If (fg)(x) = h(x) such that h of x is equal to the square root of the quantity 8 times x plus 6 end quantity which of the following could accurately represent f and g?

Answer: 420 minutes in 7 hours. 2 minutes in 120 seconds.

Step-by-step explanation: Multiply 7x60, as there are 60 minutes per hour. Divide 120/60 to find how many minutes are within those many seconds.

Answer:

Area of park = 2976 ft²

Length of park = 62 ft

Width of park = ?

Area of park = length ×width

2976 = 62 × width

width = 2976/62

=48 ft

Considering the relationship between velocity, distance and time, it is found that the total distance traveled was of 380 miles.

Velocity is distance divided by time, that is:

v = d/t.

For the first day, we have that:

v = 40, t = t + 2, d = d + 20, hence:

40 = (d + 20)/(t + 2)

For the second day, we have that:

v = 60

60 = d/t

d = 60t

Then, replacing in the first equation:

40 = (60t + 20)(t + 2)

60t + 20 = 40t + 80

20t = 60

t = 3.

Then the distances are given by:

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Answer:

X = 2

Y = 1

Step-by-step explanation:

Solve by substitution

[tex]y = x - 4 \\ 2x + y = 5 \\ \\ y = x - 4 \\ 2x - 5 = - y \\ \\ y = x - 4 \\ - y = 2x - 5 \\ \\ add \: the \: two \: equations \\ \\ 0 = 3x - 9 \\ 9 = 3x \\ \frac{9}{3} = \frac{3x}{x} \\ x =3 \\ \\ substitute \: 3 \: for \: x \: in \: one \: of \: the \: equations \: to \: find \: y \\ \\ y = x - 4 \\ y = 3 - 4 \\ y = - 1 \\ \\ solution \: (3. - 1)[/tex]

See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

Area models are shapes used to model or illustrate products, multiplications, divisions and quotients

The equation is given as:

4x^2+12x+9 = (2x+3)^2

Express (2x+3)^2 as the product of (2x+3) and (2x+3)

4x^2+12x+9 = (2x+3) * (2x+3)

The above means that the area model is a square.

So, the side lengths of the model must be equal, where the side lengths are 2x + 3 and the area of the square is 4x^2+12x+9

See attachment for the area model of the equation 4x^2+12x+9 = (2x+3)^2

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If an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.

Given that arc has measure of 7π/4.

We are required to convert the measure from radian to degree measure.

Converting means chaning of units from one to another.

To convert 7π/4 into degrees we have to just put π=180 then we will get the value in degrees.

7π/4=7*180/4

=7*45

=315 degrees

Now we have to convert 60 degrees into radians.

60 degrees=60*π/180

=π/3

Hence if an arc has measure 7π/4 radians then it will be having 315 degrees and 60° in radian is π/3.

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Answer: 40 inches

Step-by-step explanation: If the 20 points on the line were spaced 1 inch apart, the result would be 20 inches. Each point you're going to is 1 inch in spacing and there is only going to be 20 inches of spacing (1 inch per point.)

For 2 inches spaced apart, the result would be simply 40 inches. You just need to add the distance of 20 more to the already distance of 20 points, since if 2 were to be divided, it would be 1, which is 20 inches in distance as stated. Another 20 points would be another inch in distance, and adding them gives you 2 inches in distance or 40 inches all together.

I apologize if I wasn't clear enough, I couldn't find a way to explain it as good as I thought it was in my mind.

Hope it helped though!

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Given : Chords A C and B D intersect at point E.  Length of Different segments is given in terms of x

To find :  Length of chord BD

Solution:

Chords A C and B D intersect at point E.

=> AE * CE   = BE * DE

AE = x

CE = x + 12

BE = x + 2

D = x + 5

=> x(x + 12) = (x + 2)(x + 5)

=> x² + 12x  = x²  + 7x + 10

=> 5x = 10

=> x = 2

BD = BE + DE

= x + 2 + x + 5

= 2x + 7

putting x = 2

=> BD = 2 (2) + 7

Applying the intersecting chord theorem, the length of segment CE in is: 2.5 units.

In geometry, the intersecting chords theorem is the theorem that defines the relation of the four line segments formed when two chords of a circle intersect each other at a point in the circle.

According to the intersecting chords theorem, the products of the lengths of the line segments that are formed on each chord are congruent or equal to each other.

In the diagram given, we have chords AC and BD intersecting at point E to form the following line segments:

BE = BD - DE = 7 - 2 = 5 units

DE = 2 units

AE = 4 units

CE = ?

Based on the intersecting chord theorem, we have:

(BE)(DE) = (AE)(CE)

Plug in the values

(5)(2) = (4)(CE)

10 = 4(CE)

Divide both sides by 4

10/4 = 4(CE)/4

2.5 = CE

CE = 2.5 units

Thus, applying the intersecting chord theorem, the length of segment CE in the circle given is: 2.5 units.

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58 min/day  rate did she practice in minutes per day.

What is  time?

1 day = 2030 min ÷ (5 weeks × 7 days)

1 day = 2030 ÷ 35

1 day = 58 minutes

rate = 58 min/day

Therefore, 58 min/day  rate did she practice in minutes per day.

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Answer:

Step-by-step explanation:

6*[4-(42-63)]=

6*[4-(-21)]=

6*[4+21]=

6*25=150.

6*[4-9÷3]=

6*[4-27]=

6*(-23)=-138.

6*[4-3]=

6*1=6.

Answer:

No real solutions.

Step-by-step explanation:

To solve this, we need to use Quadratic Formula.

Quadratic Formula:

[tex]x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ [/tex]

in the form of:

[tex]a {x}^{2} + bx + c[/tex]

Given information from the question, we can deduce:

a = -1

b = -2

c = 5

Let's substitute these values into the formula.

[tex]x = \frac{ - ( - 2) + - \sqrt{ {( - 2)}^{2} - 4( - 1)( -5)} }{2( - 1)} \\ = no \: real \: solutions[/tex]

if you punch these into the calculator.

The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.

Hence, f(-3/5) = 101/25.

Given the function; f(x) = ( 8x² - 2x + 4 ) / 2

To determine the value of the function when x = -3/5, we simply replace the variable x with -3/5 in the function.

f(x) = ( 8x² - 2x + 4 ) / 2

f(-3/5) = ( 8(-3/5)² - 2(-3/5) + 4 ) / 2

Divide each term by 2

f(-3/5) = 4(-3/5)² - (-3/5) + 2

f(-3/5) = 4(9/25) - (-3/5) + 2

f(-3/5) = 36/25 +3/5 + 2

f(-3/5) = ( 36 + 3×5 + 2×25 ) / 25

f(-3/5) = ( 36 + 15 + 50 ) / 25

f(-3/5) = 101/25

The value of the function f(x) = ( 8x² - 2x + 4 ) / 2 when x = -3/5 is 101/25.

Hence, f(-3/5) = 101/25.

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Answer:

(-4, -18).

Step-by-step explanation:

f(x = x^2 + 8x - 2         Completing the square on x^2 + 8x:-

     = (x + 4)^2 - 16 - 2

     = (x + 4)^2 - 18

- which is the vertex form of f(x)

The vertex of

(x - h)^2 + k  is at (h, k)

So the vertex of f(x) is at (-4, -18)

Answer:

  2.57

Step-by-step explanation:

The mean absolute deviation is the mean of the absolute values of the differences from the mean.

The mean of the dataset is the sum of values, divided by their number:

  mean = (20 +16 +21 +16 +22 +16 +15)/7 = 126/7 = 18

The absolute values of the differences from 18 will have an average of ...

  mean(|differences|) = (2 +2 +3 +2 +4 +2 +3)/7 = 18/7

  mad(data) ≈ 2.57

__

Additional comment

Some calculators have the mad( ) function built-in. See the second attachment, for example.

Answer: Third Graph

Step-by-step explanation:

Given inequality

|x| + 1 > 2

Subtract 1 on both sides

|x| + 1 - 1 > 2 - 1

|x| > 1

Simplify the absolute value sign

x > 1 or x < -1

Apply the inequality to the graph

Since it is less than or greater than, the circle should be hollow

Since it is less than -1 or greater than 1, one line should point to the left and another should point to the right

Therefore, it should be the Third Graph

Answer:

Step-by-step explanation:

here is an solution :

Answer:

Its (-3,-5)

Step-by-step explanation:

Hope This Helps:))

From the calculations below, it is seen that the measure of angle WZY is gotten to be 71°

The lines ZY and ZW are tangents to the attached circle which is centered at x.

From the properties of circles, the tangents (ZY and ZW) from an external point to the circle make an angle of 90° to the radius of the circle. i.e. XW and ZY respectively.

From the attached diagram, we see that angles ZWX and ZYX are 90° each. Since WXYZ is a quadrilateral the sum of its internal angles is 360°.

Out of the four angles of the quadrilateral, the three angles are seen as 109°, 90°, 90°. Therefore, the fourth angle is;

∠WZY = 360° - (90° + 90° + 109°)

∠WZY = 360° - 289°

∠WZY = 71°

Therefore, we can conclude from the calculations above that the measure of angle WZY is gotten to be 71°

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Answer:  B. 71°

Step-by-step explanation:  TRUST ME!!! Answer is correct on Edge!!! :)

I got it right!

Answer:

Step-by-step explanation:

Answer:

speed equals distance over time.

To and fro, distance=speed×time(ts)

distance=900×18=16,200km.

therefore, ts=16,200

since, speed = distance/time

therefore, time taken is inversely proportional to speed making D the best option.

the volume of the hexagonal prism is 184. 75 cm^3

It is important to note that the volume of a hexagonal prism is given as;

V = (2/√3) × ap2 × h

Where

From the information given, we have the values of the following parameters;

height = 10cm

apothem = 4cm

base edge = 6cm

Now, let's  substitute the value of the parameters

Volume = (2/√3) × ap^2 × h

Volume = 2/√3 × 4^2 × 10

Multiply through

Volume = 1. 1547 × 16 × 10

Volume = 184. 75 cm^3

Thus, the volume of the hexagonal prism is 184. 75 cm^3

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The amount made per minute is $1.28 * 10^7

Fractions are written as a ratio of two numbers. For instance a/b is a fraction.

According to the question, a certain animated movie earned $1.1 * 10^9 every 9.1 * 10^1 minutes.

$1.1 * 10^9 = 9.1 * 10^1

In order to determine the amount earned per minute;

x = 1minute

Divide both expressions

1.1 * 10^9/x = 9.1 * 10^1

x = 1.1 * 10^9 /9.1 * 10^1

Divide the result

x = 1.1 * 10^9 /9.1 * 10^1

x = 0.12 *10^8
x = $1.28 * 10^7

Hence the amount made per minute is $1.28 * 10^7

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The amount of cloth needed to make 1 headband is 10 meters.

Cloth needed to make 1 headband = Number of headbands Anne made / Total clothes used

= 6 ÷ 3/5

= 6 × 5/3

= (6 × 5) / 3

= 30/3

= 10 meters

Therefore, the amount of cloth needed to make 1 headband is 10 meters.

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Given the:

ln(x + 6) - ln(2x - 1) = 1

Using the logarithm rule:

We know,

Simplifying we get,

By cross multiplication we get,

Therefore, the value of x is 1.97.

The correct option in the exercise ln (x + 6) - ln (2x - 1) = 1 is alternative "D".

The distributions of data can be characterized along three aspects or dimensions, namely location, spread, and shape. The spread (variance, range, interquartile range) aspects represent variation of the data or the spread of the data distributions.

About the Distribution of Data:

The idea of a distribution is fundamental to illustrating any output from a production process. Any manufacturing process output will not always produce the same value when it is measured, leading to distributions.

The measured values will naturally disperse around a central tendency value. A distribution is the name given to this dispersion around a core value. It is characterized by 3 aspects - location, spread, and shape.

Mean or median represent the location of the distribution numerically. Most common numerical measures that represent the spread are variance, range, and interquartile range. Skewness or kurtosis tell about the shape of the distribution.

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The y-intercept of the line is (0,7).

Given the pairs of a line in the coordinate plane are (x, y) (-72,25), (-54,13) and (-36,11).

First we will find the slope of the linear equation

The formula for calculating the slope between two points is equal to

m = (y₂-y₁) / (x₂-x₁)

take points (-54,13) and (-36.,11)

by substituting the values ​​in the above formula, we get

m = (11-13) / (- 36 - (- 54))

m = -2 / 18

m = -1 / 9

Now, we will find the equation for the line in point-slope form

y-y₁ = m (x-x₁)

we have m = -1 / 9 and (x₁, y₁) = (- 36.11)

Further, substitute the values ​​in the above equation, we get

y-11 = (- 1/9) (x + 36) ..... (1)

Convert the equation to the form of a slope intercept

y = mx + b

isolate the variable y in equation (1), we get

y-11 = (- x / 9) -4

y = (- x / 9) - 4 + 11

y = (- x / 9) +7

Here, b=7

Hence, the y-intercept of the line for the pairs of lines in the coordinate plane(x,y) is (-72,25), (-54,13) and (-36,11) is the point (0,7).

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Answer:

C. 4≤x≤6

Step-by-step explanation:

First things first, let’s learn the difference between domain and range. Domain is the spread of the x values and range is the spread of the y values. This means that in this question, you can rule out options A and B because those could potentially show range. Now we are left with options C and D. When we look at the first x coordinate, we see that it’s a 4. The last x coordinate is a 6. This means that the domain is greater than or equal to 4, but less than or equal to 6. You can also represent it as 4≤x≤6.

Hope that helps! Have a fantastic day!

The volume of the cube that perfectly fits an 18 ft³ pyramid is calculated as (C) 54 ft³.

To find the volume of the cube that perfectly fits an 18 ft³ pyramid:

We have been provided that:

Therefore, the volume of the cube that perfectly fits an 18 ft³ pyramid is calculated as (C) 54 ft³.

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The correct question is given below:

The volume of a pyramid that fits exactly inside a cube is 18 cubic feet. what is the volume of the cube?

(A) 6 cubic feet

(B) 18 cubic feet

(C) 54 cubic feet

(D) 72 cubic feet

A vertically opposite angle is a pair of angles formed due to the intersection of two lines, and are said to be equal. Thus the angle that is the same as <BPD is <APC.

ii. The value of x is [tex]47^{o}[/tex].

The intersection of two or more lines at a point will always produce a set of angles. Some of these angles when compared may have similar measures or properties.

Two angles can be equal with respect to their measure if they are vertically opposite. Vertically opposite angles are angles formed when two lines intersect, such that a pair of opposite angles about the point of intersection are equal.

Thus from the given question, the angle that is the same as <PBD is <APC.

i.e <BPD ≅ <APC (vertically opposite property)

Also,

x + 133 = 180 (sum of angles on a straight line)

x = 180 - 133

  = 47

x = [tex]47^{o}[/tex]

Therefore the value of x is [tex]47^{o}[/tex].

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