If FG = 10x − 10, GH = x + 4, and FH = 16, what is FG?

The elevation at the lower end of a drain is 119.8 feet. For the second drain difference in feet will be 10.55 feet and in inches will be 126.6 inch.

The height above or below a fixed reference point, most frequently a reference geoid, which is a mathematical representation of the Earth's sea level as an equipotential gravitational surface, determines a location's elevation. A vertical surface is depicted in an elevation when viewed from a point perpendicular to the viewer's picture plane. You are looking at the front elevation, for instance, if you are standing directly in front of a building and viewing its front. The height between a point and a horizontal surface is known as HEIGHT. The height of a point above (or below) sea level is known as its ELEVATION.

Here,

a. The length of drain= 52 feet

the gradual decrease=0.125 ft

elevation at high end=126.30 feet

elevation at low end,

=126.3-(52*0.125)

=126.3-6.5

=119.8 feet

b. The elevation at one end=94.67 feet

The elevation at other end=84.12 feet

The difference in elevation,

=94.67-84.12

=10.55 feet

=10.55*12

=126.6 inches

The elevation of a drain's lower end is 119.8 feet. The second drain will differ by 10.55 feet in feet and 126.6 inches in inches.

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The average rate of change of f(x) on the interval  30 ≤ x ≤ 60 is r = 1/5.

For a function f(x), we define the average rate of change over an interval:

a ≤x ≤b is given by:

( f(b) - f(a))/(b - a)

In this case we have the function defined by the table and the interval:

30 ≤ x ≤ 60

On the table we can see:

f(60) = 19

f(30) = 13

Then the average rate of change is:

r = (19 - 13)/(60 - 30) = 6/30 = 1/5

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Answer: 2-i

Step-by-step explanation:

multiply the fraction by 3-i/3-i

Answer:

whats the question

The time spent exercising for a student who spends 6 hours texting is 6 hours.

The scatter plot is given in the question,

As per the given scatter plot, we take the two points (9, 1) and (3,7).

The equation of the line of best fit:

Let the approximate equation would be as:

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

x₁ = 9, y₁ = 1

x₂ =3, y₂ = 7

y - y₁ = (y₂ - y₁)/(x₂ -x₁ )[x -x₁]

y - 1 = (7 - 1)/(3 - 9)](x - 9)

y - 1 = (- 6/6)(x - 9)

y - 1 =  -1(x - 9)

y = -x + 9+ 1

y = -x + 10 ...(i)

The time spent exercising by a student who spends 4 hours texting

This means that x = 4.

Substitute the value x =4 in the equation (i), and solve for y

y = -4 + 10

y = 6

Hence, the time spent exercising for a student who spends 6 hours texting is 6 hours.

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The equation that shows the relationship between the number of hours Jack's crew works, x, and the total number of yards of pavement laid, y will be;

⇒ y = 40 + 15x

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

Sanjay and his paving crew laid 40 yards of new pavement.

And, They can lay 15 yards of new pavement per hour.

Now,

Let the number of hours Jack's crew works = x

And, The total number of yards of pavement laid = y

Hence, We can formulate;

An equation that shows the relationship between x and y will be;

y = 15x + 40

Thus, The equation that shows the relationship between the number of hours Jack's crew works, x, and the total number of yards of pavement laid, y will be;

⇒ y = 40 + 15x

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Answer:

1st: One solution

2nd: Infinite many solutions

3rd: No solution

4th: No Solution

5th: One Solution

Step-by-step explanation:

1st:

The solution is (6,9)

x = 6 if a vertical line going though (6,0)

y = 9 is a horizontal line going through (0,9)

The two lines with intersect at (6,9)

2nd:

3y = 15x + 6  If you divide all the way through by 3, you get

y = 5x + 2

This is identical to the first equation given.  Since it is the same line, the answer is infinite many solutions.

3rd:

3y = x + 2  Divide all the way through by 3

y = 1/3 x + 2/3

9y = 3x + 7  Divide all the way through by 9

y = 1/3 x + 7/9

Since the slopes are the same in both equations (1/3), these line are parallel and will never intersect.

4th:

Since the slopes are both the same (2), the lines are parallel and they will never intersect, so the answer is no solution.

5th:

2y = 3x  Divide both sides by 2

y = 3/2

-5y = -10  Divide both sides by -5

y = 2x

These equations are proportional so they go through the origin.  They both have a y intercept of zero, so they intersect at (0,0).  The answer is one solution.

Answer:

x = 12 m

Step-by-step explanation:

the area (A) of a rectangle is calculated as

A = length × width

here A = 44 , then

x × 3 [tex]\frac{3}{4}[/tex] = 44 ( change mixed number to improper fraction )

x × [tex]\frac{11}{3}[/tex] = 44 ( multiply both sides by 3 to clear the fraction )

11x = 132 ( divide both sides by 11 )

x = 12 m

The image after a 270 rotation is (4, -3)

If the point of rotation is not the origin, the steps are as follows:

1. Subtract the point of rotation off each vertex point of

the shape

2. Rotate as you would around the origin

3. Add the point of rotation back to each vertex point of

the shape

Given: R(1, 2) after a 270 rotation about (0, - 2)

step1: (1-0, 2-(-2)) = (1, 4)

step 2: For rotation about the origin through 270°, the image is (y, -x). Thus, (1, 4) => (4, -1)

step 3: (4, -1) => (4+0, -1+(-2) ) = (4, -3)

Therefore, the image of R(1, 2) after a 270 rotation about (0, - 2) is (4, -3)

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The differentiation of the given function is [tex]9x^2tan(x^4)[/tex] + [tex]12x^{6}sec^2(x^4)+8x^3sec^2(x^4)[/tex].

In the given question we have to differentiate the given function with respect to x.

The given function is f(x)= [tex]tan(x^4)\cdot(3x^3+2)[/tex].

We have to differentiate the given function so we differentiate using the Product Rule.

The Product Rule of Differentiation is

d/dx[h(x)g(x)]=h(x) d/dx g(x)+g(x) d/dx h(x)

In the given function the value of

h(x) = [tex]tan(x^4)[/tex] and g(x) = [tex](3x^3+2)[/tex]

So;

f'(x)= [tex]tan(x^4)[/tex]d/dx [tex](3x^3+2)[/tex] + [tex](3x^3+2)[/tex] d/dx [tex]tan(x^4)[/tex]............(1)

We firstly find the value of d/dx [tex](3x^3+2)[/tex] and d/dx [tex]tan(x^4)[/tex].

We firstly find the value of d/dx [tex](3x^3+2)[/tex]

As we know that d/dx of x^n =nx^(n-1) and d/dx a=0

So;

d/dx [tex](3x^3+2)[/tex]= 3 d/dx [tex]x^3[/tex]+d/dx 2

d/dx [tex](3x^3+2)[/tex]=3(3[tex]x^2[/tex])+0

d/dx [tex](3x^3+2)[/tex]=9[tex]x^2[/tex]

Now finding the value of d/dx tan([tex]x^4[/tex])

d/dx [tex]tan(x^4)[/tex] = d/dx [tex]tan(x^4)[/tex] d/dx [tex]x^4[/tex]

d/dx [tex]tan(x^4)[/tex]= [tex]sec^2(x^4)\cdot(4x^3)[/tex]

d/dx [tex]tan(x^4)[/tex]= [tex]4x^3sec^2(x^4)[/tex]

Now putting the values of differentiation in equation 1

f'(x)= [tex]tan(x^4)\cdot9x^2[/tex] + [tex](3x^3+2)\cdot4x^3sec^2(x^4)[/tex]

f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]3x^3\cdot4x^3sec^2(x^4)+2\cdot4x^3sec^2(x^4)[/tex]

Simplifying

f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]12x^{3+3}sec^2(x^4)+8x^3sec^2(x^4)[/tex]

f'(x)= [tex]9x^2tan(x^4)[/tex] + [tex]12x^{6}sec^2(x^4)+8x^3sec^2(x^4)[/tex]

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Answer:

x+7=4/3x-1/3 One solution was found : x = 22 Rearrange: Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : ... 3x-9/4x-12: correct answer right here

Step-by-step explanation:

The pitcher that has the lowest number of runs allowed per inning is Randy.

In order to determine the pitcher that has the lowest number of runs per innings, divide the number of runs of each player by the number of innings of that player.

Division is the mathematical operation that is used to calculate the quotient of two or more numbers. It entails grouping a number into equal parts using another number.

Number of runs per innings = number of runs / number of innings

Number of runs per innings for Randy : (2 / 3) = 0.667

Number of runs per innings for Felix : (4 / 5) = 0.80

Number of runs per innings for Johan: (5 / 7) = 0.714

Here is the complete question:

A baseball team has three different pitchers. Randy pitched 3 innings and allowed 2 runs, Felix pitched 5 innings and allowed 4 runs, and Johan pitched 7 innings and allowed 5 runs.

Which pitcher has the lowest number of runs allowed per inning?

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Answer:

[tex]\dfrac{1}{2}[/tex]

Step-by-step explanation:

   Number of cards = 52

 Number of black cards = 13 (club) + 13 (spade)

                                        = 26

[tex]\sf P(\text{getting a black card})=\dfrac{26}{52}[/tex]

                                     [tex]\sf =\dfrac{1}{2}[/tex]

Answer:

I=PRT/100

I100=PRT dbs by Rt

l100/RT = P

48000*100/6*6

P=

[tex]{ \qquad\qquad\huge\underline{{\sf Answer}}} [/tex]

Here we go ~

[tex] \textsf{1. Numbers are : 36, 3, 12 } [/tex]

[tex] \textsf{HCF = product of total common factors of} [/tex][tex] \textsf{all three numbers, i.e : 2 } [/tex]

[tex] \textsf{LCM = product of highest power of each factor } [/tex][tex] \textsf{present in any three of them,} [/tex][tex] \textsf{i.e : 2⁵ × 3 = 32 × 3 = 96} [/tex]

Similarly,

[tex] \textsf{2. Numbers are : 6, 54, 12} [/tex]

[tex] \textsf{GCD = 2 × 3 = 6 } [/tex]

[tex] \textsf{[ 2 and 3 are the only ones common} [/tex] [tex] \textsf{among all three ]} [/tex]

[tex] \textsf{LCM = 2² × 3³ = 4 × 27 = 108} [/tex]

[tex] \textsf{3. Numbers are : 16, 8, 12 } [/tex]

[tex] \textsf{GCD = 2 × 2 = 4 } [/tex]

[tex] \textsf{LCM = 2⁴ × 3 = 16 × 3 = 48} [/tex]

Answer:

Numbers are : 36, 3, 12

36 = 2 × 2 × 2 × 2 × 2 × 1

3 = 3 × 1

12 = 2 × 2 × 3

HCF = product of total common factors of all three numbers, i.e : 2

LCM = product of highest power of each factor present in any three of them, i.e : 2⁵ × 3 = 32 × 3 = 96

Similarly,

2. Numbers are : 6, 54, 12

6 = 2 × 3

54 = 2 × 3 × 3 × 3

12 = 2 × 2 × 3

GCD = 2 × 3 = 6

[ 2 and 3 are the only ones common among all three ]

LCM = 2² × 3³ = 4 × 27 = 108

3. Numbers are : 16, 8, 12

16 = 2 × 2 × 2 × 2

8 = 2 × 2 × 2

12 = 2 × 2 × 3

GCD = 2 × 2 = 4

LCM = 2⁴ × 3 = 16 × 3 = 48

Answer:

  (x, y) = (1, 3)

Step-by-step explanation:

You want to solve the system of equations x-y= -2; x+y=4 by the addition method.

The addition method seeks to eliminate one of the variables by adding the equations with appropriate multipliers so that one of the coefficients becomes zero.

Here, we observe that the coefficient of y in one equation is the opposite of that in the other equation. This means adding the two equations will cancel the y-terms:

  (x -y) +(x +y) = (-2) +(4)

  2x = 2 . . . . . . . . . . . . . . . . simplify; y-term is eliminated

  x = 1 . . . . . . divide by 2

  1 +y = 4 . . . . . . . substitute for x in the second equation

  y = 3 . . . . . . . . . subtract 1

The solution is (x, y) = (1, 3).

The complete table of values of the function is

x | f(x)

0 | 1

1 | 2

2 | 4

3 | 8

The ordered pairs are (x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)

The equation of the function is given as

f(x) = 2ˣ

On the incomplete table of values, we have the following x values

x = 0, 1, 2, 3

Next, we substitute x = 0, 1, 2, 3 in the equation f(x) = 2ˣ

So, we have:

f(0) = 2⁰ = 1

f(1) = 2¹ = 2

f(2) = 2² = 4

f(2) = 2³ = 8

So, the complete table is

x | f(x)

0 | 1

1 | 2

2 | 4

3 | 8

When represented as ordered pairs, we have

(x, y) = (0, 1), (1, 2), (2, 4) and (3, 8)

See attachment for the graph

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Answer:

Step-by-step explanation: 348 miles and 6 hours

Answer:

The first column is usually for the categories of the data set and the second or third column is usually for the frequency of each category.

The number written on the right of each category is its frequency

Step-by-step explanation:

The probability that the sample proportion of a large shipment of stereos will differ from the population proportion by more than 6% is 0.0063

The probability is calculated using z score, this is used to determine the amount of standard deviations a sample, X is from the mean

The z score is given by the formula

z = (X - μ) / σ

Definition of variables

mean, μ  = p = 18% = 0.18

sample size, n = 306

standard deviation, σ

= √{(p(1 - p)) / n}

= √{(0.18(1 - 0.18)) / 306}

= √{(0.18 * 0.82) / 306}

= 0.02196

The probability

differ from the population proportion by less than 3%

|X - 0.18| > 0.06

X < 0.12 OR X > 0.24

P(z < 0.12) + P(z > 0.24 )

z score for z < 0.06

z = (0.12 - 0.18) / 0.02196

= -2.7322

p value for z < -2.7322 = 0.003146

z score for z > 0.06

z = (0.24 - 0.18) / 0.02196

= 2.7322

p value for z > 2.7322 = 1 - 0.99685 = 0.003146

The probability required = 0.003146 + 0.003146 = 0.006292 = 0.63%

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Answer:

x = 22

Step-by-step explanation:

Solve for x:

x/11 = 2

multiply both sides by 11:

11(x/11) = 11(2)

x = 22

Answer:

x = 22

Step-by-step explanation:

[tex] \sf \frac{x}{11} = 2[/tex]

Use cross multiplication.

[tex] \frac{x}{11} = \frac{2}{1} \\ \\ \sf x = 2 \times 11 \\ \\ \sf \: x = 22[/tex]

Answer:

9 units

Step-by-step explanation:

We see that on the x-axis, everything is equal.

On the y-axis, there are -2 and 7.

So we are finding the distance between -2 and 7

|-2|+|7|=9

So the distance between the points is 9 units.

The solution for the variable w according to the given equation; -21 ⅓ w + 6 = 15 as required in the task content is; w = -27/64.

It follows from the task content that the value of variable w is time determined according to the given equation as in the task content.

Given the equation; -21 ⅓ w + 6 = 15.

First, the mixed number must be converted to a fraction so that we have;

-21 ⅓ = -64/3.

Hence, the equation becomes;

-64w/3 + 6 = 15

Multiply both sides of the equation by 3 so that we have;

-64w + 18 = 45

-64w = 45 - 18

-64w = 27

w = -27/64.

Ultimately, the solution for variable w according to the equation as given in the task content is; w = -27/64.

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The lines p and q are parallel.

Alternate Exterior Angles are a pair of angles on the outer side of each of those two lines, but on opposite sides of the transversal.

Given a figure,

Since, ∠ 1 ≅ ∠ 5 and they are alternate exterior angles, then we can conclude that p║q by alternate exterior angles theorem.

Hence, The lines p and q are parallel.

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Answer:

1350 ml

Step-by-step explanation:

(1800 : 4) * 3

450 * 3

1350 ml

Answer:

Commutative Property of Addition2. Distributive propertyStep-by-step explanation:Given[tex]Line 1: 4(8+9x)

Answer:

21 gallons

Step-by-step explanation:

[tex]\frac{9}{198} \times 462 \\ \\ =\frac{462}{22} \\ \\ =21[/tex]