Mason has 2/3 of a foot of ribbon. He needs to divide the ribbon into 1/6 -foot pieces.
How many pieces can he cut from the ribbon?

Answer:

  z = √30

Step-by-step explanation:

Given similar right triangles with hypotenuse segments marked 3 and 7, you want to know the length of short leg z adjacent to the segment marked 3.

The fact that all of these triangles are similar gives rise to some "geometric mean" relationships:

  hypotenuse/short side = 10/z = z/3

  30 = z² . . . . . . . multiply by 3z

  z = √30 . . . . . . take the square root

__

Additional comment

The other two geometric mean relations are ...

  x = √(7·10) . . . . . hypotenuse/long side: 10/x=x/7

  y = √(7·3) . . . . . . short side/long side: y/7=3/y

The triangles are similar by AA: each has a right angle, and an angle in common with the largest triangle. Triangles similar to the same triangle are similar to each other.

Both Candice and Joel used a proof by contradiction.

Candice began her proof by assuming the statement was false (by supposition) and then used the vertical angles theorem, definition of congruence, and additional property of equality to arrive at a contradiction.

By demonstating that assuming a proposition to be false results in a contradiction, proof by contradiction establishes the truth or validity of a proposition in logic.

Joel began his proof by assuming the statement was true and used the angle addition postulate, vertical angles theorem, definition of congruence, and subtraction property of equality to arrive at a conclusion that the statement was true.

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a) The block-spring system has an elastic potential energy equal to 2.517 joule.

b) The block has speed of approximately 1.513 meters per second.

In this problem we must analyze the energy and kinematics of spring-block system with no irreversibilites (no friction). Part A - Elastic potential energy is determined when spring is entirely deformed:

U = (1 / 2) · k · x²

Where:

If we know that k = 895 N / m and x = 0.0750 m, then the elastic potential energy of the block-spring system is;

U = (1 / 2) · (895 N / m) · (0.0750 m)²

U = 2.517 J

The elastic potential energy of block-spring system is 2.517 joule.

Part B - And the speed can be determined by principle of energy conservation and work-energy theorem:

K = U

Where K is translational kinetic energy, in joules.

(1 / 2) · m · v² = U

v² = 2 · U / m

v = √(2 · U / m)

If we know that U = 2.517 J and m = 2.20 kg, then the speed of the block is:

v = √[2 · (2.517 J) / (2.20 kg)]

v ≈ 1.513 m / s

The speed of the block after leaving the spring is approximately 1.513 meters per second.

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The predicted value of y when I = 5 is equal to D) 30.

To determine the predicted value of y when I = 5, we can use the equation of the simple linear regression model:

y = b0 + b1x

where b0 and b1 are the regression coefficients and x is the predictor variable.

We can find b1 using the formula:

b1 = r(Sy/Sx)

where r is the sample correlation coefficient, Sy is the standard deviation of the y variable, and Sx is the standard deviation of the x variable.

Plugging in the given values:

b1 = -0.98(8/2) = -4

We can find b0 using the formula:

b0 = ybar - b1*xbar

where ybar and xbar are the mean of the y variable and the x variable respectively.

Plugging in the given values:

b0 = 10 - (-4)*10 = 50

Therefore, the equation of the simple linear regression model is:

y = 50 - 4x

So when I = 5, the predicted value of y is:

y = 50 - 4(5) = 50 - 20 = 30

The closest answer choice is D. 30.

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Answer:

One Half

Step-by-step explanation:

1/3 = 2/6

2/6 + 1/6 = 3/6 = 1/2

The value of dividing 316 by 4 will be 79.

An expression is simply used to show the relationship between the variables that are provided or the data given regarding an information.

In this case, it is vital to note that they have at least two terms which have to be related by through an operator. Some of the mathematical operations that are illustrated in this case include addition, subtraction, etc.

It should be noted that dividing 316 by 4 will be:

= 316 / 4

= 79

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Complete question

Divide 316 by 4

The required set of positive two-digit even numbers less than 36 that do not contain the digit 2 is 11,13,14,15,16,17,18,19,30,31,33,34,35.

An integer is a whole number (not a fractional number) that can be positive, negative, or zero. Zero is not a fraction or decimal of any number. It is neither positive nor negative.

Given:

Set D is the set of positive two-digit even numbers less than 36 that do not contain the digit 2.

According to the given question, we have

2-digit numbers are numbers that have two digits and they start with the number 10 and end with the number 99.

Starting at 11 and going up the two-digit numbers even numbers less than 36 that do not contain the digit 2.

11,13,14,15,16,17,18,19,30,31,33,34,35.

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There is a possible translation of the form g(x) = f(x) + k for which the graph y=g(x) will have no x-intercepts.

A translation is a movement to a graph or figure in which only the position of the figure changes, either left, right, up or down, keeping the inclination, orientation and congruence.

The translations are represented as follows:

Hence, for the function to have no x-intercepts, the function must be shifted up as though the minimum value of the function is greater than zero.

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When you divide two numbers the answer is called the quotient.

Divide the dividend by the divisor to find the quotient of a division problem.

This may be accomplished by using repeated subtraction or lengthy division.

The quotient of two numbers, two fractions, or two algebraic expressions can be found.

According to the remainder theorem, when a polynomial p(x) is divided by (x – a), the remainder Equals f. (a). This is demonstrated by Euclid’s Division Lemma. Using this, p(x) = q(x) (x – a) + r if q(x) is the quotient and r is the remainder.

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Herb spent 55 hours at the library.

Fractions defines a part of a whole and are represented as a numerical value. A fraction can be a portion or section of any quantity out of a whole, where the whole can be any number, a specific value, or a thing.

Total time spent in the Library = 1/6 + 1/4 + 1/2

Total time spent = 11/12 x 60 mins

Total time spent = 55 hours

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(a) The maximum value of g(x) = -8[tex]x^2[/tex] + 5x - 2 is 5/16.

(b) The maximum value of h(x) = -(1/3)[tex]x^2[/tex] + 3x is 9/2.

(c) The maximum value of k(x) = 8[tex]x^2[/tex] - 5x - 7 is 5/16.

(d) The maximum value of j(x) = -(71/99)[tex]x^2[/tex] + 210 is 0.

(e) The maximum value of f(x) = 4[tex]x^2[/tex] - 3x + 7 is 3/8.

(f) The maximum value of F(x) = -[tex]x^4[/tex] + [tex]x^3[/tex] + 9 is 0/0. We cannot say anything about that function.

The general form of a quadratic function;

f(x) = a[tex]x^2[/tex] + bx + c and a < 0,

Then the function f has a maximum value when x = -b/2a

(a) The function is g(x) = -8[tex]x^2[/tex] + 5x - 2

We can find the maximum value at x = -b/2a.

On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = -8 and b = 5

Now putting the value at x = -b/2a

x = -5/2(-8)

x = (-5)/(-16)

x = 5/16

(b) The function is h (x) = -(1/3)[tex]x^2[/tex] + 3x

We can find the maximum value at x = -b/2a.

On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = -(1/3) and b = 3

Now putting the value at x = -b/2a

x = (-3)/2(-1/3)

x = (3×3)/2

x = 9/2

(c) The function is k(x) = 8[tex]x^2[/tex] - 5x - 7

We can find the maximum value at x = -b/2a.

On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = 8 and b = -5

Now putting the value at x = -b/2a

x = -(-5)/(2×8)

x = 5/16

(d) The function is j(x) = -(71/99)[tex]x^2[/tex] + 210

We can find the maximum value at x = -b/2a.

On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = -(71/99) and b = 0

Now putting the value at x = -b/2a

x = 0/2(-(71/99))

x = 0

(e) The function is f(x) = 4[tex]x^2[/tex] - 3x + 7

We can find the maximum value at x = -b/2a.

On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = 4 and b = -3

Now putting the value at x = -b/2a

x = -(-3)/(2×4)

x = 3/8

(f) The function is F(x) = -[tex]x^4[/tex] + [tex]x^3[/tex] + 9

We can find the maximum value at x = -b/2a.

On comparing with f(x) = a[tex]x^2[/tex] + bx + c, we get a = 0 and b = 0

Now putting the value at x = -b/2a

x = 0/0

We cannot say anything about that function.

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The complete question is given below:

It is proven that the other nth roots of z can be found by multiplying the initial one by the nth roots of unity.

A complex number satisfying the equation [tex]z^{n-1} = 0[/tex] is known as the nth root of unity. There are about n nth roots of a unit, according to the fundamental theorem of algebra. We know that,[tex]1=e^{2\pi i}[/tex]. Then, the nth root is written as [tex]\omega=e^{2\pi i/n}[/tex].

The integer of powers of this root between 0 and n-1 provides the other nth roots. Then, the roots are [tex]1, \omega, \omega^2 ,\cdots \cdots, \omega^{(n-1)}[/tex]. Now, factorize the equation [tex]z^{(n-1)} = 0[/tex] we get the required identity as, [tex]z^{(n-1)} = (z- 1)(z^{(n-1)}+ z^{(n-2)} + \cdots \cdots+ z + 1) = 0[/tex].  

This indicates that the equation [tex]1+\omega+ \omega^2+\cdots \cdots+ \omega^{(n-1)}[/tex] is true for all nth roots of unity other than 1.

Roots of unity also have the great quality of being periodic, which results from the fact that n = 1. It is equal to a power of that power mod n if the power is bigger than n.

When ω is a third root of unity, [tex]\omega^5 + \omega^4 + 1 = \omega^2 + \omega + 1 = 0[/tex].

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The equation in slope-intercept form that models the total cost of attendance is y = 4487x + 750.

We know lines have various types of equations, the general type is

Ax + By + c = 0, and the equation of a line in slope-intercept form is

y = mx + b.

Where slope = m and b = y-intercept.

the slope is the rate of change of the y-axis with respect to the x-axis and the y-intercept is the (0,b) where the line intersects

the y-axis at x = 0.

To find the equation in the slope-intercept form,

We'll sum all the annual fees and subtract the scholarship amount and 'x' will represent the number of years while the one-time fee will be our constant term.

So, (6125 + 2112 + 1250 - 5000).

= 4487.

Therefore, The equation in slope-intercept form is,

y = 4487x + 750.

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Step-by-step explanation:

it is a parallelogram.

in comparison to a rectangle one side is shifted a bit, but the endpoints of the shifted side are still positioned the same way relative to each other.

and particularly, their relative offset from each other must be the same as for the endpoints of the other, parallel side.

let's look at

(0, -1) and (2, 7).

their relative offset is given by

x + 2 (from 0 to 2)

y + 8 (from -1 to 7)

the missing point must have the same offset from (-5, -3), as this line is parallel to the one above :

-5 + 2 = -3

-3 + 8 = 5

so, the missing point is (-3, 5).

Answer: Let x be the original cost of the jersey.

We know that the jersey was on sale at a 30% discount, so the sale price is x - (30/100)*x = x(1- 0.3) = 0.7x

We also know that Tyrone spent a total of $83.39 and the hat cost $37.89, so the jersey cost is 83.39 - 37.89 = 45.5

So we can write the equation:

0.7x = 45.5

To find the original cost of the jersey, we can divide both sides by 0.7:

x = 45.5 / 0.7

x = 65

So the original cost of the jersey is $65.

Step-by-step explanation:

The area of the rectangle is and using the length and breadth

area of rectangle = length × breadth

area of rectangle = 2.5m × (4n +5)

area of rectangle = 10mn + 12.5m

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Question:

The dimensions, in feet, of a rectangle, are represented by expressions, as shown in the diagram below. The area of the rectangle is 10mn + 12.5m. Explain your work.

Answer:

First, find out how many guests have ordered chicken: 240 guests * 3535/10000 = 84 guests

Then subtract that number from the total number of guests to find the number of guests who haven't ordered chicken: 240 guests - 84 guests = 156 guests

Then find how many of those guests have ordered gluten-free meals: 156 guests * 12.5% = 19.5 guests

Then round down the number of guests who have ordered gluten-free meals to the nearest whole number to find the exact number of guests who ordered gluten-free meals: 19 guests

Then subtract that number from the number of guests who haven't ordered chicken to find the number of guests who haven't ordered their meals yet: 156 guests - 19 guests = 137 guests

So 137 people haven't ordered their meals yet.

The sum of four consecutive integers is,

⇒ 4n + 6

The process of combining two or more numbers is called the Addition. The 4 main properties of addition are commutative, associative, distributive, and additive identity.

We have to given that;

⇒ n = first integer of the four.

Now, Let four consecutive integers with n is first integer of the four are,

⇒ n, n + 1, n + 2, n + 3

Hence, The sum of four consecutive integers is,

⇒ S = n + (n + 1) + (n + 2) + (n + 3)

      = 4n + 6

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The order of the group generated by a and b under matrix multiplication is a^2b^3.

Start with the identity matrix:

I = [1 0 ; 0 1]

Multiply it by a:

a*I = [1 1; 0 1]

Multiply it by b:

b*a*I = [1 2; 0 1]

Multiply it by a:

a*b*a*I = [2 3; 0 1]

Multiply it by b:

b*a*b*a*I = [2 5; 0 1]

Multiply it by a:

a*b*a*b*a*I = [4 3; 0 1]

Therefore, the order of the group generated by a and b is a^2b^3.

The order of the group generated by a and b under matrix multiplication is a^2b^3.

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The population of Calculus City can be modeled by an exponential function, g(t) = 10(1.3) ^t, where t is the number of years since 2019. Evaluating g (6) means calculating the population of Calculus City after 6 years, which is 10(1.3) = 39.5 thousand people.

(a) The population of Calculus City can be modeled by an exponential function, g(t) = 10(1.3) ^t, where t is the number of years since 2019.

(b) g (6) = 10(1.3) = 46.6 thousand. This means that the population of Calculus City will be 46.6 thousand in the year 2025.

(c) Solving the equation g(t) = 16.9 yields t = log1.3(16.9/10) = 4.7 years. This means that the population of Calculus City will be 16.9 thousand in the year 2023.7.

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The lines L₁ and L₂ given by the vector equations is perpendicular.

In order to prove that the lines are perpendicular,

L₁: r(t) = (-5+ 3t)i + (3 + t)j

L₂: r(s) = (2+2s)i + (4 - 6s)j

To determine whether the lines L₁ and L2 are parallel, perpendicular, or neither, we need to compare their direction vectors.

The direction vector for L₁ is given by <3,1> and the direction vector for L₂ is given by <2,-6>.

The dot product of the direction vectors is (32) + (1-6) = -8. Since the dot product is zero, the vectors are perpendicular, and therefore the lines are perpendicular.

Therefore, the lines are PERPENDICULAR.

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So. the left Riemann sum is 23.74 ft^2.

Given the information in the table:

(a) To use a left Riemann sum with three subintervals to approximate the integral of A(h) with respect to h, we need to divide the interval of integration [0,10] into three equal subintervals. The width of each subinterval is (10-0)/3 = 3.33 ft. The left Riemann sum can be calculated as:

(A(0) * 3.33) + (A(2) * 3.33) + (A(5) * 3.33) = (50.3 * 3.33) + (14.4 * 3.33) + (6.5 * 3.33) = 16.80 + 4.78 + 2.16 = 23.74 ft^2

(b) This approximation represents the total area of the horizontal cross section of the tank up to a specific height h.

(c) The Riemann sum is an underestimate of the actual integral. This is because the Riemann sum uses the left endpoint of each subinterval to approximate the area under the curve, but the actual area under the curve is always greater than or equal to the area of the rectangles.

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Answer:

9 books

Step-by-step explanation:

If their assembly rates continue, based on an equation, Summer will catch up with Jin in 52 minutes.

An equation refers to a statement claiming the equality of two or more mathematical expressions.

Using the equation sign (=) mathematicians show that expressions are equal or equivalent.

Jin's assembling rate per minute = 12 parts

Summer's assembling rate per minute = 15 parts

The number of parts already assembled by Jin before Summer started = 156 parts

Let the minutes used by Jin or Summer = n

The total parts assembled by Jin in n minutes = 156 + 12n

The total parts assembled by Summer in n minutes = 15n

For Summer to catch up to Jin, 15n = 156 + 12n

Grouping like terms:

15n - 12n = 156

3n = 156

n = 52

Thus, in 52 minutes, the number of assembly parts by Summer will equal Jin's.

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The value for x is 1 or -6. The solution has been obtained by using logarithm.

A logarithm is the power to which a number must be raised in mathematics in order to produce other numbers. It is the most useful way to express really large numbers.

We are given [tex]log_3 \frac{3(2-x)}{x(x+2)} = 0[/tex]

Solving the equation, we get

[tex]log_3 \frac{3(2-x)}{x(x+2)} = 3^0[/tex]  (Using the property of log)

On multiplying both sides by x(x+2), we get

[tex]log_3 \frac{3(2-x)}{x(x+2)} x(x+2) = 3^0 x(x+2)[/tex]

⇒3 (2−x) = x(x+2)

⇒ 6 - 3x=x² +2x

= x²+5x-6=0

⇒ x²+6x-x-6=0

⇒ (x+6)(x-1)=0

⇒ x = 1,-6

Hence, the value for x is 1 or -6.

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After the raise, Lisa much will pay $9 in federal income taxes Annually.

For the stated question:

Lisa's salary =  $215.20 a week.

After increment of $40 per week.

$215.20  + $40 = $255.2

She gets 3 allowances and is married.

After raise,

Federal income taxes = $9. (taken from the table)

Thus, After the raise, Lisa much will pay $9 in federal income taxes Annually.

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a. The table for the weekly weight of Julie is illustrated below.

b. The recursive definition for this sequence is y = 180 - 2x.

An equation is written in the form of variables and constants separated by the operation of multiplication and division,

An equation states that terms in different forms on both sides of the equality sign are equal.

Multiplication and division do not separate the terms of an equation.

Given, Julie is trying to lose weight.

She now weighs 180 pounds and every week for eight weeks, she was able to lose 2 pounds.

The list of her weight every week for eight weeks is,

week 1 = 180 - 2 = 178 pounds.

week 2 = 178 - 2 = 176 pounds.

week 3 = 176 - 2 = 174 pounds.

week 4 = 174 - 2 = 172 pounds.

week 5 = 172 - 2 = 170 pounds.

week 6 = 170 - 2 = 168 pounds.

week 7 = 168 - 2 = 166 pounds.

week 8 = 166 - 2 = 164 pounds.

The equation that represents her weekly weight loss is,

y = 180 - 2x, Where 'x' represents the number of weeks and y represents the final weight.

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Answer:

$ 148.75

Step-by-step explanation:

       Principle = $ 425

         Rate = 7%

       Time = 5 yeats

[tex]\sf \boxed{Simple \ Interest = \dfrac{Principle*rate*time}{100}}[/tex]

                           [tex]= \dfrac{425*7*5}{100}\\\\=\dfrac{17*7*5}{4}\\\\\\=\dfrac{595}{4}\\\\=148.75[/tex]

Answer:

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

Let the husband's age be h and wife's age be w.

The difference of their age is 3 and sum is 73:

The difference between the squares is:

Answer:

219

Step-by-step explanation:

H-W=3

H+W =73

2H=76

H=38

W=35

38² -35² = 219

The solution of the system of equations is given by the ordered pair (10, 85).

The solution tells us that the height of both Drone A and Drone B would be the same after 10 minutes.

In this scenario, heights of drones are represented by the following system of equations:

y = 8x + 5     .......equation 1.

y = 6x + 25    .......equation 2.

where:

By equating equation 1 and equation 2, number of minutes since the drones were released can be calculated as follows;

8x + 5 = 6x + 25

8x - 6x = 25 - 5

2x = 20

x = 20/2

x = 10 minutes.

Next, we would determine the height when x = 10 minutes:

y = 8(10) + 5

y = 80 + 5

y = 85 meters.

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