What is the perimeter of this composite figure?

The value of f(g(x)) in the form a + bxⁿ is 1 -5x⁻². Where a = 1, b = -5 and n = -2

From the question, we are to determine the value of f(g(x)) in the form a + bxⁿ

From the given information,

[tex]f(x) = \frac{x}{x+5}[/tex]

and

[tex]g(x) = x^{2} -5[/tex]

Then,

[tex]f(g(x)) = \frac{(x^{2} -5)}{(x^{2} -5) +5}[/tex]

∴ [tex]f(g(x)) = \frac{x^{2} -5}{x^{2} }[/tex]

Simplifying

[tex]f(g(x)) = \frac{x^{2} }{x^{2} } -\frac{5}{x^{2}}[/tex]

[tex]f(g(x)) = 1 -\frac{5}{x^{2}}[/tex]

[tex]f(g(x)) = 1 -5x^{-2}[/tex]

Hence, the value of f(g(x)) in the form a + bxⁿ is 1 -5x⁻². Where a = 1, b = -5 and n = -2.

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Answer:

  x = 2

Step-by-step explanation:

The two points have the same x-coordinates, so lie on the same vertical line:

  x = 2

Step-by-step explanation:

the slope of a line or linear equation is always the factor of the driving variable.

usually in the form of

y = ax + b

x is the variable, and a the slope.

but in our case the variable is called "n".

it does not matter, the same principle applies.

the slope is the factor of n : 1050.

and as the slope is always the ratio y/x, we are looking for a fraction form, and that would be 1050/1.

so, the third answer is correct.

Answer:

7

Step-by-step explanation:

The sides are in proportion.

Answer:

7

Step-by-step explanation:

Given,

△ABC ~ △DEF

( ~ means similar )

To find : missing side length

Similar triangle rule : -

If two triangles are similar, their corresponding sides are similar.

So,

AB ~ DE

BC ~ EF

AC ~ DF

Let the missing side length ( DF ) be " x ".

Note : -

When the corresponding sides are divided, their ratios will be same.

That is,

AB / DE

= 20 / 4

= 5 / 1

= 5 : 1

BC / EF

= 40 / 8

= 5 / 1

= 5 : 1

AC / DF should also be equal to 5 : 1.

AC / DF = 5 : 1

35 / x = 5 / 1

Cross multiply,

x * 5 = 35 * 1

5x = 35

Divide 5 on both sides,

x = 35 / 5

x = 7

Therefore,

the missing side length is 7.

Step-by-step explanation:

24.

AC = 12 = cos(angle) × AB = cos(angle) × 13

imagine a circle with center in A and radius 13.

that is why we can say AC = cos(angle) × radius, and BC = sin(angle) × radius.

cos(angle) = 12/13 = 0.923076923...

angle = 22.61986495...°

so, B is the right answer.

25.

we have a right-angled triangle.

from the point in the ground, where the ladder starts, to the point on the wall, where the ladder ends, and the point on the ground right under the wall point.

at this ground point there is the right angle.

at the ladder ground point we have 70°.

so, the angle at ladder/wall point is

180 - 90 - 70 = 20°.

remember, the sum of all angles in a triangle is always 180°.

the ladder itself (20 ft) is the Hypotenuse (the baseline opposite of the 90° angle).

the height of the ladder/wall point is one leg (and what we need to calculate), and the ground distance from the ladder/ground point to the point right under the ladder/wall point is the second leg.

we can use the law of sine :

a/sin(A) = b/sin(B) = c/sin(C)

with the sides being always opposite of the associated angles.

so, we have

20/sin(90) = 20/1 = 20 = height/sin(70)

height = 20×sin(70) = 18.79385242... ft

so, D is the right answer.

Answer:

104.65 m

Step-by-step explanation:

The plane with the smaller angle of depression is closer to the raft.

Taking the tan values of both planes :

Plane 1 (57°)

Plane 2 (48°)

Equate Equations 1 and 2 :

Taking the sin ratio to find distance :

The equation of function g(x) = 2(x -7)² - 1, and the values of h and k are 7 and -1, respectively.

A quadratic equation is the second-order degree algebraic expression in a variable.

The standard form of this expression is  ax² + bx + c = 0 where a. b are coefficients and x is the variable and c is a constant.

The function is given as:

f(x) = 2x² - 1

When the function is translated with 7 units left, the transformation rule is:

(x,y) -> (x + 7, y)

So,

g(x) = 2(x -7)² - 1

A quadratic function is expressed as:

g(x) = a(x -h)² + k

By comparison, the values of h and k are 7 and -1, respectively.

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The number of the standard versions downloaded will be 2790 standard versions.

Division means the separation of something into different parts, sharing of something among different people, places, etc.

A Web music store offers two versions of a popular song.

The size of the standard version is 2.1 megabytes (MB).

The size of the high-quality version is 4.9 MB.

Yesterday, the high-quality version was downloaded four times as often as the standard version.

The total size downloaded for the two versions was 5859 MB.

Then the number of the standard versions were downloaded will be

→ 5859 / 2.1

→ 2790 standard versions

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An expression is defined as a set of numbers, variables, and mathematical operations. The simplification of the given expression 9 + (2×24) is 57.

In mathematics, an expression is defined as a set of numbers, variables, and mathematical operations formed according to rules dependent on the context.

The prime factorization of the expression can be done as,

9 + (2×24)

= (3×3) + (2×2×2×2×3)

= 3 [3+(2×2×2×2)]

= 3 [3 + 16]

= 3 (19)

= 57

Hence, the simplification of the given expression 9 + (2×24) is 57.

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Answer:

Everything is in the picture

Answer:

A. (h+(h-2) =14)...

I hope this is right! And go on your test! :)

First one is B second one is B last one is C

Answer:

  x = 70°

Step-by-step explanation:

The relevant relations are ...

__

Triangle OBQ is isosceles, so angle OQB = 40°. Triangle OPQ is isosceles, so angle OQP is x. The sum of angles OQB and OQP is angle BQP, which is supplementary to angle OPQ. That is, ...

  (40° +x) +x = 180°

  2x = 140° . . . . . . subtract 40°

  x = 70° . . . . . . divide by 2

_____

There are many ways to find x. The one shown here is just one of them. In general, right triangles, isosceles triangles, symmetry, inscribed angles can all be used to write relations involving the known angles and x.

The area of the given figure is 787.5 square centimeter

The area of Rectangle is length times of width.

The given figure has a rectangle whose length is 23 cm

width is 14 cm

Area of rectangle = 23×14

=322 square centimeter

Area = 15+34/2 ×19

=931/2

Total area = 322+931/2

=787.5 square centimeter

Hence, the area of the given figure is 787.5 square centimeter

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The number of T-shirts and shorts did Dots sell in the month of April with the total sales of $570 are 60 and 30 respectively.

A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.

Dots sells T-shirts ($5) and shorts ($9).

Let suppose the number of T-shirts sold is x and shorts sold is y. Dots sells T-shirts ($5) and shorts ($9) with total sales of $570. Thus,

[tex]5x+9y=570[/tex]

Solve it further,

[tex]5x+9y=570\\9y=570-5x\\y=\dfrac{570-5x}{9}[/tex]                  ....1

People bought 2 times as many T-shirts as shorts. Thus,

[tex]x=2y[/tex]                          ....1

Put the value of y form equation in this equation as,

[tex]x=2\times\dfrac{570-5x}{9}\\9x=1140-10x\\10x+9x=1140\\x=\dfrac{1140}{19}\\x=60[/tex]

Put this value of x in equation 2 as,

[tex]x=2\times y\\60=2\times y\\y=\dfrac{60}{2}\\y=30[/tex]

Thus, the number of T-shirts and shorts did Dots sell in the month of April with the total sales of $570 are 60 and 30 respectively.

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Answer:

3. (3, 6)
4. (3, 7)
5. (3, 36)

Step-by-step explanation:

These are slope functions, so there's is no definite answer for x as it tells you to solve when x is 3. So put simply lets do that. Knowing that x is now 3, we can solve for all the functions. This will give you y, which is f(x) which just tells you the equations represents a function or slope on a graph. All these equations create lines. Solving for question 3, 3 + 3 is 6, so f(x) = 6, and the answer is (3, 6). For 4, you do 3 x 3 - 2, which is 9 - 2 = 7. So (3, 7). So on and so forth.

The third graph from the figure represents the exponential function f(x) = 3ˣ, since the function contains the point (x, y) = (5, 243) on the cartesian plane.

In this question we must compare a given exponential function with a set formed by four functions. As the function is crescent and monotonous, then  we can choose the correct graph by a evaluating the function for a given x-value and find the graph that matches with such finding:

f(5) = 3⁵

f(5) = 243

The third graph from the figure represents the exponential function f(x) = 3ˣ, since the function contains the point (x, y) = (5, 243) on the cartesian plane.

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Answer:

The perimeter of the rhombus is 20 units

Step-by-step explanation:

One important fact about a rhombus is that all four of its sides are equal, so we only need to solve for one side in order to find the perimeter. We can use the Pythagorean Theorem to solve the side length of the rhombus. Using line AD as a reference, we know that the length of AD is the square root of the change in x squared plus the change in y squared, or [tex]\sqrt{3^{2}+4^{2} } =\sqrt{9+16} =\sqrt{25}=5[/tex] units. Multiply the length of AD by 4 and you'll get that the perimeter of rhombus ABCD is 5 × 4 = 20 un.

The perimeter of the rhombus ABCD is 20 units.

Option B is the correct answer.

A rhombus is a quadrilateral that has four equal sides.

Some of the properties we need to know are:

- The opposite sides are parallel to each other.

- The opposite angles are equal.

- The adjacent angles add upto 180 degrees.

We have,

We can use the distance formula to find the length of each side of the rhombus, and then add them up to find the perimeter.

The distance between points A and B is:

[tex]AB = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\= \sqrt{(-2 - 1)^2 + (-3 - 1)^2}\\ = \sqrt{9 + 16}\\= \sqrt(25) \\= 5[/tex]

The distance between points B and C is:

[tex]BC = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\= \sqrt{(-5 - (-2))^2 + (1 - (-3))^2}\\ = \sqrt{9 + 16}\\= \sqrt{25}\\= 5[/tex]

The distance between points C and D is:

[tex]CD = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\ = \sqrt{(-2 - (-5))^2 + (5 - 1)^2}\\ = \sqrt{9 + 16}\\ = \sqrt{25}\\ = 5[/tex]

The distance between points D and A is:

[tex]DA = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}\\ = \sqrt{(1 - (-2))^2 + (1 - 5)^2}\\ = \sqrt{9 + 16}\\= \sqrt{25}\\ = 5[/tex]

Since a rhombus has all sides of equal length, we can add up the lengths of the sides to find the perimeter:

P = AB + BC + CD + DA = 5 + 5 + 5 + 5 = 20

Therefore,

The perimeter of the rhombus ABCD is 20 units.

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The only value of the angles that could not be the value of the θ is determined as 240⁰.

If sinθ is given as [tex]\frac{\sqrt{3} }{2}[/tex], then the value of θ is determined as follows;

sinθ = √3/2

sinθ = 0.866

θ = sin⁻¹(0.866)

θ = 60⁰

When the angle is translated in radians, θ  = π/3 = 180/3 = 60⁰

thus, θ  = π/3

2(π/3) = 2(60) = 120⁰

using the following formula, we can obtain the rest;

θ = π/3 + 2πk

when k = 1;

θ = π/3 + 2π(1)

θ = 60 + 2(180)

θ = 420⁰

Thus, the only value of the angles that could not be the value of the θ is determined as 240⁰.

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Answer:

20 g/cm³

Step-by-step explanation:

mass = 180g

volume = 9 cm³

density =mass/volume

=180/9= 20 g/cm³

Answer:

2

Step-by-step explanation:

I don't know why am I so bad at math???

Answer:

Soln.

Given that we have proven:AB =CD and BC=DA

we will be said that the A and C is the angle of 90° and we will add the letters to get the results so let's started the A+90°+ 90°+ B+C+ D=90°

A+180°+B+C+D

180°+90°

=270°

Answer:

219.8 square cm

Step-by-step explanation:

[tex]s = 2\pi r^{2} +2\pi rh\\s=2(3.14)5^{2} +2(3.14)(5)(2)\\s = 6.28(25)+6.28(10)\\s = 157+62.8\\s=219.8 cm^{2}[/tex]

Explanation:

ratio of two cubes: 2 : 5

Perimeter of one face of cube: 4 × side

For small cube: 4 × 2 = 8

For big cube: 4 × 5 = 20

Ratio of perimeter of one face: 8 : 20 = 2 : 5

Total surface area of cube: 6a²

For small cube: 6(2)² = 24

For big cube: 6(5)² = 150

Ratio of total surface area: 24 : 150 = 4 : 25

Volume of cube: a³

For small cube: (2)³ = 8

For big cube: (5)³ = 125

Ratio of volume: 8 : 125

#1

Perimeter=4a

Find ratio

Samd

#2

TSA=6a²

#3

Volume=a³

When the ball hits the ground,

h=0

vt�16t^2=0

64t-16t^2=0..

t(64-16t)=0

t=0 (reject, not reasonable)

or

64-16t=0

16t=64

t=64/16=4

How long will it take for the ball to hit the ground? 4 seconds

Answer:

$ 53,333.33

Step-by-step explanation:

The formula for simple interest is I = PRT. So, we are trying to solve for P(original investment). To do this, we get the formula P = I / RT. This is the formula we will be using.

Work:

First, converting R percent to r a decimalr = R/100 = 5%/100 = 0.05 per year,putting time into years for simplicity,18 months ÷ 12 months/year = 1.5 years,then, solving our equation

P = 4000 / ( 0.05 × 1.5 ) = 53333.333333333

P = $ 53,333.33

Answer:

84 degrees

Step-by-step explanation:

180-96=84

Answer:

It is a cluster from $1.00 to $7.00 and

has no gaps.

Step-by-step explanation:

Answer:

A

Step-by-step explanation:

Answer:

B. g(x) = (x + 2)²

Step-by-step explanation:

We got the graph of g by translating the graph of the parent function

f(x) = x² two units to the left

Therefore the equation of the graph of g is (x + 2)²