The ...... is the ratio of new/old.reductioncenter of dilationenlargementscale factor

The total cost of the pita bread and hummus dips will be $305.00.

To determine the cost of the pita bread and hummus dips, Toula can use the following expressions:

Cost of pita bread:

Number of crates needed = (150 bags) / (50 bags/crate) = 3 crates

Cost of each crate = $15.00

Total cost of pita bread = (Number of crates needed) × (Cost of each crate) = 3 crates × $15.00/crate = $45.00

Cost of hummus dips:

Number of boxes needed = (65 containers) / (5 containers/box) = 13 boxes

Cost of each box = $20.00

Total cost of hummus dips = (Number of boxes needed) × (Cost of each box) = 13 boxes × $20.00/box = $260.00

Therefore, the expressions Toula can use to determine the costs are:

Cost of pita bread = 3 crates × $15.00/crate

Cost of hummus dips = 13 boxes × $20.00/box

The total cost will be the sum of the costs of pita bread and hummus dips:

Total cost = Cost of pita bread + Cost of hummus dips

Total cost = $45.00 + $260.00

Total cost = $305.00

Therefore, the total cost of the pita bread and hummus dips will be $305.00.

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Answer:

Step-by-step explanation:

Let's denote the volume of the cube as V and the length of each edge as x. Given that the volume of a cube is V = x^3, we can find the rate at which the length of each edge is changing.

We're given that the rate of change of the volume is dV/dt = 56 in³/sec. We want to find the rate of change of the length of each edge, which is dx/dt, when the length of each edge is 6 inches.

First, we differentiate the volume equation with respect to time t:

V = x^3

dV/dt = d(x^3)/dt

Using the chain rule:

dV/dt = 3x^2 * (dx/dt)

Now, we know that dV/dt = 56 in³/sec and x = 6 in. Plugging these values into the equation, we get:

56 = 3 * (6)^2 * (dx/dt)

Solving for dx/dt:

56 = 108 * (dx/dt)

dx/dt = 56 / 108

dx/dt ≈ 0.5185 in/sec (rounded to four decimal places)

So, the rate at which the length of each edge is changing is approximately 0.5185 inches per second when the edges are 6 inches long.

The exterior angle of a triangle is equal to the sum of the two interior opposite angles, so : f° = a° + b° .

A triangle is a polygon which has 3 sides. The triangles can be divided into 3 types based on the value of the angles: Equilateral, isosceles ,scalene and right angled.

One of the internal angles of a right triangle (also known as a right-angled triangle) measures 90 degrees (a right angle). The hypotenuse, the triangle's longest side, is the side that faces the right angle. The triangle's other two sides are referred to as its legs. Right triangles adhere to the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the two legs.

We know when we add all the angles of any given triangle it is 180°

∴ a° + b° + c° = 180°

or, a° + b° = 180° - c°

Now we know that a linear pair the sum of the angles is 180°.

∴c° + f° = 180°

or, f° = 180° - c°

So from the above two equations we can say that

f° = a° + b°

Therefore in the triangle the exterior angle of the triangle is equal to the sum of the two interior opposite angles.

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Using the cross product for the proff of Pythagoras theorem, the correct step is

By the cross product property, AB² =  BC multiplied by BD

The cross product property is typically used to solve equations with two values, where the product of the extremes (the outer terms) is equal to the product of the means (the inner terms).

For the similar triangles, the ratio is as follows

BD / BA = BA / BC

BA² = BD * BC

and AB = BA, hence

BA² = BD * BC

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A function is a relation that gives one input for every one output thus the value of g(10) is -31.

A certain kind of relationship called a function binds inputs to essentially one output.

The machine will only accept specified inputs, described as the function's domain, and will potentially produce one output for each input.

As per the given function,

g(x) = -3x - 1

The value of the function at x = 10

g(10) = -3(10) - 1

g(10) = -30 - 1 = -31

Hence "A function is a relation that gives one input for every one output thus the value of g(10) is -31".

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Answer:

A: the starting height?

B: a plant with a starting height of 1.75 grows to a height 20% taller than its previous height?

Step-by-step explanation:

Answer:

163.5 cubes

Step-by-step explanation:

Answer:

A gift box has dimensions of: 8 12 inches, 5 12 inches, and 2 12 inches, respectively. How many cubes with side lengths of 12 inches would be needed to fill the gift box?

116.875 cubes

163.5 cubes

935 cubes

1870 cubes

163.5 cubes

Step-by-step explanation:

A gift box has dimensions of: 8 12 inches, 5 12 inches, and 2 12 inches, respectively. How many cubes with side lengths of 12 inches would be needed to fill the gift box?

116.875 cubes

163.5 cubes

935 cubes

1870 cubes

163.5 cubes

The time Jack left Santa Clara is 1 : 55 pm

A word problem in math is a math question written as one sentence or more. These statements are interpreted into mathematical equation or expression.

The time for Jack to walk to lose Altos is 25 min and he uses another 25mins to work to Palo alto.

Therefore, the total time he spent is

25mins + 25 mins = 50 mins

He arrived Palo at 2 :45 pm, therefore the time he left Santa Clare will be ;

2:45 pm = 14 :45

= 14:45 - 50mins

= 13:55

= 1 : 55pm

Therefore he left at 1:55 pm

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The correct expanded form using Laws of exponents is:

Two-thirds times two-thirds times two-thirds times two-thirds

Some of the laws of exponents are:

1) When multiplying like bases, keep the base the same and add the exponents.

2) When raising a base with a power to another power, keep the base the same and multiply the exponents.

3) When dividing like bases, keep the base the same and subtract the denominator exponent from the numerator exponent.

Now, we want to solve the expression given as: (²/₃)⁴

When we expend this, we arrive at:

²/₃ × ²/₃ × ²/₃ × ²/₃

This among the options is Option A which is:

Two-thirds times two-thirds times two-thirds times two-thirds

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Answer:

  D.  $10

Step-by-step explanation:

The cost per yard of soil at Luke's can be found using the slope formula.

  m = (y2 -y1)/(x2 -x1)

  m = (182.50 -123.50)/(5 -3) = 59/2 = 29.50

The y-intercept of the cost graph can be found from ...

  b = y1 -m·x1

  b = 123.50 -(29.50)(3) = 35.00

This is the charge when no soil is included in the delivery, so it is the delivery charge.

The difference between Luke's $35 delivery charge and Hope's $25 delivery charge is ...

  $35 -25 = $10 . . . difference in delivery charges

Answer:

Step-by-step explanation:

So we know he arrived at 8:11 am. He should've arrived at 8:05 am if he rode the bus. So, we know that it took 27 minutes for him to get to school by walking. If he arrived at 8:11, then he started walking at 7:44 am. Since the school bus arrived 2 minutes before he started walking, we can say that the school bus arrived at 7:42 am.

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The expected total dollar net operating Income for next year = $70,000

1) The contribution format income statement for the game last year, and the degree of operating leverage is computed below:

Contribution format income statement for the game last year Sales (15,000 × $20) = $300,000

Variable expenses (15,000 × $6) = $90,000

Contribution margin = $210,000

Fixed expenses = $182,000Net operating income = $28,000

Degree of operating leverage = Contribution margin / Net operating income= $210,000 / $28,000= 7.5 2)

The expected percentage increase in net operating income for next year:

The expected sales in next year = 18,000

games selling price per game = $20

Therefore, Total sales revenue = 18,000 × $20 = $360,000

Variable expenses = 18,000 × $6 = $108,000

Fixed expenses = $182,000

Expected net operating income = Total sales revenue – Variable expenses – Fixed expenses

= $360,000 – $108,000 – $182,000= $70,000

The expected percentage increase in net operating income = (Expected net operating income - Last year's net operating income) / Last year's net operating income*100= ($70,000 - $28,000) / $28,000*100= 150%

The expected total dollar net operating income for next year = $70,000

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On solving the provided question we can say that The following is the data table of the function.

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output. A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or scope. Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

here,

the provided functions that can be formed are

           x            -infinity < x < -10

f(x) =    2x + 10          -10 < x < 10

           4X - 10       10 < x < infinty

The following is the data table of the function.

x              y

-20          -20

-15          -15

-10          -10

-5             0

0              10

5               20

10              30

15              50

20              70

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An example of the piecewise defined function is: \(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

The subject of mathematics includes quantities and their variations, equations and related structures, shapes and their locations, and places where they can be found. The term "function" refers to the relationship between a set of inputs, each of which has an associated output.

A connection between inputs and outputs in which each input leads to a single, distinct result is known as a function. Each function is given a domain and a codomain, or range.

Usually, f is used to denote functions (x). input is an x. There are four main types of functions accessible. based on the following factors: on functions, one-to-one functions, many-to-one functions, inside functions, and on functions.

The following is the data table of the function.

x               y

-20          -20

-15           -15

-10           -10

-5              0

0              10

5              20

10              30

15              50

20             70

The provided functions that can be formed are

\(f(x)= \begin{cases}x & -\infty < x \leq-10 \\ 2 x+10 & -10 < x \leq 10 \\ 4 x-10 & 10 < x < \infty\end{cases}\)

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Answer:

7)  Domain:  (-∞, ∞)

    Range:  [-1, ∞)

8)  Domain:  (-∞, ∞)

    Range:  (-∞, ∞)

Step-by-step explanation:

Interval notation

( or ) : Use parentheses to indicate that the endpoint is excluded.

[ or ] : Use square brackets to indicate that the endpoint is included.

Domain & Range

The domain is the set of all possible input values (x-values).

The range is the set of all possible output values (y-values).

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

From inspection of the graph, the minimum y-value is y = -1.  

The end behavior of the relation is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow + \infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the range of the relation is restricted:  [-1, ∞)

From inspection of the graph, the line is continuous.

The arrows either end of the line indicate that the line continues indefinitely in those directions.

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

The end behavior of the function is:

\(y \rightarrow + \infty, \textsf{as } x \rightarrow - \infty\)

\(y \rightarrow -\infty, \textsf{as } x \rightarrow +\infty\)

Therefore, the domain of the relation is unrestricted:  (-∞, ∞)

Answer:

Step-by-step explanation:

The sum of the rates of painting, in fences per hour, is ...

  1/9 + 1/7 = (9+7)/63 . . . . fences per hour

The total rate in hours per fence is the inverse of that:

  63/16 = 3 15/16 ≈ 3.9 . . . hours to paint the fence

__

The relevant relationship is ...

  distance = speed × time

Let t represent Tom's speed in miles per hour. Then George's speed is (t-36). They both have traveled the same total distance at the point where Tom catches up.

  (2+3)(t-36) = 3t

  2t = 180 . . . . . . . add 180-3t

  t = 90 . . . . . . divide by 2

Tom's average speed is 90 miles per hour.

Answer:A. x= .100

Step-by-step explanation:because of the distance in miles

The division of two complex numbers is another complex number, whose real part is   \((ac + bd)/(c^2 + d^2)\) and imaginary part is  \((bc-ad)/(c^2 + d^2)\) .  the simplified expression is   \(8(\cos(22°) + i\sin(22°))\) .

To simplify the expression, we can use the formula for the division of two complex numbers:

\(\frac{Z_1}{Z_2} = \frac{r_1}{r_2} \cos (\Theta _1 - \Theta _2)\)

where  \(z_1 = r_1 \text{cis}(\theta_1)$ and $z_2 = r_2 \text{cis}(\theta_2)\) are complex numbers in polar form.

Using this formula with \(z_1 = 56(\cos(33°) + i\sin(33°))$ and $z_2 = 7(\cos(11°) + i\sin(11°))\)   , we get:

\(\frac{56(\cos(33°) + i\sin(33°))}{7(\cos(11°) + i\sin(11°))} &= \frac{56}{7} \text{cis}(33°-11°) \&= 8\text{cis}(22°)\)

Therefore, the simplified expression is   \(8(\cos(22°) + i\sin(22°)).\)

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What is cosine?

Well, cosine is adjacent side divided by the hypotenuse.

cos M = 20/36

Reducing 20/36 to the lowest terms we get

cos M = 5/9

cos N = 30/36

Reducing 30/36 to the lowest terms we get

cos N = 5/6

Answer:

\(y=\frac{4}{7} x-\frac{9}{7}\)

Step-by-step explanation:

The yellow points are on (4,1) and (8,8).

The slope is \(\frac{8-4}{8-1} =\frac{4}{7}\)

In point-slope form the equation is y-1=\(\frac{4}{7}\)(x-4)

Expand and add 1 to get y=\(\frac{4}{7}\)x-\(\frac{9}{7}\)

Using the Pythagoras theorem, we can find the value of x to be = 10ft.

Option B is correct.

The right-angled triangle's three sides are related in line with the Pythagoras theorem, also referred to as the Pythagorean theorem. The hypotenuse of a triangle's other two sides add up to a square, according to the Pythagorean theorem, which states that.

Here in the question,

We have 2 right-angled triangles.

So, base of the large triangle, x

= √ (13² - 12²) + √ (13² - 12²)

= √ 5² + √ 5²

= 5 + 5

= 10ft.

Therefore, the length of the side, x = 10ft.

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The simplification form of the given mathematical equation 4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 is \(4^{8}\)

In the given question, it is given

We know the simplification property of the division of numbers as,

Division in exponential form

\(\frac{a^{x} }{a^{y} }\) = \(a^{x-y}\) , and

Multiplication in exponential form

\(a^{x} . a^{y}\) = \(a^{x+y}\)

Similarly, we'll apply the same property to solve this question,

\(4^{5+3+2+3 + ( -2 -1 -2)}\)

\(4^{5+3+2+3 - ( 2 + 1 + 2)}\)

\(4^{13 - 5}\)

\(4^{8}\)

Hence, the simplification form of the given mathematical equation 4^5 x 4^3 x 4^2 x 4^3 / 4^2 x 4 x 4^2 is \(4^{8}\)

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Answer:

The vertex of the function is at (–3,–16)

The graph is increasing on the interval x > –3

The graph is positive only on the intervals where x < –7 and where

x > 1.

Step-by-step explanation:

The graph of \(f(x)=(x-1)(x+7)\) has clear zeroes at \(x=1\) and \(x=-7\), showing that \(f(x) > 0\) when \(x < -7\) and \(x > 1\). To determine where the vertex is, we can complete the square:

\(f(x)=(x-1)(x+7)\\y=x^2+6x-7\\y+16=x^2+6x-7+16\\y+16=x^2+6x+9\\y+16=(x+3)^2\\y=(x+3)^2-16\)

So, we can see the vertex is (-3,-16), meaning that where \(x > -3\), the function will be increasing on that interval

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

2x - 8 + 2x + 3

-8 = 3 so the statment is false for any value of x

We are not given the radius of the circle or any other relevant data, so I assumed the radius of the circle r=5

Answer:

The y-coordinate of Q is 3

Step-by-step explanation:

Circles and Lines

The figure below shows a circle of radius r=5 and a segment that goes from the center of the circle to a point of the circumference, where x=4.

We can find the y-coordinate of that point by using Pithagora's theorem:

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

Solving for y:

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

\(y^2=5^2-4^2\)

\(y^2=25-16=9\)

\(y=\sqrt{9}=3\)

The y-coordinate of Q is 3

Answer:

When the absolute value of the scale factor is less than one, a compression occurs. When the absolute value of the scale factor is equal to one, neither an expansion nor a compression occurs.

each video is 15 minutes long

Step-by-step explanation:

The number that can complete the equation 5y + 2(3y − 1) = ⬜y − (y + 2) is

5y + 2(3y − 1) = 12 y − (y + 2)

The number that can complete the equation is computed by simplifying the equation at the left hand side of the equality sign and comparing with the right side of the equality side

The comparison will show the number that can fit in the blank

Simplifying the equation at the left hand side of the equation

= 5y + 2(3y − 1)

= 5y + 6y − 2

= 11y - 2

Simplifying the equation at the right hand side of the equation

=  ⬜y − (y + 2)

let x represent the missing number

=  xy − (y + 2)

=  xy − y - 2

comparing both equations

11y - 2 =  xy − y - 2

11y =  xy − y

11y + y =  xy

12y = xy

x = 12

The missing value = 12

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Step-by-step explanation:

Collinear points have the same gradient

find the gradient(slope) between AB first

\( = \frac{1 - 2}{3 - 1} \\ = \frac{ - 1}{2} \)

Find the one for BC

\( = \frac{4 - 1}{ - 3 - 3} \\ = \frac{3}{ - 6} \\ = \frac{ - 1}{2} \)

Find the gradient between AC now

\( = \frac{4 - 2}{ - 3 - 1} \\ = \frac{2}{ - 4} \\ = \frac{ - 1}{2} \)

YOUR LAST STATEMENT NOW WILL BE

POINTS A,B AND C ARE COLLINEAR SINCE THE GRADIENTS BETWEEN THEM IS THE SAME!!!

Answer:

The answer should be b. (0,2) because that the order pair for y

Answer:

(2,3) makes the equation false.

Step-by-step explanation:

a. -1 = 1/2(0)-1

-1 = -1

b. 0 = 1/2(2) - 1

0 = 1 - 1

0 = 0

c. 2 = 1/2 (3)-1

2 = 3/2 - 1

2 = .5

d. 1=1/2(4)-1

1=2-1

1=1