Answers
The area under the curve y = x² + 5x + 4 and the x-axis is \(1\frac{2}{3}\) square units.
To find the area under the curve y = x² + 5x + 4 and the x-axis, we need to integrate the given function over a specific interval.
We need to find the definite integral of the function over a suitable interval.
Let's find the definite integral of the function from its roots (where the curve intersects the x-axis).
First, let's find the roots of the function by setting y = 0:
x² + 5x + 4 = 0
Factoring the quadratic equation:
(x + 1)(x + 4) = 0
Setting each factor equal to zero:
x + 1 = 0 => x = -1
x + 4 = 0 => x = -4
The roots of the function are x = -1 and x = -4.
To find the area under the curve, we integrate the function from x = -4 to x = -1:
∫[x=-4 to -1] (x² + 5x + 4) dx
Integrating the function:
∫[x=-4 to -1] (x² + 5x + 4) dx = [1/3x³ + (5/2)x² + 4x] from -4 to -1
Substituting the limits:
[1/3(-1)³ + (5/2)(-1)² + 4(-1)] - [1/3(-4)³ + (5/2)(-4)² + 4(-4)]
Simplifying:
[-1/3 + 5/2 - 4] - [-64/3 + 40/2 - 16]
\(1\frac{2}{3}\)
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Related Questions
Megan has $45.12 in her purse. She spends $7.89 for lunch and $21.25 for a pair of sunglasses.
What is the exact amount that Megan has left?
Answers
Answer:
15.98 dollars
Step-by-step explanation:
its really easy
we need to subtract the total amount that she has spent from the total amount that she had in her purse
the total amount in Megan's purse=$45.12
total amount that Megan spent=$7.89+$21.25 =$29.14
now,
the exact amount that Megan has left = $45.12-$29.14=$15.98
find the domain of the function, picture included
Answers
Answer:
[4,∞)
Step-by-step explanation:
x≥4
[4,∞)
which of the following lines represents the equation -3/5x-2?
Answers
Answer:
A
Step-by-step explanation:
Answer:
Line A
Step-by-step explanation:
Line A is the only one that starts at -2
Perform the following mathematical operation and report the answer to the appropriate number of significant figures.
We know the least precise place value is in the 10's place.
67.4 +43 +30 + 42.10 = [?]
it's not 182.5 / 137.9 / 182
Answers
Answer:
200
Step-by-step explanation:
The sum is 182.5, which is 200 to 1 significant figure.
HELP PLEASE! ILL MARK BRAINLIEST!
A rental car company charges $53.75 per day to rent a car and $0.07 for every mile driven. Alexander wants to rent a car, knowing that: He plans to drive 425 miles. He has at most $320 to spend. Write and solve an inequality which can be used to determine dthe number of days Alexander can afford to rent while staying within his budget .
Answers
Answer:
5 days
Step-by-step explanation:
425x0.07=29.75
320-29.75=290.25
290.25÷53.75=5.4
Answer:
Inequality: 53.75d + 29.75 ≤ 320
Answer: d ≤ 5.4
Step-by-step explanation:
An IV of 550 mL infused in 940 minutes. The IV infused at ______ mL/hr. Round your final answer to 2 decimal places if necessary.
Answers
To find out the unit rate in mL/h
Divide the total milliliters by the total time in hours
Remember that
1 hour=60 minute
so
940 minutes=940/60=47/3 hours
therefore
\(550\div\frac{47}{3}=\frac{550*3}{47}=35.11\text{ ml/h}\)The answer is 35.11 ml/hQuestion 9 of 60
Which symbol correctly compares the fractions below? 3/7 ? 4/14
O A. =
B. >
O C. <
OD. None of these are correct.
SUBMIT
Answers
Find the value of x. Round to the nearest tenth.
Answers
explanation: pythagorean theorem
the exact value of sin 5pi/12 is
Answers
The exact value of sin(5π/12) is (√6 + √2)/4
Calculating the exact value of sin 5pi/12From the question, we have the following parameters that can be used in our computation:
sin 5pi/12
Express properly
So, we have
sin(5π/12)
Convert the angle to degrees
This gives
sin(5π/12) = sin(5/12 * 180)
Evaluate
sin(5π/12) = sin(75)
The actual value of sin(75) is (√6 + √2)/4
This means that
sin(5π/12) = (√6 + √2)/4
Hence, the exact value of sin(5π/12) is (√6 + √2)/4
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The exact value of sin 5π/12 is (√6 + √2)/4
What is trigonometric function?The trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.
Angle in trigonometry can be measured in either degree or radian.
π is a measurement in radian which is equivalent to 180° in degrees.
Therefore:
5π/12 = 5 × 180/12
= 75°
Therefore sin5π/12 = sin75°
sin75 = sin( 45+30) = sin45cos30+ cos 45sin30
= 1/√2 × √3/2 + 1/√2 × 1/2
= √3/2√2 + 1/2√2
= (√3+1)/2√2
rationalizing;
(2√6 + 2√2)/8
dividing through by 2
=(√6 + √2)/4
therefore tan75 =(√6 + √2)/4
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The value of a coin in 2010 was $40. The value of the coin has increased in value at a rate of 16.9% annually.
What was the value of the coin in 2019?
Enter your answer in the box rounded to the nearest dollar.
Answers
The value of the coin in 2019 would be approximately $132.
To calculate the value of the coin in 2019, we need to consider the annual increase rate of 16.9% from 2010 to 2019. We can use the compound interest formula to find the final value.
Starting with the initial value of $40 in 2010, we can calculate the value in 2019 as follows:
Value in 2019 = Initial value * (1 + Rate)^n
where Rate is the annual increase rate and n is the number of years between 2010 and 2019.
Plugging in the values:
Value in 2019 = $40 * (1 + 0.169)^9
Value in 2019 ≈ $40 * 2.996
Value in 2019 ≈ $119.84
Rounding the value to the nearest dollar, we get approximately $120. Therefore, the value of the coin in 2019 would be approximately $120.
However, please note that the exact value may vary depending on the specific compounding method and rounding conventions used.
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stick of butter weight a quarter of a pound how much do 13 sticks of butter weight
Answers
you get 3 1/4 pounds as a mixed number, 3.25 pounds as a decimal, and 13/4 pounds as a fraction. Hope this helped!
Which number(s) have a 5 that is 10 times the value of the 13,725 in ?
Answers
Answer:
I will give you three, but the answer is the number that has a 50
Step-by-step explanation:
52
654
7657
50 is the numbers that have a 5 in 10 times the value of the 13,725.
What is place value?Place value is the value of each digit in a number.
For example, the 5 in 350 represents 5 tens, or 50; however the 5 in 5006 represents 5 thousands, or 5000.
Now the given number is,
13,725
10 times of the number is givens as,
13,725*10
or, 137,250
here place value of 5 in 137,250 is 5 tens or 50.
Therefore, 50 is the numbers that have a 5 in 10 times the value of the 13,725.
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Please help me i will give all of my points 14
Please help i need this right now
Answers
Answer:
3 7/12
Step-by-step explanation:
43,678 to the nearest ten
Answers
Answer:
43,680
Step-by-step explanation:
4 in below let him go
5 and above bump him up
8>5 so we bump him up
so 7-> 8
Answer:
43,680
Step-by-step explanation
Rounding numbers to the nearest 10 means finding which 10 they are nearest to. For example, 78 rounded to the nearest 10 is 80.
plzzzzzz helpppppppp
Answers
Answer:
x^7=5(12)
=60
So answer would be c
Answer:
function of D. π7 = 17 be in touch with the
The formula P= 2/+ 2w means that the perimeter of a rectangle is equal to
twice the sum of its length and its width.
Solve P = 21+ 2 w for /
Answers
Answer:
D. \( l = \frac{P - 2w}{2} \)
Step-by-step explanation:
Given:
\( P = 2l + 2w \)
Required:
Solve for l
Solution:
To solve for l, we would make l the subject of the given formula.
\( P = 2l + 2w \)
\( P = 2(l + w) \)
Divide both sides by 2
\( \frac{P}{2} = \frac{2(l + w)}{2} \)
\( \frac{P}{2} = l + w \)
Subtract w from both sides
\( \frac{P}{2} - w = l + w - w \)
\( \frac{P}{2} - w = l \)
\( \frac{P}{2} - \frac{w}{1} = l \)
\( \frac{P - 2w}{2} = l \)
Rewrite
\( l = \frac{P - 2w}{2} \)
please help!!! the photo below
Answers
Answer:its (-2,1), (-6,-15)
Step-by-step explanation:
F. Why would a linear function describing an investment made at a bank have a minimum
value but no maximum value? Explain your reasoning.
Answers
Answer: The function would have a minimum value because the least you will ever have is 0$. It cannot go below 0, so that is the minimum. However, depending on how much time has passed, the maximum amount of money you have can change. It can always go up more, so there is no set maximum.
Step-by-step explanation:
NEED HELP NEOWWWWWWWWWWWW
What is the area of this polygon?
units2
Answers
Answer the photo please and do my other ones
Answers
Answer:
C
Step-by-step explanation:
If you were to put the number of turkey out in order from least to greatest, the median is 12. Doing the same thing to the ham, the median is 9.
Subtracting Turkey (12) from Ham (9) your answer is C, or 3.
the product of 9 and the difference of four and a number
Answers
Answer:
9(4-n)
Step-by-step explanation:
Hope this helps
Tell me if I'm wrong
diameter = 10.5in.we are learning something about area of circle.
Answers
Use the formula for the area of a circle:
\(A=\pi\cdot r^2\)First, we need to find the radius r. Since the radius is half the diameter, then:
\(\begin{gathered} r=\frac{10.5\text{ in}}{2} \\ \therefore r=5.25in \end{gathered}\)Substitute the value for r in the formula for the area of the circle:
\(\begin{gathered} A=\pi\cdot(5.25in)^2 \\ \approx86.6in^2 \end{gathered}\)Therefore, the area of a circle of diameter 10.5 in is approximately 86.6 squared inches.
What is the greatest common factor of the polynomial's terms?
18a6+36a3
(A) 54a9
(B) 18a3
(C) 6a3
(D) 9a3
Answers
Answer-
B) 18a3 is the highest common factor
How many 2-letter words can be made from the letters MATH if
Answers
Answer:
ham
tam
mat
hat
at
ha
am
ma
Step-by-step explanation:
help me pls this is middle school work
Answers
Answer: 5 or 5 \(\frac{0}{3}\)
Step-by-step explanation:
3*1=3 ==> 1st box value
3*2/3=6/3=2 ==> 2nd box value
3+2=5
5=5 \(\frac{0}{3}\)
There are 4 bottles of vitamins in
each box of vitamins. Each bottle of vitamins has
20 vitamins. If the clinic wants to have a supply of 400
vitamins how many more boxes should it order
Answers
Answer:
the clinic needs 20 more bottles of vitamins to have a supply of 400 vitamins.
Step-by-step explanation:
400 divided by 20 = 20.
Vicky made some purchases at the
Sunflower Market. She bought strawberries
for $3.50, carrots for $2.25 and a bouquet of
flowers for $9.95. If sales tax is 5%, what will
Maria pay altogether?
1. $16.48
2. $15.70
3. $16.49
4. $16.50
Answers
Step-by-step explanation:
Vicky Bought:
Strawberries $3.50
Carrots $2.25
Flowers $9.95
Subtotal $3.50 + $2.25 + $9.95
= $15.70
5% Sales Tax (5% of Subtotal) = 5/100 x $15.70
= $0.785 (will not round off here as it is not the final answer.)
Total = Subtotal + 5% Sales Tax
= $15.70 + $0.785
= $16.485
= $16.49 (rounded off to nearest cent)
Part A: Timothy said that AKLM was dilated by a scale factor of 1.5 centered at the origin. Is Timothy CORRECT? Explain your answer or show your work.
Answers
Yes, Timothy is correct because triangle AKLM was dilated by using a scale factor of 1.5 centered at the origin.
What is dilation?In Mathematics, dilation can be defined as a type of transformation that is typically used for enlarging or reducing the size of a geometric object but not its shape, based on the scale factor.
For the given coordinates of the preimage triangle KLM, the dilation with a scale factor of 1.5 from the origin (0, 0) would be calculated as follows:
Coordinate K (-1, 3) → Coordinate K' (-1 × 1.5, 3 × 1.5) = Coordinate K' (-1.5, 4.5).
Coordinate L (8, 4) → Coordinate L' (8 × 1.5, 4 × 1.5) = Coordinate L' (12, 6).
Coordinate M (10, -3) → Coordinate M' (10 × 1.5, -3 × 1.5) = Coordinate M' (15, -4.5).
In conclusion, the coordinates of the image triangle K'L'M after a dilation with a scale factor of 1.5 from the origin are (-1.5, 4.5), (12, 6), and (15, -4.5) as shown in the graph above, therefore, Timothy is correct.
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The table represents a linear relationship
X—2 0 4
Y-4 3 1
Which equation represents the table
Y=1/2x+5
y=-1/2x+3
Y=2x-3
Y=-4x+2
Answers
The linear relationship illustrated in the provided table can be effectively described by the equation Y = -4x + 2. Option D.
To determine the equation that represents the given table with the values of x and y, we can observe the pattern and find the equation of the line that fits these points.
Given the table:
X: 2 0 4
Y: -4 3 1
We can plot these points on a graph and see that they form a straight line.
Plotting the points (2, -4), (0, 3), and (4, 1), we can see that they lie on a line that has a negative slope.
Based on the given options, we can now evaluate each equation to see which one represents the line:
Y = 1/2x + 5
When we substitute the x-values from the table into this equation, we get the following corresponding y-values: -3, 5, and 6. These values do not match the given table, so this equation does not represent the table.
Y = -1/2x + 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: 4, 3, and 2. These values also do not match the given table, so this equation does not represent the table.
Y = 2x - 3
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -4, -3, and 5. These values do not match the given table, so this equation does not represent the table.
Y = -4x + 2
When we substitute the x-values from the table into this equation, we get the corresponding y-values: -6, 2, and -14. Interestingly, these values match the y-values in the given table. Therefore, the equation Y = -4x + 2 represents the table.
In conclusion, the equation Y = -4x + 2 represents the linear relationship described by the given table. So Option D is correct.
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can you help me for this m.c.m is of 10, 3 and 90.
Gracias (Thaks youuuuuuuuuuuuuuuuu)
Answers
Answer:
AR 27-10 supplements the MCM and is the ... available. The installation Trial Defense Service office will provide a military lawyer. If the. 3-1 ... away or assaulting you, enlist others to help.