There is a vertical asymptote at x = 0.
A vertical asymptote is a vertical line that the graph of a function approaches but never touches or crosses. In the case of a rational function such as f(x) = x^3/(x^2-4), vertical asymptotes occur where the denominator of the function is equal to zero.
In this case, the denominator is x^2 - 4, which is equal to zero when x = ±2. However, we need to check whether these values are in the domain of the function. Since the interval of interest is (–18, 19), we see that only x = 2 is in the domain of the function.Therefore, the only vertical asymptote of the function f(x) = x^3/(x^2-4) on the interval (–18, 19) is at x = 0, which is the value of x where the denominator is closest to zero.
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4x + 8y = 3x + 7y + 14; y=2
Answer:
Step-by-step explanation:
as we alderdy have value of y,we can substuite it in the place of y
4x+8(2)=3x+7(2)+14
4x+16=3x+14+14
4x-3x=28-16
x=12
Dante has a tent shaped like a triangular prism. The tent has equilateral triangle bases that measure 5 feet on each side. The tent is 8 feet long and 4. 3 feet tall
The tent has a volume of 86 cubic feet.
How we get the volume of tent?The tent owned by Dante is in the shape of a triangular prism, which means it has two identical equilateral triangle bases that measure 5 feet each. The tent's length is 8 feet, and its height is 4.3 feet.
To calculate the tent's volume, we can use the formula for the volume of a triangular prism, which is [tex]V = (1/2) * b * h * l[/tex], where b is the base, h is the height, and l is the length of the prism.
Plugging in the given values, we get [tex]V = (1/2) * 5 * 4.3 * 8[/tex] = 86 cubic feet. The volume of a tent is an important consideration when deciding which one to purchase or use for a particular activity, as it determines how much space is available inside for people and belongings.
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Please help I need it ASAP, also needs to be rounded to the nearest 10th
Answer: 161.2
Step-by-step explanation:
Plug into formula
6.9² = 13²+17.8²-2(17.8)(13) cos C >simplify numbers
-438.23 = -2(17.8)(13) cos C >Divide both sides by -2(17.8)(13)
cos C=.947 > use [tex]cos^{-1}[/tex] C to solve for angle
<C=180-18.75 = 161.2 > neded to subtract from 180 for this
one
The triangular cross section of a prism is an isosceles right-angled triangle.
The volume of the prism is 203 cm
Use approximations to estimate the value of y.
You must show your working.
Your final line should say, Estimate for y is.
y cm
4. 13 cm
y cm
Using approximation as x = 10, the estimation of y = 4.06 cm.
We need to find the area of the triangular cross-section of the prism. Since it is an isosceles right-angled triangle, we know that the two legs are equal in length, so let's call them x.
The area of a triangle is 1/2 * base * height, and in this case, the base and height are both x, so the area is 1/2 * x * x, or x^2/2.
Now, we can use the formula for the volume of a prism, which is V = area of base * height. In this case, the volume is 203 cm, and the height is y, so we can write:
203 = x^2/2 * y
To estimate the value of y, we need to make an assumption about the value of x. Since we don't have any information about it, let's assume it is about 10 cm (this is just an approximation).
Plugging in x = 10, we get:
203 = 10^2/2 * y
203 = 50 * y
y = 203/50
y ≈ 4.06 cm
So our estimate for y is 4.06 cm. Remember to include all the necessary terms and the final line, which should say: Estimate for y is 4.06 cm.
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Quality-control research determined that of all new
cars sold by Sherman Motors, 8% will require a
minor repair during the first year of ownership.
Suppose you survey the owners of three cars from
Sherman Motors. Find the probability to the nearest
percent that exactly one car will require a minor
repair in the first year
The probability that out of three exactly one car will require a minor repair in the first year = 33%
P(E ) = no. of favorable outcome/total no. of outcome
E here represents exactly one car that requires a minor repair.
out of three cars, exactly one car will need a minor repair
No. of favorable outcome = 1
Total no. of outcome = 3
Now, putting value in P(E) we get
P(E) = 1/3
P(E) = 0.333
To get percentage we multiply by 100
P(E) = 0.333 × 100
P(E) = 33.3
The probability to the nearest percent = 33%
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If the an average American makes around $ 40,000 per year for his or her lifetime and works from age 22 to 65, what amount will he or she pay in taxes for their entire lifetime?
We can see here that the amount he or she will pay in taxes for their entire lifetime is: $344,000
What is tax?Tax is a financial obligation that all people, businesses, and other types of entities must fulfill for a government organization.
Let us say that an average American makes $40,000 for his or her lifetime and works from age 22 to 65, and pays a combined federal and state income tax rate of 20%, the amount of taxes paid per year would be:
$40,000 x 0.20 = $8,000
Over a 43-year period (from age 22 to 65), the total amount of taxes paid would be: $8,000 x 43 = $344,000
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The price of a visit to the dentist is
$
50
$50dollar sign, 50. If the dentist fills any cavities, an additional charge of
$
100
$100dollar sign, 100 per cavity gets added to the bill.
In general, the cost of the visit will depend on the number of cavities found by the dentist as: Cost = $50 + $100 * n.
What is equation?An equation is a mathematical statement that says that two expressions are equal. It consists of two sides, the left-hand side (LHS) and the right-hand side (RHS), separated by an equal sign (=). An equation expresses a relationship between the quantities involved and represents a balance or equality between the two sides. Equations are used in various fields of mathematics, science, and engineering to model real-world situations and solve problems. They can be linear or nonlinear, simple or complex, and involve different types of variables, functions, and operators. Solving equations is an essential skill in mathematics and involves applying various techniques and strategies to find the solution or solutions to the equation.
Here,
If the dentist finds n cavities, the cost of the visit will be:
Cost = $50 + $100 * n
So, if the dentist finds, for example, 3 cavities, the cost of the visit will be:
Cost = $50 + $100 * 3 = $350
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Complete question:
The price of a visit to the dentist is $50 if the dentist feels any cavities in additional charge of $100 per cavity get added to the bill. If the dentist finds n cavities What will the cost of the visit be?
What is the solution of |x – 6| ≥ 1? 5 < x < 7 x ≤ –7 or x ≥ –5 x ≤ 5 or x ≥ 7 –7 < x < –5
Answer:
(c) x ≤ 5 or x ≥ 7
Step-by-step explanation:
You want the solution to |x -6| ≥ 1.
UnfoldThe absolute value relation represents two relations, one for the domain x < 6, and one for the domain x ≥ 6.
x < 6In this domain, the inequality becomes ...
-1 ≥ x -6
5 ≥ x . . . . . . add 6
x ≤ 5 . . . . . . . put x on the left
x ≥ 6In this domain, the inequality is ...
x -6 ≥ 1
x ≥ 7
The disjoint solution sets are x ≤ 5 or x ≥ 7.
__
Additional comment
For |x -a| ≤ b, we can "unfold" this to the compound inequality ...
-b ≤ (x -a) ≤ b
copying the inequality symbol to the left side, and writing the opposite of the constant there.
We can do the same thing with the inequality ...
|x -a| ≥ b
but it doesn't really make sense as a compound inequality.
Instead, we have to write it as ...
-b ≥ (x -a) or (x -a) ≥ b
in recognition of the fact that the solution spaces are disjoint.
Arnav was 1.5 \text{ m}1.5 m1, point, 5, start text, space, m, end text tall. In the last couple of years, his height has increased by 20\%20%20, percent
Over the last couple of years, Arnav's height has increased by 20% so his current height is 1.8 meters.
Arnav's height initially was 1.5 meters. Over the last couple of years, his height increased by 20%. To find the new height, we can use the formula: new height = initial height × (1 + percentage increase).
In this case, the initial height is 1.5 meters and the percentage increase is 20%, which can be expressed as a decimal (0.2). Using the formula, we can calculate Arnav's new height as follows:
New height = 1.5 meters × (1 + 0.2) = 1.5 meters × 1.2 = 1.8 meters.
After the 20% increase in height over the last couple of years, Arnav's current height is 1.8 meters.
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i need help !!!!!!!!!!!!!!!!!!
Answer:
[tex]\displaystyle\textsf{a) }\binom{8}{4}\\\\\textsf{b) }\binom{-8}{4}[/tex]
Step-by-step explanation:
Given a translation vector ...
[tex]\displaystyle \binom{g}{h}[/tex]
moves g to the right and h up, you want the vectors for 8 right, 4 up, and for 8 left, 4 up.
SubstitutionWhen we have g = units to the right, and we want 8 units to the right, we know that g = 8. Similarly, h = units up, and we want 4 units up, so h = 4.
Putting these values in the vector form, we have ...
a) 8 right, 4 up matches vector ...
[tex]\displaystyle \boxed{\binom{8}{4}}[/tex]
b) Left is the opposite of right, so 8 units left will be represented by ...
g = -8
As before, 4 units up means h = 4.
[tex]\displaystyle \boxed{\binom{-8}{4}}[/tex]
<95141404393>
Answer this Question
The missing numbers on the grids are given as follows:
2 and -6.
How to obtain the amounts?The amounts are obtained by a system of equations, for which the variables are given as follows:
x and y.
The top grid represents the sum of the measures, hence:
x + y = -4.
The bottom grid represents the subtraction of the measures, hence:
x - y = 8.
Adding the two equations, the value of x, representing the left grid, is given as follows:
2x = 4
x = 2.
Then the value of y, representing the right grid, is given as follows:
2 + y = -4
y = -6.
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Consider a point with rectangular coordinates (x,y).
if x<0 then the polar coordinates of the point are (r,θ) where r≥0 and −π/2≤θ<3π/2and:
r=
θ=
if x≥0 then the polar coordinates of the point are (r,θ) where r≥0 and −π/2≤θ<3π/2 and:
r=
θ=
Polar coordinates for rectangular coordinates if x<0: r=√(x²+y²) and θ=tan⁻¹(y/x)+π if y≥0 or θ=tan⁻¹(y/x)−π if y<0, For x≥0: r=√(x²+y²) and θ=tan⁻¹(y/x) if y≥0 or θ=tan⁻¹(y/x)+2π if y<0.
The polar coordinates of a point with rectangular coordinates (x,y) depend on the sign of x.
If x<0, the polar coordinates are (r,θ) where r≥0 and −π/2≤θ<3π/2. If x≥0, the polar coordinates are (r,θ) where r≥0 and −π/2≤θ<3π/2.
If x<0, t
hen r=√(x²+y²) and
θ=tan⁻¹(y/x)+π if y≥0
or θ=tan⁻¹(y/x)−π if y<0.
The value of r is the distance from the origin to the point and θ is the angle between the positive x-axis and the line segment from the origin to the point.
If x≥0, then r=√(x²+y²) and θ=tan⁻¹(y/x) if y≥0 or θ=tan⁻¹(y/x)+2π if y<0.
In this case, θ is the angle between the positive x-axis and the line segment from the origin to the point, measured counterclockwise.
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Can someone help with this math equation from study island…????
The solution of the exponents is shown below.
What is the solution of the exponents?Exponents are mathematical shorthand for multiplying a number by itself a certain number
We have that;
5^n = 1
5^n = 5^0
n = 0
2) 2^-7/2^n = 2^2
2^-7 - n = 2^2
-7 - n = 2
-n = 2 + 7
n = -9
3) 6^5 * 6^n = 6^1
6^ 5 + n = 6^1
5 + n = 1
n = 1 - 5
n = -4
4) (8^n)^7 = 8^21
8^7n = 8^21
7n = 21
n = 3
5) 4^n = (1/4)
4^n = 4^-1
n = -1
In each of the cases, we have applied the laws of the exponents as we know them.
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The equation of the forms are matched as;
2⁻⁷/2ⁿ = 2², n = -9
6⁵ * 6ⁿ = 6. n = -4
(8ⁿ)⁷ = 8²¹, n = 3
4ⁿ = 1/4 , n = -1
What are index forms?Index forms are simply described as mathematical forms that are used to represent numbers of variables that are too large or small.
To multiply index forms, you need to add the exponents of the same bases.
To divide index forms, you need to subtract the exponents of the same bases.
From the information given, we have that;
2⁻⁷/2ⁿ = 2²
cross multiply the values
2⁻⁷ = 2²⁺ⁿ
Then,
-7 = 2 + n
n = -9
6⁵ * 6ⁿ = 6
take the exponents
5 + n= 1
n =- 4
(8ⁿ)⁷ = 8²¹
We have;
7n = 21
Make 'n' the subject
n = 3
4ⁿ = 1/4
4ⁿ = 4⁻¹
n =-1
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What expression represents the volume of the cylinder, in cubic units? 4πx2 2πx3 πx2 2x 2 πx3
The expression that represents the volume of the cylinder, in cubic units, is:
[tex]$$V = 2\pi x^3$$[/tex]
The expression that represents the volume of a cylinder in cubic units is given by the formula:
[tex]$$V = \pi r^2h$$[/tex]
where [tex]$r$[/tex] is the radius of the base of the cylinder and [tex]$h$[/tex] is the height of the cylinder.
Now, let's consider each option provided:
[tex]1. $4\pi x^2$[/tex]
This expression only includes the radius, but it does not include the height of the cylinder, so it cannot be the correct answer.
[tex]2. $2\pi x^3$[/tex]
This expression includes both the radius and the height of the cylinder, but it does not include the squared term for the radius, so it cannot be the correct answer.
[tex]3. $\pi x^2$[/tex]
This expression includes the squared term for the radius, but it does not include the height of the cylinder, so it cannot be the correct answer.
[tex]4. $2x$[/tex]
This expression only includes a single variable, which is neither the radius nor the height of the cylinder, so it cannot be the correct answer.
[tex]5. $2\pi x^3$[/tex]
This expression includes both the squared term for the radius and the height of the cylinder, so it is the correct answer.
Therefore, the expression that represents the volume of the cylinder, in cubic units, is:
[tex]$$V = 2\pi x^3$$[/tex]
This formula can be used to calculate the volume of a cylinder given the value of its radius and height.
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Suppose a friend or family asked you how it could be possible that an annual interest rate is higher than 100%. write out an explanation of what you might say to them
If someone asked me how it could be possible for an annual interest rate to be higher than 100%, I would explain that it is actually quite common in certain situations, particularly in the case of loans with very short terms or loans with high fees.
For example, let's say you borrowed $100 from a lender and agreed to pay back $110 in one week. The lender is essentially charging you 10% interest for the one-week loan period, but if you annualize that rate, it comes out to over 520%. This is because the lender is charging you a very high interest rate for a very short period of time.
Another example would be if you took out a payday loan, which typically have very high fees attached to them. For instance, you might borrow $500 and have to pay back $575 in two weeks. The interest rate on this loan might be calculated as the $75 fee divided by the $500 borrowed, which comes out to 15%. However, if you annualize that rate, it comes out to over 390%.
In both of these examples, the interest rate is very high because the loan term is very short and/or the fees are very high. It's important to note that borrowing at such high interest rates can be extremely costly and can lead to a cycle of debt, so it's generally recommended to avoid loans with high interest rates whenever possible.
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What is the slope of the line that passes through the points (9, 1) and (10, -1)?
Write your answer in simplest form.
Answer:
m=2
Step-by-step explanation:
I need helpp
5x+3=2x-15
Answer:
x = -6
Step-by-step explanation:
5x + 3 = 2x - 15
3x + 3 = -15
3x = -18
x = -6
Let's Check
5(-6) + 3 = 2(-6) - 15
-30 + 3 = -12 - 15
-27 = -27
So, x = -6 is the correct answer.
Answer:
x = -6
Step-by-step explanation:
Equation is 5x + 3 = 2x - 15
First, we can subtract the constants
5x = 2x - 18
Then, we can subtract 2x on both sides
3x = -18
Divide both sides by 3 to isolate x
x = -6
Consider the function f(x) = 5 – 2x^2, -5 ≤ x ≤ 2. The absolute maximum value is
and this occurs at x = The absolute minimum value is and this occurs at x =
As a result, the function's absolute maximum and minimum values are 5 and -45, respectively, at x = -5 and x = 2, respectively.
what is function ?Every element in a set (referred to as the domain) in mathematics is connected by a rule known as a function to exactly one component in some other set (called the range or codomain). In other terms, a role is a connection among 2 sets where every element in the domain matches exactly one member in the range. Using a formula or equation with a variable input, function notation is a common way to represent functions. As an illustration, the formula f(x) = 2x + 1 gives each true figure x the value 2x + 1.
given
We can apply the second derivative test to determine whether this critical point is a maximum or minimum. By taking f'(xderivative, )'s we arrive at:
f''(x) = -4
The critical point at x = 0 is a local maximum since f"(0) = -4 is a negative value.
Secondly, we must determine whether the interval's endpoints of -5 x 2 provide values that are higher or lower than the crucial point. By entering x = -5 and x = 2, we obtain:
[tex]f(-5) = 5-2(-5) (-5)^2 = 5 – 50 = -45[/tex]
[tex]f(2) = 5 - 2(2) (2)^2 = -3[/tex]
As a result, the function's absolute maximum and minimum values are 5 and -45, respectively, at x = -5 and x = 2, respectively.
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A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall between t = 0.5 s and t=1.4 s? Use Galileo's formula u(t) = -32t ft/s.
Answer = _______
The distance is negative because it's a fall, so the cat falls 27.36 ft between t = 0.5 s and t = 1.4 s.
To find the distance the cat falls between t = 0.5 s and t = 1.4 s, we need to use the formula for velocity and distance.
we first need to find the position at each of these times using the given formula u(t) = -32t ft/s.
The formula for distance fallen is:
distance(t) = initial position + initial velocity × t + (1/2) × acceleration × t²
Since the cat falls with zero initial velocity and starts from the tree, we can simplify the formula:
distance(t) = (1/2) × acceleration × t²
First, let's find the velocity of the cat at t = 0.5 s and t = 1.4 s using Galileo's formula:
u(0.5) = -32(0.5) = -16 ft/s
and, u(1.4) = -32(1.4) = -44.8 ft/s
Now, we can use the formula for distance:
distance = (velocity at t = 0.5 s + velocity at t = 1.4 s) / 2 x (t = 1.4 s - t = 0.5 s)
⇒ distance = (-16 ft/s + (-44.8 ft/s)) / 2 x (1.4 s - 0.5 s)
⇒ distance = (-60.8 ft/s) / 2 x (0.9 s)
⇒ distance = -27.36 ft/s x s
Therefore, the cat falls 27.36 feet between t = 0.5 s and t = 1.4 s.
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A van can ferry a maximum of 12 people. By setting up an inequality, find the maximum number of vans that are needed to ferry 80 people
By setting up an inequality, the maximum number of vans that are needed to ferry 80 people are 7 vans.
To find the maximum number of vans needed to ferry 80 people using the given terms, let's set up an inequality. Let's use the variable "v" to represent the number of vans.
Since a van can ferry a maximum of 12 people, we can write the inequality as:
12v ≥ 80
Now, let's solve for "v":
Divide both sides of the inequality by 12.
v ≥ 80/12
Simplify the inequality.
v ≥ 6.67
Since we cannot have a fraction of a van, we need to round up to the nearest whole number:
v ≥ 7
Therefore, the maximum number of vans needed to ferry 80 people is 7 vans.
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Determine the distance between the points (−3, −6) and (5, 0).
[tex]~~~~~~~~~~~~\textit{distance between 2 points} \\\\ (\stackrel{x_1}{-3}~,~\stackrel{y_1}{-6})\qquad (\stackrel{x_2}{5}~,~\stackrel{y_2}{0})\qquad \qquad d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2} \\\\\\ d=\sqrt{(~~5 - (-3)~~)^2 + (~~0 - (-6)~~)^2} \implies d=\sqrt{(5 +3)^2 + (0 +6)^2} \\\\\\ d=\sqrt{( 8 )^2 + ( 6 )^2} \implies d=\sqrt{ 64 + 36 } \implies d=\sqrt{ 100 }\implies d=10[/tex]
Regina writes the expression y + 9 x 3/4. Which expression is equivalent to the one Regina writes?
The expression that is equivalent to the one Regina wrote is y + 27/4
Which expression is equivalent to the one Regina wrote?From the question, we have the following parameters that can be used in our computation:
y + 9 x 3/4
This means that
Expression = y + 9 x 3/4
When expanded, we have
Expression = y + 27/4
Using the above as a guide, we have the following:
The expression that is equivalent to the one Regina wrote is y + 27/4
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Find the missing sector areas and arc lengths.
The areas of the sector in the circle are 18π, 3π, 10π and 5π
Finding the sector areas and arc lengths.The orange sector
This is calculated as
Sector area = central angle/360 * πr²
Where
Radius, r = 6central angle = 180 degreesSo, we have
Sector area = 180/360 * π * 6²
Sector area = 18π
The yellow sector
This is calculated as
Sector area = central angle/360 * πr²
Where
Radius, r = 6central angle = 30 degreesSo, we have
Sector area = 30/360 * π * 6²
Sector area = 3π
The green sector
This is calculated as
Sector area = central angle/360 * πr²
Where
Radius, r = 6central angle = (180 - 50 - 30) = 100 degreesSo, we have
Sector area = 100/360 * π * 6²
Sector area = 10π
The purple sector
This is calculated as
Sector area = central angle/360 * πr²
Where
Radius, r = 6central angle = 50 degreesSo, we have
Sector area = 50/360 * π * 6²
Sector area = 5π
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When do you hit the water and what is your maximum height above the pool?
The time till you hit the water, given your height above the water, would be 0.76 seconds.
The maximum height above the pool you would get is 15.39 feet.
How to find the maximum height and time ?We are given h ( t ) = - 16 t ² + 5t + 15
You hit the water at 0 so the formula is:
0 = - 16 t ² + 5t + 15
Using the quadratic equation, we can solve:
t = ( - b ± √ ( b ² - 4 ac ) ) / 2a
t = ( - 5 ± √ ( 5 ² - 4 ( - 16 ) ( 15 ) )) / 2 (- 16)
t = (- 5 ± √ 985 ) / -32
t = 0. 76 seconds
The vertex of the parabolic function would be:
= - b / 2a
= - 5 / ( 2 x - 16 )
= 0. 15625 seconds
Maximum height is therefore:
= -16 ( 0. 15625 ) ² + 5 ( 0. 15625 ) + 15
= 15.39 feet
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The monthly income of a man is Rs 53000. He deposits 20% of his yearly income in civil investment fund and 10% in charity. If 1 % social security tax should be paid on First Rs 300000and 15% tax is imposed yearly ,how much tax should he pay?
The man needs to pay a total tax of Rs 69780 (3000 for social security and 66780 for yearly tax).
How to find the tax should he pay?To find the tax, let's find the man's yearly income:
Yearly income = Monthly income x 12
Yearly income = 53000 x 12 = 636000
Next, let's find how much he deposits in civil investment fund and charity:
Amount deposited in civil investment fund = Yearly income x 20%
Amount deposited in civil investment fund = 636000 x 0.2 = 127200
Amount deposited in charity = Yearly income x 10%
Amount deposited in charity = 636000 x 0.1 = 63600
Now, let's calculate the total taxable income:
Total taxable income = Yearly income - Amount deposited in civil investment fund - Amount deposited in charity
Total taxable income = 636000 - 127200 - 63600 = 445200
Since the man's taxable income is above Rs 300000, he needs to pay 1% social security tax on Rs 300000:
Social security tax = 1% of 300000 = 3000
Now, let's calculate the yearly tax imposed at a rate of 15%:
Yearly tax = Total taxable income x 15%
Yearly tax = 445200 x 0.15 = 66780
Therefore, the man needs to pay a total tax of Rs 69780 (3000 for social security and 66780 for yearly tax).
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Now that you have chosen your mode of transportation, use your choice to answer the questions that follow.
What would the cost of your transportation be if you drove:
a. 10 miles? b. 25 miles? c. 42 miles? d. 68 miles?
Make sure to list your chosen mode of transportation and then answer all parts and show your work
(a) The cost of City Bus for driving 10 miles = $3.
(b) The cost of City Bus for driving 25 miles = $7.5.
(c) The cost of City Bus for driving 42 miles = $12.6.
(d) The cost of City Bus for driving 68 miles = $20.4.
We previously choose City Bus as our mode transport since the per mile cost for City Bus is less.
Let the model for City Bus be f(x) = cx + d, where f(x) is total cost and x is number of miles.
From the table of Taxi we get, f(2) = 0.60; f(4) = 1.20; f(6) = 1.80 and f(8) = 2.40.
So, 2a + b = 0.60 and 4a + b = 1.20
(4a + b) - (2a + b) = 1.20 - 0.60
2a = 0.60
a = 0.60/2 = 0.30
Now, f(8) = 2.40
8*0.30 + b = 2.40
2.40 + b = 2.40
b = 2.40 - 2.40 = 0
So the function rule for City Bus is, f(x) = 0.3x.
(a) Total cost to drive 10 miles is,
f(10) = 0.3*10 = 3
(b) Total cost to drive 25 miles is,
f(25) = 0.3*25 = 7.5
(c) Total cost to drive 42 miles is,
f(42) = 0.3*42 = 12.6
(d) Total cost to drive 68 miles is,
f(68) = 0.3*68 = 20.4
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What is the surface of the prism
Answer:
The third answer is correct
Step-by-step explanation:
Given:
A net of a rectangular prism
l (length) = 11,75 cm
w (width) = 5,75 cm
h (height) = 4 cm
Find: A (surface area) - ?
The surface area is equal to the sum of the areas of all the sides
There are:
2 sides with dimensions of 11,75 cm and 4 cm
2 sides with dimensions of 5,75 cm and 11,75 cm
2 sides with dimensions of 4 cm and 5,75 cm
[tex]a(surface) = 4 \times 11.75 \times 2 + 5.75 \times 11.75 \times 2 + 4 \times 5.75 \times 2 = 275.125 = 275 \frac{1}{8} \: {cm}^{2} [/tex]
The surface area of a triangular pyramid is 450 square meters. The surface area of a similar triangular pyramid is 50 square meters.
What is the ratio of corresponding dimensions of the smaller pyramid to the larger pyramid?
The ratio of the corresponding dimensions of the smaller pyramid to the larger pyramid is 1/3.
What is a dimension?Dimension is the measure of the distance or length of an obeject.
To calculate the ratio of the corresponding dimensions of the smaller pyramid to the larger pyramid, we use the formula below
Formula:
l/L = √(a/A) ........................ Equation 1
Where:
l/L = Ratio of the dimension of the smaller pyramid to the larger onea = Area of the smaller pyramidA = Area of the larger pyramidFrom the question,
Given:
a = 50 m²A = 450 m²Substitute these values into equation 1
l/L = √(50/450)l/L = √(1/9)l/L = 1/3Learn more about dimension here: https://brainly.com/question/27404871
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An investor purchases 500 shares of Exxon-mobil stock at $98. 93 per share. His broker charges 2% of the cost of the stock. What is the cost of the stock?
The cost of the stock for the investor would be calculated as follows:
Cost of 1 share = $98.93
Number of shares purchased = 500
Total cost of the stock = Cost per share x Number of shares
Total cost of the stock = $98.93 x 500
Total cost of the stock = $49,465
The broker charges 2% of the cost of the stock, so the broker's fee would be calculated as:
Broker's fee = 2% x Total cost of the stock
Broker's fee = 2% x $49,465
Broker's fee = $989.30
Therefore, the total cost of the stock for the investor including the broker's fee would be:
Total cost of the stock + Broker's fee = $49,465 + $989.30
Total cost of the stock + Broker's fee = $50,454.30
So the cost of the stock for the investor including the broker's fee is $50,454.30.
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a) ¿Cuál es el coeficiente del término 23x5?
Answer:
El coeficiente del término 23x^5 es 23.
Step-by-step explanation: