In this figure, AB∥CD and m∠3 = 114°.

What is m∠6?

The area of the square is increasing at a rate of 36 cm/s2.

What is the rate of expansion of a solid?

For physics, The term "thermal expansion" refers to a material's change in length, width, height, or volume when its temperature is raised or lowered. Solids exhibit particularly noticeable thermal expansion due to their closely packed atoms. There are numerous uses for the thermal expansion of solids in daily life.

A solid's atoms vibrate more quickly around their fixed positions when it is heated. As a result, there is little relative growth in the size of solids during heating. In order to prevent buckling when exposed to heat from the sun, metal train tracks feature tiny gaps.

Calculation

L = length of a side

A = L2

dA/dt = 2L dL/dt

dL/dt = 2 cm/s

A = 81 sqcm ⇒ L = √A = √81 cm = 9 cm

dA/dt = 2(9cm)(2 cm/s) = 36 sqcm

Hence the rate is the area of the square increasing is 36sqcm

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Using the rate of change of area ,

If the area of a square is 81 cm² the area of the square increases at a rate of 36 cm²/s.

Suppose that initially there were no squares, but suddenly squares began to form at a constant rate. At the end of the first second, the sides were 2 cm long each, and at the end of the second second they were 4 cm each. Therefore, we can say that the rate of change of increasing sides is 2 cm/s. If a square has a side of S cm, this is expressed mathematically.

dS/dt = 2 cm/s ---(1)

Since we know the area of the square is given by

A=S² cm²

the derivative of the area function shows the variation of area with respect to side S

dA/dS=2S

So , when area of square is 81 cm² , its side length is 9 cm. Since we need rate of change of area w.r.t. time, we need to multiply both the sides by dS/dt .

dA/dS×dS/dt=2S×dS/dt

=> dA/dt=2S×dS/dt

=> dA/dt = 2×9 ×2 = 36 cm²/s

Hence, the required area increasing rate is 36 cm²/s.

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From the given exponential function  y = 7.1(1.03)ˣ, the amount produced in 2006 was approximately 7.8 billion pounds and the estimated amount in 2014 will be approximately 9.8 billion pounds

An exponential function is a function of form f (x) = ax, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.

In the function given;

y = 7.1(1.03)ˣ

a) What is the estimated number in 2006

x in 2006 = 3

x = 3

Insert the values into the formula above;

y = 7.1(1.03)³

y = 7.76 ≅ 7.8 billion pounds

b)

The cheese produced in 2014

x in 2014 = 11

Insert in the value and solve

y = 7.1(1.03)¹¹

y = 9.83 ≅ 9.8 billion pounds

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Answer:

9

Step-by-step explanation:

3 x 3 = 9

4 x 4 = 16

16 - 11 = 5

11 - 9 = 2

2 is less than 5 which makes it closer to 11.

Answer:

Ans = 9

Step-by-step explanation:

3 x 3 =9

4 x 4 =16

2 x 2 =4

If the car's speed is 65 kilometers per hour, if it possible that the bus speed 75 kilometers per hour it is not possible.

Distance is a numerical representation of the distance between two items or locations. Distance refers to a physical length or an approximation based on other physics or common usage considerations.

It is given that:

if the car's speed is 65 kilometers per hour, if it possible that the bus speed 75 kilometers per hour

Time = 2 hours

Distance = speed x time

Distance(for car ) = (65)(2) = 130 km

Distance(for bus ) = (75)(2) = 150 km

Total distance = 130 + 150 = 280 km

But the distance between car and bus is 350 km.

Thus, if the car's speed is 65 kilometers per hour if it possible that the bus speed 75 kilometers per hour it is not possible.

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The value of the longest of the four side lengths is 26 feet.

Let the integers be x, x + 2, x + 4 and x + 6.

Since the perimeter is given as 92 feet. This will be:

x + x + 2 + x + 4 + x + 6 = 92

4x + 12 = 92

Collect like terms

4x = 92 - 12

4x = 80

Divide

x = 80 / 4

x = 20

The longest side will be:

= x + 6.

= 20 + 6.

= 26 feet.

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Answer:

y=-1,5x+17

Step-by-step explanation:

(10,2) => x=10, y=2

a - slope

a=-1,5

y=ax+b -linear equation

2=(-1,5)*10+b

2=-15+b

b=17

y=-1,5x+17

The answer of this 70/cos 20° round to 1 decimal place  is 74.5

To solve the equation 70/cos 20° , firstly we need to find out the value of the cos 20°.

From the simple calculator we can find the value of cos 20° which is 0.9397.

Now we use this value to solve the above equation.

70/cos 20°;

70/0.9397;

74.491.

written that we  have to round of the value to first decimal place, so the answer will become 74.5

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Answer:

A and D

Step-by-step explanation:

|3x + 4| − 9 = 0

|3x + 4| = 9

3x+4 = 9 v 3x+4 = -9

3x=5 v 3x=-13

x=⁵/₃ v x=-¹³/₃

x=1 ²/₃ v x=-4¹/₃

Answer:

(0,15) The time it take to fill the ball with air

Step-by-step explanation:

On edge 2022

Answer:

0

Step-by-step explanation:

The y -axis intercept  also called the y intercept occurs when x = 0

y = 4/3 x    put in x = 0

y = 4/3 (0) = 0

Answer:

The y-intercept is 0.

Step-by-step explanation:

The y-intercept is where the graph meets the y-axis.

The equation for the logarithmic function that has the following transformation from the parent logarithmic function. The other factors are mentioned in the answer below.

An essential tool for arithmetic calculations is the logarithmic function. John Napier, a Scottish mathematician, physicist, and astronomer, made the discovery of logarithms in the 16th century. It has a wide range of uses in complex scientific and astronomical calculations. Exponential functions and logarithmic curves are closely related, and the latter is thought of as the inverse of the former.

Parent function is y = log x

1. Shifted 3 units left,

y = log (x+3)

2. The vertical compression by a factor of 2,

y = 2 log(x+3)

3. Reflection across the y-axis,

y = 2 log(-x+3)

4. Shifting down by 5 units,

y = 2 log(-x+3)-5

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Answer:

[tex]x=-2\frac{9}{23} , y=\frac{16}{23 }[/tex]

Step-by-step explanation:

7x - 9y = -30 ------ equation (1)

-3x - 6y = 3 ------ equation (2)

From equation (2),

3x + 6y = -3

 x + 2y = -1

      ∴ x = -2y - 1 ------ equation (3)

Substitute equation (3) into equation (1):
7(-2y - 1) - 9y = -30

-14y - 14 - 9y = -30

             -23y = -16

               23y = 16

∴ y = [tex]\frac{16}{23}[/tex]

Substitute y = [tex]\frac{16}{23}[/tex] into equation (3):

x = -2([tex]\frac{16}{23}[/tex]) - 1

  = -[tex]\frac{32}{23}[/tex] - 1

  = -[tex]\frac{55}{23}[/tex] = -[tex]2\frac{9}{23}[/tex]

The number of tickets sold at a regular price is 20.

The linear equation:

an algebraic equation of the form y=mx + b. involving only a constant and a first-order (linear) term, where m is the slope and b is the y-intercept.

Let x be the number of regular admission and y be the number of students.

The first statement is 48 tickets are sold. By this we get the first equation:

x + y = 48 ----------(1)

The second statement is the total collection for the ticket is $300. Form this we get the second equation:

8x + 5y = 300 --------(2)

Multiplying the equation by 5 we have:

5x + 5y = 240 --------(3)

Now subtracting equation (3) from (2) we get:

3x = 60

x = 20

Therefore we get that the ticket sold at regular price is 20.

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[tex](\stackrel{x_1}{-1}~,~\stackrel{y_1}{14})\qquad (\stackrel{x_2}{2}~,~\stackrel{y_2}{r}) \hspace{5em} \stackrel{slope}{m}\implies \cfrac{\stackrel{rise} {\stackrel{y_2}{r}-\stackrel{y1}{14}}}{\underset{run} {\underset{x_2}{2}-\underset{x_1}{(-1)}}} ~~ = ~~\stackrel{\stackrel{\textit{\small slope}}{\downarrow }}{-2} \\\\\\ \cfrac{r-14}{2+1}=-2\implies \cfrac{r-14}{3}=-2\implies r-14=-6\implies r=8[/tex]

Answer:

n = 49

Step-by-step explanation:

49 has a factor of -7 which can also add up to -14

Eg : -7(-7) = 49, -7 + (-7) = -14

49

x²-14x+49=(x-7)²

An algebraic expression that is created by squaring a binomial expression is known as a perfect square trinomial.

It is of the form (ax2 + bx + c).

Real numbers a, b, and c are present here, and a ≠0.

The given equation is x2 + 14x + c

To find the value of c

We can take half of the linear coefficient and square it

14/2 = 7

72 = 49

Therefore, the value of c is 49.

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Answer:

15.4

Step-by-step explanation:

Round: 17.98 to 18 and 2.596 to 2.6

Do the math: 18-2.6=15.4

Conclusion: We rounded the numbers (17.98 to 18 and 2.596 to 2.6). Then we did the subtraction and got our answer.

Therefore, your answer is 15.4.

Answer:

x=60

Step-by-step explanation:

180 = 100 + 20 + x

180 = 120 + x

-x = 120 - 180

-x = -60

x = 60

Answer:           bro you gotta figure dis out

Step-by-step explanation:hhahahahahahahahahahaahahhaha

Answer:

Connie - [tex]x^{2} + 10[/tex]

Step-by-step explanation:

10 more means that you are adding ten to the square of x

The critical t-distribution values converge to the critical z-distribution values as a particular family of t-distributions that t2 has 2 degrees of freedom (df) and t9 has 9 degrees of freedom.

The maximum number of logically independent values—that is, values with the freedom to change—in the data sample is referred to as the degree of freedom. When calculating degrees of freedom, one is subtracted from the total number of items in the data sample. Degrees of freedom, also known as numerical freedom of variance, are the maximum number of logically independent values that can be present in sample data. Degrees of freedom are frequently brought up when discussing various mathematical hypothesis testing techniques, like the chi-square.

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Answer:

293,000.

Step-by-step explanation:

Just round to the nearest thousandth, and add 500 since you originally had 292,500.

Answer:

Step-by-step explanation:

292500 to the nearest 1000 is 293000.

The measure, x, which is of one of the base angles of the isosceles triangle in the question is 71°

The value of x is 71°

An isosceles triangle is a triangle that has congruent base angles

The description of the specified triangle mare as follows;

The length of the sides are;

21 and 21

Therefore;

The triangle is an isosceles triangle

The base angles of an isosceles triangle are congruent, therefore;

The measure of the  angle adjacent the angle x is also m∠x

Which indicates;

38° + x° + x° = 180° (Angle sum property of a triangle)

38° + 2·x°  = 180°

2·x° = 180° - 38° =  142°

x = 142° ÷ 2 = 71°

x = 71°

The measure of the angle x is 71°

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Answer:

the conversion factor

Step-by-step explanation:

Answer:

  7.8

Step-by-step explanation:

You want the distance between P(8, 2) and Q(3, 8).

The distance between points is given by the distance formula:

  d = √((x2 -x1)² +(y2 -y1)²)

  d = √((3 -8)² +(8 -2)²) = √((-5)² +6²) = √61

  d ≈ 7.8

The distance between points P and Q is about 7.8 units.

__

Additional comment

You will notice that the desired distance is the length of the hypotenuse of a right triangle with legs that are 5 and 6. The Pythagorean theorem tells you that length is √(5² +6²) = √61, as above. The distance formula is based on the Pythagorean theorem.

You can find the relevant triangle leg lengths by counting grid squares on the graph. Of course, the distance formula does the same thing by subtracting coordinate values.

Answer:

19

Step-by-step explanation:

P.E.M.D.A.S

2X8=16

15/5= 3

Answer:

27

Step-by-step explanation:

1) Write it out using operations

2) Organise it into PEMDAS

P: There are no brackets

E: There are no exponents (powers)

M: We need to put  2 × 8 in brackets (to make sure we know what to do first

D: We need to put 15 ÷ 5 in brackets

A&S: As the numbers we need to add and subtract will be part of the brackets we can move on!

3) Solve!

First we need to do the brackets

Then the rest

Hope this helps, have a great day!!

For the given condition after he makes his milkshake and muffins, one and seven-twelfths cups of berries will Rasheed have left. Option D is correct.

Fraction number consists of two parts, one is the top of the fraction number which is called the numerator and the second is the bottom of the fraction number which is called the denominator.

It is given that, Rasheed has two and three-fourths cups of berries. He uses four-sixths of a cup of berries to make a milkshake. He then uses one-half of a cup of berries.

The number of cups of berries will Rasheed has left is found by subtracting the total used amount from the total amount,

=2 3/4-(4/6+1/2)

=11/4-(4/6+1/2)

=11/4 - 7/6

=19/12

=1 7/12

1.58

Thus, for the given condition after he makes his milkshake and muffins, one and seven-twelfths cups of berries will Rasheed have left. Option D is correct.

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Answer:

20xy^2 + 15x^2 + 10x

Step-by-step explanation: