Five times a number decreased by nine is equal to twice the number increased by 23. Which equation could be usedto solve the problem?5x - 9 = x + 235x - 9 = 2x + 235x + 23 + 2x = 235x + 23 = 2x + 23

Answer:

Step-by-step explanation:

it is d

Answer:

(6x- 4) (x+2)

Step-by-step explanation:

Hope this will help you

Answer:

9 hours

Steps:

3x + 20 = 47

3x = 27

x = 9

Step-by-step explanation:

The starting temperature is 20°F, and it rises 3° every hour.

We know in x hours, the temperature will be 47°F.

So our equation is 3x + 20 = 47

Since the temperature is already 20°, we will subtract 20 from 47, leaving us with 27.

What number, multiplied by 3, is 27?

9.

Therefore, we know in 9 hours, the temperature will be 47°F.

Hope this helped :)

The functions f(x) = -x² + 9 and g(x) = 6 - 2x can be plotted on the same system of axes with their intercepts labeled.

To draw the functions f(x) = -x² + 9 and g(x) = 6 - 2x on the same system of axes, we need to determine their intercepts with the x and y-axes.

Intercepts with the x-axis:

To find the x-intercepts, we set y = 0 for each function and solve for x.

For f(x):

0 = -x² + 9

x² = 9

x = ±√9

x = ±3

So, the x-intercepts of f(x) are x = -3 and x = 3.

For g(x):

0 = 6 - 2x

2x = 6

x = 6/2

x = 3

Therefore, the x-intercept of g(x) is x = 3.

Intercepts with the y-axis:

To find the y-intercepts, we set x = 0 for each function and solve for y.

For f(x):

y = -0² + 9

y = 9

So, the y-intercept of f(x) is y = 9.

For g(x):

y = 6 - 2(0)

y = 6

Therefore, the y-intercept of g(x) is y = 6.

Now, we can plot the points (-3, 0), (3, 0), (0, 9), and (0, 6) on the graph. Connect the points with a smooth curve to represent the function f(x) = -x² + 9.

The line representing g(x) = 6 - 2x will be a straight line with a slope of -2 and a y-intercept of 6.

The graph should show the curve of f(x) passing through the points (-3, 0), (3, 0), and (0, 9), and a straight line for g(x) passing through the points (3, 0) and (0, 6).

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The zeros of the polynomial function are x = -1 and x = 5

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

y = x⁴ - 4x³ - 4x² - 4x - 5

To calculate the zeros of the polynomial function, we create a graph of the polynomial

The point where the graph intersect with the x-axis are the zeros of the polynomial function

using the above as a guide, we have the following:

Zeros: x = -1 and x = 5

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The p value is calculated as 0.116

Null u = 70

alternate u ≠ 70

The alternate is a two tailed test

the test statistic calculation

t = x - u / s/√n

x = 85 + 77 + 82 + 68 + 72 + 69 / 6

= 75.5

standard deviation s = \(\sqrt{\frac{(85- 75.5)^2+(77- 75.5)^2+...(69- 75.5)^2}{6-1} }\)

= 7.01

Test stat = (75.5 - 70) / 7.01/√6

= 1.92

degree of freedom = 6 - 1 = 5

this is 2 tailed

p value using excel = tdist( 1.8, 5 , 2)

= 0.116

We fail to reject the null hypothesis because it is greater than the level of significance

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Answer:

X=110

Step-by-step explanation:

The height of the cliff is 109.58 meters.

Angle of elevation is the angle which is between a horizontal line and the line of sight which is pointed upwards.

Given that,

We get a right angled triangle ABC where A represents the base of the cliff and C is the point of the top of the hill.

B is the point which is at a distance of 235 meters from the base of a cliff.

Length of AB = 235 meters

Angle of elevation to the cliff top, ∠B = 25 degrees

AC represents the height of the cliff. Let it be x.

Using the trigonometric ratio,

tan B = AC / AB

tan 25 = x / 235

x = 235 × tan 25

  = 109.58 meters

Hence the height of the cliff is 109.58 meters.

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Therefore , the solution of the given problem of function comes out to be  (g - f)(-1) = 29.

The math lesson covers an extensive variety of subjects, including geometry, integers, one's divisions, construction, and both real and imagined geographic places. A work covers the connections between various variable that all work together to produce the same result. A utility is made up of a variety of distinctive components that cooperate to create distinct results for each input.

Here,

We must first evaluate g(-1) and f(-1) before subtracting the results to obtain (g - f)(-1).

We possess

=> g(x) = 5x + 18

=>  g(-1) = 5(-1) + 18 = 13

=>  f(x) = x² - 17

=>  f(-1) = (-1)² - 17 = -16

Therefore:

=>  (g - f)(-1) = g(-1) - f(-1) = 13 - (-16) = 29

So, (g - f)(-1) = 29.

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Yes, there is an analogous ratio between 2:1 and 20:10.

We just cancel by a common factor. So 4:2=2:1 . The simplest representation of the ratio 4 to 2 is the ratio 2 to 1. Also, since each pair of numbers has the same relationship to one another, the ratios are equivalent.

By dividing the terms of each ratio by their greatest common factor, we may simplify both ratios to explain why.

As the greatest common factor for the ratio 2:1 is 1, additional simplification is not necessary.

The greatest common factor for the ratio 20:10 is 10. When we multiply both terms by 10, we get:

20 ÷ 10 : 10 ÷ 10

= 2 : 1

As a result, both ratios have the same reduced form, 2:1, making them equal.

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Answer

The Answer is A C D

Step-by-step explanation:

Answer:

124 degrees since all angles should equal 180 degrees.

Answer:

So if you think about it, 180° is a full angle. So if you take the 180° and subtract the 19° and the 37° you should get your remaining angle. the answer I got for the angle is 124°. To check your work, 124° + 19° + 37° = 180°

Step-by-step explanation:

Hope that this has helped you out! :)

The Galois group of f over R is isomorphic to the symmetric group S4. The given statement "Each intermediate field of F/Q is a Galois extension of Q." is true because f is separable.

The roots of f are given by

x = ±(√(5) + √(2)), ±(√(5) - √(2))

Let φ be the automorphism defined by

φ(√(5) + √(2)) = √(5) + i√(2)

φ(√(5) - √(2)) = √(5) - i√(2)

φ(-√(5) + √(2)) = -√(5) - i√(2)

φ(-√(5) - √(2)) = -√(5) + i√(2)

where i is the imaginary unit. Then φ has order four since φ⁴ is the identity automorphism. Let σ be the automorphism defined by

σ(√(5) + √(2)) = -√(5) + √(2)

σ(√(5) - √(2)) = √(5) - √(2)

σ(-√(5) + √(2)) = -√(5) - √(2)

σ(-√(5) - √(2)) = √(5) + √(2)

Then σ has order two since σ² is the identity automorphism. It can be shown that the Galois group of f over Q is generated by φ and σ. Since φ has order four and σ has order two, the Galois group is a non-abelian group of order eight.

To prove or disprove that each intermediate field of F/Q is a Galois extension of Q, we need to show that each intermediate field is a splitting field of a separable polynomial over Q. Since F is the splitting field of f over Q, any intermediate field of F/Q is also a splitting field of f over Q. Since f is separable (its roots are distinct), every intermediate field of F/Q is a Galois extension of Q, and hence a splitting field of a separable polynomial over Q. Therefore, the statement is true.

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Answer:1/30 is the correct answer

Step-by-step explanation:

first, calculate the total number of chips: 4+5+1=10

since we know that chips are not replaced.

probability of finding the first white chip: 4/10 (4 white chips,10 total)

after removing 1 white chip remaining white chips=3, total chips=9

probability of finding the second white chip:3/9 (3 white chips,9 total)

after removing 1 white chip remaining white chips=2, total chips=8

probability of finding the third white chip 2/8 (2 white chips,8 total)

after removing 1 white chip remaining white chips=1, total chips=7

Now the probability of finding 3 white chips is:

probability=(4/10) * (3/9) * (2/8)=1/30

The given function has

x-intercepts: x = 0, x = 4, x = -4, x = -4i and x = 4i.

Positive or Negative:  The function f(x) = x(x − 4)³(x+4)² is positive for x > 0 and negative for x < 0.

Even or Odd: The function f(x) = x(x − 4)³(x+4)² is an even function.

End behavior: x approaches positive or negative infinity the value of f(x) approaches positive infinity.

What is a function?

A function is a mathematical relationship between a set of inputs (referred to as the domain) and a set of outputs (referred to as the range). In other words, a function assigns a unique output to each input value in the domain.

Given the function f(x) = x(x − 4)³(x+4)²

x-intercepts: The x-intercepts are the points at which the function crosses the x-axis, meaning the y value is equal to zero. To find the x-intercepts we need to set f(x) = 0 and solve for x.

x(x - 4)^3(x+4)^2 = 0

the x-intercepts of the function f(x) = x(x - 4)^3(x+4)^2 are x = 0, x = 4, x = -4, x = -4i and x = 4i.

Positive or Negative: The function f(x) = x(x − 4)³(x+4)² is positive for x > 0 and negative for x < 0.

Even or Odd: The function f(x) = x(x − 4)³(x+4)² is an even function.

End Behavior: The end behavior of this function is that as x approaches positive or negative infinity the value of f(x) approaches positive infinity.

Hence, the given function has

x-intercepts: x = 0, x = 4, x = -4, x = -4i and x = 4i.

Positive or Negative:  The function f(x) = x(x − 4)³(x+4)² is positive for x > 0 and negative for x < 0.

Even or Odd: The function f(x) = x(x − 4)³(x+4)² is an even function.

End behavior: x approaches positive or negative infinity the value of f(x) approaches positive infinity.

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Answer Key:

1. Since the question says Mr. Smith runs 2.7 miles every day of the week, you will need to multiply it with 365, the days of the year. The total answer you would get D. 985.5 miles.

| I just want to help you with #2 anyway