im(z)Im(w)[/tex]
2. The sum to infinity of an exponential sequence with a positive common ratio is 25 and the first two terms is 16. find fifth term
Answer:
0
Step-by-step explanation:
hi
hi
haha
and
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are doing
dog food
0 answer
(scroll to bottom for answer)The equation you want to be using is A(n)+1=(A(n))r because this is a exponential sequence
r represents the ratio, which you said was 25, so basically you said
A(n)
____ = 25
A(n)-1
rthe sum of the first 2 terms are 16, the first two terms being A1 and A2, they need to follow the equation:
A2
__ = 25
A1
lets give them variables to make this a bit easier-
A1 will be x and A2 will be y
x+y=16(1st equation)
y/x=25, 25x=y(2nd equation)
(if you multiply y/x=25 by x you will get that 25x=y, which is where that other equation came from)
going back to x+y=16
subtract y from both sides
x=16-y
use substitution and solve for the second equation
25(16-y)=y
distribute
400-25y=y
add 25y to both sides to get rid of the -25y on the left side while keeping the equation equal
400=26y
divide both sides by 26 and you get 400/26 which simplifies to 200/13
after all that you need to multiply 200/13 by 25, 3 separate times
200 1875000
___ x 25 x 25 x 25= _________
13 13
pull it into a calculator and you get something like
142846.153846
Need help please thank you
Answer:
D. x = -7/3
Step-by-step explanation:
A graphical solution is often easier when the problem is written in the form f(x) = 0. That way, the x-intercept(s) of the function f(x) will be the solution.
F(x) = 0The desired form can be found by subtracting 16 from both sides of the equation:
[tex]\left(\dfrac{1}{64}\right)^{-x-3}=16\qquad\text{given}\\\\\left(\dfrac{1}{64}\right)^{-x-3}-16=0\quad\Longrightarrow\quad f(x)=\left(\dfrac{1}{64}\right)^{-x-3}-16[/tex]
A graph is attached, showing x=-7/3 is the solution.
Algebraic solutionUsing powers of 4, the equation can be rewritten ...
[tex]\left(\dfrac{1}{4^3}\right)^{-x-3}=4^2\qquad\text{given}\\\\4^{3(x+3)}=4^2\\\\3(x+3)=2\qquad\text{equating exponents, or taking base-4 logs}\\\\x=\dfrac{2}{3}-3=\boxed{-\dfrac{7}{3}}\qquad\text{divide by 3, subtract 3}[/tex]
10005²³ x + cos x = 11 sin²x = 9
What is the mean of 13, 7, 8 and 4
Answer:
16
Step-by-step explanation:
Mean is same as average. To find the average, add all items and divide the sum by the number of items in the list.
Avg = (13 + 7 + 8 + 4) / 2 = 32 / 2 = 16
Hi there,
please see below for solution steps :
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
To find the mean you first need to add all numbers and divide by how many there are :
[tex]\sf{\dfrac{13+7+8+4}{4}}[/tex]
⨠ simplify
[tex]\sf{\dfrac{32}{4}}[/tex]
[tex]\boxed{\sf 8}[/tex] [tex]\tiny\pmb{\sf{Frozen \ melody}}[/tex]
‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗‗
Again I need help, If you tell me the answer that would be very nice! ,
Find the surface area of the composite figure :
The surface area of the given two rectangular prism is given as follows:
498 cm².
What is the surface area of a rectangular prism?The surface area of a rectangular prism of length l, width w and height h is given as follows:
S = 2(lw + wh + hl).
For this problem, there are two prisms, with dimensions given as follows:
l = 12 cm, w = 7 cm, h = 7 cm.l = 2 cm, w = 7 cm, h = 2 cm.Hence the surface area of the figure is the combined surface area of each figure, hence:
S = 2(7 x 7 + 12 x 7 + 12 x 7) + 2(2 x 7 + 2 x 2 + 7 x 2) = 498 cm².
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The answer to this problem please and thank you
Answer:
C
Step-by-step explanation:
The red dotted line we see is the asymptote, which is a line that the functions will never cross.
The asymptotes we see currently is:
x = -3
and
x = 2
We can find the vertical asymptotes using the denominator of the function since the x value that makes the denominator 0 is the asymptote. Since -3 and 2 is the asymptote, the denominator of the function will be:
(x-2) (x+3)
If we look at the answer choices, we can see that C is the only option with a denominator of (x-2)(x+3), so that is our answer.
Answer:
C
Step-by-step explanation:
there are 2 vertical asymptotes at x = - 3 and x = 2
then the factors on the denominator will be (x + 3) and (x - 2)
then
f(x) = [tex]\frac{1}{(x-2)(x+3)}[/tex]
A large party balloon is being filled with helium at a constant rate. After 8 seconds, there is 2.5L of helium in the balloon.
b) The balloon will burst if there is more than 10 L of helium in it. How long will it take to fill the balloon with that much helium?
Answer:
32 seconds
Step-by-step explanation:
first 8 secknds gives us the value of set 2.5l
2.5L to make 10 =
10÷2.5=4
That said 2.5L fills 1pL by 4 giving us;
4×2.5= 10L
Write an equation for a rational function with: Vertical asymptotes at x = 4 and x = 1 x-intercepts at x = -3 and x = 6 y-intercept at 5
The rational equation with the desired asymptotes and intercepts is given by:
[tex]f(x) = \frac{-10(x^2 - 3x - 18)}{9(x^2 - 5x + 4)}[/tex]
What are the asymptotes of a function f(x)?The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.The vertical asymptotes are related to the roots of the denominator, hence:
[tex]f(x) = \frac{a}{(x - 4)(x - 1)} = \frac{a}{x^2 - 5x + 4}[/tex]
The x-intercepts are related to the numerator of the function, hence:
[tex]f(x) = \frac{a(x + 3)(x - 6)}{x^2 - 5x + 4} = a\frac{x^2 - 3x - 18}{x^2 - 5x + 4}[/tex]
The y-intercept is to find a, hence, when x = 0, y = 5, thus:
-18a/4 = 5
18a = -20
a = -10/9
Hence the function is:
[tex]f(x) = \frac{-10(x^2 - 3x - 18)}{9(x^2 - 5x + 4)}[/tex]
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Type the correct answer in each box.
[3 x 6 1 -8 5] and -5A = [-15 35 -30 -5 40 y]
The value of x in A is ___ and the value of y in B is ___
The value of x in A is 7 and the value of y in B is -15
Functions and valuesFunctions are represented as a function of variable. Given the following sets of numbers.
A = [3 x 6 1 -8 5] and;
-5A = [-15 35 -30 -5 40 y]
Equate the individual values to have:
-5A= -15
Divide both sides by -5
-5A/-5 = -15/-5
A = 3
Determine the value of y
-5A = y
-5(3) = y
y = -15
Similarly;
5x = 35
x = 35/5
x = 7
Hence the value of x in A is 7 and the value of y in B is -15
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Answer:
The value of x in A is -7
The value of y in B is -25
Step-by-step explanation:
Everything in the first matrix can be multiplied by -5 to equal everything in the second matrix, since we are dealing with x and y, only the first and third rows matter.
In the first row, we know that 3 times -5 equals -15 and x times -5 equals 35
therefore, -5x=35, with basic algebra we find that X = -7
In the third row, we know that 8 times -5 is 40 and 5 times -5 equals y.
This takes just basic multiplication to find that Y = -25
Mary walks from corner D to corner E to corner F on a city block that measures 264 feet wide and 900 feet long. Kate walks diagonally across the city block from corner D to corner F. How much less distance did Kate walk than Mary to get to corner F? Round your answer to the nearest whole foot. Enter only the number.
Step-by-step explanation:
we have a rectangle, that is then cut in half diagonally into 2 right-angled triangles.
in our problem it does not matter which side is the larger and which is the shorter one, because the distance calculation for both cases involve one short and one long side. the sequence does not matter.
Mary walks one short and one large side to get to the opposite corner (from D to F) :
264 + 900 = 1,164 ft
Kate walks diagonally. and that diagonal is the Hypotenuse of the right-angled triangle with a short and a long side of the rectangle.
so, Pythagoras applies :
c² = a² + b²
with c being the Hypotenuse (the side opposite of the 90° angle), and a and b are the legs.
in our case that means
diagonal² = 264² + 900² = 69,696 + 810,000 =
= 879,696
diagonal = sqrt(879,696) = 937.9211054... ft ≈ 938 ft
so, Kate walked
1,164 - 938 = 226 ft
less than Mary.
the set of integers less than -20
In mathematical notation, the set of integers less than -20 as follows:
{-21, -22, -23, -24, -25, ...}
The set of integers less than -20 is the set of all whole numbers that are smaller than -20. Integers include both positive and negative whole numbers, as well as zero.
In mathematical notation, we can represent the set of integers less than -20 as follows:
{-21, -22, -23, -24, -25, ...}
The set includes all numbers that are smaller than -20, going indefinitely in the negative direction. Each number in the set is obtained by subtracting 1 from the previous number in the set.
For example:
-21 is the integer immediately smaller than -20, so it is included in the set.
-22 is the next integer, smaller than -20, so it is also included in the set.
And this pattern continues indefinitely, encompassing all the integers less than -20.
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What is 6 wholes divided by 2/3 ?
Answer:
9
Step-by-step explanation:
6 ÷ 2/3 = 6 / (2/3 ) = (6/1) / (2/3) = 6/1 x 3/2 = 18/2 = 9
find the x-intercept of the graph of the equation y=(x+2)(x-1)
Answer:-2,0 & 1,0
Step-by-step explanation:
Substitute them in with zero product property
f(x)=ax+b/2 then f^-1 (x-1) =2x-5/2 find a and b
From the given inverse function, we have
[tex]f^{-1}(x-1) = 2x - \dfrac52 \\\\ \implies f^{-1}(x) = f^{-1}((x+1)-1) = 2(x+1) - \dfrac52 = 2x-\dfrac12[/tex]
By definition of inverse function,
[tex]f\left(f^{-1}(x)\right) = x[/tex]
so that
[tex]f\left(2x-\dfrac12\right) = x[/tex]
[tex]a\left(2x-\dfrac12\right) + \dfrac b2 = x[/tex]
[tex]2ax - \dfrac a2 + \dfrac b2 = x[/tex]
[tex]\implies\begin{cases}2a=1 \\\\ -\dfrac a2+\dfrac b2 = 0\end{cases}[/tex]
[tex]\implies \boxed{a=\dfrac12}[/tex]
[tex]\implies \dfrac b2 = \dfrac a2 \implies \boxed{b=\dfrac12}[/tex]
If the vertex of a parabola is (-4,-7), what is the axis of symmetry?
Answer:
-4
Step-by-step explanation:
Given vertex, the axis of symmetry is x = h.
if X + Y = 212 and xy = 27 find the value of (x³+y³)
Which expression represents the
number of reams of paper the company
produced during the second year?
The expression that represents the number of reams of paper produced in the second year is 4.704 x [tex]10^{10}[/tex] (option d)
What is the expression that represents the reams produced in the second year.The quantity of paper produced in the first year is written in scientific notation. Scientific notation is used to compress larger numbers into smaller numbers.
In order to write a number in scientific notation, the number is written as a decimal number, between 1 and 10 and multiplied by a power of 10.
For example, The number 5 x 10³ is equivalent to 500
Paper produced in the second year = paper produced in the first year x 5.6
(8.4 x [tex]10^{9}[/tex] ) x 5.6 = 47.04 x [tex]10^{9}[/tex]
4.704 x [tex]10^{9 + 1}[/tex]
= 4.704 x [tex]10^{10}[/tex]
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Write the following number in scientific notation. 788,000
Answer:
7.88 x 10^5 is 788,000 is scientific notation
Let A, B, C be three points on a circle
with AB = BC. Let the tangents at A and
B meet at D. Let DC meet again
at E. Prove that the line AE bisects the segment
BD. (Hint: Why do we care about a chord bisecting a tangent line?)
The proof that the line AE bisects the segment can be seen below.
How to get the proof
Let us have
Γ1 and 2 are the two intersecting circles. to be the circumcircle of the shape ADE. Then we can see that Γ1 is tangent to the line DB.
A common tangent would have to touch T1 at A and also touch T2 at B
Such that what we would have would be
<ADB = 180◦ − 2<ABD = <ABC = <AEC
This would then tell us that the line is tangent to the segment.
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Multiply each of the following(2a-3b)and(a^2+2b^2)
Answer: [tex]\Large\boxed{2a^3+4ab^2-3a^2b-6b^3}[/tex]
Step-by-step explanation:
Given expression
(2a - 3b) (a² + 2b²)
Apply the FOIL method (First Outer Inner Last)
Please refer to the attachment below for a graphical understanding
= 2a · a² + 2a · 2b² - 3b · a² - 3b · 2b²
Simplify by multiplication
=2 (a · a²) + 4 (a · b²) - 3 (b · a²) - 6 (b · b²)
[tex]\Large\boxed{=2a^3+4ab^2-3a^2b-6b^3}[/tex]
Hope this helps!! :)
Please let me know if you have any questions
Answer:
Your answer is 2a³ + 4ab² - 3a²b - 6b³.
Step-by-step explanation:
(2a - 3b) (a² + 2b²)
=2a (a² + 2b²) -3b (a² + 2b²)
=2a.a² + 2a.2b² - 3b.a² - 3b.2b²
=2a³ + 4ab² - 3a²b - 6b³ ans.
Hope its helpful :-)
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Peter and Blair recently reviewed their future retirement income and expense projections. They hope to retire in 29 years and anticipate they will need funding for an additional 20 years. They determined that they would have a retirement income of $54,000 in today's dollars, but they would actually need $75,017 in retirement income to meet all of their objectives. Calculate the total amount that Peter and Blair must save if they wish to completely fund their income shortfall, assuming a 2 percent inflation rate and a return of 6
Based on the number of years that Peter and Blair have till retirement, the total amount that they need to save to completely fund their income shortfall is $65,545.72.
What amount do Peter and Blair need to save?First, find the income shortfall:
= 75,017 - 54,000
= $21,017
The amount they need to save to cover this shortfall is the future value of this amount at retirement. The rate will be the real rate which is:
= 6% - 2% inflation
= 4%
The future value is:
= Income shortfall x future value interest factor, 4%, 29 years
= 21,017 x 3.1187
= $65,545.72
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A bird flies 50km everyday to collect food for his offspring and 20km to drink water. To fly this distance takes him 1 hour and 40 minutes. What’s his average speed over the whole day?
Answer:
42km/h
Step-by-step explanation:
70km=100 minutes
7km= 10min
42km=60min
42km/h
Question: You can work 40 hours per pay period while attending school earning $12.50 an hour. There are two pay periods per month. NOW Assume you have deductions for health care of $25 per pay period and 401K deduction of $50 per pay period. These deductions are pretax.
Gross Pay per pay period: $
Taxable Income per pay period:
You pay 11% in federal taxes. Federal tax withholding per pay period: $
___
Use the state tax rates below and calculate State tax withholding per pay period: $
(round to two decimals)
_____
From the image:
Calculate FICA withholding per pay period: $
Calculate Medicare withholding per pay period: $
(round to two decimals)
What is your Net pay per pay period: $
(round to two decimals)
1) Based on the information, the following taxation calculations can be made:
a) Gross Pay per pay period: $500
b) Taxable Income per pay period: $425
c) Since you pay 11% in federal taxes, the Federal tax withholding per pay period is $46.75.
2) The State tax withholding per pay period is $20.
3) The calculation of FICA, Medicare, and the Net Pay per pay period is as follows:
FICA withholding per pay period: $25.50
Medicare withholding per pay period: $6.16
Net Pay per pay period = $326.59
Data and Calculations:Total hours worked per pay period = 40 hours
Rate per hour = $12.50
Pay periods per month = 2
Gross pay per pay period = $500 (40 x $12.50)
Deductions per pay period:Health care = $25
401K deduction = $50
Total deductions per pay period = $75
Taxable income per pay period = $425 ($500 - $75)
Federal taxes = 11%
Federal tax withholding per pay period: $46.75 ($425 x 11%)
Annual taxable income = $10,200 ($425 x 24)
State withholding tax (annual) = $480 {$120 + ($10,200 - $5,000) x 5%}
State withholding tax per pay period = $20 ($480/24)
FICA withholding per pay period: $25.50 ($425 x 6.2%)
Medicare withholding per pay period: $6.16 ($425 x 1.45%)
Net Pay per pay period:Gross Pay $500
Total deductions $75
Taxable income = $425
Federal Withholding = $46.75
State Withholding = $20
]FICA Withholding = $25.50
Medicare Withholding = $6.16
Net Pay per pay period = $326.59
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Maytag Company earns $2.60 per share. Today the stock is trading at $46. The company pays an annual dividend of $1.60 a. Calculate the price-earnings ratio (Round your answer to the nearest whole number.) Price-earings natio b. Calculate the stock yield. (Round your answer to the nearest tenth percent.) Stock yield
a. The price-earnings ratio of Maytag Company's stock is 17.
b. The stock yield of Maytag Company's stock is 3.48%.
What are the price-earnings ratio and stock yield?The price-earnings ratio is a financial measurement of the worth of Maytag Company.
The price-earnings (P/E) ratio is computed as the current stock price divided by the company's earnings per share.
The P/E ratio shows the potential investor how much to pay per share for each $1 of earnings.
The stock yield is a financial measurement that shows the dividends paid relative to the market value per share.
Data and Calculations:Earnings per share = $2.60
Current share price = $46
Annual dividend = $1.60
a. Price-earnings ratio = Price per share/earnings per share
= 17 ($46/$2.60).
b. Stock yield = Annual dividend per share/Current stock price x 100
= 3.48% ($1.60/$46 x 100)
Thus, while the price-earnings ratio is 17, the stock yield is 3.48%.
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m∠1 =
✔ 131
degrees
m∠2 =
✔ 49
degrees
m∠3 =
✔ 112
degrees
Answer:
what is the question show the pic
This box plot represents the number of pages that several students in sixth grade have read in a month. Use the shape of the box plot to describe the data set. Select all that apply.
The total range of pages read is 20 .
The lowest quarter of data is more dispersed than the highest quarter of data.
One-half of the students have read between 72 and 86 pages.
The median number of pages of the sixth graders is 76.
One-fourth of the students have read weigh 72 and 76 pages.
One-fourth of the students read more than 76 pages.
One-fourth of the students have read less than 72 pages.
The true statements are:
The median number of pages of the sixth graders is 76.
One-fourth of the students have read less than 72 pages.
One-half of the students have read between 72 and 86 pages.
What are the true statements?A box plot is used to study the distribution and level of a set of scores. The box plot consists of two lines and a box. the two lines are known as whiskers.
The end of the first line represents the minimum number and the end of the second line represents the maximum number. The difference between the minimum number and the maximum number is the range.
Range = 92 - 61 = 31
On the box, the first line to the left represents the lower (first) quartile. 1/4 of the score represents the lower quartile. The next line on the box represents the median. 1/2 of the score represents the median. The third line on the box represents the upper (third) quartile. 3/4 of the scores represents the upper quartile.
First quartile = 72
Third quartile = 86
Median = 76
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