Answer:
The two numbers are 12 and -29
Step-by-step explanation:
Let x and y be the two numbers
x+y = -17
x - y = 41
Add the two equations together
x+y = -17
x - y = 41
----------------
2x = 24
Divide by 2
x = 12
Now find y
x+y = -17
12 +y = -17
Subtract 12 from each side
y = -17-12
y = -29
What is the area of the region bounded by the three lines with equations $2x+y = 8$, $2x-5y = 20$ and $x+y = 10$?
Answer:
42
Step-by-step explanation:
A graphing tool is useful for finding the points of intersection of these lines. If the equations are numbered 1, 2, 3 in the order given, we can find the points of intersection to be ...
equations 1, 2: A(5, -2)
equations 2, 3: B(10, 0)
equations (3, 1): C(-2, 12)
Then the area can be found from the coordinates using the formula ...
A = (1/2)|x1(y2-y3) +x2(y3-y1) +x3(y1-y2)|
= (1/2)|5(0-12) +10(12-(-2)) -2(-2-0))| = (1/2)|-60 +140 +4|
A = 42
The area of the triangular region is 42 square units.
For the function y=f(x), find f’(a)
Answer:
-1/4
Step-by-step explanation:
f(x) = 1/(x+1)
f(a) = 1/(a+1)
f'(a) = {(a+1)×d/da (1) - d/da (a+1) × 1}/(a+1)²
f'(a) = {(a+1)×0 - 1×1}/(a+1)²
f'(a) = (0-1)/(a²+2a+1)
f'(a) = -1/(1+2a+a²)
putting a = 1
f'(a) = -1/(1+2+1)
f'(a) = -1/4
Suppose a professional baseball player hit 55 home runs his first season, 58 his second,
and 69 his third. How many home runs would he need to hit in the current season so that
his average for the 4 years is no less than 59?
Answer:
About 54
Step-by-step explanation:
To work backwards from average, you need to multiply the average by the total number of cases, which is 4, since there are 3 current cases/seasons and you want the 4th.
59 * 4 = 236
You then subtract the total home runs that you know of from 236.
236 - 55 - 58 - 69 = 54
To find average, you are adding to the total and then dividing by the number of groups, which is essentially mean (mean is basically the average).
Which equation is represented by the table?
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now, in about how many years will it take to reach $20 per month? Use the equation 20 = 8(1.2)x to solve the problem. Round to the nearest year. 1 year 5 years 2 years 16 years
Answer:
6 years
Step-by-step explanation:
A parent increases a child’s monthly allowance by 20% each year. If the allowance is $8 per month now. This is an exponential function, An exponential function is given by:
[tex]y=ab^x[/tex]
Let x be the number of years and y be the allowance. The initial allowance is $8, this means at x = 0, y = 8
[tex]y=ab^x\\8=ab^0\\a=8[/tex]
Since it increases by 20% each year, i.e 100% + 20% = 1 + 0.2 = 1.2. This means that b = 1.2
Therefore:
[tex]y=ab^x\\y=8(1.2^x) \\[/tex]
To find the number of years will it take to reach $20 per month, we substitute y = 20 and find x
[tex]20=8(1.2)^x\\20/8=1.2^x\\1.2^x=2.5\\Taking \ natural\ log\ of \ both\ sides:\\ln(1.2^x)=ln2.5\\xln(1.2)=0.9163\\x=0.9163/ln(1.2)\\x=5.026[/tex]
x = 6 years to the nearest year
Answer:
5 years
Step-by-step explanation:444
write 32 1/2 in radical form
Answer:
Nothing further, the simplest answer is 32 1/2
Step-by-step explanation:
Find the sum of 1 + 3/2 + 9/4 + …, if it exists. This is infinite series notation. The answer is NOT 4.75.
Answer:
D
Step-by-step explanation:
First, this looks like a geometric series. To determine whether or not it is, find the common ratio. To do this, we can divide the second term and the first term, and then divide the third term and the second term. If they equal to same, then this is indeed a geometric series.
[tex](3/2)/(1)=3/2\\(9/4)/(3/2)=(9/4)(2/3)=18/12=3/2[/tex]
Therefore, this is indeed a geometric series with a common ratio of 3/2.
With just this, we can stop. This is because since the common ratio is greater than one, each subsequent value is going to be bigger than the previous one. Because of this, the series will not converge. Therefore, the series has no sum.
To see this more clearly, imagine a few more terms:
1, 1.5, 2.25, 3.375, 5.0625...
Each subsequent term will just increase. The sum will not converge.
Answer:
No Sum --- it doesn't exist.
Step-by-step explanation:
The partial sums get arbitrarily large--the go to infinity.
The geometric series you are trying to sum has common ratio = 3/2.
The sum of the infinite series exists only when |common ratio| < 1.
The formula for the partial sum of n terms is (r^(n+1) - 1) / (r - 1) = (1.5^(n+1) - 1) / 0.5, or in decimals instead of fraction.. i.e. 1 + 1.5 + 2.25 + 5.0525 + 25.628 + 656.840..... therefore It would take a long time but you'd be adding up forever and goes to infinity.
Manuel says that he can solve the equation 3n = 21 by multiplying both sides by ⅓. Explain why this is correct.
Step-by-step explanation:
はい、両側を削除して、3を掛けて7にします
Step-by-step explanation:
Given:
3n = 21
if we multiply both sides by 1/3, we will get:
3n = 21
3n x (1/3)= 21 x (1/3)
3n/3 = 21/3
n = 21/3
n = 7
Hence we can indeed solve for n by multiplying both sides by (1/3)
Janet invests a sum of EUR in an account that offers 3.5% simple interest. After ten years her investment is worth 7425 EUR. How much did she invest?
We need to find the amount of money Janet invested in 10 years to yield 7425 EUR
She invested EUR 21,214.29
Simple interest = P × R × T
Where,
P = principal = ?
R = interest rate = 3.5% = 0.035
T = Time = 10 years
Simple interest = 7425 EUR
Simple interest = P × R × T
7425 = p × 0.035 × 10
7425 = p × 0.35
7425 = 0.35p
Divide both sides by 0.35
P = 7425 / 0.35
= 21,214.285714285
Approximately,
P = EUR 21,214.29
https://brainly.com/question/10936433
What is the sum of the geometric sequence?
Answer:
B. 259
Step-by-step explanation:
6^(i - 1) for i = 1 to 4
sum = 6^(1 - 1) + 6^(2 - 1) + 6^(3 - 1) + 6^(4 - 1) =
= 6^0 + 6^1 + 6^2 + 6^3
= 1 + 6 + 36 + 216
= 259
Answer: B. 259
A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Pit Hauling cost per Ton at Site Price per ton Site 1 Site 2 Site 3 North $30 $60 $50 $100 South $60 $30 $40 $120 Now suppose that trucks (and their drivers) need to be hired to do the hauling, where each truck can only be used to haul gravel from a single pit to a single site. Each truck can haul 5 tons, and the cost per truck is five times the hauling cost per ton given above. Only full trucks would be used to supply each site.
Required:
Formulate this problem as a transportation problem with two sources and three destinations.
https://www.chegg.com/homework-help/questions-and-answers/contractor-susan-meyer-haul-gravel-three-building-sites-purchase-much-18-tons-gravel-pit-n-q8579741
Determina el valor absoluto de 13 – 11|
Responder:
2
Explicación paso a paso:
El valor absoluto de una expresión es el también conocido como valor positivo devuelto por la expresión. Una expresión en un signo de módulo se conoce como valor absoluto de la expresión y dicha expresión siempre toma dos valores (tanto el valor positivo como el negativo).
Por ejemplo, el valor absoluto de x se escribe como | x | y esto puede devolver tanto + x como -x debido al signo del módulo.
Pasando a la pregunta, debemos determinar el valor absoluto de | 13-11 |. Esto significa que debemos determinar el valor positivo de la expresión como se muestra;
= | 13-11 |
= | 2 |
Este módulo de 2 puede devolver tanto +2 como -2, pero el valor absoluto solo devolverá el valor positivo, es decir, 2.
Por tanto, el valor absoluto de la expresión es 2
Ana drinks chocolate milk out of glasses that each holds 1/8 fraction of a liter. She has 7/10 fraction of a liter of chocolate milk in her refrigerator. How many glasses of chocolate milk can she pour?
Answer:
6 glasses
I hope this helps!
Answer:
28/5
Step-by-step explanation:
looked up on khan
Find the slope of the line containing the points (7,5) and (2, 4).
Answer:
1/5
Step-by-step explanation:
the two points are(7,5) and (2,4)
let,(x1,y1)=(7,5) and (x2,y2)=(2,4)
slope (m)=y2-y1/x2-x1
=4-5/2-7
=-1/-5
=1/5(minus ,minus are cut)
:( I Need help! Show work please! Aviva has a total of 52 coins, all of which are either dimes or nickels. The total value of the coins is $4.70. Find the number of each type of coin.
Answer:
42 Dimes, 10 Nickels.
Step-by-step explanation:
Dimes are worth $0.10, nickels are worth $0.05.
If D = number of dimes, and N = number of nickels, then the following equations are true:
0.10D + 0.05N = 4.70
D + N = 52
Next, let's multiply the first equation by 10 so that we can subtract the second one from it.
D + 0.50N = 47
(-) D + N = 52
Subtracting the second equation from the first one gives:
-0.5N = -5
-0.5N/-0.5 = -5/-0.5
N = 10
Finally, substitute N in the original second equation to find D.
D + 10 = 52
D + 10 - 10 = 52 - 10
D = 42
Please help this is due at 11:59 and im really stuck.
9514 1404 393
Answer:
B B C C A A
Step-by-step explanation:
If we number the equations 1 to 6 left to right, then we have ...
B - can be put (y = 2x)B - can be put (y = (1/9)x)C - other, not a proportional relationshipC - other, y = 5/x, an inversely proportional relationshipA - has the form, k = 0.04A - has the form, k = -11five hundred seven billion,six hundred forty million,seven hundred forty-two thousand,seventy two
Answer:
507,640,142,072
Step-by-step explanation:
not sure what you are asking but I hope this helps! :D
Evaluate f(g(3)) if f(x)=6x−4 and g(x)=x2.
(Please Explain! Thank you)
Answer: 50
Step-by-step explanation:
f(x) = 6x-4 and g(x) = x^2
f(g(3)) means what is the value of the function f when it is evaluated at the value of g(3).
So g(x) is x^2 so g(3) is 3^2 = 9
Therefore we put 9 in for f(g(3))= f(9) = 6(9) - 4 = 54 - 4 = 50
if 2/-5 x=-10/x what is the value of x
Answer:
± 5
Step-by-step explanation:
2x/-5 = -10/x
2x^2 = 50
x^2 = 25
x = ± 5
Answer:
x=5
Step-by-step explanation:
Start with writing it like 2x/-5= -10/x
Then cross multiply: 2[tex]x^{2}[/tex]= 50
Divide by 2: [tex]x^{2}[/tex]=25
Square root of 25: 5
x=5
Use the model to show to help find the sum 0.34 plus 0.49
Answer/Step-by-step explanation:
The idea to use in solving this problem using the model, is to express the number of shaded boxes in fraction form.
Thus, the blue red shaded boxes has 34 boxes shaded out of 100 boxes. This represents [tex] \frac{34}{100} [/tex]. This will give us 0.34.
The other shaded boxes represents [tex] \frac{49}{100} = 0.49 [/tex].
Using the model, we can solve 0.34 + 0.49.
Add both fractions together.
[tex] \frac{34}{100} + \frac{49}{100} = \frac{34+49}{100} [/tex]
[tex] \frac{83}{100} = 0.83 [/tex]
Express b+1/3b-2 with “b” as the subject
Answer:
b = [tex]\frac{1+2a}{3a-1}[/tex]
Step-by-step explanation:
Given
a = [tex]\frac{b+1}{3b-2}[/tex] ( multiply both sides by 3b - 2 )
a(3b - 2) = b + 1 ← distribute left side
3ab - 2a = b + 1 ( subtract b from both sides )
3ab - b - 2a = 1 ( add 2a to both sides )
3ab - b = 1 + 2a ← factor out b from each term on the left side
b(3a - 1) = 1 + 2a ( divide both sides by 3a - 1 )
b = [tex]\frac{1+2a}{3a-1}[/tex]
Answer:
[tex]→a = \frac{(b + 1)}{(3b - 2)} \\ a(3b - 2) = (b + 1) \\ 3ab - 2a = b + 1 \\ 3ab - b = 2a + 1 \\ b(3a - 1) =( 2a + 1) \\ \boxed{b = \frac{(2a + 1)}{(3a - 1)} }✓[/tex]
b = (2a+1)/(3a-1) is the right answer.Simplify the following expression:
Step-by-step explanation:
[tex]{ \bf{( \frac{ - 10 {a}^{3} {b}^{5} \times 6 {a}^{6} {b}^{2} }{ {12a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{( \frac{ - 60 {a}^{9} {b}^{7} }{12 {a}^{9} {b}^{5} } ) {}^{3} }} \\ \\ = { \sf{(5 {b}^{2}) {}^{3} }} \\ = { \sf{125 {b}^{5} }}[/tex]
The state of Georgia is divided up into 159 counties. Consider a population of Georgia residents with mutually independent and equally likely home locations. If you have a group of n such residents, what is the probability that two or more people in the group have a home in the same county
Answer:
[tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]
Step-by-step explanation:
number of counties = 159
n number of people are mutually independent and equally likely home locations
considering the details given in the question
n ≤ 159
The number of ways for people ( n ) will live in the different counties (159) can be determined as [tex](\left \{ {{159} \atop {n}} \right} )[/tex]
since the residents are mutually independent and equally likely home locations hence there are : [tex]159^{n}[/tex] ways for the residents to live in
therefore the probability = [tex]\frac{159^{n} -(\left \{ {{159} \atop {n}} \right.)*n! ) }{159^{n} }[/tex]
What is the x-coordinate of the point shown in the graph?
______
Answer:
Hey there!
The x coordinate would be -5.
Let me know if this helps :)
As we can see in the Graph,
x-coordinate = - 5y-coordinate = - 7
NO LINKS OR ANSWERING QUESTIONS YOU DON'T KNOW!!! Given this frequency chart of 1490 passengers from the Titanic who died, choose the class(es) whose relative frequency would comprise just under, 1/2 of a pie chart
Answer:
b and eStep-by-step explanation:
Second and Third which gives in total:
0.112 + 0.354 = 0.466This is under 1/2 and greater than Crew.
5/3 x 6/7 real quick plz
Answer:
10/7 or 1 3/7. I hope this helps,
Step-by-step explanation:
Please help answer the following questions!!! :D I will do anything in return!
what is the formula for lineal equetion
Answer:
y=mx+c
Step-by-step explanation:
A linear equation means the equation of straight line.
The formula for equation of straight line in slope intercept form is y=mx+c
where, m is the slope of line and c is the y intercept
The formula for equation of straight line in double intercept form is x/a+y/b=1
The formula for equation of straight line in normal form is xcos α + y cos α=p
There are more formulas bur assuming you are asking for the general representation of the straight-line equation, it is y=mx+c.
Answer:
[tex]\textbf{Linear Equations : y=mx+b}[/tex]
[tex]\textbf{m= slope}[/tex]
[tex]\textbf{b= y-intercept}[/tex]
[tex]\textbf{Example:-}[/tex] [tex]\textrm{y= 6x+8}[/tex]
[tex]slope(m)=6[/tex]
[tex]y-intercept=8[/tex]
[tex]\textbf{OAmalOHopeO}[/tex]
60 is x% of 12. Find the value of x.
Answer:
20
Step-by-step explanation:
We can set up a percentage proportion to find the value of x.
[tex]\frac{12}{x} = \frac{60}{100}[/tex]
Now we cross multiply:
[tex]100\cdot12=1200\\\\1200\div60=20[/tex]
Hope this helped!
Emily made a pot cream of pumpkin soup for thanksgiving dinner she put 5 cups of cream in the soup she poured the soup into 24 small bowl show much cream measured in oz is used for each small bowl of soup?
Answer:
each bowl can contain 5/3 oz. of soup.
Step-by-step explanation:
1 cup = 8 oz.
8 oz.
5 cups x -------------- = 40 oz.
1 cup
to get the measurement of each bowl,
40 oz. divided into 24 bowls.
therefore, each bowl can contain 5/3 oz. of soup.