Ignore the Brief Introduction
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Carpenter remove [tex]3/16[/tex] inches from the top of the plank to the same thickness of wood from the top and bottom of the plank.

How many inches does the carpenter remove from the top of the plank ?

A wooden plank is [tex]5ft[/tex] long and [tex]1\frac{1}{2}[/tex] inches thick

to make the plank [tex]1\frac{1}{8}[/tex] inches thick

Carpenter needs  to cut off

[tex]=1\frac{1}{2} -1\frac{1}{8} \\=\frac{3}{2} -\frac{9}{8} \\=\frac{3}{8}[/tex]

Carpenter cuts each side

[tex]=\frac{3}{8} /2\\=\frac{3}{16} inches[/tex]

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Part A

The two factors are 5 and 4x+6.

Part B

The first factor, 5, has 1 term.

The second factor, 4x+6, has 2 terms.

Part C

The coefficient of the variable term is 4.

The five consecutive integers are -2, -1, 0, 1 and 2.

Given that;

The sum of five consecutive integers equals 5.5 times the middle integer.

Since the integers are consecutive, let the integer be;

x, x+1, x+2, x+3 and x+4.

Now, sum of the integers equals 5.5 times the middle integer.

Middle integer is x+2.

Hence we have;

x + x+1 + x+2 + x+3 + x+4 = 5.5( x+2 )

x + x+1 + x+2 + x+3 + x+4 = 5.5x + 11

We collect like terms

x + x + x + x + x - 5.5x = 11 - 1 - 2 - 3 - 4

5x - 5.5x = 1

-0.5x = 1

x = -( 1 / 0.5 )

x = -2

Since our integers are; x, x+1, x+2, x+3 and x+4.

We substitute in the value of x

x = -2

x+1 = -2 + 1 = -1

x+2 = -2 + 2 = 0

x+3 = -2 + 3 = 1

x+4 = -2 + 4 = 2

Therefore, the five consecutive integers are -2, -1, 0, 1 and 2.

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Find some points

Graph attached

Answer:

y = - [tex]\frac{1}{6}[/tex] x - 1

Step-by-step explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = 6x - 2 ← is in slope- intercept form

with slope m = 6

given a line with slope m then the slope of a line perpendicular to it is

[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex] , then

y = - [tex]\frac{1}{6}[/tex] x + c ← is the partial equation

to find c substitute (6, - 2 ) into the partial equation

- 2 = - 1 + c ⇒ c = - 2 + 1 = - 1

y = - [tex]\frac{1}{6}[/tex] x - 1 ← equation of perpendicular line

The equation exists 62 - (9 ÷ x)  then, the simplifying the equation, we get 59.

An equation exists as a mathematical statement that is created up of two expressions connected by an equal sign. For example, 3x – 5 = 16 exists an equation.

The equation is described as the state of being equal and exists often illustrated as a math expression with equal values on either side or directs to a problem where many things need to be taken into account.

Given: [tex]$62\:-\:\left(\frac{9}{3}\right)[/tex]

then substitute the value of x = 3

Removing parenthesis -(a) = -a, we get

-(9/3) = -9/3

Divide the numbers, 9/3 = 3

= 62 - 3 = 59

Therefore, the correct answer is option A. 59.

The complete question:

Evaluate 62 - (9 ÷ x) when x = 3

A. 59

B. 12

C. 27

D. 33

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Answer:

20 ft by 14 ft

Step-by-step explanation:

See attached image.

Answer:

t = -35/8

Step-by-step explanation:

Divide both sides by 2/5.

Answer:

24 % (to the nearest percent)

Step-by-step explanation:

the probability that the student is a graduate is equal to :

[tex]=\frac{\text{the total number of graduates} }{\text{the total number of students} }[/tex]

[tex]=\frac{2610}{10730} \\=0.243243243243[/tex]

Converting to percentage:

0.243243243243×100

= 24.3243243243 %

Using a geometric sequence, the number of emails sent on day 7 is given as follows:

A. 93,312.

A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.

The nth term of a geometric sequence is given by:

[tex]a_n = a_1q^{n-1}[/tex]

In which [tex]a_1[/tex] is the first term.

This situation can be modeled by a geometric sequence with first term and common ratio given as follows:

[tex]a_1 = 128, q = 3[/tex]

Hence the number of people that receive the email on day n is:

[tex]a_n = 128(3)^{n-1}[/tex]

On day 7, the amount is:

[tex]a_7 = 128(3)^{7-1} = 93,312[/tex]

Hence option A is correct.

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Answer:

51 liters.

Step-by-step explanation:

By proportion  number of litres for 1428 miles

=  17 * 1428/476

= 17 * 3

= 51 liters.

Answer:

x=4

Step-by-step explanation:

the proportion between 9 and 3 is 1/3

so u just apply the fraction to the corresponding side

so 1/3 of 12 is 4

so x is 4

Answer:

  (a)  see attached

Step-by-step explanation:

A table will represent a function if no input (x) values are repeated.

The offered tables can be evaluated as follows:

  (a) x-values {-4, -1, 1, 4}, no repeats. Is a function.

  (b) x-values {2, 2, 3, 3}, both values repeated

  (c) x-values {-5, -5, 5, 5}, both values repeated

  (d) x-values {2, 2, 7, 7}, both values repeated

Laura's walking speed is 4.50 feet per second.

Speed is the total distance travelled per time. Speed can be determined by dividing the distance walked by Laura by the time.

Average speed = total distance / total time

54 / 12 = 4.50 feet per second

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Answer:

If you divide it out and it comes out a whole number unless the original set of numbers is a fraction

The EXPERIMENTAL REGION is the range of values of the independent variables in the data used to estimate the regression model.

According to the statement

There is a region where the range of values of the independent variables in the data used to estimate the regression model.

AND

Those region is called EXPERIMENTAL REGION

So, Experimental region is called a those region in which the region within which we can make valid predictions and doesn't go outside of the bounds of the data we were provided.

So, The EXPERIMENTAL REGION is the range of values of the independent variables in the data used to estimate the regression model.

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The correct option is D. the number of sweatshirts for which cost and income are equal.

Any equation that contains only one element which squares the variable and none that raises it to a higher power.

The general form form of quadratic equation is-

ax² + bx + c = 0

According to the question;

Use the substitute method to get the quantity of sweatshirts in which cost and earnings are equal.

Step 1: Write the following system of equations as the first step.

[tex]\begin{aligned}&y=35 x \\&y=-0.05(x-400)^{2}+9492\end{aligned}[/tex]

Step 2: Replace the value of "y" in the equation (2).

[tex]35 x=-0.05(x-400)^{2}+9492[/tex]

Step 3: Make the equation above simpler.

[tex]35 x=-0.05 x^{2}-8000+40 x+9492[/tex]

Step 4: Write the preceding equation in generalised quadratic form.

[tex]0.05 x^{2}-5 x-1492=0[/tex]

The processes above lead to the conclusion that option D provides the proper statement.

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The complete question is-

In the first equation in the system of equations, y represents the money collected from selling sweatshirts. In the second equation, y represents the money spent to produce x sweatshirts with team logos on them for a professional sports league. What does the solution of the system represent in this context?

y=35x

y=-0.05(x-400)^2+9,492

A. the number of sweatshirts that generate the maximum income

B. the number of sweatshirts that generate the minimum cost

C. the number of sweatshirts for which the difference between cost and income is greatest.

D. the number of sweatshirts for which cost and income are equal

Answer:

D

Step-by-step explanation:

He said so

Due to length restriction we kindly invite to check the explanation for further details about the analysis of three quadratic equations and inherent rigid transformations.

Herein we find the graph of the parent quadratic equation f(x) = x² and two proposed resulting functions, whose difference with the former one have to be explained in terms of the kind of rigid transformations they have.

By comparing them, we find that both functions g(x) and h(x) are the result of a rigid transformation of the form f'(x) = k · f(x), where the transformation is a simple vertical dilation for k > 1, simple vertical contraction for 0 < k < 1, vertical contraction and reflection around the x-axis for - 1 < k < 0 and vertical dilation and reflection around the x-axis for k < - 1.

Function g(x) is the result of dilating f(x) by a factor of 3 and function h(x) is the result of dilating and reflecting f(x) around the x-axis by a factor of - 3.

The tables for each quadratic function are summarized below:

g(x):

 x             - 2             - 1               0             1                2

g(x)            12               3              0             3               12

f(x):

 x             - 2             - 1               0             1                2

g(x)          - 12            - 3               0           - 3            - 12

Lastly, we prepare the graph with the three functions in the image attached below.

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Generally speaking, Harriot's notation was clearer than Viète's, which made it simple for him to connect Viète's identities.

Harriot made significant contributions to the theory of equations and developed a more straightforward notation for algebra.

The employment of special notation is algebra's most evident characteristic. Variables are the symbols that are used to represent numbers.

A symbolic system known as notation is used to represent mathematical concepts and objects.

The primary components of notation are letters, symbols, figures, and signs. Notation can be made using symbols, characters, numbers, or a combination of these, such as the factorial symbol.

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By utilizing the law of the sines and Heron's formula, we find that the approximate area of the triangle is approximately 73.1 square centimeters. (Correct choice: A)

Prior to using Heron's formula, we must find the lengths of the missing sides by law of the sines:

A = 180° - 95° - 35°

A = 50°

[tex]b = 14\,cm \times \frac{\sin 35^{\circ}}{\sin 50^{\circ}}[/tex]

b ≈ 10.483 cm

[tex]c = 14\,cm \times \frac{\sin 95^{\circ}}{\sin 50^{\circ}}[/tex]

c ≈ 18.206 cm

Now, we proceed to calculate the area of the triangle:

s = 0.5 · (14 cm + 10.483 cm + 18.206 cm)

s = 21.345 cm

[tex]A = \sqrt{(21.345\, cm) \cdot (21.345\, cm - 14\,cm)\cdot (21.345\, cm - 10.483\,cm)\cdot (21.345\,cm - 18.206\,cm)}[/tex]

A ≈ 73.113 cm²

By utilizing the law of the sines and Heron's formula, we find that the approximate area of the triangle is approximately 73.1 square centimeters. (Correct choice: A)

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Combining the equations, the solution to the system of equations is: x = 3, y = 10.

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

In this problem, the equations are:

Combining(adding) them, we have that:

5x - 3y = -15.

From the second equation:

y = 3x + 1.

Replacing in the combined equation:

5x - 3(3x + 1) = -15.

-4x = -12

x = 3.

y = 3x + 1 = 3 x 3 + 1 = 10.

The solution is:

x = 3, y = 10.

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The quadratic function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).

In this question we have a graph of a quadratic equation translated to another place of a Cartesian plane, whose form coincides with the vertex form of the equation of the parabola, whose form is:

g(x) = C · (x - h)² - k     (1)

Where:

By direct comparison we notice that (h, k) = (5, 1) and C = 1. Now we proceed to check if the points (x, y) = (2, 10) and (x, y) = (8, 10) belong to the parabola.

x = 2

g(2) = (2 - 5)² + 1

g(2) = 10

x = 8

g(8) = (8 - 5)² + 1

g(8) = 10

The quadratic function g(x) = (x - 5)² + 1 passes through the points (2, 10) and (8, 10) and has a vertex at (5, 1).

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Answer: B

Step-by-step explanation:

looked at the points from the dude above, or below, anyway i hope this helps

Answer:

Step-by-step explanation:

The first part tells us that y is, or is anywhere below ½x-3

The second part tells us that above 6-2x

Since we don't know what x is, we cannot actually find y.

The best answer to this question is:

6-2x < y < ½x-3

Which reads, in words, as: six minus two-x is below y; and y is below one-half-x minus three.

Hopefully, this is what your teacher or math program is looking for. There is hardly another way to solve it, other than graphing it. The graphed version will be attached, but I highly doubt you'll need it.

Answer: 1800

Step-by-step explanation:

Exterior angles of a polygon add to 360 degrees, so this means the polygon has 12 sides.

We also know that since an interior angle and its corresponding exterior angle are supplementary, each interior angle is 150 degrees.

Therefore, the sum of the measures of the interior angles is (150)(12)=1800 degrees.

the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B

Angle of elevation can be defined as the angle formed between a horizontal line and the line of sight up to an object with the image of the object located above the horizontal line.

It is the height greater than the height of the observer.

The opposite of the angle of elevation is the angle of depression which is formed with an observer

Words associated with the angle of elevation are;

The angle of elevation is the angle between the line of sight and the horizontal line.

Hence, the angle formed by the line of sight and the horizontal line can best be described as an angle of elevation. Option B

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Using translation concepts, the inequality that represents the graph is given as follows:

f(x) > sqrt(1 - x)

A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction either in it’s definition or in it’s domain. Examples are shift left/right or bottom/up, vertical or horizontal stretching or compression, and reflections over the x-axis or the y-axis.

The parent square root function is given by:

y = sqrt(x)

It increases to right starting at x = 0, and in this problem it increases to left starting at x = 1, meaning that it was reflected over the y-axis and shifted right one unit, hence the function is:

sqrt(1 - x)

The part graphed is the values above the function, that is, the values that are greater, as the line is only dashed, hence the inequality is:

f(x) > sqrt(1 - x)

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Answer: x = 0

Step-by-step explanation:

Given equation (swapped position):

x + 3 - 5x = 3

Combine like terms:

(x - 5x) + 3 = 3

-4x + 3 = 3

Subtract 3 on both sides:

-4x + 3 - 3 = 3 - 3

-4x = 0

Divide -4 on both sides:

-4x / -4 = 0 / -4

[tex]\boxed{x=0}[/tex]

Hope this helps!! :)

Please let me know if you have any questions

Answer:

The volume of this rectangular prism is 112mm.

Step-by-step explanation:

[tex]volume \: = \: length \times width \times height \\ v = 6.4mm \times 2.5mm \times 7mm \\ v = 112mm[/tex]

The amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

In the question, we are informed that the triangle KLM, represents a section of a park set aside for picnic tables. We are also informed that the picnic area will take up approximately 400 square yards of the park.

We are asked for the amount of fencing needed to surround the perimeter of the picnic area of the park.

We know the area of a triangle can be found using the trigonometric area formula, Area = (1/2)ab sin C.

Using this in the given triangle KLM, we get:

Area = (1/2)(KL)(KM)(sin K),

or, 400 = (1/2)(KL)(45)(sin 25°),

or, KL = (400*2)/(45*sin 25°) = 800/(45*0.42262) = 800/19.017822 = 42.0658 ≈ 42 yd.

Thus, we get KL = 42 yards.

Now, the perimeter of the picnic area = the perimeter of the triangle KLM = KL + LM + MK = 42 + 20 + 45 yards = 107 yards.

Thus, the amount of fencing needed to surround the perimeter of the picnic area of the park is 107 yards. Hence, the second option is the right choice.

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