A carpenter needs to build a box to hold his wood screws. He has a sheet of wood that measures 18 inches by 12 inches. He then cuts equal squares from each corner. (a) Write an expression for the length, width, and height for the open box. (b) Write a function for the volume (use factored form).

The value of x in the given triangle is x = 12  .

Angle Sum Property of the Triangle states that the sum of measure of all three sides of the triangle is 180° .

In the question ,

a triangular figure is given

in which , the measure of angle A is (6x - 19)°

the measure of angle B is [tex]=[/tex] 84°

the measure of angle C is [tex]=[/tex] (3x + 7)°

So , By Angle sum property ,

we get

∠A + ∠B + ∠C [tex]=[/tex] 180°

substituting the values of angle A, B and C ,

we get

(6x - 19)° [tex]+[/tex] 84° + (3x + 7)° [tex]=[/tex] 180°

6x - 19 [tex]+[/tex] 84 [tex]+[/tex] 3x + 7 [tex]=[/tex] 180

9x + 72 = 180

9x = 180 - 72

9x = 108

x = 108/9

x = 12

Therefore , the value of x is [tex]=[/tex] 12

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Answer:

(2x)-8 is the correct answer

Step-by-step explanation:

Hope this helps

Answer:

1

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Answer:

1.) 150/512 in.  

2.) 64/125 in.

Step-by-step explanation:

1.) V = l x w x h                That's the formula to find the volume of a rectangle

V = 6/8 x 5/8 x 5/8 in.    Plug in the numbers

V = 150/512 in.                Multiply

V = 75/256 in.                 Simplify

Since you're asked to not reduce don't write this answer. I only put it to show that it can be simplified.

2.) V = l^3                       This is the formula to find the volume of a cube

V = (4/5)^3 in.                 Plug in the numbers

V = 64/125 in.                 Miltuply

Answer:

If two parallel lines are cut by a transversal, then the corresponding angles are congruent.

Answer:

y = x - 3

Step-by-step explanation:

Consider the equation "y = mx + b" :

y = mx + b

Since the slope is 1, you could input that into the equation:

y = (1)x + b

The variable "b" represents the y-intercept, therefore, to find the y - intercept, you would have to subtract 7 from each side of the coordinate points to get 0 as the x - coordinate to find the y - intercept:

(7    4)

-7 || -7

(0, -3)

Therefore, the y - intercept would be -3 and the equation would be:

y = x - 3

Answer:

b = 8 ft

Step-by-step explanation:

Formula we use,

→ (AC)² = (BC)² + (AB)²

Now the value of a will be,

→ (10)² = b² + (6)²

→ 100 = b² + 36

→ b² = 100 - 36

→ b = √64

→ [ b = 8 ft ]

Hence, value of b is 8 ft.

The equation in standard form is x - y = 9

From the question, we have the following parameters that can be used in our computation:

Points = (8, –1) and (2, –5)

Point-slope form is y + 1 = (x – 8).

Recall that the point-slope form is y + 1 = (x – 8).

So, we have

y + 1 = (x – 8)

Open the brackets

y + 1 = x – 8

Subtract 1 from both sides

y = x - 9

Rewrite as

-x + y = -9

Multiply through by -1

x - y = 9

Hence, the equation is x - y = 9

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Answer:

$24,067.32

Step-by-step explanation:

If you look up a compound interest calculator and put in the data correctly you should get $24,067.32

The coordinates of the centroid of a triangle with vertices X(−4, 0) , Y(−1, 4) , and Z(2, 2) is; (x, y) = (-1, 2)

Centroid of a Triangle states that  the center of the triangle can be calculated as the point of intersection of all the three medians of that same triangle, and that this median is a line drawn right from the midpoint of one side to the opposite vertex.

We are given the coordinate of the vertices of the triangle as;

X(−4, 0) , Y(−1, 4) , and Z(2, 2)

Now, the formula to find the coordinates of the centroid of the triangle is; (x, y) = (x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3

Thus, the coordinates of the Centroid is;

(x, y) = (-4 + (-1) + (2))/3, (0 + 4 + 2)/3

(x, y) = (-1, 2)

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Answer: 3

I used PEMDAS in this explanation: Parenthesis, Exponents, Multiplication, Division, Addition, Subtraction. Also known as the order of operations

Step-by-step explanation:

-5 + (5+3) :

First, add 5+3 =8

-5+8

When adding a negative to a positive, first, switch the -5 and 8 around like so.

8 + (-5)

then turn the -5 into it's opposite and subtract ---> 5

8-5=3

Unworded explanation:

-5 + (5+3) :

-5 + 8

8 + (-5)

8-5 = 3

Answer: By compare the graph of -6 ≤ x ≤-4 with the graph of x ≤-6 or x ≥-4 we can see that in first graph value is x belongs to [-6,-4] and in second graph we can see that x belongs to (-∞,-6] ∪ [-4,∞)

What does a coordinate mean in math?

a pair of values used to specify a point's position on a coordinate plane using the horizontal and vertical breakups from the two reference axes. typically represented by the pair of x-values and y-values (x,y).

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The value of x is 15

If two angles sum to 90 degrees, they are said to be complimentary angles. In other terms, a right angle is created when two complementary angles are combined (90 degrees). If the sum of angles 1 and 2 equals 90 degrees (i.e., angle 1 plus angle 2 = 90°), then the angles are complementary and are referred to as one another's complements.

∠1 and ∠2 are complementary angles i.e the sum of ∠1 and ∠2 is 90° .

Thus

∠1 + ∠2 = 90°

x° + (3x+30)° = 90°

x + 3x + 30 = 90

4x = 90-30

4x = 60

x = 15

Therefore the value of x is 15.

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The mean of the distribution of sample means is 100.

Considering the values provided in the question,

Population mean = 100

We know that,

The sample mean is a reliable indicator of the population mean.

That is, E( sample mean)=Mean(sample mean)= population mean

Here population mean is 100, therefore mean of distribution of sample means is also 100.

The total of all the values in a sample is known as the Sample Mean. It is a statistical metric used to examine different variables throughout time. It is calculated by statisticians and researchers by dividing the total sum of all data fragment values by the total number of data sets.

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Answer: 63 inches

Step-by-step explanation:

Answer:

63 inches

Hope this helps :)

This comes to $141, indicating that Ms. Patel spent that money on four sets of pliers, two wrench sets, and a chisel set.

The given condition states that;

Make a ratio first.

This ratio might be expressed as 4:2:1 (in pliers, wrenches, and chisels).

Then, multiply every one of these sums by their respective prices before adding them all up.

Pliers : 4 times 17.50 equals $70

Wrenches : $2 x $21.5 = $43

Chisels : 1 x 28 equals $28

Thus,

Sum = $70 + $43 + $28

Sum = $141

This amounts to $141, proving that she purchased a chisel set, two wrench sets, and four pairs of pliers.

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Answer:

Maximum height of 32 feet after 1.25s

Step-by-step explanation:

Solving the  system of equations using the algebraic method gives x = 1 or x = -4

Given: y = x²+x-1 and y+2x=3

In order to solve the system of equations algebraically

First, rewrite y+2x=3 to make y the subject:

y = 3-2x

Then, equate the two y of the equations and solve for x:

x²+x-1 = 3-2x

x²+x-1-3+2x = 0

x²+3x-4 = 0      (factorize)

x²+4x-1x-4 = 0

(x-1)(x+4) = 0

x-1 = 0 or x+4 = 0

x = 1 or x = -4

Therefore, the solution of the system of equations is x = 1 or x = -4

I pick the algebraic method because it is easier, faster and more accurate

I can check my answer by substituting the values of x into the equation  

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Answer:

(-4, 11) and (1, 1)

Step-by-step explanation:

Given system of equations:

[tex]\begin{cases}y=x^2+x-1\\y+2x=3\end{cases}[/tex]

The solutions to the given system of equations are the points of intersection of the two graphs.

To solve the given system of equations algebraically, first rearrange the second equation to make y the subject:

[tex]\implies y=3-2x[/tex]

Substitute the found expression for y into the first equation:

[tex]3-2x=x^2+x-1[/tex]

Rearrange to a quadratic equation and factor:

[tex]x^2+3x-4=0[/tex]

[tex]x^2+4x-x-4=0[/tex]

[tex]x(x+4)-1(x+4)=0[/tex]

[tex](x+4)(x-1)=0[/tex]

Apply the zero-product property to solve for x:

[tex](x+4)=0\implies x=-4[/tex]

[tex](x-1)=0\implies x=1[/tex]

To find the y-values of the solutions, substitute the found x-values into the rearranged second equation:

[tex]x=-4 \implies y=3-2(-4)=11[/tex]

[tex]x=1\implies y=3-2(1)=1[/tex]

Therefore, the solutions to the given system of equations are:

From a set of whole numbers less than 25, the probability of getting a number either divisible by 5 or divisible by 3 is 11/25

The set of whole numbers = {0, 1,2,3,4,5.....}

The set of whole numbers less than 25 = {0,1,2,3,4,......,24}

The numbers divisible by 5 = {5, 10, 15, 20}

The numbers divisible by 3 = {3, 6, 9, 12, 15, 18, 21, 24}

The common term is 15

The probability = Number of favorable outcomes /  Total number of outcomes

The number of favorable outcome = 11

Total number of outcomes = 25

Substitute the values in the equation

The probability = 11/25

Hence, from a set of whole numbers less than 25, the probability of getting a number either divisible by 5 or divisible by 3 is 11/25

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By graphing, the solution of the system of equations is: (6, -2).

To solve the system of equations by graphing, plot each of the line of the equations, then find the coordinates of the point where both lines intersect. Where they intersect is the solution to the systems of equations.

Given the following equations:

x + 2y = 2

y = -x + 4

x + 2y = 2 can be rewritten as y = -1/2x + 1. The graph for x + 2y = 2 will intercept the y-axis at 1 and also has a slope of -1/2. (It is the red line in the image below).

The graph of y = -x + 4 will also have a slope of -1 and intercept the y-axis at 4. (It is the blue line in the image below).

The graph of the equations are shown below, and they intersect at (6, -2), which is the solution to the system of equations.

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Answer:

60°

Step-by-step explanation:

As we can conclude from the equal measured side lengths, this is an equilateral triangle so all angles have equal measurement.

Since the sum of interior angles in a triangle is equal to 180 to find the measure of angle V we need to divide 180 by 3:

180 ÷ 3 = 60

The P value of the question in the given condition is less than 0.05 hence it reject the null hypothesis.

According to the null hypothesis, an independent variable and a dependent variable have no association with one another. The results might be the result of an experimental or sampling error if the hypothesis indicates a link between the two factors. There is a relationship in the measured phenomena, but, if the null hypothesis is incorrect.

First we find the value of small z

z = (x - μ) / (α / [tex]\sqrt{100}[/tex])

z = (7275 - 7100) / (1500/[tex]\sqrt{100}[/tex])

z = (175) / 150

z = 1.1667

As we have verified the test statistic value and it matched.

Then,

P value approach

Hence P value must be equal to 0.0013

As p value is less than 0.05 , Reject the null hypothesis.

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The number of kilometers in 5 square gigameters is  5. 0 × 10^18

Proportion can be described as an expression or equation in which two ratios are made equal to each other.

It is also known as the mathematical comparison between two numbers or elements.

From the information given, we have;

1 gigameter = 1.0×10^6 kilometers

But,

5 square gigameters = 5. 1.0×10^6 . 1.0×10^6

Add the powers

5 square gigameters = 5..0×10^12

If 1 gigameter = 1.0×10^6 kilometers

Then 5. 1.0×10^12 gigameter = x

cross multiply

x = 5.0×10^12 ×  1.0×10^6

x = 5. 0 × 10^18 kilometers

Hence, the value is 5. 0 × 10^18 kilometers

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Based on the image attached, the relationship are:

a). AB and BC - Both the segments are said to be perpendicular and they are intersecting at the point B.

b). AE and BF - Both segments are said to be parallel

c). EF and ED - Both are skew

d). Plane ABC and plane ABF - Both of the planes do  intersect at point AB

e). Plane AED and plane BFC - Both of the given planes are known to be parallel

if the ratio equality is accurate, parallel. If the lines are not parallel or if you can solve them as a system of simultaneous equations, the lines will intersect. If two crossing lines have a zero dot product, they are perpendicular.

If the lines are not parallel or intersecting, they are said to skew. Lines that are parallel never cross.

Therefore,

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Answer:

Step-by-step explanation:

A=P(1+r/n)^nt

Let the Beth deposite is x.Here r and n will be 1.

A=x(1+1/1)^5

Similarly
B=2x(1+1/n)^nt

B=2x(1+1/1)^5

There combined interest is:
A+B=x(1+1/1)^5+2x(1+1/1)^5

21=32x+64x

21=96x

x=21/96 is the beth deposite.

2x=2*21/96 is the Reena deposite

If the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12

The given matrix is

C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]

The matrix is defined as the set of numbers that arranged in rows and columns to form a rectangular array. The numbers in the matrix are called the elements of the matrix.

Here we have to find the determinant of the matrix C

The determinant of the matrix is defined as the scalar value calculated for a given square matrix.

The determinant of C is represented by |C|

Then,

C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex]

|C| = -6×4 - 6×-2

= -24 -(-12)

= -24 + 12

= -12

Hence, if the matrix C = [tex]\left[\begin{array}{cc}-6&6\\-2&4\end{array}\right][/tex], then the determinant of the matrix |C| = -12

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With the help of some mathematical operations, we can conclude that after 42 months, coach will have a total amount of $8,356 in his bank account.

So, we know that coach gets 2.3% simple interest monthly.

Now, calculate the total amount after 42 months as follows:

Then, on monthly basis, the coach gets $97.75 as interest.

Then, for 42 months:

Hence, the total amount after 42 months:

Therefore, with the help of some mathematical operations, we can conclude that after 42 months, coach will have a total amount of $8,356 in his bank account.

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Correct question:

Coach deposits $4250 in the bank and gets 2.3% simple interest monthly. He keeps the money in the bank for 42 months without any deposits or withdrawals. How much money will he have in the bank after 42 months? Round to the nearest cent.

A total of 549 of people at the convention are bored by the cable news

From the question, we have the following parameters that can be used in our computation:

Not bored = 122

Bored = 9/11 of the people

This means that

Not bored = 1 - Bored

So, we have

Not bored = 1 - 9/11

Evaluate

Not bored = 2/11

Recall that Not bored = 122

So, we have

2/11 * x = 122

Where x = the number of people

This gives

x = 122 * 11/2

Evaluate

x = 671

Recall that

Bored = 9/11 of the people

So, we have

Bored = 9/11 * 671

Evaluate

Bored = 549

Hence, the number of people at the convention that are bored is 549

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The total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.

Given, Joh rent a kayak at a nearby state park.

He pay a fee of 12.99 plus 3. 75 for each hour that he spend in the water.

We have to find the amount he spend when he was in the water for 4(1/2) hours.

Total amount = 12.99 + hourly amount

Hourly amount = 3.75×4(1/2)

Hourly amount = 3.75×9/2

Hourly amount = 16.875

Total amount = 12.99 + 16.875

Total amount = 29.865

Hence, the total amount Joh spend when he was in the river for 4(1/2) hours is 29.865.

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