A 13 ​-ft ladder is leaning against a house when its base starts to slide away. By the time the base is 12 ft from the​ house, the base is moving away at the rate of 15 ​ft/sec.
a. What is the rate of change of the height of the top of the​ ladder?
b. At what rate is the area of the triangle formed by the​ ladder, wall, and ground changing​ then?
c. At what rate is the angle between the ladder and the ground changing​ then?

Answer:

 1.5

Explanation:

Given that:

While solving this problem, the above following is not required to use.

[tex]\rightarrow \sf log_b ([b^3])^{1/2}[/tex]

apply log rule

[tex]\rightarrow \sf \dfrac{1}{2}\log _b\left(b^3\right)[/tex]

[tex]\boxed{\sf \log _b\left(b^3\right)=3}[/tex]

[tex]\rightarrow \sf \dfrac{1}{2}(3)[/tex]

distribute

[tex]\rightarrow \sf \dfrac{3}{2} \quad or \quad 1.5[/tex]

Answer:

-6 and 10

Step-by-step explanation:

i did this before. np kiddo

Answer:

  -6, +10

Step-by-step explanation:

You are looking for factors of -60 that have a sum of 4. It can be helpful to list them so that they have a positive sum.

  -60 = (-1)(60) = (-2)(30) = (-3)(20) = (-4)(15) = (-5)(12) = (-6)(10)

The sums are 59, 28, 17, 11, 7, 4. The factor pair of -60 that has a sum of 4 is ...

  -6 and 10

_____

Additional comment

The square root of 60 is between 7 and 8, neither of which are factors of 60. That means the above list includes all of the factor pairs of 60. We have chosen the signs so that the sums are positive and the product is negative.

Answer:

-21

Step-by-step explanation:

37 - 45 - 13 is translated

-8 - 13

-21

Answer:

π(5²)(13)+⅓π(5²)(12)

Step-by-step explanation:

You can find the volume of the cylinder by:

V=πr²h

which is V1=π(5²)(13)

and the volume of the crooked cone by:

⅓πr²h

which is V2=⅓π(5²)(12)

and you need the volume of the whole shape. you can find by adding V1+V2

Answer:

he.....a red cap.(wants/want)

Answer:

Step-by-step explanation:

2x-10=8

2x = 10 + 8

2x = 18

x = 18 : 2 =

x = 9

-----------------------

check

2 * 9 - 10 = 8                         (remember PEMDAS)

18 - 10 = 8

8 = 8

the answer is good

Answer:

There are 7 sides.

Step-by-step explanation:

Let's Use the formula that states that the sum of the angles of an n-sided polygon is given by.

S=(n−2)180

Since we are given that the two angles are right, the angles and each of the remaining angles is 144.

And Therefore, the sum is:

S=90

(n−2)144

(n−2)180

=90

+90

+(n−2)144

⇒(n−2)180

−(n−2)144

=180

⇒(n−2)(180

−144

)=180

⇒(n−2)(36

=180

⇒n−2=

36

180

​⇒n−2=5

⇒n=5+2=7

Hence, the polygon has 7 sides.

The number of sides of the polygon such that one angle is the right angle will be 6.

An angle is a geometry in plane geometry that is created by 2 rays or lines that have an identical terminus.

The identical endpoint of the two rays—known as the vertex—is referenced as an angle's sides.

In any closed polygon, the number of sides is equal to the number of interior angles.

Suppose the number of sides is n in the given polygon.

Sum of angles = 90° + 126° × (n - 1)

The sum of angles is given as, 180(n - 2)

90° + 126° × (n - 1) = 180(n - 2)

90 + 126n - 126 = 180n - 360

180n - 126n = 90 - 126 + 360

54n = 324

n = 6

Hence "The number of sides of the polygon such that one angle is the right angle will be 6".

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Answer:

B

Step-by-step explanation:

1/9 can be simplified to 1/3 as 1/3 x 1/3 = 1/9  and 49/25 can be simplified to 7/5 as 7/5 x 7/5 = 49/25.

Now looking at both the fraction 1/3 and 7/5

1/3 simplifies to 0.34

It is an irrational value as the 3 keeps repeating.

7/5 simplifies to 1.4

It is a rational value as the decimal value is not repeating.

Thus making the second option the answer.

The value of x will be equal to x = 79.

Triangle is a shape made of three sides in a two-dimensional plane. the sum of the three angles is 180 degrees.

For an isosceles triangle, the value of two opposite angles is equal and the opposite sides are also equal.

The Sum of the three angles is equal to 180 degrees so the third angle will be calculated as:-

Angle = 180 - 142 - 19 = 19

Now applying Lami's theorem in the triangle we will get the third side.

[tex]\dfrac{sin\angle A}{a} = \dfrac{sin\angle B}{b} = \dfrac{sin\angle C}{c}[/tex]

[tex]\dfrac{Sin 19}{42}= \dfrac{Sin142}{x}[/tex]

[tex]x = \dfrac{42\times Sin 142}{Sin19}[/tex]

x = 79

Therefore the value of x will be equal to x = 79.

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Answer:

Step-by-step explanation:

Answer:

A≈113.1

Step-by-step explanation:

A=4πr2=4·π·32≈113.09734

The Arrangement that will be the first to have a red and blue ribbon is the 15th arrangement.

The least common multiple that is divisible by both a and b is the smallest positive integer, lowest common multiple, or smallest common multiple of two numbers a and b, generally indicated by LCM.

Given the florist places a red ribbon on every third Arrangement and a blue ribbon on every fifth Arrangement. Therefore, to find the arrangement that will have both a red and a blue ribbon, you need to take the LCM of 3 and 5.

Since the LCM is 15, therefore, the Arrangement that will be the first to have a red and blue ribbon is the 15th arrangement.

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Answer:

Hi

The answer is C

Step-by-step explanation:

Because it descend means goes down so it's minus and after that it ascends means goes up so it's plus so the answer will be -

26,843-1,284+5832

Given that [tex]f(x) = 3x^2 + 5[/tex], we have

[tex]f(x + 3) = 3 (x + 3)^2 + 5 \\\\= 3 (x^2 + 6x + 9) + 5 \\\\= 3x^2 + 18x + 32[/tex]

so that

[tex]f(x+3) - (f(x) + 3) = (3x^2 + 18x + 32) - (3x^2 + 8) \\\\= \boxed{18x + 24}[/tex]

Answer:

y-4=-1/2(x-4)

Step-by-step explanation:

point slope form: y-y1=m(x-x1)

every time x increases by 8, y decreases by 4. slope can be found by rise/run. the slope is -4/8 which is -1/2, which means m=-1/2. in the given equation, it said y-4. It plugged in 4 for y1, meaning it was talking about the second given point, which was (4,4). plug in 4 for x and you get y-4=-1/2(x-4)

The correct answer to this question is the first option

The expected number of hot dogs sold when the temperature is 50° would be 23 hot dogs, If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees.

Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.

A mathematical notion called the line of the best fit connects points spread throughout a graph. It's a type of linear regression that uses scatter data to figure out the best way to define the dots' relationship.

[tex]\rm m = \dfrac{n\sum xy-\sum x \sum y}{n\sum x^2 - (\sum x)^2}[/tex]

[tex]\rm c = \dfrac{\sum y -m \sum x}{n}[/tex]

The question is incomplete.

The complete question is:

A hot dog vendor at the zoo recorded the average temperature in degrees, x, and the average number of hot dogs she sold, y.

The equation for the line of best fit for this situation is shown below.

[tex]\rm y=\dfrac{3}{10}x+8[/tex]

Based on the line of best fit, complete the given statements.

We have a line of best fits:

[tex]\rm y=\dfrac{3}{10}x+8[/tex]

Plug x = 50 in the line of best fit.

y = (3/10)50 + 8

y = 15+8

y = 23

Plug y = 35

35 = (3/10)x + 8

27 = (3/10)x

x = 90 degree

Based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.

Thus, the expected number of hot dogs sold when the temperature is 50° would be 23 hot dogs, If the vendor sold 35 hot dogs, the temperature is expected to be 90 degrees, and based on the line of best fit, for every 10-degree increase in temperature, she should sell 3 more hot dogs.

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Answer:

4 pencil & 2 ruler = $8

2 pencil & 4 ruler = $10

let the no. of Pencil be X and no. of ruler be Y

4x + 2y = 8

2x + 4y= 10

solving the equation by elimination method,

multiplying eq 2 with 2

4x + 2y = 8

4x + 8y = 20

subtracting,

- 6 y = -12

y = 2

2x + 4(2)= 10

2x + 8 = 10

2x = 10 - 8

2x = 2

x = 1

Cost of 3 ruler + 3 pencil

= 3(1) + 3(2)

= 3 + 6

= 9

Answer:

$9

Step-by-step explanation:

pencil - p

ruler - r

4p + 2r = 8

2p + 4r = 10

4p + 2r = 8 {finding p in terms of r so we can substitiute it}

    - 2r    -2r

4p = 8 - 2r

÷ 2      ÷2

2p = 4 - r  {now, we can replace "2p" in our other equation}

2p + 4r = 10 becomes...

[4 - r] + 4r = 10

4 - r + 4r = 10

4 + 3r = 10

- 4        -4

    3r = 6

  ÷3    ÷3

    r = 2

when we have 4 pencils and 2 rulers, we have:

4p + 2[2] = 8

4p + 4 = 8

     -4     -4

4p = 4

÷4      ÷ 4

p = 1

{checking with our other equation:

p = 1 ; r = 2

2p + 4r = 10

2[1] + 4[2] = 10

2 + 8 = 10

10 = 10

TRUE STATEMENT;

confirms our variables}

so , we have found that the cost of a pencil is $1, and the cost of a ruler is $2,

p = 1 ; r = 2

so, let's solve our original problem:

3 rulers + 3 pencils = ?

3(2) + 3(1) = ?

6 + 3 = 9

so, the cost of this combination would be $9

hope this helps!! have a lovely day :)

The set that represents the range of the diagram below is given as follows:

B. {3, 5, 7}.

It is the set that contains all possible output values.

In the diagram, we have that:

Hence the set that represents the range of the diagram below is given as follows:

B. {3, 5, 7}.

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Answer:

Seitokachou-sama uhuuuyy7 is

The amount of the acid will be equal to 113.75 Ml.

Concentration in chemistry is calculated by dividing a constituent's abundance by the mixture's total volume.

In chemistry, to solve this kind of exercise, dilutions, and concentrations are common to use the following equation

C1 x V1 = C2 x V2

V1 refers to volume 1, in this case, is 70mL because is the quantity I have, the solution I can use to obtain another solution. C1 refers to the concentration of the solution I also have, in this case, 65%.

C2 and V2 refer to the volume and concentration of the solution I am looking for. So, if want to know V2, which is the volume I need to add, the only thing to do is find V2 in the equation:

V2 = ( C1 x V1 ) / C2

V2 = ( 65% x 70mL) / 40%

V2 = 113.75 Ml.

Therefore the amount of the acid will be equal to 113.75 Ml.  

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The best approximation for the median is 3.6.

An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).

For the given density curve, the area under the density curve is

A=(1/2)×5×(1/2)=5/4

now, for the median, the area on the left and the area on the right of the median.

Let the median be x, then

The area criteria we get

(1/2)x(x/10)=(5/4)/2

⇒x²=5*20/4=25/2

So, we get x=5/([tex]\sqrt2[/tex])=3.5 ≈ 3.6

Hence the required answer is option 3.6

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Answer:

B. y = (x+1)(x+5)

Step-by-step explanation:

If the x-intercepts are (-1,0) and (-5,0), then the solutions (also called zeros and x-intercepts) are

x = -1 and x = -5

This is a "working backwards" kind of problem. If you were solving the equation, right before the final step, x=-1 would have been:

x + 1 = 0

Right before x=-5

would have been,

x + 5 = 0.

These two: x+1 and x+5 are called the linear factors. You multiply them back together to find the equation.

y = (x+1)(x+5)

The expressions show the total number of furniture legs in aisle 2 is 4t + 4c + 3s.

A quantity obtained by the addition of a group of numbers.

Given number of tables = t, chairs = c and stools = s.

The total number of furniture legs = 4 * t + 4 * c + 3 * s.

                                                         = 4t + 4c + 3s.

Therefore, the expressions which show the total number of furniture legs in aisle 2 is 4t + 4c + 3s.

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Answer:

X + 35° = 70° ( this is one of the property of triangle in which the sum of two interior angles of a triangle is equal to its other angle)

X = 70 - 35

X = 35°

Answer:

120

Step-by-step explanation:

10%=12

20%=12x2

100%=12x10

        =120

Answer:

Let the number be x.

Compute 10% of x and equate it to 12 to compute the value of x as follows:

[tex]x[/tex] x [tex]\frac{10}{100} = 12[/tex]

[tex]x[/tex] = 12 x [tex]\frac{100}{10}[/tex]

[tex]x[/tex] = 120

Thus, the number is 120.

Note that

108° = 90° + 18°

so

sin(108°) = sin(90° + 18°) = sin(90°) cos(18°) + cos(90°) sin(18°) = cos(18°)

Then

sin²(108°) + sin²(18°) = cos²(18°) + sin²(18°) = 1

by the Pythagorean identity.

The value of the expression sin²(108°) + sin² (18°) ​will be 0.9986.

A mathematical expression is made up of terms (constants and variables) separated by mathematical operators. A mathematical equation is used to equate two expressions. Equation modelling is the process of writing a mathematical verbal expression in the form of a mathematical expression for correct analysis, observations and results of the given problem. Trigonometric functions are real functions which relate an angle of a right-angled triangle to ratios of two side lengths. The six - trigonometric functions are -

We have the following trigonometric equation -

sin²(108°) + sin² (18°) ​

We have the following expression -

sin²(108°) + sin² (18°) ​

(0.95)² + (0.31)²

0.9025 + 0.0961

0.9986

Therefore, the value of the expression sin²(108°) + sin² (18°) ​will be 0.9986.

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