The sum of 3 consecutive even numbers is 72 what is the smallest of the three numbers

The fraction of the cornbread that Val eats from the leftover 11/12 of the cornbread after a picnic in simplest form is 1/3.

Given that:

(11)/(12) of the cornbread is left over

Val eats (2)/(11) of the leftover cornbread.

We are to find what fraction of the cornbread does Val eat.

Val eats (2)/(11) of the (11)/(12) of the cornbread = (2/11) × (11)/(12) = 2/6 = 1/3.

∴ Val eats 1/3 of the cornbread.

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Answer:

y intercept = \((0, ~-\frac{5}{2} )\)

x intercept = \((-2, ~0)\)

.

Step-by-step explanation:

\(-5x - 5y = 10\)

.

y intercept

\(\to x = 0\)

\(-5(0) - 4y = 10\)

\(-4y = 10\)

\(y = \frac{10}{-4}\)

\(y = -\frac{5}{2}\)

so, the answer is \((0, ~-\frac{5}{2} )\)

.

x intercept

\(\to y = 0\)

\(-5x - 4(0) = 10\)

\(-5x = 10\)

\(x = \frac{10}{-5}\)

\(x = -2\)

so, the answer is \((-2, ~0)\)

.

Happy to help :)

Answer:

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Step-by-step explanation:

bqhhq wjwjw wjwjw wjwj

Answer:

\(-2x^2-x\). Your answer was wrong because "x-squared" terms didn't cancel.

Step-by-step explanation:

To solve this problem, set up an equation.  We know something is supposed to be added to the expression \(2x^2+2x\), and the result should be x. So:

\(2x^2+2x+(\text{ ? })=x\)

We want to solve for the question mark... the unknown thing that we're adding to the original expression, in order to get x.

It is uncommon to put question marks in equations to represent quantities. Usually we use a letter. Since x is already being used in the equation, we should pick something else ... we could use "y".

\(2x^2+2x+(\text{ } y \text{ })=x\)

...or just...

\(2x^2+2x+y=x\)

Algebra allows us to solve the equation and find out what "y" is equivalent to.

To solve, we want to get the "y" by itself. To do so, we try to eliminate the other "terms" from the left side of the equation.

Understanding "terms" & "like terms"

Terms

"Terms" in an equation are either a number multiplied to other things, or just a single number that isn't multiplied to anything else.

For example, the various terms in our equation above are

\(2x^2\), \(2x\), \(y\), \(x\)

You might ask why the last things, which don't have a number, are considered terms.

Remember that multiplying by 1 doesn't change anything, so we could imagine each of the last two terms as being 1 times the letter.

So, we can rewrite our equation:

 \(2x^2+2x+1y=1x\)

Like terms

"Like terms" are terms where the "other stuff the numbers are multiplied to" is the same, so for instance, the \(2x\) and the \(1x\) are like terms. They are like terms because, the "other stuff" that the numbers are multiplied to are "x" for both terms. Note that \(2x\) and \(2x^2\) are not "like terms" because the "stuff" is different:

\(x\) is different than \(x^2\)

"Like terms" are important because only like terms can be "combined" into a single simplified term.

Solving equations

To solve an equation, we isolate what we're solving for, y, by disconnecting the other terms from it, and simplify.

Starting with subtracting 2x from both sides of the equation:

\(2x^2+2x+1y=1x\\(2x^2+2x+1y)-2x=(1x)-2x\)

Subtraction is the same as "adding a negative":

\(2x^2+2x+1y+(-2x)=1x+(-2x)\)

Since all terms are now connected by addition, we can add in any order we want (because of the Commutative Property of Addition), and we can combine like terms.

Thinking just about the number parts, since \(1+(-2)=-1\),  then \(1x+(-2x)=-1x\).

Returning to our main equation, the right side simplifies:

\(2x^2+2x+1y+(-2x)=1x+(-2x)\\2x^2+2x+1y+(-2x)=-1x\)

On the left side: \(2x\) and \(-2x\) are like terms.

Fact: \(2+(-2)=0\)

So, \(2x+(-2x)=0x\)

Since anything times zero is just zero, \(0x=0\). Furthermore, adding zero to anything doesn't change it.  So when the \(2x\) and \(-2x\) terms on the left side of our main equation are combined, they "disappear" (While we talked through are a lot of rules/steps to justify why that works, it is common to omit those justifications, and to just combine those like terms and make them disappear.)

So, \(2x^2+2x+1y+(-2x)=-1x\) simplifies to:

\(2x^2+1y=-1x\)

Similarly for the \(2x^2\) term, we subtract from both sides:

\(2x^2+1y=-1x\\(2x^2+1y)-2x^2=(-1x)-2x^2\\2x^2+1y+(-2x^2)=-1x+(-2x^2)\)

Combining like terms on the left, they disappear.

\(1y=-1x+(-2x^2)\)

There are no like terms on the right.

Since the two terms on the right are added together, we can use the commutative property of addition to rearrange:

\(1y=-2x^2+(-1x)\)

Addition of a negative can turn back into subtraction, and simplify multiplication by 1.

\(y=-2x^2-x\)

Remembering we chose "y" as the unknown thing we wanted to know, that's why the "correct answer" is what it is.

Verifying an answer

Verifying can double check an answer, and helps explain why the answer you chose doesn't work.

To verify an answer, the original statement said add something to the expression and get a result of "x". So, let's see if the "correct answer" does:

\(2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-2x^2-x)\\2x^2+2x+(-2x^2-1x)\\2x^2+2x+(-2x^2)+(-1x)\)

Combining the "x-squared" terms, completely cancels...

\(2x+(-1x)\)

Combining the "x" terms, and simplifying...

\(1x\\x\)

So it works.

Why isn't the answer what you chose:

\(2x^2+2x+(\text{ } ? \text{ })\\2x^2+2x+(-x^2-x)\\2x^2+2x+(-1x^2-1x)\\2x^2+2x+(-1x^2)+(-1x)\)

Combining the x-squared terms, things don't completely cancel...

\(1x^2+2x+(-1x)\)

Combining the x terms...

\(1x^2+1x\\x^2+x\)

So adding the answer that you chose to the expression would not give a result of "x", which is why it is "wrong"

The value of (f- g)(x) is  2x - 26.

This is a question of subtraction of functions.

Subtraction of functions

The subtraction of function involves the creation of a new function through the addition of two other functions.

Subtraction of one real-valued function from another.

Let h: X → and p: X → be any two real functions, where X ⊆ Real numbers. Then, we can define h - p: X → by h - p x = h(x) – p(x), for all x ∈ X.

Given that:-

f(x) = 2x + 1

g(x) = 27

We have to find the value of (f- g)(x)

We know that,

(f- g)(x) = f(x) - g(x)

Hence, we can write,

(f- g)(x) = 2x + 1 - 27 = 2x - 26

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Answer:

See explanation

Step-by-step explanation:

Required

The significance of "b" in exponential function

An exponential function is represented as:

\(y = ab^x\)

In the above equation, parameter "b" is the rate of the function

In other words, the constant multiplier of the function.

Take for instance;

\(y = 2*4^x\)

By comparison:

\(b = 4\)

Another instance is:

\(y = 2(-4)^x\)

By comparison

\(b = -4\)

Other significance of parameter b are:

If \(b > 0\) then b represents a growth factor

If \(b < 0\) the b represents the factor of decay

\(b \ne 0\) i.e. b is never 0

Set the right-hand side equal to zero to obtain the related homogeneous equation:

y'' − y' − 2y = 0

r2 - r - 2 = 0 is the characteristic equation.

The result of factoring this equation is (r - 2)(r + 1) = 0

The roots are therefore r = 2 and r = -1.

The homogeneous equation's general solution is the following:

y_h(t) equals c1*e(2t) plus c2*e(-t).

We need to identify a specific solution in order to discover the nonhomogeneous equation's general solution. The approach of indeterminate coefficients can be used to infer a form for a specific solution. We can speculate on a specific solution of the following kind because the polynomial on the right-hand side of the equation is of degree 2.

At2 + Bt + C = y_p(t)

Taking y_p(t)'s first and second derivatives, we obtain:

y_p'(t) equals 2At + B

y_p''(t) = 2A

When these expressions are substituted into the initial differential equation, we obtain:

-6t + 10t2 = 2A - (2At + B) - 2(At2 + Bt + C)

When we condense and group related terms, we get:

-6t + 10t2 = (-2A)t2 + (-2B-2A)t + (2A-B-2C)t

When like terms' coefficients are equated, we obtain:

-2A = 10, -2B - 2A = -6, 2A - B - 2C = 0

If we solve for A, B, and C, we obtain:

A = -5, B = 4, C = -11/4

The specific solution is thus:

y_p(t) = -5t^2 + 4t - 11/4

As a result, the following is the nonhomogeneous equation's general solution:

c1*e(2t) + c2*e(-t) - 5t2 + 4t - 11/4 are equivalent to y(t) = y_h(t) + y_p(t).

where the initial circumstances define the constants c1 and c2.

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Answer:221 min

Step-by-step explanation:

Given

Scott run 20 km in 85 minutes

Speed is given by

\(\Rightarrow \text{speed}=\dfrac{\text{distance}}{\text{time}}\)

Speed of Scott

\(\Rightarrow v=\dfrac{20}{\frac{85}{60}}=\dfrac{20\times 60}{85}=14.117\ km/hr\)

For 52 km, time taken is

\(\Rightarrow \text{time t}=\frac{52}{14.117}=3.683\ hr\ or\\\Rightarrow t=221\ min\)

Answer:

x = 13/3

Step-by-step explanation:

Solve for x:

3×2 (x - 4) - 2 = 0

Hint: | Multiply 3 and 2 together.

3×2 = 6:

6 (x - 4) - 2 = 0

Hint: | Distribute 6 over x - 4.

6 (x - 4) = 6 x - 24:

6 x - 24 - 2 = 0

Hint: | Group like terms in 6 x - 24 - 2.

Grouping like terms, 6 x - 24 - 2 = 6 x + (-24 - 2):

6 x + (-24 - 2) = 0

Hint: | Evaluate -24 - 2.

-24 - 2 = -26:

6 x + -26 = 0

Hint: | Isolate terms with x to the left hand side.

Add 26 to both sides:

6 x + (26 - 26) = 26

Hint: | Look for the difference of two identical terms.

26 - 26 = 0:

6 x = 26

Hint: | Divide both sides by a constant to simplify the equation.

Divide both sides of 6 x = 26 by 6:

(6 x)/6 = 26/6

Hint: | Any nonzero number divided by itself is one.

6/6 = 1:

x = 26/6

Hint: | Reduce 26/6 to lowest terms. Start by finding the GCD of 26 and 6.

The gcd of 26 and 6 is 2, so 26/6 = (2×13)/(2×3) = 2/2×13/3 = 13/3:

Answer:x = 13/3

The number that Bethany thinks of is 104, and 1/13 of that number is 8.

Word problems in mathematics involve arithmetic operations and the use of variables to solve those problems. Word problems are problems we encounter in our daily life and with the use of correct mathematical interpretation, we can provide accurate solutions to them.

Let the number that  Bethany thinks of be (x) for example. So, 6/13 of x is equal to 48.

i.e.

(6/13) * (x) = 48

By dividing both sides with (6/13), we have:

x = 48 ÷ (6/13)

x = 48 × (13/6)

x = 8 × 13

x = 104

Thus, 6/13 of the number that Bethany thinks of that gives us 48 is 104. Now, to find 1/13 of 104, we have:

1/13 × 104

= 8

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∑xn=11−x

when x

is in the radius of convergence

∑(−x)n=11+x∑(−x2)n=∑(−1)nx2n=11+x2∑(−1)n(2–√x)2n=∑(−1)n(2n)x2n11+2x2x∑(−1)n(2n)x2n=x1+2x2∑(−1)n(2n)x2n+1=x1+2x2

The series convenes by the root test if:

limn→∞|an−−√nx|<1

|an−−√n|=|2n2n+1x|<1

|x|<2√2

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Answer: This triangle is not a right triangle

Step-by-step explanation:

In a right triangle, the hypotenuse(c) is always the longest side and a and b are the shorter sides.  Thus, 5^2+9^2=13^2.  Simplify this to get 25+81=169, then 106=169.  Because 106 does not equal 169, it is not a right triangle.

Hope it helps <3

Answer:

4t - 22

Step-by-step explanation:

To find:-

Answer:-

To find out the perimeter we can simply add all the side lengths of the given figure. Since the given figure here is a rectangle, we can add up all the four sides to find the perimeter.

The four sides given to us are t-6 , t-5 , t-6 and t-5 .

Hence the perimeter of the quadrilateral would be ,

Perimeter = t-5 + t-6 + t-5 + t-6

Perimeter = 4t - 10 - 12

Perimeter = 4t - 22

Hence the perimeter of the given figure us 4t - 22.

\(\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{$\sf\large t-5$}\multiput(-1.4,1.4)(6.8,0){2}{$\sf\large t-6$}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture} \)

The correct option is B) Not valid. Consider the statement “Since some shoes are sneakers, some non-sneakers are non-shoes.”

We know that all sneakers are shoes, but all shoes are not sneakers.  Hence, some shoes are sneakers. But, this statement does not imply that “some non-sneakers are non-shoes.” This inference cannot be drawn by contraposition. So, it is not valid.Inferences cannot be drawn in contraposition all the time. Contraposition is a type of logical statement that involves reversing and negating the terms of an original proposition. It is a logical relationship between a proposition and its converse. If a proposition is true, the contrapositive is always true.An example of contraposition can be shown as follows:“If a person is a human, then they are mortal.”We can write the contrapositive of this statement as:“If a person is not mortal, then they are not human.”

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If Central angle BAC of circle A measures 23/20 π T radians. Arc BC has a length of 63.48 centimeters. The radius of the circle A is: 55.2cm.

In this case, we know the length of arc BC is 63.48 cm and the central angle BAC measures 23/20 π radians.

Now let find the radius of circle A:

So:

63.48π = (23/20 π)/2π × 2πr

63.48π = 1.15 rπ

Divide both side by 1.15

r = 63.48 /1.15

r =55.2 cm

Therefore we can conclude that the radius of circle A is approximately 55.2 centimeters.

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The complete question is:

Central angle BAC of circle A measures 23/20 π T radians. Arc BC has a length of 63.48 centimeters. What is the radius of the circle? The radius of circle A is

The answer is (a) $10,000.

The total cost of producing 200 units of output can be found by multiplying the output (200 units) by the average total cost (ATC) per unit, which is given as $50. Therefore, the total cost is:

Total Cost = Output x ATC

Total Cost = 200 x $50

Total Cost = $10,000

Therefore, the answer is (a) $10,000.

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Answer:

SA= 119 cm²

Step-by-step explanation:

the solution contain of four steps

Answer:

$400

..................

One pound is equal to approximately 2 cups.

It's important to note that this conversion is an approximation and may not be exact, especially if you are measuring ingredients like flour or sugar, which can be packed differently.

To ensure accurate measurements, it's best to use a kitchen scale to measure ingredients by weight.

In conclusion, 1 pound is approximately equal to 2 cups. When converting between pounds and cups, it's important to keep in mind that this conversion may not be exact, especially when measuring ingredients like flour or sugar.

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Answer:

60

Step-by-step explanation:

based on my previous learning.. hope it helps.. correct me if im wrong..

The scalar product P.Q = 33, P.S = -25, and Q.S = -2. The scalar product P-Q, P-S, and Q-S are not defined.

The scalar product, also known as the dot product, is a mathematical operation that takes two vectors and returns a scalar quantity. To compute the scalar product of two vectors, we multiply their corresponding components and sum the results.

For the given vectors, P = (11)i + (10)j + (11)k, Q = (3)i + (4)j - (5)k, and S = -4i + j - 2k.

To find P.Q, we multiply the corresponding components of P and Q and sum the results: P.Q = (11)(3) + (10)(4) + (11)(-5) = 33.

Similarly, P.S = (11)(-4) + (10)(1) + (11)(-2) = -25, and Q.S = (3)(-4) + (4)(1) + (-5)(-2) = -2.

However, the scalar product P-Q, P-S, and Q-S are not defined since these operations involve subtracting vectors, and the scalar product is not defined for vector subtraction.

Therefore, the scalar products P.Q = 33, P.S = -25, and Q.S = -2, while the scalar products P-Q, P-S, and Q-S are not defined.

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Answer:

Long solution

Step-by-step explanation:

(a) Let the height of the cone be h cm. The volume of the hemisphere is given by (1/2)(4/3)πr³ = (2/3)πr³. The volume of the solid is the sum of the volumes of the hemisphere and the cone, which is (2/3)πr³ + (1/3)πr²h. Since the volume of the hemisphere is one third of the volume of the solid, we have:

(2/3)πr³ = (1/3)πr²h

Simplifying, we get:

2r = h

Therefore, h is expressed in terms of r as h = 2r.

(b) The slant height of the cone can be found using the Pythagorean theorem. Let l be the slant height, then we have:

l² = r² + h²

Substituting h = 2r, we get:

l² = r² + (2r)² = 5r²

Taking the square root of both sides, we get:

l = r√5

Since k is an integer, we can write:

l = Vk cm, where k is an integer

Comparing the two expressions, we get:

Vk = r√5

Therefore, the value of k is k = ⌊r√5⌋, where ⌊x⌋ denotes the largest integer less than or equal to x.

(c) The total surface area of the solid is the sum of the curved surface area of the cone, the curved surface area of the hemisphere, and the area of the circular base of the cone. We have:

Curved surface area of the cone = πr l = πr(r√5) = πr²√5

Curved surface area of the hemisphere = 2πr²

Area of the circular base of the cone = πr²

Therefore, the total surface area of the solid, in cm², is given by:

πr²√5 + 2πr² + πr² = (πr²)(√5 + 3)

Answer:

C = 4p

Step-by-step explanation:

Because it starts at 0 pounds costs 0 dollars, we know it starts at the origin and has no y-intercept. Because it rises up 20 dollars for every 5 pounds, we can use rise/run to do 20/5 to get an increase of 4 dollars per pound.

Answer:

45°

Step-by-step explanation:

If you walk forwards, and make a 90° turn and walk the same amount, the angle will be half of 90, which is 45.

At t = 4, the object has a speed of approximately 34.5506 units per second, calculated by finding the magnitude of its velocity vector.

To find the speed of the object, we need to calculate the magnitude of its velocity vector. The velocity vector is the derivative of the position function with respect to time. Given the position function F(t) = (7t² + 4, 4t − 2, t³ + 4t), we can differentiate each component with respect to time to obtain the velocity vector.

Taking the derivatives, we have:

F'(t) = (14t, 4, 3t² + 4)

Now, substitute t = 4 into the velocity vector to get the velocity at that particular time:

F'(4) = (14(4), 4, 3(4)² + 4)

    = (56, 4, 52)

The magnitude of the velocity vector can be calculated using the formula:

Speed = ||F'(4)|| = √(56² + 4² + 52²) ≈ 34.5506

Therefore, the speed of the object at t = 4 is approximately 34.5506.

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