a 13-foot ladder is leaning against a wall. if we pull the ladder away from the wall at a rate of 1ft/s, how fast is the top of the ladder moving down the wall when the bottom of the ladder is 12ft from the wall?

{(-9,3), (8,7), (-9, -9), (2, 4)}

=======================================================

Explanation:

To find an example of a non-function, we look for (x,y) points where x repeats itself. That occurs in choice D where we have (-9,3) and (-9,-9) in the same function set.

The input x = -9 leads to multiple outputs y = 3 and y = -9 simultaneously. This is not allowed if we wanted a function.

A function is only possible if each input x leads to exactly one y output.

So this is why we look for repeated x values when trying to find non-functions. Choices A, B and C all have unique x values that don't repeat, which means those choices represent functions.

Side note: The y values can repeat, but the function won't be one-to-one.

The value of x from the given equation is 9/2

The given equation is

log₂(2x - 1) = 3

The general form of logarithm with base 2 is

          log₂ N = x

Conversion of the logarithm to exponential form is

            2ˣ = N

where x is the log₂ of N

           x is the number of times number '2' should be multiplied by intself to obtain n

Using this conversion in the above equation,

log₂(2x - 1) = 3

       (2x - 1)  = 2³    

       (2x - 1)  = 8

        2x - 1 = 8

        2x = 8 +1

        2x = 9

          x = 9/2

Therefore the value of x is 9/2

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0.868   is the probability that their mean useage time is between 4 and 7 hours.

What are examples and probability?

Given, population mean (μ) = 5.4

population standard deviation (σ) = 1.2

Sample size (n) = 5

Probability that the sum of their useage time is less than 30

= Probability that the sample mean is less than (30/5 = 6)

= p(x<6)3

Z score

 = x - μ/σ/√n

= 6 - 5.4/1.2/√5

= 0.6/1.2/2.236068

= 0.6/0.536656

= 1.11803

Area to the left of (Z = 1.11803) = 0.86822 = 0.868

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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:

The graph should look like the one below.

Step-by-step explanation:

C is lbs of chicken

S is pounds of steak

Alfred spent 30 pounds of meat for the party:

c + s [tex]\leq[/tex] 30

Alfred spend $60 on the 30 lbs of meat.

The chicken is $1.50 per pound and the steak is $2.40 per lb  then

1.5c + 2.50 [tex]\leq[/tex] 60

0.5c + 0.85 [tex]\leq[/tex] 20

The linear inequalities system that models situation is:

0.5c + 0.85 [tex]\leq[/tex] 20

c + s [tex]\leq[/tex] 30

c [tex]\geq[/tex]  0

s [tex]\geq[/tex] 0

The Graph:  

Answer:

x=11.2

Step-by-step explanation:

x/16=7/10

x=7/10×16

x= 11.2

Step-by-step explanation:

First, let's write down the equation properly:

[tex] \frac{x}{16} = \frac{7}{10} [/tex]

Then we follow these simple steps to solve the equation to find the value of x.

10x = 112

x = 11.2

Answer:

x = 3

Step-by-step explanation:

Plug in 1 for x:

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

Answer:

7/20

Step-by-step explanation:

is always right use without the s

Answer:

x = 72 and y = 0 im just guessing so dont be completey

*109

eight feral 103721

Answer: (1,4)

Step-by-step explanation:

y = 3x^2 - 6x + 7

Answer: 4

Step-by-step explanation:

This simplifies to 5/6.

So 20 / 5 = 4

and 24 / 6 = 4

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

Answer:

Equation of line is given as y = mx + c, where m is the slope and c is the y-intercept.

First find the slope.

Formula for slope is given as (y2-y1)÷(x2-x1) or (y1-y2)÷(x1-x2).

Slope = (7-1)÷(-9-9)

= -6/18

= -1/3

Equation of line is y = -1/3 + c.

Substitute either one of the points into the equation to find c.

1 = -1/3(9) + c

c = 4

Hence equation of line is y = -1/3x + 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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Answer:

21606 ft

Step-by-step explanation:

get difference between elevations with subtraction

20320 - - 1286

20320 + 1286

21606 ft

Answer: $ 7.20

Step-by-step explanation:

(9x4)/5

36/5

= 7.2

= $7.20

Answer:

B

Step-by-step explanation:

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

∠ 7 = ∠ 2 = 70°

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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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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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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[tex]{\Large \begin{array}{llll} y = ab^x \end{array}} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x=0\\ y = 10 \end{cases}\implies 10=ab^0\implies 10=a(1)\implies 10=a~\hfill \underline{y = 10b^x} \\\\[-0.35em] ~\dotfill\\\\ \begin{cases} x = 3\\ y = 80 \end{cases}\implies 80=10b^3\implies \cfrac{80}{10}=b^3\implies 8=b^3 \\\\\\ \sqrt[3]{8}=b\implies 2=b~\hfill \underline{y = 10(2)^x}[/tex]

Answer:

Common difference = 2

21st term = 73

Explicit rule : a(n) = 31 + 2n

Three terms in the sequence after 73: 77,77,79

Step-by-step explanation:

Given:

33, 35, 37, 39

If the sequence is arithmetic it  has a common difference ( same difference on each value)

d= Common difference = 35 - 33 = 37 - 35 = 39 - 37 = 2

d = 2

Explicit formula:

a(n) = a1 + d (n - 1 )

Where:

a1= first term = 33

d = common difference = 2

Replacing:

a(n)= 33 + 2 (n - 1 )

a(n) = 33 + 2n - 2

a(n) = 31 + 2n

21st term:

a(21) = 31 + 2 (21) = 31+ 42 = 73

To obtain the three terms in the sequence after 73, add the common difference 3 times.

73 + 2 = 75

75+2= 77

77 + 2 = 79

Answers:

Common difference = 2

21st term = 73

Explicit rule : a(n) = 31 + 2n

Three terms in the sequence after 73: 77,77,79

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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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Step-by-step explanation:

she reads 45 books in 15 days.

so, the reading rate is 45/15.

now, a ratio is just a fraction with a special meaning, but calculations, simplifications and so on are all the same.

so,

45/15 = 9/3 = 3/1 = 3

that means she reads 3 books in 1 day.

The evaluated value of the function is as follows:

The functions can be evaluated as follows:

To evaluate a function is to replace (substitute) its variable with a given number or expression.

In other words, evaluating a function means to substitute a variable with its given number or expression.

Therefore,

g(x) = -3x + 1

f(x) = x² + 7

h(x) = 12 / x

j(x) = 2x + 9

Hence,

a.

g(10) = -3(10) + 1

g(10) = -30 + 1

g(10) = - 29

b.

f(3) = (3)² + 7

f(3) = 9 + 7

f(3) = 16

c.

h(-2) = 12 / -2

h(-2) = -6

d.

j(7) = 2(7) + 9

j(7) = 14 + 9

j(7) = 23

e.

h(a) = 12 / a

h(a) =  12 / a

f.

g(b) + g(c) = -3(b) + 1 + -3(c) + 1

g(b) + g(c) = -3b + 1 - 3c + 1

g(b) + g(c) = -3b - 3c + 2

h.

find x when g(x) = 16

16 = -3x + 1

16 - 1 = -3x

15 = -3x

x = 15 / -3

x = -5

j.

find x when h(x) = -2

-2  = 12 / x

-2x = 12

x = 12 / -2

x = -6

k.

find x when f(x) = 23

23  = x² + 7

23 - 7 = x²

x² = 16

square root both sides

x = √16

x = 4

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The classification of the terms in the expression is given as follows:

In an addition, each term involved in the addition is called a term. Hence, the expression has three terms, which are given as follows:

Hence the first statement is correct.

The coefficients of the expression are:

Hence the second statement is correct.

In the third term, 6n is divisible by 6, hence six is a factor of the term, and the third statement is correct.

The variables of the expression are k and n, hence two variables, and the fourth statement is correct.

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