x = some unknown number
x+8 = sum of the number and 8
2(x+8) = product of 2 and the sum of a number and 8
2(x+8) = 16 is the final answer–4.5t49.5t = 40
Please help
Answer:
t= -0.18
Step-by-step explanation:
Isolate t to get the unknown number:
(-4.5t)(49.5t) = 40
Multiply (-4.5t)(49.5t):
(-4.5t)(49.5t) = -222.75t
Now, write full equation:
-222.75t = 40
Isolate t by dividing -222.75 on both sides:
[tex]\frac{-222.75}{-222.75}t=\frac{40}{-222.75}[/tex]
Cancel out left hand side:
[tex]t=\frac{40}{-222.75}[/tex]
Simplify your answer:
[tex]t=-0.17957351[/tex]
Approximate to 2 decimals:
[tex]t=-0.18[/tex]
How many terms of the series of - 3+0+3+6+9+...are needed to give a sum of 105?
Answer:
10
Step-by-step explanation:
Remember that the formula for the sum of an arithmetic series is:
[tex]S=\frac{k}{2}(a+x_k)[/tex]
Where k is the number of terms, a is the initial term, and x_k is the last term of the series.
We essentially want to find k, the number of terms, given that the sum S is equal to 105. So, substitute 105 into our equation:
[tex]105=\frac{k}{2}(a+x_k)[/tex]
To do so, we need to final term x_k. We don't know what it is yet, but that doesn't matter. All we need to do is to write it in terms of k. First, remember that the standard form for the explicit formula of an arithmetic sequence is:
[tex]x_n=a+d(n-1)[/tex]
Where a is the first term, d is the common difference, and n is the nth term.
From our sequence, we can see that the first term is -3.
Also, we can determine that our common difference is +3, since each subsequent term is 3 more than the previous one. -3+3 is 0, 0+3 is 3, 3+3 is 6, and so on.
Therefore, our explicit formula is:
[tex]x_n=-3+3(n-1)[/tex]
Therefore, our final term, x_k, will be if we substitute k for n. So, we can acquire the equation:
[tex]x_k=-3+3(k-1)[/tex]
Now that we know what x_k is, we can substitute that into our original equation:
[tex]105=\frac{k}{2}(a+x_k)[/tex]
Substitute the equation into x_k. Also, let's substitute -3 (our first term) for a. So:
[tex]105=\frac{k}{2}(-3+(-3+3(k-1)))[/tex]
And now, all we have to do is to solve for k.
First, distribute the 3:
[tex]105=\frac{k}{2}(-3+(-3+3k-3))[/tex]
Add within the parentheses:
[tex]105=\frac{k}{2}(3k-9)[/tex]
Multiply both sides by 2. This removes the fraction on the right:
[tex]210=k(3k-9)[/tex]
Distribute. We will get a quadratic:
[tex]210=3k^2-9k[/tex]
So, let's solve for k. Let's divide everything by 3:
[tex]70=k^2-3k[/tex]
Subtract 70 from both sides:
[tex]0=k^2-3k-70[/tex]
Factor. We can use -10 and 7. So:
[tex]0=(k-10)(k+7)[/tex]
Zero Product Property:
[tex]k-10=0\text{ or } k+7=0[/tex]
Solve for k for each equation:
[tex]k=10\text{ or } k=-7[/tex]
-7 doesn't make sense (we can't have -7 terms). Remove that solution. So, we are left with:
[tex]k=10[/tex]
Therefore, the number of terms we have in our series for our sum to be 105 is 10.
And we're done!
Question 5 You and a friend share a pizza cut into 8 equal slices. Suppose you each eat 3 slices. What
fraction of the pizza is left over?
Answer:
3/8
Step-by-step explanation:
Find the particular solution to ty''-(1+t)y'+y=t^2e^t.
Complete Question
Find a particular solution to [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]
[tex]y_1 = 1 + t , \ y_2 = e^t[/tex]
Answer:
The solution is [tex]y_p = -e^{2t} + t + \frac{3t^2}{2} + \frac{t^3}{2}[/tex]
Step-by-step explanation:
Now the given equation is [tex]ty''-(1+t)y'+y=t^2e^t , t > 0[/tex]
dividing through by t
We have
[tex]y'' - \frac{1 + t }{t}y' + \frac{1}{t} y = te^t \\\\ let's\ call\ it \ g(t)[/tex]
Now for the given initial value we can generate our Wronskian as follows
[tex]W(y_1 ,y_2) = | \left y_1} \atop {y_1'}} \right. \left y_2} \atop {y_2'}} \right | = | \left {(1 + t)} \atop {1}} \right. \left e^t} \atop {e^t}} \right | = (1 + t )e^t - e^t = te^t[/tex]
Now applying method of variation of parameters to obtain the particular solution
So here we assume that
[tex]y_p = v_1 y_1 + v_2 y_2[/tex]
So
[tex]v_1 = - \int\limits {\frac{y_2 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{e^t te^t}{te^t} } = - \int\limits { e^t} } = -e^t[/tex]
And
[tex]v_2 = - \int\limits {\frac{y_1 (t) g(t)}{W(t)} } \, dt = - \int\limits {\frac{(1 + t) te^t}{te^t} } = - \int\limits (1 + t) = t + \frac{t^2}{2}[/tex]
So
[tex]y_p = -e^t * e^t + t + \frac{t^2}{2} * 1 + t[/tex]
[tex]y_p = -e^{2t} + t + \frac{3t^2}{2} + \frac{t^3}{2}[/tex]
Given f(x) = |X - 9|.The vertex of the function moves from (0,0) nine units where?
left
right
up
down
Answer:
RightStep-by-step explanation:
Given function
f(x) = |x - 9|Let's try point x = 0
f(0) = | 0 - 9 | = | -9 | = 9So the vertex moves right
See attached
Point Q (-2, -2) is translated according to this rule (x - 3, y + 4). Which directions will Point Q be translated?
Answer:
it would be translated up.
Step-by-step explanation:
(-2,-2) (x-3, y+4)
-2-3= -5 -2+4= 2
(-5,2)
Let p: It is the year 2020.
q: Montclair University montclair is located in Kansas.
Is ~ PV ~ q true or false?
O True
O False
I think it's TRUE so yeah.
One number is 19 larger than the other, and the sum of these numbers is 97. What is the larger number? Plz help asap
Answer:
58
Step-by-step explanation:
I have attached an image with this answer that will help you to visualise this question. I will now explain it.
The smaller number (Number 1) has 1 unit.
The bigger number (Number 2) has 1 unit, and 19.
If you add 19 to the smaller number, you will make two of the bigger number.
[tex]97+19=116[/tex]
This is equivalent to two of the bigger number. (Try to visualise it!)
Hence, divide it by 2 to get one of the bigger number.
[tex]116\div2=58[/tex]
Answer:
58
Step-by-step explanation:
The smaller number (Number 1) has 1 unit.
The bigger number (Number 2) has 1 unit, and 19.
If you add 19 to the smaller number, you will make two of the bigger number.
This is equivalent to two of the bigger number. (Try to visualise it!)
Hence, divide it by 2 to get one of the bigger number.
Gina buys 4 packs of stickers for her scrapbook there are 9 stickers in each pack each page in the scrapbook holds 6 stickers how many pages does Gina need for these stickers
Answer:
total stick she has = 9*4 = 36
6 sticker is need in 1 page
so page required for 36 stickers = 36/6 = 6pages
Step-by-step explanation:
What type of angle is angle M? A. Acute B. Obtuse C. Straight or D. right
Step-by-step explanation:
acute angle is a tiny angle obtuse is a wide 180 straight is just a straight line and a right angle is a right angle which equals 90 degrees
Answer:
Acute angle refers to angle less than 90
Obtuse angle refers to angle greater than 90 but less than 180
straight line angle is equal to 180
right angle is equal to 90
Describe and correct the error a student made when naming the polynomial
-2x3 + 5x4 - 3x is a
cubic trinomial
+
Choose the correct answer below
O A. The student did not put the polynomial in ascending order of the degrees of the terms before naming it by the first term. It is a linear trinomial.
O B. The student did not combine like terms before naming the polynomial. It is a degree-8 polynomial.
O C. The student did not put the polynomial in standard form before naming it by the first term. It is a fourth-degree trinomial.
OD. The student did not put the polynomial in standard form before naming it by the first term. It is a quadratic trinomial.
Answer:
C. The student did not put the polynomial in standard form before naming it by the first term. It is a fourth-degree trinomial.
Step-by-step explanation:
A trinomial is a polynomial with three variables. The polynomial -2x³ + 5x⁴ - 3x has three variables hence it is a trinomial.
The degree of a polynomial is the highest degree of a variable in a polynomial equation.
The polynomial -2x³ + 5x⁴ - 3x can be arranged as The polynomial 5x⁴ - 2x³ - 3x, hence the variable with the highest degree is 5x⁴ which has a degree of 4.
Therefore The polynomial -2x³ + 5x⁴ - 3x has a degree of 4
This means the polynomial -2x³ + 5x⁴ - 3x is a trinomial with a degree of 4
1:
2
3
Deanna and Lisa are playing games at the arcade. Deanna started with $15, and the
machine she is playing costs $0.75 per game. Lisa started with $12, and the machine
she is playing costs $0.50 per game. After how many games will the two girls have
the same amount of money remaining?
Answer:
After 12 games.
Step-by-step explanation:
Deanna's money after playing 12 games =
15 - (0.75 × 12) = 6$
Lisa's money after playing 12 games =
12 - (0.50 × 12) = 6$
Find the inverse.
f(x) = 3x+28
Set [tex]y = f^{-1}(x)[/tex] and [tex]f(y) = x[/tex]
Interchange the variables [tex]x[/tex] and [tex]y[/tex]
[tex]3y + 28 = x\\3y = x - 28\\y = \frac{x - 28}{3} \\\\f^{-1}(x) = \frac{x - 28}{3}[/tex]
Find f '(a). f(x) = 1 − 2x
PLZ HELP IVE BEEN STUCK ON THIS QUESTION
Answer:
A= 16
B=?
Step-by-step explanation: srry about the second one im also confused but i tried my best.
100 POINT I need answer ASAP WITH WORK PLEASE!!
Answer:
153.2 =x
Step-by-step explanation:
Since this is a right triangle, we can use trig functions
cos theta = adjacent side/ hypotenuse
cos 40 = x/200
Multiply each side by 200
200 cos 40 = x/200 * 200
200 cos 40 =x
153.20888886=x
To the nearest tenth
153.2 =x
Answer:
AC = 153.2 m.
Step-by-step explanation:
cos(Ф) = adj / hyp
cos(40) = AC / 200
AC = cos(40) x 200
AC = 153.2 m
The zeroes of the function are
The answer is -2 , 0, and 4
Which of the following is equal to 20x + 8y - 80?
A. 3x + y - 10
B. 5x+2y-20
c. 4(5x + 2y - 20)
D. 4(5x + 2y – 40)
E. 4(5x + 8y - 20)
HELP PLEASE MY WORK HAS TO BE DUE IN A FEW MINUTES PLEASE HELP
Given: 2/3 every 30 seconds
If we cut 2/3 in half, we get 1/3. This would also mean we cut the time in half 30 / 2 = 15 seconds
Therefore, 1/3 of the length every 15 seconds.
15 + 15 + 15 = 45 seconds to go the full length of the path
If 25% of a number is 30, then what is 40% of the same number?
Divide 30 by 25% to find the full amount:
30/0.25 = 120
Now multiply the full amount by 40%:
120 x 0.40 = 30
-28 (-13)
Can someone please?
For the given linear function, what are the slope and y-intercept?
Answer:
The equation of any straight line, called a linear equation, can be written as: y = mx + b, where m is the slope of the line and b is the y-intercept. The y-intercept of this line is the value of y at the point where the line crosses the y axis.
Step-by-step explanation:
I had this question not to long ago and got it right
What is this (x^2)^5 times (x^5)^2
Answer:
[tex]x^{20}[/tex]
Step-by-step explanation:
[tex](x^{2} )^{5}[/tex]·[tex](x^{5})^{2}[/tex]
[tex](x^{10} )[/tex] · [tex](x^{10})[/tex]
[tex]x^{20}[/tex]
3x + 1 = 5X-13 if anyone knows what to do can they please help
Answer:
x = 7
Step-by-step explanation:
First, you look at the equation. Identify the locations of variable terms (both sides of the equal sign) and the constant terms (both sides of the equal sign).
If there are any parentheses, it is a good idea to use the distributive property to eliminate them. Here, there are none.
I like to start by subtracting the variable term with the smallest coefficient. Here, that is 3x, so we add -3x to both sides of the equation.
3x -3x +1 = 5x -3x -13
1 = 2x -13 . . . . . . . . . . . . combine like terms
Now, we have the only variable term on one side of the equal sign. We want it by itself, so we need to make the -13 go away. We do that by adding its opposite to both sides of the equation:
1 +13 = 2x -13 +13
14 = 2x . . . . . . . . . . . . combine like terms
Finally, we want the coefficient of 2 in the x-term to disappear. We make that happen by multiplying both sides of the equation by 1/2, the reciprocal of that coefficient.
(1/2)(14) = (1/2)(2x)
7 = x . . . . the solution
__
It is generally a good idea to check your work by seeing if your solution value satisfies the equation:
3(7) +1 = 5(7) -13 . . . . put 7 where x is in the original equation
21 +1 = 35 -13
22 = 22 . . . . . . x = 7 is the solution
_____
Additional comment
By subtracting 3x from 5x, the result is 2x with a positive coefficient. We could solve the equation just as easily by subtracting 5x from 3x. That result would be ...
-2x +1 = -13
Subtracting 1 would give
-2x = -14
and you would multiply by -1/2 to get x=7. I personally like to avoid having this many minus signs show up in the problem. That is why I choose to subtract the x-term with the smallest coefficient.
simplify the following expression 2x cubed y cubed over 4y squared
3xcubed y to the fifth over 2
Please answer ASAP, I will give you brainilest and 5 stars if you get it right and do it quick!!
Answer:
a) 3.2 cm
b) 6.25 km
There are 10 boys and 15 girls. What is the probability of picking double girls
Pls Help!!! John and his mother left their house for the market simultaneously. While John's mother was walking with a speed of 15 meters per minute, it took John 3 minutes to walk to the market and back to meet his mother. How long did it take John to get to the market, if his speed was 25 meters per minute?
Answer:
It would take 2.4 minutes
Step-by-step explanation:
Time span can never be different for the same two people. Therefore in 3 minutes, John's mother would have covered a distance of 15(3) = 45 meters. Respectively John would have covered a distance of 25(3) = 75 meters in the same time.
Distance from 'starting point' to the market: 45 m + 15 m = 60 meters,
Time that John takes to return from market, and meet with his mother
=> 15 / 25 (his speed) = 0.6,
Time it takes John to get to the market: 3 - 0.6 = 2.4 minutes
Answer:
2.4 mins
2mins 24 sec
Step-by-step explanation:
Colin Davis machine company maintains a general ledger
Step-by-step explanation:
yf.bfz
vcg ,kgu nkkgfgvvxvh
(9mn-19^4n) - (8m^2+12m^4n+9mn
Answer:
-19n^4 - 8m^2 - 12m^4n
Step-by-step explanation:
8m^2 + 12m^4n + 9mn
-
19n^4 9mn
------------------------------------------------------------------------
-19n^4 - 8m^2 - 12m^4n
Answer:
The answer is B.) -31m^4n-8m^2