Therefore, the rational function whose graph has an x-intercept at x=2.
What is function?In mathematics, a function is a rule that assigns to each input value from a set (called the domain) exactly one output value from another set (called the range). In other words, a function is a relationship between two sets of numbers, such that for each input value there is a unique output value. Functions are commonly denoted by an equation that defines the relationship between the input and output variables. For example, the equation y = f(x) defines a function f, where x is the input variable and y is the output variable.
Here,
To identify the rational function whose graph is given below, we need to determine its equation. We know that the graph has an x-intercept at x=2 and a y-intercept at y=−2/3.
We also know that the function is a rational function, which means it can be written as a ratio of two polynomials. The general form of a rational function is:
f(x) = p(x)/q(x)
where p(x) and q(x) are polynomials, and q(x) cannot be zero.
To find the specific equation of the function whose graph is shown, we can use the information about the intercepts to write down two points that are on the graph. We can use these points to set up a system of equations that we can solve for the coefficients of the polynomials p(x) and q(x).
Using the x-intercept, we know that the point (2,0) is on the graph. Using the y-intercept, we know that the point (0,-2/3) is on the graph. So we can set up the following system of equations:
p(2)/q(2) = 0
p(0)/q(0) = -2/3
Since the denominator of a rational function cannot be zero, we know that q(2) and q(0) cannot be zero. This allows us to set up a third equation:
q(x) ≠ 0
Now we can use algebra to solve for the coefficients of p(x) and q(x). We can start by writing the rational function in general form:
f(x) = p(x)/q(x)
and then multiplying both sides by q(x):
f(x)q(x) = p(x)
We can now substitute x=2 and x=0 to get two equations:
f(2)q(2) = p(2) = 0
f(0)q(0) = p(0) = -2/3
We also have the equation q(x) ≠ 0. This means that the denominator cannot have any factors that would make it equal to zero, so we can assume that q(x) has a linear factor of (x - 2), since we know that the graph has an x-intercept at x=2. We can then write:
q(x) = a(x - 2)
where a is some constant.
Now we can substitute this expression for q(x) into the equation f(x)q(x) = p(x) and simplify:
f(x)q(x) = p(x)
f(x)a(x - 2) = p(x)
We can now substitute x=0 and use the equation we found for p(0):
f(0)a(-2) = -2/3
f(0) = 1/3a
Next, we can substitute x=2 and use the equation we found for p(2):
f(2)a(0) = 0
f(2) = 0
Finally, we can substitute these values for f(0) and f(2) into the general form of the rational function and simplify:
f(x) = p(x)/q(x)
f(x) = p(x)/(a(x - 2))
We know that p(x) = f(x)q(x) from the equation we derived earlier, so we can substitute this into the equation above:
f(x) = f(x)(x - 2)/a(x - 2)
We can now cancel the f(x) terms from both sides and simplify:
1 = (x - 2)/a
a = x - 2
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HELLLLP I NEED THIS ANSWERED ASAP
Answer:
Step-by-step explanation:
3f(x) stretches the graph of the function by a factor of 3 since it is being multiplied to f(x) and 3 is greater than one.
f(x+3) shifts the graph of the function 3 units to the left since 3 equals h in the equation: f(x-h), so you switch the sign and it becomes negative thus moving left.
f(3x) compresses the graph by a factor of 1/3 since it is inside the parenthesis.
f(x) + 3 shifts the graph of the function up by 3 units since it is being added to f(x).
A 28 g serving of almonds has 160 calories. How many calories are in a 45 g serving of almonds?
Answer:
257.14 calories (about 260)
Step-by-step explanation:
To solve this problem, we can use proportions.
If a 28 g serving of almonds has 160 calories, then:
28 g / 160 calories = 45 g / x calories
where x is the number of calories in a 45 g serving of almonds.
We can cross-multiply and solve for x:
28 g * x = 160 calories * 45 g
x = (160 calories * 45 g) / 28 g
x = 257.14 calories
Therefore, a 45 g serving of almonds has 257.14 calories (rounded to two decimal places).
identify the dependant clause in the following sentence: i will put away my winter clothes and store the blankets in the upstairs closet when i no longer have to turn ob the furnace every day.
The dependent clause in the sentence is: "when I no longer have to turn on the furnace every day."
How to determine the dependent clauseThe sentence has two parts: the first part is an independent clause, which can stand alone as a complete sentence:
"I will put away my winter clothes and store the blankets in the upstairs closet."
The second part is a dependent clause, which cannot stand alone as a complete sentence, and it starts with the subordinating conjunction "when."
The dependent clause provides additional information on when the action of putting away winter clothes and storing blankets will happen, and it depends on the independent clause to make sense.
Hence, "when I no longer have to turn on the furnace every day" is the dependent clause.
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give the numerical value of the parameter n in the following binomial distribution scenario. the probability of buying a movie ticket with a popcorn coupon is 0.597 and without a popcorn coupon is 0.403. if you buy 18 movie tickets, we want to know the probability that no more than 13 of the tickets have popcorn coupons. Consider tickets with popcorn coupons as successes in the binomial distribution. Do not include n= in your answer.
Answer:
18
Step-by-step explanation:
pls give simpe working out
Answer:
b = 82
Step-by-step explanation:
Given
a =46 degrees
c = 52 degrees
Since XY is a straight line, it has an angle of 180 degrees
So, Angle a + angle b + angle c = 180 degrees
46 + angle b + 52 = 180
angle b + 98 = 180
angle b = 180 - 98
angle b = 82 degrees
Therefore angle b is equal to 82 degrees
Answer:
180 in a straight line
Step-by-step explanation:
there is 180⁰ in straight line.
46 + 52 is 98
180 - 98 is 82
6/cm
4 cm
Find the value of x.
X
x = [?]
Applying the secant-tangent theorem, the value of x is calculated as: x = 5.
What is the Secant-Tangent Theorem?The secant-tangent theorem states that if there is a point outside of a circle and we draw a tangent line and a secant line from that point to the circle, then the length of the tangent line squared is equal to the length of the secant line multiplied by the length of the part of the secant line that is outside the circle.
Therefore, applying the secant-tangent theorem:
4 * (x + 4) = 6²
4x + 16 = 36
4x = 36 - 16
4x = 20
4x/4 = 20/4
x = 5
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Blooming Flower Company was started in Year 1 when it acquired $60,000 cash from the issue of common stock. The following data summarize the company’s first three years’ operating activities. Assume that all transactions were cash transactions.
The recording of the transactions in the Blooming Flower Company for the Year 1 . The amount of depreciation expense on its Year 1 Income Statement is $9,000.
What is income tax?Income tax is a tax applied on individuals or entities concerning income or profit earned by them.
The Data Analysis as follows;
Cash $60,000 Common Stock $60,000
Equipment $40,000 Cash $40,000
Cash $72,000 Sales Revenue $72,000
Salaries Expense $25,000 Cash $25,000
Depreciation Expense - $9,000
Accumulated Depreciation $9,000 means ($40,000 - $4,000)/4
Now we have
Transaction Balance Sheet Income Statement StatemenCashFlows
Assets = Liabilities + Equity
Revenue - Expense = Net Income
1. +$60,000 = $0 + $60,000 FA
2. +40,000 - 40,000 IA
3. +72,000 = $0 + 72,000 +$72,000 OA
4. -25,000 = $0 - 25,000 - 25,000 OA
5. -9,000 = $0 - 9,000 - 9,000 N/A
$98,000 = $0 $98,000 $72,000 - $34,000 = $38,000
Where FA = Financing activity
IA = Investing activity
OA = Operating activity
N/A = Not applicable
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Test the following sequences for different types of convergence (i.e., linear, super linear, or quadratic), where n = 1, 2, 3 . . . .
a. xn = n^-2
b. xn = 2^-n
c. xn = 2^-2n
d. xn = 2^-an with a0 = a1 = 1 and an+1 = an+an-1 for n≥2
Answer:
a. The sequence x_n = n^-2 converges quadratically to zero as n approaches ∞.
b. The sequence x_n = 2^-n converges linearly to zero as n approaches ∞.
c. The sequence x_n = 2^-2n converges quadratically to zero as n approaches ∞.
d. The sequence x_n = 2^-a_n with a_0 = a_1 = 1 and a_n+1 = a_n+a_n-1 for n≥2 converges superlinearly to zero as n approaches ∞.
Step-by-step explanation:
a. The sequence {x_n} = {n^(-2)} converges quadratically to zero as n approaches ∞.
To see this, we can calculate the limit of the ratio between consecutive terms:
lim_{n -> ∞} (x_{n+1} / x_n) = lim_{n -> ∞} ((n+1)^(-2) / n^(-2)) = lim_{n -> ∞} ((n / (n+1))^2) = 1
Since the limit is equal to 1, we know that the convergence rate of {x_n} is at least quadratic. This can also be seen from the fact that the error in the nth term is O(n^(-3)), which is smaller than the error in a linearly converging sequence (which is O(n^(-1))).
b. The sequence {x_n} = {2^(-n)} converges linearly to zero as n approaches ∞.
To see this, we can calculate the limit of the ratio between consecutive terms:
lim_{n -> ∞} (x_{n+1} / x_n) = lim_{n -> ∞} (2^(-(n+1)) / 2^(-n)) = lim_{n -> ∞} (1/2) = 1/2
Since the limit is strictly less than 1, we know that the convergence rate of {x_n} is linear.
c. The sequence {x_n} = {2^(-2n)} converges quadratically to zero as n approaches ∞.
To see this, we can calculate the limit of the ratio between consecutive terms:
lim_{n -> ∞} (x_{n+1} / x_n) = lim_{n -> ∞} (2^(-(2(n+1))) / 2^(-2n)) = lim_{n -> ∞} (1/4) = 1/4
Since the limit is equal to 1/4, we know that the convergence rate of {x_n} is at least quadratic. This can also be seen from the fact that the error in the nth term is O(n^(-2)), which is smaller than the error in a linearly converging sequence (which is O(n^(-1))).
d. The sequence {x_n} = {2^(-a_n)}, where a_0 = a_1 = 1 and a_{n+1} = a_n + a_{n-1} for n >= 2, converges superlinearly to zero as n approaches ∞.
To see this, we can use the fact that a_n grows exponentially with n. We can prove by induction that a_n >= phi^n, where phi is the golden ratio. Since the terms of {x_n} are decreasing and bounded below by 0, they must converge to a limit L. Taking the limit of the ratio of consecutive terms, we get:
lim_{n -> ∞} (x_{n+1} / x_n) = lim_{n -> ∞} (2^(-a_{n+1}) / 2^(-a_n)) = lim_{n -> ∞} (2^(-a_n - a_{n-1})) = 0
This shows that the convergence rate of {x_n} is superlinear.
PLEASE PLEASE PLEASE HELP ASAP
Answer:
Step-by-step explanation:
We can start by simplifying the denominator, which is cot(a) + tan(a):
cot(a) + tan(a) = cos(a)/sin(a) + sin(a)/cos(a)
To combine these terms, we can find a common denominator of sin(a)cos(a):
cos^2(a)/(sin(a)cos(a)) + sin^2(a)/(sin(a)cos(a))
= (cos^2(a) + sin^2(a))/(sin(a)cos(a))
= 1/(sin(a)cos(a))
Now we can substitute this expression into the original equation:
sec(a)/(cot(a) + tan(a))
= sec(a) / (1/(sin(a)cos(a)))
= sec(a) * (sin(a)cos(a))
= (1/cos(a)) * (sin(a)/cos(a))
= sin(a)/cos^2(a)
= csc(a)sec(a)
Therefore, the simplified form of sec(a)/(cot(a) + tan(a)) is csc(a)sec(a).
The graph below shows a transformation of y=2^x
Write an equation for the graph above.
The equation of the graph given is y = -([tex]2^x[/tex] - 2).
What is translation?It is the movement of the shape in the left, right, up, and down directions.
The translated shape will have the same shape and shape.
There is a positive value when translated to the right and up.
There is a negative value when translated to the left and down.
We have,
y = [tex]2^x[/tex]
The transformation of the function to get the given graph.
Step 1:
Shrink vertically with a scale factor of 2.
Step 2:
Rotation of the function about the origin.
We get,
y = -([tex]2^x[/tex] - 2)
Thus,
The equation of the graph is y = -([tex]2^x[/tex] - 2).
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The venom of Conus geographus is extremely toxic to humans. The neurotoxins of the cone shell are small peptides of fewer than 30 amino acids that target the neuronal communication sequence to achieve paralysis. The normal prey of geographus are small fish. Envenomation in humans leads to a wide range of symptoms. Sixty percent of the victims experience intense pain, 75% experience swelling around the wound, and 40% have both symptoms. (a) Draw an appropriate Venn diagram for these data (b) Are the two symptoms independent of each other? (c) What is the probability that the victim will experience at least one of these symptoms? (d) If a victim experiences swelling, what is the probability he will also have intense pain? (e) What is the probability that a victim will experience pain but not swelling? (f) What is the probability that a victim will not experience either symptom?
Therefore , the solution of the given problem of probability comes out to be probability of not experiencing either symptom is 0.05.
What precisely does the probability method suggest?Calculating the likelihood that a statement is true or that an event will take place is the focus of probability theory, a branch of mathematics. Any number range between 0 and 1, where 1 is frequently used to describe certainty and 0 is commonly used to denote possibility, can be used to represent chance. A probability diagram shows the likelihood that a particular event will occur.
Here,
To determine if the two symptoms are independent, we need to check if the probability of one symptom changes depending on whether the other symptom is present or not.
P(pain | swelling) = 40% / 75% = 0.533
P(pain | no swelling) = 20% / 25% = 0.8
Since the conditional probabilities are not equal, the two symptoms are dependent.
(c) The probability that the victim will experience at least one of these symptoms is the probability of experiencing pain, swelling, or both. This can be calculated as:
P(pain or swelling) = P(pain) + P(swelling) - P(pain and swelling)
= 60% + 75% - 40%
= 95%
So the probability of experiencing at least one of these symptoms is 95%.
(d) The probability that a victim will have intense pain given that they have swelling is the conditional probability:
P(pain | swelling) = 40% / 75%
= 0.533
So the probability of having intense pain given that there is swelling is 0.533.
(e) The probability that a victim will experience pain but not swelling can be calculated as:
P(pain and no swelling) = P(pain) - P(pain and swelling)
= 60% - 40%
= 20%
So the probability of having intense pain without swelling is 20%.
(f) The probability that a victim will not experience either symptom is the complement of the probability of experiencing at least one symptom:
P(neither pain nor swelling) = 1 - P(pain or swelling)
= 1 - 0.95
= 0.05
So the probability of not experiencing either symptom is 0.05.
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In a two-digit number, the units digit is one more than the tens digit. If the digits are reversed, the sum of the reversed number and the original number is 187. Find the original number.
The tens digit is 8, and the units digit is 9 (since y = x + 1). Therefore, the original number is 89.
Describe Equation?In mathematics, an equation is a statement that asserts the equality of two expressions. An equation contains one or more variables, which are unknown values that can vary or change. The variables are usually represented by letters such as x, y, or z. The expressions on either side of the equals sign can be constants, variables, or functions of variables.
The simplest form of an equation is a linear equation, which can be represented as ax + b = c, where a, b, and c are constants and x is a variable. To solve a linear equation, we need to find the value of the variable that makes the equation true. This is done by performing arithmetic operations on both sides of the equals sign to isolate the variable.
Equations can also be more complex, involving multiple variables, powers, and functions. In such cases, algebraic techniques such as factoring, substitution, and solving systems of equations may be required to find the solution.
Equations are used to describe relationships between variables in many fields of study, including physics, chemistry, economics, and engineering. They are also used in everyday life, such as in calculating the cost of a purchase after applying a discount, or determining the amount of time it takes to travel a certain distance
Let's represent the tens and units digits with x and y, respectively. According to the problem statement, we have two equations:
y = x + 1 (the units digit is one more than the tens digit)
10x + y + 10y + x = 187 (the sum of the original number and the reversed number is 187)
Simplifying the second equation, we get:
11x + 11y = 187
x + y = 17 (dividing both sides by 11)
Substituting y = x + 1 into the second equation, we get:
x + (x + 1) = 17
2x + 1 = 17
2x = 16
x = 8
So the tens digit is 8, and the units digit is 9 (since y = x + 1). Therefore, the original number is 89.
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Which of the following operators allows you to specify a range and is often used with date criteria? a) in b) NOT c) BETWEEN d) LIKE
Therefore , the solution of the given problem of range comes out to be option c) BETWEEN .
What is the range?The variable's range is calculated by multiplying the maximum observed value by its minimum observed (minimum). Variable steel prices and different designs are two examples of potential range or central difference limits. The breadth or scope of a process or action gives a hint as to the utmost or anticipated spread of a weapon's missile. The range of a list or subgroup is the integer between its lowest and maximum.
Here,
To specify a range and is often used with date criteria
the operation which we use :
Is option c) BETWEEN
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Cuanto costaba un abrigo que , tras experimentar una rebaja del 40% y a continuación una subida del 30% ahora cuesta 56,16€?
Por lo tanto, el precio original del abrigo era de 72€
Para resolver este problema, primero debemos determinar el precio original del abrigo antes de las rebajas.
Sea x el precio original del abrigo.
Después de aplicar la primera rebaja del 40%, el precio del abrigo sería:
x - 0.4x = 0.6x
Luego, tras la subida del 30%, elprecio se incrementaría al 130% del precio anterior:
1.3(0.6x) = 0.78x
Sabemos que este precio final es de 56,16€, por lo que podemos resolver la ecuación:
0.78x = 56.16
x = 72
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if there are 12 dogs and 48 cats at a pet daycare, fill out all of the possible ratios of dogs to cats that could be made.
The possible ratios of dogs to cats that could be made is
12 : 48 , 6 : 24 , 3 : 12 , 1 : 4 and soon.
What is ratio in math?
When b does not equal 0, an ordered pair of numbers a and b, represented as a / b, is said to be a ratio. A percentage is an equation in which two ratios are made equal to one another.
As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls (for every one boy there are 3 girls)
Given ,
If there are 12 dogs and 48 cats at a pet daycare,
So, we have to fill out all of the possible ratios of dogs to cats that could be made.
ratio could be = 12 : 48
12 : 48 = 1 : 4
6 : 24 = 1 : 4
3 : 12 = 1 : 4
1 : 4 = 1 : 4
Therefore, The possible ratios of dogs to cats that could be made is
12 : 48 , 6 : 24 , 3 : 12 , 1 : 4 and soon.
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please help! math question!
Simplifying, the exponents expression, we have 63y/xu⁴
What are exponents?Exponents are the powers to which a particular number is raised.
How to simplify the expression?Given the expression 3y⁻⁴ . 3y⁵x⁸u⁻⁵.7x⁻⁹. To simplify the expression, we use the product rule of exponents which states that for a given base x, xᵃ xᵇ = xᵃ⁺ᵇ.
So, applying this rule to the expression and collecting common bases, we have that
3y⁻⁴ . 3y⁵x⁸u⁻⁵u.7x⁻⁹ = 3y⁻⁴ × 3y⁵ × x⁸ × 7x⁻⁹ × u⁻⁵ × u
= 3 × 3 × y⁻⁴ × y⁵ × 7 × x⁸ × x⁻⁹ × u⁻⁵ × u
Applying the product rule, we have that
= 3 × 3 × y⁻⁴ ⁺ ⁵ × 7 × x⁸ ⁺(⁻⁹) × u⁻⁵ ⁺ ¹
= 3 × 3 × y⁻⁴ ⁺ ⁵ × 7 × x⁸ ⁻ ⁹ × u⁻⁵ ⁺ ¹
= 3 × 3 × y × 7 × x⁻¹ × u⁻⁴
= 3 × 3 × 7 × y × x⁻¹ × u⁻⁴
Using the reciprocal rule that x⁻ⁿ = 1/xⁿ, we have that
= 3 × 3 × 7 × y × x⁻¹ × u⁻⁴
= 63 × y × 1/x × 1/u⁴
= 63y/xu⁴
So, simplifying, we have 63y/xu⁴
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You need to solve a system of equations. You decide to use the elimination method.which of these is not allowed? 2x-3y=12 equation 1 and -x+2y=13 equation 2
The solution to the system of equations is x = 34.5, y = 19.
None of the operations that can be performed on these equations violate the rules of the elimination method, so they are all allowed.
To solve the system of equations using the elimination method, you can multiply equation 2 by 2 to obtain:
-2x + 4y = 26 (equation 2, multiplied by 2)
Then, you can add this equation to equation 1 to eliminate the x variable:
(2x - 3y) + (-2x + 4y) = 12 + 26
Simplifying and solving for y, you get:
y = 19
Substituting this value of y into either equation, you can solve for x:
2x - 3(19) = 12
2x - 57 = 12
2x = 69
x = 34.5
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Use the dropdown to complete the following inequality.
1- a ? 0
The complete sentence with inequality is,
⇒ 1 - a > 0
What is Inequality?A relation by which we can compare two or more mathematical expression is called an inequality.
Given that;
The number line is shown in figure.
By figure, the value of a is in between - 1 and - 2.
Hence, It is negative number.
Thus, We can assume,
⇒ a = - x
Hence, We get;
⇒ 1 - a
⇒ 1 - (- x)
⇒ 1 + x > 0
Thus, The complete sentence with inequality is,
⇒ 1 - a > 0
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Determine if the triangles are congruent. If they are, state how you know.
*
The triangles are congruent by ''ASA congruency theorem.''
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Given that;
Two triangles PQT and PZX are shown in figure.
Now, By figure;
In both triangles PQT and PZX,
⇒ ∠ QTP = ∠ PXZ
⇒ PQ = PZ
⇒ ∠ QPT = ∠ XPZ (By definition of vertically opposite angle.)
Thus, By ASA congruency theorem both triangles are congruent.
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four out of twelve people went out of town for the holidays. what percent of the people stayed home for the holidays
Answer:
66.67
Step-by-step explanation:
8 people stayed home, 8/12=2/3=66.67(approx)
Solve for x. Show work.
Answer:
x = -7.8
Step-by-step explanation:
Solve for x:
[tex]x-(-3.9)=-3.9[/tex]
Simplify
[tex]x+3.9=-3.9[/tex]
Subtract 3.9 on both sides
[tex]x=-7.8[/tex]
DIRECTION: Determine the validity of the following arguments.
Note that the above is solved using a Truth Table. The truth table is attached accordingly. Note that the argument is invalid
What is a truth table?A truth table is a table that displays all possible combinations of truth values for the propositional variables in a logical expression and the resulting truth value of the expression.
It is an important tool in logic as it enables us to determine the validity of arguments, identify tautologies and contradictions, and simplify complex expressions. Truth tables provide a systematic and rigorous method of evaluating logical expressions and reasoning about their truth values.
With respect to the table, since there is at least one row where all premises are true but the conclusion is false (the fifth row in this case), the argument is invalid
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what is the y intercept when the coordinate is 4,-1 and the slope is -2
Answer:
y- intercept = 7
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
here m = - 2 , then
y = - 2x + c ← is the partial equation
to find c substitute (4, - 1 ) into the partial equation
- 1 = - 2(4) + c = - 8 + c ( add 8 to both sides )
7 = c
that is the y- intercept = 7
A weight hanging from a spring bobs up and down starting from a lowest height of 4 feet to a maximum height of 10 feet. It completes one full cycle in 3 seconds (that means at time t=0 the weight is at the height of 4 feet and at the time of t=3 seconds the weight is back at that same height again) a. Find a model () = (( − )) + D describing the motion of the weight. Show all work and include three values checking the model is correct. b. What will be the height of the weight at t=1.5 seconds? c. Draw a graph of the model for two periods.
The weight's height at t=1.5 seconds is roughly 8.07 feet.
a. The equation for simple harmonic motion can be used to find a model that describes the motion of the weight:
Acos(wt + phi) + D = y(t)
A represents amplitude, w represents angular frequency, phi represents phase shift, and D represents vertical shift.
The amplitude A is equal to half the difference between these two heights because we know the weight oscillates between a minimum height of 4 feet and a maximum height of 10 feet:
A = (10 - 4)/2 = 3
The weight completes a full cycle in three seconds, hence the weight's angular frequency is:
T = 2pi/3 and w = 2pi
where T, or the period, denotes the length of time for one complete cycle.
We can set phi to 0 because the weight begins at the lowest height of 4 feet. Last but not least, the vertical shift D is just the average of the highest and lowest heights:
D = (10 + 4)/2 = 7
Combining everything, we obtain:
Y(t) equals 3cos((2pi/3)*t) + 7
b. By simply entering t=1.5 into our model, we can determine the height of the weight at t=1.5 seconds:
3cos((2pi/3)*1.5)*y(1.5) + 7 + 8.07
Hence, the weight's height at t=1.5 seconds is roughly 8.07 feet.
c. We can plot y(t) for t ranging from 0 to 6 seconds in order to graph the model for two periods (two full cycles). The graph is shown here:
code
|
10 | *
| * *
| * *
| * *
7 | * *
| * *
| * *
| * *
4 | * *
+-----------------------------
0 1 2 3 4 5
The graph demonstrates that the weight oscillates sinusoidally with a period of 3 seconds between 4 and 10 feet. In contrast, the minimum height is reached at t=0 seconds and the maximum height is obtained at t=1.5 seconds and t=4.5 seconds.
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A scale factor of a famous statue uses a scale factor of 210:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?
Answer:
A scale factor of a famous statue uses a scale factor of 210:1. If the height of the drawing is 1.2 feet, what is the actual height of the statue?
The actual height of the statue is 252 feet (1.2 x 210).
Answer:
252
Step-by-step explanation:
tan(−0.9)
Find an approximate value of the given trigonometric function by using the figure and a calculator.
tan(−0.9)
We can write tan(− 0.9) as -
tan(− 0.9) = -1.26.
What is tangent function?Tangent function is defined as the ratio of perpendicular and base. Mathematically, we can write -
tan(Ф) = p/b
tan(Ф) = perpendicular/base
Given is to find the value of tan(− 0.9).
We know -
1 radian = 57.2958 degrees
0.9 radian = 57.3 x 0.9 = 51.57 degrees
0.9 radian = 51.57 degrees ... { 1 }
So, we can write -
tan(− 0.9) = tan( - 51.57°) = - 1.26
Therefore, we can write tan(− 0.9) as -1.26.
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100 POINTS If a business owner paid for all business assets with their own money, what percent of the profits will they receive?
A. 100%
B. 95%
C. 75%
D. 50%
Answer:
A. 100%
Step-by-step explanation:
Business owners will recieve 100% of their profits, because they paid for them. The recommended profits are 50% because they need to pay employees as well.
Answer please, I'll give brainlyist
Answer:
(1,-1)
Step-by-step explanation:
Answer:
Option B: [tex](1, -1)[/tex]
Step-by-step explanation:
The two equations are linear simultaneous equations, which can be solved by either the substitution, elimination or graphical method.
Substitution method:
Formulate an expression for x in terms of y by isolating x and making it the subject of the equation:
[tex]x + 2y = -1[/tex]
∴ [tex]x = -2y -1[/tex] —— (equation i)
[tex]2x - 3y = 5[/tex] ——- (equation ii)
Substitute (equation i) in (equation ii) to solve for y:
[tex]2(-2y -1) - 3y = 5[/tex]
Expand the brackets or parenthesis using the Distributive Law:
[tex]-4y -2 -3y = 5[/tex]
Bring all the like terms together. Isolate the y terms together on one side of the equation and move all the other terms to the other side:
[tex]-4y -3y = 5 + 2[/tex]
= [tex]-7y = 7[/tex]
= [tex]y = -\frac{7}{7}[/tex]
∴ y = [tex]-1[/tex]
Substitute this calculated value of y into any of the equations to solve for x:
[tex]x = -2(-1) - 1[/tex]
[tex]= 2 - 1[/tex]
∴ x = [tex]1[/tex]
Together these x and y values form an ordered pair. In addition, this ordered pair is a solution to both the equations and also considered the point of intersection of the two equations
∴ Option B: [tex](1, -1)[/tex]
6/cm
4 cm
Find the value of x.
X
x = [?] cm
The value of x is given as follows:
x = 3.
How to obtain the length of AC?Applying the secant-tangent theorem, we have that the following equation holds true:
4x² = 6².
Hence we can solve the equation for x to obtain the value of x, as follows:
4x² = 36
x² = 36/4
x² = 9
x = sqrt(9)
x = 3.
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Solve for d.
d+5≥6 solve one step liner inequality
The range of value for d is d ≥ 1
What is inequality?Inequality, In mathematics is a statement of an order relationship. Greater than, greater than or equal to, less than, or less than or equal to—between two numbers or algebraic expressions.
Greater than is >
Greater then or equal to is ≥
less than <
less then or equal to ≤
d + 5≥ 6
add the additive inverse of 5 to both sides
d+5+(-5) ≥ 6+(-5)
d ≥ 6-5
d ≥ 1
therefore the range of value of d is d ≥ 1
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