A wholesaler requires a minimum of 4 items in each order from its retail customers. The manager of one retail store is considering ordering a certain number of sofas, x, and a certain number of pillows that come in pairs, y. Which graph represents the possible combinations of sofa and pillow orders the manager can have?

[tex]\bf (\stackrel{x_1}{-2}~,~\stackrel{y_1}{5})~\hspace{10em} slope = m\implies 6 \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-5=6[x-(-2)]\implies y-5=6(x+2) \\\\\\ y-5=6x+12\implies y=6x+17\qquad \impliedby \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

Answer:

  58°

Step-by-step explanation:

A right triangle can be drawn to model the geometry of the problem. The hypotenuse of the triangle is the length of the string, 100 ft. The side opposite the angle is the height of the kite above the ground, 85 ft.

The mnemonic SOH CAH TOA reminds you of the relationship between sides and angles.

  Sin = Opposite/Hypotenuse

  sin(α) = (85 ft)/(100 ft) = 0.85

The angle whose sine is 0.85 is found using the arcsine (inverse sine) function:

  α = arcsin(0.85) ≈ 58.2°

The angle of elevation is about 58°.

_____

When using your calculator to find the values of inverse trig functions, make sure it is in degrees mode. Otherwise, you're likely to get the answer in radians (≈ 1.01599 radians).

Step-by-step explanation:

[tex] f(x) = \log_a x [/tex]

[tex] \dfrac{f(x + h) - f(x)}{h} = [/tex]

[tex] = \dfrac{log_a(x + h) - \log_a x}{h} [/tex]

[tex] = \dfrac{log_a \dfrac{x + h}{x}}{h} [/tex]

[tex] = \dfrac{1}{h}log_a ( 1 + \dfrac{h}{x} ) [/tex]

[tex] = log_a ( 1 + \dfrac{h}{x} )^{\frac{1}{h}} [/tex]

Answer:

  21.97 in

Step-by-step explanation:

Use the formula for the volume of a cone, fill in the given information, and solve for the height.

  V = (1/3)πr²h

  23 in³ = (1/3)(3.14)(1 in)²h . . . . . . . . with given numbers

  3·23 in³/(3.14 in²) = h ≈ 21.97 in . . . . . divide by the coefficient of h

Answer:

21.97 inches

Step-by-step explanation:

If a cone-shaped water cup holds 23 cubic inches and has a radius of 1 inch, the height of the cup is 21.97 inches.

Round your answer to the nearest hundredth.

Answer:

$30,000.

Step-by-step explanation:

Wave Corporation began the current year with a retained earnings balance of $25,000.

Depreciation expense was of $5000

During the current year, the company earned net income of $15,000

Also gave cash dividends of $5,000.

So, year end retained earnings will be :

Year end retained balance = total net income minus net losses and dividends.

[tex]25000-5000+15000-5000=30000[/tex] dollars

The answer is $30,000.

Answer:

1 -> f

2 -> e

3 -> d

4 ->  a

5 ->  c

6 ->  g

7 ->  b

Step-by-step explanation:

Let consider the options as a,b,c,d,e,f,g

1. Bell curve  ->     f

2. Data set   ->      e

3. Histogram   ->   d

4. Mean       ->      a

5. Normal distribution   ->   c

6. Standard deviation   ->    g

7. Variance      ->     b

The task is to match vocabulary words to their definitions, a common task in an English class. It involves comparing words with definitions and identifying matches. This helps students understand new words.

Given that the task at hand is to match vocabulary words to their correct definitions, this is a task typically found in an English class. This activity involves comparing a list of words with a list of definitions, then identifying which definition corresponds to each word. For example, the word 'gratify' can be matched with the definition 'give (someone) pleasure or satisfaction'. This process helps students better understand and remember the meanings of new words.

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Answer:

  a) {C, D}, {B, E}, A . . . . four possible equivalent answers (explanation below)

  b) Line C shows a "directly proportional" relationship

Step-by-step explanation:

Slope is the ratio of "rise" (vertical change) to "run" (horizontal change). Positive changes are "up" and "right".

Line A -- has no vertical change, so its slope is 0.

Line B -- changes 1 unit vertically for each 4 units horizontally, so its slope is 1/4.

Line C -- changes 1 unit vertically for each 2 units horizontally, so its slope is 1/2.

Line D -- changes 1 unit vertically for each 2 units horizontally, so its slope is 1/2. This is the same slope as line C, so neither is greater than the other.

Line E -- changes 1 unit vertically for each 4 units horizontally, so its slope is 1/4. This is the same slope as line B, so neither is greater than the other.

If we use alphabetical order to rank equal slopes, then the slopes (greatest to least) are ...

  C (1/2), D (1/2), B (1/4), E (1/4), A (0)

_____

A "directly proportional" relationship graphs as a straight line through the origin. The only line passing through the point where the x- and y-axes meet is line C.

  Line C represents a proportional function.

Step-by-step explanation:

[tex]l \times w + l \sqrt{( \frac{w}{2}) ^{2} + {h}^{2} } + w \times \sqrt{( \frac{l}{2} )^{2} + {h}^{2} } [/tex]

L = length base

w = width base

h = height

Answer:

[tex]S=\dfrac{ns^2}{4}\left(\cot{\left(\dfrac{180^{\circ}}{n}\right)}+\sqrt{3}\right)[/tex]

Step-by-step explanation:

A "regular pyramid" is a pyramid whose base is a regular polygon and whose edges are all the same length. Thus each face is an equilateral triangle.

A hexagonal regular pyramid will look like a hexagonal pancake, as the vertical height of it will be zero. A regular pyramid with 7 or more faces cannot exist, because the apexes of the triangular faces cannot meet at a point.

__

For an edge length of "s", the area of each triangular face is (√3)/4×s². There are n of those faces, so the lateral area (LA) will be ...

   LA = ns²(√3)/4

The area of the regular polygon base will be the product of half its perimeter and the length of its apothem (a). The apothem is ...

  a = (s/2)cot(180°/n)

So, the area of the base (BA) is ...

  BA = (1/2)(ns)(s/2)cot(180°/n) = ns²cot(180°/n)/4

The total surface area of the regular pyramid is then ...

  S = BA + LA

  S = (ns²/4)(cot(180°/n) +√3) . . . . for edge length s and n faces (3≤n≤5)

Answer:

  see below

Step-by-step explanation:

The formula for the sum of an infinite geometric series with first term a1 and common ratio r (where |r| < 1) is ...

  sum = a1/(1 -r)

Applying this to the given series, we get ...

a. sum = 5/(1 -3/4) = 5/(1/4) = 20

b. sum = d/(1 -1/t) = d/((t-1)/t) = dt/(t-1)

_____

The derivation of the above formula is in most texts on sequences and series. In general, you write an expression for the difference of the sum (S) and the product r·S. You find all terms of the series cancel except the first and last, and the last goes to zero in the limit, because r^∞ → 0 for |r| < 1. Hence you get ...

  S -rS = a1

  S = a1/(1 -r)

Answer:

  A:  -2

Step-by-step explanation:

You want some factor k such that k(5x) +(10x) = 0. That is, 5k+10 = 0. The solution to this is k=-2, corresponding to selection A.

k = -2 for sure

I normally multiply 5x+10y=15 by -2 to cancel out the x's.

This is because you can only solve the problem if one of your variables is canceled out and then you solve!

Answer:[tex]y=2x^2[/tex]

Step-by-step explanation:

Given Curve passes through [tex]\left ( 0,5\right )[/tex]

Also the slope of the curve at every point p is twice the Y-coordinate of p

Let the coordinate of p be[tex] \left ( x,y\right )[/tex]

Therefore

[tex]\frac{\mathrm{d} y}{\mathrm{d} x}=2y[/tex]

[tex]\frac{dy}{y}=2dx[/tex]

Integrating both sides

[tex]\int \frac{dy}{y}=\int 2dx[/tex]

[tex]\ln y=2x+c[/tex]

Substituting values

[tex]\ln 5=c[/tex]

[tex]\ln \frac{y}{5}=2x[/tex]

[tex]y=2x^2[/tex]

Answer: 1) Each friend had contributed $6.25.

2)The expression to show how many books Aaron read in p months :

[tex]y=9p[/tex]

He reads 54 books in 6 months.

Step-by-step explanation:

1) Given : The total number of friends who contributed equal amounts of money to buy a present. : 4

The total amount they have = $25

Since all the friends contributed the same amount.

Thus , the amount each had contributed :

[tex]=\dfrac{\text{Amount collected}}{\text{Number of friends}}\\\\=\dfrac{25}{4}=6.25[/tex]

Hence, each friend had contributed $6.25.

2) Given : The number of books Aron reads each month = 9 books

Let the number of months be 'p'.

Then the expression to show how many books Aaron read in p months .

[tex]y=9p[/tex]

Then , the  number of books Aaron read if he read for 6 months.

[tex]y=9(6)=54[/tex]

Hence, he reads 54 books in 6 months.

Answer:

  10 weeks

Step-by-step explanation:

Let w represent the number of weeks Anthony will be saving. Then he wants ...

  165 + 40w = 500 +0.10×500

  40w = 385 . . . . . subtract 165 and simplify

  w = 9.625 . . . . . . divide by 40

It will take Anthony 9.625 ≈ 10 weeks to save that amount.

Answer:

[tex]8\frac{2}{8}[/tex]

Step-by-step explanation:

x = number of granola bars

[tex]\frac{3}{4} + 7\frac{1}{2} = \frac{6}{8} + 7\frac{4}{8} = 7\frac{10}{8} = 8\frac{2}{8}[/tex] = x[/tex]

Solve the equation

He can conclude that the system of equations has no solution since one equation in it always results with false equivalency.

Hope this helps.

r3t40

He can conclude that the system of equations is inconsistent, i.e. it has no solution.

We know that we get a no solution when we get a expression which is always false.

Here,

Vineet solved a system of equations by substitution.

In his work, he substituted an expression for one of the variables and solved for the value of the other.

This resulted in the equation 7 = 9.

which is a false identity.

since 7 can never be equal to 9.

Hence, the system of equations is inconsistent , it has no solution.

The answer x = 7 is false here is why.

[tex]3x+52=13\Longrightarrow3x=-39[/tex]

This further simplifies to solution,

[tex]x=-\dfrac{39}{3}\Longrightarrow\boxed{x=-13}[/tex]

Hope this helps.

r3t40

Final answer:

The two-column proof format shows that the solution to the given equation 3x + 52 = 13 is x = -13, which contradicts the statement x = 7 to be proven. Either the given equation or the proof is incorrect as x = 7 cannot be derived from the equation provided.

Explanation:

Two Column Proof

When given the equation 3x + 52 = 13, we are asked to prove that x = 7. To do this, we can use a methodical approach in a two-column proof format where we list each step of the solution process alongside the reason for each step, as follows:

3x + 52 = 13: Given equation.

3x = 13 - 52: Subtract 52 from both sides.

3x = -39: Simplify.

x = -39 / 3: Divide both sides by 3.

x = -13: Simplify.

This results in x = -13, which contradicts the initial statement that we need to prove (x = 7). Therefore, either there is a mistake in the given equation or the proof is incorrect. Based on the provided information, x = 7 cannot be directly proven from the equation 3x + 52 = 13.

Answer:

  a.  6x^3 - 24x^2 + 6x + 36

Step-by-step explanation:

These are expanded using the distributive property, which is also used for collecting terms.

  (2x - 6)(3x2 - 3x - 6) = 2x(3x^2 - 3x - 6) - 6(3x^2 - 3x - 6)

  = 6x^3 -6x^2 -12x -18x^2 +18x +36

  = 6x^3 +(-6-18)x^2 +(-12 +18)x +36

  = 6x^3 -24x^2 +6x +36 . . . . . . matches selection A

_____

Comment on strategy

For multiple-choice questions, it often works well to find a way to identify a viable answer with the minimum amount of work. Comparing these answer choices, you can see that determining the correct values of the x-term and the constant term will let you pick the right choice.

The constant term is easy, because it is simply the product of the constants (-6)(-6) = 36. This narrows the choices to A and C.

The x-term will be the sum of products of x-terms and constants:

  2x(-6) +(-6)(-3x) = -6(2x-3x) = -6(-x) = 6x

This narrows the choices to A alone.

Observational study.

------APEX

Answer:

Step-by-step explanation:

The choices for this question are

a. Double-blind study

b. Experiment

c. Sample survey

d. Observational study

The right answer would be d. Observational study, because this type of study is defined as an empirical and non-experimental research where all information is obtained by observation. When we apply this study, we try to find a cause-effect relation by observing the phenomenon as it naturally happens, that is, without interfering with the course of events like experimental investigations do.

So, in this case, Matilda is just observing, without altering anything that could influence the birds. She just sits observe and recover information, that's an observational study.

Therefore, the right answer is d.

Answer:

.6094

Step-by-step explanation:

Answer:

Step-by-step explanation:

A man steps out of a plane at 4,000m of height above the ground.The point at which he jumps out of the plane would make a good reference point. However, if his acceleration is going to change as a result of him opening his parachute 2000m above the ground, a good reference point would be there. Keep in mind though, that his velocity at that instant would need to be known for it to be useful- otherwise the airplane reference point would be just as good with appropriate modeling....

Answer:4000m easy !!

Answer:

20 seconds

Step-by-step explanation:

Given:

Position of car = s(t) = 60t-1.5t^2

The speed is the change in position.

So,

[tex]Speed\ of\ car=\frac{ds}{dt} = \frac{d}{dt} (60t) -\frac{d}{dt} (1.5t^2)\\=60-2t(1.5)\\=60-3t[/tex]

When the car will stop, the speed will be zero.

[tex]60-3t=0\\3t=60\\t = \frac{60}{3}\\ t=20[/tex]

Therefore, the car will stop after 20 seconds of applying the break ..

The best predicted value of y for x = 5 is 27.

A regression equation is a mathematical model that represents the relationship between a dependent variable and one or more independent variables. It expresses the linear or nonlinear association between these variables and is derived from statistical methods like linear regression analysis.

To predict the value of y for x = 5 using the regression equation, you can substitute x = 5 into the equation y = 5x + 2:

y = 5(5) + 2 = 27

Therefore, the predicted value of y for x = 5 is 27.

The best predicted value of [tex]\( y \) for \( x = 5 \) is \( y = 27 \).[/tex]

To find the best predicted value of [tex]\( y \) for \( x = 5 \),[/tex]we substitute [tex]\( x = 5 \)[/tex] into the regression equation:

[tex]\[ y = 5x + 2 \] \[ y = 5(5) + 2 \] \[ y = 25 + 2 \] \[ y = 27 \][/tex]

To reconcile this discrepancy, if we assume that the provided value of [tex]\( y = 18.3 \)[/tex] corresponds to [tex]\( x = 5 \),[/tex] then we would set the regression equation equal to 18.3 and solve for \( x \):

[tex]\[ 18.3 = 5x + 2 \] \[ 16.3 = 5x \] \[ x = \frac{16.3}{5} \] \[ x = 3.26 \][/tex]

Answer:

Step-by-step explanation:

Circumference of the wheel = (pi)d = 45*3.14 = 141.3 inches

----

Distance traveled in inches: 5*141.3 = 706.5 inches

---

Distance traveled in feet: 706.5/12 = 58.875 feet

Answer:

0.60b + 0.30w = 150; 60 + 0.30w = 150

Step-by-step explanation:

Answer:

C. 0.60b + 0.30w = 150; 60 + 0.30w = 150

Step-by-step explanation:

Answer:

  f(x) = -2|x-2| +4

Step-by-step explanation:

Step 1: recognize this as an inverted, scaled, and translated absolute value function.

Step 2: identify the scale factor as 2, because each section has a "rise" of 2 for each "run" of 1. The scale factor is -2 because the function is inverted (reflected across the x-axis).

Step 3: identify the vertex* as (2, 4).

Step 4: Use the scale factor and translation information to make the transformation ...   (let abs(x) represent the absolute value function)

  f(x) = (scale factor)×abs(x -horizontal shift) + (vertical shift)

  f(x) = -2|x -2| +4

_____

* The vertex is an identifiable point on the graph of this function. Knowing how the vertex is translated tells you how the whole function is translated. In general, you want to use an identifiable point (a turning point, point of symmetry, extreme point, whatever) when you're trying to determine the translation. For some functions, like a line, there is no specific identifiable point, so determining any specific translation is difficult or impossible.

_____

Comment on writing functions from graphs

One of the reasons for studying different functions is so you can learn to recognize their shape, and associate a formula and certain properties with that shape.

_____

The attached graph shows the parent absolute value function in blue and the transformed function f(x) in red.

"Alia gets 4^2 fewer than Kelly, who gets 3^3."

So it's about a subtraction.

[tex]\boxed{3^3-4^2}[/tex]

Hope this helps.

r3t40

Answer:

  D. 3^3 - 4^2

Step-by-step explanation:

4^2 fewer than 3^3 is ...

  3^3 - 4^2 . . . . . matches choice D

Answer:

  b:  10% decay

Step-by-step explanation:

Expressed as a percentage change, the growth is usually the value of the base of the exponential function after 1 has been subtracted. That result is expressed as a percent:

  0.9 - 1 = -0.10 = -10% . . . . . 10% decay

_____

The "t/12" exponent means this is the decay that is experienced over 12 units of time. This might be the annual decay, where t is expressed in months, for example.

Answer:

proof my answer is correct

Step-by-step explanation:

The exact value of cosθ in simplified form is -5√61 / 61.

One area of mathematics known as trigonometry examines the relationship between the sides and angles of a right triangle. The relationship between sides and angles is defined for 6 trigonometric functions.

We have,

The terminal side of θ passes through the point (−5,−6).

Now, Hypotenuse

= √(-5)² + (-6)²

= √25+36

=√61

Using Trigonometry

cos θ = Adjacent side/ Hypotenuse

cos θ = -5/ √61

Now, rationalizing

cos θ = -5/√61 x √61/√61

cos θ = -5√61 / 61

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Answer:

  4/9

Step-by-step explanation:

The easiest segment to work with is BC, since the y-values are the same for coordinates B and C and for B' and C'.

The length of BC = 9 -(-9) = 18.

The length of B'C' = 7 -(-1) = 8.

The scale factor is B'C'/BC = 8/18 = 4/9.

Find the perimeter of the yard ( the distance around the yard).

A rectangle has two sides of each dimension.

The perimeter is 20 + 20 + 45 + 45 = 130 feet.

Now multiply the total feet by the cost per foot:

130 feet x 25 per foot = $3,250 total.

Danny needs to spend on his yard $3250 to fencing.

The rectangle is a geometrical figure in which opposite sides are equal.

The angle between any two consecutive sides will be 90 degrees.

Area of rectangle = length × width.

Perimeter of rectangle = 2( length + width).

Length of fence = Perimeter of his yard(rectangle)

Perimeter of rectangle = 2( length + width).

Perimeter of fence =2 ( 20 + 45 )

The perimeter of fence =130 foot.

Now

Cost = $25 per foot

So,

Cost of 130 feet at the rate of  $25 per foot

⇒ 130 × 25 = $3250

Hence, Danny needs to spend on his yard $3250 to fencing.

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