(8-6b)(5-3b)=

You have to find the product this is geometry

The solution of the equation y = (2/3)x + 3 is 5/3

The given equation is

y = (2/3)x + 3

The slope of the line is the change in y coordinates with respect to the change in x coordinates.

This is the linear equation in the the slope intercept form

y = mx + b

Where m is the slope of the line

b is the y intercept

y is the y coordinates

x is the x coordinates

The value of x = -2

Substitute the value of x in the equation

y = (2/3) × -2 + 3

Do the arithmetic operations

= -4/3 + 3

Add the numbers

= 5/3

Therefore, the solution is 5/3

I have solved the question in general, as the given question is incomplete

The complete question is:

What is the solution of the equation y = (2/3)x + 3x, when x = -2?

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add all the sides!

[side one] + [side two] + [side three]

[7y + 10] + [7y + 10] + [y - 4]

= 14y + 20 + y - 4

= 15y + 16

hope this helps :) !!

Answer:

15y + 16

Step-by-step explanation:

2(7y + 10) + y - 4

14y + 16 + y

15y + 16

Answer:

For example, the phrase "3 more than an unknown number" becomes the mathematical expression "x + 3." Because the unknown number has no explicitly stated value, we label it with a variable x. To get a value three more than x, simply add 3 to it.

hope it helps ya mate. ~^~

Answer:

3 + x

Step-by-step explanation:

"More than" means addition. 3 more than x is saying 3 plus x. In an algebraic expression, this would look like:

3 + x

Answer:

18

Step-by-step explanation:

24*0.74 = 18

Answer:

There are infinite solutions for this plug in any number for t, and you will always get 0

Step-by-step explanation:

Hope this helps:)

The coordinates of A'', B'' and C'' are (-1, 4), (-4, 3) and (-1, 2) respectively.

Transformation of geometrical figures or points is the manipulation of a given figure to some other way.

Different types of transformations are Rotation, Reflection, Glide reflection, Translation and Dilation.

Given triangle has coordinates,

A(2, -2), B(5, -3) and C(2, -4).

First the triangle is translated by the rule (x, y) → (x - 1, y + 6)

A(2, -2) becomes A'(2 - 1, -2 + 6) = A'(1, 4).

B(5, -3) becomes B'(5 - 1, -3 + 6) = B'(4, 3)

C(2, -4) becomes C'(2 - 1, -4 + 6) = C'(1, 2)

Then the translated triangle is reflected across the Y axis.

When reflected a point (x, y) across the Y axis, y coordinate remains same and x coordinate flips.

A'(1, 4) becomes A''(-1, 4)

B'(4, 3) becomes B''(-4, 3)

C'(1, 2) becomes C''(-1, 2)

Hence the vertices of the triangle after undergoes translation and reflection becomes A''(-1, 4), B''(-4, 3) and C''(-1, 2).

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In order to find the volume, we will use the next formula

where l is the length, w is the width and h is the height.

In our case

l=28 ft

w=25 ft

h=12 ft

we substitute the data

The volume is 8400 cubic feet

Step-by-step explanation:

The americium is represented as 1. Every 432 years it decreases by 50%.

First half-life:

432 years.

\(1 \div 2 = 0.50\)

0.50 (1/2) of americium remains after 432 years.

Second half-life:

\(432 \times 2 = 864\)

\(0.5 \div 2 = 0.25\)

0.25 (1/4) of the americium remains.

Third half-life:

\(432 \times 3 = 1296\)

\(0.25 \div 2 = 0.125\)

0.125 (1/8) of the americium remains.

Last half-life:

\(432 \times 4 = 1728\)

\(0.125 \div 2 = 0.0625\)

0.0625 (1/16) of the americium remains.

Option B is correct.

Answer:

p < 4

Step-by-step explanation:

We are given 0.4p + 1.7 < 3.3.

We solve it like a normal equation by isolating the variable p. Subtract 1.7 from both sides:

0.4p + 1.7 - 1.7 < 3.3 - 1.7

0.4p < 1.6

Divide both sides by 0.4:

p < 1.6/0.4

p < 4

Thus, our possible solutions are p < 4.

~ an aesthetics lover

Answer:

7

Step-by-step explanation:

Make the fractions have a denominator of 20.

2/5 times the top and bottom by 4 (because 5 times 4 = 20) = 8/20

So 8 socks are white

1/4 times 5 = 5/20

So 5 socks are black

Add them and subtract from 20 to get the number of gray socks

20-13=7

Answer:

The ratio of paper bags to hard bags is 6:2, which can also be written as 6/2 = 3/1. This means that for every 3 units of paper bags, there is 1 unit of hand bags.

If there are 192 bags in total, and the ratio of paper bags to hard bags is 3:1, then there must be 3 + 1 = 4 parts in total. We can find the number of bags in each part by dividing the total number of bags by the number of parts: 192 bags / 4 parts = 48 bags/part.

Since there are 3 parts of paper bags for every 1 part of hard bags, there must be 3 * 48 bags/part = 144 paper bags. Answer: {144}.

Step-by-step explanation:

=======================================================

Explanation:

I'll use the quadratic formula to find the roots or x intercepts. This slight detour allows us to factor without having to use guess-and-check methods.

The equation is of the form ax^2+bx+c = 0

This leads to...

\(x = \frac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\x = \frac{-(-11)\pm\sqrt{(-11)^2-4(12)(-5)}}{2(12)}\\\\x = \frac{11\pm\sqrt{361}}{24}\\\\x = \frac{11\pm19}{24}\\\\x = \frac{11+19}{24} \ \text{ or } \ x = \frac{11-19}{24}\\\\x = \frac{30}{24} \ \text{ or } \ x = \frac{-8}{24}\\\\x = \frac{5}{4} \ \text{ or } \ x = -\frac{1}{3}\)

Now use those roots to form these steps

\(x = \frac{5}{4} \ \text{ or } \ x = -\frac{1}{3}\\\\4x = 5 \ \text{ or } \ 3x = -1\\\\4x - 5 =0 \ \text{ or } \ 3x+1 = 0\\\\(4x-5)(3x+1) = 0\)

Refer to the zero product property for more info.

Therefore, the original expression factors fully to (4x-5)(3x+1)

Use the FOIL rule to expand it out and you should get 12x^2-11x-5 again.

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

We did that factoring so we could find the side lengths of the rectangle.

I'm using the fact that area = length*width

The order of length and width doesn't matter.

From here, we can then compute the perimeter of the rectangle

P = 2(L+W)

P = 2(4x-5+3x+1)

P = 2(7x-4)

P = 14x - 8

The correct statement is Most of the songs were between 3 minutes and 3.8 minutes long.

Based on the given information from the graph, we can determine the following:

The graph shows an upward trend from 2.8 to 3.4 on the horizontal axis.

Then, there is a downward trend from 3.4 to 4 on the horizontal axis.

From this, we can conclude that most of the songs played during the one-hour interval were between 3 minutes and 3.8 minutes long. This is because the upward trend indicates an increase in length from 2.8 to 3.4, and the subsequent downward trend suggests a decrease in length from 3.4 to 4.

Therefore, the correct statement is:

Most of the songs were between 3 minutes and 3.8 minutes long.

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Answer:

A

Step-by-step explanation:

To determine the number of women (w) and men (m) who donated money at the circus booth, while ensuring that the total donation does not exceed $4,268, a system of inequalities can be used.

The system of inequalities is: w + m > 249 and 16w + 18m ≤ 4,268.

The first inequality, w + m > 249, represents the condition that the total number of women and men who donated is greater than 249 people. This ensures that more than 249 people donated money.

The second inequality, 16w + 18m ≤ 4,268, represents the condition that the total donation amount does not exceed $4,268. The average donation for women is $16, so the total donation by women is 16w. Similarly, the average donation for men is $18, so the total donation by men is 18m. Adding these two amounts together should be less than or equal to $4,268.

By solving this system of inequalities, we can determine the possible values of w and m that satisfy both conditions.

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The volume of the solid is 243/2 cubic units. To find the volume of the solid, we need to integrate the function z = 9 - y - x^2 over the bounded region in the first octant.

The region is bounded by the coordinate planes, so we have the limits of integration as follows:

0 ≤ x ≤ √9-y
0 ≤ y ≤ 9

The solid is bounded, so the integral will give us a finite volume:

V = ∫∫z dA, where the double integral is taken over the bounded region.

V = ∫[0,√9-y]∫[0,9] (9-y-x^2) dx dy

We can simplify the integrand by integrating with respect to x first:

V = ∫[0,9] ∫[0,√9-y] (9-y-x^2) dx dy
V = ∫[0,9] (9y - y^2 - 3(9-y)^2/2) dy
V = ∫[0,9] (-3y^2 + 54y - 243/2) dy
V = [-y^3/3 + 27y^2 - 243/2 y] [0,9]
V = 243/2

Therefore, the volume of the solid is 243/2 cubic units.

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Answer:

The answer is B. 9.7

Step-by-step explanation:

sin 14°=x/40

=> sin 14° X 40 = x

∴ x = 9.67≈ 9.7

Answer:A. h(t) = -16(t - 403)^2 + 3

B. h(t) = -16(t - 5)^2 + 3

C. h(t) = -16(t - 3)^2 + 403

D. h(t) = -16(t - 5)^2 + 403

Step-by-step explanation:

To find the area of the region bounded by the parabola y = 4x², the tangent line to this parabola at (2, 16), and the x-axis, we will integrate the area between the curve and the x-axis on the interval (0,2) and then subtract the area of the triangle formed by the tangent line, x-axis, and the vertical line x=2.

Here's the complete solution:Step 1: Find the equation of the tangent line at (2,16)The derivative of y = 4x² is:y' = 8xThus, the slope of the tangent line at (2,16) is:y'(2) = 8(2) = 16The point-slope form of the equation of a line is:y - y₁ = m(x - x₁)Using point (2,16) and slope 16, the equation of the tangent line is:y - 16 = 16(x - 2)y - 16 = 16x - 32y = 16x - 16Step 2: Find the x-coordinate of the intersection between the parabola and the tangent line.To find the x-coordinate, we equate the equations:y = 4x²y = 16x - 16Substituting the first equation into the second gives:4x² = 16x - 16Simplifying, we get:4x² - 16x + 16 = 04(x - 2)² = 0x = 2Since the x-coordinate of the point of intersection is 2, this is the right endpoint of our integration interval.Step 3: Integrate the region bounded by the parabola and the x-axis on the interval (0,2)We need to integrate the curve y = 4x² on the interval (0,2):∫(0 to 2) 4x² dx= [4x³/3] from 0 to 2= (4(2)³/3) - (4(0)³/3)= (32/3)Thus, the area between the curve and the x-axis on the interval (0,2) is 32/3.Step 4: Find the area of the triangle formed by the tangent line, x-axis, and the vertical line x=2To find the area of the triangle, we need to find the height and base.The base is the vertical line x=2, so its length is 2.The height is the distance between the x-axis and the tangent line at x=2, which is 16. Thus, the area of the triangle is:1/2 * base * height= 1/2 * 2 * 16= 16Step 5: Subtract the area of the triangle from the area of the region bounded by the parabola and the x-axis on the interval (0,2)Area of the region = (32/3) - 16= (32 - 48)/3= -16/3Therefore, the area of the region bounded by the parabola y = 4x², the tangent line to this parabola at (2, 16), and the x-axis is -16/3.

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The parabola is defined by the equation \(y = 4x².\)

We need to find the area of the region bounded by this parabola, the tangent line to this parabola at (2, 16), and the x-axis.

This is illustrated in the figure below: Let's first find the equation of the tangent line at (2, 16).

The derivative of y = 4x² is:y' = 8x

\(y = 4x² is:y' = 8x\)

The slope of the tangent line at \((2, 16) is therefore: y'(2) = 8(2) = 16\)

The equation of the tangent line is therefore:y - 16 = 16(x - 2) => y = 16x - 16

\(y - 16 = 16(x - 2) => y = 16x - 16\)We can now find the intersection points of the parabola and the tangent line by solving the system of equations:\(4x² = 16x - 16 => 4x² - 16x + 16 = 0 => (2x - 4)² = 0\)

Therefore, x = 2 is the only intersection point.

This means that the region is bounded by the x-axis on the left, the parabola above, and the tangent line below.

To find the area of this region, we need to integrate the difference between the parabola and the tangent line from x = 0 to x = 2.

This gives us the area of the shaded region in the figure above.

Using the equations of the parabola and the tangent line, we have:\(y = 4x²y = 16x - 16\)

The difference between these two functions is:\(y - (16x - 16) = 4x² - 16x + 16\)

To find the area of the region, we need to integrate this function from x = 0 to x = 2.

That is, we need to compute the following definite integral: \(A = ∫[0,2] (4x² - 16x + 16) dxIntegrating term by term, we get: A = [4/3 x³ - 8x² + 16x]₀² = [4/3 (2)³ - 8(2)² + 16(2)] - [4/3 (0)³ - 8(0)² + 16(0)] = [32/3 - 32 + 32] - [0 - 0 + 0] = 32/3\)

Therefore, the area of the region bounded by the parabola \(y = 4x², the tangent line to this parabola at (2, 16), and the x-axis is 32/3 square units.\)

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Answer:

- 3,  2/3

Step-by-step explanation:

Given:

3·x² + 7·x - 6 = 0

General Equation:

a·x² + b·x + c = 0

a = 3;

b = 7;

c = - 6.

Discriminant:

D = b² - 4·a·c = 7² - 4·3·(-6) = 49 + 72 =  121

√ (D) = √ (121) = 11

Solution:

x₁₂ = ( - b ± √(D) ) / (2·a);

x₁ = ( - 7 - 11 ) / (2·3) =  ( - 18) / 6 =  -3

x₂ = ( - 7 + 11 ) / (2·3) =  4 / 6 = 2 / 3

The true statement is "Every seventh-grade class has 12 more students than a kindergarten class." (option d).

For the seventh-grade class, the mean is 32, which is larger than the mean for the kindergarten class. This means that, on average, seventh-grade classes have more students than kindergarten classes. The MAD for the seventh-grade class is 2, which is larger than the MAD for the kindergarten class.

This suggests that the deviation from the mean for each data point in the seventh-grade class is larger, on average 2 students, than for the kindergarten class. This means that the size of seventh-grade classes is more variable than kindergarten classes.

Option D is correct because while the difference between the means of the two classes is 12, this does not mean that every seventh-grade class has 12 more students than every kindergarten class.

Hence the c correct choice is option (d).

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13 and 13√2 is the value of x and y in the given diagram

The given diagram is a right triangle, we need to determine the value of x and y.

Using the trigonometry identity

tan45 = opposite/adjacent
tan45 = x/13

x = 13tan45
x = 13(1)
x = 13

For the value of y

sin45 = x/y

sin45 = 13/y
y = 13/sin45

y = 13√2
Hence the exact value of x and y from the figure is 13 and 13√2 respectively.

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The wavelength of the wave is approximately 2.09m, and the speed of the wave is approximately 1.99m/s. values were obtained by analyzing given expression and utilizing relationships between wave parameters.

To find the wavelength, we can use the formula λ = v/f, where λ represents the wavelength, v represents the speed of the wave, and f represents the frequency of the wave. However, in the given expression, we are not directly given the frequency. Instead, we have the angular frequency ω, which is related to the frequency as ω = 2πf.By comparing the given expression with the general wave equation, we can identify that the wave number k = 3.00m^(-1). Since the wave number is related to the wavelength as k = 2π/λ, we can rearrange the equation to find the wavelength: λ = 2π/k. Plugging in value for k, we get λ = 2π/(3.00m^(-1)), which simplifies to approximately λ = 2.09m.

To determine the speed of the wave, we can use the formula v = λf, where v represents the speed of the wave, λ represents the wavelength, and f represents the frequency. As mentioned earlier, we have the angular frequency ω instead of the frequency f. However, we know that ω = 2πf, so we can rearrange this equation to find f = ω/(2π). Plugging in the given angular frequency ω = 6.00s^(-1), we get f = 6.00s^(-1)/(2π), which simplifies to approximately f = 0.955Hz.Now that we have the wavelength λ = 2.09m and the frequency f = 0.955Hz, we can use the formula v = λf to find the speed of the wave. Plugging in the values, we get v = (2.09m)(0.955Hz), which gives us the speed of the wave v = 1.99m/s.

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Answer:

2x - 12

Step-by-step explanation:

Hello!

So, let's simplify using the distributive property.

Let's look at 3(2x - 4). You want to multiply 3 by every term inside the parentheses.

3*2x = 6x

3*-4= - 12

So now our expression looks like this:

(6x - 12) - 4x

Now we combine like terms. Our only like terms are 6x and -4x.

6x - 4x = 2x. So, our simplified expression is:

2x - 12.

∑ k = 1 88 2.5 ⁢ ( 1.2 ) k  is this series written in sigma notation.

What is the series written in sigma notation?

Given:

2.5 + 2.5(1.2) + 2.5(1.2)2 + ⋯ + 2.5(1.2)87

If we look at the power it is always one less the term i.e., for first term the value of k=0.

So, the series in the form of summation can be written as

∑ k = 1 88 2.5 ⁢ ( 1.2 ) k

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Answer:

n ÷ 20.7 = 9

Step-by-step explanation:

Let n be the unknown number

Quotient is division and is means equals.

n ÷ 20.7 = 9

Answer:

C. x<4

Step-by-step explanation:

1. Subtract 2 from both sides

2. You get x<4

Answer:

C) x < 4

Step-by-step explanation:

x + 2 < 6

x < 6 - 2

x < 4

Answer:

Perpendicular bisector

Step-by-step explanation:

Given

The above statement

Required

What describes the given statement?

The term that describes the given statement is the perpendicular bisector.

This is so because:

- The perpendicular bisector passes through midpoints

- The point of intersection is at the \(90^o\)