Find the length of the segment indicated round your answer to the nearest tenth if necessary

When we're solving with functions, it's no different than solving from a regular equation.

In most cases, we only need to substitute x with a given value.

[tex]g(x)=\dfrac{1}{4}x+1[/tex]

⇒ To find g(-16), plug in -16 as x:

[tex]g(-16)=\dfrac{1}{4}(-16)+1\\\\g(-16)=-4+1\\\\g(-16)=-3[/tex]

-3

Step-by-step explanation:

f(x} = 3x + 1

g(x} = 2x -- 3

f(g(x)) = 3x + 1. (Calm down right?)

Let the x in the expression be (2x -- 3)

N.B x = g{x}

f(g(x)) = 3(2x --3} + 1

Open bracket

f(g(x)) = 6x -- 9 + 1

f(g(x)) = 6x -- 8...

2... Solve for g(f(x)), using the same strategy

g(f(x)) = 2x -- 3

x = f(x)

g(f(x)) = 2(3x + 1) -- 3

g(f(x)) = 6x + 2 -- 3

g(f(x)) = 6x -- 1

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Answer:

Step-by-step explanation:

f(g(x)) means substituting g(x) in f(x)

ie, 3(2x-3)+1 = 6x-9+1 = 6x - 8

g(f(x)) means substituting f(x) in g(x)

ie, 2(3x+1)-3 = 6x2-3 = 6x - 1

Answer:6

Step-by-step explanation:

8-6 = 2

Answer:

10

Step-by-step explanation:

Let the number be equal to y

A statement that is assumed to be true without proof is a(n) Theorem

A statement that has been shown to be true by vigorous application of logic is a(n) ---> Conjecture

A(n) Axiom is a statement that is believed to be true but hasn't been proven.

A definition is both a precise and a general statement of the significance of a mathematical term.

It does this by laying down all of the characteristics of the word together with the structures that need to be true.

This is how the meaning of the word is defined. A mathematical assertion that can be demonstrated using logically sound mathematical reasoning is called a theorem.

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Answer: 4

Step-by-step explanation:

This simplifies to 5/6.

So 20 / 5 = 4

and 24 / 6 = 4

When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b.

Flora needs 3 bags of dog food.

When the second number in the ordered pair, b, is not equal to 0, the ratio is expressed as a/b.

An equation in which two ratios are made equal is known as a percentage.

As an illustration, you could express the ratio as 1: 3 if there is 1 guy and 3 girls.

Given,

Dog eats 2 cups in a day

There are 24 cups in each bag

Solution:

Dog eats one bag of food in  24 cups/2 cups = 12 days

One food bag is sufficient to feed the dog for 12 days

For 35 days, the number of food bags needed is

1/x = 12/35 where x be the number of food bags needed for the dog.

x = 2.92  

That is 3 bags of dog food are needed for 35 days to feed the dog.

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*109

eight feral 103721

From the given figure < BAC = 180 - ( < ABC + < BCA ) because they are sum of angles in a triangle

given data

< ABC = 52 degrees

< BCA = 88 degrees

calculation for angle BAC

< ABC + < BCA + < BAC = 180 degrees ( sum of angles in a triangle )

< BAC = 180 - ( < ABC + < BCA )

< BAC = 180 - < ABC - < BCA

plugging in the values gives

< BAC = 180 - 52 - 88

< BAC = 180 - 140

< BAC = 40 degrees

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The two surfaces meet in an ellipse in some plane with [tex]0\le z\le5[/tex], since

[tex]4x^2 + 4y^2 = 5 - 6x^2 - y^2 \implies 10x^2 + 5y^2 = 5 \implies 2x^2 + y^2 = 1[/tex]

so the solid is bounded by the elliptical cylinder with this equation. In cylindrical coordinates, with

[tex]\begin{cases}x = \frac1{\sqrt2} r \cos(\theta) \\ y = r \sin(\theta) \\ z = \zeta \\ dV = dx\,dy\,dz = \frac1{\sqrt2} r \, dr \, d\theta \, d\zeta\end{cases}[/tex]

the solid is the set

[tex]\begin{array}{c} R = \left\{(r,\theta,\zeta) ~:~ 0\le r\le1 \text{ and } 0 \le\theta\le2\pi \text{ and } \right. \\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ \left.3r^2 - r^2 \cos(2\theta) \le \zeta \le 5 - 2r^2 - r^2 \cos(2t)\right\} \end{array}[/tex]

and the volume is given by the integral

[tex]\displaystyle \iiint_R dV = \frac1{\sqrt2} \int_0^{2\pi} \int_0^1 \int_{3r^2 - r^2 \cos(2\theta)}^{5 - 2r^2 - r^2 \cos(2\theta)} r \, d\zeta \, dr \, d\theta \\\\ ~~~~ = \frac1{\sqrt2} \int_0^{2\pi} \int_0^1 r(5 - 5r^2) \, dr \, d\theta \\\\ ~~~~ = \frac{10\pi}{\sqrt2} \int_0^1 (r - r^3) \, dr \\\\ ~~~~ = 5\sqrt2\,\pi \left(\frac12 - \frac14\right) = \boxed{\frac{5\pi}{2\sqrt2}}[/tex]

After solving the question using Pythagoras' theorem we get, The ladder moving down the wall at 8 feet per second.

According to the question,  

The bottom(base) of the ladder is 12 feet,

the height of the ladder is 13 feet.

Now, We have to find the top of the ladder moving down the wall

by using Pythagoras' theorem,

hypotenuse ^2 = base^2 + perpendicular ^2

13^2 = x^2 + y^2

169 =  x^2 + y^2

After using Pythagoras' theorem

we have this equation and now we will differentiate both sides:  

0  =2x*dx/dt + 2y*dy/dt    

0  =24*1 + 3* dy/dt  

dy/dt = - 8 feet per second  

Positive whole number we have to take.

So,   dy/dt = 8 feet per second

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Answer:

1. C

2. D

5. C

Step-by-step explanation:

Answer:

C as j is a variable

D

C as 13+9+1.9= 23.9

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Answer:    she gets 540

Step-by-step explanation:

   She earns 540 dollars since the saleswoman only gets 9% of it and she sold $6000 dollars worth of merchandise you divide by percentage

 Example:  1. Find the percentage of the original or real number. In this case, it's 500.

2. Multiply the final number by 100. 500 x 100 = 50,000.

3. Divide the result of the multiplication by the percentage. 50,000 divided by 40% = 1,250. Thus, 500 is 40% of 1,250.

The expression when a = 2 and x = -4, given 2a-x. The value will be 8.

In mathematics, an operation is a function that transforms zero or more arguments or operands into a clearly defined output value. The number of operands in the operation determines how difficult it is.

Unary operations (i.e., operations of arity 1), which include additive inverse and multiplicative inverse, as well as binary operations (i.e., operations of arity 2), which include addition and multiplication, are the operations that are most frequently studied. The nullary operation, also referred to as a zero-arity operation, is a constant. The mixed product is an example of a ternary operation, also referred to as an operation of arity 3.

The arity is typically assumed to be limited. Even yet, infinitary operations are occasionally taken into account, in which case the "typical" operations of finite dimensionality are referred to as finiteary operations.

Similar to an operation, but with partial function in place of a function, is the definition of a partial operation.

Since, a= 2 and x= -4, then,

2(2)-(-4)= 8

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Answer: b

Step-by-step explanation:

:)

Answer:

7/20

Step-by-step explanation:

is always right use without the s

Using the properties of an arithmetic sequence we can conclude that the total number of match boxes is 66.

There is a consistent distinction between the words in a sequence of numbers known as a "arithmetic progression" or "arithmetic sequence" (AP).

We know that the bottom row of the pyramid has 11 matchboxes .

As we can see in the figure that the each succeeding step has one matchbox less.

Therefore the number of matchboxes in each row is in an AP.

Therefore the AP has a common difference of  -1 and the first term is 11

The last term of the AP is 1.

Therefore

aₙ = a + (n-1)d

or, 1 = 11 + (n-1)(-1)

or, n = 11

We know that the sum of all terms of an AP is given by

S=n/2{2a+(n-1)d}

or, S = 11/2 {2×11 + (10)(-1)}

or, S = 66

Therefore from the arithmetic progression we calculate that the total number of match boxes is 66.

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Disclaimer: The missing diagram is attached below.

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Answer:

x = 3

Step-by-step explanation:

Plug in 1 for x:

- | 1 + 1 | + 5 = - |2| + 5 = -2 + 5 = 3

The numbers which correctly represents the y-coordinates of the given pairs; (-8-6) and (-1,0) as in the task content are; -6 and 0 respectively.

It follows from simple definition that the x -y plane, is a two dimensional plane which contains the x and y axis. The x and y axis happen to be used in the description of plane shapes which are two- dimensional in nature.

Also, it is noteworthy that each point on the xy-coordinate is described by a pair of coordinates and takes the form; (x, y).

In which case, the x-coordinate is written first and y-coordinate is written second as indicated above.

On this note, the y's of the pair of coordinates, (-8-6) and (-1,0) as given in the task content by convention can be observed to be; -6 and 0 respectively.

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Answer:

Number of balls of clay: 10

Step-by-step explanation:

The volume of the cube is  [tex]$V_{\text{cube}}=7^3=343,$[/tex]

and the volume of a clay ball is: [tex]$V_{\text{ball}}=\frac43\cdot\pi\cdot2^3=\frac{32}{3}\pi.$[/tex]

Since the balls can be reshaped but not compressed, the maximum number of balls that can completely fit inside a cube is

[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor=\left\lfloor\frac{343}{\frac{32\pi}{3} }\right\rfloor.\][/tex]

Approximating with [tex]$\pi\approx3.14[/tex]

We have:

[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor=10.23565228[/tex]

We simplify to get:

[tex]\[\left\lfloor\frac{V_{\text{cube}}}{V_{\text{ball}}}\right\rfloor\approx10[/tex]

So:

[tex]\boxed{number\ of\ balls = 10}.$[/tex]

The theorem can be used to readily show the corollary because, according to its statement, it considerably depends on it. Consequently, the assertion is accurate.

The given statement is True.

The term "corollary" refers to an outcome that follows logically from another action. You could claim that your rediscovered passion of reading is a corollary to the recent opening of a bookstore in your area. The term corollary describes the result of an action, such as the need to study more as a corollary to receiving a poor grade.

A theorem states that two angles that add up to 180° and form a straight line are regarded as "supplementary."

A corollary of this is known as the "Vertical Angle Theorem," which asserts that where two lines intersect, their angles across from each other are equal (in the diagram, a=c and b=d).

The theorem can be used to readily show the corollary because, according to its statement, it considerably depends on it. Consequently, the assertion is accurate.

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Answer:

Step-by-step explanation:Answer: using identity[(a+b)(a-b) = a^2 - b^2]. (m+n)(m-n) = m^2 - n^2. m^2 - n^2 = (3)^2 - (4)^2 = -7.

Answer: 3 5/11 should be 3.4545454545 as a decimal

Hope this helps!

Answer:

3 + 0.4545454545454545 =  3.454545454545455

Step-by-step explanation:

3 5/11 as a decimal exspansion

3 + (5 : 11) =

3 + 0.4545454545454545 =

3.454545454545455

Given the equation 13.25y = 79.5, the value of y is A. 6.00.

An equation is a mathematical statement that states that two mathematical expressions are equal in value.

Equivalent values are also expressed as algebraic equations sharing the same root.

We depict equations by using the equation symbol (=).

13.25y = 79.5

y = 6 (79.5/13.25)

Check:

13.25y = 79.5

13.25(6) = 79.5

79.5 = 79.5

Thus, given the equation 13.25y = 79.5, the value of y cannot be 66.25, 92.75, or 1,053.38 but Option A.

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Answer:

2

Step-by-step explanation:

[tex]6(1+2r)-3(1-8r)=75 \\ \\ 6+12r-3+24r=75 \\ \\ 3+36r=75 \\ \\ 36r=72 \\ \\ r=2[/tex]

The mean of Class 1 is 78.83.

The median of Class 1 is  88

The mode of Class 1 is 90

The mean of Class 2 is 79.42

The median of Class 2 is 85.50

The mode of Class 2 is 90

The mean of Class 3 is 79.42

The median of Class 3 is 78

The mode of Class 3 are 75 and 80

The standard deviation of Class 1 is 18.81

The standard deviation of Class 2 is 16.15

The standard deviation of Class 3 is 12.70.

The class that had the higher standard deviation is class 1.

The class that did better on the exam is class 3 because it has the higher mean and the lowest standard deviation.

Mean is the average of a set of numbers.

Mean = sum of numbers / total number

Mean of Class 1 = (45 + 50 + 55 + 68 + 77 + 86 + 90 + 90 + 90 + 95 + 100 + 100) / 12 = 78.83

Mean of Class 2 = (40 + 64 + 65 + 70 + 80 + 84 + 87 + 88 + 90 + 90 + 95 + 100) / 12 = 79.42

Mean of Class 3 = (55 + 65 + 70 + 75 + 75 + 76 + 80 + 80 + 88 + 90 + 99 + 100) / 12 = 79.42

Median is the number that is at the center of the dataset that is arranged in either ascending or descending order.

Median of Class 1 = (86 + 90) / 2 = 88

Median of Class 2 =  (84 + 87) / 2 = 85.50

Median of Class 3 = (76 + 80) / 2 = 78

Mode is the number that occurs most frequently in a dataset.

Standard deviation is used to calculate the average variation of a dataset.

Standard deviation = [tex]\sqrt{\frac{(x - u)^{2} }{n} }[/tex]

Where:

Standard deviation of Class 1 = 18.81

Standard deviation of Class 2 = 16.15

Standard deviation of Class 3 = 12.70

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Answer:

Down below!

Step-by-step explanation:

A.

The mean 78.83.

The median  88

The mode 90

The range 55

B.

The mean 79.42

The median 85.50

The mode 90

The range 60

C.

The mean 79.42

The median 78

The mode 75 and 80

The range 45

D. 18.81

E. 16.15

F. 12.70

G. The class that had the higher standard deviation is class 1.

H. The class that did better on the exam is class 3 because it has the higher mean and the lowest standard deviation.

Answer:

B

Step-by-step explanation:

∠ 2 and ∠ 7 are alternate exterior angles and are congruent, then

∠ 7 = ∠ 2 = 70°

Answer: -2+i

Step-by-step explanation:

By the conjugate root theorem, since the coefficients are real, the complex conjugate of a root must also be a root.

Answer: $ 7.20

Step-by-step explanation:

(9x4)/5

36/5

= 7.2

= $7.20