Please I need help , thanks

The steps peter could use in solving the quadratic equation is by applying the quadratic formula; x = –1 Plus or minus StartRoot StartFraction 5 Over 8 EndFraction EndRoot

8x² + 16x + 3 = 0

using Quadratic formula

The following steps are involved

\(x = \frac{ -b \pm \sqrt{b^2 - 4ac}}{ 2a }\)

\(x = \frac{ -16 \pm \sqrt{16^2 - 4(8)(3)}}{ 2(8) }\)

\(x = \frac{ -16 \pm \sqrt{256 - 96}}{ 16 }\)

\(x = \frac{ -16 \pm \sqrt{160}}{ 16 }\)

\(x = \frac{ -16 \pm 4\sqrt{10}\, }{ 16 }\)

\(x = \frac{ -16 }{ 16 } \pm \frac{4\sqrt{10}\, }{ 16 }\)

\(x = -1 \pm \frac{ \sqrt{10}\, }{ 4 }\)

\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)

\(x = -0.209431\)

or

\(x = -1.79057\)

Therefore, the steps peter could follow will give the result

\(x = -1 \pm \frac{ \sqrt{5}\, }{ 2 }\)

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It will take 3.5 hours for the two cars to be 280 miles apart.

To determine the time it takes for the two cars to be 280 miles apart, we can use the concept of relative velocity.

Since the cars are traveling in opposite directions, their velocities can be added together to find their relative velocity:

Relative velocity = Velocity of car traveling east + Velocity of car traveling west

Relative velocity = 60 mph + 20 mph

Relative velocity = 80 mph

The relative velocity of the cars is 80 mph, which means that they are moving away from each other at a combined speed of 80 mph.

To find the time it takes for them to be 280 miles apart, we can use the formula:

Time = Distance / Speed

Plugging in the values, we have:

Time = 280 miles / 80 mph

Time = 3.5 hours

Therefore, it will take 3.5 hours for the two cars to be 280 miles apart.

During this time, the car traveling east would have covered a distance of 60 mph × 3.5 hours = 210 miles, while the car traveling west would have covered a distance of 20 mph × 3.5 hours = 70 miles.

The sum of these distances is indeed 280 miles, confirming the result.

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A. To construct a grouped frequency distribution for the given data, we first need to determine the range of the data:

Range = Maximum value - Minimum value

Range = 39 - 5

Range = 34

Next, we need to decide on the width of each class interval. A common rule is to choose the number of classes to be between 5 and 20, and then choose a class width that is a convenient number. In this case, we will choose 8 classes and a class width of 5.

Class width = Range / Number of classes

Class width = 34 / 8

Class width ≈ 4.25

We can round up the class width to 5 to get a convenient number. The class intervals are:

5 - 9.99

10 - 14.99

15 - 19.99

20 - 24.99

25 - 29.99

30 - 34.99

35 - 39.99

40 - 44.99

Next, we count the number of observations that fall into each class interval. This gives us the frequency of each interval. The grouped frequency distribution is:

Class Interval Frequency

5 - 9.99 5

10 - 14.99 8

15 - 19.99 9

20 - 24.99 16

25 - 29.99 7

30 - 34.99 6

35 - 39.99 1

40 - 44.99 0

B. To draw the histogram, frequency polygon, and cumulative frequency curves, we first need to calculate the cumulative frequencies. The less than cumulative frequency is the running total of the frequencies up to each class interval, while the more than cumulative frequency is the running total of the frequencies from each class interval to the end.

Class Interval Frequency Less than Cumulative Frequency More than Cumulative Frequency

5 - 9.99 5 5 62

10 - 14.99 8 13 57

15 - 19.99 9 22 49

20 - 24.99 16 38 40

25 - 29.99 7 45 24

30 - 34.99 6 51 17

35 - 39.99 1 52 11

40 - 44.99 0 52 10

Now we can draw the graphs:

Histogram:

   20 |

       |           __

       |          |  |

       |    __    |  |

       |   |  |   |  |

       |   |  |   |  |

       |   |  |   |  |

       |___|__|___|__|__

           5  10  15  20

Frequency polygon:

   25 |

       |  __

       | |  |     __

       | |  |    |  |

       | |  |    |  |

       | |  |

Answer:

-6x

Step-by-step explanation:

2x - 8x = -6x

Answer:

7.6

Step-by-step explanation:

Mean = (sum of numbers)/amount of numbers

11 + 4 + 6 + 7 + 5 +10 +9 + 21 + 3 + 0 = 76

76/10 = 7.6

Answer:

area is 3.14 r2

Step-by-step explanation:

here r = 5 inch

area = 3.14 × 25

so 78.5 in2

Answer:

E: since irrational is non-terminating and the ... means it goes on forever which cannot be represented by a fraction

Answer: 73

Step-by-step explanation:

Answer:

3/8

Step-by-step explanation:

since there are 8 balls in total and 3 of them are green, you write the ratio as 3:8. This is the same as 3/8

Answer: help me pls

Step-by-step explanation:

A train traveled at a constant speed for six hours and traveled a distance of 408 miles. What is the best estimate of the number of miles the train could travel in 2.5 hours? *

Answer:

0.333333333.......

Step-by-step explanation:

Answer:

divergent

Step-by-step explanation:

We can use the root test.

The root test states that if the limit of the nth root of the absolute value of the nth term of a series is less than 1, then the series is convergent. If the limit is greater than or equal to 1, then the series is divergent. If the limit is indeterminate, then the root test is inconclusive and we need to use a different test.

To apply the root test to the series √ 1/4 +√ 2/6 + √ 3/8 + ........​, we can take the nth root of the absolute value of the nth term of the series for each value of n. In this case, the nth term of the series is √ (n-1)/(2n). Therefore, we can take the nth root of the absolute value of this expression for each value of n:

√|√ (1-1)/(21)| = 1

√|√ (2-1)/(22)| = 1/√2

√|√ (3-1)/(23)| = 1/√3

√|√ (4-1)/(24)| = 1/2

As we can see, the limit of the nth root of the absolute value of the nth term of the series is 1, which is greater than or equal to 1. Therefore, according to the root test, the series √ 1/4 +√ 2/6 + √ 3/8 + ........​ is divergent.

I hope this helps! Let me know if you have any other questions or need further assistance.

Answer:

0.0819

Step-by-step explanation:

The function that is decreasing on the same interval as the given function f(x) is h(x) = 2x^2 + 8x + 3.

To determine if a function is increasing or decreasing, we look at the sign of its derivative. If the derivative is positive, the function is increasing, and if the derivative is negative, the function is decreasing.

Taking the derivative of h(x) with respect to x, we get h'(x) = 4x + 8. To find the interval on which h(x) is decreasing, we need to find the values of x for which h'(x) < 0.

Setting h'(x) < 0, we have 4x + 8 < 0. Solving this inequality, we find x < -2.

Therefore, h(x) is decreasing for x < -2. Since the interval where h(x) is decreasing matches the interval for the given function f(x), we can conclude that h(x) = 2x^2 + 8x + 3 is the function that is decreasing on the same interval as f(x).

Overall, the function h(x) = 2x^2 + 8x + 3 is decreasing on the interval x < -2, which aligns with the interval of the given function f(x).

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\(\sqrt[3]{a^2+b^2} = (a^2+b^2)^{\frac{1}{3}}\)

Using common factor method, sum of the given expressions is 17.14m + 9.37

what is common factor ?

In mathematics, a common factor is a factor that two or more numbers have in common. For example, the numbers 12 and 18 have common factors of 1, 2, 3, and 6. The greatest common factor (GCF) is the largest number that divides evenly into two or more numbers.

In algebra, we often use the term "common factor" when referring to expressions. When two or more algebraic expressions have a factor in common, we can use the distributive property to factor out the common factor.

According to the question:
To add the expressions (5.19+4m)+(4.18+3.95m), we can first group the like terms:

(5.19 + 4.18) + (4m + 3.95m)

9.37 + 7.95m

So, the sum of the expressions is:

(5.19+4m)+(4.18+3.95m) = 9.37 + 7.95m

Now, we can use the distributive property to factor out a common factor of m from 7.95m:

9.37 + 7.95m = 4m + (5.19 + 7.95)m

We can factor out a common factor of 1 from (5.19 + 7.95)m:

4m + (5.19 + 7.95)m = (4 + 5.19 + 7.95)m

Adding the coefficients, we get:

4 + 5.19 + 7.95 = 17.14

Therefore, the sum of the expressions is:

(5.19+4m)+(4.18+3.95m) = (4m+5.19)+(3.95m+4.18)= 17.14m + 9.37.

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Amount of $150,000 represents 42.86% of $350,000.

Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem.

We have Danny’s home cost $350,000. The federal government program for flood damage insurance covers only $150,000.

Assume that it represents [x%] percent of the total value. Then, we can write -

x = (150000/350000) x 100

x = 42.86%

Therefore, $150,000 represents 42.86% of $350,000.

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Differentiating both sides of

xy = 99

with respect to t yields

x dy/dt + y dx/dt = 0

When x = 11, we have

11y = 99   ==>   y = 9

and we're given that dy/dt = -4 at this point, which means

11 (-4) + 9 dx/dt = 0   ==>   dx/dt = 44/9

Step-by-step explanation:

it seems you solved the tricky part yourself already.

just to be sure, let's do the first derivative here again.

the easiest way would be for me to simply multiply the functional expression out and then do a simple derivative action ...

f(t) = (t² + 6t + 7)(3t² + 3) = 3t⁴ + 3t² + 18t³ + 18t + 21t² + 21 =

= 3t⁴ + 18t³ + 24t² + 18t + 21

f'(t) = 12t³ + 54t² + 48t + 18

and now comes the simple part (what was your problem here, don't you know how functions work ? then you are in a completely wrong class doing derivatives; for that you need to understand what functions are, and how they work). we calculate the function result of f'(2).

we simply put the input number (2) at every place of the input variable (t).

so,

f'(2) = 12×2³ + 54×2² + 48×2 + 18 = 96 + 216 + 96 + 18 =

= 426

Answer: 21.15 ft²

Step-by-step explanation:

We can use the formula for the area of a triangle:

(b×h)/2

In this case, the base is 9 and the height is 4.7.

So, we substitute the variables with the numbers in this problem.

(9 × 4.7)/2

9 × 4.7 = 42.3

42.3/2 = 21.15

So, our final answer is 21.15 ft²

Answer:

x≥√πax≥πa or x ≤−√πa

Step-by-step explanation:

Answer:it is A or D

Step-by-step explanation:

The City A and Abilene are nearest to each other

The Austin and Abilene are farthest apart from each other

Here the two angles of the triangle = 59 degrees and 64 degrees

The sum of the angles in a triangle is 180 degrees

Then the third angle will be

59 + 64 + x = 180

123 + x = 180

x = 180 - 123

x = 57 degrees

The third city name is not visible so consider it as city A

Part a

Here the smallest angle is 57 degrees

Opposite side of the angle will be the smallest distance

That is the distance between city A and Abilene

Part b

Here the largest angle is 64 degrees

The opposite side of the angle will be largest distance

That is the distance between Austin and Abilene

Therefore, the City A and Abilene are nearest to each other and Austin and Abilene are farthest apart from each other

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Answer:

2/11

Step-by-step explanation:

Answer:

To calculate 2 3/4 of 500 grams, follow these steps:

1. Convert the mixed number to an improper fraction:

2 3/4 = (2 x 4 + 3)/4 = 11/4

2. Multiply the improper fraction by 500:

11/4 x 500 = (11 x 500)/4 = 2,750/4

3. Simplify the fraction by dividing the numerator and denominator by their greatest common factor, which is 2:

2,750/4 = (2 x 1,375)/(2 x 2) = 1,375/2

Therefore, 2 3/4 of 500 grams is equal to 1,375/2 grams or 687.5 grams.

Step-by-step explanation:

Four triangles can create a set of pattern blocks that includes a total of four rhombuses.

To understand why, it's essential first to understand what pattern blocks are. Pattern blocks are shapes that are commonly used in early childhood education to teach math concepts like geometry, spatial reasoning, and fractions. They come in different shapes, including triangles, squares, hexagons, trapezoids, and rhombuses.

To create a set of pattern blocks using triangles, one can use four equilateral triangles with the same side length. When these triangles are arranged together, they form a larger equilateral triangle, as each external side of each small triangle connects to a side of another triangle. This larger equilateral triangle can then be divided into four smaller rhombuses by using two diagonals (lines connecting opposite corners) to form a "X" shape. Each of these four smaller rhombuses is made up of two adjacent triangles and forms a diamond shape. Therefore, it can be said that four equilateral triangles can form a set of four rhombuses within an equilateral triangle pattern block set.

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The point (2, 5) is a solution to the system of equations: y = x + 2.

Let's test each system of equations:

y = x - 8

2x + y = 7

Substituting x = 2 and y = 5 into the equations:

5 = 2 - 8 (not true)

2(2) + 5 = 7 (not true)

The point (2, 5) is not a solution to this system of equations.

y = x + 2

y = x + 5

y = -1/2 * x + 6

y = 3x - 1

y = 2/3 * x + 6

Substituting x = 2 and y = 5 into the equations:

5 = 2 + 2 (true)

5 = 2 + 5 (not true)

5 = -1/2 * 2 + 6 (not true)

5 = 3 * 2 - 1 (not true)

5 = 2/3 * 2 + 6 (not true)

The point (2, 5) is a solution to the equation y = x + 2.

3y + 6x - 18 = 0

Substituting x = 2 and y = 5 into the equation:

3(5) + 6(2) - 18 = 0

15 + 12 - 18 = 0

27 - 18 = 0

9 = 0 (not true)

The point (2, 5) is not a solution to this equation.

Based on the tests, the point (2, 5) is a solution to the system of equations: y = x + 2.

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Answer:

A

Step-by-step explanation:

General formula to find Volume is Base Area x Height

1. Volume of triangular prism:

  10cm x 12cm² = 120cm³

3. Volume of rectangular prism:

   10cm x (3cm x 4cm) = 10cm x 12cm² = 120cm³

If the train travels at an average speed of 50 Km/h, it would be late by 10 minutes.

Speed is simply referred to as distance traveled per unit time.

It is expressed as:

Speed = distance / time

Given that the train running between two stations 50 Km apart arrives on time if it travels at an average speed of 60 km/h.

The time taken by the train to travel 50 km at an average speed of 60 km/h can be calculated using the formula:

Speed = distance / time

time = distance / speed

time = 50 km / 60 km/h

time = 5/6 hour

Next, if the train travels at an average speed of 50 km/h, the time taken to cover the same distance of 50 km would be:

Speed = distance / time

time = distance / speed

time = 50 km / 50 km/h

time = 1 hour

Now, the difference in time between the two scenarios would be:

time difference = 1 hour - 5/6 hour

time = 1/6 hour

Convert to minutes

time = 1/6 × 60

time = 10 minutes

Therefore, the train would be late by 10 minutes.

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