4. Five hamburgers and two French fries together contain 2160 calories, while four hamburgers and five French fries contain 2680 calories. What’s the calorie count in one hamburger and one pack of French fries?

Answer:

389.1 units² (nearest tenth)

Step-by-step explanation:

Regular polygon: all side lengths are equal, all interior angles are equal.

Apothem: a line drawn from the center of any polygon to the midpoint of one of the sides

Radius: a line drawn from the center of the polygon to a vertex.

Therefore, we have been given the apothem of this regular dodecagon.

[tex]\textsf{Area of a regular polygon}=\dfrac{n\:l\:a}{2}[/tex]

where:

[tex]\textsf{Length of apothem (a)}=\dfrac{l}{2 \tan\left(\frac{180^{\circ}}{n}\right)}[/tex]

where:

First, calculate the length of one side of the regular dodecagon by substituting a = 11 and n = 12 into the apothem formula:

[tex]\implies 11=\dfrac{l}{2 \tan\left(\frac{180^{\circ}}{12}\right)}[/tex]

[tex]\implies l=11 \cdot 2 \tan\left(\frac{180^{\circ}}{12}\right)[/tex]

[tex]\implies l=44-22\sqrt{3}[/tex]

Now substitute n = 12, the found value of l, and a = 11 into the area formula:

[tex]\implies \textsf{Area}=\dfrac{12(44-22\sqrt{3})(11)}{2}[/tex]

[tex]\implies \textsf{Area}=389.0622274...[/tex]

[tex]\implies \textsf{Area}=389.1\: \sf units^2 \: (nearest\:tenth)[/tex]

Answer:

389.1 square units

Step-by-step explanation:

Area of the Dodecagon (12-sided polygon)

Area Formula

Finding the length (l)

Apothem Formula

Finding Area

Answer:

1/428

Step-by-step explanation:

There are 428 pages,

Each page likely to be turned onto as equally as every other page,

and there is one possible correct page.

Since the pivot pillar is 1 m above the ground, maximum angle can the seesaw beam move is 26.39°

The maximum angle can be gotten using trigonometric ratios answer the question,

Trigonometric ratios are the ratios of the sides of a triangle.

Angles are a measure of rotation or bearing.

Given that the seesaw plank is 4.5 m long and the pivot pillar is 1 m above the ground, when the seesaw is at maximum angle, it forms a right angled triangle with the ground.

It also forms a smaller similar triangle with the same maximum angle Ф which is gotten from the trigonometric ratio

sinФ = h/L where

So, Ф = sin⁻¹(h/L)

= sin⁻¹(1 m/2.25 m)

= sin⁻¹(1/2.25)

= sin⁻¹(0.4444)

= 26.39°

So, maximum angle can the seesaw beam move is 26.39°

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Answer:

2x + 10 = x

Step-by-step explanation:

Let him mows x

Robert mows

[tex]\displaystyle \dfrac{\dfrac{4c^2-36}{8c^2-24c}}{\dfrac{12c+36}{2c^2 -6c}}\\\\\\=\left(\dfrac{4c^2 -36}{8c^2 -24c}\right) \cdot \left(\dfrac{2c^2 -6c}{12c+36}\right)\\\\\\=\left[\dfrac{4(c^2 -9)}{8(c^2-3)}\right]\cdot\left[\dfrac{2(c^2-3)}{12(c+3)}\right]\\\\\\=\dfrac{8(c^2-3^2)}{8 \cdot 12(c+3)}\\\\\\=\dfrac{(c+3)(c-3)}{12(c+3)}\\\\\\=\dfrac{c-3}{12}[/tex]

[tex]\text{Hence the answer is d.}[/tex]

Answer:

d

Step-by-step explanation:

separate the 2 divisions and simplify each , that is

[tex]\frac{4c^2-36}{8c^2-24c}[/tex] ← factor numerator/ denominator

= [tex]\frac{4(c^2-9)}{8c(c-3)}[/tex] ← factor difference of squares on numerator

= [tex]\frac{4(c-3)(c+3)}{8c(c-3)}[/tex] ← cancel (c - 3) and 4/8 on numerator/ denominator

= [tex]\frac{c+3}{2c}[/tex]

---------------------------------------------------

[tex]\frac{12c+36}{2c^2-6c}[/tex] ← factor numerator/ denominator

= [tex]\frac{12(c+3)}{2c(c-3)}[/tex] ← cancel 12 and 2 on numerator/ denominator

= [tex]\frac{6(c+3)}{c(c-3)}[/tex]

----------------------------------------------------------

to divide the top fraction by the lower fraction

leave top fraction, change division to multiplication, turn lower fraction upside down.

[tex]\frac{c+3}{2c}[/tex] × [tex]\frac{c(c-3)}{6(c+3)}[/tex] ← cancel (c + 3) and c on numerator/ denominator

= [tex]\frac{c-3}{2(6)}[/tex]

= [tex]\frac{c-3}{12}[/tex] → d

The area inside one leaf of the rose: r=6sin(6θ) is 3π/2 after evaluating the integral over the limit 0 to  π/6

It is defined as the mathematical calculation by which we can sum up all the smaller parts into a unit.

We have:

r=6sin(6θ)

First we have to find the limits:

r = 0

6sin(6θ) = 0

θ = nπ/6

n = 0 to n = 1

θ = 0 to  θ = π/6

[tex]\rm Area = \int\limits^{\dfrac{\pi}{6}}_0 {6sin6\theta} \, d\theta[/tex]

After calculating the above definite integral, we will get:

Area = 3π/2

Thus, the area inside one leaf of the rose: r=6sin(6θ) is 3π/2 after evaluating the integral over the limit 0 to  π/6

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Answer:

50

Step-by-step explanation:

since the Pythagorean theorem is

[tex]c=[/tex] √[tex]a^2+b^2[/tex]

b is the bottom line (48)

a is the right line (14)

c is the top line (c)

plug that in

[tex]c =[/tex] √[tex]14^2 + 48^2[/tex]

then do the exponets

[tex]14^2[/tex] = 14 * 14 = 196

[tex]48^2[/tex] = 48 * 48 = 2304

then add them together

196 + 2304 = 2500

[tex]c =[/tex] √2500

the sqrt of 2500 is 50 (50 * 50 = 2500)

c = 50

your answer is 50

hope this helps:)

[tex]\qquad\qquad\huge\underline{{\sf Answer}}[/tex]

Let's calculate the value of c using Pythagoras theorem ~

[tex]\qquad \sf  \dashrightarrow \: c {}^{2} = a {}^{2} + {b}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: c {}^{2} = {14}^{2} + {48}^{2} [/tex]

[tex]\qquad \sf  \dashrightarrow \: c = \sqrt{196 + 2304} [/tex]

[tex]\qquad \sf  \dashrightarrow \: c = \sqrt{2500} [/tex]

[tex]\qquad \sf  \dashrightarrow \: c = 50 \: units[/tex]

Answer:

Step-by-step explanation:

The mode is the number of most repeated data in the set.

Given set 2, 1, 4, 7, 1 has mode 1 (repeated twice).

If we add 1 to the set the mode will remain 1 as it will repeat three times, so the mode won't change.

There is no change in mode, so the mode decrease is zero.

Answer:

The mode would not decrease

Step-by-step explanation:

Given set of numbers:  2, 1, 4, 7, 1

The mode is most frequently occurring data value.

Therefore, 1 is the mode of the given data set as there are two of this data value.

If we add 1 to the data set, the set becomes:  2, 1, 4, 7, 1, 1

Therefore, 1 is still the mode since there are now three of this data value.

In conclusion, the mode would stay the same.

Answer:

750 mL

Step-by-step explanation:

Unit Conversion Rate

Solving

Answer:

750

Step-by-step explanation:

.75 x 1000 = 750

multiply volume value by 1000

hope this helps!

6540 g

Convert kilograms (kg) into grams (g) by multiplying the amount of kilograms (kg) by 1000 :

[tex]\boxed{\rm{6.45\:kg\:\:\:\:\:\:\:}}[/tex]  times 1,000 --> [tex]\boxed{\rm{6540\:g\:\:\:\:}}[/tex]

[tex]\Large\text{6540\:g}[/tex]

[tex]\small\text{hope\:helpful~}[/tex]

This solution shows that 6 is included in the solution due to the equal sign and not true for the inequality  4x − 5 < 19 since 6 is excluded

Inequalities are equation not separated by an equal sign

Given the inequality expression

4x − 5 ≤ 19

4x ≤ 19 + 5

4x ≤  24

x≤ 6

This solution shows that 6 is included in the solution due to the equal sign and not true for the inequality  4x − 5 < 19 since 6 is excluded

Given the equation

4x + 3 = 23

4x = 23 - 3

4x =20

x = 5

Hence 5 is the solution from the given set

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Answer:

Rational

Step-by-step explanation:

All fractions are rational numbers but it is not necessary that all rational numbers are fractions.

Have a nice day! :)

If d is the common difference between consecutive terms, then

[tex]a_4 = a_3 + d = a_2 + 2d[/tex]

We have [tex]a_2 = 64[/tex] and [tex]a_4 = 100[/tex], so

[tex]a_4 - a_2 = 100 - 64 = 36 = 2d \implies d = 18[/tex]

Then the 1st term in the sequence is

[tex]a_2 = a_1 + d \implies 64 = a_1 + 18 \implies a_1 = 46[/tex]

and the n-th term would be

[tex]a_n = a_1 + (n-1) d \implies a_n = 46 + 18 (n-1) \implies \boxed{a_n = 18n + 28}[/tex]

The movement of the particle on the circle is its displacement.

The value of dy/dt at this time is -9/2.

Differentiation is a process, in Maths, where we find the instantaneous rate of change in function based on one of its variables.

A particle moves on the circle x^2 + y^2=25 in the XY-plane for time t≥0. At the time when the particle is at the point (3,4), dxdt=6.

The equation of the circle is given as:

[tex]\rm x^2 + y^2=25[/tex]

Differentiate with respect to time

[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0[/tex]

Substitute all the values in the equation

[tex]\rm 2x \times \dfrac{dx}{dt}+2y \times \dfrac{dy}{dt}=0\\\\2(3) \times 6+2(4)\times \dfrac{dy}{dt}=0\\\\ 6 \times 6+8 \times \dfrac{dy}{dt}=0\\\\ 36+8\times \dfrac{dy}{dt}=0\\\\ 8\times \dfrac{dy}{dt}=-36\\\\ \dfrac{dy}{dt}= \dfrac{-36}{8}\\\\ \dfrac{dy}{dt}= \dfrac{-9}{2}[/tex]

Hence, the value of dy/dt at this time is -9/2.

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You are given a vector in the XY plane that has a magnitude of 87. 0 units and a y component of -66. 0 units. The direction of the vector V is;

We know that the formula for 2 vectors like this in the x and y directions is; A = xi^ + yj^

Where A is the magnitude of the resultant

x is the value of the x-component

y is the value of the y-component

We are given;

Magnitude of vector = 84 units

Y-component of the vector = -67 units

Thus,

[tex]A = \sqrt(x^2 + y^2)\\\\87 = \sqrt(x^2+ (-66)^2)\\\\87^2= x^2+ 4356\\\\7569 = x^2+ 4356\\\\x= \sqrt(7569 - 4356)\\\\x = 56.68 units[/tex]

From A above, let us take the positive value of the x-component and as such our original vector will be;

A = 56.68i^ - 66j^

The direction of the vector V is;

[tex]\theta = tan^{-1} \dfrac{y}{x} \\\\\theta = tan^{-1} \dfrac{-66}{56.68} \\\theta =-27.15°[/tex]

Since it points entirely to the negative x-axis, then the angle is;

180 - (-27.15) = 207.15°

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To solve this problem, we can to simply plot using a graphing tool and the region under the area would be given. We would see there's no solution for this compound inequality

The given inequalities in this question are

When we plot this, we would see that no solution exists for this compound inequality problem.

Kindly check the attach image for more details.

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Answer:

$332.64

Step-by-step explanation:

Since we are applying a discount to a price tag, we will be decreasing the amount of that price tag.

In this case, we will be taking 20% off of $415.80. This means that our new price tag will be 80% of what it originally was. To find the answer, we must first change 80% into a decimal.

80% ->  [tex]\frac{80}{100}[/tex] -> 0.980

Next, we multiple $415.80 by 0.80 as shown below:

[tex]415.80(0.80)[/tex]

Our answer will be:

$332.64

Area of three rectangles

Area of two triangles

Total

Answer:

The rule is +2

This is the 194th term

Step-by-step explanation:

This is an arithmetic sequence because 2 is added every time.

2x + 1 = 389

2x = 388

x = 194

194* 2 + 1 = 389

mark brainliest please!

Answer:

398 i think

Step-by-step explanation:

Answer:

= 0,16m

Step-by-step explanation:

we are given the ratio there the 2 is for the image 9 is for the car so we say 9 divide by 11 multiply by 0,2

The horizontal and vertical axes of a graph can have any names you like. If the independent variable represents something in particular, the horizontal axis is usually named so as to indicate that.

A coordinate system is a system in geometry that uses one or more integers, or coordinates, to determine the position of points or other geometric components in a unique way.

The horizontal and vertical axes of a graph can have any names you like. If the independent variable represents something in particular, the horizontal axis is usually named so as to indicate that. In a graph of distance versus time, for example, the independent variable is likely to be time, and the horizontal axis is likely to be named something that suggests that--"t," for example, or perhaps "days".

It is fairly convenient to use "x" to name a general independent variable. The corresponding dependent variable in a two-variable relation is conventionally called "y". The horizontal axis in x-y graphs is usually labelled "x" and is called the "x-axis."

This convention is sufficiently well-used that we often call the horizontal number line of the graph the "x-axis" even if it is labelled something else.

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Answer:

6

Step-by-step explanation:

first, we start with 2 dozen = 2 * 12 = 24 cookies

next, cole eats 2/3 of the cookies

2/3 of the cookies = 2/3 * 24 = 16

we are then left with

original # - # of cookies cole ate = 24 - 16 = 8

next, jim eats 1/4 of the cookies left

cookies left = 8

1/4 of cookies left = 1/4 * 8 = 2

cookies left - cookies jim eats = cookies still in jar = 8 - 2 = 6

The density of the gold substance is 3.53 g/cm^3

The density of a substance is the degree of compactness of a substance and it can be determined by the ratio of the mass of the substance to volume.

Mathematically, the density can be computed as:

[tex]\mathbf{Density = \dfrac{mass}{volume}}[/tex]

[tex]\mathbf{Density = \dfrac{14.12 \ g}{4 \ cm^3}}[/tex]

Density = 3.53 g/cm^3

Therefore, we can conclude from the above calculation that the density of the gold with a mass of 14.12 grams and a volume of  4 cubic centimeters is 3.53 g/cm^3.

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Answer:

A 3.53 g/cm^3 if it not a it still 3.53g/cm^3

Step-by-step explanation:

A first step in solving the equation 1/4 x + 1/2 = 3/4x will be answer A multipllied by 4 on both sides.

What is an equation?

The equation is actually a relationship between the numbers and the variables.The given equation is  1/4 x + 1/2 = 3/4x

Now the solution of the equation will be:-

1/4 x + 1/2 = 3/4x

By multiplying with 4 the equation will become:-

x+2=3x

3x-x=2

2x=2

x=1

Hence the solution of the given equation will be x=1

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Answer:A

Step-by-step explanation:

Multiplying each by 1/4.We have;4x1/4 + 4x1/2 = 4x3/44/4 + 4/2 = 12/41 + 2 = 33=3This is the most effective way.

Answer:

Step-by-step explanation:

jfift

Answer:

m = 3

Step-by-step explanation:

see image.

6/8 = 3/4

Use the picture in the problem or use algebra to find m. See image.

Answer:

24

Step-by-step explanation:

6/2 = x/8

x=24

24 oil changes

Answer:

[tex]\frac{1}{3}[/tex]

Step-by-step explanation:

1. Convert both mixed numbers into improper fractions:

[tex]\frac{15}{4} x = \frac{5}{4}[/tex]

2. Multiply both sides by 4:

4 · [tex]\frac{15}{4} x=\frac{5}{4}[/tex] · 4

15x = 5

3. Isolate x:

x = 1/3

hope this helps!

Step-by-step explanation:

i got confused whether it is 7/2 or /2-1