algebra II engenuity

Answer:

9

Step-by-step explanation:

Whatever you do to the denominator, you've got to do to the numerator, and vice versa. So for 8 to become 24, you multiply by 3. do that to the numerator 3 as well. 3 × 3 is 9.

For the sake of showing work I will replace the empty space with an x like so...

[tex]\frac{3}{8} =\frac{x}{24}[/tex]

To find out what x is you must cross multiply (aka butterfly)

***Image of this step is attached below

3*24 = 8*x

72 = 8x

Next divide 8 to both sides to finish isolating x. Since 8 is being multiplied by x, division (the opposite of multiplication) will cancel 8 out (in this case it will make 8 one) from the right side and bring it over to the left side.

72 ÷ 8 = 8x ÷ 8

9 = 1x

9 = x

To make these fractions equivalent the empty spot must be 9

[tex]\frac{3}{8} = \frac{9}{24}[/tex]

Hope this helped!

~Just a girl in love with Shawn Mendes

The equivalent expression to 4 √6 divided by 3 √2 is 4/3 × √3. This is achieved by expressing the square roots as fractional exponents and simplifying.

The student is asking which expression is equivalent to the following mathematical expression: √(4 √6) / (3 √2).

To simplify this expression, we'll use the properties of exponents and radicals.

The square root of a number x can be written as x raised to the power of 0.5, so:

√6 = 60.5

√2 = 20.5

The given expression thus becomes:

(4 × 60.5) / (3 × 20.5) = 4/3 × 60.5/20.5

Since the exponents are the same, we can simplify the radicals by dividing the numbers inside the radicals:

4/3 × (6/2)0.5 = 4/3 × (3)0.5

And as (3)0.5 is the square root of 3:

4/3 × √3

Therefore, the equivalent expression is 4/3 × √3.

Answer:

Distribute the -9 into the values in the parentheses.

STEP BY STEP

-9(-2x-3)

-9*-2x=18x

-9*-3=27

Therefore, the equation then becomes: 18x+27.

The answer is the first choice, or A.

The percent of the cash discount being offered is 5%.

The terms 5/10 EOM mean that the customer is eligible for a cash discount of 5% if the invoice is paid within 10 days from the end of the month. In this case, the invoice date is August 1st, so the end of the month is August 31st. To calculate the number of days allowed for the cash discount, we subtract 10 days from August 31st, which gives us August 21st. Therefore, the cash discount is valid until August 21st and the percent of the cash discount being offered is 5%.

Answer:

b. 3

Step-by-step explanation:

In a 30°-60°-90° triangle, the short side is ½ the hypotenuse [the long side is double the short side].

30°-60°-90° Triangles

x√3 → long side

x → short side

2x → hypotenuse

45°-45°-90° Triangles

x → two legs

x√2 → hypotenuse

I am joyous to assist you anytime.

Answer:

$720

Step-by-step explanation:

1 hour of tutoring  =  $45

16 hours of tutoring = $45 x 16 hours = $720

Answer:

$720

Step-by-step explanation: just multiply 45 and 16 together, boom theres your answer

Answer:

D

Step-by-step explanation:

To evaluate f(5) substitute x = 5 into f(x)

f(5) = (3 × 5) + 2 = 15 + 2 = 17 → D

[tex]f(5)=3\cdot5+2=17\Rightarrow\text{D}[/tex]

Answer:

(1/2)x+3/2

or

0.5x+1.5

Step-by-step explanation:

Hopefully you mean to have that dot between f and g closed because if it open it means something totally different.

So closed dot means multiplication

Open dot means you are composing a function with another one

So here you are just doing (x+3)  *  (1/2)

Just use distributive property   (1/2)x+(1/2)(3)

(1/2)x +3/2

or

0.5x+1.5

Answer:

Multiply 9 by 6

Step-by-step explanation:

7:9 is the ratio

We multiply the first term by 6.

What we do to one side, we do to the other

7*6=42

9*6 = 54

That way we keep the ratio in the same proportion

42:54

Answer: Multiply 9 by 6.

Step-by-step explanation:

Answer:

Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction

Step-by-step explanation:

Samantha will be offered the choice of using the coupon or the sale discount. If she chooses tht 50% coupon, her savings will be $30. If she chooses the marked sale discount, her savings will be $15.  

The scenario above assumes she gets 50% off the sale price of $45, so saves $15+22.50 = $37.50 off the original price.

Answer: Samantha will save $37.50 because she must first find the 25% sale price before taking the extra 50% reduction so the answer is B

Step-by-step explanation:

Linear data is data lying across a straight line. The runner which kept the most consistent pace was runner B.

Firstly, there is a data set. Then, we try to fit a line which will tell about the linear trend. This line is made using the least squares method.

For the given case, the second runner(runner B)'s data is almost forming a linear trend, whereas, for the first runner, its more spread, and the third graph, its a quadratic trend.

For non-linear trends like in third graph(runner C), we use polynomial regression to fit polynomial curves of higher degrees.

Thus, as the runner B's data set is lying more near to a line than other runners, thus,

The runner which kept the most consistent pace was runner B.

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Answer:

f(6)  =  68

Step-by-step explanation:

f(6)

f(n+1)=f(n)-8

n = 5, so

f(6)=f(5)-8

and with n = 4

f(5)=f(4)-8 , so

f(4) = f(3) - 8

f(3) = f(2) - 8 = 100 - 8 = 92

f(3)  = 92

Then, we can go and find the result

f(4) =[92] - 8  = 84

f(5)=[84] - 8 = 76

f(6)  = [76] -8 = 68

[tex]f(n+1)=f(n)-8\\f(2)=100\\\\f(3)=100-8=92\\f(4)=92-8=84\\f(5)=84-8=76\\f(6)=76-8=68[/tex]

Step-by-step explanation:

The wheel has a diameter of 250 feet, so its circumference is:

C = 2πr = πD

C = 250π feet

It makes one revolution in 30 seconds, or half a minute, so the linear speed of the passenger is:

v = d / t

v = 250π / 0.5

v = 500π ft/min

v ≈ 1571 ft/min

This is about the same as 17.9 mph.

Final answer:

The linear speed of a passenger on the original Ferris wheel with a diameter of 250 feet, making one revolution every 30 seconds, was approximately 1570.8 feet per minute.

Explanation:

The question asks to calculate the linear speed of a passenger on the edge of the first Ferris wheel, which was 250 feet in diameter, and made one revolution every 30 seconds. To find the linear speed, we first need to determine the circumference of the Ferris wheel, which can be done by using the formula for the circumference of a circle, C = πd, where d is the diameter.

For the first Ferris wheel:

Diameter (d) = 250 feet

Circumference (C) = π * 250 feet = 785.398163 feet (approximately)

Time for one revolution = 30 seconds

Since the question requires the speed in feet per minute, we need to convert the time for one revolution to minutes:

30 seconds = 0.5 minutes

The linear speed (v) can be found using the formula v = C / time. Substituting our values in:

v = 785.398163 feet / 0.5 minutes = 1570.79633 feet per minute

Therefore, the linear speed of a passenger at the edge of the Ferris wheel was approximately 1570.8 feet per minute.

Answer:

82 notes

Step-by-step explanation:

3×8=24

16×3=48

4×3=12

24+48+12=84

Final answer:

To find the total number of notes played throughout the song, add the notes from each measure (8 + 16 + 4 = 28) and multiply by the times they are played (28 x 3), resulting in 84 notes played in total.

Explanation:

The question pertains to calculating the total number of notes played in a song where specific measures of music are repeated a certain number of times. First, we need to calculate the number of notes in a single iteration of the three measures:

Measure 1: 8 notes

Measure 2: 16 notes

Measure 3: 4 notes

Adding these together, we get a total of 28 notes for one iteration of the 3 measures. Since these measures are played 3 times throughout the song, we multiply 28 by 3, which equals 84 notes. Therefore, 84 notes are played throughout the song.

Answer: 24

Step-by-step explanation:

Break down the numbers until they have no way to be broken down anymore

8 = 4*2 = 2*2*2

24 = 6*4 = 3*2*2*2

The one that has more products is 24, so, it is 24.

Answer:

False

Step-by-step explanation:

a^2+b^2=c^2 so the biggest number would be c and that would be 11 9^2=81 4^2=16 adding these together gets 97. 97=/=11^2 which is 121

Answer:

A. True.

Step-by-step explanation:

We have been given lengths of three segments. We are asked to determine whether the given segments could form a triangle or not.

Triangle inequality theorem states that sum of two sides of triangle must be greater than third side of the triangle.

Using triangle inequality theorem, we will get:

[tex]9+4>11[/tex]

[tex]13>11[/tex] True

[tex]9+11>4[/tex]

[tex]20>4[/tex] True

[tex]4+11>9[/tex]

[tex]15>9[/tex] True

Since our given segments satisfies triangle inequality theorem, therefore, the given segments could form a triangle.

Answer: 30

Step-by-step explanation: Start off by multiplying the two numbers.

3 x 10 = 30.

30 is a common multiple. Find any multiples below 30. Let’s start off using the biggest number of the two, which is 10, to see what other numbers can be multiples. 10, 20, and 30 can be. 3 can’t be divided into 10 or 20, so your least common multiple is 30.

Answer:

6 more than 5 times the measure of mn is (5mn + 6)

Step-by-step explanation:

Answer:

3 1/3

Step-by-step explanation:

8 1/6 - 4 5/6    Borrow 1 or 6/6 from the 8 so you have something to subtract.

7 7/6 - 4 5/6    Subtract the whole numbers.

7 - 4 = 3           Subtract the fractions.

7/6 - 5/6          Do the subtraction

2/6                   Reduce

2/6 = 1/3          Put the two parts together.

3 1/3

the result of subtracting the two mixed numbers is  [tex]3\frac{1}{3}[/tex]

To subtract the mixed numbers [tex]8\frac{1}{6}[/tex] and [tex]4\frac{5}{6}[/tex] we need to first understand how to subtract it. To subtract mixed numbers we need to first convert them to improper fraction. For the new fraction, the denominator remains same but new numerator is calculated by finding the product of whole number and denominator and then adding it to the numerator. This can be done as follows:

[tex]8\frac{1}{6} = \frac{ 8 \times 6 +1}{6} = \frac{49}{6}[/tex]

[tex]4\frac{5}{6} = \frac{ 4 \times 6 +5}{6} = \frac{29}{6}[/tex]

Now we subtract them as follows:

[tex]\frac{49}{6} - \frac{29}{6} = \frac{20}{6} = \frac{10}{3}[/tex]

To convert this back into mixed fraction we divide 10 by 3 and the quotient becomes the whole number while the remainder becomes numerator and 3 remains as denominator

[tex]\frac{10}{3} = 3\frac{1}{3}[/tex]

Therefore, the result of subtracting the two mixed numbers is  [tex]3\frac{1}{3}[/tex]

Answer:

1155

Step-by-step explanation:

Answer:

41

Step-by-step explanation:

:))

Answer:

$[tex]1g[/tex]

Explanation:

If the number of granola bars is represented by the variable [tex]g[/tex], and each granola bar costs $1, then we need to multiply the amount per granola bar by the number of granola bars.

This is $[tex]1 * g[/tex], or $[tex]1g[/tex].

In this scenario, the total cost of the granola bars can be represented by the mathematical expression 'g', as each granola bar costs $1.

If each granola bar costs $1 and 'g' is representing the number of granola bars, then the total cost of the granola bars can be represented by the expression 1 * g or simply g. This is because for every granola bar you buy, you are adding $1 to your total. So if you bought 'g' granola bars, your total cost would be $1 times the number of granola bars 'g'. This is an example of direct proportionality, where the total cost increases with the increase in number of granola bars.

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x+19= 26

x+19-19= 26-19

x= 7

Check answer by using substitution method

x+19= 26

7+19= 26

26= 26

Answer is x= 7 (D.)

To find the solution we need to solve for x

We need to get x alone to solve for x.

To remove any number, always do the opposite operation

Opposite of +19 is -19

To remove +19 , subtract 19 from both sides

x+19=26

x+19 -19 =26-19 =7

x=7

So the value of x=7

The solution to this equation Option D.  x=7

An equation is a mathematical statement that is made up of two expressions connected by an equal sign. For example, 3x – 5 = 16 is an equation. Solving this equation, we get the value of the variable x as x = 7.

There are three major forms of linear equations: point-slope form, standard form, and slope-intercept form.

An equation is a mathematical statement that two things are equal. It consists of two expressions, one on each side of an 'equals' sign. For example x=y is an equation where two expressions x and y are equal. Whereas f(x)=x is a function with variable x and hence f(x)=x is not an equation.

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A fifth-degree polynomial has three real roots and two imaginary roots.

The given polynomial function f(x) is a fifth-degree polynomial, meaning it has five roots. We are given three of the roots: -2, 2, and 4 + i. Since the coefficients of a polynomial with real coefficients are either real or come in conjugate pairs for complex roots, the remaining two roots must be the complex conjugates of 4 + i, which are 4 - i. Therefore, f(x) has three real roots -2, 2, and 4, and two complex roots 4 + i and 4 - i.

Answer: D. f(x) has three real roots and two imaginary roots.

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The function f(x), a fifth degree polynomial, has three real roots and two complex (imaginary) roots due to the Conjugate Root Theorem. The roots are –2, 2, 4, 4 + i and 4 - i. Therefore, option D is correct.

The function f(x) is a fifth degree polynomial. Given the roots available, –2, 2, and 4 + i, we already have three roots, two real and one complex (or imaginary). From the Conjugate Root Theorem, which states that if a polynomial has real coefficients, then any imaginary root must have its conjugate as a root. Thus, the conjugate of 4 + i, which is 4 - i, is also a root of this function. Therefore, the fifth degree polynomial has three real roots –2, 2, and 4, and two imaginary roots 4 + i and 4 - i, indicating that option D: 'f(x) has three real roots and two imaginary roots' is correct.

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Answer:

The sequences are arithmetic

1).-8.6, -5.0, -1.4, 2.2, 5.8

2).  5, 1, -3, -7, -11

3). -3, 3, 9, 15, 21

Step-by-step explanation:

If a sequence is a an AP then there is a common difference d.

1) Check sequence 1

-8.6, -5.0, -1.4, 2.2, 5.8

-5.0 - - 8.6 = 3.6

-1.4 - -5.4 = 3.6  It is an AP

2) Check sequence 2

2, -2.2,2.42, -2.662, 2.9282

-2.2 - 2 = -4.2

-2.662 - 2.42 = -5.082 Not AP

Similarly AP sequences are

5, 1, -3, -7, -11

-3, 3, 9, 15, 21

The sequence that are arithmetic are as follows:

5, 1, -3, -7, -11.

-3, 3, 9, 15, 21

-8.6, - 5.0, -1.4, 2.2, 5.8

Arithmetic sequence is a list of numbers with a definite pattern. Therefore, let's find the sequence with a definite pattern.

5, 1, -3, -7, -11.

This is a sequence as it as a definite pattern. The value are reduced by 4. Therefore, the common difference is 4.

-3, 3, 9, 15, 21

This is a sequence because it has a common difference of 6.

-8.6, - 5.0, -1.4, 2.2, 5.8

This is a sequence because it has a common difference of 3.6.

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Answer:

x = 11/6

Step-by-step explanation:

You need to reduce this fraction to the lowest terms.

This can be done by dividing out those factors that appear both in the numerator and in the denominator.

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Answer:  [tex]\bold{x=-\dfrac{4}{3}\qquad x=5}[/tex]

Step-by-step explanation:

[tex]\dfrac{2}{x-2}+\dfrac{7}{x^2-4}=\dfrac{5}{x}\\\\\\\text{Multiply each term by the LCD x(x-2)(x+2) to clear the denominator:}\\\dfrac{2}{x-2}[x(x-2)(x+2)]+\dfrac{7}{x^2-4}[x(x-2)(x+2)]=\dfrac{5}{x}[x(x-2)(x+2)]\\\\\\\text{Simplify - cross out like terms:}\\2[x(x+2)]+7[x]=5[(x-2)(x-2)]\\\\\\\text{Distribute:}\\2x^2+4x+7x=5x^2-20\\\\\\\text{Set equation equal to zero and Add like terms:}\\0=5x^2-2x^2-7x-4x-20\\0=3x^2-11x-20\\\\\text{Factor, set each factor equal to zero, and solve for x:}[/tex]

[tex]0=(3x+4)(x-5)\\0=3x+4\qquad 0=x-5\\\large\boxed{x=-\dfrac{4}{3}\qquad x=5}[/tex]

Answer:

18

Step-by-step explanation:

First you need to plug in the numbers for each variable.

3(3)+(5+2(8))-12

Now you solve

3(3)+(21)-12

9+21-12

18

a box plot is drawn with end points at 10 and 35. The box extends from 13 to 30 and a vertical line is drawn inside the box at 21.

Answer:

(x - 15)(x + 3)

Step-by-step explanation:

Consider the factors of the constant term (- 45) which sum to give the coefficient of the x- term (- 12)

The factors are - 15 and + 3, since

- 15 × 3 = - 45 and - 15 + 3 = - 12, hence

x² - 12x - 45 = (x - 15)(x + 3)

The equation of f(x) is  B. F(x) = -√x. Therefore , B. F(x) = -√x is correct.

Here's why:

The parent function of the graph is the square root function, which means the original equation is f(x) = √x.

The graph is reflected across the x-axis.

This means that the y-values are multiplied by -1. In other words, if the original point was (x, √x), the reflected point would be (x, -√x).

Therefore, the equation of the reflected function is f(x) = -√x.

The other options are incorrect because:

A. F(x) = √x is the original equation, not the reflected equation.

C. F(x) = √x - 1 shifts the graph down one unit, but it does not reflect it across the x-axis.

D. F(x) = √x + 1 shifts the graph up one unit, but it does not reflect it across the x-axis.