To simplify the given expression, subtract the terms in the numerator, and then simplify the terms in the denominator. Finally, divide the numerator by the denominator.
Explanation:To perform the indicated operation a-a^4/a^2+a+1, we need to simplify the expression using the order of operations. First, we simplify the terms in the numerator: a - a^4. Then, we simplify the terms in the denominator: a^2 + a + 1. Finally, we divide the simplified numerator by the simplified denominator to get the final answer.
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To perform the given operation, we need to follow the order of operations and simplify the exponents before performing the division, addition, and subtraction.
Explanation:To perform the indicated operation a - a^4 / a^2 + a + 1, we need to follow the order of operations, which is often remembered using the acronym PEMDAS. This stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Simplify the exponents: a^4 = a * a * a * a and a^2 = a * a.Perform the division: a^4 / a^2.Perform the addition: a^2 + a + 1.Perform the subtraction: a - (result of division) / (result of addition).Learn more about Order of Operations here:https://brainly.com/question/15840745
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Which expression is modeled by the diagram above?
PLEASE HELP ASAP!
Answer:
[tex]3\frac{1}{4}[/tex] divide by [tex]\frac{3}{4}[/tex]
Step-by-step explanation:
[tex]3\frac{1}{4}[/tex] is a mixed fraction and it can be written as
[tex]\frac{3*4+1}{4}=\frac{13}{4}[/tex]
13/4 can be break into
[tex]\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{3}{4}+\frac{1}{4}[/tex]
[tex]\frac{13}{4}[/tex] can be divided into [tex]\frac{3}{4}[/tex] and it is left with
[tex]\frac{1}{4}[/tex]
[tex]3\frac{1}{4}[/tex] divide by [tex]\frac{3}{4}[/tex]
A and B are two events.
P(A) = 0.6, P(B) = 0.3, P(A and B) = 0.1.
What is the value of P(A or B)?
Answer:
0.8
Step-by-step explanation:
We can solve P(A or B) by using the following:
[tex]P(AorB)=P(A)+P(B)-P(AandB)[/tex]
Since we know P(A) = 0.6, P(B) = 0.3 and P(A and B) = 0.1 we obtain:
[tex]P(AorB)=0.6+0.3-0.1=0.8[/tex]
Answer: 0.8
Step-by-step explanation:
In a geometric sequence, a2=108 and as 256. Write the explicit formula for this sequence.
Answer:
C. 81[-4/3]^n-1
Step-by-step explanation:
The explicit formula for a geometric sequence is given by a_n = a * r^(n-1). Using the provided values of a2 = 108 and a5 = 256, we can establish two equations to solve for 'a' and 'r'. This results in two possible explicit formulas for the sequence.
Explanation:In a geometric sequence, each term after the first is obtained by multiplying the previous term by a fixed, non-zero number called the common ratio. If we denote the first term of the sequence by 'a' and the common ratio by 'r', then the explicit formula of the sequence is: a_n = a * r^(n-1). Given that a2 = 108 (the second term is 108) and a5 = 256 (the fifth term is 256), we have two equations: a*r = 108 and a*r^4 = 256. Dividing the second equation by the square of the first equation, we get r^2 = 256/108^2 = 0.022. So, r is about +- 0.148. Substituting r into the first equation, we can solve for a. This gives us two possible explicit formulas for the sequence depending on whether we take the positive or negative value of r.
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Simplify the algebraic expression: 7x2 + 6x – 9x – 6x2 + 15.
A. x2 – 3x + 15
B. x4 – 3x + 15
C. x2 + 15x + 15
D. 13x2 + 3x + 15
Answer:
The correct answer option is A. x2 – 3x + 15.
Step-by-step explanation:
We are given the following expression and we are supposed to simplify it:
[tex]7x^2+6x-9x-6x^2+15[/tex]
Before solving it, a good idea will be to arrange all the like terms together in their decreasing power and write the expression as:
[tex]7x^2-6x^2+6x-9x+15[/tex]
Simplifying it to get:
[tex]x^2-3x+15[/tex]
Therefore, the first option A is the correct answer x2 – 3x + 15.
Answer:
A. [tex]x^{2} - 3x +15[/tex]
Step-by-step explanation:
Given:
7x^2 + 6x – 9x – 6x^2 + 15.
On combining the x^2, and "x" terms we get,
= (7x^2 – 6x^2) + (6x – 9x) + 15
Now, here simple addition of integers takes places
= x^ - 3x + 15
Help please in explain
Answer:
they are different numbers
Step-by-step explanation:
when you subtract 35-15 it comes out to 20 and the other one comes out to 17
You save $3,260.00 in a savings account earning a 3.55% APR compounded monthly. How much is the total interest earned by the end of the third month? a) $23.56 b) $21.02 c) $28.59 d) $27.01
Answer:
$29.02
Step-by-step explanation:
We will use compound interest formula to find the amount of interest after 3 months.
[tex]A=P(1+\frac{r}{n})^{nT}[/tex], where,
A= Amount after T years.
P= Principal amount.
r= Annual interest rate in decimal form.
n= Number of times interest is compounded per year.
T= Time in years.
Let us convert our given interest rate in decimal form.
[tex]3.55\%=\frac{3.55}{100}=0.0355[/tex]
Let us convert our given time in years.
[tex]3\text{ months}=\frac{3}{12}\text{ years}=0.25\text{ years}[/tex]
Let us substitute our given values in above formula.
[tex]A=3260(1+\frac{0.0355}{12})^{12\times 0.25}[/tex]
[tex]A=3260(1+0.0029583333333333)^{3}[/tex]
[tex]A=3260(1.0029583333333333)^{3}[/tex]
[tex]A=3260\times 1.0089012810988858948[/tex]
[tex]A=3289.018176382368017048[/tex]
We will use formula [tex]A=P+I[/tex] to find the amount of interest.
[tex]3289.018176382368017=3260+I[/tex]
[tex]3289.018176382368017-3260=I[/tex]
[tex]29.018176382368017=I[/tex]
[tex]I\approx 29.02[/tex]
Therefore, the total interest earned by the end of the third month will be $29.02.
Answer:
$28.59
Step-by-step explanation:
GradPoint doesn't seem to have the correct answer. THe closest I could get was to take 3,260 x .0355 x 90/365 = 28.54
The steps below show the incomplete solution to find the value of q for the equation 4q - 2q - 4 = -1 + 21
Step 1: 4q - 2q - 4 = -1 + 21
Step 2: 4q - 2q - 4 = 20
Step 3: 2q - 4 = 20
Which of these is most likely the next step?
Answer:
As you did not provide any "next steps", I would do it this way:
2q - 4 = 20 // add 4 to both sides
2q = 24 // divide both sides by 2
q = 12
Answer:
2q-4=20
Step-by-step explanation:
A website's views were increasing exponentially at a rate of 14% per year.
What was the monthly growth rate?
Enter your answer, rounded to the nearest tenth of a percent, in the box.
Answer:
see below PLEASE GIVE BRAINLIEST
Step-by-step explanation:
14% ÷ 12 (MONTHS IN THE YEAR) = 1.16666667
If rounding to the nearest 10th of a percent the answer is 1.2% increase per month.
Answer:
1.1%
Step-by-step explanation:
Annual rate: 14 % = [tex]\frac{14}{100} = 0.14[/tex]
Monthly rate = [tex](1 + r )^{\frac{1}{12} } - 1[/tex]
= [tex](1 + 0.14 )^{\frac{1}{12} } - 1[/tex]
= [tex](1.14 )^{\frac{1}{12} } - 1[/tex]
= 1.01097 - 1
= 0.01097
In percent it becomes: 0.01097 * 100 = 1.097%
Rounded to the nearest tenth: 1.1%
The quotient of twice a number and 7 is 20. “Translate using an equation or an inequality, do not solve.”
Answer:
2n/7=20
Step-by-step explanation:
let n be the number
Answer: 2x/7 =20
Step-by-step explanation:
Hi, to answer this question we have to write an equation.
Quotient means the result of the division of 2 numbers. In this case we have to divide twice a number (a number "x" multiplied by 2) by 7.
Mathematically speaking:
2x/7
That quotient is equal to 20.
So, the final equation is:
2x/7 =20
Feel free to ask for more if needed or if you did not understand something.
Based on the graph, which inequality is correct for a number that is to the right of -3?
4 > −3
−3 > 4
−2 < −3
−3 < −6
Answer:
4 > −3
Step-by-step explanation:
To find a number to the right of -3, it must be bigger than -3
The open part of the inequality faces the bigger number.
4 is bigger than -3
4>-3
help?? #10 please!!
Answer:
∠CAT = 140°
Step-by-step explanation:
Since AB bisects ∠CAT then ∠BAT = ∠CAB, hence
5x + 20 = 2x + 50 ( subtract 2x from both sides )
3x + 20 = 50 ( subtract 20 from both sides )
3x = 30 ( divide both sides by 3 )
x = 10
∠CAT = ∠BAT + ∠CAB = 5x + 20 + 2x + 50 = 7x + 70
substitute x = 10 into the expression
∠CAT = (7 × 10) + 70 = 70 + 70 = 140°
help quickly please!
Im not too sure, but C might work as an answer...
Sorry if it's wrong :(
Jennifer is making a cold cut platter using turkey and ham for an event that she is catering. She uses 90 slices of meat. If 63 of the slices of meat are turkey, what percent of the meat on the platter are ham? ALSO, PLEASE EXPLAIN. Thanks! :)
Answer:
30% of the meat on the platter is ham.
Step-by-step explanation:
90 slices = 100%
10% = 9 slices
90 - 63 = 27 slices (this is the amount of ham)
10% x 3 = 30% = 27 slices of ham
Answer:
27 slices of ham which is about 30% of the meat.
Step-by-step explanation:
In this problem we have given
no. of slices of meat=90
no of slices of turkey's meat=63
Percent of ham in platter=?
No of ham slices= Total slices -turkey slices
=90 - 63
= 27 slices
therefore no of ham slices=27
percent of ham slices=Ham slicesx100/total slices
=27x100/90%
=30%
Therefore percent of ham's in patter=30%
Which of the following is NOT a congruence transformation
A. A reflection over the x-axis
B. A dialation with scale factor 0.5
C. A translation 1 unit left
D. A dialation with scale factor 1
Can 12 be part of more than one fact family? Explain.
Rearrange the equation so b is the independent variable. 4a+b=−52
Answer:
[tex]a= \frac{-52-b}{4}[/tex]
Step-by-step explanation:
Rearrange the equation so b is the independent variable.
To get 'b' as a independent variable , we need to get 'a' alone
WE need to solve for 'a' so that 'a' depends on variable b and 'b' becomes independent variable
4a+b=−52
To get 'a' alone , subtract 'b' from both sides
4a = -52-b
Divide by 4 on both sides
[tex]a= \frac{-52-b}{4}[/tex]
Answer:
a=-13-1/4b
Step-by-step explanation:
I got it on khan academy I didn’t get what the guy before got but sorry if it’s wrong
A line passes through the point (-9,3) and has a slope of -2/3?
Write an equation in point slope for this line.
The point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
We have the slope m = -2/3 and the point (-9, 3). Substitute:
[tex]y-3=-\dfrac{2}{3}(x-(-9))[/tex]
[tex]y-3=-\dfrac{2}{3}(x+9)[/tex] use distributive property
[tex]y-3=-\dfrac{2}{3}x-\dfrac{2}{3}\cdot9[/tex]
[tex]y-3=-\dfrac{2}{3}x-(2)(3)[/tex]
[tex]y-3=-\dfrac{2}{3}x-6[/tex] add 3 to both sides
[tex]\boxed{y=-\dfrac{2}{3}x-3}[/tex]
Plz I need by tonight
Answer: $9.75
Step-by-step explanation: I think this is how you do it. 20h=195 so you divide 195 by 20 to find our how much he gets an hour.
Answer:
9.75
Step-by-step explanation:
You have to divide the both by 20 since there is any like terms or anything to use, but you can use division on both sides since its 20h = 195.
20h = 195
-------------20 20
-------------h = 9.75
Evaluate The Expression 3(× - 1)² +2× - 7 for × = 3
[tex]\bf 3(x-1)^2+2x-7\implies \stackrel{\stackrel{x=3}{\cfrac{}{}}}{3[(3)-1]^2+2(3)-7}\implies 3[2]^2+6-7 \\\\\\ 3[4]+(-1)\implies 12-1\implies 11[/tex]
What is the solution to the equation fraction 1 over 4x = 5?
A) x = fraction 4 over 5
B) x = fraction 5 over 4
C) x = 20
D) x = 1
Your brother is going to buy a car when he graduates, but he doesn't have enough money to pay for it in cash. He takes a loan out at a bank that charges 4% simple interest. If the initial cost of the car is $18,500 and he takes out a 5-year loan, what is the total amount your brother will be paying for the cost of his car?
Answer:
Step-by-step explanation:$18,500 × .04=
$740×5= $3,700 + $18,500=
$22,200 for total loan
A store sells 12 cans of nuts for $33. How much would it cost you to buy 5 cans of nuts?
[tex]\bf \begin{array}{ccll} cans&\$\\ \cline{1-2} 12&33\\ 5&x \end{array}\implies \cfrac{12}{5}=\cfrac{33}{x}\implies 12x=165 \\\\\\ x=\cfrac{165}{12}\implies x=13.75[/tex]
Answer:
$13.75
Step-by-step explanation:
Divide $33 by 12 to find out how much each can of nuts costs, which is $2.75. Now multiply that by 5 to get the cost of 5 cans of nuts. $13.75.
Using the completing-the-square method, rewrite f(x) = x2 − 8x + 3 in vertex form.
A) f(x) = (x − 8)^2
B) f(x) = (x − 4)^2 − 13
C) f(x) = (x − 4)^2 + 3
D) f(x) = (x − 4)^2 + 16
Answer:
B
Step-by-step explanation:
f(x) = [tex]x^{2} -8x+3[/tex]
=> f(x)= [tex]x^{2} -2(x)(4)+4^{2}-4^{2}+3[/tex]
=> f(x) = [tex](x-4)^{2}-4^{2}+3[/tex]
=> f(x) = [tex](x-4)^{2}-16+3[/tex]
=> f(x) = [tex](x-4)^{2}-13[/tex]
Answer:
f(x) = (x - 4)² - 13
Step-by-step explanation:
f(x) = x² − 8x + 3
x² − 8x + 3 = 0
x² - 8x = -3
x² - 8x + 4² = -3 + 4²
x² - 8x + 4² = -3 + 16
x² - 8x + 4² = 13
(x - 4)² = 13
(x - 4)² - 13 = 0
The vertex form of a quadriatic function f(x) = x2 − 8x + 3 is;
f(x) = (x - 4)² - 13
8 lb 1 oz − 3 lb 6 oz
Answer:
Since you want me to answer 3 lb 1 oz - 1 lb 15 oz instead, the answer is 18 oz
Step-by-step explanation:
First, convert pounds and ounces to just ounces, then subtract the total ounces. Finally, convert back to pounds and ounces to get the result of 8 lb 1 oz minus 3 lb 6 oz, which is 4 lb 11 oz.
Subtracting Mixed Measurements
To find the result of 8 lb 1 oz − 3 lb 6 oz, follow these steps:
Convert everything to ounces for easier subtraction (since there are 16 ounces in a pound).
Subtract the ounces first, then subtract the pounds.
Step-by-Step Solution
Step 1: Convert to ounces
8 lb 1 oz = (8 × 16) + 1 = 128 + 1 = 129 ounces
3 lb 6 oz = (3 × 16) + 6 = 48 + 6 = 54 ounces
Step 2: Subtract the ounces
129 ounces - 54 ounces = 75 ounces
Step 3: Convert back to pounds and ounces
75 ounces = 4 lb 11 oz (since 75 ÷ 16 = 4 remainder 11)
Therefore, 8 lb 1 oz − 3 lb 6 oz = 4 lb 11 oz.
Destiny reached the 3-km mark of the race at 10:36am and the 5-km mark at 10:44am. WHat is her running rate
Answer:
Running rate of Destiny is 15 kmph
Step-by-step explanation:
Running rate of Destiny is the speed at which Destiny is running.
It can be calculated by finding the difference in the distance covered to the difference in the time taken.
So,
Running rate = Difference in distance covered / Difference in time taken
Difference in distance covered = 5-3 = 2 km
Difference in time taken = 10:44 am - 10:36 am = 44 -36 minutes = 8 mins =8/60 hour = 2/15 hour
Running rate = 2/(2/15) kmph =(2*15)/2 = 15 kmph
∴Running rate of Destiny is 15 kmph
What are the zeros of the quadratic function f(x)=2x^2+16x-9
Answer:
D
Step-by-step explanation:
The quadratic formula is
[tex]x=\frac{-b+\sqrt{b^2-4ac} }{2a}[/tex].
It is important because while some quadratics are factorable and can be solved not all are. The formula will solve all quadratic equations and can also give both real and imaginary solutions. Using the formula will require less work than finding the factors if factorable. We will substitute a=2, b=16 and c=-9.
[tex]x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}\\x=\frac{-(16)+/-\sqrt{(16)^2-4(2)(-9)} }{2(2)}\\x=\frac{-16+/-\sqrt{256+72} }{4}[/tex]
We will now simplify and solve.
[tex]x=\frac{-16+/-\sqrt{328}}{4}\\x=-4+/-\sqrt{\frac{328}{16}}\\x=-4+/-\sqrt{\frac{41*8}{2*8}}\\x=-4+/-\sqrt{\frac{41}{2}}[/tex]
From the information in the graph, which team showed the least amount of improvement over last year?
A.
Jets
B.
Bears
C.
Colts
D.
Rangers
Answer:
The rangers
Step-by-step explanation:
Their number of wins didn't go up. In fact their wins decreased the most.
Answer:
D
Step-by-step explanation:
Improvement means positive change. The one with the least positive difference is the Rangers because they became WORSE by more than 10, which is bigger than even the Jets' negative amount.
Write the equation of the circle with center (3,-2), and passes through the point (0,2).
Final answer:
To find the equation of the circle, we need the center coordinates and the radius. In this case, the center is (3, -2) and the circle passes through the point (0, 2). Using the distance formula, the radius is found to be 5. Therefore, the equation of the circle is [tex](x - 3)^2 + (y + 2)^2 = 5^2[/tex].
Explanation:
To find the equation of a circle, we need the center coordinates and the radius. In this case, the center is (3, -2) and the circle passes through the point (0, 2). We can use the distance formula to find the radius, which is the distance between the center and the point on the circle.
Using the distance formula, [tex]d = \sqrt{((x2 - x1)^2 + (y2 - y1)^2)[/tex], we have:
[tex]d = \sqrt{((0 - 3)^2 + (2 - (-2))^2)} = \sqrt{((-3)^2 + (4)^2)} = \sqrt{(9 + 16)} = \sqrt{(25)} = 5[/tex]
So, the radius is 5. Therefore, the equation of the circle is
[tex](x - 3)^2 + (y + 2)^2 = 5^2[/tex]
To find the equation of the circle with center at (3, -2) and passing through the point (0, 2), use the standard form and calculate the radius. Then, the equation is (x - 3)² + (y + 2)² = 25.
To find the equation of a circle with center at (3, -2) and passing through the point (0, 2), we can use the standard form of the equation of a circle, which is:
(x - h)² + (y - k)² = r²
Here, (h, k) is the center of the circle, and r is the radius. Given the center (3, -2), we substitute h = 3 and k = -2:
(x - 3)² + (y + 2)² = r².
Next, we find the radius by calculating the distance between the center (3, -2) and the point (0, 2) using the distance formula:
r = [tex]\sqrt{(0 - 3)^2 + (2 + 2)^2}[/tex]
= √(9 + 16)
= √(25)
= 5.
With r = 5, we can now write the full equation of the circle:
(x - 3)² + (y + 2)² = 25
To summarize, the equation of the circle with center at (3, -2) and passing through the point (0, 2) is (x - 3)² + (y + 2)² = 25.
find f'(x) for f(x)=e^(x)ln(x)
Answer:
df/dx = e^x(1/x+ ln(x))
Step-by-step explanation:
f(x) = e^x * ln(x)
We can solve this by partial derivatives
df/dx = u dv + v du
let u = e^x and v = ln(x)
df/dx = e^x * 1/x + ln(x) * e^x
Factor out the e^x
df/dx = e^x(1/x+ ln(x))
solve the equation by completing the square. x^2 -6x -21=0 if the solution is not a real number enter no solution (ANSWER -2.48 and 8.48 )this is what the lesson says i just dont know how to show this
Answer:
see explanation
Step-by-step explanation:
given x² - 6x - 21 = 0 ( add 21 to both sides )
x² - 6x = 21
to complete the square
• add ( half the coefficient of the x-term)² to both sides
x² + 2 (- 3)x +9 = 21 + 9
(x - 3)² = 30 ( take the square root of both sides )
x - 3 = ± [tex]\sqrt{30}[/tex] ( add 3 to both sides )
x = 3 ± [tex]\sqrt{30}[/tex]
x = 3 - [tex]\sqrt{30}[/tex] = - 2.48 ( to 2 dec. places ) or
x = 3 + [tex]\sqrt{30}[/tex] = 8.48 ( to 2 dec. places )