A wooden plank is $5$ feet long and $1\frac{1}{2}$ inches thick. To make the plank $1\frac{1}{8}$ inches thick, a carpenter removes 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

Answer:

12

Step-by-step explanation:

What is GCF(greatest common factor)?

The GCF of a, b is the largest positive number that divides both a and b without a remainder

Prime factors of a number are the prime numbers that when multiplied together result in the number

Prime factors of 24
24 = 2 x 12

12 = 3 x 4

4 = 2 x 2

So prime factorization  of 24 are 2 x 3 x 2 x 2 = 2³ x 3

Prime factors of 60:
60 = 2 x 30

30 = 2 x 15

15 = 3 x 5

Prime factorization  of 60: 2 x 2 x 3 x 5 = 2² x 3 x 5

Find the factors that are common to both 24 and 60:

2² and 3

2² x 3 = 4 x 3 = 12

So the GCF is 12

This is the greatest number that can divide 24 and 60 without a remainder

The given statement as an expression is y = 7 + 2x

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

A mathematical statement

The mathematical statement is given as

7 points more than twice the number of points scored by the other team

Represent the points with x and y

So, we have the following representation

7 points more than twice x is  y

is equal to implies =

So, we have:

7 points more than twice x = y

more than implies +, twice implies 2 times

This gives

7 + 2 * x = y

Evaluate

7 + 2x = y

Rewrite as

y = 7 + 2x

The question does not require that we solve the expression

So, we leave it at y = 7 + 2x

Hence, the required expression is y = 7 + 2x

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To solve the expression 4e + d + 12 - 2e for given values of d and e, we need to substitute the given values in place of the variables in the expression and then perform the calculations.

Given that d = 6 and e = 2

So, the expression becomes:

4(2) + 6 + 12 - 2(2)

Now we can perform the calculation:

8 + 6 + 12 - 4 = 10 + 12 = 22

Therefore, the value of the expression 4e + d + 12 - 2e when d = 6 and e = 2 is 22.

Answer:

[tex] \sf \: d + 2e + 12 = 22 [/tex]

Step-by-step explanation:

Now we have to,

→ Simplify the given expression.

The expression is,

→ 4e + d + 12 - 2e

Now we have to use,

→ d = 6

→ e = 2

Let's simplify the expression,

→ 4e + d + 12 - 2e

→ d + 4e - 2e + 12

→ (d) + (4 - 2)e + (12)

→ d + (2)e + 12

→ d + 2e + 12

→ 6 + 2(2) + 12

→ 6 + 4 + 12

→ 10 + 12 = 22

Therefore, the answer is 22.

Answer:



Step-by-step explanation:

Get a common denomenator, add the two fractions together and subtract the sum from 1 whole.

The additive inverse of 6 /- 13 is -6 /+ 13, which means that the two numbers have the same magnitude but opposite signs.

The additive inverse of a number is the number that needs to be added to the original number to get a result of zero. In other words, the additive inverse of a number is the opposite of the number in terms of sign. To find the additive inverse of 6 /- 13, we must multiply the negative sign of -13 by -1 to change it to a positive. This means that the additive inverse of 6 /- 13 is -6 /+ 13. This means that the two numbers have the same magnitude but opposite signs. To verify this, we can add the two numbers together. 6 /- 13 + -6 /+ 13 = 0. Therefore, the additive inverse of 6 /- 13 is -6 /+ 13.

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The minimum value is 0.5 and the maximum value is 3.5.

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The quotient of 3 8 and 2 3 is equal to 4. This can be determined by dividing 3 8 by 2 3 and simplifying the fractions. The result is 4.

To determine the quotient of 3 8 and 2 3, begin by dividing 3 8 by 2 3. This can be done by multiplying the numerator (3) and denominator (8) of 3 8 by the reciprocal of 2 3, which is 3 2. Doing this yields 9 16. Now, reduce the fraction by dividing both the numerator and denominator by the greatest common factor (GCF) of 9 and 16, which is 3. The result is 3 5. Finally, convert the fraction to a whole number by dividing the numerator (3) by the denominator (5). The result is 4. Therefore, the quotient of 3 8 and 2 3 is 4.

3 8 ÷ 2 3 = (3 × 3 2) ÷ (8 × 3 2) = 9 16 ÷ 9 2 = 9 16 ÷ 3 = 3 5 = 3 ÷ 5 = 4

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To obtain a 40% alcohol solution from a 22% solution, you need to add 18% more alcohol.

100 ml of 22% alcohol solution contains 22 ml of pure alcohol and 78 ml of other ingredients.

Therefore, to obtain a 40% solution, you need 40 ml of pure alcohol in every 100 ml of solution.

So, 18 ml of pure alcohol should be added to 100 ml of 22% solution to obtain 40% solution.

Another way to calculate this is:

You can calculate the amount of pure alcohol you need to add by multiplying the initial volume of the solution (100ml) by the percentage increase in alcohol content (18%) .

100ml * 18% = 18ml

So you would need to add 18ml of pure alcohol to 100ml of 22% alcohol solution to obtain a 40% alcohol solution.

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A conversion of this equation in point-slope form into standard form is y = x/2 + 1.

In Mathematics, the slope-intercept form of a line can be calculated by using this linear equation:

y = mx + c

Where:

Based on the information provided about the line, it is represented by this equation;

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

Making y the subject of formula in the above equation, we have the following:

y = x/2 - 2 + 3

y = x/2 + 1

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There are two points: one at x1, y1 and the other at x2, y2. A point with an x value of x one plus x .

The number of rotations that a geometry can fit into is determined by its order of rotational symmetry. The degree of rotational symmetry is expressed as 360°A°, where A° is the lowest angle by which a figure may be rotated from its rotated shape to its original shape. 360 degrees The number of rotations a perfect circle can undergo while still preserving its shape is a measure of a shape's degree of rotational symmetry. A full 360° revolution won't look the same until a triangle is placed back in its initial starting position.

given

There are two points: one at x1, y1 and the other at x2, y2. A point with an x value of x one plus x .

two all divided by two lies directly between the two points. Its y coordinate is equal to y1 plus y2 divided by 2.

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The standard form of polynomial 2x³ + 8x² -23x +6.

A polynomial is a mathematical equation that solely uses the operations addition, subtraction, multiplication, and non-negative integer exponentiation of variables. Variables are sometimes known as indeterminates in mathematics.

An expression that consists of exponents, constants, and variables that are concatenated using mathematical operations is referred to as a polynomial.

Given:

(x+6)(2x²-4x+1)

Multiplying the polynomial

= 2x³  -4x² + x + 12x² - 24x + 6

= 2x³ -4x² + 12x² + x -24x + 6

= 2x³ + 8x² -23x +6

Hence, the required polynomial is  2x³ + 8x² -23x +6.

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Answer:

33 containers.

Step-by-step explanation:

Dividing 296 by 9 gives you 32.89, rounding up to the next whole number gives you 33 containers.

Answer:

What is this on

Step-by-step explanation:

answer:B. 90 good luck I hope you pass

The answer is B which is 90

12b+12p can be written as (9b + 9p) + (3b + 3p) to show the fruit for Nathan's kebabs and Linda's kebabs separately.

Expressions in math are mathematical statements that have a minimum of two terms containing numbers or variables, or both, connected by an operator in between. The mathematical operators can be of addition, subtraction, multiplication, or division.

Given,

Each kebab needs the same number of blueberries, b, and the same number of pineapple pieces, p.

Total number of kebabs = 12

Fruits needed to make them = 12b + 12p

Fruits needed to make 3 kebabs by Linda = 3b+3p

If Linda makes 3 kebabs

then Nathan would make 12 -3 = 9 kebabs

Fruits needed make 9 kebabs by Nathan = 9b + 9p

thus, to show the fruit for Nathan's kebabs and Linda's kebabs separately, 12b + 12p can be written as

12b + 12p

= 9b + 3b + 9p + 3p

Grouping,

= (9b + 9p) + (3b + 3p)

Hence, (9b + 9p) + (3b + 3p) is the rewritten form of 12b+12p so that it shows the fruit for Nathan's kebabs and Linda's kebabs separately.

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[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

The angle measures of the triangle are :

And since it has an angle measuring 90° (right angle), so conclusion can be made that the given triangle is a right angled triangle.

Hence, correct choice is ;

[tex]\qquad \sf  \dashrightarrow \: \bf right[/tex]

The domain of this function is all real numbers from -54 to 60.

Real numbers are any number that can be expressed on the number line. They include natural numbers, whole numbers, integers, rational numbers and irrational numbers. Real numbers can be expressed as decimals, fractions, or in scientific notation. Real numbers can also be positive, negative, or zero. They are used in mathematics to represent a wide variety of physical quantities, such as distances, velocities, and forces.

Real numbers are numbers that represent an exact quantity, such as whole numbers and fractions. To find real numbers, you can use the standard number line or the decimal point system. The number line is a graphical representation of all real numbers, and it starts with the positive numbers on the right and the negative numbers on the left. The decimal point system assigns place values to each digit in a number, and the real numbers are the numbers that have non-repeating digits.

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So the possible values of (z+1/z) are 6 and 0 for z=5 and z=-1 respectively.

An algebraic expression in mathematics is an expression created using variables, constant algebraic numbers, and algebraic operations. A good example of an algebraic expression is 3x2 2xy + c.

A constant has a fixed value and does not vary over time. For instance, the size of a shoe, a piece of clothing, or any other article of clothing will never alter. x+y = 8 is an algebraic equation, and 8 is a constant that cannot be altered. Variables are concepts that change or fluctuate throughout time.

We can start by multiplying both sides of the equation by (z+1/z) to get:

(z-1/z)(z+1/z) = 6(z+1/z)

This simplifies to:

z^2 - 1 = 6z + 6

We can then solve for z by isolating it on one side of the equation.

z^2 - 6z - 5 = 0

(z-5)(z+1) = 0

So the solutions to this equation are z = 5 and z = -1

Now we can substitute the value of z back into the original expression to find the value of (z+1/z)

For z = 5, (z+1/z) = (5+1/5) = 6

For z = -1, (z+1/z) = (-1+1/(-1)) = 0

So the possible values of (z+1/z) are 6 and 0.

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Answer:

-152

Step-by-step explanation:

Given that h(t) = 161-4t and g(t) = 3-2t,

g(-1) = 3-2(-1) = 3+2 = 5

h(1) = 161-4(1) = 161-4 = 157

Therefore, g(-1)-h(1) = 5 - 157 = -152

So the value of g(-1)-h(1) is -152

Answer:

The answer is

30 degrees is acute angle

60 degrees is also acute angle

90 degrees is right angle

Step-by-step explanation:

anything below 90 degrees is acute angle

90 degrees creates a perfect square which is a right angle

Answer:

108

Step-by-step explanation:

x=2

12x+84

12(2)+84

24+84=108

The second derivative test for a multivariable function is generally in a positive definite quadratic form.

In mathematics, the second partial derivative test is a method in multivariable calculus which used to determine if a critical point of a function is a local minimum, maximum or saddle point.

A partial derivative of a multivariable function is a derivative with regard to one variable with other variables adhered constant. It is used to describe the concepts of gradient, divergence, and curl in terms of partial derivatives.

The second derivative of a function is directly the derivative of the function's derivative. Let's consider, as an example, the function f(x) = x^3 + 2x^2.

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The coordinate A , B and C will be A(2,2), B(2,6) and C(10,2)

A coordinate system is a method for determining how to position points or other geometrical objects on a manifold, such as Euclidean space, uniquely using one or more integers, or coordinates.

In order to make it simple to identify the points, a cartesian plane divides the plane space into two dimensions. The coordinate plane is another name for it. The horizontal x-axis and the vertical y-axis are the two axes of the coordinate plane. The origin is the place where these coordinate axes connect, and they split the plane into four quadrants (0, 0). Additionally, each point in the coordinate plane is denoted by the coordinates (x, y), where x represents the point's location in relation to the x-axis and y represents its position in relation to the y-axis.

Since it is factored by 2

The coordinate A , B and C will be

A (1*2, 1*2) = A(2,2)

B(2,6) and C(10,2)

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Answer:

the radius is 8.5

Step-by-step explanation:

54 divided by pie/3.14 = 17 (plus decimals)

17 Divide by 2 = 8.5

Answer:

t=2

Step-by-step explanation:

t>o and t² - 4 = 0

[tex]t^2=4[/tex]

[tex]t=\sqrt{4}[/tex]

[tex]t=+2/-2[/tex]

As t>0

Therefore, t=+2

Thus, if t>o and t² - 4 = 0, the value of t=+2

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As per the given discount rate, the discount amount is $500 and the sale price is $2000

The term discount in math is defined as the process of equals the difference between the price paid for and it's par value.

Here we have given a department store has its mid year sale.

And here we have given that a knapsack originally priced at 2500 has a discount rate of 20%

Here let us consider that x be the discount, and then it can be calculated as,

=> discount amount = original price x 20%

Here we have to apply the values on the equation, then we get,

=> discount amount = 2500 x 20/100

=> discount amount = 500

Therefore, the sales price is calculated as,

=> Sales price = original price - discount price

=> sales price = 2500 - 500

=> sales price = 2000

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The total volume of the tank is 400π + 78.72 cubic metres. To the nearest cubic meter, it is approximately 400π + 79 cubic metres.

What is the volume of a cylinder?

The volume of a cylinder is the amount of space inside the cylinder. It can be calculated by multiplying the area of the base by the height of the cylinder. The formula for the volume of a cylinder is V = πr²h, where r is the radius of the base of the cylinder and h is the height.

The tank is shown as a cylinder with a rectangular prism on top. To find the volume of water the tank can hold, we will need to find the volume of the cylinder and the rectangular prism separately, and then add them together.

The cylinder has a radius of 5 metres and a height of 8 metres. The volume of a cylinder is given by the formula V = πr²h, where r is the radius and h is the height. So the volume of the cylinder is V = π(5²)(8) = 400π cubic metres.

The rectangular prism has a length of 4.2 metres, a width of 2.2 metres and a height of 8 metres. The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width and h is the height. So the volume of the rectangular prism is V = (4.2)(2.2)(8) = 78.72 cubic metres.

So the total volume of the tank is 400π + 78.72 cubic metres. To the nearest cubic meter, it is approximately 400π + 79 cubic metres.

Please note that since π is an irrational number, the value of 400π is not an exact value, but an approximation.

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MN, RS, and NP in this triangle are, respectively, 410, 400, and 320 when MN = 5x + 10.

Given that it has three sides and three vertices, a triangle is a polygon. It is one of the fundamental geometrical forms. Triangle ABC is the term used to describe a triangle containing the vertices A, B, and C.A triangle is a polygon because it has three sides and three corners. The points at which the three sides of the triangle converge are referred to as its corners. Three triangle angles can be multiplied to get 180 degrees.

given

as AMNP-ARST

the x = 80

so MN = 5 * 80 + 10

= 410

RS = 6* 80 - 8

= 400

MN, RS, and NP in this triangle are, respectively, 410, 400, and 320 when MN = 5x + 10.

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In mathematics, there are several types of inequalities that are commonly studied, including linear inequalities, quadratic inequalities, absolute value inequalities, rational inequalities, logarithmic inequalities and trigonometric inequalities.

Linear inequalities: These are inequalities involving a linear function and a single variable. They can be represented in the form of "ax + b > c" or "ax + b < c" where a, b, and c are constants, and x is the variable.

Quadratic inequalities: These are inequalities involving a quadratic function and a single variable. They can be represented in the form of "ax^2 + bx + c > 0" or "ax^2 + bx + c < 0" where a, b, and c are constants, and x is the variable.

Absolute value inequalities: These are inequalities involving the absolute value of a variable or expression. They can be represented in the form of "|x| > a" or "|x| < a" where x is the variable and a is a constant.

Rational inequalities: These are inequalities involving a rational function (a function with a fraction) and a single variable. They can be represented in the form of "f(x) = (ax+b)/(cx+d) > 0" or "f(x) = (ax+b)/(cx+d) < 0" where a, b, c, d are constants, and x is the variable.

Logarithmic inequalities: These are inequalities involving logarithmic functions and a single variable. They can be represented in the form of "loga(x) > b" or "loga(x) < b" where a and b are constants, and x is the variable.

Trigonometric inequalities: These inequalities involve trigonometric functions such as sine, cosine, and tangent. These inequalities can be used to describe the range of possible values for an angle or a real-valued function.

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