The equation that models this situation is y = 35x + 30, where y is the amount of money she spent and x Is the number of chairs she bought

Answer:

x = 4

Step-by-step explanation:

Given

4x - 6 + 2x = 18 ← simplify left side by collecting like terms

6x - 6 = 18 ( add 6 to both sides )

6x = 24 ( divide both sides by 6 )

x = 4

The solution to the equation 4x - 6 + 2x = 18 is x = 4.

To solve the equation 4x - 6 + 2x = 18, we need to combine like terms and isolate the variable x.

First, let's combine the like terms on the left side of the equation:

4x + 2x - 6 = 18

This simplifies to:

6x - 6 = 18

Next, we can isolate the variable x by adding 6 to both sides of the equation:

6x - 6 + 6 = 18 + 6

This simplifies to:

6x = 24

To solve for x, we can divide both sides of the equation by 6:

(6x)/6 = 24/6

This simplifies to:

x = 4

Therefore, the solution to the equation 4x - 6 + 2x = 18 is x = 4.

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Answer:

$878.25

Step-by-step explanation:

Continuously compounded interest is:

A = Pe^(rt)

where A is the final amount, P is the initial amount, r is the interest rate, and t is the number of compoundings.

Here, P = 560, r = 0.09, and t = 5.

A = 560e^(0.09×5)

A = 878.25

Final answer:

To calculate the future value of an investment compounded continuously, use the formula A = Pert. In this case, the investment will be worth approximately $877.29 in 5 years.

Explanation:

To calculate the future value of an investment compounded continuously, we can use the formula A = Pert, where A is the future value, P is the initial principal, r is the annual interest rate, and t is the time in years. In this case, P = $560, r = 0.09, and t = 5. Plugging these values into the formula, we get:

A = 560e^(0.09⋅5)

A ≈ 560e^0.45

A ≈ 560 ⋅ 1.5662

A ≈ $877.29

Therefore, the investment will be worth approximately $877.29 in 5 years.

Answer:

B. 37.5 sq. units

Step-by-step explanation:

The area of a triangle is given by

A = 1/2 bh where b is the length of the base and  h is the height

A = 1/2 (5 * 15)

A =37.5 units^2

Answer:375 units

Hope this helps

The answer choice that matches the box plot you draw would be B.

A box plot can be used to represent the distribution of a data set using the five-number summary. The five-number summary include the following:

To plot a box plot for the given data, we need to determine the value of each of the five-number summary of the data set.

Given:

12, 14, 17, 23, 25, 30, 32, 37, 38, 40, 41

The minimum: Lowest data value in the data set is the minimum = 12

The maximum: Highest data value = 41

Median: The middle data value (the 6th data point) = 30

First Quartile: The middle value of the first part of the data set before the median (the 3rd data point) = 17

Third Quartile: The middle value of the second part of the data set after the median (the 9th data point) = 38

Next is to plot the five-number summary on a box plot.

Min value, 12, is displayed and represented by the whisker you have at your far left.

Max value, 41, is displayed and represented by the whisker you have at your far right.

Median value, 30, is displayed and represented by the vertical line that divides the rectangular box into two you.

Q1 value, 17, is displayed and represented at the beginning of the rectangular box.

Q3 value, 38, is displayed and represented at the end of the rectangular box.

The box plot of the given data when drawn would match the following as shown in the attachment below.

Therefore, the answer choice that matches the box plot drawn is B.

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Answer:

x = 0, 6, -1

Step-by-step explanation:

We need to set f(x) = 0 to find the values of x for this expression.

So

[tex]x^3-5x^2-6x=0[/tex]

We will factor out an x and do middle term factorization to arrive at our answer for x (there will be 3 x values):

[tex]x^3-5x^2-6x=0\\x(x^2-5x-6)=0\\x(x-6)(x+1)=0\\x=0,6,-1[/tex]

These are the 3 values for x.

Answer:

0.75m/s

Step-by-step explanation:

Speed formula: ⇒ [tex]S=\frac{V}{T}[/tex]

Divide by the numbers from left to right.

S=18

T=24

18/24=0.75

0.75m/s is the correct answer.

I hope this helps you, and have a wonderful day!

[tex]\frac{3}{4}[/tex] millimeter per second

You simply need to divide [tex]\frac{18}{24}[/tex].  This is a fraction, so you can just simplify it.

Divide the numerator and the denominator each by 6, which is the greatest common factor.  [tex]\frac{\frac{18}{6}}{\frac{24}{6}} = \frac{3}{4}[/tex]

This is as simple as the result can get, so [tex]\frac{3}{4}[/tex] millimeter per second is the final answer.

Answer: [tex](-4,-7)[/tex]

Step-by-step explanation:

By definition, the equation of parabola in Vertex form is:

[tex]y=a(x - h)^2 + k[/tex]

Where (h, k) is the vertex of the parabola.

You need to remember that multiplication of signs:

[tex](+)(+)=+\\(-)(-)=+\\(-)(+)=-[/tex]

Then given the equation [tex]y = -(x + 4)^2 - 7[/tex], you know that this is:

[tex]y = -(x -(-4))^2 +(-7)[/tex]

You can observe that the value of "h" and the value of "k" of this equation are:

[tex]h=-4\\k=-7[/tex]

Therefore, the vertex is:

[tex](-4,-7)[/tex]

Answer:

h = 147 - 16t^2.

Step-by-step explanation:

Use the following equation of motion

h = ut + 1/2 gt^2    where  h = height, u = initial velocity , g = acceleration due to gravity and t = the time.

So here we have:

h = 14t + 1/2 * -32 * t^2

h = 14t - 16t^2

Answer:

Height of jump, s(t) = 14t - 16.09t²

Step-by-step explanation:

We have equation of motion s = ut + 0.5 at².

For the this vertical motion we have

              s = height of jump

              u = initial velocity = 14 ft/s

               t = time

               a = acceleration due to gravity = -32.17 ft/s²

Substituting

                 s = 14 x t + 0.5 x (-32.17) x t²

                 s = 14t - 16.09t²

Height of jump, s(t) = 14t - 16.09t²

Answer:

$409.86

Step-by-step explanation:

230 is the before markup

We must apply the markup (or even discount) before the tax is applied.

Marked up 65% means we must do .65(230)  <---This will tell us how much more the tent is going to sell for

.65(230)=149.5

So we started with 230 and it is going up by 149.5, so the new price before tax is 230+149.5=379.5

Now the tax is applied to what you are paying (before tax).

So 8% of 379.5 is .08(379.5)=30.36

So new price + tax is the total cost

    379.5        +30.36

=409.86

Answer:

-12

Step-by-step explanation:

We can just try and find what works! since we can subtract 12 from -2 and get -14, we might try subtracting 12 every time. After we test it out, we see that is is correct!

Answer:

10-12n

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

B because the line doesn't go through any of the data points.

Answer:

y-6 = -3(x+1)

Step-by-step explanation:

The point-slope form of a line is the following:

y-yo = m(x-xo), where 'm' is the slope and (xo, yo) is any point where the line passes through.

In this case, m=-3 and (xo, yo) = (-1, 6).

Therefore: y-yo = m(x-xo) = y-6 = -3(x+1)

In conclusion, the point-slope form of the equation that represents the line that passes through the point (-1, 6) and has a slope of -3 is:

y-6 = -3(x+1)

For this case we have that the equation of a line in the point-slope form is given by:

[tex](y-y_ {0}) = m (x-x_ {0})[/tex]

Where:

m: It's the slope

[tex](x_ {0}, y_ {0})[/tex]: It is a point through which the line passes

According to the data we have to:

[tex]m = -3\\(x_ {0}, y_ {0}) = (- 1,6)[/tex]

So the equation is:

[tex](y-6) = - 3 (x - (- 1))\\(y-6) = - 3 (x + 1)[/tex]

Answer:

[tex](y-6) = - 3 (x + 1)[/tex]

Answer: the answer is C. (1, 2)

Step-by-step explanation: because the origin is 0 and slope is rise over run. so if you start at 0, go up one, and over two, your point is at (1,2) .

Answer:

Option D.

Step-by-step explanation:

A line will be in the form of y = mx + c

Where m = slope of the line and c = y-intercept

In this question slope of the line is given as [tex]\frac{1}{2}[/tex] and it passes through origin.

Since line passes through origin then there will be no y-intercept that means c=0

So equation will be y = [tex]\frac{1}{2}[/tex]x

Now check each option that satisfy the equation of the line.

Option A. ( 0, [tex]\frac{1}{2}[/tex] )

                 y = 0 ≠ [tex]\frac{1}{2}[/tex] so invalid option

Option B. ( [tex]\frac{1}{2}[/tex], 1 )

               y = [tex](\frac{1}{2})[/tex] [tex](\frac{1}{2})[/tex] = [tex](\frac{1}{4})[/tex] ≠ 1 Invalid option

Option C. ( 1,2)

               y = [tex](\frac{1}{2})[/tex] × 1 = [tex](\frac{1}{2})[/tex] ≠ 2 Invalid option

Option D. ( 2, 1 )

              y = [tex](\frac{1}{2})[/tex] × 2 = 1 correct option

Option D. is the correct answer.

Final answer:

To complete the square for the equation x² - 9x + _____ = 6, the constant term should be (81/4). This is obtained by dividing the coefficient of x by 2 and then squaring it.

Explanation:

The constant term required to complete the square for the equation x² - 9x + _____ = 6 can be found using a specific algebraic method. To complete the square, the coefficient of the x term should be divided by 2 and then squared. Therefore, for the equation provided, we take (-9/2) and square it, which results in (81/4). The complete equation after adding the constant term will be x² - 9x + 81/4 = 6 which, after completing the square, can be written as (x - 9/2)² = 6 + 81/4.

Answer:

option number 1st is the correct answer.

Answer:

the second  because it shows you the way its  

Step-by-step explanation:

The equation to show how many dogs Ida walked Saturday is A.10x = 70

A system of linear equations exists usually a set of two linear equations with two variables.

A linear equation only includes one or two variables. No variable in a linear equation exists raised to a power greater than 1 or utilized as the denominator of a fraction. When you discover pairs of values that create a linear equation true and plot those pairs on a coordinate grid, all of the points lie on the same line.

Given,

Ida gets paid $10 for every dog walked and made a total of $70 on Saturday.

It will be A. She earned 10 dollars per hour 10x= 70.

Hence, the correct answer is option A. 10x = 70

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Answer:

-4

Step-by-step explanation:

Factor by the numbers from left to right.

[tex]64^\frac{1}{3}[/tex]

[tex]64=4^3[/tex]

[tex](\frac{4}{3})^\frac{1}{3}=4^3^*^\frac{1}{3}=4[/tex]

It changes to positive to negative.

-4

-4 is the correct answer.

[tex]3(2x+5) = 3x+4x\\6x+15=7x\\x=15[/tex]

Answer:

x = 15

Step-by-step explanation:

Given

3(2x + 5) = 3x + 4x ← collect like terms

3(2x + 5) = 7x ← distribute parenthesis on left side by 3

6x + 15 = 7x ( subtract 6x from both sides )

15 = x ⇒ x = 15

Answer:

Step-by-step explanation:

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Answer:

The side of the square = x/√2

Step-by-step explanation:

All the sides of a square are equal. All the angles are equal to 90°

To find the side of a square

From the figure attached with this answer shows a square.

Let 'x' be the diagonal of the square.

The diagonal make two right angled triangle with angle 45°, 45° and 90°

Therefore the sides are in the ratio 1 : 1 : √2

Here diagonal = x

 side : side : x= side : side : √2

Therefore one side length = x/√2

Answer:

Area = x²/2 square units

Step-by-step explanation:

The key to solving this question is to understand that:

a) the sides of a square are the same length

b) the length of the diagonal may be calculated via Pythagoras' theorem (c² = a² + b², where c is the length of the hypotenuse of a triangle and a and b the lengths of the other two sides)

1. Now, let's call the sides of the square length y and the diagonal is length x.

Using c² = a² + b², we can substitute our values to get:

x² = y² + y²

x² = 2y²

2. Stepping away from Pythagoras' theorem for a little bit, let us think of the general formula for the area of a square:

A (for Area) = a², where a is the length of the sides of the square (which are all of equal length)

Given that we defined our square as having length y, let us substitute this value in to get:

A = y²

3. Now we have two formulas that we can work with:

1) x² = 2y²

2) A = y²

4. Given that A = y², we can say that 2y² = 2A

Therefor, if x² = 2y², then x² = 2A

Thus, if we want to find the formula for area in terms of x, we need to simply rearrange the given formula to make A the subject, giving us:

A = x²/2 square units

Hope that helps :)

Answer:

a = 4

Step-by-step explanation:

Assuming you require to solve for a

Given

3 = a(4 - 7)² - 33 = a(- 3)² - 33 = 9a - 33

Add 33 to both sides

9a = 36 ( divide both sides by 9 )

a = 4

Answer:

r=3

Step-by-step explanation:

24π=2π(r^2+r)

Divide each side by 2 pi

24π/2π =2π/2π(r^2+r)

12 = r^2 +r

Subtract 12 from each side

12-12 = r^2 +r -12

0 =  r^2 +r -12

Factor

What number multiply to -12 and add to 1

4*-3 = -12

4-3 = 1

0= (r+4) (r-3)

Using the zero product property

r+4 =0          r-3 =0

r+4-4 =0-4   r-3+3=0+3

r = -4           r = -3

Assuming r is the radius, r must be positive

r =3

Answer: Option C

[tex]y=5[/tex], [tex]x=10[/tex]

Step-by-step explanation:

If the lines m and n are parallel then the large triangle and the small triangle are similar triangles, because they have equal angles.

By definition for similar triangles it is satisfied that if they have sides of length a, b, c and a', b',  c'  then:

[tex]\frac{a}{a'}=\frac{b}{b'} =\frac{c}{c'}[/tex]

In this case

[tex]a = 12\\a' = 4\\c = 15\\c' = y[/tex]

So:

[tex]\frac{12}{4}=\frac{15}{y}[/tex]

Now solve the equation for the variable y

[tex]3=\frac{15}{y}[/tex]

[tex]y=\frac{15}{3}[/tex]

[tex]y=5[/tex]

We know that

[tex]x+y=15[/tex] and  [tex]y=5[/tex]

Then

[tex]x+5=15[/tex]

[tex]x=10[/tex]

Finally the answer is:

[tex]y=5[/tex], [tex]x=10[/tex]

Answer:

5.29

Step-by-step explanation:

Answer:

5.29

Step-by-step explanation:

Answer:

6a^2

Step-by-step explanation:

Answer:

1/6.

Step-by-step explanation:

Total number of tokens in the bag = 4 + 14 + 6 = 24.

There are 4 red tokens so the probability of picking a red

=  4/24

= 1/6.

Answer:

A trapezoid is a quadrilateral with exactly one pair of parallel sides. In a trapezoid the parallel sides are called bases. ... A trapezoid with the two non-parallel sides the same length is called an isosceles trapezoid. This conjecture tells us that the base angles of an isosceles trapezoid are equal in measure

Step-by-step explanation:

Answer:

A trapezoid with the two non-parallel sides the same length is called an isosceles trapezoid.

Answer:

x = 2

Step-by-step explanation:

Using the rules of logarithms

• log [tex]x^{n}[/tex] ⇔ nlog x

• log x + log y ⇔ log(xy)

• log x = log y ⇒ x = y

Given

3 ln2 + ln8 = 2ln(4x)

ln2³ + ln8 = ln(4x)²

ln8 + ln8 = ln16x²

ln(8 × 8) = ln16x²

ln64 = ln16x², hence

16x² = 64 ( divide both sides by 16 )

x² = 4 ( take the square root of both sides )

x = [tex]\sqrt{4}[/tex] = 2

Answer: x=2 so B on edg