The equivalent expression for the given expression 132/11 is 12.
1) Given that, 132/11
Here, the equivalent expression is 132/11 =12
2) 126/7 = 18
3) 7)98(14
7
_______
28
28
________
0
4) Sixty-four divided by four
That is, 64/4 = 16
5) 28÷2
= 28/2
= 14
6) 28/2 = 14
7) 48/3 = 16
8) 36÷2
= 36/2
= 18
9) 36÷3
= 36/3
= 12
Therefore, the equivalent expression for the given expression 132/11 is 12.
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Find relative extrema (x, y) of a function h(x) = x^3 + 3x^2 − 2 using
(a) the first derivative test
(b) the second derivative test
Which test is easiest?
a) Based on the first derivative test, h(x) has a relative minimum at x = -2 and a relative maximum at x = 0.
b) For x = -2: h''(-2) = 6(-2) + 6 = -6 < 0, so h(x) has a relative maximum at x = -2.
For x = 0: h''(0) = 6(0) + 6 = 6 > 0, so h(x) has a relative minimum at x = 0.
What is the calculus?Calculus is a branch of mathematics that deals with the study of rates of change, accumulation, and the properties and behavior of functions.
(a) First derivative test:
The first derivative test involves finding the critical points of the function, where the first derivative is equal to zero or undefined, and then checking the sign of the first derivative in the intervals between the critical points to determine whether the function has relative extrema at those points.
Find the first derivative of h(x):
h'(x) = 3x² + 6x
Set h'(x) = 0 and solve for x to find the critical points:
3x² + 6x = 0
x(x + 2) = 0
x = 0 or x = -2
Test the intervals between the critical points using the sign of the first derivative:
For x < -2: Choose x = -3, h'(-3) = 27 + (-18) = 9 > 0, so h(x) is increasing.
For -2 < x < 0: Choose x = -1, h'(-1) = 3 - 6 = -3 < 0, so h(x) is decreasing.
For x > 0: Choose x = 1, h'(1) = 3 + 6 = 9 > 0, so h(x) is increasing.
Based on the first derivative test, h(x) has a relative minimum at x = -2 and a relative maximum at x = 0.
(b) Second derivative test:
The second derivative test involves finding the critical points of the function using the first derivative, and then checking the sign of the second derivative at those points to determine whether the function has relative extrema at those points.
Find the second derivative of h(x):
h''(x) = 6x + 6
Evaluate the second derivative at the critical points found in step 2 of the first derivative test:
For x = -2: h''(-2) = 6(-2) + 6 = -6 < 0, so h(x) has a relative maximum at x = -2.
For x = 0: h''(0) = 6(0) + 6 = 6 > 0, so h(x) has a relative minimum at x = 0.
Hence, the ease of a test may vary for different individuals and their familiarity with calculus concepts.
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Find f(−3), f(0) and f(1) for the following function.
f(x)=2x
Answer:
-6, 0, 2Step-by-step explanation:
f(x)=2x
note: putting anything in the f(x) parentheses replaces x in the function with that value
so,
f(-3) = 2(-3) = -6
f(0) = 2*0 = 0
f(2) = 2(2) = 4
A store has 300 televisions on order, and 90% are high definition. How many televisions on order are high
definition? You may find the bar model useful in completing this problem.
20% 30% 40%
70%
0%
0
10%
30
The store has
50% 60%
high-definition televisions on order.
80%
90%
100%
300
Answer:
90% of 300 = .90 × 300 = 270 high- definition televisions on order.
Given (x – 7)2 = 36, select the values of x. x = 13 x = 1 x = –29 x = 42
The solution for x in the equation (x – 7)^2 = 36 are x = 13 and x = 1
Solving for x in the equationWe can solve for x by taking the square root of both sides of the equation:
(x – 7)^2 = 36
Taking the square root of both sides:
x - 7 = ±6
Adding 7 to both sides:
x = 7 ± 6
Therefore, the values of x are:
x = 7 + 6 = 13
x = 7 - 6 = 1
So the correct answers are x = 13 and x = 1. The values x = -29 and x = 42 are not solutions to the equation.
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12,59,294,1469,7344 what is the pattern rule
Both equations give the correct terms, so we can conclude that the pattern rule is: [tex]an^2 - 131n + 80[/tex] , where [tex]a=63[/tex] .
What is the consecutive terms?To find the pattern rule for the given sequence 12, 59, 294, 1469, 7344, we need to observe the differences between consecutive terms. Let's find the differences between each pair of terms:
[tex]59 - 12 = 47[/tex]
[tex]294 - 59 = 235[/tex]
[tex]1469 - 294 = 1175[/tex]
[tex]7344 - 1469 = 5875[/tex]
The differences are not constant, so we need to find the differences between these differences:
[tex]235 - 47 = 188[/tex]
[tex]1175 - 235 = 940[/tex]
[tex]5875 - 1175 = 4700[/tex]
Now, the second differences are constant (equal to 940), which suggests that the pattern rule is a quadratic equation. Let's assume the pattern rule is of the form:
[tex]an^2 + bn + c[/tex]
where n is the term number (starting with n=1 for the first term).
To find the coefficients a, b, and c, we can use the first three terms of the sequence. Let's substitute n=1,2,3 into the equation and equate it to the corresponding terms:
[tex]a + b + c = 12 (for n=1)[/tex]
[tex]4a + 2b + c = 59 (for n=2)[/tex]
[tex]9a + 3b + c = 294 (for n=3)[/tex]
We can solve these equations simultaneously to get the values of a, b, and c:
[tex]a = 63[/tex]
[tex]b = -131[/tex]
[tex]c = 80[/tex]
Therefore, the pattern rule for the sequence is:
[tex]an^2 - 131n + 80[/tex]
where a=63.
To check if this pattern rule works for the other terms of the sequence, we can substitute n=4 and n=5:
[tex]a(4^2) - 131(4) + 80 = 1469[/tex]
[tex]a(5^2) - 131(5) + 80 = 7344[/tex]
Therefore, Both equations give the correct terms, so we can conclude that the pattern rule is:
[tex]an^2 - 131n + 80, where a=63.[/tex]
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Solve for w.
w − 5
4
= 2
The value of the variable w is 56
What are algebraic expressions?Algebraic expressions are described as expressions that are composed of terms, variables, factors, coefficients and constants.
Also, algebraic expressions are made up of mathematical or arithmetic operations, such as;
AdditionBracketSubtractionParenthesesMultiplicationDivisionFrom the information given, we have the algebraic equation as;
w - 54 = 2
To determine the value of the variable, we take the steps;
collect the like terms
w = 2 + 54
Now, add the values
w = 56
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Please help me who knows how to do this
Can someone help me I dont understand this :(
Check the picture below.
the set of five number each of which is divisible by 3
Answer:
{3, 6, 9, 12, 15}
Each of these numbers is divisible by 3
Step-by-step explanation:
Pre calculus trigonometry
The result of the division of the two complex numbers is equal to z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)].
How to find the division of two complex numbers
In this problem we find two complex numbers in rectangular form, whose division must be found. This can done by easily by means of complex numbers in polar form and definition of division:
Complex number (rectangular form)
z = r · (cos θ + i sin θ)
Complex number (polar form)
[tex]z = r\cdot e^{i\cdot \theta}[/tex]
Where:
r - Normθ - DirectionDivision between two complex numbers in polar form:
[tex]\frac {z_{1}}{z_{2}} = \left(\frac{r_{1}}{r_{2}}\right)\cdot e^{i\cdot (\theta_{1}-\theta_{2})}[/tex]
This number is equivalent to the following expression in rectangular form:
z₁ / z₂ = (r₁ / r₂) · [cos (θ₁ - θ₂) + i sin (θ₁ - θ₂)]
If we know that r₁ = 8, r₂ = 9, θ₁ = π / 10 and θ₂ = π / 12, then the division of the two complex numbers is:
z₁ / z₂ = (8 / 9) · [cos (π / 10 - π / 12) + i sin (π / 10 - π / 12)]
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The formula v= √√2gh gives the velocity v, in feet per second, of an object after it falls h feet accelerated by gravity g, in feet
per second squared. If g is approximately 32 feet per second squared, find how far an object has fallen if its velocity is 96 feet
per second.
We can rearrange the formula to solve for h:
v = √√2gh
Squaring both sides: v^2 = 2gh
Dividing both sides by 2g: h = v^2 / 2g
Substituting v = 96 ft/s and g = 32 ft/s^2, we get:
h = (96 ft/s)^2 / (2 × 32 ft/s^2)
h = 288 ft
Therefore, the object has fallen 288 feet.
In ΔFGH, g = 910 cm,
m∠G=98° and
m∠H=51°. Find the length of h, to the nearest 10th of a centimeter.
In ΔFGH, the length of h is 714.2 cm
Let us assume that in ΔFGH, f represents the opposite side to angle F, g represents the opposite side to angle G, and h represents the opposite side to angle H.
Consider the following figure.
Using sine rule for triangle FGH,
sin F/f = sin G/g = sin H/h
Consider equation sin G/g = sin H/h
sin(98°) / 910 = sin(51°) / h
We solve this equation for h.
h = (sin(51°) × 910)/ sin(98°)
h = (0.777 × 910)/ 0.99
h = 714.21
h = 714.2 cm
This is the required length of h.
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P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3
What is P(J)?
O 0.1105
O 0.8143
O 0.8895
O 0.1857
The conditional value probability is solved and P ( J ) = 0.1105
Given data ,
P(JIK) = 0.35, P(KJ) = 0.95, P(K) = 0.3
We can use Bayes' theorem to find P(J):
P(J | K) = P(K | J) * P(J) / P(K)
0.35 = 0.95 * P(J) / 0.3
0.35 * 0.3 = 0.95 * P(J)
0.105 = 0.95 * P(J)
P(J) = 0.105 / 0.95
P(J) = 0.1105
Hence , the probability is P ( J ) = 0.1105
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if you help I would be so thankful
Answer:
I put the answer on the attachment please look
Anna baked 4 batches of cookies with c cookies in each batch she then ate 8 cookies there were 72 cookies left after Anna ate her cookies
The expression for the number of cookies Anna has left is [tex]3c - 8[/tex].
What does an expression means?An expression refers to statement that have minimum of two numbers or variables or both and an operator connecting them.
The total number of cookies Anna baked is:
= 3 batches * c cookies/batch
= 3c cookies
After eating 8 cookies, Anna has left:
= 3c cookies - 8 cookies
So, the expression for the number of cookies Anna has left is [tex]3c - 8[/tex].
Full question "Anna baked 3 batches of cookies with c cookies in each batch she then ate 8 cookies. How many cookies does anna have left write your answer as an expression.
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‼️‼️‼️‼️WILL MARK BRAINLIEST‼️‼️‼️‼️
Answer:
S = 2π(14^2) + 2π(14)(154)
= 2π(196) + 2π(2,156)
= 4,704π = 14,778.1 ft^2
Using 3.14 for π:
S = 4,704(3.14) = 14,770.6 ft^2
3d *5d*2=?
Please what is 3d times 5d times 2
Answer:
[tex]30d^2[/tex]
Step-by-step explanation:
Evaluate the determinant
1
03
03
0)2
w2
1 , where w is a cube root
co
2 1 o
of unity.
In this case, the cube root is = 0
Why is this so?We can use the rule Sarrus to evaluate the determinant
1 w w²
w w² 1
w² 1 w
Starting with the first column, we can wrte out the terms for the diagonal products and
then sum the terms for the products of the diagonal elements that wrap around
(1 x w² x w) +(w x 1 x w²) + (w² x w x w) - (w ² x w x 1) - (w x w² x w) - (1 x w x w ²)
Simplifying each term:
w³ + w³ + w³ - w³ -w³ - w³
We can see that all the terms cancel out, leaving us with a determinant of 0. So it is clear that
|1 w w²|
|w w² 1 |
|w² 1 w | = 0
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Full Question:
Although part of your question is missing, you might be referring to this full question:
Evaluate the determinant 1 w w2 , w w2 1, w2 1 w. where w is a cube root of unity.
where should the linear inequality y ≤ 3/2x + 3 be shaded?
Answer:
Step-by-step explanation:
it should be shaded at the 76
what is the suface area of 11cm and 14cm
Answer:
429 i think
Step-by-step explanation:
What is the equation through the points: (-7, -3), (1, 2)
ASAP please
The equation of the line passing through the points (-7, -3) and (1, 2) is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].
What is the equation of the line?The formula for equation of line is expressed as;
y = mx + b
Where m is slope and b is y-intercept.
First, we determine the slope of the line.
Given the two points are (-7, -3) and (1, 2)
We can find the slope of the line by using the slope formula:
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
Substituting the values, we get:
m = (2 - (-3)) / (1 - (-7))
m = 5/8
Using the point-slope form, plug in one of the given points and slope m = 5/8 to find the equation of the line.
Let's use the point (-7, -3:
y - y₁ = m(x - x₁)
[tex]y - (-3) = \frac{5}{8}( x - (-7) ) \\\\y + 3 = \frac{5}{8}(x + 7 )\\\\y + 3 = \frac{5}{8}x + \frac{35}{8} \\ \\y = \frac{5}{8}x + \frac{35}{8} - 3\\\\y = \frac{5}{8}x + \frac{11}{8}[/tex]
Therefore, the equation of the line is [tex]y = \frac{5}{8}x + \frac{11}{8}[/tex].
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At the time of her grandson's birth, a grandmother deposits $14,000 in an account that pays 4.5% compounded
monthly. What will be the value of the account at the child's twenty-first birthday, assuming that no other deposits
or withdrawals are made during this period?
i Click the icon to view some finance formulas.
The value of the account will be $
(Round to the nearest dollar as needed.)
4
Answer:
The value of the account will be $5,628
Step-by-step explanation:
Step-by-step explanation:
we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
therefore
The value of the account will be $5,628
Help please!!!!
Whoever answers right gets brainliest!
Answer:
25
Step-by-step explanation:
To solve this problem you have to use this formula [tex](\frac{b}{2})^{2}[/tex] it. So in this case b is the term next to the x term. This number is 10. So all we have to do is insert it into the formula. This would give us:
[tex]=(\frac{10}{2})^{2}\\\\=(5)^{2}\\\\= 25[/tex]
The constant term is 25.
Could I get Brainilest, please? I'm trying to get to the expert level
Function f is an exponential function. It predicts the value of a famous painting, in thousands of dollars, as a function of the number of years since it was last purchased.
What equation models this function?
ANSWER: 8(1.25)x just took the test
Answer:
[tex]f(t) = 8e^{0.223144t}[/tex]
The earrings that Mrs.Moore wants to buy are $55.00. She won’t buy them until they are at least 45% off. What is the most that Mrs.Moore is willing to spend?
Answer:
$30.25
Step-by-step explanation:
55% of 55$ is $30.25. she wants 45 % off of 55$. which is $24.75. 55-24.75 is 30.25
$30.25
since it's 45% off, you need to subtract 45% from 100%
100%-45%=55%
then turn the % into a decimal
55%/100=0.55
now multiply the original price by 0.55
0.55*55=30.25
The height y(in feet) of a ball thrown by a child isy=−114x2+2x+3
where x is the horizontal distance in feet from the point at which the ball is thrown.
(a) How high is the ball when it leaves the child's hand? (Hint: Find y
when x=0)
Your answer is y=____
(b) What is the maximum height of the ball? _____
(c) How far from the child does the ball strike the ground?_____
Seven days a year, Tiger Stadium becomes the fifth largest city in the state of Louisiana. Over 92,000 fans pack the stadium to watch the Tigers play. After the game, if the fans leave at a rate of 10% per minute, how long will it take before the stadium is half empty?
1. Find the data using at least 10 numbers in the x column.
2. Create a scatter plot. Label the graph and show increments.
3. Write an exponential equation.
4. Interpret the meaning of the "a" and "b" in your function y=ab^x including the units.
5. Find out how long it will take before the stadium is half empty and all the way empty.
Two mechanics worked on a car. The first mechanic worked for 20 hours, and the second mechanic worked for 15 hours. Together they charged a total of $2600. What was the rate charged per hour by each mechanic if the sum of the two rates was $155
per hour?
the first mechanic charged $55 per hour and the second mechanic charged $100 per hour. we solve this by forming equation by by given data.
what is equation ?
An equation is a mathematical statement that shows that two expressions are equal. It typically consists of two sides separated by an equal sign (=). The expressions on each side of the equal sign can contain variables,
In the given question,
Let's assume that the first mechanic charged x dollars per hour and the second mechanic charged y dollars per hour.
From the problem, we know that:
The first mechanic worked for 20 hours, so he charged 20x dollars.
The second mechanic worked for 15 hours, so he charged 15y dollars.
Together, they charged a total of $2600, so we have:
20x + 15y = 2600
The sum of the two rates was $155 per hour, so we have:
x + y = 155
We can use these two equations to solve for x and y. First, we can rewrite the second equation as:
y = 155 - x
Then, we can substitute this expression for y into the first equation:
20x + 15(155 - x) = 2600
Simplifying and solving for x, we get:
20x + 2325 - 15x = 2600
5x = 275
x = 55
Now that we know x, we can use the second equation to find y:
y = 155 - x = 155 - 55 = 100
Therefore, the first mechanic charged $55 per hour and the second mechanic charged $100 per hour.
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The amount of money in a saving account increases bu D. 2% every month
Write a function for the amount of money in the accounts, after t months with an initial deposit of tr $ 100
By what' factor does the amount in the account increases ever meant every year?
The exponential function giving the balance of the account after t months is:
[tex]y = 100(1.02)^t[/tex]
The yearly growth factor is given as follows:
26.82%.
How to define an exponential function?An exponential function has the definition presented as follows:
[tex]y = ab^x[/tex]
In which the parameters are given as follows:
a is the value of y when x = 0.b is the rate of change.The parameter values for this problem are given as follows:
a = 100 -> initial deposit.b = 1.02 -> increase of 2% every month -> 1 + 0.02 = 1.02.Hence the function is:
[tex]y = 100(1.02)^t[/tex]
The yearly growth factor can be obtained as follows:
[tex](1.02)^{12} = 1.2682[/tex]
Increase of 26.82% each year, which is composed by 12 months.
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solve for x, neg x over 4 = 12 A 48 or B -3 or C 3 or D -48?
The solution for x is -48, the answer is D) -48.
What is Algebraic expression ?
An algebraic expression is a mathematical phrase that contains variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. It represents a value that can change based on the values assigned to the variables.
Starting with:
x:4 = 12
Multiplying both sides by -1 gives:
(-x÷4) = -12
Simplifying the left side:
x÷4 = -12
Multiplying both sides by 4 gives:
x = -48
Therefore, the solution for x is -48, the answer is D) -48.
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