The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).
How many properties are used to simplify the expression 4 + 3(9 + 2) into 37?The properties that were used to simplify the expression 4 + 3(9 + 2) into 37 are:
Distributive property: The expression was rewritten as 4 + (3 × 9) + (3 × 2) by distributing the 3 over the parentheses.
Associative property: The order of the terms (3 × 9) and (3 × 2) was rearranged without changing the result because of the associative property of multiplication.
Commutative property: The order of the terms 4, 27, and 6 was rearranged without changing the result because of the commutative property of addition.
Identity property: The property was not explicitly used in this example, but it is worth noting that adding 0 to any number leaves it unchanged (i.e., a + 0 = a).
The properties used to simplify the expression are Associative property of addition, Commutative property of addition, and Distributive property and Identity property of addition. Therefore, the correct option is A, C, E and F.
The properties used to simplify the expression are as follows.
1. Distributive property (E): 4 + 3(9 + 2) = 4 + (3 × 9) + (3 × 2)
This property is applied when a number is multiplied with the sum of two or more numbers. In this case, the number 3 is distributed over the numbers 9 and 2.
2. Identity property of addition (F): 4 + 27 + 6 = 4 + 6 + 27
This property states that adding zero to any number does not change its value. Although this property isn't explicitly shown in the given steps, it is implied by the fact that we can rearrange the terms in the addition without changing their value.
3. Commutative property of addition (C): 4 + 6 + 27 = 10 + 27
This property states that changing the order of numbers in an addition does not change the sum. Here, the numbers 4 and 6 were rearranged to make it easier to add them together.
4. Associative property of addition (A): (10 + 27) = 37
This property states that the grouping of numbers in an addition does not affect the sum. In this case, the parentheses are unnecessary since the numbers were already grouped correctly.
In summary, the properties used to simplify the expression are: A) Associative property of addition, C) Commutative property of addition, and E) Distributive property and F) identity property of addition.
Note: The question is incomplete. The complete question probably is: The real number properties can be used to simplify numerical expressions. in this section, you will identify which properties were used to simplify several expressions. Which properties were used to simplify the following expression? select all that apply.
4 + 3(9 + 2)
4 + (3 × 9) + (3 × 2)
4 + 27 + 6
4 + 6 + 27
10 + 27
37
A) associative property of addition B) associative property of multiplication C) commutative property of addition D) commutative property of multiplication E) distributive property F) identity property of addition G) identity property of multiplication
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How do you use the definition of a derivative to find f' given f(x)=√4x+3 at x>-3/4?
The derivative of f(x) is -3/4.
How to find derivative?To find the derivative, use the definition of a derivative:
f'(x) = lim h→0 [f(x + h) - f(x)] / h
Substitute f(x) = √(4x + 3) into this definition:
f'(x) = lim h→0 [√(4(x + h) + 3) - √(4x + 3)] / h
Multiplying by the conjugate of the numerator:
f'(x) = lim h→0 [(√(4(x + h) + 3) - √(4x + 3)) * (√(4(x + h) + 3) + √(4x + 3))] / [h * (√(4(x + h) + 3) + √(4x + 3))]
Expanding the numerator, we get:
f'(x) = lim h→0 [(4(x + h) + 3) - (4x + 3)] / [h * (√(4(x + h) + 3) + √(4x + 3)) * (√(4(x + h) + 3) + √(4x + 3)))]
f'(x) = lim h→0 [4h] / [h * (√(4(x + h) + 3) + √(4x + 3)))]
Canceling out the h terms, we get:
f'(x) = lim h→0 4 / (√(4(x + h) + 3) + √(4x + 3)))
Now, we can evaluate the limit as h approaches 0:
f'(x) = 4 / (√(4x + 3) + √(4x + 3))
f'(x) = 4 / (2√(4x + 3))
f'(x) = 2 / √(4x + 3)
Therefore, the derivative of f(x) is -3/4.
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Can someone please help me ASAP? It’s due tomorrow
Applying the concept of combination, the number of different sandwiches that can be created is determined as: D. 6.
How to Apply the Concept of Combination to Determine How May Sandwiches to be Created?To determine the number of different sandwiches that can be created with two different meats, we can use the concept of combinations.
In this case, we need to choose 2 meats out of 4 options. The number of combinations of 2 items that can be chosen from a set of 4 items is given by the formula:
nCr = n! / r!(n-r)!
where n is the total number of items, r is the number of items to be chosen, and the exclamation mark (!) denotes the factorial function.
In this case, we have:
n = 4 (since there are 4 meat options)
r = 2 (since Regan wants to choose 2 meats)
Therefore, the number of different sandwiches that can be created is:
4C2 = 4! / 2!(4-2)! = 6
This means there are 6 different ways to choose 2 meats out of 4, and hence 6 different sandwich options.
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Find g(x), where g(x) is the translation 1 unit left of f(x)=x2.
write your answer in the form a(x–h)2+k, where a, h, and k are integers.
To find g(x), the translation 1 unit left of f(x) = x², we need to replace x with (x+1) because moving left means we need to subtract 1 from x. Therefore, g(x) = f(x+1) = (x+1)².
To write g(x) in the form a(x-h)² + k, we need to expand (x+1)² first. Using the formula (a+b)² = a² + 2ab + b², we get:
g(x) = (x+1)² = x² + 2x + 1
Now we can write g(x) in the vertex form by completing the square. We add and subtract (2/2)² = 1 to the expression to get:
g(x) = x² + 2x + 1 - 1 + 1
= (x+1)² + 0
Therefore, g(x) = (x+1)² + 0 is the vertex form of g(x), where a=1, h=-1, and k=0. This means that the vertex of the parabola g(x) is (-1,0), and it opens upwards. The translation 1 unit left of f(x)=x² results in a horizontal shift of the parabola to the left by 1 unit without changing its shape or orientation.
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Ellen mixed 1over 4 kg of flour with 2 over 9 kg of sugar. Determine a reasonable estimate for the amount of flour and sugar combined
A reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.
To determine a reasonable estimate for the amount of flour and sugar combined, we first need to add the fractions 1/4 and 2/9. To do this, we need to find a common denominator. The least common multiple of 4 and 9 is 36. We can convert 1/4 to 9/36 by multiplying both the numerator and denominator by 9. We can also convert 2/9 to 4/36 by multiplying both the numerator and denominator by 4. Now we can add the fractions:
9/36 + 4/36 = 13/36
So Ellen mixed 13/36 kg of flour and sugar combined. To convert this to a decimal, we can divide the numerator by the denominator:
13 ÷ 36 ≈ 0.36
Therefore, a reasonable estimate for the amount of flour and sugar combined is approximately 0.36 kg.
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order: baraclude (entecavir) 0.5mg PO daily. The drug is an oral
solution with strength of 0.05 mg/mL. How many mL will you
administer?
10mL of the baraclude oral solution to the patient.
To determine the amount of the oral solution of baraclude (entecavir) to administer, we need to use the following formula:
Amount to administer (mL) = Desired dose (mg) / Strength (mg/mL)
In this case, the desired dose is 0.5mg and the strength is 0.05mg/mL. Plugging in these values, we get:
Amount to administer (mL) = 0.5mg / 0.05mg/mL = 10mL
Therefore, you will administer 10mL of the baraclude oral solution to the patient.
Hi! To calculate the number of mL to administer, you need to consider the prescribed dose and the strength of the oral solution. The order is for Baraclude (entecavir) 0.5mg PO daily, and the solution's strength is 0.05 mg/mL.
To find the required mL, divide the prescribed dose by the solution's strength:
0.5 mg (prescribed dose) ÷ 0.05 mg/mL (solution's strength) = 10 mL
You will administer 10 mL of Baraclude (entecavir) oral solution daily.
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rewrite the expression 4^-2 x 8^0 x 5^6
In a recent Game Show Network survey, 30% of 5000 viewers are under 30. What is the margin of error at the 99% confidence interval? Using statistical terminology and a complete sentence, what does this mean? (Use z*=2. 576)
Margin of error:
Interpretation:
The margin of error at the 99% confidence interval is 1.39%. Interpretation: we can be 99% confident that the true proportion of viewers under 30 in the population falls within the range of 30% ± 1.39%.
To calculate the margin of error at the 99% confidence interval, we can use the formula:
Margin of error = z* × √(p × (1 - p) / n)
where z* is the critical value (2.576 for a 99% confidence interval), p is the sample proportion (0.30), and n is the sample size (5000).
Margin of error = 2.576 × √(0.30 × (1 - 0.30) / 5000) ≈ 0.0139 or 1.39%
The interpretation of this result is that we can be 99% confident that the true proportion of viewers under 30 in the population falls within the range of 30% ± 1.39%. In other words, if we were to conduct the survey multiple times, we would expect the proportion of viewers under 30 to fall within this interval 99 out of 100 times. This information is useful for understanding the level of uncertainty in the survey results and can help guide decision-making based on the findings.
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I forgot please help me out here. Is 25 fl oz greater than 1 pint, or 1 pint greater than 25 fl oz. Please help me out thank you so much
The 25 fluid ounces is greater than one pint is correct statement .
Relation between fluid ounces and pint ,
There are 16 fluid ounces in one pint.
Conversion of fluid ounces to pint
This implies that,
1 fluid ounces is equal to one by sixteen pint.
To be precise,
25 fluid ounces is equal to 25 / 16pints
⇒ 25 fluid ounces is equal to 1.5625.
However, since 1.5625 is greater than 1,
This implies that 25 fluid ounces is greater than 1 pint.
So, 25 fluid ounces is greater than 1 pint.
Because 25 is greater than 16.
And 1 pint is not greater than 25 fluid ounces.
Therefore, the 25 fluid ounces is greater than one pint.
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!!I NEEEDD HELPPP!! Please helppp :(
The customer would save $492 in the first year by switching to Intellivision.
The customer would save $207 in the second year by switching to Intellivision.
For the third year, it would be cheaper to stick with ElectroniSource.
How to find the savings ?To calculate the savings for the first year, we need to find the total cost for ElectroniSource and compare it to the flat fee from Intellivision for all three services.
The savings for the first year by switching to Intellivision would be:
$1,632 - $1,140 = $492
Therefore, the customer would save $492 in the first year by switching to Intellivision.
After the first year, Intellivision raises the rates by 25%. So the new flat fee for the second year would be:
$95 + ($95 x 25%) = $118.75
The savings for the second year by switching to Intellivision would be:
$1,632 - $1,425 = $207
Therefore, the customer would save $207 in the second year by switching to Intellivision.
For the third year, Intellivision raises the rates by 16% compared to the second year. So the new flat fee for the third year would be:
$118.75 + ($118.75 x 16%) = $137.78
Therefore, for the third year, it would be cheaper to stick with ElectroniSource, which costs $1,632 for the year, compared to Intellivision, which costs $1,653.36 for the year.
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what is the radius of a circle if 24-meter chord is 5 meters from center
Susan set up a lemonade stand to raise money for a children's hospital. She's selling cups of lemonade for $2. 50 each and brownies for $1. 50 each. She sells 280 items and raises $540.
How much money does Susan raise from selling lemonade?
If she sells 280 items and raises $540, then Susan raises $300 from selling lemonade.
To determine how much money Susan raises from selling lemonade, we'll set up a system of equations using the given information.
Let x be the number of lemonade cups and y be the number of brownies sold. We know:
1. x + y = 280 (total items sold)
2. 2.50x + 1.50y = 540 (total money raised)
First, we'll solve for x in equation 1:
x = 280 - y
Now, substitute this expression for x in equation 2:
2.50(280 - y) + 1.50y = 540
Simplify and solve for y:
700 - 2.50y + 1.50y = 540
-1.00y = -160
y = 160
Now that we have the number of brownies (y), we can find the number of lemonade cups (x):
x = 280 - 160
x = 120
Finally, calculate the money Susan raises from selling lemonade:
Money from lemonade = 120 * $2.50 = $300
So, Susan raises $300 from selling lemonade.
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Kellen runs for at least 1 hour but for no more than 2 hours. He runs at at an
average rate of 6. 6 kilometers per hour. The equation that models the distance he
runs for t hours is = 6. 6t
Find the theoretical and practical domains of the equation.
Select ALL correct answers.
The correct answers are:
The theoretical domain is 1 ≤ t ≤ 2.
The practical domain is 1 ≤ t ≤ 2.
Find out the theoretical and practical domain?The equation that models the distance Kellen runs for t hours is given as 6.6t, where t is the time in hours.
The theoretical domain of the equation refers to all the possible values that t can take in the equation without any restrictions. In this case, the only restriction is that Kellen runs for at least 1 hour but for no more than 2 hours. Therefore, the theoretical domain of the equation is:
1 ≤ t ≤ 2
The practical domain of the equation refers to the values of t that make sense in the context of the problem. Since Kellen runs for at least 1 hour, the practical domain should start at 1 hour. Also, since he cannot run for more than 2 hours, the practical domain should end at 2 hours. Therefore, the practical domain of the equation is:
1 ≤ t ≤ 2
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In the following equation, what is the value of c?
8^c = (8^-4)^5
Please help, I don't understand this geometry problem!!
Nisha is looking out the window of her apartment building at a sculpture in a park across the street. The top of Nisha's window is 60 feet from the ground. The angle of depression from the top of Nisha's window to the bottom of the sculpture is 25°. What is the distance along the ground between the building and the sculpture? Round your answer to the nearest hundredth.
25.36 feet
27.98 feet
100.22 feet
128.67 feet
The distance along the ground between the building and the sculpture is approximately 27.98 feet. Rounded to the nearest hundredth, the answer is 27.98 feet.
How to calculate the distance along the ground between the building and the sculptureFrom the problem statement, we know that angle BAC is 25 degrees and AC is 60 feet. We want to find AB, which is the horizontal distance between A and B.
We can use trigonometry to find AB. Let's use the tangent function:
tan(25) = AB / AC
Solving for AB, we get:
AB = AC * tan(25)
Substituting the values we know, we get:
AB = 60 * tan(25)
Using a calculator, we get:
AB ≈ 27.98 feet
Therefore, the distance along the ground between the building and the sculpture is approximately 27.98 feet. Rounded to the nearest hundredth, the answer is 27.98 feet.
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Problem List Previous Problem Next Problem = (1 point) An alternating current E(t)=120sin(12t) has been running through a simple circuit for a long time. The circuit has an inductance of L=0.31 henrys, a resistor of R=7ohms and a capacitor of capcitance C=0.029 farads. What is the amplitude of the current I?
The amplitude of the current I is 16.9 Amperes
How to determine the amplitude of the current ITo find the amplitude of the current I in the given circuit with an alternating current E(t) = 120sin(12t), inductance L = 0.31 H, resistance R = 7 ohms, and capacitance C = 0.029 F, we need to determine the impedance (Z) of the circuit first.
The impedance Z can be calculated using the formula:
Z = √((R²) + (XL - XC)²)
Where XL is the inductive reactance, and XC is the capacitive reactance. XL can be calculated as:
XL = 2πfL
And XC can be calculated as:
XC = 1/(2πfC)
Here, f is the frequency of the alternating current, which can be determined from the given function E(t) = 120sin(12t) as:
f = 12/(2π) = 1.91 Hz
Now, we can calculate XL and XC:
XL = 2π(1.91)(0.31) = 3.74 ohms
XC = 1/(2π(1.91)(0.029)) = 2.89 ohms
Next, we can find the impedance Z:
Z = √((7²) + (3.74 - 2.89)²) = √(49 + 0.72) = 7.1 ohms
Finally, we can find the amplitude of the current I using Ohm's law:
I = E(t)/Z
Since we're looking for the amplitude, we only need the maximum value of E(t), which is 120 V:
I = 120/7.1 = 16.9 A
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Evaluate the iterated integral by converting to polar coordinates.∫8−8∫√64−x20(x2+y2) dy dx
To convert to polar coordinates, we need to express x and y in terms of r and θ. We have:
x = r cos θ
y = r sin θ
Also, we need to change the limits of integration. The region of integration is the circle centered at the origin with radius 8, so we have:
-π/2 ≤ θ ≤ π/2 (for the upper half of the circle)
0 ≤ r ≤ 8
Now we can express the integrand in terms of r and θ:
[tex]x^2 + y^2 = r^2[/tex] (by Pythagoras)
[tex]20(x^2 + y^2) = 20r^2[/tex]
So the integral becomes:
∫-π/2π/2∫[tex]08r^3 cos^2 θ sin θ dr dθ[/tex]
We can simplify cos^2 θ sin θ using the identity cos^2 θ sin θ = (1/3)sin^3 θ, so we get:
∫-π/2π/2∫[tex]08r^3 (1/3)sin^3 θ dr dθ[/tex]
The integral with respect to r is easy to evaluate:
∫0^8r^3 dr = (1/4)8^4 = 2048
The integral with respect to θ is also easy to evaluate using the fact that sin^3 θ is an odd function:
∫-π/2π/2(1/3)[tex]sin^3[/tex] θ dθ = 0
Therefore, the value of the iterated integral is:
2048(0) = 0
The volume of the solid is zero. This makes sense because the integrand is an odd function of y (or sin θ) and the region of integration is symmetric with respect to the x-axis.
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9.
What is the solution set for this inequality?
negative five D plus five and one over two symbol seventeen.
Answer:
Step-by-step explanation:
A plane rose from take-off and flew at an angle of 11° with the ground. When it reached an
altitude of 500 feet, what was the horizontal distance the plane had flown?
A plane rose from take-off and flew at an angle of 11° with the ground, the horizontal distance the plane had flown when it reached an altitude of 500 feet is approximately 2755.3 feet.
To solve this problem, we can use trigonometry. We know that the angle between the ground and the plane's path is 11°, and the altitude of the plane is 500 feet. Let x be the horizontal distance the plane has flown.
We can use the tangent function, which is defined as the ratio of the opposite side to the adjacent side of a right triangle, to find x. In this case, the opposite side is the altitude (500 feet) and the adjacent side is x. So we have:
tan(11°) = 500/x
To solve for x, we can multiply both sides by x and then divide by tan(11°):
x = 500 / tan(11°)
Using a calculator, we get:
x ≈ 2755.3 feet
Therefore, the horizontal distance the plane had flown when it reached an altitude of 500 feet is approximately 2755.3 feet.
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An animal reserve is home to 8 meerkats. It costs the reserve $1.50 per day to feed each meerkat. Write an equation with two variables that can be used to determine the total cost of feeding the reserve's meerkats for any number of days.
Answer:
y = 12x
Step-by-step explanation:
First let's find the total cost of feeding all the meerkats per day:
8*1.5 = 12
That means it costs $12 to feed all the meerkats each day. Now we can construct our equation
Let y = cost
Let x = days
y = 12x
This equation tells us the cost for feeding the meerkats an x number of days
Bonnie bought 12 bottles of pineapple juice and apple juice. The bottles of pineapple juice, p, were on sale for $1 per bottle, and the bottles of apple juice, a, were on sale for $1.75 per bottle. Bonnie spent a total of $15. How many bottles of pineapple juice and apple juice did Bonnie buy?
Answer:
Step-by-step explanation:
Let's use a system of equations to solve the problem.
We know that Bonnie bought a total of 12 bottles, so:
p + a = 12
We also know that Bonnie spent a total of $15, so:
1p + 1.75a = 15
We can solve this system of equations by substitution or elimination. Here, we'll use substitution:
p = 12 - a (from the first equation)
1(12 - a) + 1.75a = 15 (substituting p in the second equation)
12 - a + 1.75a = 15
0.75a = 3
a = 4
So Bonnie bought 4 bottles of apple juice. We can find the number of bottles of pineapple juice by substituting a=4 into the first equation:
p + 4 = 12
p = 8
Therefore, Bonnie bought 8 bottles of pineapple juice and 4 bottles of apple juice.
find the missing side. round your answer to the nearest tenth
The value of the missing side is 58. 75
How to determine the valueTo determine the value of the missing side, we need to know the different identities and their ratios.
These trigonometric identities are;
secantcosecanttangentcotangentsinecosineWe have their ratios as;
sin θ = opposite/hypotenuse
tan θ = opposite/adjacent
cos θ = adjacent/hypotenuse
We have that the;
Angle = 57 degrees
Adjacent = 32
Hypotenuse side = x
Then, we have;
Substitute the values for the cosine identity, we get
cos 57 = 32/x
cross multiply
x = 58. 78
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Find u × v, v x u, and v x v.
u = 2i + 6k
v = 4i + 7j - 5k.
To find u × v, we use the cross product formula:
u × v = | i j k |
| 2 0 6 |
| 4 7 -5 |
Expanding the determinant, we get:
u × v = (0*-5 - 6*7) i - (2*-5 - 6*4) j + (2*7 - 0*4) k
u × v = -42i - 22j + 14k
To find v × u, we use the same formula but switch the order of u and v:
v × u = | i j k |
| 4 7 -5 |
| 2 0 6 |
Expanding the determinant, we get:
v × u = (7*6 - (-5)*0) i - (4*6 - (-5)*2) j + (4*0 - 7*2) k
v × u = 42i + 18j - 14k
Finally, to find v × v, we again use the cross product formula with v as both inputs:
v × v = | i j k |
| 4 7 -5 |
| 4 7 -5 |
Expanding the determinant, we get:
v × v = (7*(-5) - (-5)*7) i - (4*(-5) - (-5)*4) j + (4*7 - 7*4) k
v × v = 0i - 0j + 0k
v × v = 0
So the cross product of v with itself is the zero vector.
To find u × v, v × u, and v × v, we'll use the cross product formula:
u × v = (u_yv_z - u_zv_y)i + (u_zv_x - u_xv_z)j + (u_xv_y - u_yv_x)k
Given u = 2i + 6k and v = 4i + 7j - 5k, we have:
u_x = 2, u_y = 0, u_z = 6
v_x = 4, v_y = 7, v_z = -5
Now, calculate u × v:
(0 * (-5) - 6 * 7)i + (6 * 4 - 2 * (-5))j + (2 * 7 - 0 * 4)k
= (-42)i + (34)j + (14)k
u × v = -42i + 34j + 14k
Next, calculate v × u:
(7 * 6 - (-5) * 0)i + ((-5) * 2 - 4 * 6)j + (4 * 0 - 7 * 2)k
= (42)i + (-34)j + (-14)k
v × u = 42i - 34j - 14k
Finally, calculate v × v:
(7 * (-5) - (-5) * 7)i + ((-5) * 4 - 4 * (-5))j + (4 * 7 - 7 * 4)k
= (0)i + (0)j + (0)k
v × v = 0i + 0j + 0k
In summary:
u × v = -42i + 34j + 14k
v × u = 42i - 34j - 14k
v × v = 0i + 0j + 0k
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please help with question 9
The value of the function g(x) = 4x⁴ - 4x³ - 10x - 51
What are functions?Functions are defined as those expressions or equations showing the relationship between two variables.
From the information given, we have the functions;
f(x) = 4x³ + 3x² - 12x - 32
h(x) = 4x⁴ - 3x² + 2x - 19
(f + g(x) = h(x)
To determine the function, let us follow the expression
f(x) + g(x) = h(x)
Make g(x), the subject of formula
g(x) = h(x) - f(x)
Substitute the expressions
g(x) = 4x⁴ - 3x² + 2x - 19 - 4x³ + 3x² - 12x - 32
Now, collect the like terms, we get;
g(x) = 4x⁴ - 4x³ - 3x² + 3x² + 2x - 12x - 19 - 32
Add or subtract the values
g(x) = 4x⁴ - 4x³ - 10x - 51
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The table shows the amount of pet food in cups remaining in an automatic feeder as a function of the number of meals the feeder has dispensed.
number of meals dispensed. n. 1. 3. 6. 7. amount of pet food remaining . f of n. cups. 21. 15. 6. 3.
based on the table, which function models this situation?
The function that models this situation is f(n) = -3n + 24.
To find the function, we need to analyze the relationship between the number of meals dispensed (n) and the amount of pet food remaining (f(n)).
1. Observe the change in f(n) when n increases by 1 meal. From n=1 to n=3, f(n) decreases from 21 to 15, a change of -6. From n=6 to n=7, f(n) decreases from 6 to 3, a change of -3.
2. The decrease in f(n) is not constant, so the function is not linear. However, the decrease becomes smaller as n increases.
3. Consider the average rate of change in f(n) per meal: (-6/2) = -3, (-3/1) = -3.
4. Since the average rate of change is constant, the function is linear.
5. The function has the form f(n) = -3n + b. To find b, plug in the value of n and f(n) from the table: 21 = -3(1) + b, which gives b = 24.
6. Therefore, the function that models this situation is f(n) = -3n + 24.
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A triangle has side lengths 6 cm, 7 cm, and √13 cm. Is this triangle a right triangle? Do these side lengths form a Pythagorean triple? Explain.
A triangle with side lengths 6 cm, 7 cm, and √13 cm is right triangle and the side lengths form a Pythagorean triple.
To determine if the triangle with side lengths 6 cm, 7 cm, and √13 cm is a right triangle and if these side lengths form a Pythagorean triple, we'll use the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
Identify the longest side. In this case, it's the side with length 7 cm.
Check if the Pythagorean theorem holds true for these side lengths:
(6 cm)² + (√13 cm)² = (7 cm)²
Calculate the squares of the side lengths:
(6 cm)² = 36 cm²
(√13 cm)² = 13 cm²
(7 cm)² = 49 cm²
Check if the sum of the squares of the two shorter sides equals the square of the longest side:
36 cm² + 13 cm² = 49 cm²
Compare the results:
49 cm² = 49 cm²
Since the equation holds true, the triangle is indeed a right triangle, and the side lengths 6 cm, 7 cm, and √13 cm form a Pythagorean triple.
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Peter owns a currency conversion shop.
Last Monday, Peter changed a total of £20,160 into a number of different currencies.
He changed
3/10
of the £20,160 into euros.
He changed the rest of the pounds into dollars, rupees and francs in the ratios 9:5:2
Peter changed more pounds into dollars than he changed into francs.
Work out how many more.
If Peter changed more pounds into dollars than he changed into francs then Peter changed £6,168 more into dollars than into francs.
First, we need to find out how much money Peter changed into euros:
(3/10) × £20,160 = £6,048
Next, we need to find out how much money Peter changed into dollars, rupees, and francs combined:
£20,160 − £6,048 = £14,112
We can use the ratios to find out how much of this total amount goes to each currency:
- Dollars: (9/16) × £14,112 = £7,932
- Rupees: (5/16) × £14,112 = £4,420
- Francs: (2/16) × £14,112 = £1,764
We can see that Peter changed more pounds into dollars than into francs. To find out how many more, we can subtract the amount changed into francs from the amount changed into dollars:
£7,932 − £1,764 = £6,168
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The figure shown is composed of two congruent triangles and a square Measurements are given in inches 6 in 5 in 4 in A 5 in What is the total area of the figure in square inches 5 in 4 in 5 in
Answer:
60 square inches
Step-by-step explanation:
Pt refers to Pythagoras Theorem. You know two sides of a right angled triangle, how do you find the 3rd side? Pythagoras Theorem. Then the rest is easy. Just do the area of all of the 4 triangles and the area of the square and add them up
28 Laney's art teacher, Mr. Brooks, has four different colors of clay. Laney and some of her classmates will be using this clay to make different figures. The following table shows the number of pounds of each color of clay Mr. Brooks has available. Clay Amount Color (pounds) Biue 11 5 Green 8 Yellow 2 Red 15 4. Use this information to help you answer parts A through E of this problem. Part A Laney noticed that one color of clay was exactly twice the amount of clay of another color. Which color of clay weighs exactly twice the number of pounds of another color of clay? A. Blue B. Green C. Yellow D. Red. â
Blue color of clay weighs exactly twice the number of pounds of another color of clay. The correct option is a.
We need to find the color of clay that weighs exactly twice the number of pounds of another color of clay. We can start by comparing the amounts of clay for each color:
- Blue: 11 pounds
- Green: 8 pounds
- Yellow: 2 pounds
- Red: 15 pounds
To find the answer, we need to see if any of these values is exactly twice another value. We can start by dividing each amount by 2:
- Blue: 11 ÷ 2 = 5.5
- Green: 8 ÷ 2 = 4
- Yellow: 2 ÷ 2 = 1
- Red: 15 ÷ 2 = 7.5
From this, we can see that the amount of blue clay (11 pounds) is exactly twice the amount of green clay (5.5 pounds). Therefore, the answer is A. Blue.
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the area of a rectangle is 65 sqare meters. the lenght of the rectrangle is 3 m less thans twice the width. find the dimensions of the rectangle
The dimensions are;
Length = 7 meters
Width = 5 meters
How to determine the valueThe area of a rectangle is expressed as;
Area = length × width
From the information given, we have that;
Length = 2w - 3
Area = 65
Substitute the values
65 = (2w - 3)w
expand the bracket
65 = 2w² - 3w
solve the quadratic equation;
2w² + 13w - 10w - 65
Factorize the terms
w(2w + 13) - 5(2w + 13)
w = 5
Substitute the value
Length = 2w - 3 = 2(5) - 3 = 7
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Please help me!!!
b) use your answer from part (a)to determine the value of y when x = –6.
the value of y is -5/8. So, In part (a), we found that the rational function f(x) = (5x + 20)/(x^2 - 20) had a vertical asymptote at x = -2√5 and x = 2√5, a horizontal asymptote at y = 0, an x-intercept at (-4, 0), a y-intercept at (0, -1), and a hole at (-4, 5/18).
To find the value of y when x = -6, we simply substitute -6 for x in the function:
f(-6) = (5(-6) + 20)/((-6)^2 - 20)
We simplify this expression by first multiplying 5 and -6 to get -30, and then adding 20 to get -10 in the numerator. In the denominator, we evaluate (-6)^2 to get 36, and then subtract 20 to get 16. So, we have:
f(-6) = -10/16
This fraction can be simplified by dividing both the numerator and denominator by 2:
f(-6) = (-10/2)/(16/2) = -5/8
Therefore, when x = -6, the value of y is -5/8.
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