Simplify the expression: x+7x2+3x+2=x+7(x+1)(x+2)
The form of the partial fraction decomposition is
x+7(x+1)(x+2)=Ax+1+Bx+2
Write the right-hand side as a single fraction:
x+7(x+1)(x+2)=(x+1)B+(x+2)A(x+1)(x+2)
The denominators are equal, so we require the equality of the numerators:
x+7=(x+1)B+(x+2)A
Expand the right-hand side:
x+7=xA+xB+2A+B
Collect up the like terms:
x+7=x(A+B)+2A+B
The coefficients near the like terms should be equal, so the following system is obtained:
{A+B=12A+B=7
Solving it (for steps, see system of equations calculator), we get that A=6, B=−5
Therefore,
x+7(x+1)(x+2)=6x+1+−5x+2
Answer: x + 7x\textasciicircum{2} + 3 x + 2=6x+1+−5x+2
sophia used 1/10 of a liter of water to fill 1/4 of a fish aquarium. How much water, in liter is required to fill the aquarium?
Answer:
4/10 of a liter
Step-by-step explanation:
if 1/10 of a liter fills 1/4 of the aqauium then your ratio is .1:.25 out of 100 so
100/25=4
please help me solve this anyone! plz don’t guess just for points this was due a few weeks ago and i have to have good grade
Answer:
[tex] - 23[/tex]
Step-by-step explanation:
Substitute -3 for X in the expression then solve.
Answer:
-23
Step-by-step explanation:
They give us the variable's value, which is [tex]x=-3[/tex]. All we have to do from here is plug it into the expression that they gave us!
So, let's do exactly that! The expression that they gave us is [tex]5x-8[/tex], and we know the value of x because they gave it to us!
Let's plug it in.:
[tex]5(-3)-8[/tex]
Let's follow P.E.M.D.A.S. and our order of operations to determine what to do first. Since we have multiplication going on within parenthesis, let's do that first.
[tex]5(-3)=-15[/tex] because a negative number times a positive number equates to a negative number. Now, we have the following expression: [tex]-15-8[/tex]
Let's subtract this now! Remember, subtracting a number from another number is basically adding the opposite of the second number; essentially, you're following keep, change, flip. You keep the first number without doing anything to it, you change the sign of the operation, and you flip the sign of the 2nd number. Let's revise this problem now with these rules.: [tex]-15 + (-8)[/tex], now we have something that we can work with! Since both numbers are negative and are being added, we keep the sign, and just add their absolute value, leaving us with the expression being -23.
. If a random variable x has a discrete uniform distribution
1
fx(x) = 2
for x = 1,2, ..., 2k; 0 Otherwise.
Derive p.g.f. of X and Compute E(2X + 3)
Shelby loves to knit scarves. Normally, it takes her 15 minutes to knit 5 inches of a scarf. She plans to make a scarf that is 30 inches long.
If she knits at the same rate, how many minutes will it take Shelby to knit the scarf?
Answer:
90 minutes
Step-by-step explanation:
let x=amount of time it would take for Shelby to knit the scarf
[tex]\frac{15}{5} =\frac{x}{30}[/tex]
cross multiply
15*30=5x
450=5x
450/5=x
x=90
It would take Shelby 90 minutes to knit a scarf that is 30 inches long.
can someone help me with this
Answer:0.98
hope this helps have a good day
Step-by-step explanation:
the product of a number and -8 is 72
Answer:
-9.
The product of -9 and -8 is 72.
Step-by-step explanation:
Product means the answer of a multiplication, so we're given 72 and -8.
We can solve this by using inverse operations.
The inverse operation of multiplication is division, so we divide 72÷ -8
This will give us -9.
You order pizza on Door Dash. It costs $39. Sales tax is 7% and you want to leave 20%
for tip. What is the total cost including the sales tax and tip? (HINT: regular price + sales
tax + tip = total cost
Answer:
$47.4
Step-by-step explanation:
prize = $39
sales tax = $7
total cost = x
tip = 20% of the tax
tip = 20% of 7
=$ 1.4
total cost = 39 +7+ 1.4
= $47.4
Answer:
$49.53
Explanation:
Convert 7 % to a decimal.
0.07 x 39Multiply 0.07 by 39 .
2.73Repeat, but with 20%.
7.8Add the tax and tip to the original price:
39 + 2.73 = 41.73
41.73 + 7.8 = $49.53
$1,580 at 10% for 8 years
Use triangles to find the sum of the interior angle measures of the polygon
Answer:
145
Step-by-step explanation:
2x squared times 6 =
A:10x squared
B:8x squared
C:12x squared
Answer:
C: 12x squared
Step-by-step explanation:
the equation would look like [tex]2x^{2}[/tex] · [tex]6[/tex] or [tex]6(2x^{2})[/tex]
you only multiply the coefficients, leave the exponent alone for this one
so 2 times 6 would be 12 and the [tex]x^{2}[/tex] remains the same giving you [tex]12x^{2}[/tex]
Pls answer this is very easy
Answer:
A and B
Step-by-step explanation:
The original equation simplifies down to -4m - 2
Answer A and B also simplify down to -4m -2, and therefor are equivalent
A: -2(4m + 1) + 4m
-8m - 2 + 4m
-4m - 2
B: 2(2m - 1) - 8m
4m - 2 - 8m
-4m - 2
Please help and explain how you got the answer. Im giving out brainliest. || Q3
Answer:6:8
Step-by-step explanation:
An elevator is traveling underground at a constant rate. The equation y= -2x - 10 can be used to represent this situation, where y is the position of the elevator underground in feet and x is the number of seconds the elevator has been traveling Which statement best describes the position of the elevator, given this equation?
O From a starting position of 2 feet underground, the elevator is descending 10 feet per second
O From a starting position of 10 feet underground, the elevator is descending 2 feet per second
O From a starting position of 2 feet underground, the elevator is ascending 10 feet per second
O From a starting position of 10 feet underground, the elevator is ascending 2 feet per second
4 is correct
reason is because the number next to x is the constant number and the end number is where you started
Which of the following would you expect to find on a monthly account statement? a. A new set of checks and deposit slips for the coming month. b. A list of credits and debits made during the period. c. A comparison of ending balances for the past 12 months. d. A tally of all credits and debits in the account’s history.
Answer:
b. A list of credits and debits made during the period.
Step-by-step explanation:
Edge 2021
On a monthly account statement, what you are expected to find is a A list of credits and debits made during the period.
What is a monthly account statement?This can be referred to as a statement of the debits and the credits that occurred in a given period of one month.
The account statement is a statement of the transactions that have occurred in an establishment over a period.
Read more on account statements here:
https://brainly.com/question/24498019
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Which expression is equivalent to 1/3(9x + 12) + 4x + 6?
A: 7x + 18
B7x + 10
C:13x x +6
D:13x + 18
The expression is equivalent to 1/3(9x + 12) + 4x + 6 will be 7x + 10. Then the correct option is B.
What is an equivalent?The equivalent is the expression that is in different forms but is equal to the same value.
The definition of simplicity is making something simpler to achieve or grasp while also making it a little less difficult.
The expression is given below.
⇒ 1/3(9x + 12) + 4x + 6
Simplify the expression, then we have
⇒ 1/3(9x + 12) + 4x + 6
⇒ 3x + 4 + 4x + 6
⇒ 7x + 10
The expression is equivalent to 1/3(9x + 12) + 4x + 6 will be 7x + 10. Then the correct option is B.
More about the equivalent link is given below.
https://brainly.com/question/889935
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Help asap if you get it right ill give 30 points no cap. Zach created a blueprint using only similar parallelograms.
Which statement about the parallelograms must be true?
The parallelograms have corresponding angles that are not congruent.
The parallelograms have corresponding sides that are congruent.
The parallelograms have proportional corresponding sides.
The parallelograms all have congruent sides and angles.
Answer: Hello!
Step-by-step explanation:
Your answer would be D :)
Data on investments in the high-tech industry by venture capitalists are compiled by a corporation. A random sample of 18venture-capital investments in a certain business sector yielded the accompanying data, in millions of dollars. Determine and interpret a 95%confidence interval for the mean amount, mu,of all venture-capital investments in this business sector. Assume that the population standard deviation is $1.70million. (Note: The sum of the data is $102.52million.)
Answer:
$4.911 million or $6.481 million
Thus, we are 95% confident that the mean amount of all venture-capital investments in the high-tech industry is somewhere between $4.911 million and $6.481 million.
Step-by-step explanation:
Given that:
sample size n = 18
standard deviation σ = 1.70
confidence interval = 95%
Sample mean [tex]\overline x =\dfrac{ \sum x }{n}[/tex]
[tex]\overline x =\dfrac{ 102.52 }{18}[/tex]
[tex]\overline x =[/tex] 5.696
The level of significance = 1 - C.I
= 1 - 0.95
= 0.05
The critical value of [tex]Z_{\alpha/2} = Z_{0.025} = 1.960[/tex] from the Z tables
The 95% C.I for the mean is;
[tex]= \overline x \pm Z_{\alpha/2} \times \dfrac{\sigma}{\sqrt{n}}[/tex]
[tex]=5.696 \pm 1.960 \times \dfrac{1.70}{\sqrt{18}}[/tex]
[tex]=5.696 \pm 1.960 \times \dfrac{1.70}{4.243}[/tex]
[tex]=5.696 \pm 1.960 \times 0.4007[/tex]
= 5.696 ± 0.785372
= (5.696 - 0.785372 , 5.696 + 0.785372 )
= ( 4.910628 , 6.481372 )
≅ $4.911 million or $6.481 million.
Thus, we are 95% confident that the mean amount of all venture-capital investments in the high-tech industry is somewhere between $4.911 million and $6.481 million.
complete the table of values for y=2-x
x= -1, 0, 1, 2, 3, 4,
y= , , , , -1, ,
Answer:
x = -1, 0, 1, 2, 3, 4
y = 3, 2, 1, 0, -1, -2
Answer:
x = -1, 0, 1, 2, 3, 4
y = 3, 2, 1, 0, -1, -2
The Quality Control Department employs five technicians during the day shift Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing process last week.
Technician Shutdown
Taylor 4
Hurley 3
Gupta 5
Rousche 6
Huang 3
Required:
a. How many samples, without replacement, of size two are possible?
b. Compute the mean of the sample means and compare it to the population mean. (Round your answers to 1 decimal place.)
Solution :
Number of different samples of two technicians possible is = 10, as 2 technicians are to be chosen from a total of 5 technicians.
a). Therefore, 10 different samples are possible of size two.
b).
Sample Shut down Mean
1. Taylor, Hurley 4, 3 3.5
2. Taylor, Gupta 4, 5 4.5
3. Taylor, Rousche 4,6 5
4. Taylor, Huang 4, 3 3.5
5. Hurley, Gupta 3,5 4
6. Hurley, Rousche 3,6 4.5
7. Hurley, Huang 3,3 3
8. Gupta, Rousche 5,6 5.5
9. Gupta, Huang 5,3 4
10. Rousche, Huang 6,3 4.5
42
Now mean of sample means [tex]$=\frac{42}{10}$[/tex] = 4.2
Mean of population is = [tex]$\frac{4+3+5+6+3}{5}$[/tex] = 4.2
Thus both the means are equal.
What's the midpoint between 3 and -5
Answer:
Step-by-step explanation:
just imagine you are on a number line and the numbers are
-5....-4.....-3.....-2....-1....0....1....2.....3
as you see the midpoint is -1
Write a function formula for g using the function f.
g(x)=
Write a function formula for f using the function g.
f(x)=
9514 1404 393
Answer:
g(x) = f(x -2) -1
Step-by-step explanation:
The transformation g(x) = f(x -h) +k causes the graph of function f(x) to be translated h units to the right and k units up. Here, g is translated 2 units right and 1 unit down, so (h, k) = (2, -1). The translated function is ...
g(x) = f(x -2) -1
What is the surface area of the right trapezoidal prism? To receive credit, you must show the work used to arrive at a final answer.
Answer:
210 cm²
Step-by-step explanation:
The net of the right trapezoidal prism consists of 2 trapezoid base and four rectangles.
Surface area of the trapezoidal prism = 2(area of trapezoid base) + area of the 4 rectangles
✔️Area of the 2 trapezoid bases:
Area = 2(½(a + b)×h)
Where,
a = 7 cm
b = 11 cm
h = 3 cm
Plug in the values
Area = 2(½(7 + 11)×3)
= (18 × 3)
Area of the 2 trapezoid bases = 54 cm²
✔️Area of Rectangle 1:
Length = 6 cm
Width = 3 cm
Area = 6 × 3 = 18 cm²
✔️Area of Rectangle 2:
Length = 7 cm
Width = 6 cm
Area = 7 × 6 = 42 cm²
✔️Area of Rectangle 3:
Length = 6 cm
Width = 5 cm
Area = 6 × 5 = 30 cm²
✔️Area of Rectangle 4:
Length = 11 cm
Width = 6 cm
Area = 11 × 6 = 66 cm²
✅Surface area of the trapezoidal prism = 54 + 18 + 42 + 30 + 66 = 210 cm²
Each week, Tasha saves 80% of the money she earns babysitting and spends the rest. This week she earned $80.00.
How much more money did she save than spend this week?
Answer:
48$
Step-by-step explanation:
80% of 80 is 64 which means she spent 16$ and saved 64$
so 64-16=48$
answer = 48$
If a=5 what is the value of the card 4a-2
Answer:
18
General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to RightStep-by-step explanation:
Step 1: Define
4a - 2
a = 5
Step 2: Evaluate
Substitute in a: 4(5) - 2Multiply: 20 - 2Subtract: 18Answer:
The card "4a-2" is equal to 18
4a-2 = 18
Step-by-step explanation:
#1. Replace a with 5 and Your equation should look like the following:
4(5)-2
#2. Now Simplify, we all know that multiplication goes before subtraction or addition:
20-2
#3. Celebrate:
18
Woohoo
Hope this helps!
Have a nice day!
If you find my answer helpful
Pls consider marking my answer as Brainliest! It would mean a lot!
Determine the two ordered pair solutions of the equation y = 2x2 + 3x , given (0, ), and (-2, ).
Answer:
We conclude that the two ordered pairs (0, 0) and (-2, 2) are the solutions of the equation y = 2x² + 3x.
Step-by-step explanation:
Given the expression
y = 2x² + 3x
Substituting x = 0
y = 2(0)² + 3(0)
y = 0+0
y = 0
so when x = 0, y = 0Thus, the ordered pair is: (0, 0)
Now, substituting x = -2
y = 2x² + 3x
y = 2(-2)² + 3(-2)
y = 8 - 6
y = 2
so when x = -2, y = 2Thus, the ordered pair is: (-2, 2)
Therefore, we conclude that the two ordered pairs (0, 0) and (-2, 2) are the solutions of the equation y = 2x² + 3x.
Reid's Hardware discounts all riding lawnmowers 9% to customers paying in cash. If Trey paid $1,390.49 in cash for a riding lawnmower, which of the following equations can be used to determine the original price of the lawnmower?
Answer:
The original price of the lawnmower is $ 1,528.
Step-by-step explanation:
If Reid's Hardware makes a 9% discount on cash payments, and Trey paid $ 1,390.49 for his lawnmower, to determine the initial cost of the same, the following calculation must be performed:
100 - 9 = 91
91 = 1,390.49
100 = X
(100 x 1,390.49) / 91 = X
139.049 / 91 = X
1.528 = X
Thus, the original price of the lawnmower is $ 1,528.
8. Lisa types 6 pages in 36 minutes. Frank types 5 pages in 30 minutes. Do they type at the same rate? Use a proportion to explain.
Answer:
Yes
Step-by-step explanation:
Lisa and Frank type at the same rate.
They both type 1 page every six minutes.
Lisa types 6 pages every 36 minutes, and if we divide the minutes by the pages, we get
[tex]\frac{36}{6} = 6[/tex]
And Frank types 5 pages ever 30 minutes, when we divide we get
[tex]\frac{30}{5} = 6[/tex]
-10x-3y=-18
-7x-8y=11 solve system using elimination
Answer:
(-7) (-10x - 3y = -18)
(10) (-7x - 8x = 11)
--------------------------
70x + 21y = 126
+ -70 - 80x = 110
---------------------------
-59x = 236
x = -4
Answer
[tex] \huge{ \boxed{ \text{(3 \:, - 4)}}}[/tex]
✑ [tex] \underline{ \underline{ \text{First ,\: let's \: know \: about \: elimination \: method}}}[/tex] :
☇ In this method , we add or subtract the given equations to eliminate one of the two variables by making their coefficients equal. Then , a single equation with one variable so obtained is solved to find the value of the variable. The value of the variable is substituted to any one equation to find the value of the eliminated variable.
☯ [tex] \underline{ \underline{ \text{Let's \: solve}}} : [/tex]
[tex] \underline{ \text{Original \: system}} : [/tex]
[tex] \text{ - 10x - 3y = - 18 - - - - Equation\: (i)}[/tex]
[tex] \text{ - 7x - 8y = 11 - - - - Equation \: (ii)}[/tex]
[tex] \text{Step \: 1} : [/tex] Take L.C.M ( Lowest Common Multiple ) of 10 and 7. For this , find the prime factors of each number. Then, take out the common prime factors and other remaining prime factors and multiply them.
prime factors of 10 = 1 × 2 × 5prime factors of 7 = 1 × 7L.C.M = Common factors × Remaining Factors
= 1 × 2 × 5 × 7
= 70
[tex] \text{Step \: 2} : [/tex] Multiply equation ( i ) by 7
[tex] \text{7( - 10x - 3y ) = - 18 * 7}[/tex]
⇢ [tex] \text{ - 70x - 21y = - 126 - - - - equation \: (iii)}[/tex]
[tex] \text{Step \: 3} : [/tex]Multiply equation ( ii ) by 10
[tex] \text{10( - 7x - 8y) = 11 \: * \: 10}[/tex]
⇢ [tex] \text{ - 70x - 80y = 110 - - - - equation \: (iv)}[/tex]
[tex] \text{Step \: 4} : [/tex] Subtract equation ( iv ) from equation ( iii ) :
Also Remember that while subtracting , sign of each term of the second equation changes. Here , we are eliminating x . So to make the coefficient of y same , equation ( i ) is multiplied by 7 and equation ( ii ) is multiplied by 10.⇩
[tex] \text{ - 70x - 21y = - 126}[/tex]
[tex]\text{+70x + 80y = - 110}[/tex]
___________________
[tex] \text{ \: \: \: \: \: \: 59y = - 236}[/tex]
Solve :
⇢ [tex] \text{59y/59 = - 236/59}[/tex]
⇢ [tex] \boxed{ \bold{ \text{y = - 4}}}[/tex]
[tex] \text{Step \: 5} : [/tex]
Substitute the value of y into equation ( iii ) , we get :
[tex] \text{ - 70x - 21y = - 126}[/tex]
➳ [tex] \text{ - 70x - 21( - 4) = - 126} [/tex]
➳ [tex] \text{ - 70x - ( - 84) = - 126} [/tex]
➳ [tex] \text{ - 70x + 84 = - 126}[/tex]
➳ [tex] \text{ - 70x = - 126 - 84}[/tex]
➳ [tex] \text{ - 70x = - 210}[/tex]
➳ [tex] \text{ - 70x/ - 70 = - 210/ - 70}[/tex]
➳ [tex] \boxed{ \bold{ \text{x = 3}}}[/tex]
[tex] \bold{ \underline{ \text{Hence ,\: x = 3 \: and \: y = - 4}}}[/tex]
Hope I helped!
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Need help! Which matrix equation represents the system of equations?
[2x+ y =5
[5x+3y -12
Step-by-step explanation:
The given equations are :
2x+ y =5 ....(1)
5x+3y = 12
We need to find the matrix equation that represents the system of equations.
[tex][A]=\left[\begin{array}{cc}2&1&\\5&3\end{array}\right][/tex]
[tex][B]=\left[\begin{array}{cc}5\\12\end{array}\right][/tex]
And
[tex][X]=\left[\begin{array}{cc}x\\y\end{array}\right][/tex]
Hence, the matrix equation is :
[tex]\left[\begin{array}{cc}2&1&\\5&3\end{array}\right] \left[\begin{array}{cc}x\\y\end{array}\right]=\left[\begin{array}{cc}5\\12\end{array}\right][/tex]
Hence, the correct option is (b).
WILL GIVE BRAINLIEST TO WHOEVER ANSWERS FASTEST!
Answer:
speed i answerd first U.U
Step-by-step explanation: