A restaurant raises the price of its signature dish by 15%
The new price of the dish is 14.50

What was the original price of the dish?

Answer:

5 > [tex]\sqrt{18[/tex]

Step-by-step explanation:

The square root of 18 is approximately 4.24.

5 is greater than 4.24, so we can use the inequality sign >.

The line of symmetry of the parabola is t = 1.875 and the vertex of the parabola is (1.875, 77).

A function is a mathematical concept that relates an input value (or values) to an output value (or values) according to a specific rule or set of rules. It can be thought of as a machine that takes in one or more inputs and produces a corresponding output. Functions are often represented using function notation, such as f(x) or g(t), where the variable in the parentheses (x or t) represents the input and the value of the function (f(x) or g(t)) represents the output.

To identify the line of symmetry and vertex of the parabola given by the function [tex]f(t) = -16t^2 + 60t + 16[/tex], we need to use the formula:

t = -b/2a

where "a" is the coefficient of the [tex]t^2[/tex] term (-16 in this case) and "b" is the coefficient of the t term (60 in this case).

Part A: Identify the line of symmetry of the parabola.

Using the formula above, we get:

t = -60 / 2(-16) = 1.875

So the line of symmetry of the parabola is t = 1.875.

Part B: Identify the vertex of the parabola.

To find the vertex, we need to substitute the value we found for t into the original function:

[tex]f(1.875) = -16(1.875)^2 + 60(1.875) + 16 = 77[/tex]

So the vertex of the parabola is (1.875, 77).

Therefore, the line of symmetry of the parabola is t = 1.875 and the vertex of the parabola is (1.875, 77).

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Answer:

 a.  1492 kg

  b.  20.8 m

Step-by-step explanation:

Given a tree is initially 20 m high and has a diameter of 0.5 m, you want the mass of the trunk if its density is 380 kg/m³. If it adds a growth ring of 4 mm per year and adds height of 0.2 m in the first year, you want the height of the tree after 5 years, assuming the same amount of wood is added each year.

The volume of the tree trunk is that of a cylinder. The formula is ...

  V = (π/4)d²h

  V = (π/4)(0.5 m)²(20 m) ≈ 3.9270 m³

The mass is the product of volume and density:

  M = Vρ

  M = (3.9270 m³)(380 kg/m³) ≈ 1492 kg

The mass of the tree trunk is about 1492 kg.

In the first year, the diameter of the tree increases by 8 mm, and the height increases by 0.2 m,. This means the volume of the tree increases to ...

  V = (π/4)(0.508 m)²(20.2 m) ≈ 4.0942 m³

The volume increase is the same each year for 5 years, so after 5 years, the volume is ...

  3.9270 m³ + 5(4.0942 -3.9270) m³ ≈ 4.7630 m³

At that time, the diameter is about 0.540 m. Solving the volume equation for the height, we find it to be ...

  h = 4v/(π·d²)

  h = 4(4.7630 m³)/(π·(0.54 m)²) ≈ 20.797 m

The height of the trunk after 5 years is about 20.8 m.

__

Additional comment

We note that the wood added in the first year includes the cylindrical shell represented by the tree ring, and a cylindrical "plug" that is 0.2 m high and equivalent in diameter to the rest of the tree. This seems an odd way for the tree to grow, but may be a reasonable approximation to the actual growth.

The height, diameter, and growth are all given to 1 significant figure. Hence the 4- and 3-significant figures used in the answers may be unsupported by the precision of the given numbers. Keeping 2 significant figures, we might report the initial mass as 1500 kg, and the final height as 21 m.

The graph is drawn by a function formulated to have the correct height at the x-intercept: v(d, h) - (final volume) = 0.

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The expression that can be used to find out the amount of time it would take Sal to finish the remaining homework is C. 4 / 9 x 3 / 5 .

To find the expression that would show the time it would take for Sal to finish his homework, the formula would be:

= Proportion of questions remaining x Time taken to finish one question

Proportion of questions remaining:

= 1 - 5 / 9

= 4 / 9

Time taken to finish one question:

= 3 / 5 minutes

The expression is therefore:

4 / 9 x 3 / 5

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Yellow to red hence has a 4 to 1 ratio. Solution: B. 4 to 1 as 2 red times 5 purple (Instead of purple).

A percent is a claim that two factors are equal in mathematics. When two quantities are compared by dividing them, the result is expressed as a ratio as a fraction. For instance, the number of girls to boys in a class can be expressed as "girls: boys" or "girls/boys." One way to express a percentage is as follows: a/b = c/d in which a, b, c, and d were four values that prevent b and d from being equal to zero. As a result, the ratio of a to b is the same as the ratio of c to d. The first term (a) is therefore equal to the reelection campaign (b), and the τ (c) is equal to the fourth term.

given

The given equalities can be used to calculate the proportion of yellow to red:

5 green times 6 yellow (Subtract both sides by 5)

(6/5) Yellow is equivalent to green.

3 purple + 4 green (substitute for green)

4 (6/5) Purple x 3 yellow

(24/5) Purple x 3 yellow (divide both sides by 4)

(8/5) Purple x yellow

2 red times 5 purple (Instead of purple)

(5/8) yellow Equals 2 red.

2 red x 8 yellow (divide both sides by 5)

Red + 4 yellows

Yellow to red hence has a 4 to 1 ratio. Solution: B. 4 to 1 as 2 red times 5 purple (Instead of purple).

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If a varies inversely as b³, the value of a when b=3 is 4/9.

Given that, a varies inversely as b³.

Here, a∝1/b³

a=k/b³

Substitute a=3/2 and b=2 in a=k/b³, we get

3/2 = k/2³

3/2 = k/8

3 = k/4

k = 12

Substitute k = 12 in a=k/b³, we get

a=12/b³

When b=3

a = 12/3³

a=12/27

a=4/9

Therefore, if a varies inversely as b³, the value of a when b=3 is 4/9.

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The length of the side b of the right triangle is 76 units.

A right angle triangle is a triangle that has one of its angles as 90 degrees. Therefore, the side b of the right triangle can be found as follows:

tan 30° = opposite / adjacent side

where

opposite side = a = 44 units

adjacent side = b

Therefore,

tan 30° = 44 / b

cross multiply

b = 44 / tan 30

b = 44 / 0.57735026919

b = 76.2102710661

Therefore,

b = 76 units

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Answer:

Step-by-step explanation:

Perimeter: 34 yd

Area: 37 yd²

The answer of the given question based on the circle and rectangle is , the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².

Perimeter is a measurement of the distance around the edge of a two-dimensional shape. It is the sum of the lengths of all the sides of the shape. The perimeter is often measured in units of length, such as centimeters, meters, or feet.

To find the perimeter and area of the composite shape formed by a rectangle and two semicircles, we can break it down into its individual components and then add them up.

First, let's find the perimeter. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The perimeter can be calculated as:

Perimeter = 2 × (semicircle circumference) + rectangle perimeter

The circumference of circle is by the formula 2πr, where r is the radius. Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the circumference of each semicircle is:

C = 2πr = 2π(7.5) = 15π feet

The perimeter of the rectangle is simply the sum of its four sides, which is:

P = 2(length + width) = 2(15 + 4) = 38 feet

Putting it all together, we have:

Perimeter = 2 × 15π + 38 ≈ 83.8 feet

Now let's find the area. The shape consists of two semicircles, each with a diameter of 15 feet, and a rectangle with a width of 4 feet and a length equal to the diameter of the semicircles, which is 15 feet. The area can be calculated as:

Area = (semicircle area) + rectangle area

The area of a circle is given by the formula πr². Since each semicircle has a diameter of 15 feet, its radius is 7.5 feet. Therefore, the area of each semicircle is:

A = (1/2)πr² = (1/2)π(7.5)² = 44.18 feet²

The area of the rectangle is simply its length multiplied by its width, which is:

A = length × width = 15 × 4 = 60 feet²

Putting it all together, we have:

Area = 2 × 44.18 + 60 = 148.4feet²

Therefore, the perimeter of the shape is approximately 83.8 feet, and its area is approximately 148.4 feet².

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Answer:

To find the lower and upper quartiles and the interquartile range, we first need to order the data from smallest to largest:

20, 22, 25, 28, 29, 30, 32, 33, 34

Next, we find the median (middle value) of the entire dataset:

Median = (29 + 30) / 2 = 29.5

This median value divides the data into two halves. We then find the median of the lower half of the data, which includes all values less than or equal to 29.5:

Lower half: 20, 22, 25, 28, 29

Median of lower half = (25 + 28) / 2 = 26.5

This value, 26.5, is the lower quartile (Q1).

Similarly, we find the median of the upper half of the data, which includes all values greater than or equal to 29.5:

Upper half: 30, 32, 33, 34

Median of upper half = (32 + 33) / 2 = 32.5

This value, 32.5, is the upper quartile (Q3).

Finally, we can calculate the interquartile range (IQR) as the difference between the upper and lower quartiles:

IQR = Q3 - Q1 = 32.5 - 26.5 = 6

Therefore, the lower quartile is 26.5, the upper quartile is 32.5, and the interquartile range is 6.

The solution is, :

(See attachment below)

Here, we have,

we know ,

Axial symmetry is symmetry around an axis; an object is axially symmetric if its appearance is unchanged if rotated around an axis.

The following information is derived from the graphic:

X-Intercepts: (-3,0), (1,0)

Y-Intercepts: (0,-3)

Vertex: (-1,-4)

Axis of symmetry of the function: x = -1

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A feature of function gif g(x) = f(x-4) is D. horizontal asymptote of y = 4

A horizontal asymptote is a straight line on a graph that a function approaches but never touches as the independent variable (usually denoted as x) increases or decreases without bound. In other words, the function gets closer and closer to the horizontal line as x becomes very large or very small, but it never actually touches or crosses it.

A function can have at most two horizontal asymptotes - one on the left side of the graph and one on the right side. The horizontal asymptotes of a function are determined by the highest degree of the polynomial in the numerator and the denominator of the function.

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Answer:

C. 84.8 m

Step-by-step explanation:

Circumference of circle = D x 3.14

D = 27 m

Let's solve

27 x 3.14 = 84.78 m

So, the circumference of the circle is C. 84.8 m

Answer:

Option C) 84.8 is the correct answer.

Step-by-step explanation:

Here we have given that the diameter of circle is 27 m and we have to find the circumference of circle. The formula to find circumference of circle is :

[tex]\dashrightarrow\sf{C = \pi d}[/tex]

Where :

Thus, finding the circumference of circle by substituting the given values in the formula :

[tex]\dashrightarrow\sf{C = \pi d}[/tex]

[tex]\dashrightarrow\sf{C = \pi \times d}[/tex]

[tex]\dashrightarrow\sf{C = 3.14 \times 27}[/tex]

[tex]\dashrightarrow\sf{C = 84.78 \: m}[/tex]

[tex]\dashrightarrow\sf{C \approx 84.8\: m}[/tex]

Hence, the circumference of circle is 84.8 m.

For the given:  linear function: y = 3x and quadratic function: y = 7x², the graph is plotted.

f(x) = ax² + bx + c, where such a, b, and c are numbers and an is not equal to zero, is a quadratic function. A parabola is the shape of a quadratic function's graph.

Although the "width" or "steepness" of a parabola can vary as well as its direction of opening, they all share the same fundamental "U" form.

Given functions:

y = 3x and y = 7x²

For the linear function:

y = 3x

Put x = 1, y = 3*1 = 1 ; (1,3)

Put x = 2 , y = 3*2 = 6 ; (2,6)

For the quadratic function: y = 7x²

Put x = 1; y = 7(1)² = 7 ; (1, 7)

Put x = 2 ; y = 7(2)² = 28; (2,28)

Plot the obtained points on the graph;

The graph for the given function is obtained using the graphing tool.

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Correct question:

Sketch the region enclosed by y = 3x and y = 7x². Find the area of the region.

The zero product property's assistance.  The RP measures 14 cm in length.

The length of a thing refers to its size or length measured from end to end. Or, to put it a different way, it is the larger of a geometrical shape's upper two or three dimensions.

(x+x+2) * (x+2) = (4+6)*4

Conjoin similar terms

(2x+2)(x+2)=10*4

2(x+1)(x+2) = 40

Divide by 2

(x+1)(x+2) = 20

FOIL

x²+2x+x+2=20

x²+3x+2=0

Subtract 20

x²+3x-18=0

Factor

(x +9) (x-6) = 0

Utilising the zero sum property

x+9=0   x-6 =0

x= -9    x=6

The length cannot be negative, hence

x=6

RP = x+2+x

= 6+2+6

= 14

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Step-by-step explanation:

Volume = 20×70×80 = 112000 cm³

Volume of cubes = 20×20×20 ×5 = 8000 ×5 = 40000 cm³

Volume of space in the tank = 112000-40000 = 72000 cm³ = 72000 mL = 72 L

Volume of water from tap = 158 × 1 = 158 L

Volume of water spilt out = 158 - 72 = 86 L

Answer: 30000cm³

Step-by-step explanation:

Capacity of tank-> 30x70x80

                               =168000

Volume of 1 cube->20x20x20

                              =8000

Volume of 5 cubes->8000x5

                                  =40000

Volume of space which can be occupied by water->168000-40000

                                                                                        =128000

Volume of water running for 158 min-> 158x1000

                                                                  =158000

Volume of water spilt out->158000-128000

                                             =30000( Ans)

The volume and surface area of a triangular prism is 1,848 cubic meters and 1,694 square meters.

What is surface area?

The space occupied by a two-dimensional flat surface is called the area. It is measured in square units. The area occupied by a three-dimensional object by its outer surface is called the surface area.

the volume and surface area of a right triangular prism with base dimensions of 24 m and 7 m height and a length of 22 m.

The volume of a right triangular prism is given by the formula:

V = (1/2) * b * h * l

where b is the base width, h is the height, and l is the length. Plugging in the given values, we get:

V = (1/2) * 24 m * 7 m * 22 m = 1,848 m³

Therefore, the volume of the right triangular prism is 1,848 cubic meters.

The surface area of a right triangular prism is given by the formula:

SA = 2 * (b * h + l * h + b * l)

Plugging in the given values, we get:

SA = 2 * (24 m * 7 m + 22 m * 7 m + 24 m * 22 m) = 1,694 m²

Therefore, the surface area of the right triangular prism is 1,694 square meters.

Hence, the volume and surface area of a triangular prism are 1,848 cubic meters and 1,694 square meters.

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Applying the Two-Tangent Theorem, the length of segment LM in the circle is: A. 18.

What is the Two-Tangent Theorem?

If two tangent segments are drawn to one circle from the same external point, the Two-Tangent Theorem states that both segments are congruent together.

Applying the theorem, we have:

4x - 2 = 3x + 3

Find the value of x:

4x - 3x = 2 + 3

x = 5

Find the length of LM:

LM = 3x + 3

Plug in the value of x:

LM = 3(5) + 3

LM = 18

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Equation: [tex]6xt^4yz^3 + 10a = 1[/tex]. Number of terms: 2, Coefficients: 6, 10 and Constants: 1.

Equation: [tex]25abc^2ab + 3ac6bc + 25[/tex], Number of terms: 3. Coefficients: 25, 3, 6. Constants: 25

What is equation and an expression?

A random combination of integers, variables, functions, etc. can be described as an expression. An expression is, for instance, 3x - 2. An equation, on the other hand, is created when two independent expressions are joined by the equal to sign. An equation, for instance, is when 3x - 2 = 5 + x.

Equation/Expression: 6xt⁴yz³ + 10a = 1

Number of terms: 2

Coefficients: 6, 10

Constants: 1

Equation/Expression: 25abc²ab + 3ac6bc + 25

Number of terms: 3

Coefficients: 25, 3, 6

Constants: 25

Equation/Expression: 25y³xy + 5 = 100

Number of terms: 2

Coefficients: 25, 1

Constants: 5, 100

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The equation that  matches this problem is 15 + 3p = 117

Let the cost of one pair of pants be represented by the variable p.

Then, the cost of three pairs of pants is 3p.

We are also given that the cost of a t-shirt is $15.

The total cost of Amelia's purchase is $117.

Therefore, the equation that matches this problem is:

15 + 3p = 117

This equation represents the total cost of Amelia's purchase, which includes the cost of one t-shirt and three pairs of pants.

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according to the question the distance between the points (1, 5) and (3, 8) is √13 units.

Distance is an object's total, aimless movement. Without regard to whether an object represents a starting or finishing point, distance can be defined as the total distance travelled. Distance is referred to as the breadth or height of the difference between two locations. It should be highlighted that the distance between each of the vantage points as well as the distance travelled from one to the other are not the same thing. The total length of a path connecting two locations counts as the distance travelled. Distance is the real distance that a body travels. It also goes by the name "path length." For instance, the length of the route for an object moving from point O to point P would be OP = 360 m.

given,

To find the distance between the points (1, 5) and (3, 8), we can use the distance formula:

distance = √[(x2 - x1)² + (y2 - y1)²]

Substituting the given values, we get:

distance = √[(3 - 1)² + (8 - 5)²]

distance = √[4 + 9]

distance = √13

Therefore, the distance between the points (1, 5) and (3, 8) is √13 units.

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Answer:

Step-by-step explanation:

Its B i think sry if im wrong

If the function f(x) = x, the effect of f(x) - 8 is: is (D) The y intercept decreases.

The function f(x) = x is a linear function with a slope of 1, which means that for every increase of 1 in the x-value, the y-value also increases by 1.

If we subtract 8 from the function, we get:

f(x) - 8 = x - 8

This is still a linear function with a slope of 1, but it has been shifted downwards by 8 units.

Therefore, the effect of f(x) - 8 is that the y-intercept decreases by 8 (since the y-intercept of f(x) is 0 and the y-intercept of f(x) - 8 is -8), while the slope remains the same.

So the correct answer is (D) The y intercept decreases.

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Answer:

please let me know what is the name of the shape. Thank you

The answer for it is diagram B because it does not cross or have parallel lines

The total number of 6 tickets will be earned when 54 points are earned.

Given that the total number of tickets earned for 9 points was earned = 1 ticket

the tickets earned when every 18 points are earned = 2 tickets

the tickets earned when every 27 points are earned = 3 tickets

Let's divide the points by tickets to find out how many points are earned for each ticket.

9/1 = 18/2 = 27/3 = 9

This shows for every ticket 9 points are earned. So, to find out the no. of tickets for 54 points, we can divide the 54 by 9.

no. of tickets earned for 54 points = 54/9 = 6 tickets.

From the above analysis, we can conclude that the 6 tickets are earned for 54 points.

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We can use the formula for the volume of a cylinder: V = Ah, where A is the base area and h is the height.

Substituting the given values, we have:

720 cm³ = 36 cm² x h

Simplifying, we can divide both sides by 36 cm²:

20 cm = h

Therefore, the height is 20 cm.

The percent of the whole group are in the Navy is 27%.

Percent is a term used to express a fraction or a ratio out of 100. It is represented by the symbol "%". For example, if there are 20 red balls out of a total of 100 balls, we can say that the percentage of red balls is 20%.

To calculate the percentage, we can use the following formula:

Percentage = (Part / Whole) x 100

where "Part" is the value we want to express as a percentage, and "Whole" is the total value.

The percent of the whole group are in the Navy is:

= 135/500 × 100

= 27%.

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Answer:

27%

Step-by-step explanation:

135 of the 500 total members are in the Navy. Meaning that 135 out of 500 is 27%

The proof that f(2x)=3f(x)+1/f(x)+3 is shown below.

To show that f(2x) = 3f(x) + 1/f(x) + 3, we substitute 2x for x in the expression for f(x):

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

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

Next, we substitute x into the expression for f(x) and add the result to itself twice:

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

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

= 3x - 3 / 3x + 3

We can simplify the expression by dividing both the numerator and denominator by 3:

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

= (1/3) (3x - 3) / (1/3) (3x + 3)

= (x - 1) / (x + 1)

= f(x)

Now, we substitute f(x) and f(2x) back into the original equation:

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

3f(x) + 1/f(x) + 3 = 3(x - 1 / x + 1) + 1/(x - 1 / x + 1) + 3

= (3x - 3 / x + 1) + (1 / (x - 1 / x + 1)) + 3

= (3x - 3 + (x + 1) / (x - 1)) / (x + 1)

= (2x + 2) / (x + 1)

= 2(x + 1) / (x + 1)

= 2

Thus, we have shown that f(2x) = 3f(x) + 1/f(x) + 3.

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