write each fraction as a decimal use bar notation if necessary 8 / 15

Answer:

10

Step-by-step explanation:

Given expression:

                   20 - \(\frac{15 + 3(5)^{2} }{5^{2} - 4^{2} }\)

     To solve this problem, we use the order of operation:

P - Parentheses

E - exponents

M - multiplication

D - division

A - Addition

S - Subtraction

  Now solve the parentheses first;

     =   20 - \(\frac{15 + 3x 25}{5^{2} - 4^{2} }\)

     =    20 - \(\frac{15 + 75}{5^{2} - 4^{2} }\)

     Now solve the exponents:

    = 20 - \(\frac{15 + 75}{25 - 16}\)

    Now solve the division:

     = 20 - \(\frac{90}{9}\)

     = 20 - 10

     = 10

There is no real Value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

(i) Zeroes of the polynomial:

In the graph, we have two points where the curve intersects the x-axis: one is at (-1,0), and the other is at (2,0).The corresponding values of x are -1 and 2, and they are the zeros of the polynomial. Therefore, the zeros of the polynomial are -1 and 2.(ii) Forming the quadratic polynomial:

From the graph, we can observe that the curve intersects the y-axis at the point (0,5), implying that the constant term of the polynomial is 5.

We can use the formula to find the quadratic polynomial if we have two zeros and one constant term. Thus, the quadratic polynomial is given by:(x + 1)(x - 2) = x² - x - 2x + 2 = x² - 3x + 2. Therefore, the quadratic polynomial is x² - 3x + 2.(iii) Value of k if a, 1/a are the zeroes of the polynomial 2x² - x + 8k:

We know that a and 1/a are the zeroes of the polynomial 2x² - x + 8k. Therefore, we can find the sum and product of the roots and use them to determine the value of k.

The sum of the roots is a + 1/a, and their product is a(1/a) = 1. Using the sum and product of the roots, we can write: a + 1/a = 1/2 (1/2 is the coefficient of x)Substituting a with 1/a in the above equation, we get: 1/a + a = 1/2Multiplying both sides of the equation by 2a, we get: 2 + 2a² = a

Simplifying the equation, we get: 2a² - a + 2 = 0Multiplying both sides by 2,

we get: 4a² - 2a + 4 = 0Dividing both sides by 2, we get: 2a² - a + 2 = 0

Using the quadratic formula, we get: a = [1 ± √(1 - 4(2)(2))]/(2(2))

Simplifying, we get: a = [1 ± √(-31)]/4Since the discriminant of the quadratic formula is negative, the roots are imaginary. Therefore, there is no real value of k that will satisfy the equation 2x² - x + 8k = 0 if a and 1/a are the roots of the polynomial.

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Answer: It is the second one, third one, and last one

Step-by-step explanation:

Answer:

2z-4

Step-by-step explanation:

By using distributive property, 2/3 * 3z =  2z and 2/3 * -6 = -4

This means the answer is 2z-4

\(Answer: \large\boxed{2z-4}\)

Step-by-step explanation:

To solve:

\(\frac{2}{3} (3z-6)\)

We must use the distributive property and distribute 2/3 to the 3z and -6

...

\(\frac{2}{3} (3z-6)\)

\(=\frac{2}{3} (3z) + \frac{2}{3} (-6)\)

\(=\frac{6z}{3} + -\frac{12}{3}\)

\(=2z-4\)

Answer:

<6 and <4

Step-by-step explanation:

Complemetary angles are angles that their measure add up to 90 degrees

the angles meet this requirment in this image are angle <6 and angle <4

Answer:

2001

Step-by-step explanation:2001

Using the definition of a confidence interval, it is found that the 90% confidence interval for the average cost for healthcare of a senior citizen receiving Medicare is ($12,000, $14,000).

A confidence interval is the sample mean plus/minus the margin of error.

Hence:

$13,000 - $1,000 = $13,000

$13,000 + $1,000 = $14,000

The interval is ($12,000, $14,000).

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Answer:

3x-5?

Step-by-step explanation:

I hope im right.

Answer:

its 72

Step-by-step explanation:

i did itand it showed 72

Answer:

30 x^2

Step-by-step explanation:

(5x)(7x)-5x^2=30x^2

Simplify the following:

5×7 x x - 5 x^2

5 x×7 x = 5 x^2×7:

5×7 x^2 - 5 x^2

5×7 = 35:

35 x^2 - 5 x^2

35 x^2 - 5 x^2 = 30 x^2:

Answer: 30 x^2

If the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

The first quartile (Q1) of the ages of the 256 employees of CCNHS – Main Campus being 39 years old implies that 25% of the employees have an age equal to or less than 39 years old.

In statistical terms, the first quartile represents the point below which 25% of the data falls. It divides the data set into four equal parts, with each part containing 25% of the data. Therefore, if the first quartile is 39 years old, it means that approximately one-fourth of the employees at CCNHS – Main Campus are 39 years old or younger.

This information provides insight into the age distribution of the employees at the institution. It indicates that a significant portion of the employees are relatively young, with a quarter of them falling below the age of 39. Understanding the age demographics of the workforce can be useful for various purposes, such as planning professional development programs or implementing age-specific policies.

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Answer:

B; There is only one (x,y) solution and y is negative

Step-by-step explanation:

First, I graphed the two equations. Attached is an image of the equations graphed. Next, I looked for overlapping points. Wherever the two points overlap, there is a solution. When looking at the graph, we can see the lines overlap at only one point, (0,-1). Since y is negative, the answer must be B; there is only one (x,y) solution and y is negative.

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Answer:

3n = 9n - 110

Step-by-step explanation:

Let's suppose that Patrick and Hall play n number of songs to earn the same amount of money.

For Patrick, the amount of money he earns is given by:

Money earned by Patrick = 3n

For Hall, the amount of money he earns after paying the $110 fee is given by:

Money earned by Hall = 9n - 110

To find the number of songs they will have to play in order to earn the same amount of money, we need to set these two expressions equal to each other and solve for n:

3n = 9n - 110

Simplifying this equation, we get:

6n = 110

Dividing both sides by 6, we get:

n = 110/6

n = 18.33 (rounded to two decimal places)

Since n represents the number of songs, it cannot be a fractional value. Therefore, we can conclude that they will have to play 18 songs to earn the same amount of money.

Therefore, the equation that could be used to find n, the number of songs they will have to play in order to earn the same amount of money, is:

3n = 9n - 110

Hope this helps!

The graph of g(x) = 2x + 5 is identical to the graph of f(x) = 2x in terms of slope but differs in terms of y-intercept. The graph of g(x) is shifted upward by 5 units compared to the graph of f(x), resulting Parallel lines.

The graph of g(x) = 2x + 5 is a linear function, while the graph of f(x) = 2x is also a linear function. Let's compare the two graphs:

1. Slopes:

Both functions have the same slope of 2. The coefficient of x in both equations is 2, which represents the rate of change or the slope of the line. This means that the two graphs have the same steepness.

2. y-intercepts:

The y-intercept of g(x) = 2x + 5 is 5, while the y-intercept of f(x) = 2x is 0. The y-intercept is the value of y when x is equal to 0. For g(x), when x = 0, y = 5, so the graph of g(x) intersects the y-axis at the point (0, 5). However, for f(x), when x = 0, y = 0, so the graph of f(x) passes through the origin (0, 0).

3. Parallel Lines:

The graphs of g(x) = 2x + 5 and f(x) = 2x are parallel lines. Since the slopes of both lines are the same, the lines will never intersect. They will remain equidistant from each other as they extend to infinity.

The graph of g(x) = 2x + 5 is identical to the graph of f(x) = 2x in terms of slope but differs in terms of y-intercept. The graph of g(x) is shifted upward by 5 units compared to the graph of f(x), resulting in parallel lines.

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Answer: 0

Explanation:

I hope this helped!

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- Zack Slocum

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The correct pairings are:

a) Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3

b) Five times the difference of a number squared and six: 5(n² - 6)

c) Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4

d) O twice the difference of nine and a number squared: 2(9 - n²)

The correct pairings of descriptions and expressions are as follows:

Four less than the quotient of a number cubed and seven, increased by three: (n³/7) - 4 + 3

This expression represents taking a number, cubing it, dividing the result by seven, subtracting four, and then adding three.

Five times the difference of a number squared and six: 5(n² - 6)

This expression represents taking a number, squaring it, subtracting six, and then multiplying the result by five.

Nine more than the quotient of six and a number cubed, decreased by four: (6/n³) + 9 - 4

This expression represents taking the cube of a number, dividing six by the cube, adding nine, and then subtracting four.

O twice the difference of nine and a number squared: 2(9 - n²)

This expression represents taking a number, squaring it, subtracting it from nine, and then multiplying the result by two.

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Answer:

C) (-6,0)(2,0)

For x-intercept, f(x) = 0:

\({ \tt{ {x}^{2} + 4x - 12 = 0 }} \\ { \tt{(x - 2)(x + 6) = 0}} \)

Answer:

C) (-6,0)(2,0)

Step-by-step explanation:

f(x)= x²+4x-12

(x-2)(x+6)=0

x=2

x=-6

The number of candy still in the bag is the dependent variable, while the independent variable, x, stands for the length of time spent eating, as the number of candies still in the bag relies on the length of time spent eating. A function relating these variables is H(x) = 60 - 5x. So H (10) = 40, meaning there are 40 candies left in the bag.

H(x) = 60 - 5x

H(10) = 60 - 5(10)

H(10) = 60 - 50

H(10) = 10

The independent variable, x, represents the number of minutes eating and the dependent variable is the number of candies left in the bag because the number of candies left depends on the number of minutes eating. This is a linear relationship, meaning that the rate at which the candies are being eaten is constant, so the decrease in the number of candies is proportional to the number of minutes eating. A function relating these variables is H(x) = 60 - 5x. This is a linear equation, with a slope of -5, which means for every minute eating, the number of candies left decreases by 5. So, when x = 10, H(10) = 60 - 5(10) = 60 - 50 = 10, meaning there are 10 candies left in the bag. This function can be used to determine the number of candies left in the bag at any point in time.

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Answer:

The ratio of their volumes is not the same 4:1, but \((4:1)^3\) = 64:1.

Step-by-step explanation:

Measurements in Similar Figures

In similar figures, if the ratio of any of these corresponding lengths is expressed as a:b then the ratio of the other corresponding lengths can also be expressed as a:b.

In similar figures, if the ratio of any of these corresponding lengths is expressed as a:b then the ratio of the areas can be expressed as (a:b)^2 and the ratio of the volumes can be expressed as (a:b)^3.

We are given the ratio of the sides of two similar prisms as 4:1. The ratio of their volumes is not the same 4:1, but \(\mathbf{(4:1)^3}\) = 64:1.

Answer:

125 ft²

Step-by-step explanation:

Hello!

Let the length be called \(l\) and the width be called \(w\).

If the length is 5 times the width, that means \(l = 5w\).

We also know that the perimeter is 60ft, or \(2(l + w) = 60\)

Substitute \(5w\) for \(l\) and solve for the dimensions:

That means \(l\) is 5(5) or 25.

The area is 125 ft².

Answer:

See below

Step-by-step explanation:

For the second step, \(\angle T\cong\angle R\) by Alternate Interior Angles. The rest of the steps appear to be correct.

Answer:

17.32 meters

Step-by-step explanation:

Let’s call the height of the tower H. The distance from the point to the base of the tower is 10 m. The angle of elevation from the point to the top of the tower is 60 degrees.

Using trigonometry, we can calculate that:

tan (60) = H / 10

H = 10 * tan (60)

H = 10 * √3

H = 17.32 m

Therefore, the height of the tower is 17.32 meters.

Let me know if I helped :)

The value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

To perform the calculation and express the answer in standard form, follow these steps:

Multiply 0.045 by 2.05:

0.045 × 2.05 = 0.09225

Divide the result by 0.0025:

0.09225 / 0.0025

= 36.9

Convert the answer to standard form by writing it as a decimal multiplied by a power of 10:

36.9 = 3.69 × 10

Therefore, the value of 0.045 × 2.05 / 0.0025 in standard form is 3.69 × 10.

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Answer:

hi

Step-by-step explanation:

5x+10+2x+10+90=180

5x+2x=180-10-10-90

7x=70

x=10

have a nice day