Ethan sold some watches at $14 each and 20 bookmarks at $1.50 each. Roy sold the same number of watches at $13.50 each and 20 bookmarks at $1.80 each. They collected the same amount of money. How many watches did Ethan sell? Ethan Roy watches 17-114 watches come total Bookmarks 20 × $1.56-30 Bookmarly 20-11-80-36 Same total​

Answer: -10x+1.5

Step-by-step explanation:

[tex]-2(5x-0.75)=-10x+1.5[/tex]

Answer:

[tex]3x^{2} +2x[/tex]

Step-by-step explanation:

Using the rainbow expansion method:

[tex]x(3x+2)=3x*x+x*2\\ = 3x^{2} +2x[/tex]

Answer:

3x² + 2x

Step-by-step explanation:

x (3x + 2)

= x*3x + x*2

= 3x² + 2x

Answer:

4

Step-by-step explanation:

When we substitute the blank for 4 and divide by 4, 7,504,124/4 is 1,876,031 :)

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Answer:

about x=38.1

Step-by-step explanation:

9x38.1=342.9

Evaluating the function in x = -1, we get:

H(-1) = 7

When we have a function:

y = f(x)

Evaluating the function in a value, like x = a gives:

y = f(a).

This means that we need to replace all the "x" in the equation by the number "a".

In this case:

H(x) = 6 - x

And we want to get:

H(-1)

So we need to replace the x by -1.

H(-1) = 6 - (-1) = 7

H(-1) = 7

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Step-by-step explanation:

[tex] \log(x) = - 1[/tex]

[tex] \log(y) = 6[/tex]

[tex] \log(z) = 2[/tex]

[tex] \: [/tex]

[tex] = \log( \frac{ {x}^{3}y }{ {z}^{2} } )[/tex]

[tex] = \log( {x}^{3} \times y \div {z}^{2} )[/tex]

[tex] = \log( {x}^{3} ) + \log(y) - \log( {z}^{2} )[/tex]

[tex] = 3 \log(x) + \log(y) - 2 \log(z)[/tex]

[tex] = 3.( - 1) + 6 - 2[/tex]

[tex] = - 3 + 6 - 2[/tex]

[tex] = 1[/tex]

Answer:

The volume = 5 276.66928645188 cm³

Step-by-step explanation:

let V be the volume of the given sphere.

V = (4/3)×π×r³ ,where r is the radius of the sphere

r = 21.6÷2 = 10.8 cm

Then

V = (4÷3)×π×(10.8)³

   = 5 276.66928645188 cm³

Answer:

Step-by-step explanation:

[tex]\frac{a+b}{a^2b} +\frac{a-b}{ab^2} \\=\frac{b(a+b)+a(a-b)}{a^2b^2} \\=\frac{ab+b^2+a^2-ab}{a^2b^2} \\=\frac{b^2+a^2}{a^2b^2} \\or\\=\frac{1}{a^2} +\frac{1}{b^2}[/tex]

The equation that can be used for finding the lengths in the Pythagoras theorem include:

b² = c² - a²

a² = c² - b²

c² = a² + b²

It should be noted that a Pythagoras theorem is simply the theorem that's used in finding the missing length of a right angled triangle.

In this case, the equation that can be used to find the sides in a Pythagoras theorem has been given.

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Answer:

the answer is 3power 7

3^7

Answer:

3^8

Step-by-step explanation:

Sam paid $ 124.032 as tax deduction each week.

An equation is a mathematical statement formed when an algebraic expression is equated by an equal sign by a constant or algebraic expression.

It is given that

weekly earnings of Sam is $912

Tax deduction is 13.6 %

Let the amount of Tax deduction is represented by $x

Then the equation formed is

x = 13.6 % 912

x = 13.6 *912 /100

x = $ 124.032

Therefore Sam paid $ 124.032 as tax deduction each week.

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The algebraic expression is:

x + (2x - 11) = 13

And the solution is x = 8.

Let's say that the number is defined by the variable x, then we can write the algebraic expression:

x + (2x - 11) = 13

Now we can solve this expression for x:

x + 2x - 11 = 13

3x = 13 + 11 = 24

x = 24/3 = 8

x = 8

The solution is x equal to 8.

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Answer:

[tex]-\dfrac{463}{7}[/tex]

Explanation:

Given equation: 2x² - 6x - 7 = 0

In quadratic equation: ax² + bx + c

[tex]Sum \ of \ roots : \alpha + \beta = \dfrac{-b}{a}[/tex]

[tex]product \ of \ roots : \alpha \beta = \dfrac{c}{a}[/tex]

So, here given:

[tex]Sum : \alpha + \beta = \dfrac{-(-6)}{2} = 3[/tex]

[tex]Product : \alpha \beta = \dfrac{-7}{2} = - 3.5[/tex]

For finding value:

[tex]\dfrac{\alpha^3}{\beta } + \dfrac{\beta^3 }{\alpha }[/tex]

join fractions

[tex]\dfrac{\alpha^4+ \beta^4}{\alpha \beta }[/tex]

factor out

[tex]\dfrac{(\alpha^2 + \beta ^2)^2 -2\alpha ^2 \beta ^2 }{\alpha \beta }[/tex]

when factored more

[tex]\dfrac{((\alpha + \beta)^2 -2\alpha \beta )^2 -2(\alpha \beta)^2 }{\alpha \beta }[/tex]

insert values inside

[tex]\dfrac{((3)^2 -2(-3.5) )^2 -2(-3.5)^2 }{-3.5 }[/tex]

calculate for value

[tex]-\dfrac{463}{7}[/tex]

The x-intercepts of the parabola are (3, 0) and (7,0)

The given parameters are:

Vertex (h, k) = (5, -12)

Point (x, y) = (0, 63)

The equation of a parabola is:

y = a(x - h)^2 + k

Substitute (h, k) = (5, -12)

y = a(x - 5)^2 - 12

Substitute (x, y) = (0, 63)

63 = a(0 - 5)^2 - 12

Evaluate

63 = 25a - 12

Add 12 to both sides

25a = 75

Divide by 26

a = 3

Substitute a = 3 in y = a(x - 5)^2 - 12

y = 3(x - 5)^2 - 12

Set y to 0 to determine the x-intercepts

0 = 3(x - 5)^2 - 12

Add 12 to both sides

3(x - 5)^2 = 12

Divide by 3

(x - 5)^2 = 4

Take the square root of both sides

[tex]x - 5 = \pm 2[/tex]

Add 5 to both sides

[tex]x = 5 \pm 2[/tex]

Expand

x = (5 - 2, 5 + 2)

Evaluate

x = (3, 7)

Hence, the x-intercepts of the parabola are (3, 0) and (7,0)

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Answer:

You can find the mean, by adding all the terms in each data set and dividing by the number of terms.  For example, if there were four data points, you would add them all up and divide by four.

hope this helps!

The coordinates of the vertex of the parabola are (-6,5).

The coordinates of a vertex of a parabolic equation are those x and y points for which the parabola crosses its axis of symmetry.

The vertex of an up-down facing parabola of the form y = ax² + bx + c is [tex]\mathbf{x_v = -\dfrac{b}{2a}}[/tex]

[tex]\mathbf{x_v = -\dfrac{2}{2(1/6)}}[/tex]

[tex]\mathbf{x_v = -6}[/tex]

From the equation:

[tex]\mathbf{y = \dfrac{1}{6}x^2+2x+11}[/tex]

[tex]\mathbf{y_v = \dfrac{1}{6}(-6)^2+2(-6)+11}[/tex]

[tex]\mathbf{y_v =5}[/tex]

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The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. The given triangle can be solved as shown below.

The sine rule of trigonometry helps us to equate the side of the triangles to the angles of the triangles. It is given by the formula,

[tex]\dfrac{Sin\ A}{\alpha} =\dfrac{Sin\ B}{\beta} =\dfrac{Sin\ C}{\gamma}[/tex]

where Sin A is the angle and α is the length of the side of the triangle opposite to angle A,

Sin B is the angle and β is the length of the side of the triangle opposite to angle B,

Sin C is the angle and γ is the length of the side of the triangle opposite to angle C.

For the given triangle, using the sine rule the ratio of the angle and the sides of the triangle can be written as,

[tex]\dfrac{Sin\ A}{18} =\dfrac{Sin\ B}{11} =\dfrac{Sin\ C}{c}\\\\\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ y^o}{11} =\dfrac{Sin\ x^o}{c}[/tex]

Taking the first two ratios,

[tex]\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ y^o}{11}\\\\y = 35.54^o[/tex]

The sum of all the angles of a triangle is 180°.

72° + 35.54° + x° = 180°

x = 72.46°

Now, using the sine ratio,

[tex]\dfrac{Sin\ 72^o}{18} =\dfrac{Sin\ 72.46^o}{c}\\\\c = 18.046[/tex]

Hence, the given triangle is solved.

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Step-by-step explanation:

[tex]( \sec(x) + \tan(x) )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]

[tex]( \frac{1}{ \cos(x) } + \frac{ \sin(x) }{ \cos(x) } )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]

[tex]( \frac{1 + \sin(x) }{ \cos(x) } )( \frac{1 - \sin(x) }{ \cos(x) } )[/tex]

[tex] \frac{1 - \sin {}^{2} (x) }{ \cos {}^{2} (x) } [/tex]

[tex] \frac{ \cos {}^{2} (x) }{ \cos {}^{2} (x) } [/tex]

[tex] = 1[/tex]

Answer:

b

Step-by-step explanation:

Answer:

  (a)  (5, -3)

Step-by-step explanation:

The "substitution method" for solving a system of equations requires that you write an expression that can be substituted for a variable in one or more of the other equations in the system.

The given equations are ...

We notice the first equation gives an expression for y. This is exactly what we want to substitute for y in the second equation.

When the expression (x-8) is substituted for y in the second equation, you get ...

  2x +3(x -8) = 1

This simplifies to ...

  5x -24 = 1

This 2-step equation can now be solved in the usual way:

  5x = 25 . . . . . . add 24 to isolate the variable term

  x = 25/5 = 5 . . . . . divide by the coefficient of x

Note that we now know what the correct answer choice is.

Using the expression for y, we find ...

  y = x -8 = 5 -8 = -3

The solution is (x, y) = (5, -3).

__

The attached graph confirms this solution.

Thoughts:  The best that I was able to do was simplify it in this form.

Answer:    V    

Answer:

(a)  5165.42 rupees

(b)  $1.35

Step-by-step explanation:

Given information:

Part (a)

To find how many rupees $103.64 was worth, multiply the number of dollars by the number of rupees per dollar:

⇒ 103.64 × 49.84 = 5165.42 rupees (nearest hundredth)

Part (b)

To find how many dollars 67.36 rupees was worth, divide the number of rupees by the number of rupees per dollar:

⇒ 67.36 ÷ 49.84 = $1.35 (nearest hundredth)

Answer:

3081.24 cm³ (nearest hundredth)

Step-by-step explanation:

Formulas

[tex]\textsf{Circumference of a circle}=\sf 2 \pi r\quad\textsf{(where r is the radius)}[/tex]

[tex]\textsf{Volume of a cylinder}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}[/tex]

If a rectangular piece of paper is rolled along its length to form a cylinder:

To calculate the volume of the formed cylinder, determine the radius by using the circumference formula:

[tex]\implies \sf 2 \pi r = 44[/tex]

[tex]\implies \sf r = \dfrac{44}{2 \pi}[/tex]

[tex]\implies \sf r =\dfrac{22}{\pi}[/tex]

Substitute the round radius into the formula for Volume and solve for V:

[tex]\implies \sf V=\pi \left(\dfrac{22}{\pi}\right)^2(20)[/tex]

[tex]\implies \sf V=\pi \left(\dfrac{484}{\pi^2}\right)(20)[/tex]

[tex]\implies \sf V=\left(\dfrac{484}{\pi}\right)(20)[/tex]

[tex]\implies \sf V=\dfrac{9680}{\pi}[/tex]

[tex]\implies \sf V=3081.239698...cm^3[/tex]

Therefore, the volume of the cylinder is 3081.24 cm³ (nearest hundredth).

Her boss would give Kim a total of $2x

The given parameters are:

Distance = 26 km

Assume that the amount raised during the marathon is

Amount = x

From the question, we have:

Boss = Double the amount

This means that:

Boss = 2 * Amount

Substitute Amount = x

Boss = 2x

Hence, her boss would give Kim a total of $2x

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The value of x is 4.

Two objects are similar if they have the same shape, or one has the same shape as the mirror image of the other.

Given:

In ΔCDB and ΔEAB

<CDB = <ABE    (alternate interior angle)

<DBC = <EAB    (alternate interior angle)

By AA similarity criteria

ΔCBD ~ ΔEAB

Now,

EB/ CD= EA/CB

6/x-1 = 4/x-2

6X-12= 4X-4

2x= 8

x=4

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Answer:

Milk and Eggs = 552

Step-by-step explanation:

First add all of the other percentages together. (70%), 100%-70%=30%. 30% of 1840 = 552.

Answer:

H.  552

Step-by-step explanation:

Circle graph information:

Total consumption = 1840 pounds per person

First, calculate the percentage of milk and eggs (the value of x).

Total percentages = 100%

⇒ x + 38 + 10 + 10 + 8 + 4 = 100

⇒ x + 70 = 100

⇒ x = 30

Therefore, 30% of food consumption is milk and eggs.

To calculate the number of pounds of milk and eggs the average American consumes each year, simply find 30% of the total consumption:

= 30% of 1840

= 30% × 1840

[tex]=\sf \dfrac{30}{100} \times 1840[/tex]

= 552

Therefore, the average American consumes 552 pounds of milk and eggs each year.

Answer:

y=3/2x + 18

Step-by-step explanation:

So when two lines are perpendicular, that simple means the slope are reciprocals, and the signs are opposite. So for example if one equation had a slope of [tex]\frac{a}{b}[/tex], the equation that is perpendicular, would have a slope of [tex]-\frac{b}{a}[/tex]. So the first step would be to find the slope of 2x+3y=4. To find the slope we can convert it into slope-intercept form which is y=mx+b where m is the slope, and this is done by isolating y, as you can see the y is alone in the slope-intercept form.

Original equation:

2x + 3y = 4

subtract 2x from both equations:

3y = -2x + 4

Divide both sides by 3

y = -2/3x + 4/3

The y-intercept doesn't really matter in this case, what really matters is the slope, and the slope is the coefficient of x, since as x increases by 1, it will increase by the amount of the coefficient, because the slope is rise/run and since the run is 1, if you increase x by 1, the run is the slope, which is the coefficient. The slope in this case is -2/3. So the reciprocal of the slope is 3/2 (notice how the sign is the opposite as well). Now we have the equation

y=3/2x + b

To find the y-intercept, you simply use the point that was given (-2, 15). Plug in -2 as x, and 15 as y to find the value of b

Original equation

y=3/2x + b

Plug in known values:

15 = 3/2(-2) + b

Multiply the fraction:

15 = -6/2 + b

Simplify the fraction:

15 = -3 + b

Add 3 to both sides

18 = b

This gives you the equation

y=3/2x + 18

It is false that x is a function of y

The equation is given as:

x = y^2

Set y = 2

x = (2)^2

x = 4

Set y = -2

x = (-2)^2

x = 4

Different values of y give the same x value.

This means that x is not a function of y

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Answer:

He have to invest $527.777778 .

Step-by-step explanation:

X : 4.75% = $10,000 : 90

Answer:

Infinitely many solutions.

Step-by-step explanation:

Let's solve your system by elimination.

x−3y=9;−x+3y=−9

x−3y=9

−x+3y=−9

Add these equations to eliminate x:

0=0

Answer:

Infinitely many solutions.