How many terms are in the expression below.

15+7x-8+4

The volume of the given rectangular prism is of 72 cm³.

The volume of a rectangular prism of length l, width w and height h is given by the multiplication of the dimensions, that is:

V = lwh.

The volume of a cube of side a is a³, hence each cube has side of 1 cm, and the dimensions of the rectangular prism are:

w = 6 cm, h = 4 cm, l = 3 cm.

Hence the volume is given by:

V = 6 cm x 4 cm x 3 cm = 72 cm³.

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Answer:

E. \( \purple { \bold{ \frac{2}{3} ( \frac{x - 1}{x} ) \sqrt{\frac{x - 1}{x} } + c }}\)

Step-by-step explanation:

\( \int \sqrt{ \frac{x - 1}{ {x}^{5} } } dx \\ \\ = \int \sqrt{ \frac{x - 1}{ {x}^{4} .x} } dx \\ \\ = \int \frac{1}{ {x}^{2}}\sqrt{ \frac{x - 1}{ x} } dx \\ \\ = \int \frac{1}{ {x}^{2}}\sqrt{ 1 - \frac{1}{ x} } dx \\ \\ let \: 1 - \frac{1}{ x} = t \\ \\ \implies \: \frac{1}{ {x}^{2} } dx = dt \\ \\ \implies \int \frac{1}{ {x}^{2}}\sqrt{ 1 - \frac{1}{ x} } dx = \int \sqrt{t} dt \\ \\ = \int {t}^{ \frac{1}{2} } dt \\ \\ = \frac{t ^{ \frac{3}{2} } }{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} t ^{ \frac{3}{2} } + c \\ \\ = \frac{2}{3} \sqrt{ {t}^{3} } + c \\ \\ = \frac{2}{3} t\sqrt{ {t} } + c \\ \\ = \frac{2}{3} (1 - \frac{1}{x} ) \sqrt{1 - \frac{1}{x} } + c \\ \\ \red{ \bold{= \frac{2}{3} ( \frac{x - 1}{x} ) \sqrt{\frac{x - 1}{x} } + c }}\\ \\ \)

The requried scale factor of the dilation from NOPQ to N'O'P'Q' is 3/4.

The scale factor is defined as the ratio of the modified change in length to original length.

Here,
The parallelogram N'O'P'Q' is a dilation for the parallelogram NOPQ.
length of the one diagonal of NOPQ is = 12
length of the one diagonal of N'O'P'Q' is = 9

Now,
The scale factor for quadrilateral = Length of diagonal N'O'P'Q' / NOPQ
                                                  = 9/12
                                                  = 3/4

Thus, the requried scale factor of the dilation from NOPQ to N'O'P'Q' is 3/4.

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Answer:

-3/4

Step-by-step explanation:

If you take two points, the rise is 3. Also, the change in y is 4. Since the line is going downwards from left to right, it has to be negative.  

Answer:

7x-2 = 7x-2

Step-by-step explanation:

The time taken to get to the 4th can be obtained by dividing the distance given by the speed of the lift.

Distance, height from ground to 4th floor = 42 feets

Time taken to get to the 4th floor = t

Recall :

Time = Distance / speed

The time taken to get to the 4th floor will be :

Therefore, to obtain the time taken, divide the distance or height of the 4th floor by the speed of the lift.

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Answer: x=1/2=0.5

Step-by-step explanation:

Given

3(2x) - 4(3x) + 3= 0

Expand parenthesis

6x - 12x + 3 = 0

Combine like terms

-6x + 3 = 0

Subtract 3 on both sides

-6x + 3 - 3 = 0 - 3

-6x = -3

Divide -6 on both sides

-6x / -6 = -3 / -6

x = 1/2 = 0.5

Hope this helps!! :)

Please let me know if you have any questions

Answer:

5.x^8.y^3

Step-by-step explanation:

15.x^10.y^5.z^2 ÷ 3.x^2.y^2.z^2

= 15/3. x^(10-2). y^(5-2). z^(2-2)

= 5.x^8.y^3.z^0

= 5.x^8.y^3

\(\\ \rm\hookrightarrow \dfrac{15x^{10}y^5z^2}{3x^2y^2z^2}\)

\(\\ \rm\hookrightarrow 5x^{10-2}y^{5-2}z^{2-2}\)

\(\\ \rm\hookrightarrow 5x^8y^3\)

Option B has type error or none of the above

Answer:

V≈235.62 ft

Step-by-step explanation:

just plug into cylinder equation

Answer:

The correct equation would be:

\(x=\frac{-3±\sqrt{3^{2}-4(-2)}}{2(-2)}\)

-Therefore, the correct option is D

Answer:

d

Step-by-step explanation:

Answer: $88.90

Step-by-step explanation:

$39.95 x 2 + 0.06 x 150

Answer:

vertex is (6, -11)

Step-by-step explanation:

Given equation
f(x) = x² - 12x + 25

is that of an upward-facing parabola(since the coefficient of x² is positive).

The vertex will be at a minimum and its x-coordinate can be found by finding the first derivative of f(x), setting it equal to zero and solving for x

f'(x) = d/dx(x² - 12x + 25)

= 2x - 12

f'(x) = 0 ==> 2x - 12 = 0

2x = 12

x = 6

Substitute x = 6 in f(x) to get

f(6) = 6² - 12(6) + 25

= 36 - 72 + 25

= -11

So the vertex is at (6, -11)

Answer:

y = 5/24

Step-by-step explanation:

2/3 = 24/36

3/4 = 27/36

8/9 = 32/36

32-27 = 5

5/36 / 2/3 = 15/72 = 5/24

Answer:y=5/13

Step-by-step explanation:

8/9-3/4 is 5/36

divide by 2/3 is

∠BAC=80° (vertical angles)

p=45° (sum of angles in a triangle)

m=55° (corresponding angles theorem)

n=135° (exterior angle theorem)

Answer:

x = 13

Step-by-step explanation:

Step 1: Define

f(x) = (x - 1)/2

f(x) = 6

Step 2: Substitute and solve for x

6 = (x - 1)/2

12 = x - 1

x = 13

Answer:

B 13/2

Step-by-step explanation:

2x² + 7x - 15 = 0

First we want to find the two solutions

We can do this by using the quadratic formula

Quadratic formula:

\( \frac{- b + or - \sqrt{b {}^{2} - 4(a)(c)} }{2(a)} \)

Where the values of a,b and c are derived from the equation.

The equation is put in ax² + bx + c = 0 form

2x² + 7x - 15 = 0

so a = 2, b = 7 and c = - 15

We now plug these values into the quadratic formula

(-(7) + or - √7² - 4(2)(-15) ) / 2(2)

first solution: -(7) + √7² - 4(2)(-15) ) / 2(2)

remove parenthesis on 7

(-7 + √7² - 4(2)(-15) ) /2(2)

Apply exponents 7²

(-7 + √49 - 4(2)(-15) ) /2(2)

Multiply -4,2 and -15

(-7 + √49 + 120 ) / 2(2)

add 49 and 120

(-7 + √ 169 ) / 2(2)

Take square root of 169

(-7 + 13 ) / 2(2)

add 13 and -7

6/2(2)

multiply 2 and 2

= 6/4

The first solution is 6/4 or 1.5

Now the second solution: -(7) - √7² - 4(2)(-15) ) / 2(2)

For the second solution we basically go through the same steps as for finding the first solution, the only difference is instead of adding -b and √b² - 4(a)(c) we are subtracting.

So we would have ( -7 - 13 ) / 2(2) instead of (-7+13)/2(2)

So second solution: ( -7 - 13 ) / 2(2)

subtract 13 from -7

-20/2(2)

multiply 2 and 2

-20/4

divide

The second solution is -5

Now that we have found the solutions we want to find r - s if r and s are the solutions to the equation and that r > s

The two solutions are 6/4 and -5.

6/4 > -5 so we know that r must equal 6/4 and s must equal -5 because r has to be greater than s

So if r = 6/4 and s = -5

Then r - s = 6/4 - (-5) = 6/4 + 5 = 13/2

So the answer is B. 13/2

Answer:

Mean: 9.6

Median: 7

Mode: 7

Range: 17

Step-by-step Explanation:

Mean: add all the numbers then divide the sum by how many numbers there are

19 + 7 + 16 + 2 + 10 + 6 + 7 = 67

67 / 7 = 9.57 --> 9.6

Median: arrange your numbers in numerical order, count how many numbers you have (if odd, divide by 2 and round up to the position of a median number, if even, divide by 2 and go to that number in position)

2, 6, 7, 7, 10, 16, 19 (7 numbers = since its odd, divide by 2 which equals 3.5, round it up to 4 and go to the number in the 4th position, in this case 7)

Mode: Put the number in order again and determine which number appears the most

2, 6, 7, 7, 10, 16, 19  = 7 appears twice while the rest only appears once

Range: subtract the lowest value from the highest value

19 - 2 = 17

Step-by-step explanation:

19, 7, 16, 2, 10, 6, 7

In ascending order:

2,6,7,7,10,16,19

mean:

(2+6+7+7+10+16+19)/7

=67/7

=9.6

Median:  7

Mode: 7

Range:

19 - 2 = 17

Answer:

1. is moving to the left by 4 and 2. is moving up by 4

Step-by-step explanation:

True. Data Envelopment Analysis (DEA) is best used in an environment of low diverges and high complexity. In such situations, DEA can effectively analyze and compare the efficiency of decision-making units, even when dealing with multiple inputs and outputs.

Data Envelopment Analysis (DEA) is a method used to measure the efficiency of decision-making units. It works by analyzing a set of inputs and outputs to determine the relative efficiency of each unit. DEA is best suited for situations where there is low diverges among the units being analyzed, meaning they are all operating under similar conditions. Additionally, DEA is most effective in situations of high complexity, where there are multiple inputs and outputs that need to be considered. Therefore, the statement that DEA is best used in an environment of low divergence and high complexity is true.

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Answer:

\(\dfrac{1}{729}\)

Step-by-step explanation:

\(\left(\dfrac{}{}(-3)^2\dfrac{}{}\right)^{-3}\)

First, we should evaluate inside the large parentheses:

\((-3)^2 = (-3)\cdot (-3) = 9\)

We know that a number to a positive exponent is equal to the base number multiplied by itself as many times as the exponent. For example,

\(4^3 = 4 \, \cdot\, 4\, \cdot \,4\)

       ↑1 ↑2 ↑3 times because the exponent is 3

Next, we can put the value 9 into where \((-3)^2\) was originally:

\((9)^{-3}\)

We know that a number to a negative power is equal to 1 divided by that number to the absolute value of that negative power. For example,

\(3^{-2} = \dfrac{1}{3^2} = \dfrac{1}{3\cdot 3} = \dfrac{1}{9}\)

Finally, we can apply this principle to the \(9^{-3}\):

\(9^{-3} = \dfrac{1}{9^3} = \boxed{\dfrac{1}{729}}\)

The antiderivative function F(x) is verified.

The most general antiderivative of the function f(x) = x2 − 7x 3 is given below.

We know that the antiderivative of f(x) is a function F(x) such that F′(x) = f(x).So, integrating f(x), we get; ∫f(x)dx = ∫(x2 − 7x 3)dx = [ x3/3 − 7/4 x 4/4 ] + c, where c is the constant of the antiderivative.Therefore, the most general antiderivative of the function f(x) = x2 − 7x 3 is given by;

F(x) = x3/3 − 7/4 x 4/4 + c

To check the answer, let us differentiate the above antiderivative function F(x) and we will get back the given function f(x).Differentiating F(x) w.r.t x, we get;

F′(x) = (x3/3)' − (7/4 x 4/4)' + c' = x2 − 7x 3 + 0 = f(x)

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The value of f.ds = 20π.

The quantity of electric or magnetic field lines that flow across a surface in a specific period of time is known as flux. Field lines offer a way to visualise the size and direction of the field under study.

Given:

f = <3xy²,3x²y,z³>

Using Divergence Theorem

P= 3xy²

Q= 3x²y

R = z³

So, dP/ dx= 3y²

dQ/ dy = 3x²

dQ/ dz = 3z²

So, \(\int\limits\int\limits\int\limits dV\)= \(\int\limits\int\limits\int\limits (dP/ dx + dQ/dy+ dR/dz)\)

= \(\int\limits\int\limits\int\limits\) (3y² + 3x² + 3z²)

= \(\int\limits\int\limits\int\limits\) 3 (y² + x² + z²)

Since the radius is 5.

= \(\int\limits\int\limits\int\limits\) 3(5)

= 15 \(\int\limits\int\limits\int\limits\) dV

= 15 (4/3)π

= 20π

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Answer:

nn

Step-by-step explanation:

nnnnnn

The  reverse of multiply by 44 is: 0.02272727.

Instead of multiplying by 44  we can  divide by the reciprocal of 44 reason been that division is the multiplicative reverse. Dividing by a digit is the same things as multiplying by the reciprocal of the digit.

Hence,

reverse of multiply by 44

Let the multiplicative reverse by x

44 (x)=1

x=1/44

x= 0.02272727

Prove:

0.02272727×44

=1

Therefore the  reverse of multiply by 44 is: 0.02272727.

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Answer:The answer is B

Step-by-step explanation:

A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options. The equation StartFraction 1 over 8 EndFraction (x + 16) = StartFraction 76 over 8 EndFraction represents the situation, where x is the food bill. The equation StartFraction 1 over 8 EndFraction (x + 16) = 76 represents the situation, where x is the food bill. The solution x = 60 represents the total food bill. The solution x = 60 represents each friend’s share of the food bill and tip. The equation 8 (x + 16) = 76 represents the situation, where x is the food bill.

Answer:

y=−2x+7

Step-by-step explanation:

Y+1=-2(x-4)

Y+1= -2x+8 step 1: multiply -2(x-4)

Y= -2x+7 Step 2: subtract 1 from both sides

So, your answer is Y=-2x+7

The expression states that for every linear polynomial p with real coefficients and a nonzero coefficient of x, there is exactly one real root r.

For all linear polynomials with real coefficients and a nonzero coefficient of x, there exists exactly one real root. This can be expressed using the universal quantifier "for all" and the existential quantifier "there exists", connected by the logical connective "and". Additionally, the statement "exactly one real root" can be expressed using the quantifier "there exists" and the logical connective "and".

Using quantifiers and logical connectives, we can express the given fact as follows:

∀p ∃!r ((isLinearPolynomial(p) ∧ hasRealCoefficients(p) ∧ coefficientOfX(p) ≠ 0) → hasRealRoot(p, r))

Explanation:

- ∀p: For every polynomial p
- ∃!r: There exists exactly one real root r
- isLinearPolynomial(p): p is a linear polynomial (degree 1)
- hasRealCoefficients(p): p has real coefficients
- coefficientOfX(p) ≠ 0: The coefficient of x in p is nonzero
- hasRealRoot(p, r): p has a real root r

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Answer:

uh I don't even know what this is

Answer: x = 500

Step-by-step explanation:

Use the Pythagorean Theorem

a²+b²=c²

300² + 400² = x²

90000 + 160000 = x²

250000 = x²

√250000 = √x²

500 = x

hope i explained it :)

The answer is (-1, 2).

Given that the parabola is y = x - x² and the point is (1, 0). In order to find the equation of the normal, we can follow the steps below:

The gradient of the tangent is equal to the derivative of the equation of the parabola: y = x - x² dy/dx = 1 - 2x

The gradient of the tangent at (1,0) is 1 - 2(1) = -1

The gradient of the normal is the negative reciprocal of the tangent gradient at the point of tangency.

The gradient of the normal at (1,0) is therefore 1.

The equation of the normal to the curve at the point (1,0) is therefore y = 1(x - 1) + 0, that is, y = x - 1.

Now we can find the coordinates of the point of intersection of the normal and the parabola by substituting y in the equation of the parabola:

y = x - x²  x - x² = x - 1 x² = 1 x = ±1The normal line to the parabola y = x - x² at the point (1,0) intersects the parabola a second time at the point (-1, 2).

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Answer:

17x+11

Step-by-step explanation:

-10x+20-9+27x

-10x+27=17x

20-9=11

17x+11

Answer:

Step-by-step explanation:

Here you go :)

Step 1

5(-2x + 4) - 9(1 - 3x)  Question

Step 2

5(-2x + 4) - 9(1 - 3x)  Remove parenthesis

-10x+20+-9+27x

Step 3

-10x+20+-9+27x  combine terms

17x+11

Answer

17x+11