The inverse Laplace transform of the given function is f(t) = (7/5) * sin(5t).
To find the inverse Laplace transform of the given function, we will use the formula:
L-1 {F(s)} = (1/2πi) ∫C e(st) F(s) ds
Where C is a Bromwich contour, i is the imaginary unit and F(s) is the Laplace transform of the function we are interested in.
Using Theorem 7.2.1, we can express the given function as:
7/([tex]s^2[/tex]+[tex]5^2[/tex]) = 7/[tex]5^2[/tex] * 1/(1+(s/5)2)
This is the Laplace transform of the function f(t) = (7/5) e(-5t) sin(5t), according to Table 7.1.
Therefore, applying the inverse Laplace transform formula, we have:
= (1/2πi) ∫C e(st) [7/([tex]5^2[/tex])] [1/(1+(s/5)2)] ds
To evaluate this integral, we need to close the Bromwich contour C in the left half of the complex plane, since the function has poles at s = ±5i, which are located in the right half of the plane.
Therefore, we can use the residue theorem to obtain:
L-1 {7/([tex][tex]s^2[/tex][/tex]+52)} = (1/2πi) (2πi i/5) e(-5t) sin(5t)
= (1/5) e(-5t) sin(5t)
So the inverse Laplace transform of 7/(s2+25) is f(t) = (1/5) e^(-5t) sin(5t).
Therefore, the answer to this question is:
L^-1 {7/s^2+25} = (1/5) e(-5t) sin(5t)
The inverse Laplace transform of A/([tex]s^2[/tex] + [tex]w^2[/tex]) is given by (A/w) * sin(wt).
In this case, A=7 and w=5, so we can plug these values into the formula: L^(-1){7/(s^2+25)} = (7/5) * sin(5t).
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To find the inverse Laplace transform of 7/(s^2 + 25), we first need to use appropriate algebra to simplify the expression. We can factor out a 7 from the numerator to get 7/(s^2 + 25).
Then, we can use Theorem 7.2.1 which states that the inverse Laplace transform of 1/(s^2 + a^2) is sin(at)/a. In our case, a = 5 (since a^2 = 25) and the inverse Laplace transform of 7/(s^2 + 25) is therefore 7sin(5t)/5. This function represents the time-domain response of the original Laplace-transformed signal.
To find the inverse Laplace transform of the given function, L^-1 {7/(s^2+25)}, we'll use appropriate algebra and Theorem 7.2.1, which states that the inverse Laplace transform of F(s) = k/(s^2 + k^2) is f(t) = sin(kt).
1. Identify the values of k and the constant in the given function. In this case, k^2 = 25, so k = 5. The constant is 7.
2. Apply Theorem 7.2.1 to the function. Since F(s) = 7/(s^2 + 25), the inverse Laplace transform f(t) = 7 * sin(5t).
So, the inverse Laplace transform of L^-1 {7/(s^2+25)} is f(t) = 7 * sin(5t).
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7 1/3t - (10 2/3t - 6)
Answer:
[tex]-3 \frac{1}{3}t+6[/tex]
Step-by-step explanation:
Given expression:
[tex]\sf 7\frac{1}{3}t-\left(10 \frac{2}{3}t-6\right)[/tex]
Remove the parentheses:
[tex]\implies \sf 7\frac{1}{3}t-10 \frac{2}{3}t+6[/tex]
Factor out the common term t:
[tex]\implies \sf \left(7\frac{1}{3}-10 \frac{2}{3}\right)t+6[/tex]
Change the mixed numbers into improper fractions:
[tex]\implies \sf \left(\dfrac{7 \cdot 3+1}{3}-\dfrac{10 \cdot 3+2}{3}\right)t+6[/tex]
[tex]\implies \sf \left(\dfrac{22}{3}-\dfrac{32}{3}\right)t+6[/tex]
Subtract the fractions:
[tex]\implies \sf \left(\dfrac{22-32}{3}\right)t+6[/tex]
[tex]\implies \sf \left(\dfrac{-10}{3}\right)t+6[/tex]
Convert the improper fraction back into a mixed number:
[tex]\implies -3 \frac{1}{3}t+6[/tex]
3 1/2k + 3/4 = -7/8
50 points reward! I need help immediately.
The value of k in the given equation is -0.104839
What is the equation in maths?A mathematical expression with an equals sign is referred to as an equation. Algebra is widely used in equations. When performing calculations but unsure of the precise amount, algebra is utilized.The point-slope form, standard form, and slope-intercept form are the three main types of linear equations.Finding an equation's solutions, which are values (numbers, functions, sets, etc.) that satisfy the equation's condition and often consist of two expressions connected by an equals sign, is known as solving an equation in mathematics.The definition of an equation in algebra is a mathematical statement that demonstrates the equality of two mathematical expressions. For instance, the equation 3x + 5 = 14 consists of the two equations 3x + 5 and 14, which are separated by the 'equal' sign.Evaluate
[tex]\frac{31}{2}[/tex]k + [tex]\frac{3}{4}[/tex] = - [tex]\frac{7}{8}[/tex]
Move the constant to the right side
[tex]\frac{31}{2}[/tex]k = [tex]-\frac{7}{8} - \frac{3}{4}[/tex]
Subtract the terms
[tex]\frac{31}{2}[/tex]k = [tex]-\frac{13}{8}[/tex]
Multiply both sides
[tex]\frac{31}{2}[/tex]k x [tex]\frac{2}{31} = - \frac{13}{8} * \frac{2}{31}[/tex]
k = [tex]-\frac{13}{124}[/tex]
k = - 0.104839
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Explain how to balance the equation. p-56=139
Anyone knowwwwwwwwwwww
The average rate of change is 19 3 ≤19 ≤15
What is average rate of change ?It is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graph.To find the average rate of change, divide the change in y-values by the change in x-values. Finding the average rate of change is particularly useful for determining changes in measurable values like average speed or average velocityIt is a measure of how much the function changed per unit, on average, over that interval. It is derived from the slope of the straight line connecting the interval's endpoints on the function's graphTo learn more about average rate of change refers to:
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Use a trigonometric ratio to solve for a. Round to two decimal places as necessary!!
HELP, and can someone explain how to get the answer?
help please and thank you
The product of a, b and c would be 6.
What is an expression?
An expression is a mathematical phrase that can contain numbers, variables, and operators. Expressions do not contain an equal sign and they can't be solved for a single value. They are used to represent a value or a set of values.
The given expression is [tex]\frac{\sqrt[4]{16xy^4}}{x^{\frac{1}{2}}y^{\frac{1}{2}}}[/tex]
In order to write the expression in the form of [tex]ax^by^c[/tex], we need to simplify it.
First, we simplify the fourth root of [tex]16xy^4[/tex] by taking the fourth root of 16, which is 2. So, the expression becomes
[tex]2\frac{xy^4}{x^{\frac{1}{2}}y^{\frac{1}{2}}}[/tex]
Next, we simplify the fraction by canceling out the[tex]x^{\frac{1}{2}} $$ and $ y^{\frac{1}{2}}[/tex] from the numerator and denominator. This gives us [tex]2xy^3[/tex]
So the expression in the form of [tex]ax^by^c[/tex] is [tex]2xy^3[/tex], where a = 2, b=1, and c=3.
the product of a, b, and c is 2 * 1 * 3 = 6.
Hence, the product of a, b and c would be 6.
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The perimeter of a rectangle is 50 inches the length of the rectangle is 10 inches.
We will use the method of linear equations to get the width of the rectangle, which is 15 inches.
Here we are given that the length of the rectangle is 10 inches and the perimeter is 50 inches.
We know that the perimeter of a shape is the length of the boundary of that shape.
The formula for the perimeter of a rectangle is 2(l + b)
= 2 X (length of the rectangle + breadth of the rectangle)
Here length, l = 10 inches, the perimeter is 50 inches, and we have been to consider breadth to be w inches.
Hence we can use the formula of the perimeter and the method of a linear equation to get the width.
Hence we get
2(10 + w) = 50
or, 10 + w = 25
or, w = 25 - 10
or, w= 15 inches.
Hence the width is 10 inches wide.
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Complete Question
The perimeter of a rectangle is 50 inches. The length of the rectangle is 10 inches. Which method can be used to find w, the width of the rectangle?
A virus is spreading around Brookfield. At the moment, 685 people are infected. If the virus is
spreading at a rate of 13% each day, how many people in all will have caught the virus in 3
days?
If necessary, round your answer to the nearest whole number.
A virus spreading around Brookfield will infect 988 people in the next 3 days.
What is an equation?
A mathematical definition of an equation is a claim that two expressions are equal when they are joined by the equals sign ("=").
Number of people infected by the virus = 685
The rate at which the virus is infecting = 13%
The virus is spreading at 13% rate each day.
To deduce the number of people who will get infected in next 3 days.
The final equation will be -
= 685 × ( 1 + 13%)³
= 685 × (113/100)³
= 685 × (1.13)³
= 685 × 1.442
= 987.77 ≈ 988
Therefore, the number of people who will get infected is 988.
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Identify the transformations of the function g(x)=-½(x-6)2+3 compared to the parent function f(x)=x2
If [tex]f(x)=x^2[/tex] and [tex]g(x) = -\frac{1}{2}(x-6)^2 + 3[/tex],
then:
the negative is a reflection over the x-axis.the [tex]\frac{1}{2}[/tex] is a vertical compression by a factor of 1/2the [tex]{}-6[/tex] shifts the graph 6 units to the rightthe [tex]{}+3[/tex] shifted the graph up by 3 units.So the graph has been flipped upside-down, squished vertically, moved right and up.
graph each equation. determine the solution of the system of equations. x+2y=4 3x+2y=0
Answer:
(-2,3) or x= -2 and y= 3
Step-by-step explanation:
I didn't graph this, but you could.
For the first equation: Subtract x from both sides to get 2y= -x +4
Next divide both sides by 2 to get y= -1/2x + 2 (Now graph this)
For the second equation subtracted both sides by -3x to get 2y= -3x
Next, divide both sides by 2 to get y= -3/2x (Now graph this)
I used elimination. I wrote both equations out then subtracted 2y from both of them then did -2x = 4
x= -2
then I substitued -2 + 2y = 4
6 = 2y
y=3
Equation to represent lengths of triangle DEF
Answer:
Step-by-step explanation:
watch the other parralleles cotés
The Pythagorean Theorem, one of the most well-known mathematical formulas, tells us how a right triangle's sides relate to one another. The hypotenuse, along with the two legs, make up a right triangle. The hypotenuse, the longest side of the right triangle and the side opposite the right angle, is where the two legs of a right triangle come together at a 90° angle.
Equation to represent the length -
a2 + b2 = c2
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What two events are independent
The equation that must be true for event C and D to be independent are P(C│D) = P(C) and
P(D│C ) = P(D).
What are independent event ?Two events are independent if the occurrence of one event does not affect the chances of the occurrence of the other event. The mathematical formulation of the independence of events A and B is the probability of the occurrence of both A and B being equal to the product of the probabilities of A and B (i.e., P(A and B)
For two events C and D. For the two events to be independent events then;
P(C│D) = P(C∩ D)/ P(D) = P(C)
or
P(D│C) = P(D∩ C)/ P(C) = P(D)
For example if a fair die is rolled,
P(D ) = Probability of getting a 3
P(C) = Probability of getting an even number
P(C│D) = P(C∩ D)/ P(D)
P(C∩ D)= 1/3 × 1/2 = 1/6
P(C│D) = P(C∩ D)/ P(C) = 1/6 ÷ 1/3 = 1/2
therefore P(C│D) = P(C) and
P(D│C ) = P(D).
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Points C and D on the coordinate grid below show the positions of two midfield players of a soccer team:
The coordinate grid is shown from negative 4 to positive 4 on the x-axis and negative 4 to positive 4 on the y-axis. From the origin, point C is 1.5 units to the left and 3 units up. From the origin, point D is 1.5 units to the right and 3 units up.
Which statement best describes the relationship between the positions of the two midfield players?
The correct option 3. D is C reflected across the y-axis; only the signs of the x-coordinates are different for C and D.
Explain the meaning of reflection of the coordinates?A figure is transformed into a reflection by a transformational process. In a point, linear line, or a plane, figures can be reflected. The image and preimage coincide when reflecting a graphic in a line or a point.The locations of C and D's coordinates are supplied to us as follows:
Point C is 1.5 units towards the left as well as 3 units up from the origin.x = -1.5 units away from the origin. Origin is at 1.5 and 3 up, or y = 3.As a result, C is the first coordinate just on axis (-1.5, 3).
Point D is 1.5 units toward the right as well as 3 units up from the origin.X is equal to 1.5 units to the origin's right, while Y is equal to 3 units to the origin.As a result, D is the second coordinate upon that axis (1.5, 3).
We can observe that the sign of the x-coordinates for C and D is opposite.It would be a reflection over the y-axis if the sign of the x coordinates were opposite.Thus, the statement D is C mirrored across the y-axis, with the only difference between C and D being the sign of the x-coordinates, best captures the relationship between the locations of the 2 midfield players.
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The complete question is-
Points C and D on the coordinate grid below show the positions of two midfield players of a soccer team:
Coordinate grid shown from negative 4 to positive 4 on x-axis and negative 4 to positive 4 on y-axis. From the origin, point C is 1.5 units to the left and 3 units up. From the origin, point D is 1.5 units to the right and 3 units up.
Which statement best describes the relationship between the positions of the two midfield players?
D is C reflected across the x-axis; only the signs of the x-coordinates are different for C and D.D is C reflected across the x-axis; only the signs of the y-coordinates are different for C and D.D is C reflected across the y-axis; only the signs of the x-coordinates are different for C and D.D is C reflected across the y-axis; only the signs of the y-coordinates are different for C and D.Isabella spends $4.87 on paintbrushes and paint. How many of each item does she buy? $0.99 each for a jar of paint. $0.95 each for a paintbrush
Answer:
Isabella can buy together 5 paintbrushes ( p ) and jars of paint ( p ) : j + p = 5, She can`t buy 4 items ( because 4 * $0.99 = $3.96 < $4.87 ) and she also can`t buy 6 items ( 6 * $0.95 = $5.70 > $4.87 ). So: p = 5 - j. Another equation is: 0.95 * ( 5 - j ) + 0.99 j = 4.87, 4.75 - 0.95 j + 0.99 j = 4.87; 0.04 j = 0.12; j = 0.12 : 0.04; j = 3, p = 5 - 3 = 2. We can prove it: 0.95 * 2 + 0.99 * 3 = 1.90 + 2.97 = 4.87. Answer: Isabella buys 2 paintbrushes and 3 jars of paint.
What is the equation of the line that passes through (0, 3) and is perpendicular to y = 34x + 5?.
The equation of a line that is perpendicular to the line y = 34x + 5 and passes through the point (0, 3) is y = -34x + 3
The slope-intercept form of the equation of a line is y = mx + c, where
m is the slope of the line c is the y-intercept.The slope of a line perpendicular to another line is the negative reciprocal of the original line's slope. In this case, the original line has a slope of 34, so the slope of the line that is perpendicular to it is -1/34.
To find the y-intercept of the line, we can use the point (0,3) that the line passes through. Substituting the x and y values of this point into the equation of the line, we get 3 = -34(0) + c, which simplifies to c = 3.
So the equation of the line that is perpendicular to y = 34x + 5 and passes through (0, 3) is y = -1/34x + 3
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What is an inequality Class 7?
An inequality is a mathematically explicable relationship between two expressions that can be represented by any of the following symbols: >, <, ≤, ≥, and ≠.
A mathematical statement known as an inequality uses the inequality symbol to represent the connection between two expressions. The terms on each side are not equal when there is an inequality sign present.
It suggests that the left and right expressions should be greater or smaller than one another, or the opposite. Literal inequalities are ones where the inequality symbols indicate the connection between two algebraic expressions.
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Need help with this question
Answer:
87=3x+24
Solve for x.
Step-by-step explanation:
AD=1/2*AB
5y-3=1/2(7y)
Solve for y.
Is this set of 4 vectors a basis for R3?
A basis of R3 cannot have more than 3 vectors, because any set of 4 or more vectors in R3 is linearly dependent.
Vectors v1, v2, . . . , v k ∈ V is called linearly dependent if they satisfy a relation of:
r₁v₁+r₂v₂+ · · · + rkvk = 0,
where the coefficients r1, . . . , r k ∈ R are not all equal to zero.
Otherwise vectors v1, v2, . . . , v k are called linearly independent. That is, if
r₁v₁+r₂v₂+ · · · +rkvk = 0 =⇒ r₁ = · · · = rk = 0.
An infinite set S ⊂ V is linearly dependent if there are some linearly dependent vectors v₁, . . . , v k ∈ S.
Otherwise, S is linearly independent.
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the inequality x>3 is read as x is greater than 3.The solution set of this equality is represent by the blue ray and includes all numbers greater than 3.
How many numbers are greater than 3?
The amount of numbers that are greater than 3 is given as follows:
Infinity.
How to model the inequality?The four inequality symbols, along with their meaning, are presented as follows:
> x: greater than x.< x: less than x.≥ x: at least x.≤ at most x.The inequality for this problem is defined as follows:
x > 3.
Meaning that the graph is composed by all the values that are greater than 3.
Perhaps the biggest difference between an equality and an inequality is the number of solutions. While an equality has a fixed number of solutions, an inequality has infinity solutions, as all the values in the solution set are solutions to the inequality.
(the solution set in this problem is all the values to the right of x = 3).
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Urgent help needed urgent urgent
The polynomial for x2 -4 in function notation is (x+2)(x-2) since a function produces an output from an input.
what is function ?Mathematics deals with numbers and their variants, equations and related structures, shapes and their locations, and locations where they might be found. The term "function" describes the connection between a group of inputs, each of which has a corresponding output. A function is an association between inputs and outputs where each input results in a single, unique output. A domain and a codomain, or scope, are assigned to each function.The input is an x. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four main categories of functions that are available.
given
A function creates an output from an input.
The name of the function, f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, and the output, f (x) f(x) f(x)f, left parenthesis, x, right parenthesis, are all enclosed in parentheses.
x2 -4
(x2 - 2*2)
= (x+2)(x-2)
The polynomial for x2 -4 in function notation is (x+2)(x-2) since a function produces an output from an input.
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How do you find the length of a segment with the midpoint and endpoint?
To find the length of a line segment given the coordinates of the midpoint and one endpoint, you can use the distance formula. The distance formula is:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) and (x2, y2) are the coordinates of two points, and d is the distance between the points.
Given the midpoint (mx, my) and one endpoint (ex, ey) you can use the following steps to find the length of the segment:
Calculate the difference in the x-coordinates and square it: (ex - mx)^2Calculate the difference in the y-coordinates and square it: (ey - my)^2Add the two values from steps 1 and 2Take the square root of the result from step 3. This is the length of the line segment.For example, if the midpoint of a segment is (5,7) and one endpoint is (7,10), the length of the segment is:
d = √((7-5)^2 + (10-7)^2)
d = √((2)^2 + (3)^2)
d = √(4+9)
d = √13
the length of the segment is √13 units.
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What if these particles is able to leave the atom?
1.Electrons
2.Protons
3.Neutrons
A chemical element's atom is a particular type of particle of substance. A positively charged electron or many negatively charged electrons encircle the central nucleus of an atom.
What if these particles is able to leave the atom?Electrons: If an electron leaves an atom, it is said to be ionized. Ionization can occur through various processes, such as collision with another particle or exposure to electromagnetic radiation.
Protons: Protons are found in the nucleus of an atom, and are held in place by the strong nuclear force. If a proton were to leave the nucleus, it would no longer be a stable atom and it would become an ion.
Neutrons: Neutrons are also found in the nucleus of an atom and are held in place by the strong nuclear force. If a neutron were to leave the nucleus, it would no longer be a stable atom, and it would become a different element.
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Identify the relation that is a function.
1) city name to state name
2) last name to phone number
3)days of the week to the months of the year
4)number of apples purchased to the cost of the apples
Decide on the input values. Choose the output values. You should classify a connection as a function if each input value results in only one output value.
Which relation is also a function?Any possible input value will result in exactly one output value, which is the definition of a function. "The output is a function of the input" is how we phrase it. The range is comprised of the output values, whereas the domain is made up of the input values. But not all relations are functions, and vice versa.
Formulas or graphs are typically used to depict functions.There are many different kinds of relations and functions, including empty relations, universal relations, reflexive relations, symmetric relations, transitive relations, equivalence relations, constant functions, polynomial functions, identity functions, on-to-one functions, onto functions, bijective functions, etc.
No relationship has the characteristics of a function if each input does not have a distinct output.There are nine different forms of mathematical relations: empty relation, full relation, reflexive relation, irreflexive relation, symmetric relation, anti-symmetric relation, transitive relation, equivalence relation, and asymmetric relation.
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Please I need an answer ASAP!
The marching band is holding a fundraiser. The band is selling t-shirts for $22 and yearbooks for $23. The goal is to sell at least $2,400 in merchandise. Which of the following is a solution to this scenario?
50 t-shirts and 56 yearbooks
51 t-shirts and 55 yearbooks
52 t-shirts and 54 yearbooks
53 t-shirts and 55 yearbooks
The solution for this scenario is,
⇒ 53 t-shirts and 55 yearbooks
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that;
The band is selling t-shirts for $22 and yearbooks for $23.
And, The goal is to sell at least $2,400 in merchandise.
Now, Let x = number of $22 t-shirt
Let y = number of $23 yearbook
Hence, We can formulate;
⇒ 22x + 23y ≥ 2400
By option 4;
There are 53 t-shirts and 55 yearbooks.
Hence, Substitute x = 53 and y = 55 in above equation,
⇒ 22x + 23y ≥ 2400
⇒ 22×53 + 23×55 ≥ 2400
⇒ 1166 + 1265 ≥ 2400
⇒ 2431 ≥ 2400
Thus, The correct option is,
⇒ 53 t-shirts and 55 yearbooks
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A seagull flies 15 feet above the surface of the
ocean. The table shows the location of several
other objects in relation to the ocean's surface.
Sort the objects into the appropriate bins by their
distances to the ocean surface as compared to
the seagull's distance.
Submarine
Petican
Fish
Airplane
Farther from the Ocean's
Surface than the Seagull is
Shark
Object
Fish
Shark
Airplane
Submarine
Pelican
Closer to the Ocean's
Surface than the Seagull is
Location in
Comparison to the
Ocean's Surface (feet)
-6
-50
150
-218
9
Answer: A seagull flies 15 feet above the surface of the ocean. The table shows the location of several other objects in relation to the ocean’s surface. Object Location in Comparison to the Ocean’s
Step-by-step explanation: Surface:Fish: –6 feet Shark: –50 feet Airplane: 150 feet Submarine: –218 feetPelican: 9 feet
For a family gathering, Bianca made 5 meat loaves using 8 pounds of ground beef. She also made 16 hamburgers using 6 pounds of ground beef. Part A Each meat loaf was made with the same amount of ground bee How much ground beef was in each meat loaf?
A. 1- 8/5
B. 5/8
C. 1- 3/5
D. 8- 1/5
Answer: Each meat loaf was made with the same amount of ground beef, and Bianca made 5 meat loaves using 8 pounds of ground beef. To find the amount of ground beef in each meat loaf, we can divide the total amount of ground beef used to make the meat loaves by the number of meat loaves.
So, the amount of ground beef in each meat loaf is 8 pounds / 5 meat loaves = 1.6 pounds
In terms of the options provided, 1.6 pounds is equal to 8/5 (Option A)
Step-by-step explanation:
What are the 4 types of exponents?
The 4 types of exponents are positive, negative, zero, and rational.
When an expression or statement of specific natural numbers (0 to ∞), is represented as repeated power by multiplication of its units, then the resulting number is an Exponent.
For example, take the value 7⁵. Here the number 7 is called “base” and the number 5 (up) is called the exponent or power of that mathematical sequence. Now, to precisely calculate the value of this exponent, simply multiply the base number as many times as denoted by the power. So, for this case, it would be 7×7×7×7×7 = 16807.
Thus, 16807 can be represented in the form of exponents as 7⁵.
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Can somebody help me?
What is the number below is in the thousandths place value in 45.1672
Step-by-step explanation:
The number in the thousandths place value in 45.1672 is 6.
Could the points A(-2,1), B(4,7), and C(1,4) be three vertices of rectangle ABCD?
O No, since AB and BC are not perpendicular.
OYes, since a fourth point can always be determined to form a rectangle.
OYes, since AB and BC form a right angle.
O No, since AB and BC are not parallel.
Since, AB and BC are not perpendicular,
No, Points A(-2,1), B(4,7), and C(1,4) cannot be three vertices of rectangle ABCD.
The correct option is A.
What is rectangle?A rectangle is a quadrilateral in which all the angles are equal and the opposite sides are equal and parallel.
A rectangle is a closed two-dimensional figure with four sides, all the angles of a rectangle are equal to 90°.
Given points
A(-2,1),
B(4,7), and
C(1,4)
For being vertices of rectangle
Angle between line segment AB and BC should be 90°.
Slope of line AB
m = (y - y')/(x-x')
m = (7 - 1)/(4 - -2)
m = 6/6
m = 1
Slope of line BC
m' = (y - y")/(x - x")
m' = (7 - 4)/(4-1)
m' = 3/3 = 1
Since slope of the two lines is same that is both are parallel, which is only possible when A, B, C are in a straight line.
Hence, points A(-2,1), B(4,7), and C(1,4) cannot be three vertices of rectangle ABCD.
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