Which expression can be used to find the output numbers in the table???

Answer: Option D.

Step-by-step explanation:

You can  observe that the dimensions of the bedroom in the scale drawing are:

[tex]length=2"\\width=1.5"[/tex]

You know that [tex]\frac{1}{2}"=3feet[/tex]

Then you need to convert these dimensions to the actual dimensions. So, you get:

[tex]actual\ lenght=\frac{(2")(3ft)}{\frac{1}{2}" }=12ft\\\\actual\ width=\frac{(1.5")(3ft)}{\frac{1}{2}" }=9ft[/tex]

Therefore, you can calculate the actual area of the bedroom. This is:

[tex]Area=(actual\ lenght)(actual\ width)\\Area=(12ft)(9ft)\\Area=108ft^2[/tex]

Answer:

Option D.

Step-by-step explanation:

From the given figure it is clear that

Length of the bedroom in scale drawing = 2''

Width of the bedroom in scale drawing = 1.5''

It is given that

Scale [tex]\frac{1}{2}''=3feet[/tex]

[tex]1''=6feet[/tex]

Using this conversion we get

[tex]2''=12feet[/tex]

[tex]1.5''=9feet[/tex]

Actual length of the bedroom = 12 feet

Actual width of the bedroom = 9 feet

Area of a rectangle is

[tex]Area=length\times width[/tex]

Actual area of the bedroom is

[tex]Area=12\times 9[/tex]

[tex]Area=108[/tex]

The actual area of the bedroom is 108 ft2.

Therefore, the correct option is D.

hi there the answer is 7:30 see the picture

Answer: 12b

Step-by-step explanation: you multiply 4 by 3 but keep the b

Answer:

C ---> 12b

Step-by-step explanation:

First you would distribute the 4 to the 3b which will give you 12b.

4(3b)

4*3=12

12b

The conditional statement is:

We know that a conditional statement is the statement which is written in the form of:

        If  p then q  i.e.  p → q

where p is the hypothesis of the statement.

and q is the conclusion  of the statement which is based on the hypothesis.

Here we are given a statement as:

 Two parallel lines lie in the same plane.

i.e. the hypothesis of the conditional statement is:

Two lines are parallel.

and conclusion is: They will lie in the same plane

( Because if two lines lie in the same plane then we can't conclude that they will be parallel )

[tex]\vec F(x,y,z)=4x^2\,\vec\imath+4y^2\,\vec\jmath+3z^2\,\vec k\implies\nabla\cdot\vec F=8x+8y+6z[/tex]

Let [tex]S[/tex] be the surface of the rectangular prism bounded by the planes [tex]x=0[/tex], [tex]x=a[/tex], [tex]y=0[/tex], [tex]y=b[/tex], [tex]z=0[/tex], and [tex]z=c[/tex]. By the divergence theorem, the integral of [tex]\vec F[/tex] over [tex]S[/tex] is given by the integral of [tex]\nabla\cdot\vec F[/tex] over the interior of [tex]S[/tex] (call it [tex]R[/tex]):

[tex]\displaystyle\iint_S\vec F\cdot\mathrm d\vec S=\iiint_R(\nabla\cdot\vec F)\,\mathrm dV[/tex]

[tex]=\displaystyle\int_0^c\int_0^b\int_0^a(8x+8y+6z)\,\mathrm dx\,\mathrm dy\,\mathrm dz=\boxed{abc(4a+4b+3c)}[/tex]

Answer:

[tex]\displaystyle \iiint_D {\nabla \cdot \textbf{F}} \, dV = \boxed{6875}[/tex]

General Formulas and Concepts:

Calculus

Differentiation

Derivative Property [Multiplied Constant]:
[tex]\displaystyle (cu)' = cu'[/tex]

Derivative Rule [Basic Power Rule]:

Integration

Integration Rule [Reverse Power Rule]:
[tex]\displaystyle \int {x^n} \, dx = \frac{x^{n + 1}}{n + 1} + C[/tex]

Integration Rule [Fundamental Theorem of Calculus 1]:
[tex]\displaystyle \int\limits^b_a {f(x)} \, dx = F(b) - F(a)[/tex]

Integration Property [Multiplied Constant]:
[tex]\displaystyle \int {cf(x)} \, dx = c \int {f(x)} \, dx[/tex]

Integration Property [Addition/Subtraction]:
[tex]\displaystyle \int {[f(x) \pm g(x)]} \, dx = \int {f(x)} \, dx \pm \int {g(x)} \, dx[/tex]

Multivariable Calculus

Partial Derivatives

Vector Calculus (Line Integrals)

Del (Operator):
[tex]\displaystyle \nabla = \hat{\i} \frac{\partial}{\partial x} + \hat{\j} \frac{\partial}{\partial y} + \hat{\text{k}} \frac{\partial}{\partial z}[/tex]

Div and Curl:

Divergence Theorem:
[tex]\displaystyle \iint_S {\big( \nabla \times \textbf{F} \big) \cdot \textbf{n}} \, d\sigma = \iiint_D {\nabla \cdot \textbf{F}} \, dV[/tex]

Step-by-step explanation:

*Note:
Your question is incomplete, but I have defined the missing portions of the question below.

Step 1: Define

Identify given.

[tex]\displaystyle \textbf{F} (x, y, z) = 4x^2 \hat{\i} + 4y^2 \hat{\j} + 3z^2 \hat{\text{k}}[/tex]

[tex]\displaystyle \text{Region (Boundary de} \text{fined by rectangular prism):} \left\{ \begin{array}{ccc} 0 \leq x \leq 5 \\ 0 \leq y \leq 5 \\ 0 \leq z \leq 5 \end{array}[/tex]

Step 2: Find Flux Pt. 1

Step 3: Find Flux Pt. 2

We can evaluate the Flux integral (Divergence Theorem integral) using basic integration techniques listed under "Calculus":

[tex]\displaystyle \begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 \int\limits^5_0 {4x^2 + x \big( 8y + 6z \big) \bigg| \limits^{x = 5}_{x = 0}} \, dy \, dz \\& = \int\limits^5_0 \int\limits^5_0 {\big( 40y + 30z + 100 \big)} \, dy \, dz \\& = \int\limits^5_0 {20y^2 + y \big( 30z + 100 \big) \bigg| \limits^{y = 5}_{y = 0}} \, dz \\\end{aligned}[/tex]

[tex]\displaystyle\begin{aligned}\int\limits^5_0 \int\limits^5_0 \int\limits^5_0 {\big( 8x + 8y + 6z \big)} \, dx \, dy \, dz & = \int\limits^5_0 {\big( 150z + 1000 \big)} \, dz \\& = \big( 75z^2 + 1000z \big) \bigg| \limits^{z = 5}_{z = 0} \\& = \boxed{6875} \\\end{aligned}[/tex]

∴  [tex]\displaystyle \Phi = \boxed{6875}[/tex]

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Topic: Multivariable Calculus

Unit: Stokes' Theorem and Divergence Theorem

Answer:

She will receive [tex]\$5[/tex]

Step-by-step explanation:

step 1

Find the total cost

The total cost is equal to

[tex]5(\$6.00)+4(\$7.50)=\$60[/tex]

step 2

Find the difference

[tex]\$65-\$60=\$5[/tex]

Answer:

$5

Step-by-step explanation:

65-6x5-4x7.5=5

For this case we have that, by definition, the volume of the cylinder is given by:

[tex]V = \pi * r ^ 2 * h[/tex]

Where:

h: It's the height

A: It's the radio

We have to:

[tex]h = 15\\r = 12[/tex]

Substituting:

[tex]V = \pi * (12) ^ 2 * 15\\V = \pi * 144 * 15\\V = 2160 \pi \ units ^ 3[/tex]

Answer:

Option B

Answer: 2160

Step-by-step explanation:

apex

Answer:

[tex]x=1\\y=3[/tex]

Step-by-step explanation:

You can use the Method of Elimination:

Multiply the first  equation by -1, add both equations and then solve for the variable "x":

[tex]\left \{ {{(-1)(2x + y )= 5(-1)} \atop {x + y = 4}} \right.\\\\\left \{ {{(-2x - y = -5} \atop {x + y = 4}} \right. \\.........................\\-x=-1\\\\(-1)(-x)=(-1)(-1)\\\\x=1[/tex]

Now substitute [tex]x=1[/tex] into any of the original equations and solve for the variable "y":

[tex]x + y = 4\\1 + y = 4\\y=4-1\\y=3[/tex]

[tex]x < - 10.434462 \\ x > 0[/tex]

Answer:

D

Step-by-step explanation:

The reading program really improved some of the student's reaping speeds.

Answer:

C and D

Step-by-step explanation:

3 is the base because its the number being multiplied repeatedly while the exponent would be the number of times its being multiplied.

Answer:

[tex]\boxed{\text{(v) and (viii)}}[/tex]

Step-by-step explanation:

The three step test for continuity states that a function ƒ(x) is continuous at a point x = a if three conditions are satisfied:

(i) Left-hand limit = right-hand limit.

Pass. The limit from either side is 8.

(ii) Left-hand limit = limit.  

Pass. If the limits from either direction exist, the limit exists.

(iii) Limit as x ⟶ ∞ is not part of the three-step test.

(iv) Limit as x ⟶ 1 exists. Pass.

(v)  f(1) is defined.

FAIL. f(1) is not defined.

(vi) Limit as x ⟶ ∞ is not part of the three-step test.

(vii) Passing the three-step test is not a step in the test.

(viii) The limit as x ⟶ 1 does not equal f(1).

FAIL. f(1) is undefined.

The steps in the three-step test for which the function fails are [tex]\boxed{\textbf{(v) and (viii)}}[/tex].

The volume of an oblique cone, to the nearest tenth is: 235.5 cubic units.

Volume of an oblique cone = (1/3) × π × r² × h, where r is radius and h is height of the oblique cone.

Given:

Thus:

Volume of an oblique cone = (1/3) × 3.14 × 5² × 9

Volume of an oblique cone = 235.5 cubic units.

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The approximate volume of the oblique cone is V = 235.5 cubic units

A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the center of base) called the apex or vertex.

The volume of a cone is given by the equation

Volume of Cone = ( 1/3 ) πr²h

where r is the radius of the cone

h is the height of the cone

Surface area of the cone = πr ( l + r )

where l = √ ( b² + r² )

Given data ,

Let the radius of the cone be r = 5 units

Let the height of the cone be h = 9 units

And , Volume of Cone = ( 1/3 ) πr²h

On simplifying , we get

V = ( 1/3 ) ( 3.14 ) ( 5 )² ( h )

V = 1.0467 x 25 x 9

V = 235.5 units³

Hence , the volume of cone is V = 235.5 units³

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The complete question is attached below :

What is the approximate volume of the oblique cone? Use π ≈ 3.14 and round to the nearest tenth.

a) 117.8 cubic units

b) 141.3 cubic units

c) 235.5 cubic units

d) 282.6 cubic units

The given points (-2,6) and (4,12) are the solution of the given equations. Option A is correct.

The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.

Here,
Given a system of equations,
y = x + 8  - - - - (1)

2y = x² + 8 - - - (2)

In order to determine that the points (-2,6) and (4,12) both are solutions of the given system of equations we must put the points in the equations,
So,
Put (-2, 6) in both equations,

Equation 1
put x = -2,
y = -2 + 8
y = 6

Equation 2
2y = [-2]² + 8
y = 4 + 8 / 2
y = 6

So points (-2, 6) is the solution of the given system of equation,

Similarly, by assigning the other point in the equation gives the same solutions

Thus, the given points (-2,6) and (4,12) are the solution of the given equations. Option A is correct.

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Answer:

16.92 pints of lemonade was made

Step-by-step explanation:

To estimate 47% of 77, multiply 77 by 0.47. The estimated value is approximately 36.19.

To estimate the percent of a number, we multiply the number by the percentage as a decimal. In this case, to estimate 47% of 77, we multiply 77 by 0.47. This gives us an estimated value of 36.19. Therefore, 47% of 77 is approximately 36.19.

Answer:

The conic is ellipse of equation (x - 1)²/22 + (y + 4)²/44 = 1

Step-by-step explanation:

* Lets revise how to identify the type of the conic  

- Rewrite the equation in the general form,  

 Ax² + Bxy + Cy² + Dx + Ey + F = 0  

- Identify the values of A and C from the general form.  

- If A and C are nonzero, have the same sign, and are not equal  

 to each other, then the graph is an ellipse.  

- If A and C are equal and nonzero and have the same sign, then  

 the graph is a circle  

- If A and C are nonzero and have opposite signs, and are not equal  

then the graph is a hyperbola.  

- If either A or C is zero, then the graph is a parabola  

* Now lets solve the problem

The equation is 4x² + 2y² - 8x + 16y - 52 = 0

∴ A = 4 and C = 2 ⇒ same sign and different values

∴ The equation is ellipse

* The standard form of the ellipse is

  (x - h)²/a² + (y - k)²/b² = 1

- Lets try to make this form from the general form

- Group terms that contain the same variable, and move the

  constant to the opposite side of the equation

∴ (4x² - 8x) + (2y² + 16y) = 52

- Factorize the coefficients of the squared terms

∴ 4(x² - 2x) + 2(y² + 8y) = 52

- Complete the square for x and y

# To make completing square

- Divide the coefficient  of x (or y) by 2 and then square the answer

- Add and subtract this square number and form the bracket of

 the completing the square

# 2 ÷ 2 = 1 ⇒ (1)² = 1 ⇒ add and subtract 1

∴ 4[(x² - 2x + 1) - 1] = 4(x² - 2x + 1) - 4

- Rewrite as perfect squares ⇒ 4(x -1)² - 4

# 8 ÷ 2 = 4 ⇒ (4)² = 16 ⇒ add and subtract 16

∴ 2[(y² + 8y + 16) - 16] = 2(y² + 8y + 16)² - 32

- Rewrite as perfect squares ⇒ 2(y + 4)² - 32

∴ 4(x - 1)² - 4 + 2(y + 4)² - 32 = 52

∴ 4(x - 1)² - 4 + 2(y + 4)² = 32 + 4 + 52

∴ 4(x - 1)² + 2(y + 4)² = 88 ⇒ divide all terms by 88

∴ (x - 1)²/22 + (y + 4)²/44 = 1

Using the point slope formula (y-y1=m(x-x1)) it is found to be y=1/2x+2.

Answer:

i have provided some pictures to help you i cant post the graphs though cuz they dont allow me to but if you need them i can send link pictures  :)

i also love you're Naruto profile picture uwu

Jeanne can use a system of inequalities to make at least $75.

Let X represent babysitting hours = $6 per hour.

Y represent tutoring hours = $10 per hour.

If she will work more 7.5hours or more than 7.5 hours she can make $75 easily.

$10 per hour × 7 hours = $70

& $6 per hour × 1 hour = $6

so, $70 + $6 = $76.

In the above way she can make easily $75.

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Answer:

The equation of the curve is y = x² + 3x

Step-by-step explanation:

I get your drift, but wish you had stated specifically that you wanted to find the equation of this curve.

Slope of tangent line to curve is dy/dx = 2x + 3.

Integrating that with respect to x yields y = x² + 3x + C.

The point (-3, 0) must satisfy this equation:

0 = (-3)² + 3(-3) + C, so C = 0.

The equation of the curve is y = x² + 3x

The equation of the curve where the slope at any point is 2x + 3 and it passes through the point (-3, 0) is y = x² + 3x.

The student's question involves finding the equation of a curve given that at each point (x, y) on the curve, the slope is 2x + 3, and the curve passes through the point (-3, 0). This is a problem that involves differential equations, as it asks us to find a function y(x) whose derivative with respect to x is given.

To find the equation of the curve, we integrate the slope function. Since the slope at any point is 2x + 3, we have:
∂y/∂x = 2x + 3
Integrating both sides with respect to x gives:
y = x² + 3x + C

To find the constant of integration C, we use the fact that the curve passes through (-3, 0). Substituting these values into the equation gives:
0 = (-3)² + 3(-3) + C
0 = 9 - 9 + C
Thus, C = 0, and the equation of the curve is:
y = x² + 3x.

Answer:

8

Step-by-step explanation:

When you are told to find f(-5), that means that you are to sub in a -5 for every x you see.  That -5 could be any number or expression.  Subbing in a -5 looks like this:

[tex]7(-5)^5+35(-5)^4-2(-5)^3-4(-5)^2+30(-5)+8[/tex]

Be careful with all those negatives.  Doing the math on that gives you that f(-5) = 8

Answer:

option C

y = 2

Step-by-step explanation:

Given in the question,

a co-ordinate = (-2,2)

x = -2

y = 2

Equation of the straight line

y = mx + c

here m = gradient of the line

        c = y - intercept

plug value in the equation above

y = (0)x + 2

y = 2

For the given logarithmic function, it is undefined as x approaches negative infinity, and increases without bound as x approaches positive infinity. The correct answer is B. One end increases and one end decreases.

The function [tex]f(x) = log_{10} (5x-1)[/tex] is a logarithmic function with a base of 10. Its end behavior is determined by the properties of logarithmic functions.

Logarithmic functions have one side that increases without bound (to positive infinity) and one side that approaches a certain limit, but never reaches it, hence getting infinitely close to it. In this case, as x approaches negative infinity, the function becomes undefined as (5x-1) becomes a negative number and logarithm is undefined for negative values. On the other end, as x approaches positive infinity, the function will also approach positive infinity because the log of a large number gets larger.

Thus, the correct answer would be B. One end increases and one end decreases (becomes undefined).

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The end behavior of the function is that A. one end decreases and one end approaches a constant.

The given function is f(x) = log10 (5x-1).

To determine the end behavior of the function, we can consider the limit of the function as x approaches positive and negative infinity.

As x approaches positive infinity, the argument of the logarithm, 5x-1, will become larger and larger, resulting in a logarithm that approaches positive infinity. Therefore, the right end of the graph increases.

Similarly, as x approaches negative infinity, the argument of the logarithm will become smaller and smaller, resulting in a logarithm that approaches negative infinity. Therefore, the left end of the graph decreases.

Thus, the correct answer is A. One end decreases and one end approaches a constant.

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The range of F(x) = logb x is the set of all real numbers.

TRUE

The range of F(x) = logb x is the set of all real numbers since the correct option is True.

The domain of this function is R+ or a positive real number For range if b&gt;1  function will be an increasing function and the graph will be asymptotic to the negative y-axis. which implies if x goes to infinity f(x) goes to infinity and vice versa if 0&lt;b&lt;1 function will be a decreasing and graph will be asymptotic to the positive y-axis. which implies if x goes to infinity f(x) goes to 0 and vice-versa the range of the above function is all real numbers.

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Answer:

Correct choice is A.

Step-by-step explanation:

We have to find about which of the given choices is the formula for the volume of a pyramid with base area B and height h.

We know that formula of volume of pyramid is given by:

[tex]volume = \frac{1}{3}\left(Base\ area\right)\left(Height\right)[/tex]

Plug the given values

[tex]volume = \frac{1}{3}\left(B\right)\left(h\right)[/tex]

So the correct choice is A.

Answer: A.  [tex]\dfrac{1}{3}\times\text{B}\times\text{h}[/tex]

Step-by-step explanation:

We know that the volume of a pyramid is given by :-

[tex]\text{Volume}=\dfrac{1}{3}\times\text{Base Area of the pyramid}\times\text{Height of pyramid}[/tex]

Let B be the Base Area of the pyramid and h be the Height of pyramid, then the formula for the volume of a pyramid with base area B and height h will become :-

[tex]\text{Volume}=\dfrac{1}{3}\times\text{B}\times\text{h}[/tex]

Hence, the formula for the volume of a pyramid with base area B and height h =[tex]\dfrac{1}{3}\times\text{B}\times\text{h}[/tex]

approximately 0.3 or 3/10 pizza was left for Julio to eat.

mind you some numbers were rounded. if you want the exact number then it's 9/28 which is equal to 0.32.

hope this helps

After accounting for the amounts of pizza eaten by Julio's family (parents, brothers, and sisters), you find that there was approximately 0.36 pizzas left for Julio to eat.

This question deals with some basic arithmetic and fractions. Start by counting how many pizzas Julio's family ate altogether. His parents ate 3/7 of one pizza, his brothers ate 2 3/4 pizzas, and his sisters ate 2 1/2 pizzas.

To add these amounts together, you might find it easiest to convert all the fractions to sevenths. The brothers ate 2 4/7 pizzas (as 4/7 is equivalent to 1/2) and the sisters ate 2 3.5/7 pizzas (as 3.5/7 is equivalent to 1/2). Add these to the 3/7 pizza the parents ate, you find the family ate a total of approximately 5.64 pizzas.

Since Julio's family ordered 6 pizzas in total, you then subtract the total amount eaten by the family from 6, which is approximately 0.36 pizzas. Therefore, Julio was left with 0.36 pizzas to eat.

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ANSWER

[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]

EXPLANATION

The given parabola has equation;

[tex]y = 34 {x}^{2} - 6x + 15[/tex]

Comparing this equation to

[tex]y = a{x}^{2} + bx + c[/tex]

we have

a=34, b=-6 and c=15

The x-coordinate of the vertex is given by:

[tex]x = \frac{ - b}{2a} [/tex]

[tex]x = \frac{ - - 6}{2(34)} [/tex]

[tex]x = \frac{ 6}{2(34)} [/tex]

[tex]x = \frac{ 3}{34} [/tex]

The y-coordinates of the vertex is obtained by substituting the x-value of the vertex into the equation:

[tex]y = 34( { \frac{3}{34} })^{2} - 6( \frac{3}{34}) + 15[/tex]

[tex]y = { \frac{9}{34} } - \frac{18}{34}+ 15[/tex]

[tex]y = \frac{501}{34} [/tex]

The vertex is

[tex]( \frac{3}{34} , \frac{501}{34} )[/tex]

Answer: (4,3)

He meant 3/4 not 34

Answer:

7.25

Step-by-step explanation:

Multiplying both sides of this equation by 7.25 will both eliminate the fraction and isolate (solve for) x;

7.25(x/7.25= 4) → x = 4(7.25)

                             x = 29

The answer is 29

U Multiply 7.25 and 4 and you get 29

Check your a answer by putting 29 in for x and it's correct

I hope this helped you guys

Bonnie will be 10 feet and 1inch. Because 1.5 yards is actually 4.5 feet, since 3 feet make up 1 yard. 5 feet + 4 feet= 9 feet. 7 inches plus 6 inches(which is half a foot) = 13 inches or 1 foot and 1inch. 9 feet + 1 foot and 1 inch = 10 feet and 1 inch.

Answer:

[tex]\boxed{\text{10 ft 1 in}}[/tex]

Step-by-step explanation:

1. Convert the height of stilts to inches

1.5 yd × (36 in/1 yd) = 54 in

2. Convert Bonnie's height to inches

5ft 7in = 5 ft × (12 in/1 ft) + 7 in = 60 in + 7 in = 67 in

3. Calculate Bonnie's height on stilts

67 in + 54 in = 121 in

4. Convert inches back to feet and inches

121 in × (1 ft/12 in) = 10R1 ft = 10 ft 1 in  

Bonnie will be [tex]\boxed{\text{10 ft 1 in}}[/tex] tall on stilts.

The answer to the question is D

Answer:

The measure of x is 35 and a = 8.19

Step-by-step explanation: