Suppose that you drink a 20 oz. bottle of Dr. Pepper with both lunch and dinner every day. If so, you’re adding 250 calories to each meal.
A. How many extra calories are you consuming per year compared to just drinking water, which has no calories?
B. A general rule of thumb is that an average-sized person expends about 100 calories for each mile walked. How many miles would you have to walk over the course of a year to burn off all the calories you’re getting from your daily Dr. Pepper?

The complex solution of a quadratic equation are (- 2 + i ) and

(- 2 - i ).

What is Quadratic equation?

An algebraic equation of the second degree is called a quadratic equation.

Given that;

A quadratic equation is;

3x² = -12x - 15

Now, The equation is written as;

3x² + 12x + 15 = 0

Take 3 common, we get;

3 (x² + 4x + 5) = 0

x² + 4x + 5 = 0

Factorize the equation by using Sridharacharya Formula;

x = - 4 ± √4² - 4*1*5 / 2*1

x = -4 ± √16 - 20 / 2

x = - 4 ± √-4 / 2

Since, √-1 = i

x = -4 ± 2i / 2                            

x = - 2 ± i

It gives two values of x as;

x = - 2 + i

And, x = - 2 - i

Hence, The complex solution of a quadratic equation are (- 2 + i ) and

(- 2 - i ).

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Answer:

See below

Step-by-step explanation:

60  milliliters of 13% vinegar and 150 milliliters of 6% vinegar will give him 300ml of 12% vinegar.

This is further explained below.

Generally, The ratio of their amounts is inversely proportional to the variations in their cost from the mean value when varied quantities of various components are combined to generate a mixture of a mean value, according to the rule of alligation.

In conclusion, How much of each brand is

[tex]x=\frac{13-8}{8-6}\\\\x=5/2[/tex]

For every 2 measures of the 13% vinegar, the Chef needs to add 5 measures of the 6% vinegar (meaning a ratio of 2:5)

2/7 *210=60  milliliters of 13% vinegar

and

150 milliliters of 6% vinegar will give him 300ml of 12% vinegar.

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The terms and coefficients of the expressions are found by taking the connectors as additions using the '+' symbol as follows;

A. 1. Terms; 12•x, 13•y, (-4•z), 2

2. Coefficients; 12, 13, -4, 2

B. The error is in not expressing the addition connecting the constant term.

C. The coefficient is 1

A term in an expression are the parts of the expression that are connected together using addition or subtraction

A coefficient is the number multiplying a variable within a term of the expression

Therefore;

A. The expression 12•x + 13•y - 4•z + 2, can be written as follows;

12•x + 13•y - 4•z + 2 = 12•x + 13•y + (-4•z) + 2

The terms of the given expression 12•x + 13•y - 4•z + 2, which is the same as 12•x + 13•y + (-4•z) + 2, are therefore;

1. Terms; 12•x, 13•y, (-4•z), 2

The coefficients are;

2. Coefficients; 12, 13, -4, 2

B. The given expression is 9•a + 4•b - 18

Writing the subtractions as additions, to indicate the signs of the coefficient gives;

9•a + 4•b - 18 = 9•a + 4•b + (-18)

The terms are therefore; 9•a, 4•b, and (-18)

C. The expression, b + 10, has only one variable, which is b, the coefficient of the expression is therefore the coefficient of b, which is 1.

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Answer:

m = 15

Step-by-step explanation:

Given equation,

→ 3m = 45

Solving for the value of m,

→ 3m = 45

→ m = 45/3

→ [ m = 15 ]

Hence, the value of m is 15.

Answer:

15

Step-by-step explanation:

3m=45 divide both sides by 3 and 45 by 3 is 15 thats the answer

Answer: -6

Step-by-step explanation:

Answer: 6

2 x3 =6

Step-4by-step explanation:

The length of the base and height of the triangle as described in the task content are; 6cm and 3cm respectively.

It follows from the task content that the Area of the triangle is; 9 cm².

Since, Area = (1/2)b × h. where h = (b-3).

Therefore we have;

9 = (1/2)b × (b-3)

18 = b² -3b

b² -3b -18 = 0.

On this note, by solving quadratically; we have; b = 6 or b = -3.

The base of the triangle is therefore 6 as it cannot be a negative measure.

Consequently, the height, h = (b-3) = 6-3 = 3.

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Answer:

140°

Step-by-step explanation:

Angles ABC and CBD form a linear pair, and thus add to 180°.

They have to carry 15.5 kg.

The unitary method is a technique for solving a problem by first finding the value of a single unit, and then finding the necessary value by multiplying the single unit value.

Given:

Piloncillo   14 kg

Tejocote    1½ kg-

Apple         2¾ kg

oldestq         3

Guava         0.75 kg

Plum            1.75 kg

Cane           2.40 kg

Cinnamon      ½ kg

So, if they take piloncillo and the tejocote

they carry,

=14 + 1 1/2

=14 + 3/2

=14 + 1.5

=15.5 Kg

Hence, they have to carry 15.5 kg.

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The complete and translated question is

My mom and I, yesterday we went to the supermarket and

we bought

punch

following items:

everything you need to make the

Christmas, and we bought the

Piloncillo 14 kg

Tejocote 1½ kg-

Apple 2¾ kg

oldestqx3

Guava 0.75 kg

Plum 1.75 kg

Cane 2.40 kg

Cinnamon ½ kg

If my mom took the piloncillo and the tejocote,

How many kilos did I carry in total?

13

Answer:

Third choice
x < -2; y ≤ -x -2

Step-by-step explanation:

The dotted vertical line passing through x = 2 shows it is a < inequality corresponding to x < -2. If it were a ≤ inequality, then it would be a solid vertical line

That eliminates the first two choices. Second choice is x < -3 which is not correct because we can see that the shaded region includes everything below x = -2 not below x = -3. For example, x = -2.5 is in the shaded region

So we have to choose between the third and fourth choices. Note that the line equation for choice 3 is y = -x -2 and for choice 4 it is y = -x +2

Choose (x, y) = (-3, 0)

choice 3
y ≤ -x -2
Substitute x with -3 in -x + 2 giving
-(-3) -2 = 3 - 2 = 1

Point(-3,1) lies on the line and therefore does satisfy the second inequality

choice 4
y ≤ -x + 2
Substitute x with -3 giving

-x + 2 = -(-3) + 2 = 3 + 2 =5
But (-3, 5) is not on the line. In fact, it is outside the shaded region so it does not satisfy the second inequality

So the correct choice is the third choice
x < -2, y ≤ -x -2

Answer:

76.83

Step-by-step explanation:

its like 1 plus 1 equals 2 you add the amount of salt present beforehand in the bowl and the one you've added together the sum would equate to 76.73

Answer:

the euro is 75 € ok......

75 euros increase

Step-by-step explanation:

25% 300 is 85

Answer:-11

Step-by-step explanation:

5x+2-2=4x-9-2

5x-+2-2=4x-9-2

5x=4x-9-2

5x=4x-9-2

5x=4x-11

5x=4x-11

5x-4x=4x-11-4x

5x-4x=4x-11-4x

1x=4x-11-4x

1x=4x=11-4x

x=4x-11=4x

x=4x-11-4x

x=-11

Answer:

-11

Step-by-step explanation:

Group

[tex]5x+2-4x=4x-9-4x\\5x-4x+2=4x-9-4x\\[/tex]

Simplify

[tex]1x+2=4x-9-4x\\x+2=4x-9-4x[/tex]

Group(Again)

[tex]x+2=4x-4x-9[/tex]

Simplify it

[tex]x+2=-9[/tex]

Group(Yet again)

[tex]x+2-2=-9-2[/tex]

Simplify(Final)

[tex]x=-9-2\\x=-11[/tex]

Answer:

a

Step-by-step explanation:

Answer:

Step-by-step explanation:

                                       Functions used:

[tex]\displaystyle\\\boxed {(\frac{u}{v})'=\frac{u'v-v'u}{v^2} }\ \ \ \ \ \boxed {(u+v)'=u'+v'}\ \ \ \ \ \boxed {(x^n)'=n*x^{n-1}}[/tex]

[tex]\displaystyle\\f(x)=\frac{x}{x^4-5} \\\\f'(x)=(\frac{x}{x^4-5})'\\ f'(x)=\frac{x'(x^4-5)-(x^4-5)'x}{(x^4-5)^2} \\\\f'(x)=\frac{1(x^4-5)-((x^4)'-5')x}{(x^4-5)^2}\\\\f'(x)=\frac{x^4-5-(4x^3-0)x}{(x^4-5)^2} \\\\f'(x)=\frac{x^4-5-(4x^3)x}{(x^4-5)^2}\\\\f'(x)=\frac{x^4-5-4x^4}{(x^4-5)^2} \\\\f'({x)=\frac{-3x^4-5}{(x^4-5)^2} \\\\[/tex]

[tex]\displaystyle\\f'(x)=\frac{-(3x^4+5)}{(x^4-5)^2} \\\\f'(x)=-\frac{3x^4+5}{(x^4-5)^2}[/tex]

Answer:

94

Step-by-step explanation:

Let the score she needs be x. Then,

[tex]\frac{81+58+95+x}{4}=82 \\ \\ 234+x=328 \\ \\ x=94[/tex]

keeping in mind that perpendicular lines have negative reciprocal slopes, let's check for the slope of the equation above

[tex]\cfrac{3x+2y}{5}=1\implies 3x+2y=5\implies 2y=-3x+5 \\\\\\ y=\cfrac{-3x+5}{2}\implies y=\stackrel{\stackrel{m}{\downarrow }}{-\cfrac{3}{2}} x+\cfrac{5}{2}\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]

so then, a perpendicular line to that will have a slope of

[tex]\stackrel{~\hspace{5em}\textit{perpendicular lines have \underline{negative reciprocal} slopes}~\hspace{5em}} {\stackrel{slope}{\cfrac{-3}{2}} ~\hfill \stackrel{reciprocal}{\cfrac{2}{-3}} ~\hfill \stackrel{negative~reciprocal}{-\cfrac{2}{-3}\implies \cfrac{2}{3}}}[/tex]

so we're really looking for the equation of a line whose slope is 2/3 and it passes through (-9 , -9)

[tex](\stackrel{x_1}{-9}~,~\stackrel{y_1}{-9})\hspace{10em} \stackrel{slope}{m} ~=~ \cfrac{2}{3} \\\\\\ \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-\stackrel{y_1}{(-9)}=\stackrel{m}{ \cfrac{2}{3}}(x-\stackrel{x_1}{(-9)}) \implies y +9= \cfrac{2}{3} (x +9) \\\\\\ y+9=\cfrac{2}{3}x+6\implies y=\cfrac{2}{3}x-3\implies \stackrel{\textit{multiplying both sides by }\stackrel{LCD}{3}}{3(y)=3\left( \cfrac{2}{3}x-3 \right)}[/tex]

[tex]3y=2x-9\implies -2x+3y=-9\implies 2x-3y=9 \\\\\\ 2x-3y=(9)(1)\implies {\LARGE \begin{array}{llll} \cfrac{2x-3y}{9}=1 \end{array}}[/tex]

The football team's total payroll is B. 2.5753 x [tex]10^{11}[/tex] dollars more than the baseball team's total payroll.

Option B is the correct answer.

We have,

To find how many more dollars the football team's total payroll is than the baseball team's total payroll, we need to subtract the baseball team's total payroll from the football team's total payroll.

Football team's total payroll = 2.6 x 10^11 dollars

Baseball team's total payroll = 2.47 x 10^9 dollars

Difference = Football team's total payroll - Baseball team's total payroll

Difference = [tex](2.6 \times 10^{11}) - (2.47 \times 10^9)[/tex]

To subtract these numbers, we need to make sure they have the same exponent:

2.47 x [tex]10^9[/tex] dollars = 0.247 x [tex]10^{10}[/tex] dollars

(move the decimal one place to the right)

Now, subtract:

Difference = (2.6 x  [tex]10^{11}[/tex]) - (0.247 x [tex]10^{10}[/tex])

Difference = 2.5753 x [tex]10^{11}[/tex] dollars

Thus,

The football team's total payroll is B. 2.5753 x [tex]10^{11}[/tex] dollars more than the baseball team's total payroll.

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The inverse of the given function f(x) = 3x + 1 is f⁻¹(x) = x/3 - 1/3.

Given the function in the question;

f(x) = 3x + 1

To determine the inverse of the function, write f(x) as y.

f(x) = 3x + 1

y = 3x + 1

Now, interchange the variable

x = 3y + 1

Solve for y by subtracting 1 from both sides

x = 3y + 1

x - 1 = 3y + 1 - 1

x - 1 = 3y

Reorder

3y = x - 1

Divide both term in the equation by 3

3y/3 = x/3 - 1/3

y = x/3 - 1/3

f⁻¹(x) = x/3 - 1/3

Therefore the inverse of the given function f(x) = 3x + 1 is f⁻¹(x) = x/3 - 1/3.

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Answer:

Step-by-step explanation:

y=0.75x+0.00

y=mx+b

Your slope is 0.75 because y=0.75

Your x is the number of times you multiply 0.75.

And there is no b so b=0 because the line would not go through the y line (vertical line)

So to conclude it would be y=0.75x+0

Sorry it took so long, if you are still confused please ask :)

No

Since ratios are simply proportions, they may be represented in multiple ways as long as the relationship remains equal.

Simplifying Ratios

There are 2 ways to check if these ratios are equivalent. The first is to simplify both ratios and see if they match each other. Firstly, find the greatest common factor (GCF) between the 2 numbers.

Then, divide each ratio by its GCF

Since 7:10 is not equal to 3:5, we know that these ratios are not equal. It is important to note that this method only works when both ratios have been completely simplified.

Find the Relationship as a Decimal

Another to see if 2 ratios are equivalent is to see if their relationships are equal as decimals. To find the relationship of a ratio as a decimal, simply divide the 2 numbers within a ratio.

Clearly, the ratios do not have equal relationships. Thus, the ratios are also not equivalent.

The equation of the parabola is : y = -6x² + 13x + 2

The general equation for parabola is -

y = ax² + bx + c. We will keep the values of x and y in this equation, to find the coefficients. Once we get the coefficients, again this equation will be used to find the equation of parabola based on given points.

For the point (1, 9)

9 = a(1)² + b(1) + c

9 = a + b + c : equation 1

For the point (2, 4)

4 = a(2)² + b(2) + c

4 = 4a + 2b + c : equation 2

For the point (4, -30)

-30 = a(4)² + b(4) + c

-30 = 16a + 4b + c : equation 3

Subtract equation 2 from equation 1

9 = a + b + c

-4 = 4a + 2b + c

We get: 5 = -3a -b

Rearranging the equation: 3a + b = -5 : equation 4

Subtraction equation 2 from equation 3

-30 = 16a + 4b + c

-4 = 4a + 2b + c

We get: -34 = 12a + 2b : equation 5

Multiplying equation with 2

6a + 2b = -10 : equation 6

Subtract equation 6 from equation 5

12a + 2b = -34

-6a + 2b = -10

6a = -24

a = -6

Keep value a in equation 6 to find the value of b

6(-6) + 2b = -10

-36 + 2b = -10

2b = 36 - 10

2b = 26

b = 13

Keep the value of a and b in equation 1 to find the value of c

-6 + 13 + c = 9

c = 9 - 7

c = 2

Keeping all the coefficients in general equation to find the equation of parabola -

y = -6x² + 13x + 2

Hence, the equation of parabola is : y = -6x² + 13x + 2

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The true statements are:

The amount of water is the dependent value.

The amount of rice is the independent value.

The independent variable is the variable that is considered as given in the experiment. It is the value of the independent variable that determines the value of the dependent variable. The person carrying out an experiment changes or manipulates the independent variable to determine the value of the dependent variable.

The dependent variable is the variable that is being measured in an experiment. It is usually affected by the independent variable.

The independent variable is the amount of rice. This is because the amount of water needed to cook the rice depends on the amount of rice. This makes the amount of water the dependent variable.

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The length of AD is option e √229.

Given,

ΔABD and C is a point between B and D. A and C makes a line and there forms another triangle, ΔABC.

∠B is a right angle = 90°

m ∠BAC = 30°

Length of AC = 12

Length of CD = 5

We have to find the length of AD.

First we can consider ΔABC.

Total interior angle of a triangle is 180°

We have given, ∠A as 30° and ∠B 90°.

Then ∠C = 180° - (∠A + ∠B) = 180 - (30 + 90) = 180 - 120 = 60

∠ACB = 60°

Trigonometric Function

Sin θ = (opposite side / hypotenuse)

We can find length of BC using trigonometric function.

In ΔABC,

For sin 30°, AC is the hypotenuse and BC is the opposite side.

So,

Sin 30° = (opposite side / hypotenuse)

Sin 30° = (BC/12)

BC = Sin 30° × 12

BC = 1/2 × 12

BC = 6

Now, we have to find the length of side AB.

For sin 60°, AB is the opposite side and AC is the hypotenuse.

So,

Sin 60° = (opposite side/hypotenuse)

Sin 60° = (AB/12)

AB = Sin 60° × 12

AB = √3/2 × 12

AB = 6√3

Now we can consider ΔABD.

In ΔABD, ∠B is 90°

Length of side AB = 6√3

Length of side BD = BC + CD = 6 + 5 = 11

Now, we can find the length of side AD using pythegorean theorem.

Hypotenuse = [tex]\sqrt{altitude^{2} +base^{2} }[/tex]

Here, AD is the hypotenuse, AB is the altitude and BD is the base.

So,

AD = [tex]\sqrt{AB^{2} +BD^{2} }[/tex]

AD = [tex]\sqrt{(6\sqrt{3} )^{2} +11^{2} }[/tex]

AD = [tex]\sqrt{36(3) + 121}[/tex]

AD = [tex]\sqrt{108+121}[/tex]

AD = √229

That is, the length of side AD is √229.

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Based on the given parameters, the slope of the line AC is 5

Linear equations are equations that have constant average rates of change. Note that the constant average rates of change can also be regarded as the slope or the gradient

The given parameters are

B is the midpoint of AC

A = (2, 4)

B = (6, 24)

Because the point B is the midpoint of AC, then the slope of AC is the slope of AB

The slope of AB is calcilated as

Slope = (y2 - y1)/(x2 - x1)

So, we have

Slope = (24 - 4)/(6 - 2)

Evaluate the quotient

Slope = 5

Hence, the slope of the line AC is 5

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Train A's unit rate is 68 km per hour.

Train B's unit rate is 75 km per hour.

The faster train is Train B.

The unit rate of the trains is equal to the average speed of the trains. The unit rate is the total distance travelled by the train per time.

The unit rate can be determined by dividing the total distance travelled by the total time travelled. The train that is faster would have a higher unit rate per time.

Unit rate = total distance / total time

The unit rate for Train A is 68 kilometers per hour. This is because this is the total distance covered in 1 hour.

d = (68 x 1) = 68 km / hr

The unit rate for Train B = 150 / 2 = 75km / hr

Train B is faster because it covers more kilometers in one hour when compared with Train A.

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Equation (A) 3¹ can be placed correctly in Jeremy's work.

So, in the given situation Jeremy determines that: [tex]\sqrt{9}=9^{\frac{1}{2}}[/tex]

Therefore, the equation that should be placed correctly in Jeremy's work is (A) 3¹.

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The complete question is given below:
Jeremy determines that √9= 9^1/2. Part of his work is shown

√9=3=3^1=3^1/2 + ^1/2=____=9^1/2

Which expression or equation should be placed in the blank to correctly complete Jeremy's work?

A: 3¹

B: (3^2)^1

C: 3^1/2 + 3^1/2

D: 3^1/2 x 3^1/2= (3x3)^1/2

E: 3^1/2 x 3^1/2= (3x3)^1/2+^1/2

Answer:

[tex]y=700x+48000[/tex]

[tex]52,200[/tex]

Step-by-step explanation:

Generally for a linear equation you use the slope-intercept form: [tex]y=mx+b[/tex]

In this form, [tex]m=\text{slope},\ b=\text{y-intercept}[/tex]

The y-intercept is just when x=0, so it can be seen as a "starting point". in this case the initial population was 48,000 so we know that: [tex]b=48000[/tex]

The slope is just how much y-changes as x increases by one, and in this case our "x" will represent how many years it's been since 2003. So the slope will represent how much the population increases each year, and this is given in the word problem as 700 people each year.

So now we have the equation: [tex]y=700x+48000[/tex]

From 2003 to 2009, 6 years have passed meaning the population is the y-value when x=6: [tex]y=700(6)+48000\\y=52,200[/tex]

The value of

x = 1/9

y = 1/63

We have given two equations :

   1/x - 1/3y = -12   ... eq. (1)

- 4/5x + 7y = -1/5    ... eq. (2)

First we will multiply the 1st equation by 4/5,

We get, 4/5x - 4/15y = -48/5   ... eq. (3)

Now, we will add the equation 3 and equation 2

     4/5x - 4/15y = -48/5

   - 4/5x + 7y     = -1/5

____________________

          7y - 4/15y = -49/5

     (105y - 4)/15y = -49/5

              105y - 4 = (-49/5) × 15y

              105y - 4 = -49 × 3y = -147y

        105y + 147y = 4

                         y = 4/252

                        y = 1/63

We get the value of  y which is 1/63,

Now, we will solve the eq. 1 by putting  is equal to 1/63.

                      1/x - 1/3y = -12

        1/x - (1 × 63/3 × 1) = -12

                          1/x -21 = -12

                                1/x = 21 - 12 = 9

                                 x = 1/9

Hence, we get the value of x and y as 1/9 and 1/63 respectively.

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