The expression that is equal to the rational expression when x does not equal to 5 or -1 is; (x - 7)/(x -5)
How to simplify Algebraic Expressions?
We want to simplify the algebraic expression;
(x - 7)(x + 1)/(x + 1)(x - 5)
Now, looking at the given expression, we see that (x + 1 ) is common to both numerator and denominator and as such they will cancel out to leave us with;
(x - 7)/(x -5)
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You plant a tree that is 36 inches tall. After one year, the tree is 43 inches tall. Which expression describes the percent of increase in the tree's height?
Use any method to solve the equation. If necessary, round to the nearest hundredth.
x^2 + x − 30 = 0
A. –5, 6
B. 10, –12
C. 5, –6
D. 5. 5, –5.5
Here, in order to find the solutions to the quadratic equation - x² + x - 30 = 0, we will use factorization method.
In the method, we will split 30, in such factors, which when added or subtracted gives us 1, and when multiplied gives us -30.
So, we will use, -5 and 6. When they are added they will give us 1 and when multiplied they will give us -30 as answer.
Now, the equation will be written as -
x² - 5x + 6x - 30 = 0
Taking common, we get
x(x - 5) +6(x-5) = 0
(x-5)(x+6) = 0
So, x - 5 = 0 and x +6 = 0, we will get, x = 5 and x = - 6
Thus, the correct option is C). x = 5 and -6
A 16 ounce package of cereal cost $4.00? what is the unit cost
Here, we need to find unit cost. Unit cost can be defined as a cost per unit of a product.
We are given that 16 ounce will cost $ 4.00.
That means -
Cost of 16 ounce of cereal package = $ 4.00
Cost of 1 ounce of cereal package -
(We will divide both sides by 16)
Cost of 16 ounce of cereal package ÷ 16 = $ 4.00 ÷ 16
Cost of 1 ounce of cereal package = $ 0.25.
Thus, the cost of 1 ounce of cereal package = $ 0.25.
Answer: 1 oz. Over 0.25 is your answer.
Step-by-step explanation:
A school typically sells 500 yearbooks each year for 50 dollars each. The economic calls does a project and discovers that they can sell 100 more yearbooks for every $5 decrease in price. The revenue for yearbook sales is equal to the number of yearbooks sold times the price of the yearbook. Let x represent the number of $5 decrease in price. If the expression that represents the revenue is written in the form R(x)=(500+ax)(50-bx). Find the value of a and b
Final answer:
For the expression R(x)=(500+ax)(50-bx), a represents the increase in yearbooks sold for each $5 decrease in price and b represents the corresponding decrease in price per yearbook. The correct values for a and b are 100 and 5 respectively, resulting in the revenue expression R(x) = (500 + 100x)(50 - 5x).
Explanation:
The student's question revolves around the concept of revenue generation based on the number of items sold and the selling price per item.
When examining revenue, we understand it as the product of price per unit times the number of units sold. In the given example, a school is selling yearbooks with a base scenario of 500 yearbooks at $50 each. We are given that for every $5 decrease in price, the school can sell an additional 100 yearbooks. This can be formulated as:
R(x) = (500 + ax)(50 - bx)
Here x represents the number of $5 decreases from the original price. With each decrease, the number of books sold increases by 100, and the price decreases by $5.
Therefore, variable a must represent the increase in quantity sold for each $5 price decrease (a = 100), and variable b must represent the decrease in price per yearbook for each price decrease (b = 5).
Therefore, the values of a and b are 100 and 5, respectively.
The expression for the revenue becomes:
R(x) = (500 + 100x)(50 - 5x)
24. Four golf balls are packaged in a cylindrical container as shown below. The balls just touch the top, bottom, and sides of the cylinder. The diameter of each ball is 4cm.
Brian wants to fence in his triangular plot of farm land that measures 1.1 by 1.5 by 2.2 miles. Determine the angles at which the fences of the three sides will meet.
Rounding each angle to the nearest degree: m<A=___degrees
The angles for Brian's triangular plot of farmland are approximately 27° for ∠A, 38° for ∠B, and 115° for ∠C.
To determine the angles of a triangular plot of land with sides measuring 1.1 miles, 1.5 miles, and 2.2 miles, we can use the Law of Cosines. The Law of Cosines states:
⇒ c² = a² + b² - 2ab × cos(C)
Let's label the sides as follows:⇒ a = 1.1 miles
⇒ b = 1.5 miles
⇒ c = 2.2 miles
First, we calculate ∠C (opposite side c):⇒ cos(C) = (a² + b² - c²) ÷ (2ab)
⇒ cos(C) = (1.1² + 1.5² - 2.2²) ÷ (2 × 1.1 × 1.5)
= (1.21 + 2.25 - 4.84) ÷ (3.3)
= (-1.38) ÷ (3.3)
= -0.4182
Then, we find ∠C by taking the inverse cosine (cos-1):⇒ ∠C ≈ 115°
Next, we calculate ∠A (opposite side a) using the same method:⇒ cos(A) = (b² + c² - a²) ÷ (2bc)
⇒ cos(A) = (1.52 + 2.22 - 1.12) ÷ (2 × 1.5 × 2.2)
= (2.25 + 4.84 - 1.21) ÷ (6.6)
= (5.88) ÷ (6.6)
= 0.8909
Then, we find angle A:⇒ ∠A ≈ 27°
Finally, we calculate angle B (opposite side b) using:⇒ ∠B = 180° - ∠A - ∠C
= 180° - 27° - 115°
= 38°
The angles at which the fences of the three sides will meet are approximately 27° for ∠A, 38° for ∠B, and 115° for ∠C, when rounded to the nearest degree.
Complete question:
Brian wants to fence in his triangular plot of farm land that measures 1.1 × 1.5 × 2.2 miles.
Determine the angles at which the fences of the three sides will meet.
Rounding each angle to the nearest degree:
Use the quadratic formula to solve, 2x^2=7x+6 Leave your answer in simplified radical form.
Please show all your work! (30 points)
What is the equation of a line, in general form, that passes through point (1, -2) and has a slope of .
3x - y - 7 = 0
x - 3y + 7 = 0
x - 3y - 7 = 0
Q9 Q13.) Find the products AB and BA to determine whether B is the multiplicative inverse of A.
Suppose you rolled the 6-sided number cube 120 times, how many times would you expect to roll a 6? Explain.
You would expect to roll a 6 approximately 20 times in 120 rolls. This is because, on average, in the long run, you would expect a specific outcome (in this case, rolling a 6) to occur with a frequency proportional to its probability (1/6) over a large number of trials (120 rolls).
When rolling a fair 6-sided number cube, each of the six faces has an equal probability of landing face up. The probability of rolling a 6 on a fair 6-sided number cube is 1/6.
To find out how many times you would expect to roll a 6 in 120 rolls, you can use the probability formula:
Expected number of successful outcomes = Probability of success * Total number of trials
Expected number of times to roll a 6 = (1/6) * 120
Expected number of times to roll a 6 = 20
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Find the equation for the plane through the points upper p 0 left parenthesis negative 2 comma negative 5 comma negative 4 right parenthesis, upper q 0 left parenthesis 5 comma 1 comma negative 4 right parenthesis, and upper r 0 left parenthesis negative 1 comma 2 comma 5 right parenthesis.
what value represents the horizontal translation from the graph of the parent function f(x)=x^2 to the graph of the function g(x)=(x+5)^2+3
Use spherical coordinates. let h be a solid hemisphere of radius 1 whose density at any point is proportional to its distance from the center of the base. (let k be the constant of proportionality.) (a) find the mass of h.
To find the mass of the solid hemisphere using spherical coordinates with density proportional to distance from center, integrate the density times the volume element over the hemisphere.
Explanation:To find the mass of the solid hemisphere using spherical coordinates, we first need to understand that the density at any point is proportional to its distance from the center of the base. Let's denote the constant of proportionality as k. The mass can be found by integrating the product of density and volume over the entire hemisphere. The volume element in spherical coordinates is given by ρ² sinϕ dρ dϕ dθ, where ρ is the radial distance, ϕ is the polar angle, and θ is the azimuthal angle.
We can denote the density as ρ = kρ, where ρ is the radial distance from the center. The mass element dm is then given by dm = ρ² sinϕ dρ dϕ dθ = kρ³ sinϕ dρ dϕ dθ. To obtain the mass of the hemisphere, we need to integrate the mass element over the appropriate limits, which are ρ = 0 to 1, ϕ = 0 to π/2, and θ = 0 to 2π.
Performing the integration, we get the mass as M = ∫∫∫ kρ³ sinϕ dρ dϕ dθ = πk/6.
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Find the area of the following ellipse. a = 4.5 m; b = 5.5 m
Answer:
Area of ellipse is ≈ 77.78 [tex]m^{2}[/tex]
Step-by-step explanation:
Given the dimension of ellipse
a = 4.5 m
b = 5.5 m
Now, Area of ellipse = [tex]\pi ab[/tex]
= [tex]\frac{22}{7}\times 4.5\times 5.5[/tex]
= [tex]\frac{5445}{70}[/tex]
= 77.78 [tex]m^{2}[/tex]
Hence Area of ellipse will be 77.78 [tex]m^{2}[/tex]
The area of the ellipse is calculated using the formula A = ab, with the given semi-major axis of 4.5 m and semi-minor axis of 5.5 m, estimated to two significant figures as 78 m².
The area A of an ellipse with semi-major axis a and semi-minor axis b is given by the formula A = \ab. Given that a = 4.5 m and b = 5.5 m, we can calculate the area of the ellipse using a calculator. Keeping in mind that we should report our final answer to the same number of significant figures as the least precise measurement provided (which in this case is two significant figures), we have:
A = \(4.5 m)(5.5 m)
A = 3.1415927... × 24.75 m²
A = 77.66546225 m²
However, due to the significant figures rule our reported answer should be:
A = 78 m²
how many number between 200 and 800 have the number 6?
Please help me with this
How do you solve 6<_2g?
Density is mass divided by volume. Find the mass of a gold bar if the density is 19.32 g/cm3 and the volume is 50 cm3.
Answer:
d
Step-by-step explanation:
denisity * volume = mass
Factor the monomial t^2-16t+48
a student uses a solution that contains 16 grams of water to conduct an evaporation experiment
the correct option is:
b.
Step 1:0.035 xx16=0.56
Step 2: 16-0.56=15.44
Step 3: 0.0425 xx15.44=0.6562
Step 4: 15.44-0.6562=14.7838
Let's break down the calculations:
Step 1: Calculate the amount of water lost at the end of the first hour.
[tex]\[ \text{Amount lost} = 0.035 \times 16 = 0.56 \][/tex]
Step 2: Subtract the amount lost from the initial amount to find the remaining water at the end of the first hour.
[tex]\[ \text{Remaining water} = 16 - 0.56 = 15.44 \][/tex]
Step 3: Calculate the amount of water lost at the end of the second hour.
[tex]\[ \text{Amount lost} = 0.0425 \times 15.44 = 0.6562 \][/tex]
Step 4: Subtract the amount lost from the remaining water at the end of the first hour to find the remaining water at the end of the second hour.
[tex]\[ \text{Remaining water} = 15.44 - 0.6562 = 14.7838 \][/tex]
So, the correct option is:
b.
Step 1:0.035 xx16=0.56
Step 2: 16-0.56=15.44
Step 3: 0.0425 xx15.44=0.6562
Step 4: 15.44-0.6562=14.7838
The complete Question is given below:
A student uses a solution that contains 16 grams of water to conduct an evaporation experiment.
At the end of one hour, the amount of water in the solution has decreased by 3.5% .
At the end of two hours, the amount of water in the solution has decreased by another 4.25% .
Which calculations can be used to determine the amount of water, in grams, remaining in the solution at the end of the second hour?
a.
Step 1:0.035 xx16=0.56
Step 2: 16-0.56=15.44
Step 3: 0.0425 xx15.44=0.6562
Step 4:16-0.6562=15.3438
b.
Step 1:0.035 xx16=0.56
Step 2: 16-0.56=15.44
Step 3: 0.0425 xx15.44=0.6562
Step 4: 15.44-0.6562=14.7838
c.
Step 1:0.35 xx16=5.6
Step 2: 16-5.6=10.4
Step 3: 0.425 xx10.4=4.42
Step 4:16-4.42=11.58
d.
Step 1: 0.35 xx16=5.6
Step 2: 16-5.6=10.4
Step 3: 0.425 xx10.4=4.42
Step 4:10.4-4.42=5.98
HELP ASAP PLEASE
Name the quadrant in which the point (x, y) lies.
x > 0 and y < 0
III
II
IV
I
Answer: quadrant 4
Step-by-step explanation:
PLEASE HELP You have just applied, and have been approved for a $175,000 mortgage. The rate quoted to you by the lender is 5.5% for a 30 year fixed mortgage. Use the provided table to determine how much of your first month’s payment goes towards the principal.
a.
$191.92
c.
$187.32
b.
$190.23
d.
$184.88
To calculate the portion of the first month's payment that goes towards the principal, we need the monthly payment amount, which is calculated from the loan amount, interest rate, and term. From there, we subtract the first month's interest from the monthly payment. In the absence of adequate information or a mortgage calculator, we cannot provide the correct option from (a-d).
Explanation:To determine how much of the first month's payment goes towards the principal of a $175,000 mortgage at a rate of 5.5% for a 30-year fixed mortgage, we need to calculate the monthly payment and then separate the interest from the principal.
The monthly payment M can be calculated using the formula:
M = P x (r(1+r)^n) / ((1+r)^n-1)
Where:
Next, we find the monthly interest portion by multiplying the principal by the monthly interest rate and subtract it from the monthly payment to find how much goes towards the principal.
Unfortunately, the information given does not provide a clear way to calculate the exact monthly payment or the portion applied to the principal without additional information or a financial calculator. In practice, you would use a formula or a mortgage calculator to find the total monthly payment, and then deduct the first month's interest to determine the amount applied to the principal. Without the correct formula or values, we can't determine the answer options (a-d) provided.
Which set of ordered pairs represents a function?
{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}
{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}
Answer:
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
Step-by-step explanation:
A set of ordered pairs in the format [tex](x,y)[/tex] represents a function if for each value of x, there is only one value for y.
The first set of ordered pairs is:
{(2, –2), (1, 5), (–2, 2), (1, –3), (8, –1)}
There are two values of y for [tex]x = 1[/tex]. This means that this set of ordered pairs does not represent a function.
The second set of ordered pairs is:
{(3, –1), (7, 1), (–6, –1), (9, 1), (2, –1)}
For each value of x here, there is only one value of y. This means that this set of ordered pairs represents a function. This is the answer.
The third set of ordered pairs is:
{(6, 8), (5, 2), (–2, –5), (1, –3), (–2, 9)}
There are two values of y for [tex]x = -2[/tex]. This means that this set of ordered pairs does not represent a function.
The fourth set of ordered pairs is:
{(–3, 1), (6, 3), (–3, 2), (–3, –3), (1, –1)}
There are two values of y for [tex]x = -3[/tex]. This means that this set of ordered pairs does not represent a function.
Write 2018 to the power of 2019 + 2018 as the sum of two perfect squares
Answer: I, III, and IV only
Step-by-step explanation:
In a right rectangles pyramid with base edges a= 18 cm and b= 10 cm the slant height toward a is k= 13 cm while the slant height towards b is l= 15 cm. What is the surface area of the pyramid
A number, half of that number, and one fifth of that number are added. The result is 51. What is the original number?
Final answer:
The original number is determined by setting up an algebraic equation based on the relationship given in the problem, solving for the variable, and using algebraic operations. The original number is found to be 30.
Explanation:
To find the original number when its half and fifth are added to it to get 51, we can set up an algebraic equation. Let's denote the original number as x. Half of that number would be x/2 and one fifth of that number would be x/5. The equation representing the given condition is:
x + x/2 + x/5 = 51
To solve this, we need a common denominator to combine the fractions:
Find the least common multiple (LCM) of 2 and 5, which is 10.Multiply the entire equation by 10 to clear the fractions: 10x + 5x + 2x = 510.Combine like terms: 17x = 510.Divide both sides by 17 to solve for x: x = 510 / 17, which simplifies to x = 30.Therefore, the original number is 30.
if you laid one of each size bolt end to end, how long would the row of bolts be?
3/8 inch, 1/2 inch, 5/8 inch, 7/8 inch, 1 1/4 inches.
The length of row of bolt will be calculated by adding the size of all the bolts.
Explain why a counter with an upper limit of five(101) resets at six (110)
hey can you please help me posted picture of question
Q2 Q13.) Use the given conditions to write an equation for the line in point-slope form and slope-intercept form.